Belief rule base optimization method based on penalty compensation population dynamic reconstruction

Abstract

The invention discloses a belief rule base optimization method based on penalty compensation population dynamic reconstruction. The method comprises the following steps: firstly, acquiring data of sensors at different positions of a gas turbine, establishing an initial belief rule base, vectorizing optimized parameters in the belief rule base, and setting initial parameters of six optimization algorithms; secondly, on the basis of vectorized parameters, different optimization algorithms are optimized respectively, all populations are merged every N generations, and sorting is carried out according to fitness values; and then calculating a fitness threshold, adjusting population sizes of different optimization algorithms, forming a population sharing pool by optimal individuals of all the optimization algorithms, and allocating individuals in the population sharing pool to the populations of the optimization algorithms as a new generation of populations. And finally, repeating the operation, selecting the optimization algorithm with the maximum population scale as an optimal algorithm, and obtaining a final solution, namely optimal information rule base parameters. According to the method, the problem that a single evolutionary algorithm falls into a local optimal solution is avoided, and the optimization efficiency is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of engineering safety and relates to a confidence rule base optimization method based on dynamic reconstruction of penalty compensation population. Background Art

[0002] As the core of machine operation, the engine often works in a high temperature and high pressure environment. Therefore, it is necessary to add some redundant designs during design to ensure that the working condition of the engine can be correctly monitored. A common way is to arrange sensors at different positions of the engine. When a sensor fails, the value of this sensor can be predicted based on the remaining sensors. In actual use, the signals between different sensors are often nonlinear. The information collected from multiple sensors is mostly quantitative data, but it may also contain qualitative information, such as some information supplemented by experts. The confidence rule base is based on the "IF-THEN" structure and has good processing capabilities when facing complex nonlinear systems. In addition, the confidence rule base itself has the characteristics of analysis, transparency, and interpretability. In actual use, expert experience can be used to promptly correct errors in the optimization process. Therefore, the confidence rule base model is introduced in engine state detection, and the initial confidence rule base is established using expert experience.

[0003] In most cases, the initial confidence rule base established by expert experience is often not accurate enough, and the confidence rule base model needs to be optimized using the collected historical data. The traditional method is to select an evolutionary algorithm as the optimization engine. However, different evolutionary algorithms have different advantages when facing different theoretical and practical problems. A single evolutionary algorithm is prone to fall into the problem of local optimal solution during the optimization process. Therefore, a new method is needed to fully utilize the advantages and characteristics of different evolutionary algorithms. Summary of the invention

[0004] In view of the above problems, the present invention proposes a confidence rule base optimization method based on dynamic reconstruction of penalty compensation population to achieve the purpose of identifying the best algorithm, improving optimization efficiency and obtaining better results. This method can solve a series of problems such as the traditional single optimization algorithm is easy to fall into the local optimal solution during the optimization process, different optimization algorithms have different advantages and disadvantages, and it is difficult to choose in actual use.

[0005] The present invention proposes a confidence rule base optimization method based on dynamic reconstruction of penalty compensation population, which includes the following steps:

[0006] (1) Collect sensor data from different locations of the gas turbine, divide it into training sets and test sets, and establish an initial confidence rule base based on expert experience.

[0007] (2) The parameters that need to be optimized in the confidence rule base are vectorized, and the initial parameters of the six optimization algorithms, namely, differential evolution algorithm DE, ant colony algorithm ACO, parameter estimation algorithm EDA, covariance matrix adaptive evolution algorithm CMA-ES, genetic algorithm GA, and adaptive differential evolution algorithm JADE, are set.

[0008] (3) Based on the vectorized parameters, different optimization algorithms are optimized separately. The populations of all optimization algorithms are merged every N generations and sorted according to the fitness values.

[0009] (4) Penalty compensation mechanism: Calculate the fitness threshold and adjust the population size of different algorithms based on the proportion of individuals in each algorithm that are better than the threshold.

[0010] (5) Population dynamic reconstruction mechanism: The best individuals of all optimization algorithms are merged to form a population sharing pool. According to the adjusted population size, individuals in the population sharing pool are allocated to populations of different algorithms as the new generation of population.

[0011] (6) Repeat (3) to (5), and finally select the optimization algorithm with the largest population size as the optimal algorithm and continue to optimize it separately.

[0012] (7) When the optimal algorithm selected in step (6) reaches the maximum number of iterations, the iteration stops and the final solution, i.e., the optimal confidence rule base parameters, is obtained.

[0013] Beneficial effects of the present invention:

[0014] The present invention proposes to use six evolutionary algorithms in combination and divide them into six different populations. These populations learn from each other through population dynamic reconstruction, giving full play to the characteristics of different evolutionary algorithms and avoiding the problem that a single evolutionary algorithm may fall into a local optimal solution.

[0015] The present invention proposes a population dynamic reconstruction mechanism, which extracts the best individuals from different evolutionary algorithms to form a new population for the next round of evolution, combines the advantages of multiple algorithms, and improves the optimization efficiency.

[0016] The present invention proposes a penalty compensation mechanism, which reallocates the size of the population according to the optimization effects of different evolutionary algorithms and ultimately determines the best optimization algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of the implementation of the method of the present invention;

[0018] Figure 2 It is an iterative curve diagram of the fitness values ​​of each algorithm of the method of the present invention in the training set;

[0019] Figure 3It is a distribution diagram of the sizes of the algorithm populations after the algorithms of the present invention have undergone a competitive distribution mechanism. DETAILED DESCRIPTION

[0020] The present invention proposes a confidence rule base optimization method based on dynamic reconstruction of penalty compensation population to achieve the purpose of identifying the best algorithm, improving optimization efficiency and obtaining better results. This method can solve a series of problems such as the traditional single optimization algorithm is easy to fall into the local optimal solution during the optimization process, different optimization algorithms have different advantages and disadvantages, and it is difficult to choose in actual use.

[0021] The present invention proposes a confidence rule base optimization method based on dynamic reconstruction of penalty compensation population, which includes the following steps:

[0022] (1) The data set is divided according to the 1000 sets of engine sensor data collected, and 800 sets of data are randomly selected as the training set data. , using the entire dataset as the test set , integrate expert experience and knowledge to establish an initial rule base.

[0023] (2) Establishing an optimization model: vectorize the parameters that need to be optimized in the confidence rule base, and set the initial parameters of the six algorithms: differential evolution algorithm DE, ant colony algorithm ACO, parameter estimation algorithm EDA, covariance matrix adaptive evolution algorithm CMA-ES, genetic algorithm GA, and adaptive differential evolution algorithm JADE.

[0024] (3) Different optimization algorithms are optimized separately, and the populations of all algorithms are merged every F generations and sorted according to fitness values.

[0025] (4) Penalty compensation mechanism: Calculate the fitness threshold and adjust the population size of different algorithms according to the proportion of individuals in each optimization algorithm that are better than the threshold.

[0026] (5) Population dynamic reconstruction mechanism: The best individuals of all optimization algorithms are merged to form a population sharing pool, and individuals in the population sharing pool are allocated to populations of different optimization algorithms according to the adjusted population size.

[0027] (6) Repeat (3) to (5), and finally select the optimization algorithm with the largest population size as the optimal algorithm and continue to optimize it separately.

[0028] (7) Termination condition detection: if the set number of iterations is reached, the optimization algorithm terminates; if not, return to (3) to continue execution. Repeat the above steps to achieve the purpose of updating and optimizing the population. Finally, when the termination condition is reached, the loop ends, the optimization terminates, and the optimal solution, that is, the optimal confidence rule base parameters, is obtained. Output the final confidence rule base parameters.

[0029] (8) Verification of the test data set. According to the final solution obtained in (7), the test data set Verification is carried out to prove the effectiveness of this method.

[0030] Furthermore, step (1) is specifically:

[0031] The parameter optimization goal of the confidence rule base is to reduce the error between the output predicted by the confidence rule base and the actual output, namely the mean square error (MSE). The variables that need to be initialized using expert experience include the premise attribute reference value of the confidence rule. , initial weight of rules , confidence level of output level The confidence rule base optimization model is expressed as follows:

[0032] (1)

[0033] st

[0034] (2)

[0035] (3)

[0036] (4)

[0037] (5)

[0038] in , Formula (2) indicates that the reference value of the mth premise attribute in the kth rule must be constrained within its upper and lower limits (lb m (lower limit) and ub m (upper limit)), formula (3) indicates that the initial weight of the k-th rule needs to be constrained in the interval (0,1], formulas (4) and (5) indicate that the confidence of the n-th output level in the k-th rule needs to be constrained in the interval [0,1], and the sum of the confidences of the same rule must be "1".

[0039] Furthermore, step (3) is as follows:

[0040] (3.1) DE optimization process. The core idea of ​​the differential evolution algorithm is to continuously optimize the objective function through differential mutation, crossover recombination and selection mechanisms between individuals. The mutation operation of individuals in the population is shown in the following formula (6):

[0041] (6)

[0042] in, Represents 3 different particles; F represents the mutation variable, usually the range of F is (0,2].

[0043] The crossover operation is to select temporary individuals according to the probability CR The jth position in the , or from the current individual with a probability of 1-CR Select the jth position from the list to form the final temporary individual The jth bit of is as shown in formula (7):

[0044] (7)

[0045] Among them, CR ranges from [0,1], indicating the crossover operator probability.

[0046] The DE sub-populations evolve independently through mutation and crossover steps to produce new populations of the next generation.

[0047] (3.2) GA optimization process. Genetic algorithm is an optimization method that simulates natural selection and genetic mechanism, mainly including three operations: crossover, mutation and selection.

[0048] The crossover operation is to generate a new individual by selecting two parent individuals through crossover. Single-point crossover is the simplest and most commonly used method, which starts from a random point in the two parent chromosomes and then exchanges parts of the two chromosomes to generate two new daughter chromosomes.

[0049] The mutation operation introduces a small disturbance to a certain dimension of the individual to improve diversity and prevent premature convergence.

[0050] The selection operation is based on the fitness function The roulette method is commonly used to select outstanding individuals to enter the next generation. The formula for the probability of selecting an individual is as follows:

[0051] (8)

[0052] Where N represents the size of the population, Indicates the first Individual.

[0053] (3.3) ACO optimization process. ACO mainly guides ants to search for paths through pheromones, and in this process constructs state transition probabilities. To distinguish the search intensity and direction, the calculation formula is as follows:

[0054] (9)

[0055] in Indicates Daizhongdi The fitness value of an individual, is the fitness value of the current optimal individual.

[0056] The generation of new individuals is as follows:

[0057] (10)

[0058] in is the step size factor for gradual convergence, is a uniform random number, U and L are the upper and lower bounds of the variable respectively. To control the threshold of global search.

[0059] (3.4) CMA-ES optimization process. The evolutionary strategy of covariance matrix adaptation guides the search direction by dynamically adjusting the covariance matrix. In each generation, new candidate solutions are generated based on the covariance matrix, which reflects the distribution of different directions in the search space. The generation formula of new individuals is:

[0060] (11)

[0061] in is the current individual, is the step size factor, is from the covariance matrix Describes the noise generated from a Gaussian distribution.

[0062] (3.5) EDA optimization process. The distribution estimation algorithm selects a part of the better individuals in the current population to estimate the probability distribution, and then generates a new candidate solution. The probability distribution is estimated by maximizing the likelihood estimate:

[0063] (12)

[0064] in It is the solution The probability density function of the dimension.

[0065] The generation formula of new individuals is:

[0066] (13)

[0067] in Based on the current probability distribution expectations, is a disturbance term that helps generate new individuals.

[0068] (3.6) JADE optimization process. JADE is a variant of the differential evolution algorithm (DE) that introduces an adaptive parameter adjustment strategy. The scaling factor and crossover probability of the mutation operation can be adaptively adjusted. The adaptive adjustment parameter formula is:

[0069] (14)

[0070] (15)

[0071] in and is the current mutation factor and crossover probability, and is a randomly selected factor, is the learning rate of the smoothing factor.

[0072] Furthermore, step (3) is as follows:

[0073] The optimization goal is to reduce the error between the output predicted by the confidence rule base and the actual output, using the mean square error (MSE) method, and the specific calculation formula is:

[0074] (16)

[0075] in is the actual output value, Output value for the confidence rule base model, is the number of samples in the training set.

[0076] Furthermore, step (4) is specifically:

[0077] (4.1) Threshold calculation: take the median of the fitness values ​​after sorting as the threshold;

[0078] (4.2) The population size is adjusted according to the proportion of individuals below the threshold of each optimization algorithm. The specific adjustment formula is:

[0079] (17)

[0080] in Indicates The number of populations after the optimization algorithm is adjusted. represents the sum of all algorithm populations before adjustment, Indicates The number of individuals for which the optimization algorithm is better than the threshold, ;

[0081] (4.3) Update the adjusted population size to ensure that the population size of each optimization algorithm is not less than 6, and the total population size after update is equal to the total population size before adjustment.

[0082] vector represents the population size of different optimization algorithms, Each element of represents the number of populations assigned to different optimization algorithms after step (4.2), Q represents the number of optimization algorithms used, and in this invention, Q=6. Perform preprocessing and change all elements in the input vector that are less than 6 to 6, as shown in the following formula:

[0083] (18)

[0084] in Represents the population size vector after preprocessing.

[0085] Calculate the difference between the total population size before and after adjustment as follows:

[0086] (19)

[0087] in represents the sum and difference of population numbers;

[0088] Assign the difference if , from all The elements are reduced proportionally , decreasing by 1 each time until , the final output The population size of all algorithms must remain constant and be at least 6;

[0089] Furthermore, step (5) is specifically:

[0090] (5.1) Evaluate the fitness of each individual in the population;

[0091] For Algorithms, , whose current population size is , calculate all individuals according to formula (16) The MSE, that is, the fitness value:

[0092] (5.2) Select the first half of the individuals with better performance in each population as excellent individuals and enter the shared pool;

[0093] For An optimization algorithm is used. Sort the population by fitness and select the first half of the individuals:

[0094] (20)

[0095] Build a shared pool:

[0096] (twenty one)

[0097] (5.3) Shared pool All individuals in the are sorted according to the size of the fitness value ;

[0098] (5.4) From the sorted shared pool, allocate the first individuals, as the new generation of the population.

[0099] The following is a detailed description of the embodiments of the method of the present invention with reference to the accompanying drawings:

[0100] The flowchart of the present invention is as follows Figure 1 As shown, the core parts are the penalty compensation mechanism and the population dynamic reconstruction mechanism;

[0101] The iterative curve diagram of the fitness value of the method of the present invention and the single evolutionary algorithm in the training set is as follows: Figure 2 As shown, in the first 100 iterations, the results obtained by this method are better than those obtained by using a single algorithm;

[0102] The change in the size of each algorithm population after 100 iterations of the six algorithms used in the present invention is shown in the figure Figure 3 As shown in the figure, the initial population size of the six algorithms is 20, and the penalty compensation population dynamic reconstruction mechanism is used every 10 generations.

[0103] The following is a preferred embodiment of the method of the present invention, which is based on the changes in sensor signals at different positions during the operation of the gas turbine, including the signal of the low-pressure rotor speed, the inlet pressure of the high-pressure compressor, the outlet temperature of the high-pressure compressor, the outlet temperature of the high-pressure turbine and the speed of the low-pressure rotor.

[0104] 1. Data collection and preprocessing

[0105] Collect 1000 sets of signals from sensors at different positions when the gas turbine is working, randomly select 800 sets as training sets, and the remaining 200 sets as test set data. Each set of data contains 4 inputs ( : Inlet pressure of high pressure compressor; : outlet temperature of high pressure compressor; : outlet temperature of high pressure turbine; : High pressure rotor speed) and 1 output ( : The speed of the low-pressure rotor). Then, the expert experience knowledge is comprehensively used to construct an initial confidence rule base model, a confidence rule base parameter optimization model is established, and the model is solved using the method proposed in the present invention.

[0106] 2. Algorithm parameter settings

[0107] In step (2), the size of the initial population of each algorithm is set to 20, the scaling factor of the DE algorithm is set to a random value that conforms to the standard normal distribution, and the crossover operator is set to 0.5; the mutation probability of the GA algorithm is set to 0.7 divided by the number of decision variables. In this example, the number of decision variables is 40, and the crossover probability is set to 0.9; the step size of ACO is set to the inverse of the current number of iterations, and the transition probability is set to 0.2; the elite selection strategy of the CMA-ES algorithm is the better half of the individuals in the population; the EDA algorithm selects the better half of the individuals for estimating the probability model. The total number of iterations is set to 500 times, and the penalty compensation population dynamic reconstruction strategy is executed in the first 100 generations, and the optimal algorithm selected continues to execute in the next 400 generations.

[0108] 3. Independent evolution of each algorithm

[0109] Through step (3), different evolutionary algorithms begin to perform their respective The independent optimization operations of the generation, in this case The experiment was set to 10. The experimental results used the mean square error (MSE) as the fitness evaluation function.

[0110] 4. Dynamic reconstruction process of penalty compensation population

[0111] The penalty compensation population dynamic reconstruction strategy is executed every 10 generations until the algorithm iterates to 100 generations and the optimal algorithm is selected. Through steps (4) and (5), the sizes of the DE population are [20, 38, 50, 67, 76, 90, 90, 90, 90], the GA population sizes are [20, 20, 10, 15, 16, 6, 6, 6, 6], the ACO population sizes are [20, 18, 15, 10, 6, 6, 6, 6, 6], the JADE population sizes are [20, 28, 30, 16, 10, 6, 6, 6, 6], the CMA-ES population sizes are [20, 10, 9, 6, 6, 6, 6, 6, 6], and the EDA population sizes are [20, 6, 6, 6, 6, 6, 6, 6]. By using the penalty compensation strategy multiple times, it can be concluded from the population size of each algorithm that the DE algorithm is the optimal algorithm for solving the model in the gas turbine confidence rule base parameter optimization example.

[0112] 5. Optimal Algorithm Optimization Stage

[0113] Through step (6), the optimal algorithm is determined to be DE, and DE is used to continue the remaining 400 generations of optimization.

[0114] 6. Test set verification and comparative analysis

[0115] After the final solution is obtained through step (7), it is substituted into the test set for verification, and the error size is: 2.4618E-05. DE, GA, ACO, JADE, EDA and CMA-ES are used separately, and the other optimization operation parameters are set the same as the method. Each algorithm solves the model separately to obtain the optimal solution, and substitutes it into the test set for solution. The error sizes obtained are 2.6823E-05, 3.0484E-05, 1.7239E-04, 2.6859E-05, 9.0024E-05, and 3.3353E-05 respectively. It can be seen that the effect obtained by the method of the present invention is better than the result obtained by a single algorithm, which shows the effectiveness of the method of the present invention.

Claims

1. A confidence rule base optimization method based on dynamic reconstruction of penalty compensation population, characterized in that: The following steps are involved: Step 1: Collect sensor data at different locations of the gas turbine and establish an initial confidence rule base based on expert experience; Step 2: vectorize the parameters that need to be optimized in the confidence rule base and set the initial parameters of the six optimization algorithms; Step 3: Based on the vectorized parameters, optimize different optimization algorithms separately, merge the populations of all optimization algorithms every N generations and sort them according to the fitness values; Step 4: Calculate the fitness threshold and adjust the population size of different optimization algorithms based on the fitness value; Step 5: Merge the best individuals of all optimization algorithms to form a population sharing pool, and assign individuals in the population sharing pool to populations of different optimization algorithms according to the adjusted population size as the new generation of populations; Step 6: Repeat steps 3 to 5, select the optimization algorithm with the largest population size as the optimal algorithm, continue to optimize the optimal algorithm separately to reach the maximum number of iterations, and obtain the final solution, that is, the optimally set belief rule base parameters.

2. The confidence rule base optimization method based on dynamic reconstruction of penalty compensation population according to claim 1 is characterized in that: The six optimization algorithms include differential evolution algorithm DE, ant colony algorithm ACO, parameter estimation algorithm EDA, covariance matrix adaptive evolution algorithm CMA-ES, genetic algorithm GA, and adaptive differential evolution algorithm JADE.

3. The confidence rule base optimization method based on penalty compensation population dynamic reconstruction according to claim 2 is characterized in that: In step 3, the specific process of optimizing different optimization algorithms is as follows: DE and GA optimization process: Continuously optimize the objective function through differential mutation, crossover recombination and selection mechanisms between individuals to generate a new population of the next generation; ACO optimization process: pheromones are used to guide ants to search for paths, and in this process, the probability of state transition is constructed Distinguishing between search intensity and direction, the calculation formula is as follows: ； in Indicates Daizhongdi The fitness value of an individual, is the fitness value of the current optimal individual; The generation of new individuals is as follows: ; in is the step size factor for gradual convergence, is a uniform random number, U and L are the upper and lower bounds of the variable respectively. To control the threshold value of global search; CMA-ES optimization process: guiding the search direction by dynamically adjusting the covariance matrix; EDA optimization process: select the best individuals in the current population to estimate the probability distribution and generate new candidate solutions; The JADE optimization process is the same as the EDA optimization process. JADE introduces an adaptive parameter adjustment strategy, and the scaling factor and crossover probability of the mutation operation are adaptively adjusted.

4. The confidence rule base optimization method based on dynamic reconstruction of penalty compensation population according to claim 3 is characterized in that: The different optimization algorithms are optimized respectively, and the optimization goal is to reduce the error between the output predicted by using the confidence rule base and the actual output.

5. The confidence rule base optimization method based on penalty compensation population dynamic reconstruction according to claim 4 is characterized in that: The specific implementation process of step 4 is as follows: Step 4.1, take the median of the fitness values ​​after sorting as the threshold; Step 4.2: Adjust the population size according to the proportion of individuals below the threshold of each optimization algorithm. The specific adjustment formula is: ； in Indicates The number of populations after the optimization algorithm is adjusted. represents the sum of the populations of all optimization algorithms before adjustment, Indicates The number of individuals for which the optimization algorithm is better than the threshold; Step 4.3: Update the adjusted population size so that the population size of each optimization algorithm is not less than 6, and the total population size after update is equal to the total population size before adjustment.

6. The confidence rule base optimization method based on dynamic reconstruction of penalty compensation population according to claim 5 is characterized in that: The specific implementation process of step 4.3 is as follows: First, the vector represents the population size of different optimization algorithms, Each element of represents the number of populations assigned to different optimization algorithms after step 4.2, Q represents the number of optimization algorithms used, and the vector Perform preprocessing, change all elements in the input vector that are less than 6 to 6, and then calculate the difference in the total population size before and after the adjustment ; Finally, assign the difference, if , from all The elements of are reduced by 1 each time until , the final output The population size of all optimization algorithms remains unchanged and is at least 6.

7. The confidence rule base optimization method based on dynamic reconstruction of penalty compensation population according to claim 6 is characterized in that: The specific implementation process of step 5 is as follows: Step 5.1: For optimization algorithm, the current population size is , calculate the fitness values ​​of all individuals: Step 5.2: Sort by fitness, the first half of the individuals enter the shared pool, and build a shared pool ; Step 5.3: Shared pool All individuals in are sorted according to the size of fitness value; Step 5.4: From the sorted shared pool, assign the first Individuals, as the A new generation of population for the optimization algorithm.

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