Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 7906834, 14 pages

http://dx.doi.org/10.1155/2016/7906834

## Machine Fault Detection Based on Filter Bank Similarity Features Using Acoustic and Vibration Analysis

^{1}Automatic Research Group, Universidad Tecnológica de Pereira, Pereira, Colombia^{2}Technological and Environmental Advances Research Group, Universidad Católica de Manizales, Colombia^{3}Signal Processing and Recognition Group, Universidad Nacional de Colombia, Manizales, Colombia^{4}Universidad Nacional de Colombia, Manizales, Colombia

Received 19 February 2016; Revised 10 May 2016; Accepted 8 June 2016

Academic Editor: Weihua Li

Copyright © 2016 Mauricio Holguín-Londoño et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Vibration and acoustic analysis actively support the nondestructive and noninvasive fault diagnostics of rotating machines at early stages. Nonetheless, the acoustic signal is less used because of its vulnerability to external interferences, hindering an efficient and robust analysis for condition monitoring (CM). This paper presents a novel methodology to characterize different failure signatures from rotating machines using either acoustic or vibration signals. Firstly, the signal is decomposed into several narrow-band spectral components applying different filter bank methods such as empirical mode decomposition, wavelet packet transform, and Fourier-based filtering. Secondly, a feature set is built using a proposed similarity measure termed cumulative spectral density index and used to estimate the mutual statistical dependence between each bandwidth-limited component and the raw signal. Finally, a classification scheme is carried out to distinguish the different types of faults. The methodology is tested in two laboratory experiments, including turbine blade degradation and rolling element bearing faults. The robustness of our approach is validated contaminating the signal with several levels of additive white Gaussian noise, obtaining high-performance outcomes that make the usage of vibration, acoustic, and vibroacoustic measurements in different applications comparable. As a result, the proposed fault detection based on filter bank similarity features is a promising methodology to implement in CM of rotating machinery, even using measurements with low signal-to-noise ratio.

#### 1. Introduction

Condition monitoring (CM) for rotating machinery is becoming an essential task that allows detecting faults at early stages, preventing unexpected damage and catastrophic accidents. In machine fault diagnoses, the vibration signal analysis is the most widely used nondestructive technique for extracting relevant information. Recently, data acquisition systems using acoustic signals have also gained demand over other noncontact measurement techniques when the sensor locations on the machine are unavailable or the measurement procedure has a high risk for workers [1]. Nonetheless, acoustic signals are more vulnerable to environmental noise than vibration responses [2], making employing signal preprocessing techniques necessary to reduce the undesirable interferences and improve the low signal-to-noise ratio (SNR) [3]. Furthermore, the vast majority of reported acoustic-based CM are focused on visual inspections, eluding to incorporate the signal preprocessing into automatic diagnoses systems [4].

With the aim of enhancing the signal quality influenced by noisy environments, different preprocessing methods must be used. Due to the fact that wide class of machinery faults is defined by spectrally localized energies over narrow subbands, the filter bank methods (FBM) are employed as a common suitable preprocessing method for acoustic [1, 5] and vibration signals [6]. Thus, CM usually includes a filter bank stage that splits the measured signal into a set of narrow spectral bands, which concentrate the information within a limited bandwidth related to the machine fault under consideration. In particular, wavelet packet transform (WPT) and empirical mode decomposition (EMD) are frequently applied as presented in [2, 7].

However, selection of the representative spectral components relies commonly on a priori knowledge available regarding the fault signatures, assuming each frequency band at which signatures may appear [8]. By instance, it is highly expected that bearing and gear faults appear at high frequencies. However, this knowledge is not accessible for most of the machine faults. Accordingly, there is a need for a measure that can identify the most representative spectral bands and hence perform a reliable assessment of the machine condition for a wide class of faults.

To date, several approaches have been developed to select the most discriminating narrow bands, which are mainly based on the use of similarity distances. In particular, the detection of impulsive behavior can be carried out using different measures of the relationship between narrow-band components. The structure of proposed correlation estimators can range from the baseline Pearson’s correlation coefficient [9], merit index based on skewness [10], and spectral kurtosis [8] to more elaborate quantile-quantile plot-based selectors [11] and entropy-based indexes [12]. Nonetheless, the majority of these approaches rely on assumptions of stationarity for the correlated processes. This model may be not suitable for an extensive variety of nonstationary faults having impulsive or dynamics confined in the time domain.

In this paper, a similarity measure is introduced (termed* cumulative spectral density index*, CSDI) that deals with nonstationary estimates for the pairwise relationship measure between each narrow-band spectral component and the acquired raw signal, aiming to improve the detection of faults like unbalance, misalignment, and bearing faults. For the sake of comparison, we contrast the introduced CSDI with the baseline correlation index and cross-entropy value proposed for nonstationary analysis in [13]. As filter bank methods, we analyze three filter bank methods (WPT, EMD, and conventional Fourier filter bank, FFB) to enhance the quality of signal analysis, preserving the physical meaning of the extracted features. CSDI is applied to the acquisition cases of the acoustic, vibration, and combination of vibration and acoustic signals. Using a -nearest neighbors algorithm, the classifier validation is carried out on the data measured in a turbine blade laboratory experiment and a laboratory test rig. Both setups are employed for simulating a set of multiple faults. Obtained results for classification accuracy show that the CSDI feature set, extracted from the considered components extracted by filter bank methods, leads to increasing the classification performance, mostly, in cases of low SNR for either case of acquired signal: acoustic or vibration. Moreover, the use of both data further improves the fault classification, resulting in a promising methodology to implement in CM of rotating machinery.

The agenda of this work is as follows: Section 2 summarizes the employed FBM as well as the compared similarity measures, including the introduced CSDI measure. Section 3 outlines the experimental setup used for the classifier validation carried out for two real-world databases of machine faults, holding acoustic and vibration recordings. Finally, discussion of the obtained results and regarded conclusions are given in Sections 4 and 5, respectively.

#### 2. Theoretical Background

##### 2.1. Filter Bank Methods

With the purpose of separating the information of spectral subbands, the filter bank methods (FBM) decompose bandwidth-limited signals into a set of narrow-band components. Thus, a given signal that has a finite bandwidth (with , being the sampling frequency) is decomposed into narrow-band components so that each one has a bandwidth such that . Regarding acoustic and vibration analysis, the following approaches for FBM are widely used:(i)*Decomposition Using Fourier Filter Banks* (FFB). Fourier transform, noted as , provides a straightforward approach to implementing FBM so that several ideal bandpass filters are applied to the input signal in order to build a component set such that the support of equals the closure of the corresponding bandwidth, noted as With the aim of obtaining an orthogonal FBM, all bandwidths are also required to be disjoint, that is, , with .(ii)*Wavelet Packet Transform* (WPT). Wavelet Transform can be expressed in terms of the inner product between each basis and the considered signal . Thus, the wavelet coefficients are the inner product, , defined as , where is the oscillation parameter, and are the scale and translation operation indexes, respectively. Therefore, a WPT basis function is defined as , where the initialization () and remaining recursions () are given in [14].(iii)*Empirical Mode Decomposition* (EMD). This FBM is a self-adaptive time-frequency signal analysis method based on local characteristic time scales. EMD can decompose the complex and unstable signal into several nearly stable intrinsic mode functions (IMFs) as defined in [15]

##### 2.2. Feature Estimation Based on Similarity Measures

With the aim of improving the discriminating ability of the feature set, we measure the similarity between the input signal and each extracted th narrow-band component, , quantifying their mutual statistical dependence.

A straightforward approach to measuring the statistical similarity between two processes is their product moment, termed* Pearson’s correlation coefficient *, that quantifies the linear relationship of dependence as follows:where is the variance, with . Notations and stand for the expectation operator and conjugate, respectively. Note that both and are assumed to be zero-mean stochastic process.

In a more elaborate approach, the statistical dependence between two processes can be estimated by using an information measure. In particular, we employ the* Kullback-Leibler* divergence (also termed relative entropy) that measures the difference between a couple of probability density functions, and , as follows:where is an i.i.d. sample for each corresponding distribution. Note that is not a distance in the formal sense since it is not symmetric and does not satisfy the triangle inequality. Still, it frequently serves as a similarity measure estimation between densities [16].

Nevertheless, either measure defined above, or , assumes the stationarity of correlated processes. In practice, this assumption is far from being true for most of the acquired CM data. Besides, most of the state-of-the-art techniques for fault detection lie on spectral analysis of the measured signals. With the purpose of providing the analytical support for nonstationary processes and spectral significance, we introduce the similarity measure (termed* cumulative spectral density index* (CSDI)) that is built on the cross-correlation function calculated between two second-order nonstationary processes.

Let be the signal content distribution over the frequency domain to be represented through the cross-spectral density between so that we compute the Fourier transform of the time-averaged function as follows:where

However, the complex-valued density must be mapped into a real-valued domain. To this end, we apply the expected value of the squared modulus as a positive semidefinite operator. Therefore, we obtain a measure of the spectral information shared between the signal and its set of narrow-band components

Nonetheless, the spectral density can hold powerful components (i.e., that are locally concentrated), strongly biasing the expectation operator estimator [17]. To overcome this issue, we propose to introduce the expected value over the cumulative energy function in the CSDI definition as follows:

Note that the higher the value of similarity for or , the higher the statistical association between variables. By contrast, lower values of imply a close relationship since it can be explained as the distance between both compared probability density functions.

#### 3. Experimental Setup

As shown in Figure 1, the presented fault detection methodology using acoustic and vibration signals comprises the following stages: (i) signal enhancement, applying one of the examined filter bank decompositions (EMD, WPT, or FFB), (ii) feature extraction, testing each of the proposed similarity measures (Pearson’s correlation coefficient, cross-entropy spectral analysis, and cumulative spectral density index) between the raw measured data and its decomposed narrow-band components, and (iii) classifier performance validation, feeding the extracted feature set into the classification algorithm.