WO2022156110A1 - 一种基于机器学习的蠕变疲劳寿命预测方法 - Google Patents

一种基于机器学习的蠕变疲劳寿命预测方法 Download PDF

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WO2022156110A1
WO2022156110A1 PCT/CN2021/096909 CN2021096909W WO2022156110A1 WO 2022156110 A1 WO2022156110 A1 WO 2022156110A1 CN 2021096909 W CN2021096909 W CN 2021096909W WO 2022156110 A1 WO2022156110 A1 WO 2022156110A1
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creep fatigue
fatigue life
particle
life
creep
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French (fr)
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王润梓
王栋铭
张显程
程吕一
李凯尚
张勇
涂善东
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华东理工大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/25—Design optimisation, verification or simulation using particle-based methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N20/00—Machine learning
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/048—Activation functions
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/04—Ageing analysis or optimisation against ageing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

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  • the invention relates to a creep fatigue life prediction method based on machine learning, and belongs to the field of material life prediction.
  • the purpose of the present invention is to provide a creep fatigue life prediction method based on machine learning, so as to realize the advantages of small error, low cost and high efficiency.
  • the present invention provides a creep fatigue life prediction method based on machine learning, including:
  • Each creep fatigue life data set includes experimental creep fatigue working condition parameters, intermediate calculation parameters and the corresponding log life of creep fatigue;
  • S2 Provide an ELM model, use the data in the training set to obtain the optimal weight matrix and optimal bias vector of the ELM model through the particle swarm optimization algorithm, and then obtain the creep fatigue life prediction model in the form of the PSO-ELM model;
  • S3 Verify the accuracy of the creep fatigue life prediction model according to the creep fatigue life data set in the test set.
  • the experimental creep fatigue working condition parameters of the step S1 include total strain range, tensile dwell time, compression dwell time and strain rate; intermediate calculation parameters include total stress amplitude, inelastic strain rate and inelastic strain energy density range .
  • the step S2 includes:
  • S21 Set the parameters of the PSO-ELM model, specifically including: setting the number of neurons in the input layer of the PSO-ELM model to be the same as the total number of categories of experimental creep fatigue parameters and intermediate calculation parameters, and the number of neurons in the output layer of the PSO-ELM model.
  • the number of neurons is set to 1; the number of neurons in the hidden layer is determined by the trial parameter method; the maximum number of iterations of the particle swarm optimization algorithm and the population size of the particles are set; the position and speed of the particles are randomly initialized;
  • S23 Use the normalized input data and output data to train the ELM model, and calculate the fitness value of the particle according to the training result.
  • the fitness value of the particle is the predicted value of the creep fatigue logarithmic life and the creep fatigue value.
  • the root mean square error of the logarithmic lifetime is determined, and the global extreme value of all particles is determined by the particle swarm optimization algorithm, and the position corresponding to the global extreme value of the particle is used as the optimal weight matrix and the optimal bias vector;
  • the root mean square error between the predicted value of the creep fatigue logarithmic life and the creep fatigue logarithmic life is:
  • m is the number of creep fatigue life data sets in the training set
  • y i is the creep fatigue logarithmic life in the training set
  • the step S23 includes:
  • S231 Use the normalized input data and output data to train the ELM model, determine the fitness value of the particle according to the training result, and then determine the initial individual extreme value of each particle and the global extreme value of all particles;
  • S233 Calculate the fitness value of the particle again, and update the individual extreme value of each particle and the global extreme value of all particles;
  • the update formula is as follows:
  • ⁇ (k) is the inertia weight at the kth iteration, is the velocity of each particle at the k-th iteration
  • c 1 and c 2 are acceleration factors, both set to 2 here
  • r 1 and r 2 are random numbers distributed between [0, 1]; is the spatial position of each particle corresponding to the individual with the best fitness in k iterations, is the spatial position of the best fitness corresponding to all particles in k iterations; is the spatial position of each particle at the k-th iteration, is the spatial position of each particle at the k+1th iteration; k is a positive integer;
  • the inertia weight ⁇ (k) is obtained directly by the following formula:
  • ⁇ (k) ⁇ 1 -( ⁇ 1 - ⁇ 2 ) ⁇ k/T max ,
  • ⁇ (k) is the inertia weight of each iteration
  • k is the current iteration number
  • T max is the maximum iteration number
  • ⁇ (k) ⁇ 1 -( ⁇ 1 - ⁇ 2 ) ⁇ k/T max ,
  • ⁇ (k) is the inertia weight of each iteration
  • k is the current iteration number
  • T max is the maximum iteration number.
  • the ELM model uses the Sigmoid function as the activation function.
  • the step S3 includes: taking the experimental creep fatigue working condition parameters and the intermediate calculation parameters in the test set together as the input data of the creep fatigue life prediction model, and using the obtained creep fatigue life prediction model to predict the input data, and the corresponding creep fatigue life prediction model is used to predict the input data.
  • the corresponding creep fatigue logarithmic life is compared, and the mean absolute percentage error and determination coefficient R 2 of the creep fatigue life prediction model in the test set are calculated to verify the accuracy of the model.
  • the mean absolute percentage error is:
  • the coefficient of determination R2 is:
  • n test is the number of creep fatigue life data sets in the test set
  • yi is the creep fatigue logarithmic life in the test set
  • yi is the creep fatigue logarithmic life predicted by the creep fatigue life prediction model
  • n test is the number of creep fatigue life data sets in the test set
  • the present invention adopts the above technical scheme, uses the PSO algorithm to optimize the weight matrix and bias vector of the ELM model, and takes the experimental creep fatigue working condition parameters, total stress amplitude, inelastic strain rate, and inelastic strain energy density range as the variation
  • the input data of the PSO-ELM model is used to predict the corresponding logarithmic life of creep fatigue, which has the advantages of small error, low cost and high efficiency.
  • the particles can jump out of the currently searched optimal solution position with a certain probability, and carry out the search in a larger space, thereby improving the possibility of the algorithm finding the optimal solution.
  • FIG. 1 is a flowchart of a method for predicting creep fatigue life based on machine learning according to an embodiment of the present invention
  • Fig. 2 is the schematic flow chart of the obtained PSO-ELM model of the creep fatigue life prediction method based on machine learning of the present invention
  • FIG. 3 is a comparison diagram of the predicted creep fatigue life based on the variation PSO-ELM model and the corresponding actual creep fatigue life in the test set of the machine learning-based creep fatigue life prediction method of the present invention, wherein the implicit ELM model The number of neurons in the layer is set to 10.
  • the creep fatigue life prediction method based on machine learning of the present invention is specifically based on the PSO (particle swarm optimization)-ELM (extreme learning machine) model training and prediction based on the variation of the creep fatigue logarithmic life of 224 groups of nickel-based superalloys. method.
  • the original creep fatigue life data set is randomly divided into a training set consisting of 156 sets of data and a test set consisting of 68 sets of data, the training set is used to train the variant PSO-ELM model, and then the The input data of the test set is input into the mutated PSO-ELM model after training, and the corresponding predicted value is obtained, and the predicted value is compared with the logarithmic output value of the test set to verify the accuracy of the mutated PSO-ELM model.
  • the creep fatigue life prediction method of the present invention includes the following steps:
  • Step S1 Acquire a plurality of creep fatigue life data sets to be predicted, and randomly divide them into 70% training set and 30% test set, each of which includes experimental creep fatigue life data sets.
  • Condition parameters (4 in number, including total strain range, tensile holding time, compressive holding time and strain rate), intermediate calculation parameters (3 in number, including total stress amplitude, inelastic strain rate, Elastic strain energy density range) and the corresponding creep fatigue logarithmic life 8 characteristics;
  • the parameters of experimental creep fatigue condition are artificially set before the experiment; the total stress amplitude is obtained by subtracting the valley stress from the peak stress, and the inelastic strain rate is obtained by dividing the stress relaxation during the holding period by the holding time.
  • the range of elastic strain energy density is the area of the half-life hysteresis loop; the logarithmic life of creep fatigue is obtained by experimentally determining the life of the material to be tested and taking the logarithm.
  • the logarithmic life of creep fatigue is in Experiments on MTS809A/T universal testing machine.
  • Step S2 Provide an extreme learning machine (ELM) model, use the data in the training set to obtain the optimal weight matrix and the optimal bias vector of the ELM model through the mutated particle swarm optimization (PSO) algorithm, and then obtain the form of PSO-ELM Creep fatigue life prediction model of the model;
  • ELM extreme learning machine
  • PSO mutated particle swarm optimization
  • the weight matrix and bias vector of the ELM model are used as the position of the particles in the variant PSO algorithm, the predicted value of the ELM model (that is, the predicted value of the creep fatigue logarithmic life) and the actual value (that is, the creep fatigue pair obtained in step S1).
  • the root mean square error between the number of lifetimes) is the fitness value of the particle, so the optimal weight matrix and optimal bias vector of the ELM model are obtained through the mutation particle swarm optimization algorithm.
  • the particles can jump out of the currently searched optimal solution position with a certain probability, and carry out the search in a larger space, thereby improving the possibility of the PSO algorithm finding the optimal solution sex.
  • step S2 specifically includes:
  • Step S21 Initialize the parameters of the PSO-ELM model; in this embodiment, the PSO algorithm is mutated, so the PSO-ELM model is a mutated PSO-ELM model.
  • Step S21 specifically includes: setting the number of neurons in the input layer of the PSO-ELM model to be the same as the total number of categories of experimental creep fatigue parameters and intermediate calculation parameters (that is, the number of neurons is set to 7), and the output
  • the number of neurons in the layer is set to 1 (corresponding to the logarithmic life of creep fatigue);
  • the number of neurons in the hidden layer is determined by the trial parameter method, that is, between 5, 10, 15, 20 four values Experiments were carried out, and the results showed that when the number is 10, the root mean square error of the model is the smallest, so in this embodiment, the number of neurons in the hidden layer is 10;
  • the Sigmoid function is selected as the activation function of the ELM model; the maximum value of the PSO algorithm is selected.
  • the number of iterations is set to 500, and the population size of the particles in the PSO algorithm is set to 20; the position and velocity of the particles are randomly initialized;
  • Step S22 The experimental creep fatigue condition parameters in the training set and the intermediate calculation parameters (ie total stress amplitude, inelastic strain rate, inelastic strain energy density range) are taken together as input data, and the corresponding creep in the training set is used as input data. Fatigue logarithmic life as output data; all data (i.e. input data and output data) are normalized;
  • the normalization operation can prevent input variables with different physical meanings and dimensions from being used equally, prevent the absolute value of the input data from being too large, and ensure that the small values in the output data are not "swallowed"; the normalization operation requires Used before training the model.
  • the normalized input data and output data are:
  • x is the normalized input data or output data
  • x old is the input data or output data before normalization
  • x min is the minimum value of the input data or output data before normalization
  • x max is the normalized input data or output data The maximum value of input data or output data before normalization.
  • the input data here refers to any one-dimensional variable in the experimental creep fatigue working condition parameters and intermediate calculation parameters described above
  • the output data refers to the creep fatigue logarithmic life, which has the same meaning as above. .
  • Step S23 Use the normalized input data and output data to train the ELM model, and calculate the fitness value of the particle according to the training result.
  • the fitness value of the particle is the predicted value of the creep fatigue logarithmic life and the real The root mean square error of the logarithmic life of creep fatigue, and the global extreme value of all particles is determined by the PSO algorithm, and the position corresponding to the global extreme value of the particle is used as the optimal weight matrix and optimal bias vector of the ELM model. ;
  • the obtained training result is the predicted value of the logarithmic life of creep fatigue.
  • the root mean square error (RMSE) between the predicted value of the creep fatigue log life and the actual creep fatigue log life is:
  • m is the number of creep fatigue life data sets in the training set
  • y i is the real creep fatigue logarithmic life in the training set
  • the step S23 specifically includes:
  • Step S231 use the normalized input data and output data to train the ELM model, determine the fitness value of the particle according to the training result, and then determine the initial individual extreme value of each particle and the global extreme value of all particles;
  • the initial individual extreme value of each particle is its own fitness value
  • the initial global extreme value of all particles is the particle with the best fitness (that is, the smallest fitness value) among all particles (set to 20 here).
  • the indicated fitness value because the fitness value is the root mean square error (RMSE), the smaller the error, the better, so the particle with the smallest fitness value can be described as the particle with the best fitness among all the particles.
  • RMSE root mean square error
  • Step S232 the number of iterations of the particle is increased by one, and the PSO algorithm is used to update the position and velocity of the particle;
  • the update formula is as follows:
  • ⁇ (k) is the inertia weight at the kth iteration, is the velocity of each particle at the k-th iteration
  • c 1 and c 2 are acceleration factors, both set to 2 here
  • r 1 and r 2 are random numbers distributed between [0, 1]; is the spatial position of each particle corresponding to the individual with the best fitness in k iterations, called the individual extreme value, is the spatial position of the best fitness corresponding to all particles in k iterations, which is called the global extremum; is the spatial position of each particle at the k-th iteration, is the spatial position of each particle at the k+1th iteration; k is a positive integer.
  • ⁇ (k) is the inertia weight of each iteration
  • k is the current iteration number
  • T max is the maximum iteration number.
  • a mutation operation is also performed on the PSO algorithm, specifically: in each round of iteration, a random number is set in the range of [0, 1), if the random number is greater than 0.9, the The ⁇ (k) of this iteration is set to the random number; otherwise, the inertia weight ⁇ (k) of each iteration of the PSO algorithm is obtained according to formula (5).
  • This setting allows the particles to jump out of the currently searched optimal solution position with a certain probability, and carry out the search in a larger space, thereby improving the possibility of the algorithm finding the optimal solution.
  • Step S233 Calculate the fitness value of the particle again, and update the individual extreme value of each particle and the global extreme value of all particles;
  • the position of each particle will be updated once per iteration, and the fitness value is calculated once; then by comparing the k+1th iteration of each new particle The fitness value and the fitness value of the individual extremum of each particle and the global extremum of all particles determined by the first k iterations, if the fitness value of the new particle after the k+1th iteration is better than the previous k If the individual extreme value of the particle determined in the next iteration, the individual extreme value of the particle is updated, otherwise it will not be updated; if after the k+1th iteration, there is a particle whose fitness value is better than all the values determined by the previous k iterations If the global extremum of the particle is set, the global extremum of the group will be updated, otherwise it will not be updated.
  • Step S234 Repeat steps S232 and S233 (one round of iteration is performed by performing steps S232 and S233) until the number of iterations satisfies the preset maximum number of iterations T max , and the obtained global extreme values of all particles correspond to The position of is the optimal weight matrix and the optimal bias vector, and step S24 is performed at this time.
  • Step S24 setting the optimal weight matrix as the weight matrix of the ELM model, and setting the optimal bias vector as the bias vector of the ELM model, thereby obtaining a creep fatigue life prediction model.
  • Step S3 Verify the accuracy of the established creep fatigue life prediction model according to the creep fatigue life data set in the test set.
  • Step S3 specifically includes: taking the experimental creep fatigue working condition parameters and the intermediate calculation parameters in the test set together as the input data of the creep fatigue life prediction model, and using the obtained creep fatigue life prediction model to predict the input data, corresponding to
  • the mean absolute percentage error (MAPE) and coefficient of determination R 2 of the variation PSO-ELM model in the test set are calculated to verify the accuracy of the model;
  • the mathematical expression of the mean absolute percentage error (MAPE) is is Equation (6)
  • the mathematical expression of the coefficient of determination R 2 is Equation (7):
  • ntest is the number of creep fatigue life data sets in the test set
  • yi is the real creep fatigue logarithmic life in the test set
  • yi is the creep fatigue logarithmic life predicted by the creep fatigue life prediction model
  • ntest is the number of creep fatigue life data sets in the test set
  • yi is the real creep fatigue logarithmic life in the test set
  • yi is the creep fatigue logarithmic life predicted by the creep fatigue life prediction model
  • Figure 3 is a comparison diagram of the predicted creep fatigue logarithmic life based on the variant PSO-ELM model and the corresponding actual creep fatigue logarithmic life when the number of neurons in the hidden layer of the ELM model is set to 10.
  • the prediction accuracy is reflected in the mean absolute percentage error (MAPE) of the logarithmic life and the coefficient of determination R2.
  • MAPE mean absolute percentage error
  • R2 the coefficient of determination

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Abstract

提供了一种基于机器学习的蠕变疲劳寿命预测方法，包括：获取待预测的蠕变疲劳寿命数据组，分为训练集和测试集，每一个蠕变疲劳寿命数据组均包括实验蠕变疲劳工况参数、中间计算参数和相对应的蠕变疲劳对数寿命(S1)；提供ELM模型，利用训练集中的数据通过粒子群优化算法得到ELM模型的最优权重矩阵、最优偏置向量，进而得到蠕变疲劳寿命预测模型(S2)；根据测试集中的蠕变疲劳寿命数据组对所述蠕变疲劳寿命预测模型的精度进行验证(S3)。弥补了传统方法在预测蠕变疲劳寿命时精度低、成本高的不足，可充分利用变异PSO算法优化ELM模型权重矩阵和偏置向量的优势，具有误差小、成本低、效率高的优点。

Description

一种基于机器学习的蠕变疲劳寿命预测方法 技术领域
本发明涉及一种基于机器学习的蠕变疲劳寿命预测方法，属于材料寿命预测领域。
背景技术
现代超超临界发电机组、燃气机、航空发动机等设备的工作环境越来越复杂。除了装置稳态运行的恒定负荷外，关键的限寿部件还承受着装置启停和温度波动等因素引起的交变载荷作用。其服役过程伴随着严重的蠕变-疲劳相互作用，这对构件寿命设计和预测方法提出了新的挑战。
虽然高温合金的蠕变疲劳寿命可以通过实验方法确定，但由于长期蠕变试验和昂贵合金制造，需要大量的时间成本和实验成本。尽管目前存在几种加速预测合金蠕变疲劳寿命的理论方法，如时间-温度参数法，但其缺乏严格的理论依据，且没有充分考虑蠕变疲劳过程中的微观组织演化信息。
近年来，数据驱动的机器学习方法已成功应用于材料性能预测、新材料发现或其他目的中，并在时间效率和预测性能方面具有显著的优势。基于此，期望获得一种新的蠕变疲劳寿命预测方法，以实现较高的计算效率和较低的时间成本，较为准确地预测高温合金的蠕变疲劳寿命。
发明内容
本发明的目的在于提供一种基于机器学习的蠕变疲劳寿命预测方法，以实现误差小、成本低、效率高的优点。
为了实现上述目的，本发明提供一种基于机器学习的蠕变疲劳寿命预测方法，包括：
S1：获取待预测的蠕变疲劳寿命数据组，将其随机分为70％的训练集和30％的测试集，每一个蠕变疲劳寿命数据组均包括实验蠕变疲劳工况参数、中间计算参数和相对应的蠕变疲劳对数寿命；
S2：提供一ELM模型，利用训练集中的数据通过粒子群优化算法得到ELM模型的最优权重矩阵、最优偏置向量，进而得到形式为PSO-ELM模型的蠕变疲劳寿命预测模型；
S3：根据测试集中的蠕变疲劳寿命数据组对所述蠕变疲劳寿命预测模型的精度进行验证。
所述步骤S1的实验蠕变疲劳工况参数包括总应变范围、拉伸保载时间、压缩保载时间和应变速率；中间计算参数包括总应力幅、非弹性应变率和非弹性应变能密度范围。
所述步骤S2包括：
S21：设置PSO-ELM模型的参数，具体包括：将PSO-ELM模型的输入层的神经元个数设置为与实验蠕变疲劳工况参数和中间计算参数的总类别数相同，其输出层的神经元个数设置为1；通过试参法确定其隐藏层的神经元的个数；设置粒子群优化算法的最大迭代次数和粒子的种群规模；随机初始化粒子的位置和速度；
S22：将训练集中的实验蠕变疲劳工况参数和中间计算参数共同作为输入数据，将训练集中的相对应的蠕变疲劳对数寿命作为输出数据；对输入数据和输出数据均进行归一化操作；
S23：利用归一化后的输入数据和输出数据对ELM模型进行训练，并根据训练结果来计算粒子的适应度值，粒子的适应度值为蠕变疲劳对数寿命的预测值与蠕变疲劳对数寿命的均方根误差，并通过粒子群优化算法确定所有粒子的全局极值，将粒子的全局极值所对应的位置作为所述最优权重矩阵和最优偏置向量；
S24：将所述最优权重矩阵设置为所述ELM模型的权重矩阵，将所述最优偏置向量设置为所述ELM模型的偏置向量，进而得到蠕变疲劳寿命预测模型。
所述蠕变疲劳对数寿命的预测值与蠕变疲劳对数寿命的均方根误差为：
Figure PCTCN2021096909-appb-000001
其中，m为训练集中的蠕变疲劳寿命数据组的个数，y i为训练集中的蠕变疲劳对数寿命，
Figure PCTCN2021096909-appb-000002
为蠕变疲劳对数寿命的预测值。
所述步骤S23包括：
S231：利用归一化后的输入数据和输出数据对ELM模型进行训练，根 据训练结果确定粒子的适应度值，进而确定初始的每个粒子的个体极值和所有粒子的全局极值；
S232：粒子的迭代次数加一，并使用粒子群优化算法对粒子的位置和速度进行更新；
S233：再次计算粒子的适应度值，更新每个粒子的个体极值和所有粒子的全局极值；
S234：重复所述步骤S232和步骤S233，直到迭代次数满足预设的最大迭代次数T max，所得到的所有粒子的全局极值所对应的位置为最优权重矩阵和最优偏置向量。
在所述步骤S232中，更新公式如下：
Figure PCTCN2021096909-appb-000003
Figure PCTCN2021096909-appb-000004
其中，
Figure PCTCN2021096909-appb-000005
是每个粒子第k+1次迭代时的速度，ω(k)是第k次迭代时的惯性权重，
Figure PCTCN2021096909-appb-000006
是每个粒子第k次迭代时的速度；c 1和c 2是加速度因子，这里均设置为2；r 1和r 2是分布在[0，1]之间的随机数；
Figure PCTCN2021096909-appb-000007
是每个粒子在k次迭代中对应适应度最佳的个体的空间位置，
Figure PCTCN2021096909-appb-000008
是所有粒子在k次迭代中对应的适应度最佳的空间位置；
Figure PCTCN2021096909-appb-000009
是每个粒子第k次迭代时的空间位置，
Figure PCTCN2021096909-appb-000010
是每个粒子第k+1次迭代时的空间位置；k为正整数；
优选地，直接通过以下公式来获得所述惯性权重ω(k)：
ω(k)＝ω 1-(ω 1-ω 2)×k/T max，
其中，ω(k)为每次迭代的惯性权重，ω 1＝0.9为初始惯性权重，ω 2＝0.4为最终惯性权重，k为当前迭代次数，T max为最大迭代次数；
或者，在每一轮迭代中，在[0,1)范围内设置一个随机数，如果该随机数大于0.9，则将该次迭代的惯性权重ω(k)设置为该随机数；否则，通过以下公式来获得所述惯性权重ω(k)：
ω(k)＝ω 1-(ω 1-ω 2)×k/T max，
其中，ω(k)为每次迭代的惯性权重，ω 1＝0.9为初始惯性权重，ω 2＝0.4为最终惯性权重，k为当前迭代次数，T max为最大迭代次数。
所述ELM模型采用Sigmoid函数作为激活函数。
所述步骤S3包括：将测试集中的实验蠕变疲劳工况参数和中间计算参数共同作为蠕变疲劳寿命预测模型的输入数据，利用得到的蠕变疲劳寿命预测模型对输入数据进行预测，与相对应的蠕变疲劳对数寿命进行比较，计算蠕变疲劳寿命预测模型在测试集中的平均绝对百分比误差和决定系数R 2，验证模型的精度。
优选地，所述平均绝对百分比误差为：
Figure PCTCN2021096909-appb-000011
决定系数R 2为：
Figure PCTCN2021096909-appb-000012
其中，n test为测试集中的蠕变疲劳寿命数据组的个数，y i为测试集中的蠕变疲劳对数寿命，
Figure PCTCN2021096909-appb-000013
为蠕变疲劳寿命预测模型预测的蠕变疲劳对数寿命，
Figure PCTCN2021096909-appb-000014
为测试集中的所有蠕变疲劳寿命数据组中的蠕变疲劳对数寿命的平均值。
本发明采用以上技术方案，利用PSO算法对ELM模型的权重矩阵和偏置向量进行优化，将实验蠕变疲劳工况参数、总应力幅、非弹性应变率、非弹性应变能密度范围共同作为变异PSO-ELM模型的输入数据，以预测相对应的蠕变疲劳对数寿命，具有误差小、成本低、效率高的优点。此外，PSO算法经过变异，可以让粒子以一定的概率跳出当前搜索到的最优解位置，在更大的空间中开展搜索，从而提高算法寻找到最优解的可能性。
附图说明
图1为根据本发明的一个实施例的一种基于机器学习的蠕变疲劳寿命预测方法的流程图；
图2为本发明的基于机器学习的蠕变疲劳寿命预测方法的所得到的PSO-ELM模型的流程示意图；
图3为本发明的基于机器学习的蠕变疲劳寿命预测方法的测试集中的基于变异PSO-ELM模型的预测蠕变疲劳寿命和相对应的实际蠕变疲劳寿命 的对比图，其中ELM模型的隐含层神经元个数设置为10。
具体实施方式
本发明的基于机器学习的蠕变疲劳寿命预测方法具体是基于224组镍基高温合金的蠕变疲劳对数寿命进行变异的PSO(粒子群优化)-ELM(极限学习机)模型训练和预测的方法。本实施例基于MATLAB软件平台，将原始的蠕变疲劳寿命数据组随机分为156组数据组成的训练集和68组数据组成的测试集，利用训练集对变异PSO-ELM模型进行训练，随后将测试集的输入数据输入到训练完成后的变异PSO-ELM模型，得到相对应的预测值，将预测值与测试集的对数输出值进行比较，验证变异PSO-ELM模型的精度。
请参阅图1，本发明的蠕变疲劳寿命预测方法，其包括以下步骤：
步骤S1：获取多个待预测的蠕变疲劳寿命数据组，将其随机分为70％的训练集和30％的测试集，每一个所述蠕变疲劳寿命数据组均包括实验蠕变疲劳工况参数(其数量为4个，包括总应变范围、拉伸保载时间、压缩保载时间和应变速率)、中间计算参数(其数量为3个，包括总应力幅、非弹性应变率、非弹性应变能密度范围)和相对应的蠕变疲劳对数寿命8个特征；
其中，实验蠕变疲劳工况参数是在做实验前人为设定的；总应力幅通过峰值应力减谷值应力得到，非弹性应变率通过保载期间的应力松弛除以保载时间得到，非弹性应变能密度范围是半寿命滞后回线的面积；蠕变疲劳对数寿命则通过实验确定待测材料的寿命并取对数来得到，在本实施例中，蠕变疲劳对数寿命是在MTS809A/T万能试验机上实验得到的。
步骤S2：提供一极限学习机(ELM)模型，利用训练集中的数据通过变异的粒子群优化(PSO)算法得到ELM模型的最优权重矩阵、最优偏置向量，进而得到形式为PSO-ELM模型的蠕变疲劳寿命预测模型；
其中，ELM模型的权重矩阵和偏置向量作为变异PSO算法中粒子的位置，ELM模型的预测值(即蠕变疲劳对数寿命的预测值)和实际值(即步骤S1获取的蠕变疲劳对数寿命)之间的均方根误差就是粒子的适应度值，从而通过变异粒子群优化算法得到ELM模型的最优权重矩阵、最优偏置向量。在本实施例中，由于PSO算法经过变异，因此可以让粒子以一定的概率跳出当 前搜索到的最优解位置，在更大的空间中开展搜索，从而提高PSO算法寻找到最优解的可能性。
如图2所示，所述步骤S2具体包括：
步骤S21：初始化PSO-ELM模型的参数；在本实施例中，PSO算法经过变异，因此所述PSO-ELM模型是变异PSO-ELM模型。
步骤S21具体包括：将PSO-ELM模型的输入层的神经元个数设置为与实验蠕变疲劳工况参数和中间计算参数的总类别数相同(即神经元个数设置为7)，其输出层的神经元个数设置为1(对应于蠕变疲劳对数寿命)；通过试参法确定其隐藏层的神经元的个数，即，在5、10、15、20四个数值之间进行试验，结果表明个数为10时，模型的均方根误差最小，因此在本实施例中隐藏层神经元的个数为10；选择Sigmoid函数作为ELM模型的激活函数；将PSO算法的最大迭代次数设置为500，PSO算法中粒子的种群规模设置为20；随机初始化粒子的位置和速度；
步骤S22：将训练集中的实验蠕变疲劳工况参数和中间计算参数(即总应力幅、非弹性应变率、非弹性应变能密度范围)共同作为输入数据，将训练集中的相对应的蠕变疲劳对数寿命作为输出数据；对所有数据(即输入数据和输出数据)均进行归一化操作；
其中，归一化操作可以避免具有不同物理意义和量纲的输入变量不能平等使用，防止输入数据的绝对值过大，保证输出数据中数值小的不被“吞食”；该归一化操作需要在对模型进行训练之前使用。
归一化后的输入数据和输出数据为：
Figure PCTCN2021096909-appb-000015
其中，x是归一化后的输入数据或输出数据，x old是归一化前的输入数据或输出数据，x min是归一化前的输入数据或输出数据的最小值，x max是归一化前的输入数据或输出数据的最大值。其中，这里的输入数据指的是上文所述的实验蠕变疲劳工况参数和中间计算参数中的任意一维变量，输出数据指的是蠕变疲劳对数寿命，其含义与上文相同。
步骤S23：利用归一化后的输入数据和输出数据对ELM模型进行训练， 并根据训练结果来计算粒子的适应度值，粒子的适应度值为蠕变疲劳对数寿命的预测值与真实的蠕变疲劳对数寿命的均方根误差，并通过PSO算法确定所有粒子的全局极值，将粒子的全局极值所对应的位置作为所述ELM模型的最优权重矩阵和最优偏置向量；
在本实施例中，得到的训练结果为蠕变疲劳对数寿命的预测值。
蠕变疲劳对数寿命的预测值与真实的蠕变疲劳对数寿命的均方根误差(RMSE)为：
Figure PCTCN2021096909-appb-000016
其中，m为训练集中的蠕变疲劳寿命数据组的个数，y i为训练集中的真实的蠕变疲劳对数寿命；
Figure PCTCN2021096909-appb-000017
为蠕变疲劳对数寿命的预测值，也就是上文所述的PSO-ELM模型根据输入数据所预测得到的输出结果。
所述步骤S23具体包括：
步骤S231：利用归一化后的输入数据和输出数据对ELM模型进行训练，根据训练结果确定粒子的适应度值，进而确定初始的每个粒子的个体极值和所有粒子的全局极值；
其中，初始的每个粒子的个体极值就是它自身的适应度值，初始的所有粒子的全局极值就是所有粒子(这里设置为20)中适应度最佳(即适应度值最小)的粒子所表示的适应度值。因为适应度值就是均方根误差(RMSE)，误差要越小越好，所以适应度值最小的粒子可以描述为所有粒子中适应度最佳的粒子。
步骤S232：粒子的迭代次数加一，并使用PSO算法对粒子的位置和速度进行更新；
在所述步骤S232中，更新公式如下：
Figure PCTCN2021096909-appb-000018
Figure PCTCN2021096909-appb-000019
其中，
Figure PCTCN2021096909-appb-000020
是每个粒子第k+1次迭代时的速度，ω(k)是第k次迭代时的惯性权重，
Figure PCTCN2021096909-appb-000021
是每个粒子第k次迭代时的速度；c 1和c 2是加速度因子，这里均设置为2；r 1和r 2是分布在[0，1]之间的随机数；
Figure PCTCN2021096909-appb-000022
是每个粒子在k次迭代中对 应适应度最佳的个体的空间位置，称为个体极值，
Figure PCTCN2021096909-appb-000023
是所有粒子在k次迭代中对应的适应度最佳的空间位置，称为全局极值；
Figure PCTCN2021096909-appb-000024
是每个粒子第k次迭代时的空间位置，
Figure PCTCN2021096909-appb-000025
是每个粒子第k+1次迭代时的空间位置；k为正整数。
在每一轮迭代中，根据公式(5)来获得PSO算法每次迭代的惯性权重ω(k)：
ω(k)＝ω 1-(ω 1-ω 2)×k/T max         (5)
其中，ω(k)为每次迭代的惯性权重，ω 1＝0.9为初始惯性权重，ω 2＝0.4为最终惯性权重，k为当前迭代次数，T max为最大迭代次数。
优选地，在所述步骤S232中，还对PSO算法进行变异操作，具体为：在每一轮迭代中，在[0,1)范围内设置一个随机数，如果该随机数大于0.9，则将该次迭代的ω(k)设置为该随机数；否则，则根据公式(5)来获得PSO算法每次迭代的惯性权重ω(k)。这样设置可以让粒子以一定的概率跳出当前搜索到的最优解位置，在更大的空间中开展搜索，从而提高算法寻找到最优解的可能性。
步骤S233：再次计算粒子的适应度值，更新每个粒子的个体极值和所有粒子的全局极值；
具体来说，经过第k+1次迭代后，每个粒子每次迭代就会更新一次位置，就要计算一次适应度值；然后通过比较经过第k+1次迭代后的每个新粒子的适应度值和前k次迭代确定的每个粒子各自的个体极值和所有粒子的全局极值的适应度值，如果经过第k+1次迭代后的新粒子的适应度值优于前k次迭代确定的该粒子的个体极值，则更新该粒子的个体极值，否则就不更新；如果经过第k+1次迭代后存在一个粒子的适应度值优于前k次迭代确定的所有粒子的全局极值，则更新该群体的全局极值，否则就不更新。
步骤S234：重复所述步骤S232和步骤S233(进行一次步骤S232和步骤S233就是进行一轮迭代)，直到迭代次数满足预设的最大迭代次数T max，所得到的所有粒子的全局极值所对应的位置为最优权重矩阵和最优偏置向量，此时进行步骤S24。
步骤S24：将最优权重矩阵设置为所述ELM模型的权重矩阵，将最优偏置向量设置为所述ELM模型的偏置向量，进而得到蠕变疲劳寿命预测模型。
步骤S3：根据测试集中的蠕变疲劳寿命数据组对建立的蠕变疲劳寿命预测模型的精度进行验证。
步骤S3具体包括：将测试集中的实验蠕变疲劳工况参数和中间计算参数共同作为蠕变疲劳寿命预测模型的输入数据，利用得到的蠕变疲劳寿命预测模型对输入数据进行预测，与相对应的蠕变疲劳对数寿命进行比较，计算变异PSO-ELM模型在测试集中的平均绝对百分比误差(MAPE)和决定系数R 2，验证模型的精度；其中平均绝对百分比误差(MAPE)的数学表达式为公式(6)，决定系数R 2的数学表达式为公式(7)：
Figure PCTCN2021096909-appb-000026
Figure PCTCN2021096909-appb-000027
其中，ntest为测试集中的蠕变疲劳寿命数据组的个数，yi为测试集中真实的蠕变疲劳对数寿命，
Figure PCTCN2021096909-appb-000028
为蠕变疲劳寿命预测模型预测的蠕变疲劳对数寿命，
Figure PCTCN2021096909-appb-000029
为测试集中的所有蠕变疲劳寿命数据组中的蠕变疲劳对数寿命的平均值。
实验结果：
通过本实施例，能够获得如下预测结果：
图3为ELM模型的隐含层神经元个数设置为10时，基于变异PSO-ELM模型的预测的蠕变疲劳对数寿命和相对应的实际的蠕变疲劳对数寿命的对比图。预测精度以对数寿命的平均绝对百分比误差(MAPE)和决定系数R 2体现，经计算，模型预测的蠕变疲劳对数寿命和实际蠕变疲劳对数寿命的MAPE为1.61％，R 2为0.9855。另外，由图3可见，变异PSO-ELM模型预测的蠕变疲劳对数寿命点大部分落在1.5倍误差带之内，且全部寿命点均落在2倍误差带之内，预测效果较好。
以上记载的，仅为本发明的较佳实施例，并非用以限定本发明的范围，本发明的上述实施例还可以做出各种变化。即凡是依据本发明申请的权利要求书及说明书内容所作的简单、等效变化与修饰，皆落入本发明专利的权利要求保护范围。

Claims (10)

  1. 一种基于机器学习的蠕变疲劳寿命预测方法，其特征在于，包括：
    步骤S1：获取待预测的蠕变疲劳寿命数据组，将其随机分为70％的训练集和30％的测试集，每一个蠕变疲劳寿命数据组均包括实验蠕变疲劳工况参数、中间计算参数和相对应的蠕变疲劳对数寿命；
    步骤S2：提供一极限学习机模型，利用训练集中的数据通过粒子群优化算法得到极限学习机模型的最优权重矩阵、最优偏置向量，进而得到形式为PSO-ELM模型的蠕变疲劳寿命预测模型；
    步骤S3：根据测试集中的蠕变疲劳寿命数据组对所述蠕变疲劳寿命预测模型的精度进行验证。
  2. 根据权利要求1所述的一种基于机器学习的蠕变疲劳寿命预测方法，其特征在于，所述步骤S1的实验蠕变疲劳工况参数包括总应变范围、拉伸保载时间、压缩保载时间和应变速率；中间计算参数包括总应力幅、非弹性应变率和非弹性应变能密度范围。
  3. 根据权利要求1所述的一种基于机器学习的蠕变疲劳寿命预测方法，其特征在于，所述步骤S2包括：
    步骤S21：初始化PSO-ELM模型的参数，具体包括：将PSO-ELM模型的输入层的神经元个数设置为与实验蠕变疲劳工况参数和中间计算参数的总类别数相同，其输出层的神经元个数设置为1；通过试参法确定其隐藏层的神经元的个数；设置粒子群优化算法的最大迭代次数和粒子的种群规模；随机初始化粒子的位置和速度；
    步骤S22：将训练集中的实验蠕变疲劳工况参数和中间计算参数共同作为输入数据，将训练集中的相对应的蠕变疲劳对数寿命作为输出数据；对输入数据和输出数据均进行归一化操作；
    步骤S23：利用归一化后的输入数据和输出数据对极限学习机模型进行训练，并根据训练结果来计算粒子的适应度值，粒子的适应度值为蠕变疲劳对数寿命的预测值与蠕变疲劳对数寿命的均方根误差，并通过粒子群优化算法 确定所有粒子的全局极值，将粒子的全局极值所对应的位置作为所述最优权重矩阵和最优偏置向量；
    步骤S24：将所述最优权重矩阵设置为所述极限学习机模型的权重矩阵，将所述最优偏置向量设置为所述极限学习机模型的偏置向量，进而得到蠕变疲劳寿命预测模型。
  4. 根据权利要求3所述的一种基于机器学习的蠕变疲劳寿命预测方法，其特征在于，所述蠕变疲劳对数寿命的预测值与蠕变疲劳对数寿命的均方根误差为：
    Figure PCTCN2021096909-appb-100001
    其中，m为训练集中的蠕变疲劳寿命数据组的个数，y i为训练集中的蠕变疲劳对数寿命，
    Figure PCTCN2021096909-appb-100002
    为为蠕变疲劳对数寿命的预测值。
  5. 根据权利要求3所述的一种基于机器学习的蠕变疲劳寿命预测方法，其特征在于，所述步骤S23包括：
    步骤S231：利用归一化后的输入数据和输出数据对极限学习机模型进行训练，根据训练结果确定粒子的适应度值，进而确定初始的每个粒子的个体极值和所有粒子的全局极值；
    步骤S232：粒子的迭代次数加一，并使用粒子群优化算法对粒子的位置和速度进行更新；
    步骤S233：再次计算粒子的适应度值，更新每个粒子的个体极值和所有粒子的全局极值；
    步骤S234：重复所述步骤S232和步骤S233，直到迭代次数满足预设的最大迭代次数T max，所得到的所有粒子的全局极值所对应的位置为最优权重矩阵和最优偏置向量。
  6. 根据权利要求5所述的一种基于机器学习的蠕变疲劳寿命预测方法，其特征在于，在所述步骤S232中，更新公式如下：
    Figure PCTCN2021096909-appb-100003
    Figure PCTCN2021096909-appb-100004
    其中，
    Figure PCTCN2021096909-appb-100005
    是每个粒子第k+1次迭代时的速度，ω(k)是第k次迭代时的惯 性权重，
    Figure PCTCN2021096909-appb-100006
    是每个粒子第k次迭代时的速度；c 1和c 2是加速度因子，这里均设置为2；r 1和r 2是分布在[0，1]之间的随机数；
    Figure PCTCN2021096909-appb-100007
    是每个粒子在k次迭代中对应的适应度最佳的个体的空间位置，
    Figure PCTCN2021096909-appb-100008
    是所有粒子在k次迭代中对应的适应度最佳的空间位置；
    Figure PCTCN2021096909-appb-100009
    是每个粒子第k次迭代时的空间位置，
    Figure PCTCN2021096909-appb-100010
    是每个粒子第k+1次迭代时的空间位置；k为正整数；
  7. 根据权利要求6所述的一种基于机器学习的蠕变疲劳寿命预测方法，其特征在于，直接通过以下公式来获得所述惯性权重ω(k)：
    ω(k)＝ω 1-(ω 1-ω 2)×k/T max，
    其中，ω(k)为每次迭代的惯性权重，ω 1＝0.9为初始惯性权重，ω 2＝0.4为最终惯性权重，k为当前迭代次数，T max为最大迭代次数；
    或者，在每一轮迭代中，在[0,1)范围内设置一个随机数，如果该随机数大于0.9，则将该次迭代的惯性权重ω(k)设置为该随机数；否则，通过以下公式来获得所述惯性权重ω(k)：
    ω(k)＝ω 1-(ω 1-ω 2)×k/T max，
    其中，ω(k)为每次迭代的惯性权重，ω 1＝0.9为初始惯性权重，ω 2＝0.4为最终惯性权重，k为当前迭代次数，T max为最大迭代次数。
  8. 根据权利要求1所述的一种基于机器学习的蠕变疲劳寿命预测方法，其特征在于，所述极限学习机模型采用Sigmoid函数作为激活函数。
  9. 根据权利要求1所述的一种基于机器学习的蠕变疲劳寿命预测方法，其特征在于，所述步骤S3包括：将测试集中的实验蠕变疲劳工况参数和中间计算参数共同作为蠕变疲劳寿命预测模型的输入数据，利用得到的蠕变疲劳寿命预测模型对输入数据进行预测，与相对应的蠕变疲劳对数寿命进行比较，计算蠕变疲劳寿命预测模型在测试集中的平均绝对百分比误差和决定系数R 2，验证模型的精度。
  10. 根据权利要求9所述的一种基于机器学习的蠕变疲劳寿命预测方法，其特征在于，所述平均绝对百分比误差为：
    Figure PCTCN2021096909-appb-100011
    所述决定系数R 2为：
    Figure PCTCN2021096909-appb-100012
    其中，n test为测试集中的蠕变疲劳寿命数据组的个数，y i为测试集中的蠕变疲劳对数寿命，
    Figure PCTCN2021096909-appb-100013
    为蠕变疲劳寿命预测模型预测的蠕变疲劳对数寿命，
    Figure PCTCN2021096909-appb-100014
    为测试集中的所有蠕变疲劳寿命数据组中的蠕变疲劳对数寿命的平均值。
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