Establishment and Optimization of State Feature System of Diesel Engine Fault Diagnosis

Liu Min-lin Liu Bo-yunCollege of Power Engineering，Naval University of Engineering，Wuhan 430033，China

Establishment and Optimization of State Feature System of Diesel Engine Fault Diagnosis

Liu Min-lin Liu Bo-yun
College of Power Engineering，Naval University of Engineering，Wuhan 430033，China

For too many state features are used in the diesel engine state evaluation and fault diagnosis，it is not easy to obtain the rational eigenvalues.In the paper，the cylinder subassembly of diesel engine is used to search for the method of establishing state feature system and optimal approach.The signal of diesel engine has been collected when the piston ring and airtight ring are working at different states，then with the Bootstrap method and Genetic Algorithm (GA），an optimum parameter combination is

diesel engine；fault diagnosis；bootstrap method；genetic algorithm.

CLC：U664.121Document code：AArticle ID：1673-3185(2010）03-47-05

1 Introduction

Cylinder，piston and piston ring are the kernel of diesel engine and usually work at the most abominable conditions.Piston ring has the function of keeping airproof between the piston and cylinder，transferring the heat from piston to cylinder wall and lubricating.Therefore，the condition of piston ring is substantially important to the fuel inflammation and the working state of diesel engine. According to ref.［1］，the friction loss between the piston and cylinder liner accounts for 55%～65%of the entire loss power while the fault rate is nearly 10%of all kinds of faults.If a simple approach can be found to evaluate the attrition rate or judge the fault happened or not，it will play an important role in the fault diagnosis and state evaluation of diesel engine.

Measuring the cylinder burning gas pressure is a common method for measuring operation condition of diesel engine，since some of the diesel engines are fitted with inspection hole on the cylinder lid，the parameters are easily obtained and tend to be used for fault diagnosis［2］.In this paper，more attention is paid to optimizing the pressure signature and finding a synthetic eigenvalue for fault diagnosis.

2 Experiment testing system

Using the 6135ZG type diesel engine as testing and analysis object，when it is working at 1500r/min，the output power is 120 hp.Drilling a hole in the first cylinder lid and installing a pressure transducer of piezoelectricity type.In addition，a rotating speed transducer of magnetoelectricity is fixed on the machine，it can measure rotate speed signal and top point.

There are five piston rings of each cylinder of 6135ZG type diesel engine，on top of them，three rings are gastight ring，they can prevent gas leaking from the space between piston and cylinder，and the heat of piston can transfer to cylinder wall.The rest of them are shaving oil rings.In this paper，three different topmost gap and tergal gap of gastight rings are set to simulate the fault of piston ring.Four kinds of status and parameters are listed as shown in tab.1.

In the table，the letter A denotes topmost gap，B denotes tergal gap，the subscript denotes ring number，unit is mm.As for the different states，the pressure values of the cylinder are measured respectively，disposed with filtration，four typical pressure plots are shown as fig.1.

Tab.1 Different gap of three gastight rings under four status

Analyzing the cylinder pressure of different working conditions，following parameters can be gained，such as indicated power of single cylinder，maximum blast pressure，position of maximum blast pressure，rate of pressure rise.They can be expressed by：

Where n denotes the test time in the i-th working condition.Being restricted by cost，time and other factors，n can not be too much.In order to well judge each of parameters，numerical simulation method is necessary.

3 Using Bootstrap to re-sampling test data

Suppose that we want to estimate a parameter θ that depends on a random quantity sample X= (X1，X2，…，Xn）in a complicated way.For example，θ might be the sample variance of X or the log sample variance.

Fig.1 Cylinder pressure of normal conditions

Fig.4 Cylinder pressure of heavy wear

Assume that we have an estimator： where of θ but do not know the probability distribution of Φ (X）given θ.This means that we cannot estimate the error involved in estimating θ by Φ (X）.In particular，we cannot tell if we can conclude θ≠0 from an observed Φ(X）≠0，no matter how large.The Bootstrap is a method for answering these questions without any prior assumptions about the distribution of θ(X）.The basic Bootstrap method：given a sample X=(X1，X2，…，Xn）of size n，a Bootstrap resample of X is a sample： where each value Xj*in equation(3）is a random sample with replacement.That is，given distinct values X1，X2，…，Xn： with independent choices of Xj*for 1≤j≤n.In particular，repeated values Xj1

*=Xj*2=Xi are allowed. Since the sample size of X*is n，repeated values of Xj*means that other values in X must be left out.

Tab.2 is the maximum blast pressure in the cylinder as the piston at the original state，using the Bootstrap method，then the distribution has been acquired.

Tab.2 Simulating example of the maximum blast pressure

As shown in table 2，it can be found that the restriction on the sample's number has been wiped off，and the unknown mean value distribution has been replaced by the simulating samples.Fig.5 shows 100 those distribution of every test sequence.

Fig.5 Distribution of simulation data

Observing the distribution curve of single parameter，there is not distinctness between the different working states.Since it tends to have an unjust judgment，the single parameter is not fit for fault diagnosis and working state evaluation，however it needs more parameters for the partition of different working states.Fig.6 shows the working state denoted by two parameters.

Fig.6 Two parameters denoting the state

By using different parameters shown in fig.6 we can improve the ability of fault diagnosis.If a parameter is found that can wipe off some redundant information and obtain the best combination fashion，it will be significant to fault diagnosis.GA is adopted in this paper as it is a search technique for approximate solutions to optimization as well as search problems.

4 Application of GA

GA is based on the evolutionary ideas of natural selection and genetic.It is useful and efficient when the search space is large，complex or poorly understood.Domain knowledge is scarce or expert knowledge is difficult to encode to narrow the search space.No mathematical analysis is available and the traditional search methods fail.

The basic concept of GA is designed to simulate processes in natural system necessary for evolution，specifically those that follow the principles first laid down by Charles Darwin of survival of the fittest.

The basic method is to create a population of randomly selected potential solutions to the problem.These solutions are encoded as chromosomes，and each chromosome is subjected to an evaluation function that assigns a fitness depending upon how well the solution it encodes solves the problem at hand.

Basing on the experiment and simulation data，the process of designing the GA lists as follow.

Coding

Since multiple parameters can express the working state better，we can define a formula which includs some elementary characteristics as follows： Where Pi，Pj，Pm，Pnare the parameters stochastic choosing from the former collection，adopting binary system coding.Operator using binary system coding too；a1～a4，r1，r2adopt floating point numbers coding method.They can be expressed by a tree structure.

Fitness function

The purpose of fitness function is classification，there are several ways to approach classifying the examples in a given set.For example，we have parametric approaches，semi-parametric approaches，and nonparametric approaches.

Somewhere in between these two opposite approaches lies the class of semi-parametric methods——those where we assume″a mixture of distributions″，or″a parametric model for each group in the sample″.It is under this umbrella that kmeans clustering falls.

Simply k-means clustering is an algorithm that attempts to find groups in the data.

The algorithm roughly follows this approach：

1）Choose some manner in which to initialize the mito be the mean of each group (or cluster），and do it.

2）For each example in your set，assign it to the closest group(represented by mi）.

3）For each mi，recalculate it based on the examples that are currently assigned to it.

4）Repeat steps 2）～3）until miconverge.

There are some difficulties in using k-means for clustering data.As seen from current and past researches，an oft-recurring problem has to do with the initialization of the algorithm.

The problem of initializing the centers for kmeans，as with the problem of finding the initial k or how many clusters are to be found in the dataset since to do so，one must also know how many centers exist.

In the evolution process of GA，fitness function is needed as a foundation.Fitness function is not restricted by the continuity，differentiable，and its defining region can be randomly confined.The only requirement is the output of fitness is nonnegative，and the fitness function touches the precision and efficiency of the GA.

In the paper，space between the homogeneous kind and heterogeneous kind is adopted as fitness function［4］.It defines as follows：

geneous discrete matrix

Where c is the number of kinds，niis the swatch number of ith kinds；Piis the transcendental probability of ith kind；xikis the D dimension eigenvector.

If the space of homogeneous kind Sbis small，on the other hand，the space of heterogeneous kind Swis big，the effect of classification is better.

Arithmetic operators

The mechanism for the selection of parent chromosomes is crucial as this is the driving force behind the gradual increase in average fitness of each generation as the GA evolves.A well known way to achieve this has been the so called“roulette wheel selection”.Also known in statistics as the Monte Carlo method，this is simply an algorithm for selecting parent chromosomes in proportion to their fitness.

From experience the following GA parameters were chosen：population size=30，breeding rate= 40%，minimum mutation rate=8%.The mutation rate was variable and increased with each generation if there had been no improvement in the literal count of the best chromosome.It then dropped back to 8%if improvement had occurred.The number of generations over which the GA was run was a maximum of 500.

5 Results of GA and validation

Basing on the above arithmetic，60 data were used for evolution，40 data for validation.The progress of the arithmetic was designed as follows.

//start with an initial time

t：=0；

//initialize a usually random population of individuals initpopulation P(t）；

//evaluate fitness of all initial individuals of population evaluate P(t）；

//test for termination criterion (time，fitness，etc.）

while not done so

//increase the time counter

t：=t+1；

//select a sub-population for offspring production

P'：=select parents P(t）；

//recombine the″genes″of selected parents recombine P'(t）；

//perturb the mated population stochastically mutate P'(t）；

//evaluate it's new fitness

evaluate P'(t）；

//select the survivors from actual fitness

P：=survive P，P'(t）；

end GA.

The optimal character combination for dividing the different wear and wear state has been found.

Equation (8）means in the process of evaluation，the parameter which can distinguish from the different states has reserved，on the contrary，the parameter is not sensitive to the different states eliminated through selection.

The optimal state feature compounding has reserved the parameter of single cylinder indication power，maximal blast pressure，average rate of pressure rise.These parameters reflect the diesel engine cylinder burning process from the different side face，the relativity between them is small.So we can find that in the genetic evolvement process，the parameter which embodies the abundant information can be reserved，otherwise parameter would be eliminated through selection or contest.The dividing effect of the optimal character combination is shown as below.

Fig.7 Distribution probability of parameter combination

6 Conclusion

Eigenvalue is vital to the precision and efficiency of fault diagnosis，the normal method for obtaining the fault diagnosis eigenvalue is simulation experiment.Since the number of experiment can not be too much，Bootstrap is introduced in the paper，and then using GA，an optimum parameter combination has been received.The process is valuable for the virtual fault diagnosis system.More attention should be paid to the Bootstrap and the efficiency of GA.

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10.3969/j.issn.1673-3185.2010.03.011

date：2009-08-25

Biography：Liu Min-lin was born in 1962.He is an associate professor at Naval University of Engineering. E-mail：liuminlin2008@sina.com

.Example shows this method is simple and efficient for establishing diesel engine state feature system，Thus，this method is valuable for the virtual state evaluation of similar complex system.