CN113361558B - Aeroengine fault detection method based on IHPSO-KMSVDD - Google Patents
Aeroengine fault detection method based on IHPSO-KMSVDD Download PDFInfo
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Abstract
The invention provides an aeroengine fault detection method based on IHPSO-KMSVDD, which provides a multi-sphere support vector data description algorithm, and surrounds sample data in different states by using different hyperspheres to perform anomaly detection, so that all errors in a certain state are greatly avoided, and the accuracy and the robustness of the original algorithm are improved. In addition, aiming at the defect that the super-parameter training time of the algorithm is too long, an improved particle swarm optimization algorithm for simulating the human learning behavior is provided for optimizing the super-parameter, so that the training time can be effectively shortened. The algorithm is suitable for the classification problem of medium and small scale, and has good performance in the aspect of the fault detection of the aero-engine. When the aeroengine fails due to abrasion, corrosion, blockage and the like, the health parameters of the corresponding parts can be changed, and when the normal data is doped with fault data with different degrees, the invention can continuously identify the fault data with excellent performance under the condition of mixing the fault data, thereby effectively improving the working efficiency.
Description
Technical Field
According to the invention, aiming at the fault detection of the aero-engine, a multi-sphere model is built by combining support vector data description (Support Vector Data Description) with a K-mean clustering algorithm, so that the problem of low detection precision of faults generated by components under various working states of the aero-engine is solved. Meanwhile, the super-parameters are optimized by utilizing an improved particle swarm optimization (Particle Swarm Optimization) algorithm, so that the training time is shortened, and the real-time performance of the aeroengine detection is improved.
Background
The aeroengine is a power core of each aircraft, the safety of the aeroengine always drives the chords of people, and once the aeroengine has a problem, the aeroengine directly threatens the property safety of people and even life safety. However, due to the complexity of its construction, the rigorous precision required, and the severity of the working environment, the major components are extremely prone to failure, and the direct maintenance costs for them have reached 50% or even more of the overall maintenance of the aircraft, which would result in a significant unnecessary loss of economic benefit for the airline if the aircraft engine were to be maintained directly each time. The method for accurately detecting the fault occurrence of the aero-engine and saving economic benefit as much as possible has great significance for health and safety management of the aero-engine, so that the fault detection technology of the aero-engine has become an important subject for domestic and foreign researches.
According to investigation, more than 90% of faults of the aero-engine are gas circuit faults. There are three main approaches to detect gas path failure to date: knowledge-based approaches, but this too relies on expert past experience, and is not suitable for new types of faults that occur in the rapid development of modern engines, which are very rapid and varying day by day; methods based on physical models, such as detection methods using observers and using kalman filters, but because accurate component characteristics of the engine are required for building the physical model, the development of the method is often limited as the engine technology is continuously updated and advanced; the data-based method, such as an intelligent detection method by using a support vector machine (Support Vector Machine, SVM for short) and an artificial neural network (Artificial Neural Network, ANN for short), has different levels of progress in detection efficiency and detection precision, effectively controls detection cost and lays a solid foundation for future research.
ANN is an artificial intelligence algorithm generated by simulating the operation mechanism of the human brain, and is composed of a plurality of nodes, one node corresponds to a neuron, each node can have one input or a plurality of inputs, the nodes between two adjacent layers are fully connected, and a message is transmitted through weights and threshold values. ANN is more concerned with minimizing risk of experience, which is less tolerant to false experiences and it is difficult to identify new outliers. The description of support vector data (Support Vector Data Description, SVDD for short) was proposed by Tax and Duin in 1999 on the basis of SVM, which is not limited to minimization of empirical risk, but focuses more on minimization of structural risk, and classification is achieved by finding a minimum hypersphere to surround as much data as possible, determining data outside the hypersphere as fault data, and determining data inside the hypersphere as normal data. When the training samples are only one type, the SVDD model can well identify abnormal data. Because of the high cost of obtaining the aeroengine fault data, SVDD algorithms that can perform fault detection only with normal data are widely used. However, when normal samples contain a plurality of samples under normal operation, they often exhibit a distribution of a plurality of clusters in a feature space, and it is not sufficient to construct only one hypersphere. For this purpose we propose to build a multi-sphere model which, although only one normal class, can enclose normal samples of different states with different hyper spheres, thus achieving a more accurate anomaly recognition.
Disclosure of Invention
The invention aims to: in order to solve the problem of fault detection in the process that the aeroengine is in multi-state operation, sample data in different states are surrounded by different hyperspheres to perform abnormality detection, so that all error identification of a certain state can be greatly avoided, and the accuracy and the robustness of an original algorithm are improved. In addition, aiming at the defect that the super-parameter training time of the algorithm is too long, an improved particle swarm optimization algorithm for simulating the human learning behavior is provided for optimizing the super-parameter, so that the training time can be effectively shortened.
The technical scheme is as follows:
an aeroengine fault detection method based on IHPSO-KMSVDD comprises the following steps:
step 1: collecting parameter samples of all parts of the aeroengine in a normal state within a full flight envelope range, and marking the parameter samples as positive samples and negative samples in a fault state;
step 2: carrying out normalization processing on the data set obtained in the step 1 to obtain a normalized data set;
step 3: dividing the data set obtained in the step 2 into a training data set and a test data set, wherein the training data set comprises normal samples and a part of outliers, and the rest data sets are all used as the test data set;
step 4: the training data set obtained in the step 3 is brought into an IHPSO algorithm model, and the optimal super parameters of the KMSVDD are obtained through training;
step 5: according to the optimal super parameters obtained in the step 4, carrying out KMSVDD algorithm model, and establishing a proper multi-sphere model;
step 6: and inputting test data, comparing the test data with the nearest super sphere, judging whether the test data is faulty or not, if the test data is positioned in the super sphere, determining that the test data is a normal sample, and otherwise, determining that the test data is a faulty sample.
Further, the fault state in step 1, which is represented by degradation of performance parameters, includes: compressor Flow Degradation (CFD), compressor Efficiency Degradation (CED), gas Turbine Flow Degradation (GTFD), gas Turbine Efficiency Degradation (GTED), power Turbine Flow Degradation (PTFD), power Turbine Efficiency Degradation (PTED).
Further, the parameters include: the engine altitude, engine flight Mach number, engine main fuel quantity, compressor outlet temperature, compressor outlet pressure, gas turbine outlet temperature, gas turbine outlet pressure, gas turbine output shaft speed, power turbine outlet temperature, power turbine outlet pressure, and power turbine output shaft speed.
Further, in the step 4, the IHPSO algorithm model is:
wherein t represents the iteration number, w is the inertia weight and is proportional to the intensity of the global optimizing capability, c 1 And c 2 Represent learning factor, r 1 And r 2 Is an abbreviation of function rand (x) representing a value between 0,1]Random number between r 3 Is a random number giving it compliance with standard normal distribution, i.e. r 3 E N (0, 1), if r 3 If > 0, it is considered to be an excitation learning coefficient, conversely, if r 3 < 0, it is considered a punished learning coefficient if r 3 =0, then this indicates that these bad habits or behaviors have no effect on the particles; assuming N engine sample data, they are considered as N particles, in a D-dimensional search space, i.e., each particle is a D-dimensional vector, x i Indicating the position of the ith particle：
x i ＝(x 1 ,x 2 ,…,x D ),i＝1,2,…,N (3)
v i Indicating the speed of the ith particle:
v i ＝(v 1 ,v 2 ,…,v D ),i＝1,2,…,N (4)
p i represents the individual optimum value of the ith particle:
p i ＝(p i1 ,p i2 ,…,p iD ),i＝1,2,…,N (5)
g i a global optimum value representing the whole population of particles:
g i ＝(g i1 ,g i2 ,…,g iD ),i＝1,2,…,N (6)
Gworst i the particle position representing the worst fitness function in the whole particle swarm:
Gworst t ＝argmin{f(x 1 ),f(x 2 ),…,f(x N )} (7)
where f (x) is the fitness function.
Furthermore, the value of the inertia weight w adopts an adaptive method, namely, in the iterative process of the particles, the inertia weight is generally reduced until the particles are converged to the global optimal position, the detail of each iteration reduction is determined by each particle in an adaptive way, the performance index of the current particle is used as the input of a Gompertz function to achieve the purpose of adaptively changing the inertia weight along with the change of the iteration number, wherein the Gompertz function is used as a double-index function and has very rapid reduction capability, and the convergence rate of the algorithm can be greatly improved, and the formula is that
y＝exp(-exp(x)) (8)
The formula for the inertial weight w is as follows:
w＝exp(-exp(R i t )) (9)
wherein, the performance index R of the particles i t The individual historical optimal positions of the particles and the global optimal positions of the groups are evaluated according to the following formula:
at the first iteration, the inertial weight is set to 0.9, and then the subsequent inertial weights are adaptively selected using equations (9) and (10).
Further, learn factor c 1 And c 2 The self-adaptive learning strategy is adopted for the value of the particle, so that the particle is more prone to improving global exploration capability in the initial stage, the individual history optimal experience of the particle can be better inherited, and c is set at the moment 1 ＞c 2 And the local searching capability of the particles is enhanced at the later stage of iteration, so that the optimal experience among the group particles can be better learned, and c is set 1 ＜c 2 . In addition, in order to enable the learning factor to be adaptively changed, the learning factor is related to the state of the particles, so that the self-adaptive decision can be carried out according to the state of the particles, and the judgment of the state of the particles can be evaluated by using the fitness function of the learning factor; c 1 And c 2 Expressed by the following equations, respectively:
c 1 +c 2 ＝4 (12)
wherein f (x) is a fitness function, f ave Is the average of fitness functions of all particles in a population of particles.
Further, in step 4, in order to prevent the algorithm from being in a local optimum when the IHPSO algorithm model is trained, the population diversity is utilized, that is, the difference value of the particle diversity of the two previous and subsequent iterations is smaller than a preset value Δe, and the calculation formula of the population diversity E is as follows:
wherein,represents the average value of the j-th dimension of all particles in the particle swarm; when the population diversity of the particles in the previous and later iterations is smaller than a preset value delta E, the particle swarm is possibly in a local optimal state, at the moment, a tiny disturbance is given to the particle swarm, the population diversity of the particle swarm is increased, and therefore the local optimal state is more easily jumped out:
p t+1 ＝p t ×(1+μN(0,1)) (14)
wherein p is t Representing the particle position at the t-th iteration, N (0, 1) represents a normal distribution subject to a mean of 0 and a variance of 1, and μ ε (0, 1) is a small perturbation factor.
Further, the multi-sphere model in step 5 is as follows:
wherein ε is i Denotes the relaxation factor, v denotes the hyper-parameter, |S j The I represents subset S j Number of samples in { S 1 ,S 2 ,…,S k The expression "multiple subsets" of training samples, that is, each sample x i Will be assigned to a subset S j J is {1,2, …, k }, and satisfiesAnd->{a 1 ,a 2 ,…,a k Respectively is a subset { S } 1 ,S 2 ,…,S k Sample center of }, by solving k standard SVDD models, namely:
solving equation (15) to obtain:
a k ＝∑α i x i (17)
wherein alpha is i Belonging to subset S k The lagrangian factor corresponding to the support vector in the constructed hypersphere.Are respectively subsets { S ] 1 ,S 2 ,…,S k The square of the radius of the super sphere formed is obtained by solving k standard SVDD models, and each sample x is obtained first i Distance from center:
where K (-) represents the kernel function. Then calculate each subset S k Radius of the formed hypersphere:
where n is a subset S k Is a sample number of (a) in a sample.
Further, in step 6, each test sample z is assigned a cluster to which it belongs, and the centers { a } of the k subsets are finally obtained 1 ,a 2 ,…,a k Radius and radiusAnd (3) determining:
if y=1, z is a normal sample; if y= -1, z is the faulty sample.
The beneficial effects are that: according to the invention, the fault detection is carried out on the aviation scroll engine through the IHPSO-KMSVDD algorithm, so that the detection effect is greatly improved, the more accurate detection of the engine fault is realized, the super-parameter optimization time is shortened, and the detection instantaneity is improved. Compared with the existing fault detection method, the method has the following advantages:
1. the method provides a new method and a new thought for detecting the faults of the aero-engine;
2. the method is easy to understand, and the parameter adjustment of the algorithm is simple;
3. the method is easy to realize, has strong practicability and can realize high-precision detection;
4. the method shortens the super-parameter optimization time and improves the detection instantaneity.
Drawings
FIG. 1 is an algorithm flow diagram of IHPSO-KMSVDD;
FIG. 2 is a schematic cross-sectional view of a certain type of turboshaft engine;
FIG. 3 shows the results of comparative experiments using KMSVDD with SVDD and WSVDD at a fault sample ratio of 2% (a) G-mean, (b) F1, (c) training time, and (d) test time;
FIG. 4 shows the results of comparative experiments using KMSVDD with SVDD and WSVDD at a fault sample ratio of 5% (a) G-mean, (b) F1, (c) training time, and (d) test time.
Detailed Description
In aeroengine fault detection, the acquisition costs of a normal sample and a fault sample are different, so that a way of completing fault detection when only a normal sample is needed is very popular, in view of this, the following steps are performed:
step 1: establishing an IHPSO super-parameter optimization model, and continuously iterating to know the found optimal super-parameter:
wherein t represents the iteration number, w is the inertia weight and is proportional to the intensity of the global optimizing capability, c 1 And c 2 Represent learning factor, r 1 And r 2 Is an abbreviation of function rand (x) representing a value between 0,1]Between (a) and (b)Random number, r 3 Is a random number given to it and obeys a standard normal distribution, i.e. r 3 E N (0, 1). In the aeroengine fault detection, it is assumed that N sample data, i.e., N particles, are in a 3-dimensional search space, i.e., each particle includes three super-parameters including a cluster parameter k, a super-parameter v, and a core parameter δ, where the k value should be an integer, so that a function round (x) is used in the iterative process to round the third dimension of the particle swarm.
x i Representing the position of the i-th particle:
x i ＝(ν,δ,k),i＝1,2,…,N (3)
since the search space of the particles is limited, the upper bound of the particle position is set to {2 } -1 ,2 10 5, the lower bound of the particle position is set to {2 } -10 ,2 -10 ,1}；
v i Indicating the speed of the ith particle:
v i ＝(v 1 ,v 2 ,v 3 ),i＝1,2,…,N (4)
the upper bound of particle velocity is set to {0.015,30,0.5}, and the lower bound of particle velocity is set to { -0.015, -30, -0.5};
p i represents the individual optimum value of the ith particle:
p i ＝(p i1 ,p i2 ,p i3 ),i＝1,2,…,N (5)
g i a global optimum value representing the whole population of particles:
g i ＝(g i1 ,g i2 ,g i3 ),i＝1,2,…,N (6)
Gworst i the particle position representing the worst fitness function in the whole particle swarm:
Gworst t ＝argmin{f(x 1 ),f(x 2 ),f(x 3 )} (7)
the value formula of the inertia weight w is as follows:
w＝exp(-exp(R i t )) (8)
wherein, the performance index R of the particles i t Optimization from individual histories of particlesThe global optimal position evaluation of the position and the population is as follows:
at the first iteration, the inertial weight is set to 0.9, then the subsequent inertial weight is adaptively selected using formulas (8) and (9), the upper bound w of the inertial weight max =0.9, lower bound w max ＝0.4。
Learning factor c 1 And c 2 The values of (2) are represented by the following equations, respectively:
c 1 +c 2 ＝4 (11)
wherein f (x) is a fitness function, f ave Is the average value of fitness functions of all particles in a particle swarm, and the upper bound c of a learning factor max =4.0, lower bound c max ＝0.0。
Finally, in order to prevent the algorithm from falling into local optimum, the population diversity is utilized, namely, the difference value of all particle diversity of the previous and subsequent iterations is smaller than a preset value delta E, and the calculation formula of the population diversity E is as follows:
wherein,represents the average of the j-th dimension of all particles in the particle swarm. The particle population diversity of the current and the subsequent two iterations is smaller than a preset value delta E=10 -3 In this case, a small disturbance is given to the particle swarm, so that the population diversity of the particle swarm is increased, and the local optimum is more easily jumped out:
p t+1 ＝p t ×(1+μN(0,1)) (13)
wherein the method comprises the steps of，p t Representing the particle position at the t-th iteration, N (0, 1) represents a normal distribution subject to a mean of 0 and a variance of 1, μ e (0, 1) is a small perturbation factor taking μ=0.5.
Step 2: setting up a KMSVDD multi-sphere model according to the optimal super parameters selected in the step 1:
wherein ε is i Denotes the relaxation factor, v denotes the hyper-parameter, |S j The I represents subset S j Number of samples in { S 1 ,S 2 ,…,S k The expression "multiple subsets" of training samples, that is, each sample x i Will be assigned to a subset S j J is {1,2, …, k }, the distribution formula is
And satisfy the followingAnd->{a 1 ,a 2 ,…,a k Respectively are subsets { S } 1 ,S 2 ,…,S k Sample center by solving k standard SVDD models, i.e
Solving equation (16) to obtain:
a k ＝∑α i x i (17)
wherein alpha is i Belonging to subset S k The lagrangian factor corresponding to the support vector in the constructed hypersphere.Are respectively subsets { S ] 1 ,S 2 ,…,S k The square of the radius of the super sphere formed is obtained by solving k standard SVDD models, and each sample x is obtained first i Distance from center:
where K (-) represents the kernel function. Then calculate each subset S k Radius of the formed hypersphere:
where n is a subset S k Is a sample number of (a) in a sample.
Step 3: for each given test sample z, the most likely subset is determined, the center { a } of the k subsets obtained in step 2 1 ,a 2 ,…,a k Radius and radiusAnd (3) determining:
if y=1, z is a normal sample; if y= -1, z is the faulty sample.
The following gives the flows of IHPSO algorithm and KMSVDD algorithm:
the experiment selects the Radial-Basis Function (RBF) kernel Function for training, where regularization parameters are obtained from step 1. Test selection(TP represents the number of samples predicted to +1 and actual tag to +1, TN represents the number of samples predicted to-1 and actual tag to-1, FP represents the number of samples predicted to +1 and actual tag to-1, FN represents the number of samples predicted to-1 and actual tag to +1) and->(wherein) As performance index of evaluation method, taking average value of G-mean and F1 of 10 results as evaluation of algorithm performance to avoid accidental factor. All experiments were configured as +.>Core TM I5-7400CPU, 3.00GHz main frequency, 8G memory, windows10 system and MATLAB2018b version desktop computer.
The invention is used for testing a T700 turboshaft engine, and as shown in fig. 2, the main components of the engine comprise an air inlet channel, a Compressor, a combustion chamber, a Gas Turbine (GT), a Power Turbine (PT) and a tail nozzle. Where 3 denotes a compressor outlet, 42 denotes a gas turbine outlet, and 5 denotes a power turbine outlet. The low-pressure air flows into the air compressor through the air inlet channel and the conveying device, and is converted into high-pressure air flow after being compressed by the air compressor. In the combustion chamber, fuel oil is injected into the combustion chamber and mixed with high-pressure gas to form mixed gas, and when the mixed gas flows through a gas turbine and a power turbine, the high-pressure shaft and the low-pressure shaft respectively drive the connected gas compressor and a transmission device (for providing power for tail rotor and rotor wing) to rotate. Eventually the hot gases are discharged to the atmosphere at high velocity.
The compressor, GT and PT connected to the aero-engine rotor are subject to failure at high rotational speeds, so that only failures of these three components are considered and the occurrence of failure of each component is simulated with degradation of flow and efficiency, respectively. Simulation data of the full flight envelope is collected before the experiment, wherein the simulation data comprise 2020 normal state samples, 2000 compressor flow degenerated fault samples, 1980 compressor efficiency degenerated fault samples, 2000 GT flow degenerated fault samples, 2000 GT efficiency degenerated fault samples, 2000 PT flow degenerated fault samples and 2000 PT efficiency degenerated fault samples. The normal state is classified as positive, the label is +1, the rest faults are classified as negative, and the label is-1. Each sample has 11 dimensions, namely fly height, fly mach number, GT output shaft speed, PT output shaft speed, T3, P3, T42, P42, T5, P5 and fuel flow, where T3 represents compressor outlet temperature, P3 represents compressor outlet pressure, and the remaining parameters are named according to the same rules. To verify the detection performance in 6 failure cases, outliers of 2% and 5% were added to the training samples. Samples were normalized prior to the experiment.
In tables 1 and 2, IHPSO-KMSVDD and KMSVDD algorithm using grid search method (GS-KMSVDD) were used, respectively, and the results of detecting the gas circuit faults of the turboshaft engine were compared. Experimental results show that the IHPSO-KMSVDD greatly shortens the super-parameter optimizing time on the basis of slightly improving the detection precision, and the super-parameter optimizing time of the GS-KMSVDD is three times longer than that of the IHPSO-KMSVDD in time comparison. Tables 3 and 4 show the exact comparison of KMSVDD with WSVDD and standard SVDD at different fault sample ratios, including G-mean value comparison, F1 value comparison, training time comparison, and test time comparison. The test result shows that the KMSVDD algorithm is used for detecting six faults of the turboshaft engine, the results are better than the standard SVDD algorithm and the WSVDD algorithm, and the G-mean value and the F1 value of the three algorithms are good. For a more visual comparison of the three algorithms, they are drawn in a bar graph fashion, as shown in fig. 3 and 4. The two figures show the obvious improvement of the G-mean value and the F1 value of the KMSVDD more clearly, namely the optimal performance. In addition, the KMSVDD algorithm needs more training time, but for real-time detection of the aeroengine, the test time of the KMSVDD algorithm needs to be more concerned, and the test time of the KMSVDD algorithm is slightly higher than that of the WSVDD algorithm and the traditional SVDD algorithm, but the KMSVDD algorithm has small influence on real-time because the KMSVDD algorithm is smaller in order of magnitude and is about 0.1 second, which proves that the KMSVDD algorithm has good performance in the detection process.
Table 1 results of comparative experiments using IHPSO-KMSVDD and GS-KMSVDD at a failure sample ratio of 2%
TABLE 2 comparative experiment results with IHPSO-KMSVDD and GS-KMSVDD at a failure sample ratio of 5%
TABLE 3 comparative experimental results using KMSVDD with SVDD and WSVDD at a failure sample ratio of 2%
TABLE 4 comparative experimental results using KMSVDD with SVDD and WSVDD at a 5% failure sample ratio
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Claims (9)
1. An aeroengine fault detection method based on IHPSO-KMSVDD is characterized by comprising the following steps:
step 1: collecting parameter samples of all parts of the aeroengine in a normal state within a full flight envelope range, and marking the parameter samples as positive samples and negative samples in a fault state;
step 2: carrying out normalization processing on the data set obtained in the step 1 to obtain a normalized data set;
step 3: dividing the data set obtained in the step 2 into a training data set and a test data set, wherein the training data set comprises a normal sample and a part of outliers, and the rest data sets are all used as the test data set;
step 4: the training data set obtained in the step 3 is brought into an IHPSO algorithm model, and the optimal super parameters of the KMSVDD are obtained through training;
step 5: according to the optimal super parameters obtained in the step 4, carrying out KMSVDD algorithm model, and establishing a proper multi-sphere model;
step 6: and inputting test data, comparing the test data with the nearest super sphere, judging whether the test data is faulty or not, if the test data is positioned in the super sphere, determining that the test data is a normal sample, and otherwise, determining that the test data is a faulty sample.
2. An IHPSO-KMSVDD based aeroengine fault detection method according to claim 1, wherein the fault condition in step 1, which is manifested as performance parameter degradation, comprises: compressor flow degradation, compressor efficiency degradation, gas turbine flow degradation, gas turbine efficiency degradation, power turbine flow degradation, power turbine efficiency degradation.
3. An IHPSO-KMSVDD based aeroengine fault detection method according to claim 1, wherein the parameters include: the engine altitude, engine flight Mach number, engine main fuel amount, compressor outlet temperature, compressor outlet pressure, gas turbine outlet temperature, gas turbine outlet pressure, gas turbine output shaft speed, power turbine outlet temperature, power turbine outlet pressure, power turbine output shaft speed.
4. The method for detecting the fault of the aeroengine of the IHPSO-KMSVDD according to claim 1, wherein the IHPSO algorithm model in the step 4 is as follows:
wherein t represents the iteration number, w is the inertia weight and is proportional to the intensity of the global optimizing capability, c 1 And c 2 Represent learning factor, r 1 And r 2 Is an abbreviation of function rand (x) representing a value between 0,1]Random number between r 3 Is a random number giving it compliance with standard normal distribution, i.e. r 3 E N (0, 1), if r 3 If > 0, it is considered to be an motivated learning coefficient, conversely, if r 3 < 0, it is considered a punished learning coefficient if r 3 =0, then it means that these bad habits or behaviors have no effect on the particles; assuming N engine sample data, they are considered as N particles, in a D-dimensional search space, i.e., each particle is a D-dimensional vector, x i Representing the position of the i-th particle:
x i ＝(x 1 ,x 2 ,…,x D ),i＝1,2,…,N (3)
v i indicating the speed of the ith particle:
v i ＝(v 1 ,v 2 ,…,v D ),i＝1,2,…,N (4)
p i represents the individual optimum value of the ith particle:
p i ＝(p i1 ,p i2 ,…,p iD ),i＝1,2…,N (5)
g i a global optimum value representing the whole population of particles:
g i ＝(g i1 ,g i2 ,…,g iD ),i＝1,2,…,N (6)
Gworst i the particle position representing the worst fitness function in the whole particle swarm:
Gworst t ＝argmin{f(x 1 ),f(x 2 ),…,f(x N )} (7)
where f (x) is the fitness function.
5. The method for detecting the fault of the aeroengine of the IHPSO-KMSVDD according to claim 4, wherein the value of the inertia weight w adopts a self-adaptive method, namely, in the iterative process of particles, the inertia weight is generally reduced until the particles are converged to a global optimal position, the detail of each iteration reduction is determined by each particle self-adaptation, and the performance index of the current particle is used as the input of a Gompertz function so as to achieve the purpose that the inertia weight is changed in a self-adaptation way along with the change of the iterative times; the formula of the inertia weight w is as follows:
w＝exp(-exp(R i t )) (8)
wherein, the performance index R of the particles i t The individual historical optimal positions of the particles and the global optimal positions of the groups are evaluated according to the following formula:
wherein t represents the number of iterations, t max Representing the maximum number of iterations.
6. The IHPSO-KMSVDD based aeroengine fault detection method as claimed in claim 4, wherein the learning factor c is 1 And c 2 Adopts self-adaptive learning strategy to set c in iteration 1 ＞c 2 Setting c at the later stage of iteration 1 ＜c 2 ；c 1 And c 2 Expressed by the following equations, respectively:
c 1 +c 2 ＝4 (11)
wherein f (x) is a fitness function, f ave Is the average value of fitness functions of all particles in the particle swarm, c max Represents the upper limit of the learning factor, c min Represents the lower limit of the learning factor, t represents the iteration number, t max Representing the maximum number of iterations.
7. The method for detecting the fault of the aeroengine based on the IHPSO-KMSVDD according to claim 4, wherein in order to prevent the algorithm from being in local optimum when the IHPSO algorithm model is trained in the step 4, population diversity is utilized, namely, the difference value of particle diversity of two previous and subsequent iterations is smaller than a preset value delta E, and a calculation formula of the population diversity E is as follows:
wherein,represents the average value of the j-th dimension of all particles in the particle swarm; when the population diversity of the particles in the previous and later iterations is smaller than a preset value delta E, the particle swarm is possibly in a local optimal state, at the moment, a tiny disturbance is given to the particle swarm, the population diversity of the particle swarm is increased, and therefore the local optimal state is more easily jumped out:
p t+1 ＝p t ×(1+μN(0,1)) (13)
wherein p is t Representing the particle position at the t-th iteration, N (0, 1) represents a normal distribution subject to a mean of 0 and a variance of 1, and μ ε (0, 1) is a small perturbation factor.
8. The method for detecting the fault of the aeroengine based on IHPSO-KMSVDD according to claim 1, wherein the multi-sphere model in the step 5 is as follows:
wherein ε is i Denotes the relaxation factor, v denotes the hyper-parameter, |S j The I represents subset S j Number of samples in { S 1 ,S 2 ,…,S k The expression "multiple subsets" of training samples, i.e., each sample x i Will be assigned to a subset S j J is {1,2, …, k }, and satisfiesAnd->{a 1 ,a 2 ,…,a k Respectively are subsets { S } 1 ,S 2 ,…,S k Sample center of }, by solving k standard SVDD models, namely:
wherein R represents the radius of the hypersphere formed by the standard SVDD model, N represents the number of samples, and the hypersphere is obtained by solving the formula (15):
a k ＝∑α i x i (16)
wherein alpha is i Belonging to subset S k The lagrangian factor corresponding to the support vector in the constructed hypersphere,respectively subset { S ] 1 ,S 2 ,…,S k The square of the radius of the super sphere is obtained by solving k standard SVDD models, firstly, the method comprises the steps ofEach sample x i Distance from center:
where K (-) represents the kernel function, then each subset S is calculated k Radius of the formed hypersphere:
where n is a subset S k Is a sample number of (a) in a sample.
9. The method for detecting the fault of the aeroengine based on IHPSO-KMSVDD as claimed in claim 8, wherein each test sample z is provided with a cluster to which the cluster belongs in step 6, and the center { a of k subsets is finally obtained 1 ,a 2 ,…,a k Radius and radiusAnd (3) determining:
wherein Φ (z) represents a mapping function; if y=1, z is a normal sample; if y= -1, z is the faulty sample.
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