\r\n\tSalmonella has changed its characteristics over time becoming the etiologic agent of many pathological processes such as cancer development, inflammatory process and immune-pathogenesis other than typhoid, paratyphoid and foodborne infections . \r\n\tListeria should be thoroughly studied as the most important cause of newborn meningitis and gynecological infection which can interfere with the pregnancy outcome. Listeria monocytogenes is the most important species in these pathologies. \r\n\tE. coli is a worldwide saprophyte microorganism which in specific situations can become pathogenic by secreting a large variety of exotoxins. Its antibiotic-resistance can be mediated by a strong ESBL especially found in retail meat products and in food-production cattle.
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1. Introduction
Memristors have turned out to be of considerable importance in several areas of research and application, such as analogue circuits, non-linear (chaotic) circuits, sensors, control systems, storage systems, cellular neural networks, logic circuits, power systems, neuromorphic circuits, etc. [1]. In order to research all those applications, the first step is understanding and modelling the behaviour of a memristor. In this scenario, there are, basically, three approaches: behavioural modelling, SPICE type models and emulator circuits. In the former case, smooth continuous cubic non-linear functions [2], square non-linear functions [3], piecewise linear models [4] and hyperbolic sine models [5, 6] have been proposed to emulate the Hewlett-Packard (HP) memristor behaviour. Examples of this type of modelling are TEAM model [7], VTEM model [8] and Simmons tunnelling model [9]. Although these models are approaching the HP memristor behaviour with a level of error relatively low, a full custom software is required for solving the mathematical models [10]. Furthermore, this task becomes cumbersome when applications with several memristors are addressed, since a large set of equations must first be established according to the topology, and next, the system of equations must be numerically solved. In the second approach, SPICE models have also been developed in order to model the HP memristor, principally [11, 12, 13, 14, 15, 16]. It is worth mentioning that the memristive effect is not limited to TiO2, and this effect has also been glimpsed on nickel oxide [1], Ag-loaded Si films [17], TiO2 sol-gel solutions [18], and other materials. Although this type of modelling is interesting, since the capabilities of commercially available tools are exploited, its major disadvantage is that numerical simulations of circuits based on memristors can only be done. In the latter, several emulator circuits have been proposed in the literature, which use different design methodologies and different topologies. In this way, grounded and floating memristor emulator circuits working at incremental or decremental mode and built with operational amplifiers and analogue multipliers have been proposed in [19, 20, 21, 22, 23, 24]. Other interesting topologies were reported in [25, 26], where digital and analogue mixed circuits were used. More recently, other active devices such as current feedback operational amplifiers, positive second-generation current conveyors (CCII+) and differential difference current conveyor, see [27, 28, 29, 30, 31, 32, 33] and the references cited therein, have also been used to design a memristor emulator circuit. However, some of them not only become complex and bulky, requiring rigid conditions to operate, but also some emulators do not exhibit those fingerprints that are useful to affirm that the emulator circuit is a memristor or memristive device. With this in mind and depending on the application, any emulator circuit must accomplish some properties, some of them are: the frequency-dependent pinched hysteresis loop for any kind of flux- or charge-controlled incremental or decremental memristor/memductor, in its version grounded or floating, must pass through the origin for any periodic signal with any amplitude, operating frequency and initial conditions; the possibility for controlling the initial state of the emulator circuit, i.e. adjust of the initial conditions, non-volatility, memristive/memductive behaviour at high-frequency and without offset, etc. All in all, the design of memristor emulator circuits is also important in order to study and research real applications as those mentioned above. As a consequence, a lot of emulator circuits using off-the-shelf components have been developed to imitate not only the real behaviour of a memristor but also the real behaviour of meminductors and memcapacitors [1].
In this chapter, we discuss the design of three memristor emulator circuits. The aim is to show the conceptual idea on the design of an emulator, passing for numerical simulations and until experimental tests. Each behavioural model is derived and programmed at SIMULINK under MATLAB environment. From a circuit-design perspective and of the knowledge gained, a design guide is described in order to design a memristor emulator circuit in a systematic way. Then, we introduce a novel technique for achieving the frequency-dependent pinched hysteresis loop associated to a memristor emulator circuit that is operating at high frequency, and the crossing point does not deviate of the origin. Since a memristor is basically a charge- or flux-controlled resistor, we describe how to transform a non-linear resistor with its normal pinched hysteresis loop to an inverse behaviour. Therefore, the main difference of an inverse non-linear resistor with respect to normal resistors is that the behaviour of frequency-dependent pinched hysteresis loop becomes a straight line when the operating frequency of the signal source decreases. Finally, some real analogue applications are described.
2. Analogue memristor emulators
Unlike behavioural models and SPICE type models, an emulator circuit is very useful, since real applications based on memristors can be researched and built. In this section, we describe three memristor emulator circuits.
2.1. Floating memristor emulator circuit
The topology shown in Figure 1(a) was reported in [28]. By a straightforward analysis, the behaviour equation is given by:
Figure 1.
(a) Flux-controlled floating memristor emulator circuit taken from [28] and (b) SIMULINK model of Eq. (1).
vm(t)im(t)=M(φm(t))=R1±R1R410R2R3Cz∫0tvm(τ)dτE1
From Figure 1(a), the S switch is connected to I to obtain a memristor emulator circuit operating at incremental mode, whereas if S is connected to D, then a decremental behaviour is obtained. These behaviours correspond to the signs + and − at Eq. (1), respectively. Assuming that
vm(t) = Amsin(ωt), where Am is the amplitude and ω = 2 πf in rad/s, we obtain:
vm(t)im(t)=R1±R1R4Am10R2R3Czωcos(ωt−π)E2
From Eq. (2), one can observe that the memristance is composed by a linear time-invariant resistor and a linear time-varying resistor. The relationship between both resistors is described by the ratio of their amplitudes, given as
kn=R4AmR2R3Czω10=1τf=TτE3
where τ=20πR2R3CzR4Am is the time constant of the emulator circuit and T=1f is the period of vm(t). In order to hold the pinched hysteresis loop in several operating frequencies, one can observe in Eq. (3) that τ must be updated according to f, since kn will decrease as the frequency increases. Thus, the numeric value of τ can be updated by R3 or Cz. On the other hand, Eq. (3) reveals that:
kn → 0 when f → ∞ or Am → 0. Hence, Eq. (1) is dominated by its linear time-invariant part.
kn → 1 when f → 1/τ or Am is monotonically increased. Therefore, the maximum pinched hysteresis loop is obtained.
kn → ≥1 when f ≤ 1/τ or Am increases too much. Here, the hysteresis loop is lost.
In order to ensure the behaviour of the frequency-dependent pinched hysteresis loop, the numerical value of kn must be in the interval (0, 1). Once the behavioural model of the memristor has been deduced, numerical simulations can be realized. The numerical value of each element of Figure 1(a) used during numerical simulations and experimental tests can be found in [28]. Therefore, Figure 2(a) (solid line) shows only the incremental pinched hysteresis loop behaviour obtained of Figure 1(b) when a sinusoidal waveform operating to 16 Hz is applied. For this case and that follows, the direction of the hysteresis loop is clockwise, whereas for a decremental mode, the direction is counterclockwise. Therefore, a similar behaviour is obtained for the decremental case, as illustrated in Figure 2(a).
Figure 2.
Numerical, HSPICE and experimental results of Figure 1(a) operating at: (a) 16 Hz and (b) 100 Hz.
Figure 1(a) was also simulated at HSPICE by using the macro-models associated to each active device and numerical results are shown in Figure 2(a) (dash-dot line). In order to validate the previous results, Figure 1(a) was experimentally tested, and the results are shown in Figure 2(a) (dot-dash line). On the other hand, when the operating frequency increases, the pinched hysteresis loop is gradually lost and the memristor behaviour becomes a straight line for all cases, as depicted in Figure 2(b). Furthermore, the frequency-dependent pinched hysteresis loop is a necessary condition but not sufficient for claiming that the emulator circuit is emulating the real memristor behaviour. In this case, tests of non-volatility are necessary. Since capacitors and inductors are the solely elements that are storing energy, the non-volatility property is indirectly measured across Cz of Figure 1(a). Thus, Figure 3 shows experimental tests of non-volatility of Figure 1(a) when a narrow pulse train of 1.2 V of amplitude and 2.4 μs of pulse width (yellow line) is applied. According to Figure 3, one can observe that once programmed the incremental and decremental memristance, its value is keeping when the input signal is not applied. Note that during non-pulse period, the memristance is non-volatile, and its variation is negligible. For incremental topology, the memristance increases according to the amplitude and pulse width, as depicted in Figure 3 (pink line), whereas for the decremental topology, the memristance decreases (blue line). It is important to point out that memristive behaviour in each operation mode can be reverted to its last value, when a negative pulse of the same size is applied.
Figure 3.
Experimental results of non-volatility property for incremental (pink line) and (blue line) decremental memristor. Pulse signal at yellow line.
2.2. Grounded memristor emulator circuit I
Recently in [28, 31, 32], floating and grounded memristor emulator circuits based on CCII+ were proposed. In this way, the behavioural model of the charge-controlled grounded memductor emulator circuit described in [32] and shown in Figure 4(a) is given by
Figure 4.
(a) Charge-controlled grounded memductor emulator circuit taken from [32] and (b) SIMULINK model of Eqs. (4) and (5).
where Rx and Ca are the parasitic resistance and capacitance connected in x- and z-terminal, respectively; Av and Ai are the voltage and current gains between y- and x-terminal and x- and z-terminal of CCII+. Similarly as in Subsection 2.1, an incremental behaviour is obtained when the S switch is connected to I and a decremental behaviour is obtained if S is connected to D. Each behaviour corresponds to the sign + and − at Eq. (4), respectively. According to the behaviour of the frequency-dependent pinched hysteresis loop, this is composed by two lobes with symmetric areas. Since the hysteresis loop is represented on the v-i plane, the average current occurs when the area of both lobes is zero, and hence, the hysteresis loop tends to be a straight line as f → ∞. This last effect is achieved when the linear time-varying part of the memductor is zero, and hence, from Eq. (4), we get
im(t)=vm(t)Rm+RxE5
From Eqs. (4) and (5), a SIMULINK model can be easily built, as shown in Figure 4(b). Note that to obtain a decremental memductor, the input-terminal second of the block, shown in Figure 4(b), must be negative. Considering vm(t) = Amsin(ωt) and substituting Eq. (5) in Eq. (4), we get
where τ=20π(Rm+Rx)(Cm+Ca)AvAiAm. From Eq. (7), one can intuit that kn will decrease as the frequency increases, but Eq. (7) also reveals that
kn → 0 when f → ∞ or Am → 0. Therefore, Eq. (6) becomes dominated by its linear time-invariant admittance.
kn → 1 when f → 1/τ or Am is monotonically increased. Hence, the maximum frequency-dependent pinched hysteresis loop is obtained.
kn → ≥1 when f ≤ 1/τ or Am increases too much. For this case, the hysteresis loop is lost.
In this manner, the behaviour of the frequency-dependent pinched hysteresis loop can be kept over a broad range of frequencies and amplitude Am, when the numerical value of kn is in the interval (0, 1) [32]. This means that τ must be updated according to f and Am, respectively. The numerical value of each element of Figure 4(a) for different operating frequencies and amplitudes can be found in [32].
According to [32], Figure 4(a) was configured for working at 16 Hz in both operation modes. Henceforth, numerical results of the incremental topology will be shown below in the left side, whereas the decremental topology will be shown in the right side. From Figure 4(b), numerical results for each topology are depicted in Figure 5(a) and (b) (solid lines). Let us now increase monotonically the operating frequency of vm(t) until f = 500 Hz. As depicted in Figure 5(c) and (d) (solid lines), the frequency-dependent pinched hysteresis loop for both topologies becomes dominated by the linear time-invariant admittance. In this stage, for widening the hysteresis loop of each topology and keeping f = 500 Hz, Cm or R1 must be adjusted. Afterwards, each topology shown in Figure 4(a) was simulated at HSPICE and numerical results are illustrated in Figure 5(a) and (b) (dash-dot lines) operating at 16 Hz, respectively. Similarly as above, the operating frequency was increased until 500 Hz and, as a consequence, both pinched hysteresis loops become a straight line, as depicted in Figure 5(c) and (d) (dash-dot lines). In order to demonstrate the real behaviour of the memductor emulator circuit, Figure 4(a) was built with off-the-shelf devices.
Figure 5.
Numerical, HSPICE and experimental results of Figure 4(a) operating at: (a) 16 Hz and (c) 500 Hz, for incremental mode; (b) 16 Hz and (d) 500 Hz, for decremental mode.
In this way, Figure 5(a) and (b) (dashed lines) illustrate the pinched hysteresis loops for both operation modes and the upper and lower lobe area of both hysteresis loops becomes zero when the operating frequency increases and hence the hysteresis loop tends to be a straight line, as illustrated in Figure 5(c) and (d) (dashed lines), confirming the theory described before. To experimentally test the non-volatility of the memductor emulator circuit, the voltage across Cm of Figure 4(a) was measured for each incremental and decremental configuration. In both cases, a rectangular pulse train of 5 V of amplitude with 82 μs was applied in the input of Figure 4(a). Therefore, Figure 6(a) shows the behaviour of vCm(t) for the incremental case, whereas Figure 6(b) shows the decremental case. From Figure 6, one can observe that the variation of vCm(t) is more pronounced for the decremental case. Observe, also, that the voltage is kept during non-pulse period. Again, the memductive behaviour in each operation mode can be reverted to its last value, whether a negative pulse of the same size is applied [32].
Figure 6.
Experimental results of non-volatility property for: (a) incremental mode and (b) decremental mode.
2.3. Grounded memristor emulator circuit II
As last example, we discuss the charge-controlled grounded memristor emulator circuit reported in [31] and illustrated in Figure 7(a). Simple analysis of Figure 7(a) allows us to obtain the memristive behaviour given by
Figure 7.
(a) Charge-controlled grounded memristor emulator circuit taken from [31] and (b) SIMULINK model of Eqs. (8) and (9).
vm(t)im(t)=M(qm(t))=R1±R240C1∫0tim(τ)dτE8
It is notable to point out that the positive sign in Eq. (8) correspond to the S switch connected to I in Figure 7(a) and hence, an incremental behaviour is obtained; whereas the negative sign is obtained when S is connected to D and hence a decremental behaviour. Again, following the idea described in previous subsections and reported in [28, 31], a frequency analysis can be done. According to Eq. (8), the average current will occur when the linear time-varying resistor is zero and hence from Eq. (8) we get:
im(t)=vm(t)R1E9
By merging Eqs. (8) and (9), a SIMULINK model can be built, as depicted in Figure 7(b). In this figure, the input-terminal second of the adder block must be negative to obtain a decremental behaviour. Assuming vm(t) = Amsin(ωt) and substituting Eq. (9) in Eq. (8), we obtain
where τ=40πR12C1R2Am is the time constant of the emulator circuit and T=1f is the period of vm(t). In the same way as in previous subsections, kn will decrease as the operating frequency increases, and for holding the hysteresis loop at a particular frequency, the numeric value of τ must be updated by C1. Analysing Eq. (11) for both configurations, we have
kn → 0 when f → ∞ or Am → 0. Therefore, Eq. (10) becomes dominated by R1.
kn → 1 when f → 1/τ or Am is monotonically increased. Thus, we see that the maximum pinched hysteresis loop is achieved.
kn → ≥1 when f ≤ 1/τ or Am increases too much. For this case, the hysteresis loop is lost.
According to [31], the memristor emulator circuit was configured to operate at 16 Hz in both operation modes. By using Figure 7(b), the hysteresis loop for each topology shown in Figure 7(a) is obtained, as depicted in Figure 8(a) and (b) (solid lines), respectively. By monotonically increasing the operating frequency of vm(t) until 100 Hz, both hysteresis loops become dominated by R1, as illustrated in Figure 8(c) and (d) (solid lines). It is worth stressing that to obtain the pinched hysteresis loops shown in Figure 8(a) and (b) (solid lines) but at f = 100 Hz, the numeric value of C1 must be adjusted. Therefore, one can insight that by scaling down C1, the hysteresis loop behaviour, for both topologies, can be pushed for operating at higher frequencies. On the other hand, Figure 7(a) was also simulated at HSPICE by using the numerical value of each element described in [31] and for both topologies. Simulation results are illustrated in Figure 8(a) and (b) (dash-dot lines), respectively; whereas the linear behaviours are depicted in Figure 8(c) and (d) (dash-dot lines).
Figure 8.
Numerical, HSPICE and experimental results of Figure 7(a) operating at: (a) 16 Hz and (c) 100 Hz, for incremental mode; (b) 16 Hz and (d) 100 Hz, for decremental mode.
To validate the results derived and demonstrate the real behaviour of the emulator circuit, Figure 7(a) was built and experimentally tested by using commercially available active devices. Therefore, Figure 8(a) and (b) (dot-square lines) show the experimental results for each topology and at each fundamental operating frequency; whereas Figure 8(c) and (d) (dot-square lines) show that the hysteresis loops become dominated by R1, confirming the theory described above. A notable fingerprint of any memristor emulator circuit is the non-volatility of its memristance. This means that the memristance once programmed, its last value must be kept for a long time. In order to verify this property, the voltage across C1 was first experimentally measured and next, by using Eq. (8), a post-processing was done for getting the memristance variation for each topology, as depicted in Figure 9 (top figure). The memristance variations were obtained when a pulse train of 5 V of amplitude and 0.5 ms of pulse width was applied to Figure 7(a), as illustrated in Figure 9 (lower figure).
Figure 9.
Experimental results of non-volatile memristance for incremental mode (black line) and decremental mode (red line). In the figure below, vm(t) as pulse train.
As one can observe in Figure 9, the memristance range for both emulator circuits is 7 kΩ, and although the pulse train is applied indefinitely, the maximum memristance achieved is 19 kΩ; whereas the minimum memristance for the decremental case is 5 kΩ. On the other hand, if the pulse train with −5 V of amplitude and same pulse width is applied, then the memristive behaviour is inverted for each topology shown in the top of Figure 9 [31].
3. Design guide
According to Section 2, one can observe that Eqs. (1), (4) and (8) have the form
yn(t)=x(t)(an±bn∫0tz(τ)dτ)E12
where yn(t) is the current or voltage output signal, x(t) is the voltage or current input signal and z(t) is the voltage or current control signal; an represents the linear time-invariant gain and bn represents the linear time-varying gain, which is associated with the time constant of the emulator circuit [28, 31, 32]. Assuming that z(t) = Amsin(ωt + θ), where θ is the phase in degrees, we obtain
According to [28, 31, 32], the linear time-varying gain can be computed in function of ω and Am given by
bn=anωknAmE15
where kn ∈ (0, 1) is a parameter that is used to ensure the behaviour of the pinched hysteresis loop.
In order to design a memristor emulator circuit, the following four-step design procedure is proposed
Step 1. For all memristor emulator circuit that has the form given by Eq. (12) and to ensure the pinched hysteresis loop, we choose kn = 0.5.
Step 2. Given an operating frequency and Am, use Eq. (15) to find the relation between bn and an.
Step 3. Select the numeric value of an, which is associated to the linear time-invariant resistor/conductor. As a consequence, the numeric value of bn is derived from Eq. (15).
Step 4. For each topology, bn is related with those parameters of the emulator circuit and τ. Therefore, the numeric value of each resistor and capacitor can be deduced.
If the above procedure is followed, it is most likely that a memristor emulator circuit with good features will result and with a frequency-dependent hysteresis loop with relatively symmetrical lobes.
4. Offset compensation
Some properties that any emulator circuit must satisfy to be considered as memristor were described in Section 1. One of them is the frequency-dependent pinched hysteresis loop observed on the voltage-current plane, which must pass through the origin for any periodic signal with any amplitude, operating frequency and initial conditions [1]. Thus, whether a periodic signal is applied to the memristor emulator circuit, both the voltage and current are zero when any of them is zero. Therefore, any device is a memristor or a memristive device when it has a current-voltage hysteresis curve with identical zero crossing. However, until today, all the memristor emulator circuits reported in the literature [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32] are operating in low-frequency and some of them present a deviation of the crossing point on the origin. This behaviour is more evident when the operating frequency of the stimulus signal increases, and hence, the emulator circuit does not only stop mimicking the behaviour of the memristor, but also reduces its application range. Note that below a certain critical frequency, the emulator circuit mimics well the behaviour of a memristor and beyond that of critical frequency, the circuit becomes a memristive device with an additional battery in series.
In order to overcome this shortcoming and achieve a pinched hysteresis loop operating at high frequency, an offset compensation technique must be applied. Such techniques have been reported in [33]. Basically, the technique involves adding two DC voltage sources in the analogue multiplier to vertically and horizontally control the offset of the hysteresis loop. However, as described in [33], this offset reduction technique is only applicable to floating and grounded memristor emulator circuits whose design is based on analogue multipliers. In this manner, let us consider the topologies shown in Figure 1(a) and 7(a), including the voltage sources, as depicted in Figure 10(a) and (b), respectively. According to Eq. (1), Figure 10(a) and [28, 33], the controlled incremental and decremental memristance is modified as
Similarly for Eq. (8), Figure 10(b) and [31, 33], the memristance becomes:
M(qm(t),VH,VV)=R1∓R220VV±R240C1∫0tim(τ)dτ±VHE17
where VH is a DC voltage source to control the horizontally offset and VV is other DC voltage source to control the vertical offset of the frequency-dependent pinched hysteresis loop on the voltage-current plane. Note that if VH = VV = 0, then Eqs. (16) and (17) are reduced to Eqs. (1) and (8), respectively. For both topologies shown in Figure 10, two switches, S1 and S2, are used to interchange the kind of memristor and to connect the VV voltage source in each case. To validate the offset reduction method, Figure 10(a) was configured at decremental mode and operating to 14 kHz. In a first step, VH = VV = 0 were considered and simulation results are depicted in Figure 11(a) (solid line). Note that the pinched hysteresis loop deviates of the origin. In a second step, the DC voltage sources were monotonically decreased until VH = −60.59 mV and VV = −160.3 mV, and as a consequence, the offset was reduced, as shown in Figure 11(a) (dashed line). A similar analysis procedure was realized to the topology depicted in Figure 10(b) but operating to 160 kHz. In this manner, the grounded memristor emulator circuit was connected as incremental mode and considering VH = VV = 0. HSPICE simulations were obtained and shown in Figure 11(b) (solid line). In order to reduce the offset in Figure 11(b) (solid line), the DC voltage sources were updated to VH = −195.5 mV and VV = 1.568 V, and hence, the crossing point was pulled towards the origin, as shown in Figure 11(b) (dashed line). It is worth to stress that the value of each DC voltage source associated to each topology was derived to trial and error, and it should slightly be updated for each operating frequency. Hence, an open question is how to automatically compute the numeric value of each DC voltage source associated to each topology and operation mode. Moreover, in Figure 11(b) (solid lines), one can observe that each frequency-dependent pinched hysteresis loop becomes slightly deformed, resulting at an asymmetrical behaviour with regards to the origin, and hence, the hysteresis lobe area is not equal. Nonetheless, after of the offset compensation, the hysteresis lobe area for all frequency-dependent pinched hysteresis loops become relatively equal as depicted in Figure 11(b) (dashed lines). As a result, it is predicted that the frequency behaviour of the pinched hysteresis loops for both memristor emulator circuits can be pushed for operating in higher frequencies and holding a symmetrical behaviour, since the offset voltage glimpsed can again be reduced by updating the DC voltage sources.
Figure 11.
HSPICE results for: (a) decremental topology of Figure 10(a) and (b) incremental topology of Figure 10(b). For both figures: offset uncompensated (solid lines) and compensated (dashed lines).
5. Transformation of normal non-linear resistors to inverse
A memristor/memductor is basically a resistor/conductor whose resistance/conductance can be changed by applying a voltage across its terminals or by applying a flow of current. The type of control signal depends on the type of memristor/memductor, i.e. flux- or charge-controlled. In any case, the frequency-dependent pinched hysteresis loop of a normal non-linear resistor/conductor will become a straight line if the operating frequency increases. This effect is because a normal non-linear resistor/conductor uses an integrator block and, in general, its behaviour can be modelled by Eq. (12). Since the inverse operation of an integral is the derivate, the hysteresis loop behaviour of a normal non-linear resistor can be inverted whether a differentiator block is used instead of an integrator block. Under this assumption and following the idea presented in Section 3, we have modified Eq. (12) as
yi(t)=x(t)(ai±bidz(t)dt)E18
where yi(t) is the inverse current or voltage output signal, x(t) is the voltage or current input signal and z(t) is the voltage or current control signal; ai represents the linear time-invariant gain and bi is the linear time-varying gain. Assuming z(t) = Am sin (ωt + θ), we obtain
Comparing Eqs. (14) and (20), one can observe that the sole difference is the position of ω. According to Section 3 [28, 31, 32], the linear time-varying gain can be computed in function of ω and Am given by
bi=aiωkiAmE21
where ki ∈ (0, 1). In Section 2, the behavioural model of normal flux- or charge-controlled resistors was derived and one can observe that each model has an integrative part. As first approximation and for obtaining an inverse flux- or charge-controlled resistor from a normal resistor, the integrator circuit of the latter must be replaced by a differentiator circuit in the former. This task can be done by simply interchanging C1 by R2 in Figure 1(a), as depicted in Figure 12(a), and analysing this figure we obtain
Figure 12.
Inverse versions of: (a) Figure 1(a) and (b) Figure 7(a).
vm(t)im(t)=R1±R1R3R4Cz10R2dvm(t)dtE22
Considering vm(t) = Amsin(ωt + ϕ), where ϕ is the phase in degrees and by using Eqs. (14) and (20), Eqs. (1) and (22) are rewritten as
vm(t)im(t)=R1±R1R410R2R3CzωAm2−vm2(t)E23
vm(t)im(t)=R1±R1R3R4Czω10R2Am2−vm2(t)E24
Comparing Eqs. (23) and (24) with Eqs. (14) and (20), respectively, one obtains
an=ai=R1,bn=R1R410R2R3Cz,bi=R1R3R4Cz10R2E25
At this point, our results indicate that by selecting adequately the numerical values of each element of Eq. (25) for a particular operating frequency, the emulator circuits of Figures 1(a) and 12(a) are able to generate normal and inverse pinched hysteresis loops, respectively. It is worth to stress that the transformation methodology is only applicable for those topologies where the integrator circuit is clearly defined, and when it is replaced by a differentiator circuit, the behaviour of the resulting emulator circuit, in general, is not modified. However, floating and grounded non-linear resistor emulator circuits without this requirement have also been reported in the literature [27, 28, 29, 30, 31, 32, 33]. One example of them was shown in Figure 7(a). However, whether C1 is replaced by an inductor L1 as shown in Figure 12(b), we get
vm(t)im(t)=R1±R2L140dim(t)dtE26
Afterwards assuming that im(t) = Amsin(ωt + ϕ) and by considering Eqs. (14) and (20), Eqs. (8) and (26) take the form
vm(t)im(t)=R1±R240C1ωAm2−im2(t)E27
vm(t)im(t)=R1±R2L1ω40Am2−im2(t)E28
Comparing Eqs. (27) and (28) again with Eqs. (14) and (20), respectively, one obtains
an=ai=R1,bn=R240C1,bi=R2L140E29
Note that although the behaviour of the inductor can be emulated by using gyrators, the resulting circuit becomes bulky and complex. Hence, this transformation technique does not show any advantage with respect to the methodology mentioned above. Without loss of generality, only HSPICE results of Figures 1(a) and 12(a) configured at incremental mode will be shown on the left side of Figure 13, whereas that for the decremental configuration will be shown on the right side. In a first step, both emulator circuits were configured to f = 2 kHz. HSPICE results are illustrated in Figure 13(c) and (d) and it is evident that these hysteresis loops are almost similar. Later, the operating frequency was decreased to f = 1 kHz, and as one can observe in Figure 13(a) and (b), the hysteresis loops present the behaviour forecasted. Finally, the operating frequency of vm(t) was increased to f = 4 kHz, and hence, the behaviour of the hysteresis loops was inverted, as depicted in Figure 13(e) and (f). From all these figures, we can observe that for inverse non-linear resistors, the hysteresis loop becomes a straight line when the operating frequency decreases, whereas for normal non-linear resistors, this behaviour is achieved when the operating frequency increases. Note that although the topology of an inverse non-linear resistor shows a frequency-dependent pinched hysteresis loop, this cannot be considered as memristor emulator circuit, since the property of non-volatility is not satisfied. Table 1 gives the numerical value for each passive element.
Figure 13.
Frequency-dependent hysteresis loop of Figure 1(a) (blue line) and Figure 12(a) (red line) operating to: 1 kHz for (a) incremental and (b) decremental mode; 2 kHz for (c) incremental and (d) decremental mode; 4 kHz for (e) incremental and (f) decremental mode.
Numerical variables of Eq. (25) and component list of Figures 1(a) and 12(a).
6. Analogue applications based on memristor emulator circuits
This section discusses three examples at the behavioural level of abstraction on the use of memristor emulator circuits in real analogue applications.
6.1. Frequency-shift keying (FSK) modulator
Modulator circuits are important blocks in digital communications since they are used to convert a unipolar bit sequence in an appropriate form for modulation and transmission [34]. Among the modulator circuits, frequency-shift keying (FSK) modulation is a frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier wave. Thus, the higher frequency of the modulator is assigned to signal 1 and the lower frequency is assigned to signal 0 [35]. This behaviour can be achieved by using a single-memductor controlled sinusoidal oscillator (SMCO), as shown in Figure 14(a). Through routine analysis, we get
Figure 14.
(a) FSK modulator based on SMCO by using Figure 4(a); and (b) SIMULINK model of Eq. (30).
s2+1C1(1R1−1R3)s+W2R3C1C2E30
From Eq. (30), the condition of oscillation (CO) is: R3 = R1 and the frequency of oscillation (FO) is: f0=12πW2R3C1C2. It is seen that CO and FO can independently be controlled by R1 and W2, respectively. By merging Figure 4(b) with Eq. (30), a SIMULINK model can be built. Such model is depicted in Figure 14(b) where the voltage and current gains are unitary (i.e. Av = Ai = 1). Note that the SMCO along with an incremental memductor is depicted in the upper part of Figure 14(b), whereas the SMCO along with a decremental memductor is illustrated in the bottom. More detailed analysis of Eq. (30) is found in [36]. For this application, the SMCO was designed with an oscillation centre frequency of f0 = 577 kHz and hence, R1 = 1 kΩ, R3 = 942 Ω, C1 = C2 = 140 pF and W2 = 0.33 mS. In order to vary the incremental memductance, a pulse train with 2 V of amplitude and pulse width of 3 μs is used to increase W2; whereas for the decremental memductance, a pulse of 0.3 V of amplitude and with the same pulse width mentioned before is used to decrease W2. For both cases, when negative pulses with the same amplitudes mentioned before are applied, both memductances return to their last state [32]. By applying these control signals in Figure 14(b), one obtains an FSK signal, as shown in Figure 15(a) and (b). On these last figures and into the interval [0, 2 ms], the operating frequency of the FSK modulator is the same as SMCO. Next, when a positive digital signal is applied to the incremental and decremental memductor, the memductance increases or decreases, respectively. As a consequence, the FO of the SMCO also increases or decreases, as shown in Figure 15(a) and (b) into the interval [2 ms, 4 ms], approximately. Afterwards, by applying a negative digital signal to the memductors, the FSK modulator returns to its original FO. Therefore, we can observe that a memductor (or memristor) device is useful for controlling the FO of a SMCO and they can be used to design an FSK modulator.
Figure 15.
Time response of the FSK modulator using: (a) incremental memductor and (b) decremental memductor.
Proportional-integral-derivative (PID) control has been used successfully for regulating processes in industry for more than 60 years, due to its simple and easy design, low cost and wide range of applications. A PID controller involves three parts: proportional part, integral part and derivative part, and its target is to minimize the error between the set point and the measured output. It is worth mentioning that for a complex or non-linear process, sometimes it is very difficult to find the optimal parameters of the PID controller.
In this sense, the oldest and simplest method was proposed by Ziegler and Nichols [37]. However, this tuning method provides a large overshoot and settling time, and hence, the PID parameters must subsequently be refined. Other methods that can also be used for choosing the parameters of PID controller were reported in [38]. However, this method presents drawbacks when applied to certain types of plants. Furthermore, the PID parameters are always constant and almost without knowledge of the process to control. Therefore, an efficient and effective online tuning mechanism is widely demanded. This last task can be achieved by using a memristor/memductor, since its memristance/memductance can be kept even when the current flow in the memristor/memductor is stopped [1, 28, 29, 30, 31, 32, 33, 35]. This property asserts that it is possible to update the parameters of a continuous PID controller online, i.e. the proportional gain (kp), integral gain1 (ki) and derivative gain (kd). In order to illustrate this idea, the transient response of a second-order low-pass filter is controlled by a PID controller [39]. The transfer function of the filter is given by
H(s)=1LCs2+sRC+1LCE31
The numeric value of each element of Eq. (31) is R = 100 Ω, L = 0.475 mH, and C = 1 μF. At this point, the PID controller parameters, kp = 80, ki = 1e5 and kd = 2e-3, were obtained according to [37].
Since the integral and derivative parts of the continuous PID controller are, in practice, designed with R-C elements and active devices [27], one can obtain Ri = Rd = 2 kΩ, Ci = 5 nF and Cd = 1 μF. Under this assumption, Figure 4(b), the PID controller and Eq. (31) are merged to build a SIMULINK model. It is worth mentioning that the memductor shown in Figure 4(b) was configured to operate at 300 Hz. Thus, Figure 16 shows all feedback systems to be simulated [39]. In the upper part of Figure 16, the plant with feedback is illustrated. In the second block, the PID controller with fixed parameters along with the plant is depicted. The third block is the PID controller based on incremental memductor along with the plant; and finally, the fourth block depicts the PID controller based on decremental memductor along with the plant. For the last two cases, the memductance is varied by applying a pulse train, and a square signal with 5 V of amplitude and f = 200 Hz is applied to all feedback systems. Figure 17 shows all the transient responses of Figure 16. As a first step, the square signal (magenta line) is applied to the feedback plant, and its transient response is underdamped (green line), as shown in Figure 17(a). Hence, the plant needs to be controlled. In a second step, the transient response of the second block is obtained and shown in Figure 17(a) (black line). Here, the rise- and fall-time are symmetric and cannot be modified online. In order to get that effect, the incremental and decremental memductor is used [39]. For both memductances, the pulse train was adjusted to get the following cases:
Figure 16.
PID controller based on memductors.
Figure 17.
(a) Transient response of the plant and PID controllers. (b) Pulse train for controlling the incremental and decremental memductance.
By using an incremental memductor, the rise-time (red line) of the system is largest than the rise-time gotten with fixed parameters (black line) and those obtained with the decremental memductor (blue line). In fact, the rise-time of the latter is the shortest, as depicted in Figure 17(a).
By using a decremental memductor, the fall-time (blue line) of the system is largest than the fall-time gotten with fixed parameters (black line) and those obtained with the incremental memductor (red line). In fact, the fall-time of the latter is the shortest, as shown in Figure 17(a).
In order to get the same rise-time in all cases, both memductances were adjusted by using the pulse train shown in Figure 17(b), and the result can be observed in Figure 17(a) at 5.5 ms, approximately.
Therefore, we can observe that memristors/memductors are useful for controlling the rise- and fall-time of the transient response of a feedback system.
6.3. Memristive synapses
As a last example, but not the least important, we describe the analysis and design of a synaptic circuit based on memristors. Basically, synapses are specialized sites where several neurons are connected, which receive and send information from other cells; this junction is the foundation of complex brain tasks and functions related to learning and memory. Emulation of biological synapses is the basis to build large-scale brain-inspired systems [40]. A key property of the brain is its ability to learn, this process lies in the plasticity of the synapses that allows the nervous system to adapt. Memristor is a candidate suitable to emulate a synapse, due to its non-volatility property and programmable device. But a single memristor cannot accomplish this task; in fact, there are several topologies that enable this behaviour, depending on the approach used for artificial neural network, i.e. cellular neural networks (CNN) [41], spiking neural networks (SNN) [42, 43], feed-forward neural networks (FFNN) [44] and recurrent neural networks (RNN) [45]. Few architectures based on memristors are focused on feed-forward artificial neural networks, which completely satisfies the requirements of an artificial synapse. On the other hand, there are several requirements that must be met for a synaptic learning [46]:
The weight must be stored always in the absence of learning.
The synapse must be computed as an output, i.e. the product of the input signal with the synaptic weight also called synaptic weighting.
Each synapse must occupy a reduced area.
Each synapse must operate with low power dissipation.
Each synapse must be capable of implementing a learning rule such as Hebbian or Back propagation [1, 40, 46].
Table 2 shows a comparison among the most recent memristive neural networks. Thus, the third column of the table shows whether design meets the five rules mentioned before, such that the synapse can be considered as learning synapse. Design of [41] does not meet rule 5, since to change a negative weight to positive not only additional circuitries is required, but on line training is not also possible; [43] meets some of the properties of [46], because it is implemented through an ideal memristor model whose applications are limited to simulations; [44] uses a high number of active components (i.e. 64) for building a synapse, considering the memristor emulator reported in [49]. The fourth column is the frequency of the spikes for SNN approach and for the case of MCNN and ANN the time for weight setting from its lowest to the highest value is described. If weight setting time is too long, then weight processing will take longer which affects its performance. Thus, only [44] simulates and fully implements a synapse based on a memristor emulator. Unlike [41, 42, 47], its hardware applications are not limited to HP memristor fabrication, but the number of elements and the operating frequency are parameters that restrict its performance. However, frequency is limited and the number of active components is high. On the other hand, the proposed synaptic memristive bridge circuit begins with the analysis of memristance of the flux-controlled memristor of Figure 1(a). First, memristance variation of Figure 1(a) is analysed, where Eq. (1) can be rewritten as
The maximum value of memristance for an incremental memristor is: Minc=R1+R1kn and the minimum is Minc=R1−R1kn, as shown in Figure 18(a).
Figure 18.
(a) Incremental and decremental memristance when vm = Amsin(ωt, ). (b) Simulation results of memristance for Am = 2 V, f = 8 kHz and kn = 0.8.
Considering that kn ∈ (0, 1), it is preferable to use kn → 1 to assure more range of variation; however, it is necessary to recall that memristance value is limited. In this frame of reference, several tests varying kn were performed in HSPICE with incremental and decremental memristors tested separately and in different operating frequencies, as shown in Figure 18(b). Nevertheless, secondary effects are observed when varying kn → 0.8, and therefore, the memristors have a different behaviour compared with Figure 18(a), since in this case, the incremental and decremental memristance vary within the same range of memristance. In order to obtain the same behaviour of memristance from Figure 1(a) and for several operating frequencies, each discrete element must be updated according to Table 3. Note that the proposed topology takes advantage of memristance behaviour and uses only two flux-controlled floating memristor emulators, M1(ϕm(t)), configured as decremental and M2(ϕm(t)) as an incremental memristor, along with two passive resistors Ra = Rb = 10 kΩ, as shown in Figure 19(a) [50]. The analysis of Figure 19(a) is as follows: when a positive pulse is applied, M1(φm(t)) decreases and M2(φm(t)) increases. As a consequence, vB decreases and vA increases. Moreover, when a negative pulse is applied, an inverted behaviour is glimpsed. Whether the pulse width is wide enough, the output voltage vAB = vA − vB varies gradually from negative to positive voltages and vice versa. Therefore, the memristances M1(ϕm(t)) and M2(ϕm(t)) are varied within vm − vA and vm − vB voltages, respectively. For synapse design, first the voltage v2 was considered and it is described by
Element
R1
R2 = R4
R3
Cz
F = 8 kHz
10 kΩ
100 kΩ
1.97 kΩ
2.5 nF
f = 10kHz
2 nF
f = 5kHz
3 kΩ
2.652 nF
Table 3.
Component list of Figure 1(a) configured in several operating frequencies.
Figure 19.
(a) Synaptic memristive bridge and (b) SIMULINK model of Eqs. (34)–(38).
v2=±v1α∫0tvm(τ)dτE33
Hence, considering Eq. (33), vA and vB are redefined as
Similarly, memristance variation for M1(ϕm(t)) is:
M1(ϕM1(t))=R1+R1αϕM1(t)E38
As observed in Eqs. (37) and (38), the memristances depend on Eq. (35) and each memristor in the synapse is designed with the same parameters, so their memristances vary at same rate. From Eqs. (34)–(38), a SIMULINK model is built and depicted in Figure 19(b). The synaptic memristive bridge was simulated in HSPICE and numerical simulations of Figure 19(b) were obtained at MATLAB. Thus, the memristance variation M1(ϕM1(t)) and M2(ϕM2(t) are shown in Figure 20, respectively. The vAB voltage for kn = 0.8 behave as sawtooth wave, as seen in Figure 21, and ξ is approximated by
Figure 20.
Memristance variations of Figure 19(a) when the bi-pulse signal vm = ±2 V at 8 kHz is applied: (a) MATLAB® and (b) HSPICE®.
Figure 21.
ξ variations of Figure 19(a) when the bi-pulse signal vm = ±2 V at 8 kHz in (a) MATLAB® and (b) HSPICE®.
ξ={49077t−1.53380≥t≥T2−48567+4.5373T2≥t≥TE39
whose confidence level is Q2 = 0.996. This value represents the linearity of ξ, if Q2 → 1 means that there is a linear relation between input pulses and ξ. To verify the behaviour of the synaptic memristive bridge, three basic steps are performed [44, 46].
Sign setting. This stage refers to configure a positive sing or negative weight, and assures that ξ is within the desired range. Therefore, a bi-pulse signal with vm = ±2 V of amplitude configured at several frequencies is applied, as depicted in Figure 22. To configure a positive sign, it is necessary to apply a falling edge pulse, when a rising edge pulse is applied, a negative ξ is configured.
Weight setting. Once the sign is established, it is necessary to apply a pulse width to set weight of the synapse. For the case 8 kHz, the allowed maximum pulse width is 62.5 μs, in the general case it is T/2. Therefore, pulse signal vm with pulse width of range (0, T/2) is applied to set the weight to a desired ξ. In Figure 22 a pulse vm is shown whose pulse width is 2.5 μs which sets ξ = −0.8495.
Synaptic weight processing. This operation refers to perform vs = ξvp, which is the multiplication of a narrow input pulse vp and the pre-established ξ weight. The pulse width of vp is narrow due to an effect called memristance drifting which is drifting of flux accumulation φM1 and φM1 caused by vp [1, 40]. However, the response to that narrow pulse is governed by the settling time (st) and slew rate (SR) of multiplier AD633 used in the memristor emulator circuit, whose st = 2 μs at output voltage V0 = 20 V and SR of 20 V/μs. The AD633 can be replaced by AD734 multiplier whose SR = 450 V/μs at V0 = 20 V and st = 200 ns.
Figure 22.
Synaptic multiplication when ξ = 0.8495 and a pulse signal vp = 1.5 V of amplitude with pulse width of 200 ns is applied: (a) MATLAB results and (b) HSPICE simulations.
Finally, Figure 22(a) presents a MATLAB simulation of a pulse vp = 2 V whose pulse width is 200 ns. This pulse is multiplied by ξ, obtaining vs = −1.699. On the other hand, the synaptic weight processing at HSPICE shown in Figure 22(b) is done following the same methodology [50].
7. Conclusion
Memristor emulator circuits are useful for developing real memristor-based application circuits as well as for educational purposes. In this chapter, we have studied three memristor/memductor emulator circuits whose behaviour can be configured as incremental or decremental. Two of them are grounded versions whereas the latter is floated. The behavioural model for each topology was derived and its SIMULINK model was also programmed. The design guide suggested in this chapter provides a systematic way for designing memristor/memductor emulator circuits with good features. Further, an offset compensation technique was also described in order to achieve the frequency-dependent pinched hysteresis loop that does not deviate of the origin when the operating frequency of the input signal increases. As a result, it is predicted that the frequency behaviour of the pinched hysteresis loops of memristor/memductor emulator circuits can be pushed for operating in higher frequencies and holding a symmetrical behaviour, since the offset voltage glimpsed can again be reduced by updating the DC voltage sources. Moreover, a transformation methodology for obtaining the behaviour of inverse non-linear resistors from normal non-linear resistors has also been described, and as it was observed in Section 5, the methodology consists in replacing the integrator circuit, clearly defined in the normal topologies by a differentiator circuit, so that not only an inverse behaviour is obtained, but also the resulting topology is not drastically modified with respect to the original topology. Finally, three real analogue applications based on memristors/memductors were addressed.
Acknowledgments
This work was supported in part by the National Council for Science and Technology (CONACyT), Mexico, under Grant 222843 and in part by the Program to Strengthen Quality in Educational Institutions, under Grant C/PFCE-2016-29MSU0013Y-07-23.
\n',keywords:"memristor, pinched hysteresis loop, current conveyor, non-linear resistor, behavioural modelling",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/55950.pdf",chapterXML:"https://mts.intechopen.com/source/xml/55950.xml",downloadPdfUrl:"/chapter/pdf-download/55950",previewPdfUrl:"/chapter/pdf-preview/55950",totalDownloads:999,totalViews:448,totalCrossrefCites:1,totalDimensionsCites:1,hasAltmetrics:0,dateSubmitted:"December 5th 2016",dateReviewed:"April 18th 2017",datePrePublished:"December 20th 2017",datePublished:"April 4th 2018",dateFinished:"June 9th 2017",readingETA:"0",abstract:"This chapter introduces a design guide of memristor emulator circuits, from conceptual idea until experimental tests. Three topologies of memristor emulator circuits in their incremental and decremental versions are analysed and designed at low and high frequency. The behavioural model of each topology is derived and programmed at SIMULINK under the MATLAB environment. An offset compensation technique is also described in order to achieve the frequency-dependent pinched hysteresis loop that is on the origin and when the memristor emulator circuit is operating at high frequency. Furthermore, from these topologies, a technique to transform normal non-linear resistors to inverse non-linear resistors is also addressed. HSPICE numerical simulations for each topology are also shown. Finally, three real analogue applications based on memristors are analysed and explained at the behavioural level of abstraction.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/55950",risUrl:"/chapter/ris/55950",book:{slug:"memristor-and-memristive-neural-networks"},signatures:"Carlos Sánchez-López, Illiani Carro-Pérez, Victor Hugo Carbajal-\nGómez, Miguel Angel Carrasco-Aguilar and Francisco Epimenio\nMorales-López",authors:[{id:"17480",title:"Dr.",name:"Carlos",middleName:null,surname:"Sanchez-Lopez",fullName:"Carlos Sanchez-Lopez",slug:"carlos-sanchez-lopez",email:"carlsanmx@yahoo.com.mx",position:null,institution:null},{id:"161703",title:"Dr.",name:"Victor H.",middleName:null,surname:"Carbajal-Gomez",fullName:"Victor H. Carbajal-Gomez",slug:"victor-h.-carbajal-gomez",email:"victhug26@gmail.com",position:null,institution:null},{id:"203246",title:"MSc.",name:"Illiani",middleName:null,surname:"Carro-Pérez",fullName:"Illiani Carro-Pérez",slug:"illiani-carro-perez",email:"icarrop@itesm.mx",position:null,institution:null},{id:"203247",title:"Dr.",name:"Miguel Angel",middleName:null,surname:"Carrasco-Aguilar",fullName:"Miguel Angel Carrasco-Aguilar",slug:"miguel-angel-carrasco-aguilar",email:"macarras2010@gmail.com",position:null,institution:null},{id:"203248",title:"MSc.",name:"Francisco Epimenio",middleName:null,surname:"Morales-López",fullName:"Francisco Epimenio Morales-López",slug:"francisco-epimenio-morales-lopez",email:"molf2503@hotmail.com",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Analogue memristor emulators",level:"1"},{id:"sec_2_2",title:"2.1. Floating memristor emulator circuit",level:"2"},{id:"sec_3_2",title:"2.2. Grounded memristor emulator circuit I",level:"2"},{id:"sec_4_2",title:"2.3. Grounded memristor emulator circuit II",level:"2"},{id:"sec_6",title:"3. Design guide",level:"1"},{id:"sec_7",title:"4. Offset compensation",level:"1"},{id:"sec_8",title:"5. Transformation of normal non-linear resistors to inverse",level:"1"},{id:"sec_9",title:"6. Analogue applications based on memristor emulator circuits",level:"1"},{id:"sec_9_2",title:"6.1. Frequency-shift keying (FSK) modulator",level:"2"},{id:"sec_10_2",title:"6.2. Proportional-integral-derivative (PID) controller",level:"2"},{id:"sec_11_2",title:"6.3. Memristive synapses",level:"2"},{id:"sec_13",title:"7. Conclusion",level:"1"},{id:"sec_14",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'Adamatzky A, Chua LO. Memristor Networks. Switzerland: Springer International Publishing; 2014'},{id:"B2",body:'Wang X, Li C, Huang T, Duan S. Predicting chaos in memristive oscillator via harmonic balance method. 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Berlin: Springer-Verlag, Germany; 2003'},{id:"B35",body:'Göknar IC, Öncül F, Minayi E. New memristor applications: AM, ASK, FSK and BPSK modulators. IEEE Antennas and Propagation Magazine. 2013;5(2):304-313'},{id:"B36",body:'Sánchez-López C, Aguila-Cuapio LE, Carro-Pérez I, González-Hernández HG. High-level simulation of an FSK modulator based on memconductor. Proceedings of the IEEE International Conference on Micro-Nanoelectronics, Technology and Applications. 2016;1(1):1-5'},{id:"B37",body:'Ziegler JG, Nichols NB. Optimum settings for automatic controllers. Transactions on American Society of Mechanical Engineers. 1942;64(1):759-768'},{id:"B38",body:'Cohen GH, Coon GA. Theoretical consideration of retarded control. Transactions on American Society of Mechanical Engineers. 1953;75(1):827-834'},{id:"B39",body:'Sánchez-López C, Morales-López FE, Carrasco-Aguilar MA. High-level simulation of a PID controller based on memristor. Proceedings of the IEEE International Conference on New Circuits Systems. 2016;1(1):1-4'},{id:"B40",body:'Tetzlaff R. Memristors and Memristive Systems. New York: Springer Science Business Media; 2014'},{id:"B41",body:'Hu X, Duan S, Wang L. A novel chaotic neural network using memristive synapse with applications in associative memory. Abstract and Applied Analysis. 2012;2012(1):19'},{id:"B42",body:'Cantley KD, Subramaniam A, Stiegler HJ, Chapman RA, Vogel EM. Hebbian learning in spiking neural networks with nanocrystalline silicon TFTs and memristive synapses. IEEE Transactions on Nanotechnology. 2011;10(5):1066-1073'},{id:"B43",body:'Zhang Y, Zeng Z, Wen S. Implementation of memristive neural networks with spike-rate-dependent plasticity synapses. Proceedings of International Joint Conference on Neural Networks. 2014;1(1):2226-2233'},{id:"B44",body:'Adhikari SP, Yang C, Kim H, Chua LO. Memristor bridge synapse-based neural network and its learning. IEEE Transactions on Neural Networks and Learning Systems. 2012;23(9):1426-1435'},{id:"B45",body:'Yang J, Wang L, Wang Y, Guo T. A novel memristive Hopfield neural network with application in associative memory. Neurocomputing. 2017;227(1):142-148'},{id:"B46",body:'Hasler P, Diorio C, Minch BA, Mead C. Single transistor learning synapse with long term storage. Proceedings IEEE International Symposium on Circuits and Systems. 1995;1(1):1660-1663'},{id:"B47",body:'Pershin YV, Di Ventra M. Experimental demonstration of associative memory with memristive neural networks. Neural Networks. 2010;23(7):881-886'},{id:"B48",body:'Wang L, Li H, Duan S, Huang T, Wang H. Pavlov associative memory in a memristive neural network and its circuit implementation. Neurocomputing. 2016;171(1):23-29'},{id:"B49",body:'Kim H, Sah MP, Yang C, Cho S, Chua LO. Memristor emulator for memristor circuit applications. IEEE Transactions on Circuits and Systems I Regular Papers. 2012;59(10):2422-2431'},{id:"B50",body:'Carro-Pérez I, González-Hernández HG, Sánchez-López C. High-frequency memristive synapses. Proceeding IEEE Latin American Symposium on Circuits & Systems. 2017;1(1):1-4'}],footnotes:[{id:"fn1",explanation:"This parameter should not be confused with ki parameter associated to the inverse nonlinear resistor."}],contributors:[{corresp:"yes",contributorFullName:"Carlos Sánchez-López",address:"carlsanmx@yahoo.com.mx",affiliation:'
Department of Electronics, Autonomous University of Tlaxcala, Tlaxcala, Mexico
Department of Electronics, Autonomous University of Tlaxcala, Tlaxcala, Mexico
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1. Introduction
Tsunami and earthquake seriously endanger people’s lives and properties. Efficient and accurate monitoring and assessment are of crucial importance for the fast response, management, and mitigation of the disasters [1, 2, 3]. Compared with the optical remote sensing, microwave remote sensing technology such as synthetic aperture radar (SAR) has been widely applied to monitoring natural and human-induced disasters for its all-day and all-weather working capacity [4].
Polarization is an essential property of the electromagnetic wave [5, 6, 7, 8]. The polarization state of wave will change when interacting with ground object. For example, rough natural surface such as land and water often induces the strong Bragg surface scattering, while building often presents the dominant double-bounce scattering because of the dihedral corner reflectors formed by ground and the vertical wall of building. Therefore, by analyzing the polarization of the scattering wave, we can acquire the physical and geometrical information regarding the object. This is the main task of SAR polarimetry (PolSAR) [9, 10, 11].
Tsunami is often accompanied by earthquake and flooding [1, 2, 3]. It damages and inundates the buildings and causes the collapse of the ground-wall dihedral structures as well as the enhancement of the direct surface scatterers. Therefore, by analyzing the power of double-bounce scattering and surface scattering before and after the event, we can achieve an efficient monitoring of the disasters. This simple strategy has been successfully adopted in the polarimetric microwave remote sensing of tsunami/earthquake [12, 13, 14, 15, 16, 17, 18, 19, 20, 21].
Nonetheless, the extraction of double-bounce scattering and surface scattering from PolSAR image is not so straightforward because each pixel in PolSAR is a 3×3 complex coherency matrix T with nine degrees of freedom (DoF). A widely used approach to achieve this is to decompose T on the canonical scattering models [22]. The first such decomposition was devised by Freeman and Durden [23] which expands T on the surface scattering, double-bounce scattering, and volume scattering (describes the complex scattering in vegetation area). This three-component decomposition, however, is responsible for only five DoF of T because of the symmetric reflection assumption. This assumption was tackled by Yamaguchi et al. [24] by introducing a fourth helix component and two additional models of volume scattering. The resulted four-component decomposition (Y4O) then only leaves three DoF unaccounted: the 13 element of T, i.e., T13, and the real part of the 23 element of T, i.e., ReT23. A same target will present differently by a simple rotation about the line of sight of radar. Deorientation should be first conducted on T to eliminate the influence [25]. As a result, ReT23 changes to zero and Y4O with rotation (Y4R) accounts for seven DoF [26]. Based on Y4R, Sato et al. [27] further proposed to add a new model to characterize volume scattering generated by even-bounce structure. However, Sato’s extended Y4R (S4R) still leaves T13 unaccounted. To solve this, Singh et al. [28] in 2013 proposed a general four-component decomposition (G4U) based on a special unitary matrix. G4U enables T13 included in the accounted models by conducting unitary transformation to the rotated version of T . Singh et al. [28] claimed that G4U could make full use of polarimetric parameters. As a result, in comparison with the four-component decompositions such as S4R and Y4R, G4U could enhance double-bounce scattering power over urban area while enhancing surface scattering contribution over an area where surface scattering is preferable [28]. This makes G4U very suitable to the remote sensing of tsunami/earthquake [16, 20] and establishes G4U the state-of-the-art four-component scattering power decomposition [29, 30].
This chapter is dedicated to enable an extension to G4U for better monitoring of tsunami/earthquake disaster. It is indicated that the unitary transformation in G4U adds a T13-related but redundant balance equation to the original self-contained equation system in Y4R and S4R. Then T13 is accounted for by G4U, but we obtain no exact solution to the system but the approximate ones. The general expression of the approximate solutions enables a generalized G4U (GG4U), while G4U and S4R represent two special forms. A dual G4U (DG4U) is also obtained. The general solution indicates that G4U cannot always enhance the double-bounce scattering power over urban area nor strengthen the surface scattering power over the area where surface scattering is dominant unless we adaptively integrate G4U and DG4U for an extended G4U (EG4U). Experiments on the PolSAR images of Miyagi Prefecture, Japan, acquired by the L-band spaceborne ALOS-PALSAR system before and after the March 11, 2011, Off-Tohoku 9.0 tsunami/earthquake demonstrate not only the outperformance of EG4U but also the effectiveness of polarimetric remote sensing in the monitoring of tsunami/earthquake disaster.
The remainder of this chapter is arranged as follows. Section 2 presents the basic principle of PolSAR and the polarization descriptors first. The advanced four-component scattering power decompositions are then described in Section 3 to develop the EG4U. By decomposing the ALOS-PALSAR datasets of the 2011 great Tohoku tsunami/earthquake using EG4U, Section 4 evaluates and analyzes the polarimetric monitoring of disaster damages further. The chapter is eventually concluded in Section 5.
2. SAR polarimetry and polarization descriptors
SAR is an active microwave remote sensing technique dedicated to acquire the large-scaled 2D coherent image of the earth’s surface reflectivity [9]. It transmits microwave pulses and receives the backscattering from the illuminated terrain to synthesize a high spatial resolution image. Such an active operation enables SAR an all-day working capacity independent of solar illumination. In addition, operating in the microwave region of electromagnetic spectrum avoids the effects of rain and clouds, which allows SAR an almost all-weather continuous monitoring of the earth surface [9].
Polarization characterizes the vector state of the electromagnetic wave. The polarization state of wave will change when interacting with a ground object. By processing and analyzing such change of polarization, we can obtain the material, roughness, shape, and orientation information regarding the object. The core of this change is the (Sinclair) scattering matrix S of the object, which transforms the incident electric filed EI into the scattered electric filed ES [31]:
ES=e−jkrrSEI→EHSEVS=e−jkrrSHHSHVSVHSVVEHIEVIE1
where r denotes the distance from radar to ground object, k is the wave number, and subscript H or V represents the horizontal or vertical polarization. Matrix S is obtained by first transmitting H-polarized wave (EHI) and receiving scatterings in H - and V-polarization simultaneously to measure the first column SHH and SVH and then transmitting V-polarized wave (EVI) and also receiving in H- and V-polarization simultaneously for the second column SHV and SVV. In reciprocal backscattering, we have SHV=SVH and matrix S covers five DoF then.
Generally, almost all the ground scatterers are situated in the dynamically changing environment and subjected to spatial and/or temporal variations [32]. Such scatterer is called the distributed target, and we can no longer model its scattering with a determined scattering matrix S . The 3×3 coherency matrix T is then constructed as the statistical average of the acquired scatterings to describe the second-order moment of the fluctuations [9]:
where · and superscript † represent the operations of ensemble average and conjugate transpose and k denotes the Pauli vector. The spatial/temporal depolarization pushes the DoF of T to nine. Therefore, different from the conventional SAR image, each pixel in PolSAR image is not a complex number but a 3×3 coherency matrix T.
The coherency matrix T in Eq. (2) is expressed in the H-V polarization basis; we can also formulate it in some other orthonormal basis by simply taking the unitary transformation of T:
UnitaryT=defU3TU3†E3
where U3 is the special unitary matrix that describes the relationship between H-V and the new orthonormal basis. Target deorientation is just based on the real rotation matrix [25]:
Deorientation makes T23′ become purely imaginary and reduces DoF from nine to eight. In order to eliminate the imaginary part further, Singh et al. developed an imaginary rotation matrix [28]:
3. Advanced four-component scattering power decompositions
Polarimetric incoherent decomposition plays an important role in the discrimination and recognition of the distributed target [22]. It pursues the scattering mechanism of the unknown target by extracting the dominant or average target (such as the Huynen-type phenomenological dichotomies [7, 32] and the eigenvalue/eigenvector-based target decompositions [9, 33]) from T or expanding T on the canonical models (such as the model-based target decompositions [23, 24, 25, 26, 27, 28]). Among these decompositions, the four-component scattering power decompositions such as Y4R, S4R, and G4U have been a hot topic recently [29].
3.1 Y4R and S4R
Y4R and S4R decompose the target by linearly expanding matrix T′ on the four canonical scattering models, as illustrated in Figure 1:
Figure 1.
The canonical models involved in the four-component model-based scattering power decompositions.
T′=fSTS′+fDTD′+fVTV′+fCTC′E8
where TS′, TD′, TV′, and TC′ denote the surface scattering model, the double-bounce scattering model, the volume scattering model, and the helix scattering model, respectively:
Parameters fS, fD, fV, and fC in Eq. (8) represent the contributions of the four components; β and α in TS′ and TD′ are complex parameters; a, b, c, and d in TV′ are real constants satisfying a+b+c=1, which involve in four volume scattering models and are adaptively selected according to the branch conditions [27, 28]. Combining Eqs. (8) and (9), the S4R/Y4R scattering balance equation system on unknowns fS, fD, fV, fC, α, and β is formulated [26, 27]:
Nevertheless, we obtain no scattering balance equation on T13′ in Eq. (10). Hence, there always exists a T13′ -related unaccounted residue in Y4R and S4R.
3.2 G4U
To model T13′, G4U uses U3φ to conduct unitary transformation to both sides of Eq. (10) first and then eliminates the influence of φ [28]. As a result, an additional balance equation is brought into G4U, and we obtain the following scattering balance equation system [30]:
Comparing Eq. (11) with Eq. (10), we can find that Eq. (11–2) gives a dichotomy to Eq. (10–2). The redundancy makes Eq. (11) have no such exact solution like Eq. (10) but some approximate ones. In G4U, Singh et al. preferred the first equation of (11–2) only.
3.3 GG4U: generalization of G4U
Obviously, Eq. (11) provides us a generalized G4U (GG4U). Here we focus on the general solution to (11) for the unknowns fS, fD, fV, fC, α, and β. Let
Eq. (13) comprises of five equations and six unknowns. Following Freeman-Durden [23] and Yamaguchi et al. [24], we can fix α or β in terms of the sign of S−D for the superior between surface scattering and double-bounce scattering:
where BC=S−D. Combining Eqs. (13) and (14), we can then simply obtain the scattering power of each of the four components, i.e., the surface scattering power PS, the double-bounce scattering power PD, the volume scattering power PV, and the helix scattering power PC:
where H· denotes the Heaviside step function, which is used here to adjust the value of PC for nonnegative PV ruling [27]. It can be easily validated that PS+PD+PV+PC=T11′+T22′+T33′. Thus GG4U gives a decomposition of scattering power.
3.4 Special decompositions
By taking appropriate value to μ, we can have some different decompositions, which are denoted as Gμ. Here we are particularly interested to the following special cases of Gμ.
Case (1): G+1≔G4U
C=C1=T12′+T13′−fVd=CG4U.E16
This is just the parameter C used in G4U. GG4U changes to G4U in this case.
Case (2): G−1≔DG4U
C=C2=T12′−T13′−fVd.E17
This acts as the complement of case (1); thus we name it the dual G4U (DG4U).
Case (3): G0≔S4R
C=C1+C22=T12′−fVd=CS4R.E18
This is the parameter C used in S4R, i.e., S4R also shows a special form of GG4U. Hence, the essential difference between S4R and G4U just lies in the different definition of parameter C in Eqs. (16) and (18). The unitary transformation is just to enable the T13′ entry contained in CG4U and finally in PS and PD. Parameter C defined in Eq. (12) is a generalization of CG4U and CS4R.
3.5 Theoretical evaluation of S4R and G4U
S4R can improve Y4R by strengthening the double-bounce scattering in urban area [27]. Singh et al. [28] indicated that G4U could further improve S4R in this aspect by strengthening surface scattering in the area where surface scattering is preferable to double-bounce scattering, while increasing the double-bounce scattering in the urban area where the double-bounce scattering is preferable to surface scattering. By combining the ruling in Eq. (14), we can formulate these observations as
PSG4U≥PSS4R,BC>0PDG4U≥PDS4R,BC≤0.E19
In terms of the general expression of PS and PD in (15), here we give a simple validation to Eq. (19) by combining μ=0 and μ=1 into Eqs. (12) and (15):
Then Eq. (19) will hold if 2C12−C1+C22≥0. Obviously, this condition is not always tenable. Hence, despite better performance in some areas, G4U cannot improve S4R for every target area. To tackle this, the extended G4U (EG4U) will be developed in the following as an adaptive combination of G4U and DG4U.
3.6 EG4U: adaptive combination of G4U and DG4U
Combining μ=−1 into Eqs. (12) and (15), DG4U surface and double-bounce scattering powers can be formulated as
PSDG4U=S+C22S,BC>0PDDG4U=D+C22D,BC≤0.E22
Combining Eqs. (20) and (22), after some simple deduction, we obtain
where BC1=C1−C2. Eq. (26) just lays the foundation for EG4U:
EG4U≔G±1=G+1=G4U,BC1>0G−1=DG4U,BC1≤0.E27
As the adaptive combination of G4U and DG4U, EG4U is also a special case of GG4U. So we denote it as G±1. By bringing μ=+1 or μ=−1 into Eqs. (12) and (15) based on the branch condition BC1, we can achieve the scattering powers of four components in EG4U. Furthermore, from Eqs. (25) to (27), we have
Compared with S4R and G4U, EG4U increases surface scattering in area where surface scattering is superior to double-bounce scattering and strengthens double-bounce scattering in area where double-bounce scattering is preferable to surface scattering. Therefore, EG4U achieves not only a nice improvement to S4R, but also an effective extension to G4U. This may make EG4U more suitable to the remote sensing of tsunami/earthquake. We will investigate this in Section 4. The procedure of EG4U is outlined in Algorithm 1.
Algorithm 1: EG4U
01: Input: T
02: Conduct deorientation to T for T′
03: Compute helix power PC=2ImT23′HT33′−ImT23′
04: Calculate branch condition BC
05: Determine volume scattering model based on branch condition
06: Obtain volume scattering power PV=2T33′−PC/2c
07: Compute parameters S, D, C1, and C2, as well as branch condition BC1
08: Implement SPAN reservation ruling based on S+D
09: if S+D>0
10: Adaptively select between G4U and DG4U based on BC1
11: if BC1>0
12: C=C1
13: else
14: C=C2
15: end if
16: Calculate surface scattering power PS and double-bounce scattering power
PD according to BC
17: if BC>0
18: PS=S+C2/S,PD=D−C2/S
19: else
20: PS=S−C2/D,PD=D+C2/D
21: end if
22: Implement nonnegative PS and PD ruling
23: else
24: PS=PD=0,PV=T11′+T22′+T33′−PC
25: end if
26: Output: PS,PD,PV,PC
4. Monitoring of disaster by EG4U decomposition of ALOS-PALSAR images of 2011 Tohoku tsunami/earthquake
As indicated in Subsection 3.4, G4U and S4R represent two special forms of GG4U of equal status. Hence, G4U cannot fully improve S4R only if we ascend the status of G4U by combining the duality of G4U, i.e., DG4U and G4U together for EG4U. EG4U can adaptively strengthen the surface scattering and double-bounce scattering. Therefore, it may improve the competence and performance of G4U in the remote sensing of damages caused by earthquake/tsunami disaster. We demonstrate these in the following by decomposing the ALOS-PALSAR images of the 2011 great Tohoku tsunami/earthquake using EG4U.
4.1 Great Tohoku earthquake and tsunami
The great Tohoku earthquake is also known as the great Sendai earthquake or the great East Japan earthquake, which was a magnitude 9.0–9.1 (Mw) undersea megathrust earthquake off the coast of northeast Japan (the epicenter is shown in Figure 2 as “
”) that occurred on March 11, 2011, the most powerful earthquake ever recorded in Japan [34]. The earthquake triggered powerful tsunami, which swept the mainland of Japan, killed over 10,000 people (mainly through drowning), and damaged over 1,000,000 buildings (half of them are collapsed and even totally collapsed) [35].
Figure 2.
Location of the great Tohoku tsunami/earthquake epicenter () and the ALOS-PALSAR footprint of the two selected fully polarimetric datasets (red rectangle, pre-event; blue rectangle, post-event).
4.2 Datasets
The Advanced Land Observing Satellite (ALOS) was launched in 2006 by the Japanese Space Agency (JAXA). It has three remote sensing payloads, i.e., the Panchromatic Remote-sensing Instrument for Stereo Mapping (PRISM) for digital elevation mapping, the Advanced Visible and Near Infrared Radiometer type 2 (AVNIR-2) for precise land coverage observation, and the Phased Array type L-band SAR (PALSAR) for all-day/all-weather land observation [36].
To demonstrate the capability of polarimetric remote sensing for damage monitoring, we choose two quad-polarization single-look complex-level 1.1 (ascending orbit) datasets acquired around Miyagi Prefecture, Japan, before and after the earthquake/tsunami with 138 days’ temporal baseline, as summarized in Table 1. The ALOS-PALSAR footprint of the two datasets is shown in Figure 2.
Scene ID
Acquire data
Incidence angle1
Azimuth resolution
Ground-range resolution2
ALPSRP257090760
2010-11-21
23.802°
4.5 m
23.5 m
ALPSRP277220760
2011-04-08
23.836°
4.5 m
23.5 m
Table 1.
ALOS-PALSAR datasets used in the experiment and their characteristics.
The incidence angle here indicates the incidence angle at the scene center.
The ground-range resolution is defined as the slant-range resolution/sin(incidence angle) [9], while the slant-range resolution of the two datasets is both 9.5 m.
4.3 Method
The flowchart of EG4U-based monitoring and evaluation of damages caused by tsunami/earthquake disaster is illustrated in Figure 3. We first co-register the two datasets based on the image features [37, 38, 39, 40]. The boxcar filtering [9] is then carried out to both datasets to suppress the speckles. To ensure the pixel size in both image directions comparable, the window size for ensemble average is chosen as 2 pixels in ground-range direction and 12 pixels in azimuth direction, i.e., we integrate the scattering matrix S of a total of 24 pixels for the estimation of a coherency matrix T in Eq. (2). From T we calculate the orientation angle θ according to Eq. (4) and implement the deorientation operation for the deoriented coherency matrix 〈[T′]〉 according to Eq. (5). Finally, EG4U is used to decompose 〈[T′]〉 to extract scattering powers PS, PD, PV, and PC and construct the RGB pseudo-color scattering power visualization result by encoding RGB with PDPVPS. This process is executed on each cell of the two datasets until we obtain the complete pre- and post-event scattering power images shown in Figure 4, based on which we evaluate EG4U on monitoring of the tsunami/earthquake disaster in the following.
Figure 3.
Flowchart of EG4U-based monitoring of tsunami/earthquake disaster.
Figure 4.
Color-coded scattering power image of the study area (a) before and (b) after the great Tohoku tsunami/earthquake disaster. The framed patch regions A, B, and C are extracted for particular analysis.
Despite the consistency, we can also observe the obvious difference between the pre- and post-event scattering power images. A lot of red pixels in Figure 4(a) change to blue pixels in Figure 4(b), particularly in the urban areas of Ishinomaki and Higashi-Matsushima, which illustrate the change from the dominant double-bounce scattering to the dominant surface scattering, denote the decrease of the dihedral structures, and indicate the collapse of buildings. Take Ishinomaki City framed in Patch A for instance; it is interesting to observe that the strong change mainly arises in the area by the seaside, while tiny change occurs in the area away from the coast. This finding is also validated by the corresponding optical images acquired before and after the event shown in Figure 6(a) and (b). Therefore, the severe damages brought by the Tohoku tsunami/earthquake are probably mainly due to the flooding rather than the earthquake. Flooding from the Onagawa Bay and the Mangokuura Sea also swept the town of Onagawa framed in Patch B, as shown in Figure 6(c) and (d) in terms of the pre- and post-event optical images. A large majority of red pixels of Patch B in Figure 4(a) change to blue pixels or even green pixels in Figure 4(b), which indicates that nearly all the buildings in Onagawa were badly damaged by the flooding except for a few buildings constructed in high elevation. The collapsed buildings not only present the dominant surface scattering here, but also the dominant volume scattering because of the complex scattering in such mountain area. The biggest change caused by flooding appears in the area along the Kitakami River. Take the town of Kamaya framed in Patch C, for example, as shown in Figure 6(e), besides several buildings, the most part of Kamaya is farmland. This area can be clearly distinguished from the Kitakami River in Figure 4(a) before the disaster. However, after the disaster, nearly all the land and buildings in Kamaya are flooded by the water from Kitakami River as shown in Figure 6(f), which present in Figure 4(b) as the wide distribution of blue pixels and show the dominant surface scattering here. Therefore, by decomposing the pre- and post-event PolSAR datasets with EG4U to construct the color-coded scattering power images, we can achieve a simple but accurate monitoring of the damages caused by tsunami/earthquake disaster.
From the above analysis, we can obtain that flooding which resulted from tsunami is the main contributor to the severe damages in the 3.11 great Tohoku earthquake. The flooding destroyed the buildings and inundated the lands. All these damages present themselves in the polarization domain as the change of the dominant scattering mechanism from double-bounce scattering to surface scattering and in the image domain as the change of pixel color from red to blue. The boundary condition BC has been widely used in model-based decomposition as a crucial feature to discriminate surface scattering and double-bounce scattering [23, 24, 26, 27, 28]. As expressed in Eq. (14), BC>0 indicates stronger surface scattering than double-bounce scattering, while BC≤0 denotes stronger double-bounce scattering than surface scattering. Therefore, besides the qualitative evaluation in terms of color, we can further achieve an quantitative evaluation of the damages by analyzing the dominant scattering according to BC. Figure 7(a) and (b) show the binary images of BC before and after the disaster, respectively. The white pixel denotes BC>0, i.e., the dominant surface scattering, which mainly occupies the water and land areas, while the black one denotes BC≤0, i.e., the dominant double-bounce scattering, which mainly occupies the urban and mountain areas. Before disaster, the black pixels account for 15.1641% of the whole image, while this ratio decreases to 13.0785% after the disaster, i.e., the dominant scattering mechanism of about 2.0856% area of the scene is changed from double-bounce scattering to surface scattering. As shown in Figure 7, the change mainly arises in the urban area like the Ishinomaki City and Higashi-Matsushima City, in the land area like the town of Kamaya, as well as in the water area like the Mangokuura Sea, Onagawa Bay, and Kitakami River. This further provides us a consistently quantitative evaluation of the damages. All these demonstrate the importance and value of polarimetric microwave remote sensing technique in the monitoring of tsunami/earthquake damages.
Figure 7.
Binary display of the branch condition BC extracted from (a) pre- and (b) post-event ALOS-PALSAR datasets. The white pixels correspond to BC>0, while the black pixels denote BC≤0.
Singh et al. [28] indicated that G4U could enhance double-bounce scattering over urban area while strengthen surface scattering contribution over water and land area. This establishes G4U the state-of-the-art four-component scattering power decomposition and enables its wide application to the remote sensing of forestry, agriculture, wetland, snow, glaciated terrain, earth surface, manmade target, environment, and damages caused by earthquake, tsunami, and landslide [29, 30]. Nevertheless, the rigorous derivation in Eq. (21) validates that G4U cannot always enhance the double-bounce scattering nor strengthen the surface scattering power unless we adaptively integrate G4U and its duality, i.e., DG4U, for EG4U based on another boundary condition BC1. As expressed in Eq. (27), G4U is selected only when BC1>0; otherwise, we should turn to DG4U. The binary images Figure 8(a) and (b) further show the pre- and post-event BC1, respectively, where the white pixels (i.e., BC1>0) indicate the area where G4U operates and the black pixels (i.e., BC1≤0) give the area where DG4U operates. The white pixels account for 46.4260% of the pre-event image, which conveys that G4U achieves better result than S4R only for 46.4260% area. As for the rest 53.5740% area, we should resort to DG4U for improvement. The ratio of white pixels increases to 49.5247% after the disaster. Nevertheless, there are still half a little more areas where G4U will underestimate the surface or double-bounce scattering. If we adopt G4U in this area to evaluate damages caused by tsunami/earthquake, the reduced double-bounce scattering from G4U may lead to the underestimation of building scale and overestimation of damage level. EG4U can adaptively increase the surface scattering or double-bounce scattering. Hence, it definitely improves the competence and performance of G4U in the remote sensing of damages caused by earthquake/tsunami.
Figure 8.
Binary display of the branch condition BC1 extracted from (a) pre- and (b) post-event ALOS-PALSAR datasets. The white pixels correspond to BC1>0, while the black pixels denote BC1≤0.
5. Conclusion
Flooding is the main contributor to the severe damages in the great Tohoku tsunami/earthquake. It destroyed the buildings and inundated the lands by the seaside. All these damages present themselves in the polarization domain as the change of the dominant scattering mechanism from double-bounce scattering to surface scattering and in the image domain as the change of pixel color from red to blue. The color-coded scattering power image is very useful and powerful in the qualitative evaluation of damages. The boundary condition BC further enables a nice quantitative evaluation of disaster. The unitary transformation in G4U adds a T13-related but redundant balance equation to the original self-contained equation system. The general solution enables a generalized G4U, while G4U just represents a special form. The strict derivation conveys that G4U cannot always strengthen the double-bounce scattering in urban area nor strengthen the surface scattering in water or land area unless we adaptively combine G4U and its duality for EG4U. Experiment on the ALOS-PALSAR datasets of 2011 great Tohoku tsunami/earthquake demonstrates not only the outperformance of EG4U but also the effectiveness of polarimetric remote sensing in the qualitative monitoring and quantitative evaluation of tsunami/earthquake damages. Efficient and accurate monitoring and assessment are of crucial importance for the fast response, management, and mitigation of the disasters. The all-day and all-weather working capacity is a significant advantage of microwave remote sensing. Polarimetric remote sensing is an effective technique in the discrimination and recognition of ground objects.
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grant No. 41871274 and No. 61971402 and by the Strategic High-Tech Innovation Fund of Chinese Academy of Sciences under Grant CXJJ19B10.
Conflict of interest
The authors declare no conflict of interest.
Notes
Sections 2 and 3 of this chapter are extracted from a journal paper of the authors submitted to IEEE Transactions on Geoscience and Remote Sensing on June 07, 2017. The paper is still under review at the time of publication of this chapter. For more details about the paper, please refer to Reference [30].
\n',keywords:"disaster monitoring, damage evaluation, tsunami, earthquake, microwave remote sensing, synthetic aperture radar (SAR), polarimetric SAR (PolSAR), polarimetric decomposition, scattering model, unitary transformation",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/71162.pdf",chapterXML:"https://mts.intechopen.com/source/xml/71162.xml",downloadPdfUrl:"/chapter/pdf-download/71162",previewPdfUrl:"/chapter/pdf-preview/71162",totalDownloads:221,totalViews:0,totalCrossrefCites:0,dateSubmitted:"October 25th 2019",dateReviewed:"January 17th 2020",datePrePublished:"February 20th 2020",datePublished:"December 23rd 2020",dateFinished:"February 20th 2020",readingETA:"0",abstract:"Polarization characterizes the vector state of EM wave. When interacting with polarized wave, rough natural surface often induces dominant surface scattering; building also presents dominant double-bounce scattering. Tsunami/earthquake causes serious destruction just by inundating the land surface and destroying the building. By analyzing the change of surface and double-bounce scattering before and after disaster, we can achieve a monitoring of damages. This constitutes one basic principle of polarimetric microwave remote sensing of tsunami/earthquake. The extraction of surface and double-bounce scattering from coherency matrix is achieved by model-based decomposition. The general four-component scattering power decomposition with unitary transformation (G4U) has been widely used in the remote sensing of tsunami/earthquake to identify surface and double-bounce scattering because it can adaptively enhance surface or double-bounce scattering. Nonetheless, the strict derivation in this chapter conveys that G4U cannot always strengthen the double-bounce scattering in urban area nor strengthen the surface scattering in water or land area unless we adaptively combine G4U and its duality for an extended G4U (EG4U). Experiment on the ALOS-PALSAR datasets of 2011 great Tohoku tsunami/earthquake demonstrates not only the outperformance of EG4U but also the effectiveness of polarimetric remote sensing in the qualitative monitoring and quantitative evaluation of tsunami/earthquake damages.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/71162",risUrl:"/chapter/ris/71162",signatures:"Dong Li, Yunhua Zhang, Liting Liang, Jiefang Yang and Xun Wang",book:{id:"8979",title:"Tsunami",subtitle:"Damage Assessment and Medical Triage",fullTitle:"Tsunami - Damage Assessment and Medical Triage",slug:"tsunami-damage-assessment-and-medical-triage",publishedDate:"December 23rd 2020",bookSignature:"Mohammad Mokhtari",coverURL:"https://cdn.intechopen.com/books/images_new/8979.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",isbn:"978-1-83962-176-5",printIsbn:"978-1-83962-175-8",pdfIsbn:"978-1-83962-177-2",editors:[{id:"52451",title:"Dr.",name:"Mohammad",middleName:null,surname:"Mokhtari",slug:"mohammad-mokhtari",fullName:"Mohammad Mokhtari"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"267545",title:"Dr.",name:"Dong",middleName:null,surname:"Li",fullName:"Dong Li",slug:"dong-li",email:"lidong@mirslab.cn",position:null,institution:null},{id:"268352",title:"Prof.",name:"Yunhua",middleName:null,surname:"Zhang",fullName:"Yunhua Zhang",slug:"yunhua-zhang",email:"zhangyunhua@mirslab.cn",position:null,institution:{name:"Chinese Academy of Sciences",institutionURL:null,country:{name:"China"}}},{id:"317493",title:"Dr.",name:"Liting",middleName:null,surname:"Liang",fullName:"Liting Liang",slug:"liting-liang",email:"liangliting16@mails.ucas.ac.cn",position:null,institution:null},{id:"317494",title:"Dr.",name:"Jiefang",middleName:null,surname:"Yang",fullName:"Jiefang Yang",slug:"jiefang-yang",email:"yangjiefang@mirslab.cn",position:null,institution:null},{id:"317495",title:"MSc.",name:"Xun",middleName:null,surname:"Wang",fullName:"Xun Wang",slug:"xun-wang",email:"wangxun19@mails.ucas.ac.cn",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. SAR polarimetry and polarization descriptors",level:"1"},{id:"sec_3",title:"3. Advanced four-component scattering power decompositions",level:"1"},{id:"sec_3_2",title:"3.1 Y4R and S4R",level:"2"},{id:"sec_4_2",title:"3.2 G4U",level:"2"},{id:"sec_5_2",title:"3.3 GG4U: generalization of G4U",level:"2"},{id:"sec_6_2",title:"3.4 Special decompositions",level:"2"},{id:"sec_7_2",title:"3.5 Theoretical evaluation of S4R and G4U",level:"2"},{id:"sec_8_2",title:"3.6 EG4U: adaptive combination of G4U and DG4U",level:"2"},{id:"sec_10",title:"4. Monitoring of disaster by EG4U decomposition of ALOS-PALSAR images of 2011 Tohoku tsunami/earthquake",level:"1"},{id:"sec_10_2",title:"4.1 Great Tohoku earthquake and tsunami",level:"2"},{id:"sec_11_2",title:"4.2 Datasets",level:"2"},{id:"sec_12_2",title:"4.3 Method",level:"2"},{id:"sec_13_2",title:"4.4 Evaluation and analysis",level:"2"},{id:"sec_15",title:"5. 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Key Laboratory of Microwave Remote Sensing, National Space Science Center, Chinese Academy of Sciences, China
Key Laboratory of Microwave Remote Sensing, National Space Science Center, Chinese Academy of Sciences, China
University of Chinese Academy of Sciences, China
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Bulky waste includes large items such as furniture, doors, flooring and mattresses. The management of bulky waste is a serious problem for European countries. The URBANREC project proposed a solution to this problem through the use of new technologies for the bulky waste processing. The aim of the URBANREC project is to implement an eco-innovative, integrated system of bulky waste management and demonstrate its effectiveness in various regions of Europe. The project has received funding from the European Union. In this chapter, the LCA environmental analysis was performed for the technology of grinding bulky waste using a water jet by the Ecofrag company. The calculations were carried out using SimaPro 8.5.2.0. 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OASPA
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STM
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COPE
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Creative Commons
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Crossref
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Altmetric and Dimensions from Digital Science
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iThenticate
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OASPA
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STM
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COPE
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Creative Commons
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Crossref
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Altmetric and Dimensions from Digital Science
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CLOCKSS
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Counter
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iThenticate
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Enago
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SPi Global
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Amazon
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DHL
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