Method for predicting phase change behavior of material

Abstract

The invention relates to the field of materials, in particular to a method for predicting the phase change behavior of a material, which is used for predicting the phase change behavior of a to-be-tested material by establishing a phase change judgment model for predicting the phase change behavior of the material and utilizing time sequence data capable of reflecting the external condition change of the to-be-tested material. The phase change judgment model for predicting the phase change behavior of the material is established, and the phase change behavior of the to-be-detected material is predicted by using the time sequence data capable of reflecting the external condition change of the to-be-detected material. Not only is the decomposition layer number k and penalty factor alpha of a variational mode decomposition algorithm in a VMD data processing unit globally optimized by adopting a frost ice optimization algorithm, so that the influence of noise and non-stationary signals on model prediction is greatly reduced, but also hyper-parameters of a long-short-term memory network are optimized by utilizing an improved grey wolf algorithm (IGWO). And the prediction capability of the phase change judgment model is improved to the greatest extent so as to cope with the strong non-stationarity and volatility of the phase change behavior time sequence.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of material science, and in particular to a method for predicting material phase transition behavior. BACKGROUND

[0002] In the field of material science, material phase transition refers to the phenomenon that a material changes from one (physical or chemical) state to another (physical or chemical) state when it is subjected to changes in external conditions such as temperature, pressure, magnetic field, etc. Accurate prediction of material phase transition is of great significance for the design of new materials, optimization of production processes, and prediction of equipment performance. In order to achieve efficient and accurate phase transition prediction, many techniques and algorithms have been widely used in material science research. Among them, the prediction of material phase transition behavior under conditions such as temperature, pressure dynamic change and heat treatment has become an important application scenario of related techniques and algorithms, greatly promoting the development of material science theory and practice.

[0003] So far, many traditional material phase transition prediction methods are based on thermodynamic principles and classical physical models (such as phase diagram models, thermodynamic models, etc.). Such models can predict phase transition temperature, pressure and other parameters based on known material properties and external conditions. However, these traditional methods often expose a series of problems in actual application:

[0004] On the one hand, it often needs a large amount of experimental data as support, accompanied by high computational cost. Especially when dealing with complex alloys and composite materials, the high complexity leads to a substantial increase in computational cost.

[0005] On the other hand, the application scope of traditional models is relatively narrow, and they can usually only predict the phase transition of some simple materials. When faced with multi-component, non-ideal materials, they often appear to be inadequate and difficult to effectively cope with. SUMMARY

[0006] The purpose of the present application is to provide a method for predicting material phase change behavior, which establishes a phase change judgment model for predicting material phase change behavior, and uses time series data that can reflect the external condition changes of the material to be tested to predict the phase change behavior of the material to be tested. In particular, since the phase change behavior data is significantly affected by time factors, accurate processing and analysis of the data is particularly important. The phase change judgment model established by the present application not only uses the frost ice optimization algorithm to perform global optimization on the decomposition layer number k and the penalty factor a of the variational mode decomposition algorithm in the VMD data processing unit, greatly reducing the influence of noise and non-stationary signals on model prediction, but also uses the improved grey wolf algorithm (IGWO) to optimize the hyperparameters of the long short-term memory network, greatly improving the prediction ability of the phase change judgment model to cope with the strong non-stationarity and volatility of the phase change behavior time series.

[0007] The purpose of the present application is achieved by the following scheme, a method for predicting material phase change behavior, comprising the following steps:

[0008] 1) Establishing a phase change judgment model for predicting material phase change behavior using a neural network;

[0009] 2) Collecting raw data that can reflect the external condition changes of the material to be tested to form a time series data set;

[0010] 3) Inputting the time series data set into the phase change judgment model and processing the data in the time series data set using the phase change judgment model to obtain phase change behavior prediction data of the material to be tested.

[0011] Preferably, in step 1), the phase change judgment model comprises an IGWO-LSTM prediction unit and a VMD data processing unit, the VMD data processing unit is used to input the data in the time series data set after variational mode decomposition to the IGWO-LSTM prediction unit, the IGWO-LSTM prediction unit comprises a long short-term memory network, the hyperparameters of the long short-term memory network are optimized by the improved grey wolf algorithm (IGWO), and the long short-term memory network is used to output the prediction values corresponding to each time series in the time series data set.

[0012] Preferably, the phase change judgment model further comprises a sequence reconstruction unit, which is used to superimpose the prediction values corresponding to each time series in the time series data set output by the IGWO-LSTM prediction unit to form complete prediction data.

[0013] Preferably, the phase change judgment model further comprises a reverse normalization processing unit, which is used to convert the complete prediction data formed by the sequence reconstruction unit into prediction results.

[0014] Preferably, the phase change judgment model further includes a frost optimization unit for globally optimizing the number of decomposition layers k and penalty factor α of the variational mode decomposition algorithm in the VMD data processing unit using a frost optimization algorithm.

[0015] Preferably, the phase change judgment model further includes a data cleaning unit, which is used to clean the time series data set before predicting the phase change behavior of the material to be tested.

[0016] Preferably, in step 3), predicting the phase change behavior of the material to be tested includes predicting the phase change process of the material to be tested and predicting the phase change performance.

[0017] The beneficial effects of the present invention are as follows:

[0018] ① The phase change behavior of materials is often affected by a combination of factors, such as temperature, pressure, chemical composition, etc., and there is usually a complex nonlinear relationship between these factors and the phase change. The present invention uses a neural network to construct a phase change judgment model that can combine time series data to predict the phase change behavior of the material to be tested. Through adaptive learning of time series data of changes in external conditions of the material to be tested, the ability to process multi-source heterogeneous data with complex nonlinear relationships is obtained, and implicit features are extracted as much as possible to more realistically simulate the phase change process of the material to be tested, expand the comprehensiveness of the prediction, and accurately predict the occurrence time and phase change type of the material phase change, providing strong support for the preparation, processing and application of the material;

[0019] ② The IGWO-LSTM prediction unit of the present invention includes a long-short-term memory network with excellent generalization capabilities. In the actual process of predicting material phase transitions and microstructural changes, this long-short-term memory network can adaptively capture the complex dynamic changes in time series data based on external conditions such as temperature and time data, and accurately predict the phase transition behavior and microstructural evolution of materials under various conditions;

[0020] ③ The hyperparameters of the long short-term memory network (LSTM) in the IGWO-LSTM prediction unit of the present invention are also optimized using the improved grey wolf algorithm (IGWO), which improves the performance of the phase change judgment model and ensures the accuracy and stability of the phase change judgment model when predicting the phase change behavior of the material;

[0021] The VMD data processing unit can perform variational mode decomposition on the data in the time series data set, extract nonlinear and non-stationary characteristics in the data, thereby separating effective characteristics of different time scales, and finally obtain intrinsic mode function components IMF of different frequencies, so as to remove noise interference, reduce data redundancy, avoid modal aliasing phenomenon, improve anti-interference ability, generalization ability, robustness and adaptability of the phase change prediction model, and further improve the prediction accuracy of the model.

[0022] The VMD data processing unit also uses the frost-ice optimization algorithm to globally optimize the decomposition layer number k and the penalty factor a of the VMD algorithm, so that the obtained IMF is more stable, and the influence of noise and non-stationary signals on the model prediction result is reduced as much as possible.

[0023] Nomenclature:

[0024] VMD: Variational Mode Decomposition.

[0025] LSTM: Long Short-Term Memory, a special type of recurrent neural network (RNN).

[0026] IMF: Intrinsic Mode Function.

[0027] IGWO: Improved Grey Wolf Optimization.

[0028] RIME: Frost-Ice Optimization Algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 The flowchart of the present application;

[0030] Figure 2 The flowchart of RIME-VMD in the present application;

[0031] Figure 3 The flowchart of using improved grey wolf algorithm to optimize LSTM in the present application;

[0032] Figure 4 The structure diagram of long short-term memory network in the present application. DETAILED DESCRIPTION

[0033] As shown in Figures 1 to 4 A method for predicting the phase change behavior of materials, comprising the following steps:

[0034] 1) A phase change judgment model for predicting the phase change behavior of a material is established using a neural network, and the phase change judgment model comprises a data cleaning unit, a VMD data processing unit, a frost ice optimization unit, an IGWO-LSTM prediction unit, a sequence reconstruction unit, and a reverse normalization processing unit.

[0035] 1-1) Data cleaning unit: Before predicting the phase change behavior of the material to be tested, the data cleaning unit is used to clean the time series data set.

[0036] In the present application, the data cleaning unit is used to clean the time series data set, which specifically includes repeated data processing, data inconsistency processing, data noise processing, outlier processing, missing value processing, etc. For example:

[0037] 1-1-1) Missing data processing: Check whether there are missing values in the original data set. Since the phase change behavior has continuity, the missing data needs to be filled using the mean method, that is, the sum of the two data before and after the missing data point is averaged, and the average value is used to complete the missing value;

[0038] 1-1-2) Deviation data processing: In view of the periodicity characteristics and the rule of small fluctuations in the short term of the phase change behavior, the correction method, the smoothing method, or the capping method should be used to process the outliers, so that the data meets the periodicity characteristics and the rule of small fluctuations in the short term of the time series data;

[0039] 1-1-3) The time series data set is normalized according to the following formula:

[0040]

[0041] In the formula, y i is the normalized value, x i is the original value of the data, x max is the maximum value of the data, and x min is the minimum value of the data.

[0042] 1-2) VMD data processing unit: used for inputting the data in the time series data set to the IGWO-LSTM prediction unit after the data is decomposed by the variational mode decomposition;

[0043] In the present application, the VMD data processing unit decomposes the data in the time series data set by variational mode decomposition, which specifically includes:

[0044] 1-2-1) The time series data set is used as the original input signal, and the original input signal is decomposed into k modal components u k by using the variational mode decomposition algorithm VMD;

[0045] The objective function and constraint condition of the VMD algorithm are as follows:

[0046]

[0047] In the formula, u k is the kth modal component; ω k is the center frequency of the kth modal component after decomposition, is a time derivative operator, δ(t) is a Dirac function, j is an imaginary unit, * is a convolution operator, and f(t) is an original input signal.

[0048] 1-2-2) Introducing Lagrange multipliers λ and a quadratic penalty factor α to obtain an augmented expression:

[0049]

[0050] In the formula, λ is a regularization parameter, used to weight the penalty term and control the model complexity, and α is a scaling parameter, adjusting the size of the entire loss function. is a time derivative operator, δ(t) is a Dirac function, j is an imaginary unit, u k is the kth modal component; ω k is the center frequency of the kth modal component after decomposition, * is a convolution operator, λ(t) is a Lagrange multiplier, and f(t) is an original input signal.

[0051] 1-2-3) Finally, the alternating direction method of multipliers is used for quadratic optimization, and the optimized intrinsic modal function components and center frequencies of the intrinsic modal function components are obtained to form an intrinsic modal function component set:

[0052]

[0053] In the formula, u k n+1 is the frequency domain representation of the kth mode component after optimization at the n+1 step,

[0054] is a frequency domain signal, f(ω) is a representation of the target signal f(t) in the frequency domain, ui(ω) is a certain signal or spectrum, ω k n+1 is the frequency value of the kth mode at the n+1 step, λ(ω) is the frequency domain of the regularization term, α is a regularization parameter, and ω k is a specific center frequency.

[0055] 1-3) Frosting optimization unit: the frost optimization algorithm is used to globally optimize the decomposition layer number k and the penalty factor α of the VMD data processing unit.

[0056] The frost and ice optimization algorithm proposes a frost and ice search strategy for algorithm search by simulating the movement of soft frost and ice particles. The algorithm simulates the growth behavior of soft frost and hard frost in the frost and ice formation process, and designs a soft frost search strategy and a hard frost piercing mechanism. The update formula of the rime particle is as follows:

[0057] The core formula of particle update is as follows:

[0058]

[0059]

[0060] In the formula: The new position of the updated particle is represented by i and j, which represent the i-th time and the j-th particle; R best,j The j-th particle of the optimal crystal in the frost and ice population is represented by r1 and r2, which represent random numbers; cosθ is the direction of particle movement; β represents environmental factors; h is the adhesion degree; Ub ij And Lb ij is the upper and lower bound of the particle motion space; t is the current iteration number; T is the maximum iteration number; ω represents the number of segments of the step function. E is the maximum boundary, θ is the direction parameter,

[0061] Rime piercing mechanism. Inspired by the hard rime piercing phenomenon, a mechanism is proposed to realize the exchange of algorithm particles and improve the convergence and the ability to jump out of the local optimum. The replacement formula between particles is:

[0062]

[0063] In the formula: F normr (S i ) is the normalized value of the current individual fitness value, which represents the probability of selecting the i-th rime individual; r3 is a random number with a value range of (-1, 1).

[0064] In the present application, the frost and ice optimization algorithm is used to globally optimize the decomposition layer number k and the penalty factor a of the variational modal decomposition algorithm in the VMD data processing unit, which specifically includes:

[0065] 1-3-1) RIME parameter initialization, set the population size and iteration number;

[0066] For example, assuming that the population size is 50 and the iteration number is 200. It means that 50 individuals (i.e. 50 parameter combinations) are updated in each iteration, and 200 rounds of updating are performed.

[0067] 1-3-2) Given the optimization range of the decomposition layer number k and the penalty factor a;

[0068] For example, the decomposition layer number k takes a value in the range of [2, 10]. The penalty factor a takes a value in the range of [100, 2000].

[0069] 1-3-3) The RIME algorithm optimizes the VMD envelope entropy as the fitness function.

[0070] For example, in the first round of iteration, 50 groups of parameters are randomly generated (such as k = 3, a = 1500), and the fitness value (i.e. envelope entropy) of each group of parameters is calculated. Assuming that the calculated envelope entropy is 0.35.

[0071] 1-3-4) Determine whether the fitness value of the fitness function is the minimum or remains unchanged:

[0072] If not, repeat steps 1-3-2) to 1-3-4);

[0073] If yes, output the current value of the decomposition layer number k and the penalty factor a as the optimal value of the decomposition layer number k and the penalty factor a.

[0074] Specifically, the parameters of the individual are updated by the RIME algorithm, and the updated fitness value is calculated. The new fitness value is compared with the current optimal value. If there is a lower fitness value (better solution), the current optimal solution is updated. When the number of iterations reaches 200 times or the minimum fitness value is found, the algorithm terminates.

[0075] For example, the optimal solution finally obtained is k = 6 and a = 1200.

[0076] In this way, the decomposition parameters (i.e. the decomposition layer number k and the penalty factor a) can be adjusted in real time according to the changes of the input sample, improving the adaptability and decomposition effect of the VMD data processing unit on data.

[0077] 1-4) IGWO-LSTM prediction unit: a long short-term memory network LSTM is built in. The advantages of the long short-term memory network LSTM in phase change behavior prediction mainly lie in its modeling ability for nonlinear and complex dynamic relationships, its ability to capture long-term and short-term dependencies, and its robustness to irregular and noisy data. Through automatic feature learning and multivariate input processing, LSTM provides an accurate and efficient prediction solution, and the processing effect on time series data is better.

[0078] In the present application, the hyperparameters of the long short-term memory network need to be optimized by the improved grey wolf algorithm (IGWO), and then used to output the prediction values corresponding to each time series in the time series data set. Finally, sequence reconstruction is performed, and through inverse normalization processing, the prediction values that can be used to predict the phase change behavior of materials are obtained.

[0079] That is, there are many hyperparameters in the LSTM neural network that need to be set. Otherwise, it will affect the convergence speed, generalization ability of the model and then affect the prediction effect of the model. Using IGWO to adjust the hyperparameters can avoid the uncertainty of manual adjustment, has small randomness and more stable optimization effect. The application takes the hyperparameters of the LSTM as the optimization object of the IGWO, takes the RMSE as the fitness value of the target function, finds the hyperparameters corresponding to the minimum RMSE, and trains to obtain the optimal hyperparameters of the LSTM.

[0080] In the application, the IGWO-LSTM prediction unit is constructed in the following manner:

[0081] After obtaining the K modal functions IMF by using the VMD data processing unit, the parameter range of the improved grey wolf algorithm is set, including the search space of the number of hidden layer units and the number of layers, and optimization control parameters such as the maximum number of evaluations and the initial number of sampling points, the LSTM network is constructed, and the basic architecture is initialized.

[0082] After the LSTM network is established, the root mean square error (RMSE) is defined as the target function, the improved grey wolf algorithm optimization dynamically selects the optimal parameter combination through the Gaussian process surrogate model and the acquisition function, finds the network hyperparameters that minimize the RMSE, and applies them to the LSTM network as the optimized hyperparameters, forming the IGWO-LSTM prediction unit of the application.

[0083] The improved grey wolf algorithm (IGWO) is described in detail as follows:

[0084] 1. Traditional GWO algorithm

[0085] The main advantages of the grey wolf optimization algorithm lie in the simplicity of its model parameters, the intuitive biological principle and the excellent global search ability. In GWO, the social structure of the wolf pack is divided into four levels: alpha, beta, delta and omega. Alpha wolf is the leader of the group, representing the current optimal solution; beta wolf is the helper, supporting alpha wolf and representing the suboptimal solution; delta wolf follows the guidance of alpha and beta wolves, representing the third optimal solution; and omega wolf is at the bottom of the hierarchy, obeying the instructions of alpha, beta and delta wolves. The hunting behavior of the wolf pack is divided into two steps: surrounding the prey and chasing the prey:

[0086] First, after discovering the prey, the wolf pack surrounds the prey. The mathematical model of the wolf pack surrounding the prey is:

[0087]

[0088] In the formula, t represents the current iteration number; represents the current grey wolf position; represents the prey position; and denotes the direction vector, and the calculation formula is as follows:

[0089]

[0090] wherein a is a convergence factor, which is linearly reduced from 2 to 0 with the number of iterations. and a random number between [0, 1] is taken as the modulus.

[0091] Secondly, after completing the encirclement of the prey, the alpha, beta and delta wolves guide the wolf pack to gradually reduce the encirclement circle to capture the prey through a mathematical model. The mathematical description of this process is as follows:

[0092]

[0093] wherein: denotes the positions of the alpha, beta and delta wolves; denotes the distances between the gray wolf individual and the alpha, beta and delta wolves; denotes the updated positions of the gray wolf individual generated according to the positions of the alpha, beta and delta wolves; denotes the final updated position of the gray wolf individual after the end of the tth iteration.

[0094] After the end of each iteration, the fitness of the gray wolf individual is re-evaluated, and the ranks of the alpha, beta and delta wolves are updated accordingly to approach the global optimal solution.

[0095] 2. Improvement of the traditional GWO

[0096] The IGWO introduces a dynamic updating mechanism for the weight factor and the elite position on the basis of the traditional GWO, and optimizes the calling mode of the fitness function. The specific improvements mainly include the following aspects:

[0097] The weight factor μ is introduced to mix the elite position;

[0098] In order to enhance the convergence speed and stability of the algorithm, the IGWO introduces the weight factor to perform weighted fusion of the traditional position updating and the elite position , and the formula is as follows:

[0099]

[0100] wherein the weight factor μ is defined as:

[0101]

[0102] t is the current number of iterations, and T is the maximum number of iterations. With the progress of iterations, μ is linearly decreased from 1 to 0, so that the algorithm pays more attention to global search in the initial stage, and relies more on the elite position to speed up convergence in the later stage.

[0103] In traditional GWO, a, b, and d represent the top three optimal solutions in the population, respectively. However, this approach can lead to excessive dependence on local optimal solutions. The improved GWO introduces a global optimal solution, ensuring that the algorithm always references the location of the optimal solution, thereby improving global search capabilities and avoiding getting stuck in local optima.

[0104] The update formula for elite positions is:

[0105]

[0106] where, is the optimal solution in the current population.

[0107] The calculation of the control parameter a:

[0108]

[0109] 3. Algorithm flow

[0110] The main flow of the improved GWO algorithm is as follows:

[0111] 3.1 Initialize the grey wolf population: randomly initialize the position of the grey wolf population within the given search space;

[0112] 3.2 Calculate the fitness value of each grey wolf;

[0113] 3.3 Determine the elite grey wolf: select the optimal grey wolf as a, b, and d according to the fitness value, and record the global optimal solution;

[0114] 3.4 Iterative optimization:

[0115] 3.4.1 Calculate the weight factor m and the control parameter a;

[0116] 3.4.2 Update the position of each grey wolf (merge elite position), that is, combine the position update of traditional GWO and the weighted fusion of elite position;

[0117] 3.4.3 Limit the search space of the grey wolf position, that is, limit the updated grey wolf position within the search space;

[0118] 3.4.4 Calculate the fitness value of the population uniformly;

[0119] 3.4.5 Update the elite position

[0120] 3.4.6 Record and output the current best fitness value.

[0121] 3.4.7 Determine whether the termination condition is met:

[0122] When the maximum number of iterations is reached or other termination conditions are met, the algorithm ends, returns and outputs the optimal solution.

[0123] In the present application, a subsequence dataset is formed by using the k sub-sequences output by the VMD data processing unit, and the subsequence dataset is divided into a training set and a test set, the test set is used to judge the phase transition behavior of the material to be tested, and the training set is used to build and train the long short-term memory network LSTM, which specifically includes:

[0124] 1-4-1) Determine the initial structure of LSTM, the structure of a single LSTM is as shown in Figure 4

[0125] The forget gate (f t ) provides the LSTM network with strong long-term memory capability by controlling the retention and forgetting of information in the cell state of the previous time step, and the calculation formula is as follows:

[0126] f t =σ(W f [h t-1 ,x t ]+b f )

[0127] In the formula, f t is the forget gate, σ is the activation function; W f is the weight matrix, indicating the weight of the input and the hidden state at the previous time in the forget gate calculation; h t-1 is the state vector calculated at time t-1; x t is the input data at the current time step, and b f is the bias term, which is a constant term added to the result of the weighted input and the previous hidden state.

[0128] The input gate (v t ) controls the acceptance degree of new input information through the Sigmoid activation function, and together with the candidate value generated by tanh determines the update of the memory cell state, thereby playing a key role in learning long-term dependencies and processing time series data. The calculation formula is as follows:

[0129] v t =σ(W v [h t-1 ,x t ]+b v )

[0130] In the formula, v t is the input gate, σ is the activation function, usually the sigmoid function, the output range is between 0 and 1, Wv is the weight matrix, indicating the weight of the current input and the hidden state at the previous time in the input gate calculation, h t-1x t is the input data for the current time step, b v is a bias term, a constant term added to the weighted input and the previous hidden state result.

[0131] Output gate (o t ): controls the output of the next time step. It decides which parts of the current memory cell state will be output as the hidden state. The calculation formula is shown:

[0132] o t = σ(W o [h t-1 ,x t ]+b o )

[0133] where o t is the output gate, W0 is the weight matrix, representing the current input x t and the hidden state h t-1 at the previous time in the output gate calculation; h t-1 is the state vector calculated at time t-1; x t is the input data for the current time step, b0 is the bias term, a constant term added to the weighted input and the previous hidden state result.

[0134] g t is the input state of the memory cell, the storage unit value adjusted by information, the candidate memory cell state. The calculation formula is shown:

[0135] g t = tanh(W g [h t-1 ,x t ]+b g )

[0136] where g t is the output of the candidate memory cell, tanh is an activation function (hyperbolic tangent function), the output range is [-1, 1], Wg is the weight matrix, representing the current input x t and the hidden state h t-1 at the previous time in the calculation of the candidate memory cell g t ; h t-1 is the state vector calculated at time t-1; x t is the input data for the current time step, bg is the bias term, a constant term added to the weighted input and the previous hidden state result.

[0137] The cell state of the current time step t is as follows:

[0138]

[0139] Where c t is a memory unit, σ is an activation function, usually a sigmoid function, with an output range between 0 and 1, and c t-1 is the unit state at the previous moment, indicating the memory of the previous time step, g t is the output of the candidate memory unit, v t is the input gate, f t For the Gate of Forgetfulness, Represents bitwise multiplication of the elements in a vector.

[0140] The hidden state (output) at the current time step t is as follows:

[0141]

[0142] Where h t is the hidden state at the current moment t, indicating the output at the current moment, o t is the output gate; Indicates bitwise multiplication of elements in a vector; tanh(c t ) is the cell state c t The hyperbolic tangent function (tanh) of .

[0143] 1-4-2) Use IGWO to optimize and update the LSTM hyperparameters in the following manner:

[0144] (1) Initialize the population size, determine the learning rate, the number of hidden layer neurons, and the number of samples.

[0145] (2) Use the parameters of step (3) to set up LSTM.

[0146] (3) Use the RMSE of the prediction model as the fitness function and calculate the corresponding fitness value.

[0147] The fitness value with RMSE as the objective function is to use RMSE to calculate the root mean square error between the predicted value and the true value:

[0148]

[0149] Where n is the number of observations in the test sample, y i and are the actual observed values ​​and the predicted values, respectively.

[0150] In other words, the present invention defines the root mean square error (RMSE) as the objective function, selects the optimal parameter combination by improving the Gray Wolf Algorithm, and finds the network hyperparameters that minimize RMSE. Finally, the optimized hyperparameters are applied to the LSTM network.

[0151] IGWO algorithm optimization method for LSTM:

[0152] 1. Initialize the position of the wolf pack

[0153] The position of each wolf represents an LSTM hyperparameter combination. h1, h2, …, h d : represent different hyperparameters in the LSTM model.

[0154] For IGWO, assume there are N wolves, and the behavior of each wolf is represented by its position vector

[0155] X i =(X i1 ,X i2 ,…,X id ).

[0156] 2. Calculate the fitness (loss function)

[0157] By finding the optimal LSTM hyperparameter combination to minimize the loss, the objective function: f(X i ) = Loss(LSTM(Xi));

[0158] Where Loss is the loss function of the LSTM model, X i is the position of the i-th wolf in the wolf pack, representing the combination of LSTM hyperparameters.

[0159] 3. Update the position of the wolf

[0160] In IGWO, the position update formula of the wolf is: Xi(t+1) = Xi(t) + A·D;

[0161] Where t is the current iteration number. X i (t) is the position information of the i-th wolf at the t-th round, i.e., the combination of LSTM hyperparameters; A is the coefficient, which controls the jumping step of the wolf; D is the distance difference between the current position of the wolf and the positions of other wolves.

[0162] 4. Convergence judgment

[0163] According to the preset maximum iteration number Tmax, or when the fitness (loss) changes less than the set threshold, judge whether the IGWO algorithm has converged. Stop when the maximum iteration number Tmax is reached or the loss value changes less than the set threshold, otherwise continue to update the position of the wolf pack.

[0164] IGWO algorithm will repeat the above steps, select the most potential hyperparameter combination for evaluation, continuously improve the proxy model, and finally find the optimal hyperparameter combination.

[0165] In summary, the application takes the hyperparameters of the long short-term memory network as the optimization object of the improved grey wolf algorithm, takes the RMSE as the fitness value of the target function, finds the hyperparameters corresponding to the minimum RMSE, and trains the optimal hyperparameters of the model. t b The learning rate controls the step size of each parameter update, the number of hidden layer neurons represents the number of neurons in each hidden layer, and the batch sample number represents the number of selected samples for each training (i.e., batch size).

[0166] 2) Collect original data reflecting the changes of external conditions of the material to be tested to form a time series data set;

[0167] 3) Use the time series data set and the phase change judgment model to predict the phase change behavior of the material to be tested. That is, input the time series data set into the phase change judgment model, and use the phase change judgment model to process the data in the time series data set to obtain the phase change behavior prediction data of the material to be tested. Specifically, it includes phase change performance prediction or phase change process prediction.

[0168] In the application, when the decomposition layer number k and the penalty factor a of the variational mode decomposition algorithm in the VMD data processing unit and the hyperparameters of the long short-term memory network LSTM in the IGWO-LSTM prediction unit are determined, a phase change judgment model (i.e., RIME-VMD-IGWO-LSTM hybrid model) capable of predicting the phase change behavior of the material can be formed. In this phase change judgment model, the predicted values corresponding to each time series in the time series data set output by the IGWO-LSTM prediction unit are superimposed by the sequence reconstruction unit to form complete prediction data, and then the inverse normalization processing unit of the phase change judgment model converts the complete prediction data formed by the sequence reconstruction unit into accurate prediction results.

[0169] According to experimental comparison, the average absolute percentage error MAPE (i.e., prediction error) of the predicted value and the true value of the phase change judgment model is calculated according to the following formula to judge the prediction accuracy of the phase change judgment model, as follows:

[0170]

[0171] In the formula, MAPE is the average absolute percentage error of the predicted value and the true value, y i is the true value, is the predicted value, and n is the total number of intrinsic mode function components in the intrinsic mode function component set.

[0172] ​As shown in Table 1, the phase change judgment model of the application, the LSTM model (i.e. only using LSTM to build the model), VMD-LSTM model, VMD-IGWO-LSTM model input the same data set, and compare the prediction results, the prediction error of the phase change judgment model in the application is the smallest, which can accurately predict the phase change behavior of the material to be tested.

[0173] Table 1

[0174]

[0175] In practical application, according to the different types of input and output data, the phase change judgment model can be divided into a model for predicting the phase change performance of the material, or a model for predicting the phase change process of the material, etc. According to the above method, examples 1, 2 and 3 are as follows:

[0176] Example 1 - phase change performance prediction (resistance performance)

[0177] (1) Collect original data that can reflect the change of external conditions of the material to be tested, and form a time series data set;

[0178] For example, when predicting the phase change performance, the original data includes temperature, time and resistance, and the phase change performance time series data set formed is shown in Table 1 (only part of the data is listed in this example):

[0179] Table 1

[0180]

[0181] Before predicting the phase change performance of the material to be tested, the data cleaning unit is used to clean the time series data set. For example, the phase change performance time series data set is normalized according to the following formula:

[0182]

[0183] In the formula, y i is the normalized phase change performance, x i is the original performance of the data, x max is the maximum value of the data, and x min is the minimum value.

[0184] Then, the phase change performance time series data set is used as the original input signal, and the original input signal is decomposed into k phase change performance components u k by using the variational mode decomposition algorithm VMD.

[0185] The objective function and constraint condition of the variational mode decomposition algorithm VMD in this example are as follows:

[0186]

[0187] where u k is the kth phase change performance component; ω k is the center frequency of the kth phase change performance component after decomposition, is the time derivative operator, δ(t) is the Dirac function, j is the imaginary unit, * is the convolution operator, and f(t) is the original phase change input signal.

[0188] The Lagrange multiplier λ and the quadratic penalty factor α are introduced to obtain the augmented expression:

[0189]

[0190] where λ is the regularization parameter used to weight the penalty term and control the model complexity, and α is the scaling parameter to adjust the scale of the entire loss function. is the time derivative operator, δ(t) is the Dirac function, j is the imaginary unit, u k is the kth phase change performance component; ω k is the center frequency of the kth component after decomposition, * is the convolution operator, λ(t) is the Lagrange multiplier, and f(t) is the original input signal.

[0191] Finally, the alternating direction method of multipliers is used for quadratic optimization, and the optimized intrinsic phase change performance modal function components and the center frequencies of the intrinsic modal function components are obtained to form the intrinsic modal function component set:

[0192]

[0193] where u k n+1 is the frequency domain representation of the kth mode phase change performance component after optimization at the n+1 step, (ω) is the frequency domain signal, f(ω) is the representation of the target signal f(t) in the frequency domain, ui(ω) is a certain signal or spectrum, ω k n+1 is the frequency value of the kth mode at the n+1 step, λ(ω) is the frequency domain of the regularization term, α is the regularization parameter, and ω k is the specific center frequency.

[0194] It is worth noting that in this embodiment, the RIME optimization algorithm is used to globally optimize the decomposition layer number k and the penalty factor α of the variational mode decomposition algorithm in the VMD data processing unit, which specifically includes:

[0195] a) RIME parameter initialization, set the population size and the number of iterations;

[0196] Assuming the population size is 10 and the number of iterations is 20 times.

[0197] b) optimization range of the decomposition layer number k and the penalty factor a given;

[0198] k is in the range of [2, 10] and a is in the range of [100, 2000].

[0199] c) the RIME algorithm optimizes the VMD envelope entropy as the fitness function;

[0200] In the first round of iteration, the fitness value of each group of parameters is calculated according to the randomly generated parameters.

[0201] d) whether the fitness value of the fitness function is the minimum or remains unchanged:

[0202] If not, repeat steps b) to d);

[0203] If yes, output the current value of the decomposition layer number k and the penalty factor a as the optimal value of the decomposition layer number k and the penalty factor a. Finally, k = 9 and a = 1731.578 are obtained.

[0204] Table 2 VMD decomposition mode data table

[0205] Modal_1 Modal_2 Modal_3 Modal_4 Modal_5 Modal_6 Modal_7 Modal_8 Modal_9 38246.1 304.6465 0.083066 2.943585 3.547686 0.025511 1.369735 0.323789 0.177165 38245.85 304.373 -0.11924 0.047723 -2.76261 0.15422 -2.7958 -0.55752 -0.09561 38245.45 303.927 -0.13601 -2.63332 -3.56184 0.283518 2.180117 0.461949 0.080505 38244.95 303.3562 0.315361 -2.48168 2.234382 -0.43009 0.039065 0.0546 -0.05781 38244.4 302.7122 1.264844 0.272435 3.614509 -0.23416 -2.08238 -0.69112 0.090525 38243.81 302.0009 2.327779 2.72994 -1.79675 0.73431 2.40099 1.064237 -0.21673 38243.06 301.1224 2.784714 2.173085 -3.71841 -0.13524 -0.87731 -0.87197 0.519399 38240.01 297.5482 -0.96876 -1.29792 -1.2203 0.137866 -1.1304 -0.92875 -1.73085 38238.89 296.2183 -2.34643 1.20419 -4.49342 -0.8363 -0.054 1.116549 2.213917 38237.79 294.8991 -2.81401 2.055693 0.534785 0.214659 0.665306 -0.94314 -2.77562 38236.68 293.5479 -2.35121 0.200201 4.443034 0.649989 -0.53295 0.38762 3.355734 38235.48 292.1088 -1.25318 -1.85019 0.141817 -0.40508 0.262795 0.455534 -3.86085 … … … … … … … … …

[0206] Finally, the phase change judgment model outputs the data shown in Table 3 to predict the resistance value of the material at different time points at various temperatures in the future.

[0207] Table 3

[0208]

[0209] Example 2 - Phase change performance prediction (temperature coefficient)

[0210] Similarly, using the data shown in Table 4, a phase change judgment model can be constructed to predict the future temperature coefficient characteristics of the material, and the predicted data is shown in Table 5.

[0211] Table 4

[0212] Time (h) Temperature coefficient (ppm / °C) 0 38570 10 38520 20 38460 30 38530 40 38410 50 38330 60 38260 70 38210 … …

[0213] Table 5

[0214] Time (h) Temperature coefficient (ppm / °C) 210 37540 220 37500 230 37450 240 37410 250 37350 260 37310 … …

[0215] Example 3 - Phase change process prediction

[0216] Similarly, using the data shown in Table 6, a phase change judgment model can be constructed to predict the future phase change process of the platinum film, and the predicted data is shown in Table 7.

[0217] Table 6

[0218]

[0219] Table 7

[0220]

[0221] It can be seen that the phase change judgment model constructed in this embodiment can model the evolution of each stage in the phase change process by collecting and analyzing experimental data of the material under different temperature and time conditions. Through modal decomposition of VMD, the patterns of different stages are extracted, and LSTM captures the dynamic changes in time series, effectively combines various factors (such as temperature) of the material phase change process, and improves the accuracy and reliability of material phase change prediction based on historical data. For the prediction of different situations in the material phase change behavior, the training data used is different, and the phase change judgment model established is different, for example:

[0222] ① Phase change temperature prediction:

[0223] In the present application, the variational modal decomposition (VMD) can effectively decompose the original data (such as temperature-time curve) into several intrinsic modal functions, remove noise, and extract the signal components related to phase change. The long short-term memory network (LSTM) can capture the long-term dependencies in time series, helping to accurately predict the phase change temperature of the material. By inputting the VMD decomposed data into the LSTM model, the RIME (robust information maximization estimation) algorithm can further optimize the model to ensure more accurate prediction results. For the phase change behavior of the material, capturing the long-term dependencies in time series helps to accurately predict the phase change temperature of the material, and combining its powerful nonlinear modeling capability can handle complex phase change prediction problems.

[0224] ② Phase change process prediction:

[0225] The phase change of the material not only includes the prediction of the phase change temperature, but also involves the evolution of each stage in the phase change process. By collecting and analyzing experimental data of the material under different temperature and time conditions, RIME-VMD-IGWO-LSTM can model the evolution of each stage in the phase change process. Through modal decomposition of VMD, the patterns of different stages are extracted, and LSTM captures the dynamic changes in time series, effectively combines various factors (such as thermal expansion, cooling speed, external pressure, etc.) of the material phase change process, optimizes the process parameters in the phase change process, and improves the accuracy and reliability of material phase change prediction.

[0226] ③ Phase change material performance prediction:

[0227] The RIME-VMD-IGWO-LSTM can combine the composition, structure and experimental data of the material to establish a performance prediction model of the phase change material. For the phase change material, long-term thermal cycle use can cause its performance to decline. The RIME-VMD-IGWO-LSTM can predict the performance degradation of the phase change material in multiple phase change processes based on historical data and experimental data, and provide a basis for service life evaluation of the material. For example, by modeling the phase change temperature, thermal conductivity, heat capacity and other performances of different types of phase change materials, their performances in different application scenarios can be predicted.

[0228] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification made by those skilled in the art without departing from the spirit of the present application falls within the scope of protection of the present application.

Claims

1. A method for predicting phase change behavior of a material, characterized in that: The following steps are involved: 1) Using neural networks to establish a phase transition judgment model for predicting material phase transition behavior; 2) Collecting raw data that can reflect changes in the external conditions of the material to be tested to form a time series data set; 3) Inputting the time series data set into the phase change judgment model, and using the phase change judgment model to process the data in the time series data set to obtain the phase change behavior prediction data of the material to be tested.

2. The method for predicting material phase change behavior according to claim 1, characterized in that: In step 1), the phase change judgment model includes an IGWO-LSTM prediction unit and a VMD data processing unit. The VMD data processing unit is used to perform variational mode decomposition on the data in the time series data set and input the data into the IGWO-LSTM prediction unit. The IGWO-LSTM prediction unit includes a long short-term memory network. The hyperparameters of the long short-term memory network are optimized by the improved grey wolf algorithm (IGWO) to output the predicted values ​​corresponding to each time series in the time series data set.

3. The method for predicting material phase change behavior according to claim 2, characterized in that: The phase change judgment model also includes a sequence reconstruction unit, which is used to superimpose the prediction values ​​corresponding to each time series in the time series data set output by the IGWO-LSTM prediction unit to form complete prediction data.

4. The method for predicting material phase change behavior according to claim 3, characterized in that: The phase change judgment model further includes a denormalization processing unit for converting the complete prediction data generated by the sequence reconstruction unit into a prediction result.

5. The method for predicting material phase change behavior according to claim 2, characterized in that: The phase change judgment model also includes a frost optimization unit for globally optimizing the number of decomposition layers k and the penalty factor α of the variational mode decomposition algorithm in the VMD data processing unit using the frost optimization algorithm.

6. The method for predicting material phase change behavior according to claim 2, characterized in that: The phase change judgment model further includes a data cleaning unit, which is used to clean the time series data set before predicting the phase change behavior of the material to be tested.

7. The method for predicting material phase change behavior according to claim 1, characterized in that: In step 3), the phase change behavior of the material to be tested is predicted, including the phase change process prediction and the phase change performance prediction of the material to be tested.

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