\\n\\n
These books synthesize perspectives of renowned scientists from the world’s most prestigious institutions - from Fukushima Renewable Energy Institute in Japan to Stanford University in the United States, including Columbia University (US), University of Sidney (AU), University of Miami (USA), Cardiff University (UK), and many others.
\\n\\nThis collaboration embodied the true essence of Open Access by simplifying the approach to OA publishing for Academic editors and authors who contributed their research and allowed the new research to be made available free and open to anyone anywhere in the world.
\\n\\nTo celebrate the 50 books published, we have gathered them at one location - just one click away, so that you can easily browse the subjects of your interest, download the content directly, share it or read online.
\\n\\n\\n\\n\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
IntechOpen and Knowledge Unlatched formed a partnership to support researchers working in engineering sciences by enabling an easier approach to publishing Open Access content. Using the Knowledge Unlatched crowdfunding model to raise the publishing costs through libraries around the world, Open Access Publishing Fee (OAPF) was not required from the authors.
\n\nInitially, the partnership supported engineering research, but it soon grew to include physical and life sciences, attracting more researchers to the advantages of Open Access publishing.
\n\n\n\nThese books synthesize perspectives of renowned scientists from the world’s most prestigious institutions - from Fukushima Renewable Energy Institute in Japan to Stanford University in the United States, including Columbia University (US), University of Sidney (AU), University of Miami (USA), Cardiff University (UK), and many others.
\n\nThis collaboration embodied the true essence of Open Access by simplifying the approach to OA publishing for Academic editors and authors who contributed their research and allowed the new research to be made available free and open to anyone anywhere in the world.
\n\nTo celebrate the 50 books published, we have gathered them at one location - just one click away, so that you can easily browse the subjects of your interest, download the content directly, share it or read online.
\n\n\n\n\n'}],latestNews:[{slug:"intechopen-supports-asapbio-s-new-initiative-publish-your-reviews-20220729",title:"IntechOpen Supports ASAPbio’s New Initiative Publish Your Reviews"},{slug:"webinar-introduction-to-open-science-wednesday-18-may-1-pm-cest-20220518",title:"Webinar: Introduction to Open Science | Wednesday 18 May, 1 PM CEST"},{slug:"step-in-the-right-direction-intechopen-launches-a-portfolio-of-open-science-journals-20220414",title:"Step in the Right Direction: IntechOpen Launches a Portfolio of Open Science Journals"},{slug:"let-s-meet-at-london-book-fair-5-7-april-2022-olympia-london-20220321",title:"Let’s meet at London Book Fair, 5-7 April 2022, Olympia London"},{slug:"50-books-published-as-part-of-intechopen-and-knowledge-unlatched-ku-collaboration-20220316",title:"50 Books published as part of IntechOpen and Knowledge Unlatched (KU) Collaboration"},{slug:"intechopen-joins-the-united-nations-sustainable-development-goals-publishers-compact-20221702",title:"IntechOpen joins the United Nations Sustainable Development Goals Publishers Compact"},{slug:"intechopen-signs-exclusive-representation-agreement-with-lsr-libros-servicios-y-representaciones-s-a-de-c-v-20211123",title:"IntechOpen Signs Exclusive Representation Agreement with LSR Libros Servicios y Representaciones S.A. de C.V"},{slug:"intechopen-expands-partnership-with-research4life-20211110",title:"IntechOpen Expands Partnership with Research4Life"}]},book:{item:{type:"book",id:"477",leadTitle:null,fullTitle:"Nuclear Power - Control, Reliability and Human Factors",title:"Nuclear Power",subtitle:"Control, Reliability and Human Factors",reviewType:"peer-reviewed",abstract:"Advances in reactor designs, materials and human-machine interfaces guarantee safety and reliability of emerging reactor technologies, eliminating possibilities for high-consequence human errors as those which have occurred in the past. New instrumentation and control technologies based in digital systems, novel sensors and measurement approaches facilitate safety, reliability and economic competitiveness of nuclear power options. Autonomous operation scenarios are becoming increasingly popular to consider for small modular systems. This book belongs to a series of books on nuclear power published by InTech. It consists of four major sections and contains twenty-one chapters on topics from key subject areas pertinent to instrumentation and control, operation reliability, system aging and human-machine interfaces. 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\r\n\tPlant invasion and global climate change are major global change components. The prediction of successful invasive plant species, interactions between plant invasion and other global change factors, as well as evaluation of invasive plant impact on the introduced environments, such as soil nutrient cycling and greenhouse gas emissions, are not well understood. This book aims to gather research in plant invasion studies associated with topics on prediction of successful invasive plants, interactions between plant invasion and other global change factors, and evaluation of invasive plant impacts, providing a thorough understanding of advances in plant invasion ecology on the background of global change. A better understanding of these questions will be helpful for future management of invasive plants, especially during global change mitigation processes, which are crucial for the sustainable development of human society and the maintenance of an environment-friendly world.
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From 2021-2013, he visited the Department of Ecology and Evolutionary Biology, Rice University, USA. He is currently working as a professor at the College of Forestry, Jiangxi Agricultural University, China, supervising graduate students. Dr. Zhang studies global change biology, forest ecology, plant invasion, and soil carbon and nitrogen cycling. He has published more than 50 papers related to global change ecology or forest ecology, and authored or co-authored several books on forest ecology or soil ecology in the recent years. 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This spectroscopic tool is successfully applied not only to the study of the structural properties of isolated biomolecules, such as proteins, nucleic acids, lipids, and carbohydrates, but also to the characterization of complex biological systems, for instance intact cells, tissues, and whole model organisms.
In particular, FTIR microspectroscopy, obtained by the coupling of an infrared microscope to a FTIR spectrometer, makes it possible to collect the IR spectrum from a selected sample area down to ~ 20 microns x 20 microns when conventional IR source and detector are employed, and down to of a few micrometers when more specialized and sensitive detectors and the highly brilliant synchrotron light source are used. In this way, FTIR microspectroscopy provides detailed information on several biological processes in situ, among which stem cell differentiation [1-5], somatic cell reprogramming [6], cell maturation [7, 8], amyloid aggregation [9-12] and cancer onset and progression [13-15], making it possible to disclose the infrared response not only from single cells, but also from subcellular compartments [8, 16, 17].
The FTIR spectra of biological systems are very complex since they consist of the overlapping absorption of the main biomolecules; for this reason, to pull out the significant and non-redundant information contained in the spectra it is necessary to apply an appropriate multivariate analysis, able to process very high-dimensional data. This is even more crucial when time-dependent biological processes, such as cell maturation or differentiation, are studied. Indeed, in this case it is fundamental to be able to extract from the spectral data the relevant information of the process you are investigating [18-21].
In Figure 1 we schematized the procedure that should be followed to successfully tackle the FTIR characterization of complex biological systems.
Scheme of the FTIR approach to study complex biological systems. The IR absorption spectra are analysed by resolution enhancement approaches (e.g. second derivatives) to resolve the overlapped absorption components and to monitor their variations during the process under investigation. The spectroscopic results are validated by an appropriate multivariate analysis approach, to identify firstly specific marker bands of the studied process. The interpretation of the spectroscopic data should be then confirmed by standard biochemical assays.
Several multivariate analysis approaches exist and for the scope of this book they can be divided into two main categories: regression and classification techniques. In the first category fall all methods that allow to derive a model describing the relationship between two sets of variables. The second category includes techniques to split observations into groups or classes.
In this chapter, we will firstly introduce the most widely used multivariate analysis approaches in the field of spectroscopy.
We will then illustrate the basic principles and experimental details for the application of principal component - linear discriminant analysis (PCA-LDA) to the analysis of FTIR spectral data of complex biological systems. The potential of these combined tools will be described on illustrative examples of cell biological process studies. In particular, we will discuss in details its application on our FTIR study of murine oocytes characterized by two different types of chromatin organisation around the nucleolus, strongly affecting their development after fertilization. In this case, PCA-LDA analysis made it possible to identify not only the maturation stage in which the fate separation between the two kinds of oocytes occurred, but also to disclose the most significant cellular processes responsible for the different oocyte destiny, thus validating the visual inspection of the infrared spectra [7].
Fourier transform infrared (FTIR) microspectroscopy is a powerful technique that allows to obtain a molecular fingerprint of the sample under investigation in a rapid and non-invasive way. In the case of complex biological systems it provides simultaneously, in a single measurement, information on the main biomolecules, such as lipids, proteins, nucleic acids, and carbohydrates, requiring also a very limited amount of sample. For these reasons, it became recently a very attracting tool for biomedical research [20, 22-24], being successfully employed for the study of several biological systems, from intact cells [6, 7, 25] to tissues [11, 26, 27] and whole model organisms (i.e. the nematode
As an example, in Figure 2 it is reported the FTIR absorption spectrum of a single intact murine oocyte. As shown, its IR response is very complex, being due to the absorption of the main biomolecules. In particular, between 3050 - 2800 cm-1 and 1500 - 1350 cm-1 the absorption of the lipid acyl chains occurs, while around 1740 cm-1 the ester carbonyl absorbs [29]. Moreover, the amide I and amide II bands - mainly due to the C=O stretching and the NH bending of the peptide bond respectively - give information on the protein secondary structure [30], while the spectral range between 1000 and 800 cm-1 is very informative on nucleic acid absorption, since it is due in particular to sugar vibrations sensitive to their conformation and to backbone vibrational modes [31, 32]. Finally, we should also mention the very complex spectral range between 1250 - 1000 cm-1, mainly due to phosphodiester groups of nucleic acids and phospholipids and to the C-O absorption of glycogen and other carbohydrates [31, 33, 34].
Making it possible to obtain a sample biochemical fingerprint in a rapid and non destructive way, FTIR microspectroscopy is widely applied to the in situ characterization of cellular processes, such as cell maturation, differentiation, and reprogramming [3, 5-7, 25, 35], and to the detection of several diseases, as, for instance, cancer [13-15] and neurodegenerative disorders [10, 11], whose onset is accompanied by changes in the composition and structure of several biomolecules.
Since water has a strong absorption in the mid-infrared spectral range, samples have to be dried rapidly before IR measurements, in particular when working in transmission mode (see for details the following paragraph). The suitability of such “dry-fixing” has been proved by Raman spectroscopy, a vibrational tool complementary to FTIR, whose response is not affected by water. In particular, Raman measurements performed on differentiating human embryonic stem cells, hydrated and dry-fixed, demonstrated that the rapid desiccation didn’t affect the spectroscopic response of the main biomolecules. Indeed, in both cases the same temporal pattern of the differentiation marker bands - due to tryptophan, nucleic acid backbone and base vibrations - was observed during the biological process under investigation [36].
FTIR absorption spectrum of a single intact murine oocyte. The measured absorption spectrum of a single intact murine oocyte (surrounded nucleolus, MI 10 H) is reported without any corrections. The oocyte - deposited on a BaF2 window - was measured in transmission by the IR microscope UMA 500, coupled to the FTIR spectrometer FTS 40A (both from Digilab), at a resolution of 2 cm-1. The absorption regions of the main biomolecules are indicated.
We should add that to obtain reliable results on the studied process it is crucial to standardize firstly the sample preparation, since - for instance - metabolic changes due to cell aging could result in significant spectral changes that could, in turn, hide the IR response specifically due to the process of interest, as it has been recently reported in the literature [37]. For these reasons, it is fundamental to check accurately the stage of cell growth in culture before performing spectroscopic measurements.
We should also briefly mention that, before spectral analyses, the measured IR spectra could require some corrections due to artifacts that can interfere with the spectroscopic response. For instance, single cells, or subcellular compartments, or particles of the size of the same order of that of the incident infrared light (∼3-10 microns) could give rise to Mie scattering, that significantly distorts the measured spectrum, causing misinterpretation of the results. For this reason, before further analyses, it is strongly recommended to correct the measured spectra with opportune algorithms specifically developed to this aim [38].
Since the IR spectra of complex biological systems are due to the overlapping spectral features of multiple components, their analysis requires often the employment of resolution enhancement procedures to better resolve their absorption bands, an essential prerequisite for the identification of peak positions and their assignment to the vibrational modes of the different molecules. Among these, second derivative analysis is widely applied, as described in [39]. Since second derivative band intensity is inversely proportional to the square of the original band half-width, this procedure introduces an enhancement of sharp lines, as those due to vapour and noise. For this reason, this analysis requires spectral data free of vapour absorption and with excellent signal to noise ratio.
Furthermore, due to the intrinsic complexity of biological systems, their spectral analysis requires the support of appropriate multivariate analysis approaches able to tackle the study of high-dimensional data, to verify firstly the reproducibility of the results and then to extract the most significant spectral information [18-21] (see for details paragraph 4).
FTIR microspectroscopy is realized coupling to a FTIR spectrometer an infrared microscope characterized by an all reflecting optics, since typical lenses and condensers of visible microscopy - being made of glass, not transparent to the IR radiation - cannot be employed.
The main advantage of FTIR microspectroscopy is that it offers the possibility to study selected areas of the sample under investigation, resulting particularly useful in the case of systems characterized by an intrinsic heterogeneity, such as biological systems.
Two main types of IR microscopy exist, depending on the detector employed, and both equipped with an IR thermal source (globar), whose spatial resolution is diffraction-limited.
The first, conventional, generally equipped with a nitrogen cooled mercury cadmium telluride (MCT) detector, makes it possible to measure IR absorption spectra from a microvolume within the sample, selected by a variable aperture of the microscope, whose side can be adjusted down to a few tens of microns.
The second type of IR microscope, more advanced, is equipped with a focal plane array (FPA), consisting of an array of infrared detector elements, that enables not only to collect the IR absorption spectrum of the sample, but also an IR chemical imaging, where the image contrast is given by the response of selected sample regions to particular IR wavenumbers. Depending mainly on the detection array, the spatial resolution in this kind of microscopy is approximately between 20 and 5 microns, making it possible to reach, therefore, a resolution near to the diffraction limit.
We should, however, add that the use of a synchrotron IR light source, with a brightness of at least two orders of magnitude higher than that of a conventional thermal source, makes it possible to achieve diffraction-limited spatial resolution with enhanced signal-to-noise ratio. In this way, synchrotron light could allow to explore the IR spectra at the subcellular level.
A final remark should be done concerning the spectral acquisition mode. Indeed, infrared measurements can be mainly performed in transmission, reflectance or attenuated total reflection (ATR) mode. Typically, measurements on complex biological systems are performed in transmission mode, using appropriate IR transparent supports for the deposition of the sample, such as BaF2, CaF2, ZnSe. In this case, the IR beam goes through the sample, that - depending mainly on its molar extinction coefficient - should have a uniform thickness, not exceeding 15-20 microns.
Moreover, in reflectance mode - where the sample is placed onto proper reflective slides - the IR beam passes the sample, is reflected by the slide, and passes the sample again. In particular, the sample slides reflect mid-infrared radiation almost completely and usually are also transparent to visible light, allowing sample inspection by a conventional light microscope. This approach is, for instance, useful for tissue characterizations.
Finally, in the ATR approach, where the sample is placed into contact with a higher refractive index and an IR transparent element (mainly germanium and diamond), samples with higher thickness than in transmission can be processed. In particular, the IR beam reaches the interface between the ATR support and the sample at an angle larger than that corresponding to the total reflection. In this way the beam is totally reflected by the interface and penetrates into the sample as an evanescent wave, where it can be absorbed. The beam penetration depth is of the order of the IR wavelength (a few micrometers) and depends on the wavelength, the incident angle, as well as on the refractive indices of the sample and of the ATR element. Furthermore, it should be noted that this kind of approach makes it possible to measure also samples not necessarily deposited onto an IR transparent support, as in ATR measurements it is only required that the sample be in close contact with the ATR element.
For a review of the technical aspects of FTIR microspectroscopy, see [40-42].
Several phenomena can only be described or explained by taking into account several variables at the same time. These cases represent the realm of the Multivariate statistical analysis (MVA).
We now define the structure of our data that will be kept throughout the text for all described techniques. For a given phenomenon we perform a certain measurement and store the value in a uni- or multivariate variable called
Each instance associated to the variable y is stored in a matrix
Each element of matrix
The matrix
In the following part, we will make a distinction between regression and classification techniques. However, it should be clear that the separation between these two domains is not always sharp and the same technique can be either used for regression or for classification purposes.
LMVR (or MLR) can be used to model linear relationships between one or more
The LMVR is based, as many other statistical techniques, on the generalized linear model:
In some cases linear models cannot be used and one could try to apply non-linear models.
Common models which frequently apply to natural phenomena are the exponentials (which, indeed, is a transformed linear model. A linear model can be applied upon on the logarithm of the data), logistic models or power law models.The regressed model has the general form of
The optimal values for the coefficients
When the number of observations is smaller than the number of variables (as it often happens for spectral data), the matrix
Increasing the number of observations (above the number of variables) will not always solve the problem. This is due to the so-called near-multicollinearity which means that some variables can be written approximately as linear functions of other variables. This problem is often found among spectral measurements. Even if the solution will be mathematically unique, it may be unstable and lead to poor prediction performances.
Linearly correlated or quasi-linearly correlated variables have to be removed prior to apply a regression method. In the following sections, we will describe two methods that are frequently used to remove correlations among variables, namely principal component analysis (PCA) and partial least squares (PLS).
4.2.3.1. Principal Component Analysis (PCA)
We should first recall the structure of the data. Suppose that we have
By using PCA, our intent is to develop a smaller number of uncorrelated artificial variables, called principal components (PC), that will account for most of the variance in the observed variables. The new uncorrelated variables are obtained as linear combination of the original data as
Given the sample mean of the m-dimensional vector
For uncorrelated variables, the off-diagonal values of the sample covariance matrix are zero, that is, S is diagonal. The covariance of linearly transformed variables
Thus, we want to find the matrix
The eigenvalues, which coincide with the matrix
The number of eigenvalues is equal to the number of original variables; however, since the eigenvalues are equal to the variance of the principal components and they are sorted in a decreasing order, the first
Hence, to describe our original dataset we can use only the first
Choosing which and the number of principal components that should be retained in order to summarize our data is a task that can be solved using several strategies [43, 49]. For example, one way commonly used is to retain the first k principal components that explain a given total percentage of the variance, e.g. 90% [43, 44]. Another rule is to plot the eigenvalues in decreasing order. Moving from left to right, the eigenvalues usually have an initial steep drop followed by a slow decrease. All the components after the elbow between the steep and the flat part of the curve should be discarded. This test is called screen plot.
Alternatively, one can select the principal components that can be associated to a physical meaning related to the studied system. For example, following the differentiations of a cell line growing in different experimental conditions, one principal component may represents the different conditions, while another PC may describe the maturation stage of the cells. None of the above methods are better than the other; usually more than one test should be done and the results compared.
The principal component analysis allows to obtain uncorrelated variables and then to remove the multicollinearity problem.
4.2.3.2. Principal Component Regression (PCR): multivariate regression following PCA
Once a set of
4.2.3.3. Partial Least Squares (PLS)
Another way to face the multicollinearity problem is to use PLS. The goal of PLS regression is to predict
In the PCR method described above, the principal components are selected based on their ability of explaining the variance of the
Classification methods can be divided into two main categories, supervised and unsupervised. Supervised techniques require the knowledge of the group membership of the observations and can be used to understand the structure of the data, e.g. why certain observations belong to a given group. Moreover, once the classification model is calibrated on a “training” dataset, it can be used in a predictive way to group observations whose group membership is unknown.
On the other hand, unsupervised methods try to group the observations without any knowledge of the group membership.
In the following paragraph, we will describe the main multivariate classification approaches.
Discriminant analysis is mainly a supervised technique which was originally developed by Ronald Fisher as a way to subdivide a set of taxonomic observations into two groups based on some measured features [51]. Later, DA was extended to treat cases where there are more than two groups, the so-called “multiclass discriminant analysis” [49, 52, 53].
DA can have mainly two objectives. First, it can be used in a supervised way to describe and explain the differences among the groups. As we will see later, mathematically DA finds the optimal hyperplane that separates the groups among each other. Or, in other words, it finds the optimal linear combination of the original variables that maximizes the distance among the groups. The transformed observations are called discriminant functions.
The use of a linear combination implies that each original variable is weighted by a coefficient which can be used to study the relative importance of the variable in the separation among the groups. A second possible role of DA is to classify observations into groups. An observation, which has to be assigned to a group, is evaluated by a discriminant function (already calibrated on another dataset) and it is assigned to one of the groups at which most likely it belongs [43, 44, 49]; in this view DA is used as an unsupervised method.
When only linear transformations are applied to the variables used as DA input, the discriminant analysis is called linear discriminant analysis (LDA).
In some cases, LDA alone is not suitable and the original variables can be mapped to a new space via any non-linear function. Then, the LDA is applied in this non-linear space (which is equivalent to non-linear classification in the original space). This procedure can be seen under several names such as “non-linear DA” (NLDA) or “kernel Fisher discriminant analysis” (KFD) or “generalized discriminant analysis”.
In the following sections we will focus on LDA, first describing the descriptive approach and subsequently the classification approach.
4.3.1.1. Linear DA (LDA) as a descriptive method
The initial dataset is an ensemble of multivariate observations partitioned into
Our goal in LDA is to search for the linear combination that optimally separates our multivariate observation into
The linear transformation of
Since
where
We now introduce the between groups sum of squares
and
where
Analogously, in the multivariate case (where each observation is constituted by
and
Finding the optimal linear combination that separates our multivariate observations into
We want to find
Equation 9 can be rewritten in the form
where
\n\t\t\t\t\tThe solutions of equation 10 are the eigenvalues
The discriminant functions are then obtained considering only the first
Discriminant functions are uncorrelated but not orthogonal since the matrix
In many cases the first two or three discriminant functions account for most of
The weighting vectors
If the variables are on very different scales and with different variance, to assess the importance of each variable in the group separation the standardized discriminant functions can be used. The standardization is done by multiplying the unstandardized coefficients by the square root of the diagonal element of the within-group covariance matrix.
Another way to assess the variable importance is to look at the correlation between each variable and the discriminant function. These correlations are called structure or loading coefficients. However, it has been shown that these parameters are intrinsically univariate and they only show how a single variable contributes to the separation among groups, without taking into account the presence of the other variables [49].
4.3.1.2. Linear as a classification method
After a set of discriminant functions are calibrated as described in the previous section, the discriminant analysis can be applied to classify new observations into the most probable groups. From this point of view, the linear discriminant analysis becomes a predictive tool, since it is able to classify observations whose group membership is unknown [43, 49]. The discrimination ability of our LDA model can be tested by a procedure called “re-substitution” [49]. This method consists of producing an LDA model using our dataset (i.e. finding the optimal w). Then, each observation vector is re-submitted to the classification function (
The fitting accuracy is the ability to reproduce the data, namely how the model is able to reproduce the data that were used to build the model (the training set). This corresponds to the apparent classification rate and it is obtained using the re-substitution procedure.
The prediction accuracy is the ability to predict the value or the class of an observation, that was not included in the construction of the model. This kind of accuracy is often referred to as the ability of the model to generalize. The data used to measure this accuracy are called “test set”. The prediction accuracy can be called “actual classification rate”. This is mainly used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice. To have an estimation of the actual classification rate, two main procedures can be applied: the hold-out and cross-validation [43].
In the hold-out, the dataset is divided into two partitions: one partition is used to develop the model (e.g. the discriminant functions) and the second partition is given as input to the model. The first partition is usually called “training set” or “calibration set”, while the second partition is the validation set [54].
When the number of observations is small, the cross-validation is usually preferred over the hold-out. The basic idea of the cross-validation procedure is to divide the entire dataset into L disjoint sets. L-1 sets are used to develop the model (i.e. the calibration set on which the discriminant functions are computed) and the omitted portion is used to test the model (i.e. the validation set given as input to the model). This is repeated for all the L sets and an average result is obtained.
Apparent or actual classification accuracies can be summarized in a confusion matrix. As an example, total N observations,
The confusion matrix becomes then:
Actual group | Predicted group | |
1 | 2 | |
1 | ||
2 |
A powerful analysis tool is the combination of the principal component analysis with the linear discriminant analysis [52]. This is particularly helpful when the number of variables is large. In particular, if the number of observations (
Let\'s take into account the same situation described for the many group linear discriminant analysis. The original dataset is an ensemble of multivariate observations which is partitioned into
Another way that can be used instead of PCA is to perform the PLS.
In a way analogous to the PCA-LDA procedure, here we first apply the PLS algorithm to the original data and then the LDA on the selected principal components [61].
Given that the PLS searches for a set of components that performs a simultaneous decomposition of the dependent and independent datasets, the main difference with PCA-LDA is that the principal components resulting as output of PLS better describe the relationship between independent and dependent variables. This does not necessarily mean that this method is better in general. Indeed, applying PCA or PLS on the same dataset often leads to similar results [62, 63] and the classification accuracy or the descriptive ability is mostly determined by the underlying structure of the data which can make one of the two methods more suitable than the other.
The goal of cluster analysis is to find the best grouping of the multivariate observations such that the clusters are dissimilar to each other but the observations within a cluster are similar [44].
CA is an unsupervised technique, that is, the group membership of the observations (and often the number of groups) is not known in advance.
At first we have to define a measure of similarity or dissimilarity also called distance functions. The most common distance functions are: i) the Euclidean distance; ii) the Manatthan distance; iii) the Mahalanobis distance; iv) the maximum norm.
Based on the procedure they use, clustering algorithms can be divided into three main groups: hierarchical, partitional and density-based clustering. None of the following algorithms is better than the other. The choice of the clustering method strongly depends on the structure of the data and on which kind of results one would expect.
Hierarchical clustering algorithms can be again subdivided into agglomerative or divisive. The agglomerative clustering starts with all observations placed in different clusters and in each step an observation or a cluster of observations is merged into another cluster. The most commonly employed agglomerative clustering strategies are complete-linkage, average-linkage, single-linkage, centroid-linkage. The drawback of the agglomerative clustering algorithms is that observations cannot be moved among the clusters once a cluster is made.
The divisive method starts with one single cluster containing all observations and then it divides the cluster into two sub-clusters at each step. Divisive methods have the same drawback of the agglomerative clustering, that is, once a cluster is made, an observation cannot be moved to another cluster. Divisive methods are suited when large clusters are searched for.
The partitional algorithm assigns the observations to a set of clusters without using hierarchical approaches. One of the most used non-hierarchical approach is the k-means clustering.
The density-based clustering seeks to search for regions of high density without any assumption about the shape of the cluster.
The artificial neural networks are mathematical models that were developed in analogy to a network of biological neurons [64]. Mathematically, a neuron can be modeled as a switch that receives, as input, a series of values and produces an output consisting of a weighted sum of the input eventually transformed by a function f. Many neurons can be combined to create more complex networks. Depending on the type of neurons and on how the neurons are connected to each others, different kinds of neural networks can be created. The most common type of neural network is the feed-forward neural network, in which neurons are grouped into layers, each neuron of a layer is connected to all the neurons of the next layer and the information flows from the input to the output without loops. For a comprehensive description of neural networks and their applications see [54, 65].
In the following, we will provide a few selected examples of the application of FTIR microspectroscopy coupled with multivariate analysis for biomedical relevant studies, with the aim to highlight the importance of linking the two approaches to extract the most significant spectral information from highly informative systems.
In some cases, PCA alone represents a powerful method for the analysis of multidimensional FTIR spectra. Indeed, several interesting works are reported in the literature, in which this approach is employed to support the spectroscopic investigation of complex biological systems and processes. For instance, synchrotron based FTIR microspectroscopy coupled with PCA has been applied to the characterization of human corneal stem cells [27, 66], in cancer research for the screening of cervical cancer [14], as well as to disclose the effects induced by a surface glycoprotein in colon carcinoma cells [67].
For instance, Matthew German and colleagues [68] coupled high-resolution synchrotron radiation-based FTIR (SR-FTIR) microspectroscopy with PCA to investigate the characteristics of putative adult stem cell (SC), transiently amplified (TA) cell, and terminally differentiated (TD) cell populations of the corneal epithelium. Using PCA, each spectrum, composed by many variables (the wavenumbers), is reduced to a point in a low dimensional space. Then, each observation can be visualized in a two or three dimensional score plot. Choosing the appropriate principal components, the authors were able to clearly distinguish the three cell populations confirming the ability of SR-FTIR microspectroscopy to identify SC, TA cell, and TD cell populations.
PCA alone is extremely powerful to reduce the number of variables; however, it is not a clustering algorithm and the group into clusters must be done with other techniques.
For example, Tanthanuch and colleagues applied FTIR microspectroscopy-supported by PCA and unsupervised hierarchical cluster analysis (UHCA) to identify specific spectral markers of the differentiation of murine embryonic stem cell (mESCs) and to distinguish them into different neural cell types [25]. In particular, focal plane array (FPA) - FTIR and SR-FTIR microspectroscopy measurements - performed on cell clumps and single cells respectively - allowed to obtain a biochemical fingerprint of different mESC developmental stages, namely embryoid bodies (EBs), neural progenitor cells (NPCs) and embryonic stem-derived neural cells (ESNCs). Interestingly, it should be noted that the results obtained on cell clumps and on single cells were found to be comparable, corroborating the FPA-FTIR results on cell clumps. The analysis of second derivative spectra enabled to highlight important spectral changes occurring during ES cell differentiation, mainly in the lipid CH2 and CH3 stretching region and in the protein amide I band. Noteworthy, these results overall indicated that during neural differentiation the cell lipid content increased significantly, likely reflecting modifications in cell membranes, whose lipid content is known to have a key role in neural cell differentiation and signal transduction. Moreover, changes in the profile of amide I band, mainly involving the alpha-helix component around 1650-1652 cm-1, indicated an increased expression of alpha-helix reach protein in ESNCs compared with their progenitor cells, a result that could reflect the expression of cytoskeleton protein, crucial for the establishment of neural structure and function. These results were then strongly supported by PCA, that made it possible to disclose regions of the IR spectrum which most contributed to the spectral variance, namely amide I band and C-H stretching region. Furthermore, the application of UHCA allowed to successfully discriminate and classify each stage of ESNCs differentiation, again considering the spectra in the spectral range mainly due to acyl chain vibrations and the extended region between 1750 and 900 cm-1.
As discussed previously, PCA is frequently used for preliminary dimensionality reduction before further analyses, as LDA [21]. Indeed, a limit of using PCA alone is that it does not allow to obtain an unambiguous grouping of the data into clusters, requiring therefore the application of another analysis step able to reduce the intra-category variation while maximizing that inter-category [69]. The coupling, for instance, of PCA with LDA is a well established procedure which enables not only to classify the observations into groups but to quantify the importance of the single variables for this group separation. In this view, the advantage of LDA is that it makes it possible to reveal clusters, identifying objectively also the most contributory wavenumbers responsible for spectra discrimination [21, 58]. In particular, the application of PCA-LDA to spectroscopic investigation of complex biological systems proved to be a useful tool for the identification of spectral biomarkers of the process under investigation [7, 35, 69, 70, 71].
One outstanding work, worth to mention here, was done by Kelly and colleagues [70], where the authors showed how infrared spectroscopy and multivariate techniques can be used as a novel diagnostic approach for endometrial cancer screening. They first demonstrated how SR-FTIR microspectroscopy with subsequent PCA-LDA allows the clear segregation of different subtypes of endometrial carcinoma. However, the requirement of a particle accelerator impairs the use of endometrial spectroscopy as practical diagnostic application.
Recently, Taylor and colleagues applied ATR-FTIR spectroscopy supported by PCA-LDA analysis to interrogate endometrial tissues, employing in particular a conventional IR radiation source [72], showing that this approach, that can be applied directly to liquid or solid samples without further preparation, could provide a useful and simple objective test for endometrial cancer diagnosis.
Furthermore, in the work of Walsh and colleagues [69], ATR microspectroscopy has been successfully applied to the characterization of samples of exfoliative cervical cytology of different categories, with increasing severity of atypia. The spectral analysis was supported by PCA, with or without subsequent LDA, to verify if it was possible to discriminate among normal, low grade and high grade of exfoliative cytology. Indeed, important differences were found in the spectral range between 1500 and 1000 cm-1, mainly due to proteins, glycoproteins, phosphates and carbohydrates. Noteworthy, the authors stressed that only the employment of the combined PCA-LDA allowed to maximize the inter-category variance, whilst reducing that intra-category. In particular, they found that the glycogen content strongly influenced the intra-category variance, while that inter-category resulted to be mainly due to protein and DNA conformational changes. In this view, FTIR microspectroscopy coupled with PCA-LDA could allow for an objective classification approach to class cervical cytology.
We should note that a delicate point of PCA-LDA is the choice of the principal components to be used as LDA input and, as described in the previous section about PCA, several ways have been developed to perform this task. Alternatively, the PLS method can be used instead of PCA [6, 73, 74]. For instance, Sandt and colleagues, using synchrotron infrared microspectroscopy coupled with PLS-DA, were able to characterize the metabolic fingerprint of induced pluripotent stem cells (iPSCs). In particular, they found that iPSCs are characterized by a chemical composition that leads to a spectral signature indistinguishable from that of embryonic stem cells (ESCs), but entirely different from that of the original somatic cells [6].
Recently, we applied FTIR microspectroscopy supported by PCA-LDA to the study of murine oocytes characterized by two different types of chromatin organization, namely surrounded nucleolus (SN) oocytes in which the chromatin is highly condensed and forms a ring around the nucleolus, and the not surrounded nucleolus (NSN) type where chromatin is dispersed and less condensed around the nucleolus [7, 75]. Interestingly, only SN oocytes are capable to complete the embryonic development after fertilization, while the NSN type, if fertilized, arrests at the two cell stage. To try to get new insights on the mechanisms that drive the different chromatin organization in the two kinds of oocytes, crucial for their embryonic development after fertilization, we studied the infrared absorption of single intact cells at different maturation stages, namely antral germinal vesicle (GV), metaphase I (MI, matured for 10 hours in vitro), and metaphase II (MII, matured for 20 hours in vitro).
Indeed, as we will show in the following, the FTIR spectra of the oocytes taken at the different maturation stages are very complex, since they provide information on different processes that were taking place simultaneously within the cells. For this reason, beside a fundamental visual inspection of the data, enabling the identification and assignment of the different spectral bands, it was crucial the application of PCA-LDA that made it possible to draw out the most significant spectral information responsible for the different cell behavior. Moreover, PCA-LDA allowed to identify the stage at which the separation between the SN and NSN oocytes took place, leading to their well distinct cell destinies.
As we discussed in paragraph 2, since the FTIR spectrum of cells is due to the overlapping contributes of the main biomolecules (see Figure 2), we analysed the second derivative spectra to identify the band peak positions and to assign them to the different biomolecule vibrational modes. The spectral analysis, strongly supported by PCA-LDA, allowed us to disclose the most important spectral differences between the two types of oocytes, at each maturation stage, that were found to occur mainly in the lipid and nucleic acid absorption regions, as we will discuss below. For a full discussion of the results see [7].
5.1.1.1. NSN oocytes
The analysis between 3050 and 2800 cm-1, mainly due to the lipid carbon-hydrogen stretching vibrations [29], disclosed significant variations in the lipid content of NSN oocytes during their maturation up to MII. Indeed, besides an increase of the CH2 band intensity up to MII, respectively at 2922 cm-1 and 2852 cm-1, important changes concerned mainly the unsaturated fatty acid composition, as indicated by variations of the band between 3020 and 3000 cm-1 due to the olefinic group absorption. Indeed, as shown in Figure 3A, a single peak around 3013 cm-1 was present at GV and MI stages, while a splitting in two components at ~ 3016 cm-1 and at ~ 3010 cm-1 characterized the MII stage (see the inset of Figure 3A). These results could reflect important changes in membrane fluidity, which in turn could confer to the oocyte a different division ability after fertilization [8].
5.1.1.2. SN oocytes
SN oocytes were found to be characterized - during maturation up to MII - by a significant increase of the 2937 cm-1 component that could be likely due to cholesterol and/or phospholipids (Figure 3B) [76, 77]. As discussed for NSN oocytes, the observed changes could reflect variations in the membrane properties, again highlighting the crucial role of lipids as markers of oocyte developmental competence [8, 78].
Second derivative absorption spectra of NSN (A) and SN (B) oocytes in the lipid absorption region. The second derivatives of the FTIR absorption spectra of single oocytes, measured at the antral (continuous line), MI 10 H (dotted line), and MII 20 H (dashed line) stages, are reported in the acyl chain absorption region, after normalization at the tyrosine peak (~1516 cm-1). In the inset a magnification of the olefinic group band is shown.
5.1.1.3. PCA-LDA analysis
The results obtained by the direct inspection of second derivative spectra were confirmed by PCA-LDA analysis performed on raw spectra. Firstly, the analysis was made on each type of oocyte taken at the different maturation stages. For the SN oocytes, the component carrying the highest discrimination weight resulted that at 2938 cm-1, likely due to cholesterol and / or phospholipids [76, 77], in agreement with what found by the direct inspection of the spectra.
Concerning the NSN oocytes, on the other hand, the wavenumbers with the highest discrimination weight were the 2922 cm-1, due to the CH2 stretching vibration, which increases up to MII, and the 3018 cm-1, assigned to the olefinic group =CH of polyunsaturated fatty acids, whose absorption was observed to vary during the oocyte maturation.
We, then, compared the two types of oocyte at each maturation stage - as illustrated in Figure 4 - and we found that at the antral and MII stages the spectral components with the highest discrimination weight were those due to cholesterol and /or phospholipids, while at MI was that due to the olefinic group. Furthermore, to support the crucial role played by lipids in determining at some extent the oocyte developmental capacity, we should add that when we compared by PCA-LDA the spectra of the two oocyte types at the same maturation stage in the 1800-1500 cm-1 spectral range, dominated by the amide I and amide II absorption, the wavenumber with the highest discrimination weight was the 1739 cm-1, due to the carbonyl stretching vibration of esters [7, 29].
PCA-LDA analysis of SN and NSN oocytes in the lipid acyl chain absorption region (3050 – 2800 cm-1). The separation between the two types of oocytes at each maturation stage is reported as average of PCA-LDA scores. The height of the boxes and the whiskers corresponds to 1 and 1.5 standard deviations from the mean values, respectively. The analysis has been performed on the measured spectra.
5.1.2.1. NSN oocytes
We then analyzed the nucleic acid IR response of NSN and SN oocytes during their maturation, exploring the spectral region between 1000 and 800 cm-1, where RNA and DNA vibrational modes mainly occur [31, 32].
We found that NSN oocytes maintain, in all the studied stages, an appreciable transcriptional activity as indicated mainly by the simultaneous presence of the RNA ribose component around 921 cm-1 and of the DNA deoxyribose between 895-898 cm-1 - indicative of a DNA/RNA hybrid - whose relative intensities were seen to vary during maturation (see Figure 5A). In particular, the intensity of these two components is higher at the antral stage, while it decreases at MI, to increase again up to MII. These results were also supported by the response of the complex band between 980-950 cm-1, mainly due to the CC stretching vibration of DNA backbone. Indeed, the profile of this band varies depending on the DNA structure that, in turn, could reflect a different nucleic acid activity. In particular, for the NSN oocytes we found that at the antral stage DNA is mainly in A-form - with a triplet at 975 cm-1, 966 cm-1 and 951 cm-1 - typical of the DNA/RNA hybrid during transcription. At MI, the reduction of the 975 cm-1 and 966 cm-1 bands and the appearance of that at 969 cm-1 indicate that DNA is mainly in the B-form, suggesting a sort of transcriptional “stand by state”, further supported by the reduction extent of the DNA/RNA hybrid, as discussed above. From this “stand by state” NSN oocytes seem to resume their transcriptional activity at MII, where a coexistence of DNA A and B forms was observed, as indicated by the increase of the ~ 975 cm-1 band and again in agreement with the simultaneous increase of the ribose (921 cm-1) and deoxyribose (898 cm-1) components.
Second derivative absorption spectra of NSN (A) and SN (B) oocytes in the nucleic acid absorption region. The second derivatives of the FTIR absorption spectra of single oocytes, measured at the antral (continuous line), MI 10 H (dotted line), and MII 20 H (dashed line) stages, are reported in the 1000-800 cm-1 absorption region, after normalization at the tyrosine peak (~1516 cm-1).
Furthermore, the analysis of the low frequency range, between 840-820 cm-1, allowed us to obtain information on DNA methylation. In particular, in this spectral range, bands due to DNA S-type sugar puckering modes occur, which are sensitive to changes in the DNA sugar conformation induced by cytosine methylation [32]. The possibility to monitor changes in the profile of this spectral region in whole intact cells makes it possible, therefore, to obtain information on the variation of global DNA methylation in the CpG islands. In this way, we found that in the NSN oocytes DNA methylation was high at the antral stage, while it became very low, almost negligible at MII, in agreement with what found for the transcriptional activity pattern at the different maturation stages.
Finally, significant spectral differences were found between 890 and 850 cm-1, where four different bands due to adenine and uracil vibrational modes occur (see Figure 5) [79]. Interestingly, the relative variation of these bands enables to monitor the mRNA polyadenylation extent, a crucial mechanism that regulates transcription. We found, in particular, that NSN oocytes were characterized during maturation by a low level of mRNA polyadenylation, being the polyadenylic acid band at 884 cm-1 absent at MII, while a new band at 854 cm-1 - likely due to adenine possibly not involved in polyA tail [80] – appeared. These results seem to suggest that an inadequate level of mRNA polyadenylation could preclude the possibility to resume meiosis, leaving the NSN oocytes in an unsuccessful transcriptional state.
5.1.2.2. SN oocytes
The analysis of SN oocytes (Figure 5B) in the spectral range between 1000 and 800 cm-1 led to very different results compared to NSN oocytes (see Figure 5A). Briefly, during all the studied maturation stages, the SN oocyte transcriptional activity was found to be maintained at lower levels than NSN oocytes, as revealed by the analysis of the CC stretching of the DNA backbone (980-950 cm-1) and the monitoring of the ribose (~ 922 cm-1) and deoxyribose (895-898 cm-1) vibrations. These results were supported by the temporal evolution of the DNA methylation bands that suggested a partial CpG methylation at the antral and MI stages, which dramatically increased at MII, contrary to what observed for NSN oocytes.
Noteworthy, while no evidence of mRNA polyadenylation was observed for SN oocytes at the antral stage - as indicated by the absence of the two polyadenylic acid bands around 884 cm-1 and 860 cm-1 - starting from MI the adenine and uracile bands at 870 cm-1 and 850 cm-1 appeared, to then dramatically increase up to MII. These findings likely indicate that SN MII oocytes are characterized by an adequate level of maternal polyadenylated mRNAs, making them ready to sustain a proper embryo development, contrary to NSN oocytes.
5.1.2.3. PCA-LDA analysis
The above results overall indicate that the IR spectra of oocytes at different maturation stages are very informative in the nucleic acid absorption region, allowing to obtain information on several cell processes simultaneously, including transcriptional activity, DNA methylation, and RNA polyadenylation. For this reason, PCA-LDA analysis was crucial to disclose the most significant spectral response, enabling to identify the marker bands able to discriminate between the two kinds of oocytes.
Firstly, we analyzed the different maturation stages of each kind of oocyte. In particular, NSN oocytes displayed a segregation into three separated clusters, each corresponding to a maturation stage, with a classification accuracy of about 80%. Noteworthy, the wavenumber with the highest weight (1.0) was that around 880 cm-1, due to polyadenylic acid, that, as revealed by second derivative analysis, was present only at the antral stage and disappeared upon maturation up to MII.
On the other hand, PCA-LDA analysis of SN oocytes led to an excellent discrimination accuracy (97%), with the wavenumbers with the highest discrimination weight at 817 cm-1 (1.0) and 859 cm-1 (0.83). While this last component is due to polyadenylic acid, the assignment of the 817 cm-1 band is not unequivocal, being due to overlapping contributions of DNA and polyadenylic acid.
The above results were then confirmed by the PCA-LDA analysis performed between 1400-1000 cm-1, where contributions due to nucleic acids, such as sugar-phosphate vibrations, also occur [31]. In particular, for the NSN oocytes the wavenumber with the highest discrimination weight (1.0) was the 1305 cm-1, which is due to free adenine, possibly not involved in polyadenylation [79]. In agreement with the temporal pattern of the adenine band at 870 cm-1, discussed previously, the 1305 cm-1 component displayed a higher intensity at MII, confirming that an inadequate mRNA polyadenylation could preclude NSN oocytes from a successful embryonic development (see Figure 6).
Second derivative absorption spectra of NSN oocytes in the absorption region of “free” adenine. The second derivatives of the FTIR absorption spectra of single NSN oocytes, measured at the antral (continuous line), MI 10 H (dotted line), and MII 20 H (dashed line) stages, are reported in the 1330-1270 cm-1 spectral range, where “free” adenine absorbs, after normalization at the tyrosine peak (~1516 cm-1).
We then compared by PCA-LDA the two types of oocytes taken at the same maturation stage. As reported in Figure 7, we found the largest spectral distance at MI (92% classification accuracy), with the components carrying the highest discrimination weight due to A-DNA, likely reflecting differences in the transcriptional activity. In this view, MI stage could be considered a sort of crucial checkpoint, when some molecular rearrangements occur, deciding the oocyte fate.
PCA-LDA analysis of SN and NSN oocytes in the nucleic acid absorption region (1000 - 800 cm-1). The separation between the two types of oocytes at each maturation stage is reported as average of PCA-LDA scores. The height of the boxes and the whiskers corresponds to 1 and 1.5 standard deviations from the mean values, respectively. The analysis has been performed on the measured spectra.
These findings have been strongly supported by the comparison of the SN and NSN oocytes at each maturation stage, altogether. A very good discrimination accuracy (89%) was again found analyzing the nucleic acid absorption region, between 1000 and 800 cm-1, that led to a clear cut separation into two groups (see Figure 8): one containing only the MII SN oocytes, and the other containing all the other SN and NSN stages. In particular, the wavenumbers carrying the highest discrimination weight were found at 926 cm-1 (1.00), due to ribose vibration, and at 855 cm-1 (0.97), assigned to adenine vibration, indicating again that differences in the temporal evolution and extent of transcription and polyadenylation play a crucial role in determining the different oocyte fate: the MII SN oocytes, with their proper content of maternal mRNAs polyadenylated, ready to support successfully the embryonic development; on the other hand, the MII NSN oocytes, with their mRNA lacking the appropriate polyadenylation, are kept in an unsuccessful transcriptional state.
PCA–LDA analysis of SN and NSN oocytes in the nucleic acid absorption region. The PCA–LDA analysis has been carried out on measured FTIR absorption spectra obtained from SN and NSN oocytes at each maturation stage, between 1000 and 800 cm−1. The semi-axes of ellipsoids in the 3D score plot correspond to two standard deviations of the data along each direction.
FTIR microspectroscopy has recently emerged as a powerful tool in biomedical research, thanks to the possibility of providing, in a non-invasive and rapid way, a chemical fingerprint of biological samples. In particular, being successfully applied to the study of complex biological systems, it makes it possible not only to characterize in situ biological processes, but also to provide a rapid diagnosis of several diseases, such as cancer and amyloid-based disorders.
We should, however, note that the intrinsic complexity of the IR response of biological systems - due to the overlapping absorption of the main biomolecules - requires the support of an appropriate multivariate analysis approach able to draw out the significant and non-redundant information contained in these highly dimensional data. Indeed, only a suitable combination of biospectroscopy and of multivariate analysis would provide robust and reliable results through the identification of specific biomarkers, an essential prerequisite for unbiased result interpretation [19, 20].
D. A. is indebted to the University of Milano-Bicocca (I) for the supporting postdoctoral fellowship. P. M. acknowledges a postdoctoral fellowship from Italian Institute of Technology. S.M. D. acknowledges the financial support of the FAR (Fondo di Ateneo per la Ricerca) of the University of Milano-Bicocca (I).
The authors wish to thank Carlo Alberto Redi and his collaborators at the University of Pavia (I) for the collaboration on murine oocyte maturation, and Antonino Natalello of the University of Milano-Bicocca (I) for helpful discussions.
Solar energy is a renewable energy source, clean and inexhaustible. It is based on the photovoltaic effect to convert solar energy into electricity through solar cells. PV panels was mainly installing in isolated areas to provide them the electricity but in the last few years a considerable amount of electricity has been generated from solar energy in different countries in the world. In 2019, the global installed solar energy capacity has reached 586.42 GW [1]. This significant growth will may be continuing in the future due to its several technological, environmental and economic benefits.
Like some other renewable energies, solar energy is intermittent. Its production is so related to the solar radiation received on the earth. Therefore, it is possible to forecast solar energy from a relevant forecasting of solar radiation. Different techniques have been developed in the literature to forecast solar radiation. Most of them treat it as time series. These techniques are based on the historical solar radiation data, they treated and followed the solar radiation evolution on the past. Based on the historical data, a model is created to characterize the solar radiation behavior in the past. Therefore, the forecasting of solar radiation on a given time interval is based on this created model. The aim of this chapter is the forecasting of solar radiation using ARMA model. Based on these results and taking into account some other parameters, the PV power is then modeled. A general overview of solar radiation and its different propagation forms is presented in the first part of this chapter. Then, a brief literature review on solar radiation forecasting techniques will be the subject of the next part. After that, the ARMA model will be used to forecast the annual solar radiation corresponds to an industrial company by considering the weekly radiation averages. PV power is modeled in the following section and based on the forecasting solar radiation results, it is presented for different PV panels number. The end section concludes and summarizes this chapter.
The sun is a vital element, necessary for photosynthesis, important for plants and fundamental for the thermal balance of different component of the crop. 75% of its composition is Hydrogen and the rest is Helium [2]. The sun is the primary source of electromagnetic radiation in Earth. It emits energy in the form of electromagnetic waves called solar radiation which mainly composed of visible light, ultra violet and infrared radiation. Visible light is the part of electromagnetic spectrum visible with the naked eye, its wavelength is depended to the individual. The ultra violet radiation is characterized by a wavelength greater than 800 nm, it is also called black light. This type of radiation is not visible with the naked eye. The infrared is a radiation with a wavelength less than 400 nm. It is greater than that of visible light but shorter than that of micro wave. When the solar radiation passes through the atmosphere, it is reduced due to its molecular scattering and its absorption by gas molecules. Ultra violet and infrared radiations are the two most absorbed. The amount of energy received on earth is depended to the atmosphere thickness and to some other factors such as the seasonal and cloud variations.
By propagating in the atmosphere, solar radiation can be diffused, absorbed or reflected,
Reflected radiation: the radiation is reflected by the earth’s surface and the soil reflects the radiation in a diffuse and anisotropic manner.
Diffused radiation: the radiation is diffused in all direction, this phenomenon is occurred in a medium containing fine molecules and it strongly depends to these molecules size.
Absorbed radiation: the radiation is absorbed by gas molecules that it encounters in atmosphere, this absorption is mainly due to water vapor, carbon dioxide and ozone.
These different interaction of solar radiation with atmosphere are recapitulated in the Figure 1 [3].
Interaction between solar radiation and the atmosphere [
Several theories are developed in the literature to model solar radiation [4, 5, 6]. Therefore, at a specific moment and in a given location, the solar radiation cannot be modeled without requiring some factors such as the sky nature and the sun position. As mentioned previously, solar radiation has three different components, reflected, diffused and absorbed. All these components are modeled by the global or total solar radiation as presented in the Eq. (1).
With Rtot represents the total solar radiation, Rdir, Rdif and Rref are respectively the directed, diffused and reflected solar radiation. Each of these radiations is sensitive to certain parameters and are calculated as presented in the following equations,
With Sh is a binary umbrage value, it is computed for each hour in day. Sh is assigned to 0 when the solar radiation is projected to the neighboring mountain umbrage, else it is assigned to 1. r represents the soil reflectance; it is also called the reflection factor. Sc is the constant solar equal to 1367 W/m2. To define the other parameters, a recourse to the geometry between sun and earth as well as to the characteristics of the solar flux are needed. Indeed, the position of the sun in the sky depends to the time and latitude. It is defined by two angles which characterized the altitude and the solar azimuth. The altitude angle α is defined as presented in the below Eq. [7].
With φ and η are respectively the latitude for each cell and the solar time. δ represents the solar declinaition, this parameter depends to the year day j and expressed as written in Eq. (6),
The azimuth angle β is defined as presented in the Eq. (7)
Rout represents the solar flux, it depends to the solar constant Sc and the year day j, it is written as indicated in the Eq. (8),
τM represents the transmissivity coefficient, it is defined as the fraction of the solar radiation incident on the atmosphere surface that reaches the soil along a vertical trajectory. In the mountain area, a correlation factor linked to the atmospheric pressure p/p0 must be used. The path length is presented by the lettre M and written as shown in the Eq. (9),
M0 is calculated following the Eq. (10) and the p/p0 represents the correlation factor of atmospheric pressure, it is calculated as defined in the Eq. (11).
An incidence angle i between the sun ray and the soil surface must be taken into account when the solar radiation is converged to sloping areas. This angle is depended to the sun position and to the topography and it is written as described the below equation,
With x and βs represent respectively the slope and the exposure, they are taken in degrees. It should be noted that the Eq. (1) describes the solar radiation without taking into account the clouds effects. To take them into account, a coefficient Kc must be added. So the expression of solar radiation in the presence of clouds Rtotc will be written as presented in the Eq. (13).
The Kc coefficient is depended to the cloudiness N and calculated as described in the Eq. (14).
Before forecasting, it must specify firstly the horizon forecasting. The choice of this horizon is relative to the problem to be treated. They are four forecasting horizon categories which are the very short term, the short term, the medium term and the long term. Each of these horizons is characterized by a time interval as described in the following paragraph,
Very short term: the time horizon of this forecasting category does not exceed a few hours, usually it is used for the intra-day market.
Short term: the time horizon of this category is between 48 hours and 72 hours. This type of forecasting horizon is useful for the daily dispatching electrical power.
Medium term: the time horizon of this forecasting term is done for more than one week to one month. It intervenes in the planning of the power system. It is also used for the dispatching of the conventional power plants.
Long term: the time horizon of this type is done from one month to one year. It is useful for long term planning operations such as expansion projects for power generation units.
In the literature, different techniques are proposed to the forecasting of solar radiation [7]. It is possible to classify them into four groups, the naïve models, the conditional probability models, the reference models and the connectionist models. A description of each of these techniques is described in the following sub sections.
They are the smallest techniques for time series forecasting. For a given horizon, the forecasting is based on the last observed variable [8]. The mean, the persistence and the k nearest neighbors are registered under these models.
The mean forecasting method consists to substitute the variable to be forecasted by the mean available data assigned to this variable. It is a simple technique to apply but it is so expensive in terms of history [7]. If N corresponds to the number of historical data, the forecasting of a variable x at a given horizon h is described as presented in the Eq. (15).
This technique is based on the repetition of a measurement from time t to time t+h [7]. If the considered horizon h is 1, the forecasting of a variable data at time time t+1 is defined as written in the Eq. (16).
This predictor type is often used in time series forecasting because it is so easy to implement and it does not require a large historical data base. On the other hand, it is imprecise and it does not lead to an improvement in time series.
This technique is derived from the artificial intelligence, it consists to find in time series, a set of k data similar to those that to be predicted [9]. The determination of k is done by different algorithm [7]. This technique is, in general, efficient in the time series forecasting, however, it is sensitive to the dimensionality and to the irrelevant variables.
We cite as an example for these types of models those of Marcov chains and Bayesian inferences.
This technique is rarely used for the forecasting of solar radiation [10]. It is a stochastic process that has the Markovian property [11]. A future state is modeled by a probabilistic process which depends only to the present states. Following Markov chain, the forecasting of a variable at a given horizon h is defined as presented in the Eq. (17).
With RM represents the transition matrix of Markov chain, its dimension depends to several factors such as the number of available data and the precision nature [12].
This method is mainly based on the conditional probability; it is rarely used for the forecasting of solar radiation. This method is very difficult to handle and it requires several parameters. The estimation of the probability of a series at a given horizon can be done by Bayes theorem as described in the Eq. (18).
The first artificial neuron was created by Warren McCulloch and Walter Pitts in 1943 [13]. The structure of this neuron is imitated from the biological neuron as presented in the Figure 2 [14]. An artificial neural network (ANN), is an assembly strongly connected of formal neurons. It is characterized by an excellent capacity of learning and generalization as well as a speed of processing. Its ability to learn and generalize makes it a very powerful tools. It has proven, in recent years, its effectiveness in various research fields. ANNs are subdivided into two large families, static and dynamic neural network. The choice of the one or the other of these two networks depends to the application to be processed, the available information and the complexity model [15].
Schematic diagram of an ANN structure neuron model [
These are models from the large family of Auto Regressive and Moving Average (ARMA). ARMA is the combination of two models, the Auto Regressive (AR) and Moving Average (MA). It is characterized by its ability to extract useful statistical properties. Thus, it is among the most widely used models for time series forecasting. Its effectiveness to forecast solar radiation is well proven in certain research work [16]. AR model assumes that each point can be forecasted by the sum of p previous points plus a random error term. The expression of AR model with an order p (AR(p)) is written as presented in the Eq. (19),
with αi represent the AR coefficients and εt is a white noise.
The moving average process assumes that each point is the sum of q previous errors plus its own error. The expression of MA model with an order q (MA(q)) is written as presented in the Eq. (20).
With βi are the MA coefficients. A combination of these two models forms the ARMA model with order p and q, its expression is described in the Eq. (21).
The major requirement of ARMA model is that the time series studied must be stationary. A series is considered stationary when its statistical properties such the mean and the variance are constant over time [17]. The distribution of a stationary series at time t is identical to that at time t-1. The unit root is among the stationarity tests. Autos-correlations and partial autos-correlations diagrams can be used also to prove the stationarity of time series.
If the time series is proved stationary, an approach must be followed to define the p and q orders. Box and Jenkins methodology is used to determine them, it contains four steps, identification of the model, estimation of the parameters, the validation of the selected model and finally the use of this model for forecasting.
Identification: this is the most important step, it aims to identify the p and q orders. This is done by examining the auto correlation and the partial auto correlation diagrams of the time series.
Estimation of parameters: the determination of p and q orders does not reflect the validation of this model. It is necessary to estimate the ARMA(p,q) selected. This estimation can be made by the student test.
Validation model: this validation is carried out by applying two tests on the residues, the Ljung-Box test and homoscedasticity test to ensure that the residuals are white noises.
The use of model: the selected ARMA model can be used in forecasting. However, in order to ensure the validity of this model, it must be tested on a data base already known. It should find good forecasting performances by comparing the data forecasted by this model and those already known.
The objective of this section is to forecast the solar radiation using ARMA model. The data base solar radiation considered for the forecasting is the set of solar radiation measurements corresponds to an industrial company located in Barcelona north [18]. The time interval of these measurements is five minutes, they are taken every day for a whole year as presented in the Figure 3.
Annual solar radiation evolution.
To refine the representative curve, just the weekly solar radiation averages are taken into account as presented in the Figure 4.
Weekly solar radiation averages.
To apply ARMA model, it must study the stationarity of this series. Correlograms corresponding to the auto-correlations and to the partial auto-correlation to this series are presented in the Figure 5.
(a) Auto-correlation and partial auto-correlation (b) correlograms of annual solar radiation.
The auto-correlation coefficient of order 1 is close to 1 and the correlogram shows a slow regression which is typical of non-stationary series. Dickey Fuller test is thus applied using EViews software; it proves the weak stationary of this series as shows in the Figure 6.
Dickey fuller test results for weekly solar radiation series.
The differentiation of this series is necessary in order to make it stationary. The following Figure 7 shows the evolution of the differentiated weekly solar radiation.
Differentiated weekly solar radiation evolution.
The Dickey Fuller is thus applied and it proves the stationary of this series as shown in the Figure 8. Thereafter, the different Box and Jenkins methodology steps are followed to obtain finally the optimal ARMA model that reproduces the best the behavior of this series. Orders p and q, coefficients α1, α2 and β1 of the ARMA model are recapitulated in the Table 1.
Dickey fuller test results for the differentiated weekly solar radiation series.
ARMA (p,q) | |
---|---|
Order | Coefficients |
p = 2 | α1 = −1.0342; α2 = −0.4023 |
q = 1 | β1 = 0.7483 |
Orders and coefficients of ARMA (2,1).
In this paragraph, ARMA (2,1) model is used to forecast the differentiated weekly solar radiation averages. The real solar radiation curve and the forecasted one are presented in the Figure 9. It is clear that an approximation is observed between the two curves for certain time intervals, especially when the solar radiation does not present large fluctuations. For other moments time, the forecasted solar radiation curve diverges from the real one. This is particularly observed when the solar radiation presents large fluctuations. To confirm these results, the ARMA model errors are presented in Figure 10.
Solar radiation modeled by ARMA (2,1).
Error (a) and relative error (b) of solar radiation modeled by ARMA (2,1).
Following the Figure 10b, it is clear that the relative error is small, it does not exceed 15%. It is thus observed two peaks, the first one corresponds to the 16th week of the year and the second is in the 36th week. Therefore, when we refer to the real annual solar radiation curve, we observe a sudden fluctuation during these two weeks. Indeed, 16th and 17th weeks correspond respectively to the last week of April month and the first week of May. A considerable decrease of temperature is observed during this period; this is may be the main reason to the sudden decrease of radiation. On the other hand, 37th and 38th weeks correspond to the two first weeks of September month. At the end of this period, it is observed also a sudden decrease of the temperature which affects considerably the solar radiation. Furthermore, as the weekly solar radiation averages are considered for the forecasting, it is obvious to have these large solar radiation variations especially in the switching periods from one season to another one. The influence of temperature on solar radiation evolution for April, May, September and October months are presented in the Figure 11.
Influence of temperature on solar radiation (a) April and may weeks (b) September and October weeks.
After forecasting solar radiation or any other parameters, a forecasting error should always be calculated. An error in the forecasting context does not indicate a fault or an anomaly as it is known in several other fields but rather a criterion to evaluate the forecasting performances. In this study, Mean Square Error (MSE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) are calculated as written in the Eqs. (22)–(24) [19]. ei (i=1….n) represents the error measured between the actual value and the forecasted one for sample i and n is the total number of samples. Results are recapitulated in the Table 2, the MSE presents the lowest one (0.2182), it is a small value which reflects the performances of ARMA (2,1) model to forecast the solar radiation.
Errors | Performances |
---|---|
MSE | 0.2182 |
MAE | 0.2999 |
RMSE | 0.4671 |
Errors of solar radiation forecasting using ARMA (2,1).
The forecasting of PV power has a great importance to the best management of grid connected PV systems as well as to the isolated micro grid which include PV system as renewable energy source. Based on the literature, it is possible to forecast the PV power by direct or indirect methods [20]. Direct methods consist to describe models to directly forecast the amount of PV power or forecast the PV power without using other metrological data. In this context, different approaches are suggested which mainly the ANN and the machine learning techniques [20, 21, 22]. On the other hand, the indirect methods consist to forecast the PV power based on the forecasting of another meteorological data such as the solar radiation or the temperature [20, 23]. Different physical and statistical approaches are proposed in this field. The choice for the one or the other method is depended to the available data and the forecast horizon term. In physical approaches, the PV power forecasting is based on weather variables predicted by numerical weather prediction (NWP) models and they are more suitable for the long term horizon. The statistical approaches are based on past measured time data series and generally they are appropriate for short term horizon. Moreover, the statistical approaches are simpler than the physical approaches since they require less input data and lower computation [24].
In the following section, the PV power will be modeled and forecasted based on the results of solar radiation forecasting, presented in the precedent section. Indeed, the PV power generators are very often operating with a maximum power called Maximum Power Point Tracker (MPPT) [25]. The maximum power PPV delivered by a PV generator composed of N PV panels can be expressed as indicated in the Eq. (25) [26].
With A represents the area of a single PV panel, it is expressed in m2. G is the solar radiation measured in w/m2. ηg is the PV generator efficiency and it is described as written in the Eq. (26) [27].
ηr represents the reference efficiency of PV generator, it depends to the PV cells materials. ηpt is the efficiency of power tracking equipment, it is equal to 1 if the MPPT is perfectly used, βt is the temperature coefficient, it is expressed in °C. The typical value of this coefficient varies between 0.004 and 0.006, usually, it is taken in the range of 0.005°C [26]. Tc and Tr represent respectively the tcemperature measured in the PV cells and the reference temperature. Tc depends to the ambient temperature Ta and the radiation G as presented in the Eq. (27) [26].
The typical NOCT value for polycrystalline cells is around 45°C. Taking into account Eq. (26) and Eq. (27), the PV power is described as presented in the Eq. (28).
As shown in the Eq. (28), the evolution of PV power depends to several parameters such as the temperature, the solar radiation and the PV panels number. Therefore, it is possible to forecast the PV power from the solar radiation forecasting. So, if the PV cells used is the pollicrystalline and the area of a single PV panel is 2.25m2, the evolution of PV power for different PV panels number and based on the solar radiation forecasting results is described as presented in the Figure 12.
PV power forecasting for different PV panels number (a) N=5 (b) N=20 (c) N=50 (d) N=100.
This chapter focuses to model and to forecast the PV power based on the solar radiation forecasting results. Some physical equations are presented firstly to define in general the three different forms of solar radiation. They are explained taking into account some topographical factors and geometric relations.
For solar radiation forecasting, a set of solar radiation measurements corresponds to an industrial company is considered as data base. ARMA model is used to forecast the weekly solar radiation averages. The simulation results obtained are proven the effectiveness of this model to forecast the small variation of solar radiation. On the other hand, it is observed the deterioration of ARMA model with the large solar radiation fluctuations. The forecasting of PV power is carried out based on the obtained solar radiation forecasting results and taking into account some other parameters such as the temperature, the PV cells materials and the PV panels number.
This work was supported by Tunisian Ministry of Higher Education and Scientific Research under Grant LSE-ENIT-LR 11ES15.
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\\n\\nIntechOpen nije formalno povezan niti s jednom vanjskom stranicom čije poveznice vode na www.intechopen.com, osim ako to nije izravno navedeno. Iz tog razloga IntechOpen nije odgovoran za sadržaj koji se pojavljuje na takvim stranicama. Poveznica na IntechOpenovu stranicu ne implicira povezanost sa IntechOpenom. Korištenje takvih poveznica isključiva je odgovornost korisnika.
\\n\\nZadržavamo pravo vlasništva nad cjelokupnom stranicom www.intechopen.com i nad svim materijalom na toj stranici. Koristeći se našim uslugama, slažete se da maknete sve poveznice na našu stranicu odmah nakon što to od vas zatražimo. Također, zadržavamo pravo da ove Odredbe i uvjete, i politiku o poveznicama izmjenimo u bilo koje vrijeme. Koristeći se poveznicama na naše stranice slažete se s ovim Odredbama i uvjetima.
\\n\\nAko smatrate da je bilo koja poveznica na našoj stranici sumnjiva iz bilo kojeg razloga, molimo vas da nas kontaktirate. U tom slučaju razmotrit ćemo micanje poveznice s naše stranice, iako nismo obvezni to napraviti.
\\n\\nBez prethodne privole i izričite pisane dozvole, ne možete stvarati okvire oko naših stranica ili koristiti druge tehnike koje na bilo koji način mogu promijeniti prezentaciju ili izgled naše stranice.
\\n\\nIntechOpen može ove Odredbe izmijeniti u bilo koje vrijeme i bez prethodne obavijesti. Koristeći ovu stranicu vi se slažete s trenutnim Odredbama i uvjetima koje su na snazi.
\\n\\nOve Odredbe i uvjeti su sastavljeni u skladu s odredbama prava Ujedinjenog Kraljevstva, a za sve sporove nadležan je sud u Londonu, Ujedinjeno Kraljevstvo.
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\n\nSljedeća terminologija odnosi se na Odredbe i uvjete, te na sve naše ugovore:
\n\nKlijent, stranka, vi, vaš odnosi se na vas, osobu koja pristupa ovoj stranici i prihvaća IntechOpenove Odredbe i uvjete;
\n\nKompanija, tvrtka, mi, naše odnosi se na tvrtku IntechOpen;
\n\nStranke, strane odnosi se na klijenta i na nas, ili samo na klijenta ili nas.
\n\nSve odredbe koje se odnose na ponudu, prihvat ili razmatranje plaćanja, a za koja mi pružamo asistenciju klijentu, bilo na ugovoreni ili fiksni način, a s ciljem da se ostvare potrebe i želje klijenta u svezi s našim uslugama, su podložne zakonskim odredbama Ujedinjenog Kraljevstva.
\n\nOsim ako nije suprotno navedeno, IntechOpen i/ili svi davatelji licence vlasnici su intelektualnog vlasništva nad svim materijalima na www.intechopen.com. Sva prava intelektualnog vlasništva su pridržana. Stranice sa www.intechopen.com možete gledati, preuzimati, dijeliti, dijeliti poveznice i printati za osobnu uporabu, a temeljem pravila sadržanih u ovim Odredbama i uvjetima.
\n\nMi koristimo kolačiće. Korištenjem IntechOpenove stranice slažete se s korištenjem kolačića u skladu s IntechOpenovom Politikom privatnosti. Većina modernih, interaktivnih stranica koristi kolačiće kako bi omogućila ponovno pronalaženje korisničkih detalja kod svakog posjeta. Na našoj stranici kolačići se uglavnom koriste kako bi omogućili funkcionalnost i olakšali posjetiteljima korištenje stranice.
\n\nIntechOpen ili njegovi suradnici niti u jednom slučaju neće biti odgovorni za štete (štete uključuju gubitak podataka ili profita, druge poslovne prekide, te sve ostale štete) koje nastanu zbog korištenja materijala na IntechOpenovoj stranici ili nemogućnosti da se iste koriste, čak i ako je IntechOpen ili njegov predstavnik o takvoj šteti obaviješten pismenim ili usmenim putem. Neke jurisdikcije ne dozvoljavaju ograničenja garancija ili ograničenja obveza za posljedične ili slučajne štete pa se u tom slučaju ova ograničenja možda ne odnose na vas.
\n\nMaterijali koji se pojavljuju na IntechOpenovoj stranici mogu sadržavati manje greške, tipfelere ili fotografske greške. IntechOpen može napraviti promjene na bilo kojem materijalu koji se nalazi na stranici u bilo koje vrijeme.
\n\nIntechOpen nije formalno povezan niti s jednom vanjskom stranicom čije poveznice vode na www.intechopen.com, osim ako to nije izravno navedeno. Iz tog razloga IntechOpen nije odgovoran za sadržaj koji se pojavljuje na takvim stranicama. Poveznica na IntechOpenovu stranicu ne implicira povezanost sa IntechOpenom. Korištenje takvih poveznica isključiva je odgovornost korisnika.
\n\nZadržavamo pravo vlasništva nad cjelokupnom stranicom www.intechopen.com i nad svim materijalom na toj stranici. Koristeći se našim uslugama, slažete se da maknete sve poveznice na našu stranicu odmah nakon što to od vas zatražimo. Također, zadržavamo pravo da ove Odredbe i uvjete, i politiku o poveznicama izmjenimo u bilo koje vrijeme. Koristeći se poveznicama na naše stranice slažete se s ovim Odredbama i uvjetima.
\n\nAko smatrate da je bilo koja poveznica na našoj stranici sumnjiva iz bilo kojeg razloga, molimo vas da nas kontaktirate. U tom slučaju razmotrit ćemo micanje poveznice s naše stranice, iako nismo obvezni to napraviti.
\n\nBez prethodne privole i izričite pisane dozvole, ne možete stvarati okvire oko naših stranica ili koristiti druge tehnike koje na bilo koji način mogu promijeniti prezentaciju ili izgled naše stranice.
\n\nIntechOpen može ove Odredbe izmijeniti u bilo koje vrijeme i bez prethodne obavijesti. Koristeći ovu stranicu vi se slažete s trenutnim Odredbama i uvjetima koje su na snazi.
\n\nOve Odredbe i uvjeti su sastavljeni u skladu s odredbama prava Ujedinjenog Kraljevstva, a za sve sporove nadležan je sud u Londonu, Ujedinjeno Kraljevstvo.
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After finishing his P. hD degree in 1992, he served in the Industry as a Scientific Officer and continued his academic career as a visiting scholar for a number of educational institutions. In 1996 he joined National University of Science & Technology Pakistan (NUST) as an Associate Professor; NUST is one of the top few universities in Pakistan. In 1999 he joined an International Company Lineo Inc, Canada as Manager Compiler Group, where he headed the group for developing Compiler Tool Chain and Porting of Operating Systems for the BLACKfin processor. The processor development was a joint venture by Intel and Analog Devices. In 2002 Lineo Inc., was taken over by another company, so he joined Aalborg University Denmark as an Assistant Professor.\nProfessor Akbar has truly a multi-disciplined career and he continued his legacy and making progress in many areas of his interests both in teaching and research. 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