Wind turbine simulator fault scenario.

## Abstract

The fault diagnosis and prognosis of wind turbine systems represent a challenging issue, thus justifying the research topics developed in this work with application to safety-critical systems. Therefore, this chapter addresses these research issues and demonstrates viable techniques of fault diagnosis and condition monitoring. To this aim, the design of the so-called fault detector relies on its estimate, which involves data-driven methods, as they result effective methods for managing partial information of the system dynamics, together with errors, model-reality mismatch and disturbance effects. In particular, the considered data-driven strategies use fuzzy systems and neural networks, which are employed to establish non-linear dynamic links between measurements and faults. The selected prototypes are based on non-linear autoregressive with exogenous input descriptions, since they are able to approximate non-linear dynamic functions with arbitrary degree of accuracy. The capabilities of the designed fault diagnosis schemes are verified via a high-fidelity simulator, which describes the normal and the faulty behaviour of a wind turbine plant. Finally, the robustness and the reliability features of the proposed methods are validated in the presence of uncertainty and disturbance implemented in the wind turbine simulator.

### Keywords

- fault diagnosis
- analytical redundancy
- fuzzy prototypes
- neural networks
- diagnostic residuals
- fault reconstruction
- wind turbine simulator

## 1. Introduction

The increasing level of wind-generated energy in power generation worldwide also increases the levels of reliability and the so-called ‘sustainability’ shown by wind turbines. Wind turbine systems should generate the required amount of electrical power continuously, depending on the available wind speed, the grid’s demand and possible malfunctions.

To achieve this aim, possible malfunctions affecting the process have to be properly detected and managed, before they degrade the nominal working conditions of the plant or become critical issues. Wind turbines with large rotors (i.e., of megawatt size) are very expensive systems, thus requiring an extremely high level of availability and reliability, in order to maximise the generated energy (at a reduced cost), with a minimisation of the operation and maintenance (O&M) services. In fact, the costs of the produced energy are mainly due to the installation cost of the wind turbine, while unplanned O&M costs could increase it up to about 30%, in particular when offshore installations are considered, see Odgaard [1].

These issues have motivated the development of fault diagnosis techniques that can be coupled with the fault-tolerant controllers (the so-called ‘sustainable’ systems). On the other hand, many turbine manufacturers adopt conservative approaches against faults, which lead to the shutdown of the plant in order to wait for O&M service. Hence, effective tools for coping with faults have to be investigated, in order to improve wind turbine features, particularly during faulty situations. This will lead to prevent critical failures that may affect other wind turbine components, thus avoiding unplanned replacement of functional parts, as well as the decrease of O&M costs, with the increase of the energy production. Moreover, the development of digital control systems, big data tools and artificial intelligence strategies enhance the development of new real-time condition monitoring, diagnosis and fault-tolerant control strategies for industrial processes, which can be available only on demand.

In recent years, many works have been proposed on the topics of fault diagnosis of wind turbines, as shown very recently in Habibi et al. [2] and Lan et al. [3]. Some of them are focused on the diagnosis of particular faults, for example, those affecting the drive-train system at a wind turbine level. Sometimes, these faults are better managed when the wind turbine system is considered in comparison to other parts of the whole plant, see Odgaard & Stoustrup [4]. Moreover, fault-tolerant control of wind turbines has been investigated, for example, in Parker et al. [5] and international cooperations on these problems were also proposed, see Odgaaard and Shafiei [6].

Fault diagnosis oriented to the sustainability feature when applied to safety-critical systems such as wind turbines has been proven to be a challenging issue, see Byrski and Byrski [7] and Xu et al. [8], thus motivating the research topics addressed in this chapter.

This point is fundamental as the increasing demand for energy generation using renewable sources has led to higher attention on renewable energy conversion systems, and in particular wind turbines. They represent very complex and safety-critical plants which require reliability, availability, maintainability and safety. Moreover, their efficiency to generate electrical power has to be maximised. This motivates novel research aspects, in particular in the context of diagnosis and control. The earlier diagnosis of faults and sustainable control solutions can lead to optimise energy conversion and guarantee the desired performances in the presence of possible malfunctions due to unexpected faults and disturbance.

Therefore, this chapter analyses the problem of the fault diagnosis for wind turbine systems, and the development of practical and reliable solutions for fault diagnosis, also known as fault detection and isolation (FDI). Further design of fault-tolerant controllers is not considered in this work, but it can rely on the tools considered in this chapter. In fact, the fault diagnosis module provides information on the faulty or fault-free conditions of the system, so that the controller activity can be compensated. This fault diagnosis task is enhanced by the use of fault estimators, which are obtained via data-driven approaches, as they offer effective tools for managing limited analytical knowledge of the process dynamics, together with noise and disturbance effects.

The first data-driven solution considered in this chapter uses fuzzy Takagi-Sugeno models, see Babuška [9], which are derived from a clustering algorithm, followed by an identification procedure, see Simani et al. [10]. A second solution is also considered, which relies on neural networks to describe the non-linear analytical links between measurement and fault signals. The chosen network architecture belongs to the Nonlinear AutoRegressive with eXogenous (NARX) input prototype, which can describe dynamic relationships along time. The training of the neural network fault estimators exploits standard training algorithm, that processes the data acquired from the process, see Roy and Ganguli [11].

The developed fault diagnosis strategies are verified by means of a high-fidelity simulator, which describes the normal and the faulty behaviour of a wind turbine plant. The achieved performances are verified in the presence of uncertainty and disturbance effects, thus validating the robustness features of the proposed schemes. The effectiveness verified from the achieved results suggests further investigations on more realistic applications of the proposed schemes.

The work is organised as follows. Section 2 recalls the wind turbine simulator. Section 3 illustrates the fault diagnosis methodologies relying on fuzzy and neural network prototypes. The obtained results are summarised in Section 4. Finally, Section 5 ends the chapter by outlining the key achievements of the study, and providing suggestions for future research issues.

## 2. Wind turbine simulator description

The wind turbine simulator used in this work was proposed in Odgaard et al. [12]. It describes the realistic behaviour of a three-blade horizontal-axis variable-speed pitch-controlled wind turbine coupled with a full converter generator. The overall system consists of four interconnected modules, that is, the wind driving process, the wind turbine, the measurement system and the baseline controller. The wind turbine block contains three submodels: the blade and the pitch system, the drive-train model and the generator system. The links between the system submodels are represented in Figure 1, with the fault diagnosis system to be designed. The simulator is able to generate several fault scenarios, see Odgaard et al. [12].

In the following, the description of these interconnected submodels is briefly recalled.

### 2.1. Wind turbine model

The turbine system consists of three submodels motivated by the power transmission flow. First, the blade and pitch block represents how the blades capture wind energy, which is based on the following aerodynamic law:

For each blade, Eq. (1) describes the torque acting on the rotor *R*. The coefficient

where

The drive-train system determines the power flow through the gear box from the rotor toward the electric generator, whose dynamics are described as in Eq. (3):

where

Finally, the generator submodel represents the converter dynamics by means of first-order transfer function of Eq. (4):

where

Finally, the generated power *Pg* is computed as the product of the generator torque by its speed, decreased by the efficiency coefficient

As sketched in Figure 1, the signals generated by the wind turbine system are assumed to be acquired through the measurement block, whose objective is to simulate the real behaviour of sensors and actuators. Therefore, the measured signals are modelled as sum of their actual value and white Gaussian process terms. Moreover, the wind turbine simulator includes a baseline controller, represented by a PID standard regulator, which regulates the generated power on the basis of the actual wind speed, as shown in Odgaard & Stoustrup [4] and Odgaard et al. [12].

### 2.2. Simulated fault scenario

The wind turbine simulator includes the generation of three different typical fault cases, that is, sensor, actuator and system faults, see Odgaard and Stoustrup [4] and Odgaard et al. [12].

For the case of the sensor faults, they are generated as additive signals on the affected measurements. As an example, the faulty sensor of faulty pitch angle

On the other hand, actuator faults lead to the alteration of pitch angle or the generator torque transfer functions of Eqs. (2) and (4), by modifying their dynamics. They simulate a pressure drop in the hydraulic circuit of the pitch actuator or an electronic break down in the converter device.

Finally, a system fault affects the drive train of the turbine, which is described as a slow variation in time of the friction coefficient. This can be due to the effect of wear and tear along time of the mechanical parts.

These nine fault cases are summarised in Table 1, which also highlights which measured signals are affected by them, as shown in Figure 1.

Fault case | Fault type | Affected measurement |
---|---|---|

1 | Sensor | |

2 | Sensor | |

3 | Sensor | |

4 | Sensor | |

5 | Sensor | |

6 | Actuator | Pitch system of blade #2 |

7 | Actuator | Pitch system of blade #3 |

8 | Actuator | |

9 | System | Drive train |

With these assumptions, the overall model of the wind turbine process can be represented as a non-linear continuous-time function

where in this case, the state of the system is considered equal to the monitored system output, that is, the rotor speed, the generator speed and the generated power:

On the other hand, the input vector:

consists of the measurements of the pitch angles from the three redundant sensors, as well as the measured torque. These signals are sampled with sample time *T* in order to acquire a number *N* of data

## 3. Fault diagnosis techniques

This chapter considers two data-driven approaches, relying on fuzzy system and neural network structures, which are used to design the fault diagnosis schemes. Therefore, this section briefly introduces the general scheme of the fault diagnosis strategy, by recalling the basic features of the fuzzy systems and neural networks, as addressed in Sections 3.1 and 3.2, respectively. Moreover, these architectures, which are represented by NARX structures, are exploited residual generators for solving the problem of fault diagnosis, according to the analytical redundancy principle, see Chen and Patton [13].

In order to solve the fault diagnosis problem, this work assumes that the wind turbine system is affected by *equivalent* additive faults on the input and the output measurements, as well as measurement errors, as described by Eq. (7):

where *equivalent* additive effects. Obviously, these functions are different from zero in faulty cases. In general, the vector *r* components, that is, the number of process inputs, while *m* elements, that is, the number of process outputs.

Among the possible approaches exploited for residual generation, and based on the analytical redundancy principle, this work proposes to exploit fuzzy system and neural network structures, which provide an on-line estimation

The variable *i* components of the fault vectors

The residual generation scheme exploiting the fault estimators as residual generator is depicted in Figure 2. Note that this strategy is able to provide both the fault detection and isolation tasks, that is, the fault diagnosis function, see Chen and Patton [13].

Figure 2 shows that in general the residual generators use the acquired input and output measurements *i*th fault can be simply detected via the threshold logic of Eq. (9) applied to the *i*th residual

with *i*th component of the vector *N* samples, according to Eq. (10):

Note that the parameter

Once the fault detection phase is accomplished, the fault isolation task is directly obtained by means of a bank of estimators. As described by Eq. (7), the faults are considered as equivalent signals that are injected and affect the input measurements via the signal

According to the scheme depicted in Figure 3, in order to uniquely isolate one of the input or output faults, under the assumption that multiple faults cannot occur, a bank of multi-input single-output (MISO) fault estimators is designed. In general, the number of this estimators is equal to the number of faults that have to be diagnosed, that is, which coincides with the number of input and output measurements, *i*th estimator providing the reconstruction of the fault

Figure 3 shows this fault estimator bank, where the fault estimators are driven by the input-output signals selected via the fault sensitivity analysis procedure. In this way, the residual

As already remarked, the sensitivity analysis, which has to be executed before the design of the fault estimators, suggests how to select the input-output signals feeding the fault estimator modules. After this selection procedure is performed, as described in Section 3.3, the design of the fuzzy or neural network models is achieved, as recalled in Sections 3.1 and 3.2, respectively. Finally, the threshold test logic of Eq. (9) allows the achievement of the fault diagnosis task.

### 3.1. Fuzzy system modelling and identification

This section describes the design of the fault estimators described by means of the Takagi-Sugeno (TS) prototypes, see Takagi and Sugeno [14]. Therefore, the unknown relationships between the selected measurements and the faults are described by fuzzy models, which consist of a number of rules. These rules connect the measured signals acquired from the system under diagnosis to its faults, described in form of IF⇒THEN relations, processed by a fuzzy inference system (FIS), see Babuška [9].

According to this approach, the approximation of non-linear multi-input single-output (MISO) systems can be achieved by the Takagi-Sugeno (TS) fuzzy reasoning, as described in Babuška [9]. The TS modelling approach proposed here, as addressed in Takagi and Sugeno [14], describes the consequents as deterministic functions

The fuzzy rule of the FIS has the form of Eq. (11):

where *i* refers to the number of rules. The antecedents are combined by means of membership functions

where *bi* is a scalar offset, while *i*th rule output. The number of rules is supposed equal the number of clusters *nC* used for partitioning the data into regions where the relations

The TS prototype takes the form of the expression of Eq. (13):

Using this fuzzy approach, in general, the fault

It is worth noting that the system under investigation corresponds to the wind turbine process described in Section 2, which has a dynamic behaviour. Therefore, the considered input vector

Therefore, in order to include dynamics into the static relation of Eq. (11), the consequents are described as discrete-time linear AutoRegressive models with eXogenous input (ARX) of order *o*, in which the regressor vector has the form of Eq. (14):

where *k* represents the time step, with *i*th model of the Eq. (12) are collected into the vector:

where the

A powerful approach to the design of the *i*th FIS as approximator for the system under diagnosis begins with the partitioning of the available data

With reference to this work, the design of the FIS is considered as a system identification problem from the noisy data of Eqs. (7). In fact, the estimation of the consequent parameters *bi* of Eq. (12) is required using the input-output data for designing the bank of the fault estimations reported in Figure 3. Moreover, the data are acquired from the measurements selected from the procedure suggested in Section 3.3. The identification scheme exploited in this work was proposed by the authors in Fantuzzi et al. [17]. This approach is based on the minimisation of the prediction errors of the individual TS local affine models considered as *nC*-independent estimation problems. Their solutions rely on the estimation of errors-in-variables models in Fantuzzi et al. [17], which is also the assumption represented by Eq. (7).

Another key aspect, which is not considered here, regards the determination of the optimal number of clusters *nC*, as the clustering algorithm assumes that the number of clusters *nC* has been fixed. These issues are considered in the development of the estimation procedure properly integrated by the authors, which also determines the antecedent degrees of fulfilment

### 3.2. Neural network modelling and training

This study proposes a different data-driven approach, based on neural networks, which is exploited to implement the fault diagnosis block. This section briefly recalls their general structure and properties, which are used to implement the fault estimators.

Therefore, according to the scheme shown in Figure 4, a bank of neural networks is realised in order to reproduce the behaviour of the faults affecting the system under diagnosis using a proper set of input and output measurements. The neural network structure consists of different layers of neurons, also known as *perceptron,* see Haykin [18], modelled as a static function *f*. This function is described by an *activation function* with multiple inputs properly weighted by unknown parameters that determine the learning capabilities of the whole network.

A categorisation of these learning structures concerns the way in which their neurons are connected to each other, see Xu et al. [19]. This work proposes to use a feedforward network, also called multilayer perceptron, where the neurons are grouped into unidirectional layers. The first of them, the input layer, is directly fed by the network inputs; then, a hidden layer takes the inputs from the neurons of the input layer and transmits them the output to the neurons of the third layer, the output layer, which produces the final network outputs. According to this structure, neurons are connected from one layer to the next, but not within the same layer. The only constraint is the number of neurons in the output layer, that has to be equal to the number of actual network outputs. On the other hand, recurrent networks are multilayer networks, in which the output of some neurons is fed back to neurons belonging to previous layers, thus the information flow in forward as well as in backward directions, allowing a dynamic memory inside the network, see Hunt et al. [20].

A noteworthy intermediate solution is provided by the multilayer perceptron with a tapped delay line, which is a feedforward network whose inputs come from a delay line. This study proposes to use this solution, defined as quasistatic neural network, as it represents a suitable tool to predict dynamic relationships between the input-output measurements and the considered fault functions. In this way, another NARX description is obtained, since the non-linear (static) network is fed by the delayed samples of the system inputs and outputs selected by the fault sensitivity analysis tool described in Section 3.3. Indeed, if properly trained, the NARX network can estimate the current (and the next) fault samples

Therefore, with reference to the *i*th residual generator of Figure 4, which is used to design the estimator bank of Figure 3, this NARX network is described by the relation of Eq. (16):

where *i*th fault, while *j*th and *l*th components of the measured inputs and outputs *k* is the time step, *du* and *dy* are the number of delay of inputs and outputs, respectively, which have to be properly selected.

The design parameters are represented by the number of neurons and the number of delays of the network inputs and outputs, while the value of the weights of each neuron are derived from the network training from the data acquired from the system under diagnosis, see Hunt et al. [20].

### 3.3. Fault sensitivity analysis

The design of the fault diagnosis schemes proposed for the application example considered in this chapter have been summarised in Section 4. However, the tool addressed in this chapter enhances the design of the banks of these fault estimators depicted in Figure 3.

This tool consists of a fault sensitivity analysis that has to be performed on the wind turbine simulator. It is aimed at defining the most sensitive measurements

Fault fi | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Measurements | |||||

RMSE | 11.29 | 0.98 | 2.48 | 1.44 | 1.45 |

Fault fi | 6 | 7 | 8 | 9 | |

Measurements or | |||||

RMSE | 0.80 | 0.73 | 0.84 | 0.77 |

In particular, the fault sensitivity analysis is conducted on the basis of a selection algorithm that is performed by introducing the normalised sensitivity function

The value of *Nx* indicates the effect of the considered fault case with respect to the general measured signal *Nx* equal to 1. Otherwise, a smaller value of *Nx*, that is, close to zero, represents a signal *Nx* are thus selected as the most sensitive measurements, and they will be considered in the design of the fault diagnosis modules of the bank sketched in Figure 3.

The complete results of the fault sensitivity analysis are summarised in Table 3. For each fault case, the selected signals of the wind turbine benchmark are marked as inputs or outputs.

Fault case fi | Most sensitive inputs uj | Most sensitive outputs yl |
---|---|---|

1 | ||

2 | ||

3 | ||

4 | ||

5 | ||

6 | ||

7 | ||

8 | ||

9 |

This method represents a key feature of the proposed approach to fault diagnosis. In fact, the fault estimators of the bank of Figure 3 can be designed by exploiting a reduced number of signals, thus leading to a noteworthy simplification of the overall complexity, and a decrease in the computational cost of the training and identification phases.

## 4. Simulation results

This section summarises the simulations performed with the considered wind turbine benchmark, and the performances of the proposed fault diagnosis solutions. Due to the presence of the uncertainty and disturbance effects included in the benchmark, the robustness features of the developed fault diagnosis techniques are also verified in simulation.

With reference to the wind turbine benchmark of Section 2, all simulations are driven by the same wind mean speed sequence. It was acquired from a real measurement of wind speed, which represents a good coverage of typical operating conditions, as it ranges from 5 to 20 m/s, with a few spikes at 25 m/s, see Odgaard et al. [12]. The simulations last for 4400 s, with single fault occurrences. The discrete-time simulator runs at a sampling frequency of 100 Hz, so that *N* = 440,000 samples are acquired during each simulation. With reference to the different fault cases reported in Section 2.2, Table 4 shows the shape and the timing of the fault modes affecting the process. They model input (actuator) or output (sensor) additive faults, which are used for sensitivity analysis of Section 3.3.

Fault case | Fault type | Fault shape | Occurrence (s) |
---|---|---|---|

1 | Actuator | Step | 2000–2100 |

2 | Actuator | Step | 2300–2400 |

3 | Actuator | Step | 2600–2700 |

4 | Actuator | Step | 1500–1600 |

5 | Actuator | Step | 1000–1100 |

6 | Sensor | Step | 2900–3000 |

7 | Sensor | Trapezoidal | 3500–3600 |

8 | Sensor | Step | 3800–3900 |

9 | Sensor | Step | 4100–4300 |

As an example, in order to highlight the actual fault effect on the wind turbine measurements, Figure 5 shows the fault sensitivity test. In particular, the cases of the faults 1, 2, 3 and 8 in fault-free and faulty conditions are depicted.

### 4.1. Fuzzy estimators for fault diagnosis

The problem of the fault diagnosis of the wind turbine simulator is solved in this work by designing fuzzy prototypes as fault reconstructors. The considered approach is different from the one presented in Simani et al. [21], where the fuzzy models were used as output predictors.

Section 3.1 suggested to exploit the fuzzy *c*-means clustering algorithm. When applied to the data of the wind turbine simulator, a number

The effectiveness of the fuzzy TS fault estimators used was assessed in terms of root mean squared error (RMSE), which is computed as the difference between the predicted

Fault estimator | 1 | 2 | 3 | 4 | 5 |

RMSE | 0.016 | 0.023 | 0.021 | 0.020 | 0.019 |

Fault estimator | 6 | 7 | 8 | 9 | |

RMSE | 0.021 | 0.017 | 0.021 | 0.019 |

In this case, these estimated signals *i*.

Residual | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

3.8 | 4.3 | 4.2 | 4.5 | 3.7 | 4.4 | 4.3 | 3.5 | 3.9 |

Note that, in general, each of the nine fuzzy fault estimators described by the relations of Eqs. (13) and (14) has three inputs (see Table 3), with a number of delays

In the following, the main simulation results are summarised. Two actuator faults *fu* and two sensor fault *fy* are considered, namely the fault cases 1, 4, 8 and 9 of the scenarios recalled in Section 2.2.

According to Table 3, these faults caused the alteration of the monitored input and output signal

Figure 6 depicts the reconstructed fault functions

### 4.2. Neural networks for fault diagnosis

As for the fuzzy systems, nine NARX neural networks described in Section 3.2 were designed to estimate the nine faults affecting the acquired measurements, according to the scheme of Figure 3. The neural networks selected for fault diagnosis purpose consist of 3 layers, with 3 neurons in the input layer, 16 in the hidden one, and 1 neuron in the output layer. A number of

As for the fuzzy models, the prediction efficacy of the designed neural networks was verified in terms of RMSE. The achieved results are summarised in Table 7, which were obtained by comparing the estimated faults with respect to the simulated ones.

Fault estimate | 1 | 2 | 3 | 4 | 5 |

RMSE | 0.009 | 0.009 | 0.009 | 0.012 | 0.011 |

Fault estimate | 6 | 7 | 8 | 9 | |

RMSE | 0.011 | 0.009 | 0.009 | 0.014 |

The fault diagnosis task is thus achieved by comparing the residuals *i* is summarised in Table 8.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |

4.2 | 4.9 | 4.7 | 5.1 | 4.2 | 4.6 | 4.8 | 4.1 | 4.3 |

On the other hand, Figure 7 shows an example of residual signals for the fault cases 1, 2, 3 and 4, together with the selected thresholds.

In particular, Figure 6 depicts the residuals

The achieved results show the effectiveness of the proposed fault diagnosis solutions, also with respect to disturbance and uncertainty effects on the wind turbine simulator, thus highlighting their potential application to real wind turbine systems.

## 5. Conclusion

The chapter studied data-driven tools for solving the problem of the fault diagnosis and prognosis of a wind turbine process. The design of this fault detector is based on the estimate of the fault itself, achieved by means of artificial intelligence methods. They were considered since these viable tools demonstrated to be able to cope with poor information on the process dynamics, in the presence of errors, model-reality mismatch and disturbance effects. In particular, these methodologies rely on fuzzy and neural network structures used to determine the non-linear dynamic links between measurements and fault signals. The selected structures belong to the non-linear autoregressive with exogenous input architectures, since they may model any non-linear dynamic relationship with arbitrary degree of accuracy. The fault diagnosis and prognosis strategies were validated via a high-fidelity simulator of a wind turbine process. The achieved performances in terms of reliability and robustness were thus tested by considering the presence of uncertainty and disturbance effects modelled by this wind turbine simulator. Further works will verify the features of the same fault diagnosis schemes when applied to real plants.