International Journal of Aerospace Engineering

Volume 2016, Article ID 7892875, 10 pages

http://dx.doi.org/10.1155/2016/7892875

## Aero Engine Fault Diagnosis Using an Optimized Extreme Learning Machine

^{1}Department of Aerocraft Engineering, Naval Aeronautical and Astronautical University, Yantai 264001, China^{2}College of Information and Electrical Engineering, Ludong University, Yantai 264025, China

Received 1 June 2015; Accepted 13 October 2015

Academic Editor: Roger L. Davis

Copyright © 2016 Xinyi Yang 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

A new extreme learning machine optimized by quantum-behaved particle swarm optimization (QPSO) is developed in this paper. It uses QPSO to select optimal network parameters including the number of hidden layer neurons according to both the root mean square error on validation data set and the norm of output weights. The proposed Q-ELM was applied to real-world classification applications and a gas turbine fan engine diagnostic problem and was compared with two other optimized ELM methods and original ELM, SVM, and BP method. Results show that the proposed Q-ELM is a more reliable and suitable method than conventional neural network and other ELM methods for the defect diagnosis of the gas turbine engine.

#### 1. Introduction

The gas turbine engine is a complex system and has been used in many fields. One of the most important applications of gas turbine engine is the propulsion system in aircraft. During its operation life, the gas turbine engine performance is affected by a lot of physical problems, including corrosion, erosion, fouling, and foreign object damage [1]. These may cause the engine performance deterioration and engine faults. Therefore, it is very important to develop engine diagnostics system to detect and isolate the engine faults for safe operation of an aircraft and reduced engine maintenance cost.

Engine fault diagnosis methods are mainly divided into two categories: model-based and data-driven techniques. Model-based techniques have advantages in terms of on-board implementation considerations. But they need an engine mathematical model and their reliability often decreases as the system nonlinear complexities and modeling uncertainties increase [2]. On the other hand, data-driven approaches do not need any system model and primarily rely on collected historical data from the engine sensors. They show great advantage over model-based techniques in many engine diagnostics applications. Among these data-driven approaches, the artificial neural network (ANN) [3, 4] and the support vector machine (SVM) [5, 6] are two of the most commonly used techniques.

Applications of neural networks and SVM in engine fault diagnosis have been widely studied in the literature. Zedda and Singh [7] proposed a modular diagnostic system for a dual spool turbofan gas turbine using neural networks. Romessis et al. [8] applied a probabilistic neural network (PNN) to diagnose faults on turbofan engines. Volponi et al. [9] applied Kalman Filter and neural network methodologies to gas turbine performance diagnostics. Vanini et al. [2] developed fault detection and isolation (FDI) scheme for an aircraft jet engine. The proposed FDI system utilizes dynamic neural networks (DNNs) to simulate different operating model of the healthy engine or the faulty condition of the jet engine. Lee et al. [10] proposed a hybrid method of an artificial neural network combined with a support vector machine and have applied the method to the defect diagnostic of a SUAV gas turbine engine.

However, conventional ANN has some weak points: it needs many training data and the traditional learning algorithms are usually far slower than required. It may fall in the local minima instead of the global minima. In case of gas turbine engine diagnostics, however, the operating range is so wide. If the conventional ANN is applied to this case, the classification performance may decrease because of the increasing nonlinearity of engine behavior in a wide operating range [11].

In recent years, a novel learning algorithm for single hidden layer neural networks called extreme learning machine (ELM) has been proposed and shows better performance on classification problem than many conventional ANN learning algorithms and SVM [12–14]. In ELM, the input weights and hidden biases are randomly generated, and the output weights are calculated by Moore-Penrose (MP) generalized inverse. ELM learns much faster with higher generalization performance than the traditional gradient-based learning algorithms such as back-propagation and Levenberg-Marquardt method. Also, ELM avoids many problems faced by traditional gradient-based learning algorithms such as stopping criteria, learning rate, and local minima problem.

Therefore ELM should be a promising method for gas turbine engine diagnostics. However ELM may require more hidden neurons than traditional gradient-based learning algorithms and lead to ill-conditioned problem because of the random selection of the input weights and hidden biases [15]. To address these problems, in this paper, we proposed an optimized ELM using quantum-behaved particle swarm optimization (Q-ELM) and applied it to the fault diagnostics of a gas turbine fan engine.

The rest of the paper is organized as follows. Section 2 gives a brief review of ELM. QPSO algorithm is overviewed in Section 3. Section 4 presents the proposed Q-ELM. Section 5 compares the Q-ELM with other methods on three real-world classification applications. In Section 6, Q-ELM is applied to gas turbine fan engine component fault diagnostics applications followed by the conclusions in Section 7.

#### 2. Brief of Extreme Learning Machine

Extreme learning machine was proposed by Huang et al. [12]. For arbitrary distinct samples , where and , standard SLFN with hidden neurons and activation function can approximate these samples with zero error which means thatwhere , ( and ) is the hidden layer output matrix, denotes the output of th hidden neuron with respect to , and is the weight connecting th hidden neuron and input neurons. denotes the bias of th hidden neuron. And is the inner product of and . is the matrix of output weights and () is the weight vector connecting the th hidden neuron and output neurons. And is the matrix of desired output.

Therefore, the determination of the output weights is to find the least square (LS) solutions to the given linear system. The minimum norm LS solution to linear system (1) iswhere is the MP generalized inverse of matrix . The minimum norm LS solution is unique and has the smallest norm among all the LS solutions. ELM uses MP inverse method to obtain good generalization performance with dramatically increased learning speed.

#### 3. Brief of Quantum-Behaved Particle Swarm Optimization

Recently some population based optimization algorithms have been applied to real-world optimization applications and show better performance than traditional optimization methods. Among them, genetic algorithm (GA) and particle swarm optimization (PSO) are two mostly used algorithms. GA was originally motivated by Darwin’s natural evolution theory. It repeatedly modifies a population of individual solutions by three genetic operators: selection, crossover, and mutation operator. On the other hand, PSO was inspired by social behavior of bird flocking. However, unlike GA, PSO does not need any genetic operators and is simple in use compared with GA. The dynamics of population in PSO resembles the collective behavior of socially intelligent organisms. However, PSO has some problems such as premature or local convergence and is not a global optimization algorithm.

QPSO is a novel optimization algorithm inspired by the fundamental theory of particle swarm optimization and features of quantum mechanics [16]. The introduction of quantum mechanics helps to diversify the population and ameliorate convergence by maintaining more attractors. Thus, it improves the QPSO’s performance and solves the premature or local convergence problem of PSO and shows better performance than PSO in many applications [17]. Therefore it is more suitable for ELM parameter optimization than GA and PSO.

In QPSO, the state of a particle is depicted by Schrodinger wave function , instead of position and velocity. The dynamic behavior of the particle is widely divergent from classical PSO in that the exact values of position and velocity cannot be determined simultaneously. The probability of the particle’s appearing in apposition can be calculated from probability density function , the form of which depends on the potential field the particle lies in. Employing the Monte Carlo method, for the th particle from the population, the particle moves according to the following iterative equation:where is the position of the th particle with respect to the th dimension in iteration . is the local attractor of th particle to the th dimension and is defined aswhere is the number of particles and represents the best previous position of the th particle. is the global best position of the particle swarm. is the mean best position defined as the mean of all the best positions of the population; , , and are random number distributed uniformly in , respectively. is called contraction-expansion coefficient and is used to control the convergence speed of the algorithm.

#### 4. Extreme Learning Machine Optimized by QPSO

Because the output weights in ELM are calculated using random input weights and hidden biases, there may exist a set of nonoptimal or even unnecessary input weights and hidden neurons. As a result, ELM may need more hidden neurons than conventional gradient-based learning algorithms and lead to an ill-conditioned hidden output matrix, which would cause worse generalization performance.

In this section, we proposed a new algorithm named Q-ELM to solve these problems. Unlike some other optimized ELM algorithms, our proposed algorithm optimizes not only the input weights and hidden biases using QPSO, but also the structure of the neural network (hidden layer neurons). The detailed steps of the proposed algorithm are as follows.

*Step 1 (initializing). *Firstly, we generate the population randomly. Each particle in the population is constituted by a set of input weights, hidden biases, and -variables:where , , is a variable which defines the structure of the network. As illustrated in Figure 1, if , then the th hidden neuron is not considered. Otherwise, if , the th hidden neuron is retained and the sigmoid function is used as its activation function.

All components constituting a particle are randomly initialized within the range .