Hong-chun QU，Yuan-qiang HUANG

(Aeronautical Engineering College of Civil Aviation University of China，Tianjin 300300，China)

1 Introduction

The fault diagnosis of aero-engine has very important significance for the airlines.If we can identify potential faults rapidly and accurately through analyzing the change of engine monitoring parameters，we can not only effectively avoid in-flight shut down and flight delays caused by the fault of the engine，but also make the maintenance plan better，shorten the troubleshooting time，reduce the maintenance cost，and increase the time on-wing of the engine，so as to improve the overall benefits of the airline.Recently，the common methods used for the aero-engine gas path fault diagnosis are based on the small deviations fault equation linear model，nonlinear steady-state model or artificial intelligence methods［1］.

Neural network has been considered as the most research potential diagnostic tool in artificial intelligence methods.The BP neural network has been widely applied in the field of fault diagnosis，which belongs to the gradient descent algorithm.The network initial connection weights and thresholds generally generate randomly，and the network structure and learning rate are mainly determined by experience.If the initial connection weights are valued improperly，the network can cause oscillation，misconvergence or too long in training time［2 －4］，giving rise to the fault recognition result being not ideal.Besides，it is complicated in practical diagnosis problems of the aero-engine.All of these make BP network exist many deficiencies in application of the field［1］.Genetic algorithm is a highly efficient parallel global search algorithm，which is developed from biological evolution theory.The algorithm has very good robustness and it succeeded in solving global optimization problems［5-6］.

Genetic algorithm not only can be used to design the neural network well，but also is benefit to obtain the global optimal solution and improve the generalization performance of neural network［2，7］.Therefore，this article would take use of the genetic algorithm to optimize the initial weights and thresholds of BP neural network，and then retrain the results according to gradient descent algorithm and put the optimized network into the field of fault diagnosis of engine gas path.

2 The brief introduction of BP neural networks and genetic algorithm

Back-propagation network referred to as the BP network and is a multi-layer network which generalizes the W-H learning rules and makes weights training for nonlinear differentiable function.In the practical application of the artificial neural network，80%-90%of network models employ BP network or its modified forms，on behalf of the most essential part of the artificial neural network.

Fig.1 The structure of BP network

The BP network is a multi-layer forward feedback neural network and adjusts its weights by using back propagation learning algorithms.It consists of input layer，output layer，and a number of hidden layers，the data spread from the input layer to the output layer through hidden layers.When training the network weights，the data go along the direction of reducing error，which starts from the output layer then acrosses through the middle layers to correct the network connection weights forward and thresholds layer by layer.This process will be circled which begins from the former results until meets the network’s stable error［4，8］.

A classic three-layer BP network is shown in Fig.1.(p1，p2，…，pn)represents then-dimensional fault eigenvalue input.The number of the hidden layer neurons iss1;the transfer function isF1j(j=1，2，…，s1);the threshold isb1j.The number of the output layer neurons iss2;the transfer function isF1k(k=1，2，…，s2);the threshold isb2k.w1jirepresents the weight between thej-th hidden neuron and thei-th input neuron;w2kjrepresents the weight between thekth output neuron and thej-th hidden neuron.The output values of the hidden layery1jand of the output layery2kcan be calculated by formula(1)and formula(2).

The target of each output neuron istk，so the total output errorEcan be calculated by formula(3).

Utilizing the gradient descent algorithm and error back propagation to adjust the weights of output layer，the amount of change Δw2kjcan be shown as formula(4)，where δ is the network learning rate.

Similarly，the variable quantity of each layer’s weights and thresholds could be deduced，as shown in formula(5).

The weights and thresholds can be adjusted in this way until the output results meet the convergence condition.

Genetic algorithm is an advanced random method in global search，and which can simulate the selection of bio natural evolution，the process of mutation and natural selection through the computer programming.This kind of method employs the coding space instead of questioning space，and utilizes coding population as its evolutionary basis;the fitness function is its access judgment which can evaluate the selection of gene by the operation of individual gene bit string inside of the population.Thanks to the production of many initial points and the start of researching which is guided by the fitness function，the research owns extensive area and efficient operation.This result helps realize the automatic obtainment and accumulation of valuable information existed in research space and approaches to the best solution of the target function efficiently and adaptively［10-12］.

3 The theory of BP neural networks based on genetic algorithms

3.1 Basic theory

The basic thinking of optimizing the net work through Genetic Algorithm takes advantages of its global quick researching feature and does quick research according to the relations between input training samples and output targets.This process would find and optimize the BP network structural parameters to meet the acquirement of fitness function and improve not only the convergence speed but also the convergence accuracy of BP network.The calculating process is shown in Fig.2.

Fig.2 The training process of BP network basis on genetic algorithm

3.2 Algorithm steps

The calculation steps of genetic algorithm to optimize BP neural network are as follows.

Step 1:building up structure of the network:according to the actual problem to determine BP neural network layers，the number of neurons in each layer and transfer functions.

Step 2:the input training samples and testing samples data are normalized to eliminate the effects of different dimension between the different parameters.

Step 3:coding:The initial weights and thresholds of BP network are encoded by order based on binary code method，and connect them together to form a chromosome，namely an individual.The value of weights and thresholds ranges from-1 to 1.

Step 4:the generation of initial population:individual gene code is generated randomly，and the initial populationis composed.

Step 5:decoding:decode the gene bit string of every individual in initial population，and calculate the outputs of networky2kwith training samples.

Step 6:calculating the fitness value of individuals:the fitness value size is the evaluation standard for genetic algorithm to evaluate the individual quality，and the individual with a higher fitness value has a greater probability to inherit by the next generation ［5］，where the reciprocal of the mean square error(MSE)is used as the fitness function.The calculation formula is shown as formula(6)，so if the network output error is smaller，the fitness value is greater.

Step 7:the genetic operation:to generate a higher fitness group including selection，crossover and mutation operation［5］.

Selection:the probability value of each individual to the next generation is equal to the ratio of its fitness value with the sum of all individuals by using roulette wheel method，and pick out new species group with the same population numbers.

Crossover:according to the crossover probabilitypc，choicepc*Psizeindividuals randomly from the new group and make chromosomes one-point crossover randomly.

Mutation:the individuals of new group make basic bit mutation operation with the set of mutation probabilitypm，to realize the small probability turning of the genetic code，namely 0 to 1 or 1 to 0.

Step 8:the judgment of termination condition:if the maximum genetic algebra reaches or the mean square error(MSE)meets the requirements，the evolution is terminated.

Step 9:the weights and thresholds are decoded by the best individual serve as the initial weights and thresholds of BP network，and make the second training.If they reach the required performance，the learning process end.

Step 10:input test sample data and check the network diagnosis results.

4 Fault diagnosis applications

Take the deviation of the EGT(exhaust gas temperature)，F(xiàn)F(fuel flow)，N1(low pressure rotor speed)and N2(high pressure rotor speed)by four typical faults of PW4164(100 inch)engine as fault sample data and compile fault identification target vectors shown in table.1.These four faults are difficult to distinguish in practice because the characteristic parameter data are similar and susceptible to noise.

Table1 The characteristic parameters data of four typical faults

Compile the MATLAB program to build the threelayer BP neural network by using genetic algorithm，namely GA-BP network;design four input layer neuron，five hidden layer neuron，transfer function by adopting tansig function［4］，and four output layer neuron and transfer function by applying purelin ［4］function.Set learning rate as 0.1 and network training target MSE≦10－5.

The parameters of genetic algorithm are set as follow，evolution generation is 50，population is 20，and crossover rate is 0.7.Use the method of one-point crossover and set mutation rate as 0.1.Use the reciprocal of the mean square error as the fitness function.Use forty groups of characteristic parameter data from four typical faults as the training data for GA-BP network，and another ten groups of data from table 2 to testify the GA-BP network，which were historical data recorded by the engine monitoring department of airline.

The comparisons of fitness value between initial population and the population after evolution fifty generations by genetic algorithm optimization are indicated in Fig.3(a).It’s obvious that the fitness value of individual have significantly improved and more stabilized.The fitness value of the best individual in population increases rapidly with the evolution and after evolution twelve generation，it is not only closing to the best fitness value，but also each generation is gradually stabilized，as shown in Fig.3(b).

Fig.3 Thecomparisonsof fitnessvaluebetween initial population and the population after evolution fifty generations by genetic algorithm optimization

Diagnosis results of GA-BP network are showen in Table 3.Comparing to the diagnostic output results of common BP network under the same network structure，both methods correctly detecte all the faults and the results are consistent with the actual monitoring situation，and the output precision of GA-BP network is better than that of common BP network.The comparisons of diagnosis results’error value of those two kinds of method are indicated in Fig.4(a).And the comparison of convergence curve in Fig.4(b)shows that GA-BP network outputs are in smaller error，higher precision，converge faster and better.The BP network optimized by genetic algorithm is only trained 5 times to meet performance goals，while the common BP network needs to be trained 37 times to achieve the same performance targets.The process of the common BP network training is likely to fall into local optimum，and the performance convergence curve may not be smooth.

Table3 Network outcomes comparison

Fig.4 Comparison of two methods

5 Conclusions

This paper combines genetic algorithm and BP neural network，which forms an individual firstly from initial weights and thresholds coding of the BP neural network.Then optimizes its best solution in its range by using genetic algorithm，and finally reinvests the network with optimized weights and thresholds.This method can not only make full use of the better global searching ability and convergence speed of the genetic algorithm，but also overcome the shortcomings brought by the BP algorithm as the initial weights and thresholds are selected random.The fault diagnosis example of application on aero-engine indicates that the GA-BP network is better than common BP network in the network output precision，convergence speed and smoothness.This result provides a new idea and method for the study on the field of fault diagnosis of aero-engine，and is benefit to solve many problems in practical engineering such as when fault diagnosis result is not ideal and the network convergence speed is slow.

［1］Qu Hongchun.Study on civil turbofan engine health intelligent monitoring technologies［D］.Tianjin:Tianjin University，2010.

［2］Liu Yongjian.Research on Modified Neural Network for Fault Diagnosis and Performance Prediction of Aeroengine［D］.Nanjing:Nanjing University of Aeronautics and Astronautics，2012.

［3］Cui Zhiquan.Civil Aeroengine Gas Path Parameter Deviation Mining Method with Application［D］.Harbin:Harbin Institute of Technology，2013.

［4］Zhang Defeng.MATLAB Neural Network Design［M］.Beijing:China Machine Press，2012.

［5］Lei Yingjie，Zhang Shanwen，Li Xuwu.MATLAB Genetic algorithm toolbox and application［M］.Xi’an:Xi’an University of Electronic Science and Technology Press，2005.

［6］CHEN Guo，HAO Tengfei，CHENG Xiaoyong，et al.Sensitivity analysis of fault diagnosis of aero-engine rolling bearing based on vibration signal measured on casing［J］.Journal of Aerospace Power，2014，29(12):2874-2884.

［7］HE Chen，ZHANG Xiaodong，Patton R J.Robust fault diagnosis for aero-engine compressor sensor based on LMI and discrete model［J］.Journal of Aerospace Power，2014，29(4):965-972.

［8］Chen Ming.MATLAB Examples of neural network theory and refined analysis［M］.Beijing:Tsinghua University Press，2013.

［9］HUANG Yuanqiang，QU Hongchun，ZHAO Yuechao.Research on aero-engine performance ranking by principa components analysis［J］.Aviation maintenance and engineering，2015，1:75-77.

［10］Chen Guo.Rough Set-Genetic Algorithm-Neural Network Compositive Classifier and Its Application in Rotor Faults Diagnosis［J］.Chinese Mechanical Engineering，2008，19(1):85-89.

［11］Meng Dong，F(xiàn)an Zhongjun，Wang Jiazhen.An Improvement to the BP Neural Network Algorithm Based on the Chaos Genetic Algorithm［J］.Mathematical Theory and Applications，2014，34(1):102-110.

［12］Yang Mei，Qing Xiaoxia，Wang Bo.Optimization of Neural Network Based on Improved Genetic Algorithm［J］.Computer Simulation，2009，26(5):198-201.

［13］Yan Taishan.Research on Neural Network Training Algorithm Based on Genetic Algorithm［J］.Journal of Hunan Institute of Science and Technology(Natural Sciences)，2007，20(1):31-34.