Journal of Sensors

Volume 2016 (2016), Article ID 9693651, 9 pages

http://dx.doi.org/10.1155/2016/9693651

## A Wavelet Based Multiscale Weighted Permutation Entropy Method for Sensor Fault Feature Extraction and Identification

College of Information Science & Technology, Beijing University of Chemical Technology, Beijing City Chaoyang District North Third Ring Road 15, Beijing 100029, China

Received 20 February 2016; Revised 5 May 2016; Accepted 8 May 2016

Academic Editor: Fanli Meng

Copyright © 2016 Qiaoning Yang and Jianlin Wang. 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

Sensor is the core module in signal perception and measurement applications. Due to the harsh external environment, aging, and so forth, sensor easily causes failure and unreliability. In this paper, three kinds of common faults of single sensor, bias, drift, and stuck-at, are investigated. And a fault diagnosis method based on wavelet permutation entropy is proposed. It takes advantage of the multiresolution ability of wavelet and the internal structure complexity measure of permutation entropy to extract fault feature. Multicluster feature selection (MCFS) is used to reduce the dimension of feature vector, and a three-layer back-propagation neural network classifier is designed for fault recognition. The experimental results show that the proposed method can effectively identify the different sensor faults and has good classification and recognition performance.

#### 1. **Introduction**

At present, the sensor is widely used in various processes to obtain a variety of physical quantity of data. In practical applications, due to the harsh external environments, battery depletion, aging, and other reasons, the sensor is prone to failure or even damage [1, 2]. The data obtained from the fault sensor has low reliability, and the subsequent judgment, recognition, decision, and control based on these low quality data will lose the meaning. The reliability of sensor data and the identification of sensor fault are important research subjects. Sensor fault identification mainly consists of two aspects: fault feature extraction and fault pattern classification [3, 4].

Wavelet transform is a widely used time-frequency analysis technology. Using wavelet transform, signals are decomposed into multilevel time-frequency components. Suitable wavelet basis for wavelet decomposition is important for fault information representation [5]. The selection method of wavelet base includes many kinds, such as the minimum joint entropy standard, the minimum conditional entropy standard, the maximum mutual information criterion, the minimum relative entropy standard, and maximum energy-Shannon entropy criterion [6, 7]. Maximum energy-Shannon entropy criterion takes energy intensity and energy distribution into consideration and is capable of extracting the sensor fault variations effectively. The wavelet basis with maximum entropy Shannon energy ratio is the most appropriate wavelet basis.

After wavelet decomposition, the main problem is how to extract fault information from the coefficients in decomposed subbands. The traditional Shannon entropy only considers the probability distribution of the signal value and does not consider the order structure of the signal value. Paper [8] combines the concept of Shannon entropy with the theory of symbol to propose a new complexity measure, which is the permutation entropy (PE). Permutation entropy is a time series complexity measure based on comparison of neighborhood values and the numerical mapping into symbol sequence pattern. It can describe the local structure features of time series signal and enlarge the subtle changes in the signal with low complexity and antinoise ability. PE is a kind of effective method for classification of different signal state, identification of the breakpoint in time sequence, prediction of the future trend of the time series, determination of causal relationship [9], and so forth. In order to overcome the shortcomings of PE’s single scale, Aziz and Arif [10] proposed a multiscale permutation entropy (MPE) to estimate the complexity in different scales of time series. MPE can describe the structural characteristics and complexity of time series in multiple scales and is widely used in heart sound signal analysis [10] and bearing fault diagnosis [11].

On the other hand, the disadvantage of PE is the lack of amplitude information about the signal except sequential pattern [12]. Paper [13] puts forward the weighted permutation entropy (WPE). It extracts the sequential pattern of time series and retains the amplitude information of time series. Although the amplitude information of time series is used by WPE, it can only reflect the complexity of time series in one single scale. Multiscale analysis and weighted permutation entropy are combined, and multiscale weighted permutation entropy (MWPE) emerges. MWPE represents the complexity measure of the signal on multiscale and reflects the microlocal structure complexity and the amplitude information of the signal. It is widely used in a variety of signal analysis, such as analysis for bubbly oil-in-water [14], flow bearing fault diagnosis [15–17], biomedical signal analysis [18–21], and stock information analysis [22].

From the viewpoint of structure feature presentation, PE can extract the local microstructure feature and wavelet transform can extract the global macrostructure feature. So the combination of wavelet transform with MWPE can comprehensively represent the feature of the sensor fault. A wavelet based multiscale weighted permutation entropy (WMWPE) is proposed in this paper. WMWPEs of different subbands are used to extract signal features. Because the dimensions of WMWPE features are relatively high, it may cause low identification accuracy and time consuming. So the selection of the most important features in WMWPEs is needed [23, 24]. In this paper, the multicluster feature selection (MCFS) [23] is used as feature selection method, which takes into account both the importance of each feature itself and the correlation between all features. By sorting the score of MCFS, the first features with larger MCFS score are selected as the important feature. Through the MCFS feature selection algorithm, the recognition accuracy is guaranteed, the feature vector dimension is reduced, and the computational efficiency is improved.

Naturally, after feature selecting using MCFS, the multifault classifier is needed to conduct the fault diagnosis. A three-layer BP neural network is adopted as classifier to identify fault. The features selected by MCFS are fed into the classifier to identify sensor fault.

The remainder of this paper is organized as follows. Section 2 introduces permutation entropy and multiscale permutation entropy. In Section 3, the wavelet based multiscale weighted permutation entropy and corresponding fault identification method are presented in detail. Using practical data, the performance of the proposed method is investigated in Section 4. Section 5 makes some concluding remarks.

#### 2. **Permutation Entropy and Multiscale Permutation Entropy**

##### 2.1. Permutation Entropy

The permutation entropy (PE) is defined as follows [8]. Given a time series with the length , then the dimensional embedding vector at time is defined aswhere is the embedding dimension and is time delay. has a permutation , if it satisfies thatwhere and . There are possible permutations for an -tuple vector. For each permutation, we determine the relative frequency bywhere , and represents the number of one set.

The definition of PE with dimension is defined as

The maximum value of is , when all possible permutations appear with the same probability. Therefore, the normalized permutation entropy (NPE) can be obtained as

For any time series, is satisfied. The value of depends on the selection of the embedding dimension and delay . If is too small, the scheme will not work well since there are too few distinct states. However, it is often inappropriate to choose as a large value for detecting the dynamic change of a time series.

##### 2.2. Weighted Permutation Entropy

Weighted permutation entropy (WPE) incorporates significant amplitude information from the time series when retrieving the sequential patterns. The main motivation aims at saving useful amplitude information carried by the signal. WPE is defined as follows [13].

Given a time series and dimensional embedding vector as (1) shows, the relative frequency of each motif in (3) is modified to include the weighted information for each . Weight values are calculated in (6) based on the variance or energy of each subsequence :where is the mean of :

Thus, each pair of weight value and motif type can represent full feature for each vector . By using weight value, WPE extends the concept of PE with the addition of amplitude information prior to the computing of probability occurrence of each motif defined in (6). Weighted relative frequency is defined asThen WPE of time series is

##### 2.3. Multiscale Weighted Permutation Entropy

Multiscale analysis [22] is to obtain new time series of the original time series by a coarse-grained size process, which can estimate the complexity of time signals at different scales. Multiscale weighted permutation entropy (MWPE) is the combination of weighted permutation entropy and multiscale analysis. MWPE can totally describe the microstructure complexity and amplitude information of the time series on multiscale.

The MWPE procedure is summarized in the following steps. Firstly, the original time series is divided into nonoverlapping windows of length . Secondly, the data points inside each window are averaged by (10), and the coarse-grained time series is got. The schematic illustration of the coarse-grained procedure is shown in Figure 1. Consider the following:Weighted permutation entropy of is MWPE, as shown in