A wavelet-based multivariable approach for fault detection in dynamic systems

Abstract

This paper presents a multivariable extension to a recently proposed wavelet-based technique for fault detection. In the original formulation, the Discrete Wavelet Transform is used to carry out dynamic consistency checks between pairs of signals within frequency subbands. For this purpose, moving average models with an integrative term are employed to reproduce the dynamics of the system in each subband under consideration. The present work introduces a new architecture allowing the use of subband models with more general multivariable structures. More specifically, a multivariable ARX (autoregressive with exogenous input) structure is adopted for each subband model. The proposed technique is illustrated in a case study involving a nonlinear simulation model for an aircraft with a sensor fault. The results show that the multivariable approach outperforms the original formulation in terms of residue amplification following the fault onset.

Fault Detection, Diagnosis, and Isolation Strategy in Li-Ion Battery Management Systems of HEVs Using 1-D Wavelet Signal Analysis

“…For example, in Figure 10 are implemented in MATLAB two analysis filters and other two synthesis filters for a B spline biorthogonal wavelet that can reproduce polynomials (vanishing moment property) with three vanishing moments in the reconstruction filter and five vanishing moments in the decomposition filter, very useful to be used in fault detection. More precisely, both phases analysis and synthesis require two low pass filters (LPF) to filtrate low frequencies signals, respectively two high pass filters (HPF), to filtrate the high frequencies signals [8,12,[18][19][20][21].…”

“…Furthermore, the orthogonal and biorthogonal filters banks are an arrangement of low pass, high pass, and bandpass filters that divide the signals data sets into sub- bands [12,[17][18][19][20][21]. If the sub-bands are not modified, these filters enable perfect reconstruction of the original data.…”

“…In [14] is presented an interesting fault isolation technique based on wavelet transform, and a detailed data-based FDI techniques for a nonlinear ship propulsion system are developed in [15]. Several multimedia applications of wavelet transform can be found in [16], and a better understanding of wavelet transform analysis, design and implementation of features extraction methods, for filtering, denoising, decomposition and reconstructing signals is given in [17][18][19][20][21][22][23]. From our most recent preliminary results in Li-ion battery field, modeling and SOC estimators disseminated in [11,24,25], an interesting state-of-art analysis of similar SOC AEKF estimators performance reported in the literature is done in terms of statistical performance criteria values, such as root mean square error (RMSE), mean square error (MSE), mean absolute error (MAE), standard deviation (std), mean absolute percentage error (MAPE) and R2 (R-squared).…”

1-D Wavelet Signal Analysis of the Actuators Nonlinearities Impact on the Healthy Control Systems Performance

“…In addition, can also be added your own custom wavelet filters. However, by using the wavelet filter bank architecture depicted in Figure 47 it is possible to obtain residues that change in a noticeable manner in order to offer precious information about the time detection of the faults and its severity [19,20]. The subband model is suggested in [19] of the form:…”

“…In [19] is used the 'db8' wavelet for wavelet filter bank design of level 3 decomposition [19] for a Single-Input Single-Output (SISO) plant extended in [20] for a Multivariable (MIMO) plant. A wavelet based-frequency subband analytical redundancy scheme to calculate the residuals for different faults is shown in Figure 48, and used for wavelet filter bank synthesis and analysis of level 3 decomposition in [19,20] , and also in our case study. In this scheme G(z) and H(z) represent the ztransforms of the low pass filter (LPF) and high pass filter (HPF) respectively.…”