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An abrupt variance analysis of multiple sensor signals for dimension reduction in fault diagnosis

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Among many dimensionality reduction techniques, Principal Component Analysis, Linear Discriminant Analysis and Partial Least Squares are widely used methods. A bible of dimensionality reduction techniques, PCA uses fundamental variation of each sensor to determine new principal components, which are newly created axes.

Introduction

  • Background
  • Motivation
  • Objectives
  • Outline of the thesis

With sensor selection methods that use variable subset selection, the original sensor name and information are not transformed into new space. In Chapter 2, literature reviews are presented, which consist of dimensionality reduction techniques, particularly related to sensor selection and sensor signal characteristics.

Figure I-2 Overall structure of fault diagnosis
Figure I-2 Overall structure of fault diagnosis

Literature survey

Dimension reduction techniques

  • Sensor selection by space transformation
  • Sensor selection by variable subset selection

Feature selection is also called variable selection, attribute selection or variable subset selection and so on. To clarify the terms used in this article, we will use 'sensor selection by variable subset selection' instead of variable selection and feature selection, and also use 'sensor selection by space transformation' instead of feature extraction to avoid the confusion that may arise due to different uses of the term by humans than by humans, as in Table II-2. In other words, Linear Discriminant Analysis typically focuses only on the classification, while PCA focuses on the signal representation referred to Figure II-4.

The main point of selecting a subset of variables is not to generate a new representation of the data. In this way, sensors can be selected without any transformation and preserve the physical meanings of the original data set, so in terms of interpretability, it is better than selecting sensors in the transformed space. The variable subset selection sensor selection method is mainly divided into three methods, such as filter methods, wrapper methods, and embedded methods.

In terms of selecting original sensors that are original variables, sensor selection using variable subset section methods appears to be more simple and intrinsic methods. However, when selecting a sensor using variable subset selection methods, its algorithm uses a ranking algorithm before fault diagnosis and prognosis. In conclusion, while dimensionality reduction algorithms such as PCA and LDA perform well on sets of correlated features, sensor selection methods using variable subset selection perform poorly.

Figure II-1 The importance of feature selection. Each algorithm differs by the way dealing with  irrelevant variables (a): choosing three relevant variables among 203 dimensions (b): The first 2  PCs of three relevant dimensions (c): PCA result of the whol
Figure II-1 The importance of feature selection. Each algorithm differs by the way dealing with irrelevant variables (a): choosing three relevant variables among 203 dimensions (b): The first 2 PCs of three relevant dimensions (c): PCA result of the whol

Characterization of sensor signals for fault diagnosis

While, other researchers are careful to remove redundant sensors because removing redundant sensors may ignore potential relevant sensors (Zhao et al., 2010). They even fail to select relevant variables because the score they assign to correlated features is very similar, and none of the variables is strongly preferred over another. Because of these complementary advantages and disadvantages, Janecek and Gansterer analyzed relational feature selection and classification accuracy (Janecek et al., 2008).

Subsets of the original variables are constructed using feature selection methods such as filter and wrapper techniques, as well as using PCA. In total, there are four parameters: the amplitude mean, the period mean, the mean amplitude deviation and the period mean deviation that were extracted from the amplitude, frequency and phase of the signal waveform. Here, the standard deviation of the absolute value of the normalized and centered instantaneous frequency was used as an instantaneous property.

Root mean square, short time fourier transform, and characteristic frequency-band analysis were used to extract meaningful features from original data set (Wu et al., 2006). To predict fault of equipment, Hu and Guo used fault tendency prediction based on multi-source information fusion (Hu et al., 2012). Wang applied wave packet sample entropy to predict failure tendency of rolling element bearings (F. Wang et al., 2011).

Figure II-9 Time--domain representations of the six signals (a) sinusoidal signal. (b) sum of  sinusoids (c) monocomponent, nonstationary signal (d) multicomponent, nonstationary signal
Figure II-9 Time--domain representations of the six signals (a) sinusoidal signal. (b) sum of sinusoids (c) monocomponent, nonstationary signal (d) multicomponent, nonstationary signal

Summary

They focused on the interrelationship between the source of fusion information and the way of predicting failure trends. In the failure trend prediction model, information fusion is at three levels, including data-level fusion, feature-level fusion, and decision-level fusion. In particular, in function-level fusion, the characteristic of function is the characteristic of the target equipment error rule.

Another effort to improve the efficiency of fault diagnosis and prognosis is fault propensity analysis. The Naive Bayes classification method is rarely used in fault prediction, while it is often used in fault diagnosis. In order to clearly identify the change of signals or extract important features for classification, pre-processing such as filtering, de-noising and so on could be done before feature extraction.

Bugharbee used signal pretreatment before subjecting the data to an autoregressive model in the fault diagnosis of rolling bearings. The basic idea of ​​this paper is that by analyzing the key features of sensor signals, specifically aimed at classification, sensors can be ranked. Therefore, for the first step, several key characteristics of signals are discussed and Chapter 3 proposes the way to select sensors based on the defined indices.

Characterization of sensor signals

  • Problem statement
  • Characteristics of sensor signals
  • New measures for sensor signals
    • Abrupt variance (aVar)
    • Discernibility index (DI)
    • Sparse impulse (SI)
  • Sensor selection methods
    • aVar-based PCA
    • Weighted sum approach

As shown in the Figure III-1, if signal trends of sensor2 and sensor3 are similar, which means highly correlated, one sensor can be removed in analysis. As shown in the figure III-3, even though sensor1 is in unstable state while sensor2 is in stable state, the average value of both sensors is the same so that the average value cannot distinguish these two sensors. For example, as shown in Figure III-5 and Figure III-6, total variations are similar, but detail signal changes differ from state to state.

As clearly shown in Figure III-8, two states are well observable, which means that they can be separated at a low DI value than at a high DI value. For example, in the case shown on the left in Figure III-9, the sensor is powerful in classifying the fault and no-fault states even though it has relatively low variance, while in the right case. In the first strategy, if at least one peak value exists in a time window segment, it is counted as one sparse impulse, as shown in Figure III-10 (middle).

If the mean value in a specific time window segment is greater than the threshold, it can be counted as a sparse pulse in Figure III-10 (right). In the lower left example in Figure III-2, although the number of sparse pulses is the same for both modes, the directions of the sparse pulses are opposite, so it does not subtract scores. Signals can be classified by variance and aVar into four major categories as Figure III-14.

Thus, in the same way, PCA based on aVar is also done with unexpected variance covariance. In other words, the projected data is in the space which supports the classification of fault condition and fault-free condition.

Figure III-2 Overall framework for real-time fault diagnosis
Figure III-2 Overall framework for real-time fault diagnosis

Case study

Vehicle diagnostics simulator

  • Experimental setting
  • Experimental results and discussion

Since the total number of sensors is forty, data set contains a tremendous number of signals in high dimension Figure IV-2. To select sensors, methods discussed in Chapter 3 will all be used. i) sensor selection using weighted sum of indices (ii) sensor selection using aVar-based PCA. Sensor selection methods used in this experiment are (i) sensor selection using original PCA, (ii) sensor selection using aVar-based PCA and (iii) sensor selection using composite index.

Unlike the PCA sensor selection results, some sensors such as sensor31, sensor8, sensor36 are listed below in aVar-based PCA sensor selection. These sensors were ranked high when using PCA sensor selection only because they have high variance. Also, some sensors like sensor12, sensor6, sensor37 are ranked at the top when using clustered index based sensor selection, which are ranked below when using PCA sensor selection.

Sensors with a high SI score that were ranked low in the PCA sensor selection are highlighted in bold in Table IV-2. In dimensionality reduction, the reduced dimensionality has a critical effect on the classification result, so the number of sensors used for detection varies from 5 to 15. It is shown that when the number of selected sensors is reduced, the proposed methods outperform PCA sensor selection in terms of hit rate. .

Figure IV-2 High dimensional data. Total number of sensors is 40
Figure IV-2 High dimensional data. Total number of sensors is 40

Gear system diagnostics simulator

  • Experimental setting
  • Experimental results and discussion

Using the data set produced by gear failure simulator, a total of four failure mode data is used by combining normal mode data with four failure mode data. Fault mode 1: Displacement of two axes, short axis is not parallel to long axis Fault mode 2: Mass imbalance of the rotor in long axis. Failure mode 3: Loosen the bearing housing where sensor 2 is attached. Error condition 4: Loosen the bearing housing where sensor 3 is attached.

Experimental results such as aVar, variance, SI and DI of each sensor are listed in Table IV-6. In the whole dataset, the variance of sensor1 is the smallest, which is mounted on the engine. Sensors are arranged in ascending order, meaning the sensor is at the top of the first rank.

As indicated in Table IV-6, sparse impulse scores for each signal are also similar, lower than 0.3 or around 0.3 score, which means that there is no sparse impulse signal meaningful for classification. But sensor selection of DI does not always give effective results for classification, like sensor3 in failure mode 4. In failure mode 2 and 3, sensor4 and sensor5 have the lowest DI score, which means it is the most noticeable sensor, but these sensors do not have Vis any apparent difference between error condition and error free condition by referring to the results of each signal.

Table IV-4 Hardware specification of gear system diagnostics simulator
Table IV-4 Hardware specification of gear system diagnostics simulator

Conclusion and Future research

A fault diagnosis methodology for rolling bearings based on advanced signal preprocessing and autoregression modeling. Paper presented at the CDE Conference Proceedings, Pukyong National University, Republic of Korea. Classification of blind digital modulation in program radio using an optimized classifier and feature subset selection.

Paper presented at the Quality, Reliability, Risk, Maintenance, and Safety Engineering (ICQR2MSE), 2012 international conference on. Paper presented at the New Challenges for Feature Selection in Data Mining and Knowledge Discovery. Paper presented at the Pervasive Computing and Communications Workshops (PERCOM Workshops), 2011 IEEE International Conference on.

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Figure I-1 Progress in operation and maintenance techniques
Figure I-2 Overall structure of fault diagnosis
Figure I-3 A framework for fault detection using sensor selection methods
Figure II-3 Sensor ranking using standard PCA
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