Mathematical Problems in Engineering

Volume 2016, Article ID 7939607, 10 pages

http://dx.doi.org/10.1155/2016/7939607

## Fault Diagnosis for Engine Based on Single-Stage Extreme Learning Machine

Mechanical Engineering College, 97 West Heping Road, Shijiazhuang, Hebei Province 050003, China

Received 15 March 2016; Revised 6 August 2016; Accepted 29 August 2016

Academic Editor: Yan-Jun Liu

Copyright © 2016 Fei Gao and Jiangang Lv. 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

Single-Stage Extreme Learning Machine (SS-ELM) is presented to dispose of the mechanical fault diagnosis in this paper. Based on it, the traditional mapping type of extreme learning machine (ELM) has been changed and the eigenvectors extracted from signal processing methods are directly regarded as outputs of the network’s hidden layer. Then the uncertainty that training data transformed from the input space to the ELM feature space with the ELM mapping and problem of the selection of the hidden nodes are avoided effectively. The experiment results of diesel engine fault diagnosis show good performance of the SS-ELM algorithm.

#### 1. Introduction

As representative equipment, the engine is general power source, and its safety and reliability is very important. In equipment fault diagnosis, reciprocating machinery faults are the most difficult cases. In order to solve the problem, piezoelectric pressure sensors, accelerometers, and sound sensors are widely used to measure signals from the engine. Faults are defined as the deviations from normal behaviors in the plant. Because the engine’s working condition is so bad and its structure is so complex, signals of engine fault are nonstationary and nonlinear. It is difficult to extract a threshold which can clearly reflect the fault characteristics. So the methods which combine signal processing and intelligent pattern recognition are used to actualize fault diagnosis. Firstly, signal processing methods, such as frequency spectrum analysis, wavelet transform, Hilbert-Huang transform, and mathematical morphology, are used to denoise the measured signals and extract the feature vector which could broadly reflect the fault characteristics and types. Secondly, intelligent pattern recognition methods, such as artificial neural network and support vector machine (SVM), are used to map the feature vector into a higher dimensional feature space and classify the fault mode based on iterative optimization or statistical learning.

The combination of signal processing and intelligent pattern recognition solves the diagnosis puzzler of mechanical fault in a certain extent. But so many parameters need to be tuned to achieve a preferable fault classification rate when the recognition algorithm is applied. The computational complexity and computing time cost of the recognition also limit its effective realization in embedded systems. As a novel learning algorithm, ELM has been proposed recently by Huang et al. [1] for single hidden layer feedforward neural networks (SLFNs). Different from gradient-descent-based methods, ELM randomly chooses input weights (linking the input layer to the hidden layer) and hidden bias, and the output weights (linking the hidden layer to the output layer) are analytically determined using the Moore-Penrose generalized pseudoinverse instead of tuning them. Experimental results show that the learning speed of ELM can be thousands of times faster than gradient-descent learning algorithms. So it receives wide applications such as fault prognosis of mechanical components [2], fault classification in series compensated transmission line [3], fault diagnosis on hydraulic tube tester [4], and computer aided diagnosis system [5].

However, because of random mapping from the input space to some feature space, numerical stability of the output has been generally ignored. On the other hand, random selection of the input weights and biases results in a large number of hidden units which consumes so much computing time. To solve these shortages, many improved ELM algorithms were investigated recently [6–9]. Zhao et al. [10] proposed an input weight selection algorithm for an ELM with linear hidden nodes to improve the ill-conditioned problem. Huynh and Won proposed Least Square Extreme Learning Machine (LS-ELM) [11], Regularized Least Square Extreme Learning Machine (RLS-ELM) [12], and SVD-Neural classifier [13]. Projection Vector Machine was proposed by Deng et al. [14] for high-dimension small-sample data. Although these improved algorithms have enhanced numerical stability of the ELM output in a certain extent, some output fluctuations still exist. For many applications with high security requirements, unstable judgment may cause some fatal safety accidents, such as fault diagnosis for engine, industrial process control, control of the chaotic system, and operation condition monitoring of hydroelectric generating sets [15–18]. So, in order to introduce ELM to fault diagnosis of engine effectively, we proposed Single-Stage Extreme Learning Machine (SS-ELM) in this paper. Firstly, eigenvectors extracted from signal processing methods are directly regarded as the SS-ELM network’s hidden layer output matrix. Secondly, the Moore-Penrose generalized inverse is used to calculate the output weight. Then this method has lower computational complexity and could have been replanted to the embedded systems. Experimental results show that this approach is feasible in identifying engine faults.

The rest of this paper is organized as follows. Section 2 describes extreme learning machine algorithm and its shortage on classification. Single-Stage Extreme Learning Machine is presented in Section 3. Experimental results and analysis on engine fault diagnosis are shown in Section 4. Finally, conclusion is made in Section 5.

#### 2. Extreme Learning Machine and Its Shortage on Classification

##### 2.1. Single Hidden Layer Feedforward Networks

The standard architecture of single hidden layer feedforward networks consists of an input layer with neurons, a hidden layer with neurons, and an output layer with neurons. Consider arbitrary training samples , where and are the* j*th input pattern and the corresponding desired output. Then SLFNs with activation function can be mathematically modeled aswhere is the input weight vector connecting the input neurons and the th hidden node, is the threshold of the th hidden node, is the weight vector connecting the th hidden node with the output neurons, is the real output vector of SLFNs, and is the scalar product of and .

So the main aim of training process is to minimize the following error function by adjusting the network parameters , , and , and the error function can be defined by

##### 2.2. Extreme Learning Machine

Traditionally, gradient-descent algorithm is used to train the SLFNs, in which the set of is iteratively tuned bywhere consists of parameters , , and and denotes the learning rate. As a popular training algorithm for feedforward neural networks based on gradient-descent, back-propagation (BP) learning algorithm has been used in various fields, in which parameters are adjusted with error propagation from the output layer to the input layer. However, it is clear that these algorithms have a slow learning rate, easily get overlearning, and stop at the local minimum.

Recently, an effective training algorithm for SLFNs was proposed by Huang et al. [1] and called ELM. According to Huang and Babri [19], SLFNs with at most hidden nodes and almost any nonlinear activation function can exactly learn distinct observations. So if the standard SLFNs with hidden nodes can approximate these distinct observations with zero error, it implies that there exist , , and such that

Equation (4) can be written compactly aswhere

As proposed by Huang et al. [1], is the hidden layer output matrix. The parameters and (input weights and biases) may simply be assigned with random values and need not be adjusted during the training process. Then (5) becomes a linear system, due to the fact that the matrix may not always be square matrix, so the smallest norm least-squares of the network is estimated aswhere is the Moore-Penrose generalized inverse of matrix .

##### 2.3. Shortage of Extreme Learning Machine on Classification

Although the ELM algorithm surmounts many puzzles, such as improper learning rate, overlearning, and local minima, which always lie in traditional gradient-descent approaches, random selection of input weights and biases may lead to an ill-conditioned problem so that the output of the network will be numerically unstable [10]. On the other hand, in order to get a preferable classification rate, the number of hidden nodes should be increased substantially which usually leads the complexity of network and training time to increase obviously.

In order to verify the problem of ELM with random mapping, we choose Page Blocks dataset from UCI Machine Learning Repository [20]. The initial number of hidden nodes is set as 50 and the incremental node for each simulation is set as 5. The sigmoidal function is chosen as the activation function; input weights and biases are determined randomly. Then the training and testing accuracy of ELM variations with respect to initial network parameters and hidden nodes on Satellite Image dataset are shown in Figures 1 and 2. Training and testing time of ELM with different hidden nodes are shown in Figures 3 and 4. The simulations are carried out in MATLAB 7.11.0 environment running in AMD, 2.2-GHZ CPU with 1 G RAM.