Data Normalization

Data normalization is essential in order to distinguish between changes in the observed damage features that are caused by damage and changes that are caused by variation of the EOCs. For instance, in [19], it is observed that changing thermal conditions cause alterations in the modal properties of highway bridges ranging from 5% to 10%. The effect of operational conditions is shown in [20], where the natural frequencies of a short span bridge change up to 5.4% due to traffic loading. Worden and Farrar [21] provide a thorough overview of data normalization techniques. In Figure 1.4, this overview is summarized and the techniques are distinguished based on the availability of EOC measurements. Mahalanobis squared distance (MSD) Machine learning algorithms Factor analysis Singular value decomposition (SVD) Data normalization Auto-associative neural networks (AANN) Projection methods Intelligent feature selection (e.g. PCA) Cointegration Modelling and machine learning algorithms Regression techniques Data clustering based on EOCs

EOC measurements not available EOC measurements available

Figure 1.4: Data normalization techniques categorized based on the availability of EOC

measurements.

1.3.2.1

Data Normalization without EOC Measurements

When EOC measurements are not available, data normalization can be achieved by employing machine learning algorithms that develop a model which describes the influence of varying EOCs on the damage-sensitive features. These might be: auto-associative neural networks (AANNs), singular value decomposition (SVD) of matrices containing characteristic properties of the structure (for instance, natural frequencies, mode shapes and model coefficients) and algorithms, which employ factor analysis or the Mahalanobis squared distance (MSD). All of the aforementioned methods are based on the assumption that damage causes changes in the features, which are in some way orthogonal to the changes caused by EOC

variations [21].

As their name implies, the output of AANNs reproduces patterns presented in the input layer. The special attribute of AANNs is a bottleneck in the hidden layers, which consist of fewer nodes than the input and output layers [22]. This architecture forces the network to learn the significant characteristics of the features, which, in the context of data normalization, are the correlations between the features of the training data. The trained network should be able to quantify the unmeasured sources of variability (such as EOCs), which affect the structural response. This variability is represented at the bottleneck output where the number of nodes should be equal to the number of unobserved independent factors which influence the structural response. In [23], an AANN is used along with other pattern recognition algorithms to detect damage on a 9 m long blade, which was tested under fatigue loading in LANL. On the other hand, the basic idea behind the employment of SVD for data normalization is that the rank of the state matrix, which contains some characterictic vectors of the structure, remains constant regardless of the EOCs, but increases in case of damage. The ability of SVD to identify damage is demonstrated on data from a finite element model of a truss structure and on the experimental data of a notched cantilever beam [24].

MSD is a multivariate measure of distance, which takes into account the covariance among the variables. It has an inherent normalization function, since, in its definition, the mean differences are divided by the covariance matrix. Factor analysis is a mathematical model that attempts to describe the correlation between a set of observed variables using a small number of unobserved underlying factors [25]. In [26], both MSD and factor analysis are employed for data normalization for the example of the three-story LANL structure. Finally, in [27], a data normalization procedure based on the minimization of the Euclidean distance is suggested, in order to minimize false positive warnings caused by the effects of EOCs.

1.3.2.2

Data Normalization with EOC Measurements

When EOC measurements are available, regression techniques, which model the rela- tionships between the EOCs and the structural responses, as well as data clustering algorithms can be employed, with the latter being widely used in the monitoring of wind turbines in operation. Finally, some alternative approaches for data normaliza- tion, which involve projection are: (i) intelligent feature selection (i.e., the selection of features that are insensitive to damage), (ii) principal component analysis (PCA) and (iii) cointegration, with the latter being more suitable for unsupervised SHM applications [21].

Regression or heteroassociation deals with constructing a map between a group of continuous input variables and continuous output variables on the basis of a set of samples by minimizing an objective function [28]. Regression analysis includes linear, polynomial and autoregressive (AR) models, as well as machine learning algorithms

such as support vector regression (SVR) and neural networks (NN). One of the most common applications of regression analysis in SHM involves the definition of the de- pendency between EOCs and the observed damage features.

A simple, linear relationship between traffic load and natural frequencies, which can be enhanced with a temperature-dependent variable, is used in [29] to predict the natural frequencies of the Tamar bridge. In [30], an adaptive filter is presented, which functions as a multiple linear regression model. The filter takes temporal and spatial temperature profiles as inputs and delivers the first natural frequency. The concept is validated on data from the Alamosa Canyon bridge and it is shown that it can reproduce the natural variability of the frequencies. A robust regression tool, least trimmed squares (LTS), is proposed in [31] as a means for characterizing and distinguishing the influence of EOCs on the structural response of bridges and civil engineering structures in general. In [32], a model is created for the 3.2 kW LANL wind turbine and Gaussian process regression (GPR) is used to extract features from the responses that correlate with EOCs and, at the same time, are insensitive to damage. The presented features correlate with the rotor angular velocity and nacelle yaw angle. Subsequently, measurement data of the real turbine is clustered by using these features instead of the actual EOCs. Least squares support vector regression (LS-SVR), a variation of SVR, is used in [33] to characterize the relationship between turbine power and weather variables, as well as to contribute to wind power produc- tion monitoring.

Data clustering is widely used in SHM of wind turbines in operation. Manual clustering or a variety of automatic clustering algorithms can be employed to cluster the structural data based on the EOCs. A review of clustering algorithms is provided in [34]. There are many different ways of categorizing clustering algorithms. Accord- ing to the most general, clustering algorithms can be distinguished into hierarchical methods and partitional or point assignment methods. Hierarchical methods yield a dendrogram representing the nested grouping of patterns and similarity levels at which groupings change. Initially, each point is a distinct cluster and the two nearest clusters are repeatedly combined into one. Partitional clustering algorithms obtain a single partition of the data. They are cluster-based in the sense that a certain set of clusters is maintained, while each point is assigned to its nearest cluster.

In [35], operational cases are defined manually, resulting in clusters in the rotor speed-wind speed space, and data is normalized within each cluster. In [36], affinity propagation (AP) is employed to cluster the structural data of the 3.2 kW LANL wind turbine based on environmental data. AP is a hierarchical clustering algorithm, which takes as input measures of similarity between pairs of data points, which are called preferences, and exchanges information between them. The algorithm consid- ers all data points as potential exemplars and hence does not require a predefined number of clusters [37]. In [16] the same clustering method is employed to cluster the structural data of a 5 MW offshore wind turbine based on EOCs. K-means clus- tering, a partitioning clustering algorithm, which requires predefinition of the cluster number, is used to cluster tower acceleration data of a 1.5 MW wind turbine, based

on wind speed and drivetrain acceleration data [38]. Self-organizing maps (SOPs) are a type of artificial neural network (ANN), which gives an intuitevely appealing two- dimensional map of a multidimensional dataset. In [39], SOPs are used on SCADA data for damage detection on the gearbox of a 600 kW wind turbine.