Mathematical modeling method for main equipment of pumped storage power station based on dynamic simulation

Abstract

The invention discloses a dynamic simulation-based mathematical modeling method for main equipment of a pumped storage power station, which comprises the following steps of: S1, acquiring multi-source time sequence data of the main equipment of the pumped storage power station, and preprocessing to generate a time sequence data set; s2, constructing a time sequence variation auto-encoder model, and carrying out initialization through a dynamic potential space regulation factor; s3, dynamically adjusting and optimizing hyper-parameters of the time sequence variational auto-encoder model by using a badger optimization algorithm; s4, global optimization is carried out on weight parameters of the time sequence variational auto-encoder model through a differential evolution algorithm; s5, performing prediction by using the time sequence variation auto-encoder model, and introducing a nonlinear time decay mechanism to correct a prediction result; and S6, comparing a prediction result with actual equipment operation data, and assisting power station operation and maintenance personnel to formulate an equipment operation optimization strategy. According to the method, high-precision prediction and dynamic simulation of the operation state of the main equipment of the pumped storage power station are realized, and the operation safety and maintenance efficiency of the equipment are improved.

Description

Technical Field

[0001] The present invention relates to the field of geographic information technology, and in particular to a mathematical modeling method for main equipment of a pumped storage power station based on dynamic simulation. Background Art

[0002] During the operation of the main equipment of a pumped-storage power station, the safety, stability, and efficiency of the equipment are crucial to the operation of the entire power station. During long-term operation, the main equipment of a pumped-storage power station (such as pump turbines, generator motors, transformer equipment, etc.) is affected by complex working conditions, environmental factors, and load fluctuations, and its operating status will exhibit obvious nonlinear and dynamic change characteristics. In order to ensure the safe and stable operation of the equipment, it is usually necessary to monitor and predict the operating status of the equipment in real time, so as to promptly detect potential faults or abnormal conditions and assist operation and maintenance personnel in formulating effective maintenance and optimization strategies. Therefore, constructing an accurate and efficient mathematical modeling method for the main equipment of a pumped-storage power station is of great significance for improving equipment operating efficiency, extending equipment service life, and ensuring the overall operational safety of the power station.

[0003] At present, in the field of mathematical modeling of the main equipment of pumped storage power stations, the commonly used methods mainly include physical mechanism-based modeling methods and data-driven modeling methods. Physical mechanism-based modeling methods usually rely on the equipment structure, physical characteristics and operating conditions, and simulate the operating behavior of the equipment by establishing differential equations or mechanism models. However, this type of method is highly dependent on the internal mechanism of the equipment. When the equipment operating environment is complex or the data is difficult to obtain comprehensively, the accuracy and applicability of the model will be limited. In addition, due to the presence of various uncertainties in the actual operation of the equipment (such as environmental changes, operating condition disturbances, etc.), the physical mechanism model is difficult to dynamically adjust and adaptively learn, resulting in large model prediction errors in long-term predictions or dynamic conditions.

[0004] Data-driven modeling approaches have developed rapidly in recent years. They primarily utilize machine learning and deep learning methods to analyze and model equipment operating data. These methods can extract implicit patterns in equipment operation from historical data without explicitly understanding the internal physical mechanisms of the equipment. Common models in this category include long-short-term memory (LSTM), autoregressive integrated moving average (ARIMA), and variational autoencoders (VAE). These models have demonstrated considerable advantages in equipment state prediction, particularly when handling nonlinear and time-series data. However, traditional data-driven approaches still have some shortcomings in practical applications. For example, LSTM models can suffer from the vanishing gradient problem when handling long-term dependencies, resulting in reduced prediction accuracy; ARIMA models have limited capabilities for handling nonlinear and non-stationary data; and traditional variational autoencoder (VAE) models cannot fully capture the dynamic characteristics of equipment state changes when processing time-series data, affecting prediction performance.

[0005] Therefore, how to provide a mathematical modeling method for the main equipment of a pumped storage power station based on dynamic simulation is an urgent problem that needs to be solved by those skilled in the art. Summary of the Invention

[0006] One object of the present invention is to propose a mathematical modeling method for the main equipment of a pumped storage power station based on dynamic simulation. The present invention realizes high-precision prediction of the equipment operating status through an improved time series variational autoencoder model. The present invention introduces a dynamic latent space control factor and an adaptive compensation mechanism to dynamically adjust the latent space dimension and the adaptability of the predicted data during the model encoding and decoding process. At the same time, the hyperparameters of the model, including the latent space dimension, the number of hidden layer nodes and the learning rate, are dynamically tuned by the improved honey badger optimization algorithm to achieve adaptive adjustment of the model under different dynamic working conditions. The present invention also combines the differential evolution algorithm (DE) to optimize the global weight parameters. Through an innovative fitness function, the global optimization of the model weight is ensured based on the Pearson correlation coefficient and dynamic range deviation between the equipment operating status prediction data and the time series data set. During the prediction process, a nonlinear time decay mechanism is adopted to dynamically correct the prediction results according to the prediction confidence factor to ensure data stability in long time series prediction. The present invention has high prediction accuracy, strong model stability, good dynamic adaptability, excellent generalization ability in complex dynamic environments, and can effectively improve the operating safety and maintenance efficiency of the main equipment of the pumped storage power station.

[0007] The mathematical modeling method for main equipment of a pumped storage power station based on dynamic simulation according to an embodiment of the present invention includes the following steps:

[0008] S1. Collect multi-source time series data of the main equipment of the pumped storage power station, pre-process the multi-source time series data, and generate a time series data set;

[0009] S2. Build a time series variational autoencoder model, input the time series dataset into the time series variational autoencoder model for training, map the time series data into a dynamic latent space through the encoder, and reconstruct the latent variables into device operation status prediction data through the decoder;

[0010] S3. Introducing the Honey Badger optimization algorithm to dynamically tune the hyperparameters of the temporal variational autoencoder model. Through the global exploration and local development strategies of the Honey Badger optimization algorithm, the latent space dimension, number of hidden layer nodes, and learning rate of the variational autoencoder model are dynamically adjusted.

[0011] S4. Based on the Pearson correlation coefficient between the equipment operation status prediction data and the time series dataset, the weight parameters of the time series variational autoencoder model are globally optimized using the differential evolution algorithm to minimize the prediction error based on a global search.

[0012] S5. Use the time series variational autoencoder model to predict the real-time input equipment operation data and generate predicted data of the equipment's future state. In the prediction process, a nonlinear time decay mechanism is introduced. By setting the nonlinear time decay factor, the prediction confidence is automatically adjusted during long time series prediction.

[0013] S6. Compare and analyze the prediction results with the actual data of equipment operation in the time series data set. When the prediction error exceeds the set threshold, the anomaly detection and early warning mechanism is triggered. Through equipment operation status prediction and anomaly early warning, the power station operation and maintenance personnel are assisted in formulating equipment operation optimization strategies.

[0014] Optionally, the S2 specifically includes:

[0015] S21, build encoder E, and transform the time series dataset X∈R T×n Mapped to a latent variable z∈R in a dynamic latent space d , R is a set of real numbers, R is the time step of the time series data, n is the number of data features at each time step, and d is the dimension of the dynamic latent space;

[0016] S22. Construct a decoder D to reconstruct the latent variable z into the predicted device operating status data

[0017] S23. Set up a dynamic latent space module L and dynamically adjust the latent space dimension by introducing a dynamic entropy control mechanism:

[0018]

[0019] Among them, d t+1 represents the potential space dimension of the next iteration, d t represents the potential space dimension of the current iteration, η is the control coefficient, tanh() is the hyperbolic tangent function, H(z) is the Shannon entropy of the latent variable, H max is the preset maximum entropy value;

[0020] S24. In the process of building the temporal variational autoencoder model, a multimodal adaptive mapping mechanism is introduced to dynamically set the hidden layer size h and learning rate α:

[0021] h=h0+β·tanh(δ·H(z)+(1-δ)·C(X)-H target );

[0022] α=α0·exp(-λ·[δ·H(z)+(1-δ)·C(X)]);

[0023] Among them, h0 and α0 are the initial hidden layer size and learning rate, β and λ are control factors, δ is the weight coefficient, and H targetis the target entropy value, exp() is the exponential function, and C(X) is the complexity measure of the input time series dataset X:

[0024] C(X)=log2(1+Var(X));

[0025] Where Var(X) represents the variance of the time series data set X, and log2 is the logarithmic function;

[0026] S25. Initialize the model's hyperparameters, including encoder parameters, decoder parameters, initial latent space dimension, hidden layer size, and learning rate. Integrate the encoder, decoder, and dynamic latent space modules to construct an improved temporal variational autoencoder model.

[0027] Optionally, the S3 specifically includes:

[0028] S31. Initialize the population of the honey badger optimization algorithm to form a set of hyperparameter vectors Θ hp :

[0029] Θ hp ={[d i ,h i ,α i ]|i=1,2,…,N};

[0030] Where N is the population size, d i is the potential space dimension of the temporal variational autoencoder model of the i-th individual, h i is the number of hidden nodes of the i-th individual, α i is the learning rate of the i-th individual;

[0031] S32. Define the fitness function and use the evaluation index that combines the prediction effect of the time series variational autoencoder model with the characteristics of multimodal data:

[0032]

[0033] in, Equipment operating status data The Pearson correlation coefficient between the time series data set X, is the coefficient of variation, and are standard deviation and mean, CV ref is the reference variation coefficient, ω1, ω2 and ω3 are the preset weight coefficients, is the Shannon entropy, H ref is the reference entropy value, F(Θ hp ) is the fitness function;

[0034] S33. By introducing historical optimal memory, we simulate the behavior of honey badgers searching simultaneously in multiple independent search areas and record the historical optimal hyperparameters:

[0035]

[0036] Among them, t is the current iteration number, T max is the maximum number of iterations, τ is the decay constant, φ is the balance coefficient, ρ t and ρ t-1 is the Pearson correlation coefficient, ∈ is a small constant to prevent division by zero, M is the adaptive memory factor, exp() is the exponential function, and tanh() is the hyperbolic tangent function;

[0037] S34. By simulating the honey badger to search simultaneously in multiple independent search areas, an adaptive balancing mechanism is introduced to dynamically adjust the ratio of global and local searches according to the fitness change rate during the search process, and dynamically tune each hyperparameter P∈{d,h,α}:

[0038] P t+1 =P t +ζ·[M·(P * -P t )+(1-M)·(ω·ΔP g +(1-ω)·ΔP l )];

[0039] Among them, P t is the current hyperparameter value, P * is the historical optimal hyperparameter value, ζ is the control coefficient, ΔP g and ΔP l are the adjustment items for global search and local development respectively, ω is the balance coefficient between global and local search, P t+1 Represents the updated value of the hyperparameter P during the t+1th iteration;

[0040] S35. Apply the updated hyperparameter vector to the time series variational autoencoder model to dynamically tune the hyperparameters.

[0041] Optionally, the S4 specifically includes:

[0042] S41. Construct a weight parameter population. The weight parameter matrix of the time series variational autoencoder model is: Where m is the number of neural network layers, n w is the dimension of the weight parameters of each layer, R is a real number set, and the candidate population is initialized:

[0043] {W i |i=1,2,…,NP};

[0044] Among them, NP is the population size, Wi represents the i-th candidate weight parameter vector;

[0045] S42, for each candidate solution W i Use mutation strategy to calculate mutation vector V i :

[0046] V i =W r1 +F·(W r2 -W r3 )+γ·(W i -W prev );

[0047] Among them, r1, r2 and r3 are randomly selected and different indexes in the population, F is the scaling factor, γ is the momentum factor, and W prev represents the value of the candidate solution in the previous iteration, W r1 、W r2 and W r3 ;

[0048] S43, for candidate solution W i With the mutation vector V i Perform binomial crossover operation to generate the test vector U i :

[0049]

[0050] Among them, j represents the dimension index of the weight parameter, rand j is a uniformly distributed random number, CR is the crossover probability, j rand is the randomly selected variable dimension index, V i,j is the value of the i-th mutation vector in the j-th dimension, W i,j is the value of the i-th population individual in the j-th dimension;

[0051] S44. Define fitness function F DE (W), based on equipment operating status prediction data Pearson correlation coefficient with time series dataset X, data dynamic range matching and weight regularization:

[0052]

[0053] in, represents the Pearson correlation coefficient, represents the dynamic range of the equipment operation status prediction data, DR(X) represents the dynamic range of the time series data set, ln() is the logarithmic function, ||W||2 represents the L2 norm of the weight matrix W, ω3, ω4 and ω5 are the preset weight coefficients;

[0054] S45, perform selection operation, for each candidate solution W i , if F DE (U i ) <F DE (W i ), then update the candidate solution W i =U i ; Otherwise, keep the candidate solution unchanged;

[0055] S46, repeat steps S42 to S45 until the preset number of iterations or convergence standard is reached, and the global optimal weight parameter W is obtained. * , the globally optimal weight parameters are applied to the time series variational autoencoder model to minimize the prediction error.

[0056] Optionally, the S5 specifically includes:

[0057] S51, obtain real-time equipment operation data X t ∈R T×n , where T is the time series length, n is the input feature dimension, t represents the current time step, and R is a set of real numbers;

[0058] S52, real-time equipment operation data X t Input the temporal variational autoencoder model encoder E to obtain the dynamic latent vector z t :

[0059]

[0060] Among them, f μ (X t ;φ) represents the mean function, σ(X t ;φ) represents the standard deviation function, δ(X t ) is the dynamic latent space regulation factor, ⊙ represents element-by-element multiplication, φ is the encoder parameter, E(X t ) represents the encoder's mapping of real-time device operation data, ρ is a random noise vector, is a standard normal distribution;

[0061] S53, use the variational autoencoder model decoder D to the potential vector z t Decode and generate real-time predicted equipment operating status data

[0062]

[0063] Where Δ is the predicted time step, W o is the decoder weight matrix, b is the bias vector, f θ () is a nonlinear activation function, γ(z t ,X t) is the adaptive compensation term, θ is the decoder parameter;

[0064] S54, introduce nonlinear time decay mechanism and calculate prediction confidence factor γ t :

[0065]

[0066] Where λ is the time decay coefficient, T max is the preset maximum prediction time length, is the Pearson correlation coefficient, κ is the rate control coefficient, σ(X t ) is the standard deviation, ∈ is a small constant to prevent division by zero, tanh() is the hyperbolic tangent function, and exp() is the exponential function;

[0067] S55, according to the prediction confidence factor γ t Correct the real-time predicted equipment operation status data to obtain the final equipment operation status prediction data

[0068]

[0069] S56. Output the corrected final equipment operation status prediction data as the final prediction result, and use it for equipment status monitoring and dynamic update of variational autoencoder model parameters.

[0070] The beneficial effects of the present invention are:

[0071] The present invention achieves high-precision prediction of the operating status of the main equipment of the pumped storage power station in a complex dynamic environment by introducing an improved time-series variational autoencoder model, an innovative honey badger optimization algorithm and a differential evolution algorithm, effectively solving the problems of the mathematical modeling method in the prior art being difficult to adapt to complex working conditions, low prediction accuracy, and poor dynamic adaptability. In terms of model structure, the time-series variational autoencoder model is able to dynamically adjust the latent space dimension according to changes in input data through a dynamic latent space control factor, thereby improving the model's learning ability under nonlinear dynamic data. At the same time, the adaptive compensation mechanism ensures that the predicted data can be dynamically corrected during the model decoding process, so that the model not only pays attention to historical data patterns, but can also quickly respond to changes in real-time input data, thereby improving the accuracy and robustness of the prediction results. In terms of model hyperparameter optimization, the present invention achieves dynamic tuning of hyperparameters through an improved honey badger optimization algorithm, introduces an adaptive memory factor in global search and local development, breaks the limitation of traditional optimization algorithms that make decisions based only on the current environment, and effectively improves the efficiency and effect of hyperparameter search. In addition, during the optimization of the model weight parameters, the global search capability of the differential evolution algorithm is used to introduce the Pearson correlation coefficient and dynamic range deviation between the equipment operating status prediction data and the time series data set into the fitness function, so that the model can maintain the prediction accuracy in complex dynamic working conditions while improving the stability of the prediction results. During the prediction process, the nonlinear time decay mechanism introduced by the present invention realizes the automatic correction of the prediction data during long time series prediction through the dynamic adjustment of the prediction confidence factor, thereby avoiding the expansion of the prediction error as time accumulates. Combining the above technical means, the present invention has the significant advantages of high prediction accuracy, strong model stability, good dynamic adaptability, and excellent generalization ability. It can effectively improve the accuracy and real-time performance of the operating status monitoring of the main equipment of the pumped storage power station, and provide important technical support for the safe operation, intelligent operation and maintenance, and optimization of operation and maintenance strategies of the power station equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0073] Figure 1 This is a flow chart of the mathematical modeling method for the main equipment of a pumped storage power station based on dynamic simulation proposed by the present invention;

[0074] Figure 2 This is a schematic diagram of the actual application of the mathematical modeling method for main equipment of a pumped-storage power station based on dynamic simulation proposed by the present invention in the prediction of the operating status of the main equipment of a pumped-storage power station. DETAILED DESCRIPTION

[0075] The present invention will now be described in further detail with reference to the accompanying drawings, which are simplified schematic diagrams that illustrate the basic structure of the present invention in a schematic manner.

[0076] refer to Figure 1 and Figure 2 The mathematical modeling method of the main equipment of the pumped storage power station based on dynamic simulation includes the following steps:

[0077] S1. Collect multi-source time series data of the main equipment of the pumped storage power station, pre-process the multi-source time series data, and generate a time series data set;

[0078] S2. Build a time series variational autoencoder model, input the time series dataset into the time series variational autoencoder model for training, map the time series data into a dynamic latent space through the encoder, and reconstruct the latent variables into device operation status prediction data through the decoder;

[0079] S3. Introducing the Honey Badger optimization algorithm to dynamically tune the hyperparameters of the temporal variational autoencoder model. Through the global exploration and local development strategies of the Honey Badger optimization algorithm, the latent space dimension, number of hidden layer nodes, and learning rate of the variational autoencoder model are dynamically adjusted.

[0080] S4. Based on the Pearson correlation coefficient between the equipment operation status prediction data and the time series dataset, the weight parameters of the time series variational autoencoder model are globally optimized using the differential evolution algorithm to minimize the prediction error based on a global search.

[0081] S5. Use the time series variational autoencoder model to predict the real-time input equipment operation data and generate predicted data of the equipment's future state. In the prediction process, a nonlinear time decay mechanism is introduced. By setting the nonlinear time decay factor, the prediction confidence is automatically adjusted during long time series prediction.

[0082] S6. Compare and analyze the prediction results with the actual data of equipment operation in the time series data set. When the prediction error exceeds the set threshold, the anomaly detection and early warning mechanism is triggered. Through equipment operation status prediction and anomaly early warning, the power station operation and maintenance personnel are assisted in formulating equipment operation optimization strategies.

[0083] In this embodiment, S2 specifically includes:

[0084] S21, build encoder E, and transform the time series dataset X∈R T×n Mapped to a latent variable z∈R in a dynamic latent space d , R is a set of real numbers, R is the time step of the time series data, n is the number of data features at each time step, and d is the dimension of the dynamic latent space;

[0085] S22. Construct a decoder D to reconstruct the latent variable z into the predicted device operating status data

[0086] S23. Set up a dynamic latent space module L and dynamically adjust the latent space dimension by introducing a dynamic entropy control mechanism:

[0087]

[0088] Among them, d t+1 represents the potential space dimension of the next iteration, d t represents the potential space dimension of the current iteration, η is the control coefficient, tanh() is the hyperbolic tangent function, H(z) is the Shannon entropy of the latent variable, H max is the preset maximum entropy value;

[0089] S24. In the process of building the temporal variational autoencoder model, a multimodal adaptive mapping mechanism is introduced to dynamically set the hidden layer size h and learning rate α:

[0090] h=h0+β·tanh(δ·H(z)+(1-δ)·C(X)-H target );

[0091] α=α0·exp(-λ·[δ·H(z)+(1-δ)·C(X)]);

[0092] Among them, h0 and α0 are the initial hidden layer size and learning rate, β and λ are control factors, δ is the weight coefficient, and H target is the target entropy value, exp() is the exponential function, and C(X) is the complexity measure of the input time series dataset X:

[0093] C(X)=log2(1+Var(X));

[0094] Where Var(X) represents the variance of the time series data set X, and log2 is the logarithmic function;

[0095] S25. Initialize the model's hyperparameters, including encoder parameters, decoder parameters, initial latent space dimension, hidden layer size, and learning rate. Integrate the encoder, decoder, and dynamic latent space modules to construct an improved temporal variational autoencoder model.

[0096] In this embodiment, S3 specifically includes:

[0097] S31. Initialize the population of the honey badger optimization algorithm to form a set of hyperparameter vectors Θ hp :

[0098] Θ hp ={[d i ,hi ,α i ]|i=1,2,…,N};

[0099] Where N is the population size, d i is the potential space dimension of the temporal variational autoencoder model of the i-th individual, h i is the number of hidden nodes of the i-th individual, α i is the learning rate of the i-th individual;

[0100] S32. Define the fitness function and use the evaluation index that combines the prediction effect of the time series variational autoencoder model with the characteristics of multimodal data:

[0101]

[0102] in, Equipment operating status data The Pearson correlation coefficient between the time series data set X, is the coefficient of variation, and are standard deviation and mean, CV ref is the reference variation coefficient, ω1, ω2 and ω3 are the preset weight coefficients, is the Shannon entropy, H ref is the reference entropy value, F(Θ hp ) is the fitness function;

[0103] S33. By introducing historical optimal memory, we simulate the behavior of honey badgers searching simultaneously in multiple independent search areas and record the historical optimal hyperparameters:

[0104]

[0105] Among them, t is the current iteration number, T max is the maximum number of iterations, τ is the decay constant, φ is the balance coefficient, ρ t and ρ t-1 is the Pearson correlation coefficient, ∈ is a small constant to prevent division by zero, M is the adaptive memory factor, exp() is the exponential function, and tanh() is the hyperbolic tangent function;

[0106] S34. By simulating the honey badger to search simultaneously in multiple independent search areas, an adaptive balancing mechanism is introduced to dynamically adjust the ratio of global and local searches according to the fitness change rate during the search process, and dynamically tune each hyperparameter P∈{d,h,α}:

[0107] P t+1 =P t +ζ·[M·(P * -P t)+(1-M)·(ω·ΔP g +(1-ω)·ΔP l )];

[0108] Among them, P t is the current hyperparameter value, P * is the historical optimal hyperparameter value, ζ is the control coefficient, ΔP g and ΔP l are the adjustment items for global search and local development respectively, ω is the balance coefficient between global and local search, P t+1 Represents the updated value of the hyperparameter P during the t+1th iteration;

[0109] S35. Apply the updated hyperparameter vector to the time series variational autoencoder model to dynamically tune the hyperparameters.

[0110] In this embodiment, the S4 specifically includes:

[0111] S41. Construct a weight parameter population. The weight parameter matrix of the time series variational autoencoder model is: Where m is the number of neural network layers, n w is the dimension of the weight parameters of each layer, R is a real number set, and the candidate population is initialized:

[0112] {W i |i=1,2,…,NP};

[0113] Among them, NP is the population size, W i represents the i-th candidate weight parameter vector;

[0114] S42, for each candidate solution W i Use mutation strategy to calculate mutation vector V i :

[0115] V i =W r1 +F·(W r2 -W r3 )+γ·(W i -W prev );

[0116] Among them, r1, r2 and r3 are randomly selected and different indexes in the population, F is the scaling factor, γ is the momentum factor, and W prev represents the value of the candidate solution in the previous iteration, W r1 、W r2 and W r3 ;

[0117] S43, for candidate solution W i With the mutation vector V iPerform binomial crossover operation to generate the test vector U i :

[0118]

[0119] Among them, j represents the dimension index of the weight parameter, rand j is a uniformly distributed random number, CR is the crossover probability, j rand is the randomly selected variable dimension index, V i,j is the value of the i-th mutation vector in the j-th dimension, W i,j is the value of the i-th population individual in the j-th dimension;

[0120] S44. Define fitness function F DE (W), based on equipment operating status prediction data Pearson correlation coefficient with time series dataset X, data dynamic range matching and weight regularization:

[0121]

[0122] in, represents the Pearson correlation coefficient, represents the dynamic range of the equipment operation status prediction data, DR(X) represents the dynamic range of the time series data set, ln() is the logarithmic function, ||W||2 represents the L2 norm of the weight matrix W, ω3, ω4 and ω5 are the preset weight coefficients;

[0123] S45, perform selection operation, for each candidate solution W i , if F DE (U i ) <F DE (W i ), then update the candidate solution W i =U i ; Otherwise, keep the candidate solution unchanged;

[0124] S46, repeat steps S42 to S45 until the preset number of iterations or convergence standard is reached, and the global optimal weight parameter W is obtained. * , the globally optimal weight parameters are applied to the time series variational autoencoder model to minimize the prediction error.

[0125] In this embodiment, the S5 specifically includes:

[0126] S51, obtain real-time equipment operation data X t ∈R T×n , where T is the time series length, n is the input feature dimension, t represents the current time step, and R is a set of real numbers;

[0127] S52, real-time equipment operation data Xt Input the temporal variational autoencoder model encoder E to obtain the dynamic latent vector z t :

[0128]

[0129] Among them, f μ (X t ;φ) represents the mean function, σ(X t ;φ) represents the standard deviation function, δ(X t ) is the dynamic latent space regulation factor, ⊙ represents element-by-element multiplication, φ is the encoder parameter, E(X t ) represents the encoder's mapping of real-time device operation data, ρ is a random noise vector, is a standard normal distribution;

[0130] S53, use the variational autoencoder model decoder D to the potential vector z t Decode and generate real-time predicted equipment operating status data

[0131]

[0132] Where Δ is the predicted time step, W o is the decoder weight matrix, b is the bias vector, f θ () is a nonlinear activation function, γ(z t ,X t ) is the adaptive compensation term, θ is the decoder parameter;

[0133] S54, introduce nonlinear time decay mechanism and calculate prediction confidence factor γ t :

[0134]

[0135] Where λ is the time decay coefficient, T max is the preset maximum prediction time length, is the Pearson correlation coefficient, κ is the rate control coefficient, σ(X t ) is the standard deviation, ∈ is a small constant to prevent division by zero, tanh() is the hyperbolic tangent function, and exp() is the exponential function;

[0136] S55, according to the prediction confidence factor γ t Correct the real-time predicted equipment operation status data to obtain the final equipment operation status prediction data

[0137]

[0138] S56. Output the corrected final equipment operation status prediction data as the final prediction result, and use it for equipment status monitoring and dynamic update of variational autoencoder model parameters.

[0139] Example 1:

[0140] In order to verify the feasibility of the present invention in implementation, the present invention is applied to the actual operation of a large-scale pumped storage power station. The main equipment of the power station (including water pump turbines, generator motors, transformer equipment, etc.) is subject to frequent start and stop, load changes and seasonal working condition switching, and the equipment operating status shows complex nonlinear and dynamic change characteristics. In order to ensure the safe and stable operation of the equipment, it is necessary to predict the operating status of the equipment in real time, so as to timely discover potential faults or abnormal conditions and assist operation and maintenance personnel in formulating maintenance and optimization strategies. However, when dealing with dynamic working condition changes, traditional modeling methods usually have the problems of low prediction accuracy and poor model generalization ability. Especially in long time series prediction, the prediction error is easy to accumulate and amplify, resulting in a decrease in the credibility of the prediction results.

[0141] The "mathematical modeling method for the main equipment of a pumped storage power station based on dynamic simulation" proposed in the present invention has been put into practical application in the operation of the main equipment of the power station. The method of the present invention adopts an improved time series variational autoencoder model, which shows excellent results in the prediction of equipment operating status through dynamic latent space control factors and adaptive compensation mechanisms. In terms of model hyperparameter tuning, an improved honey badger optimization algorithm is used to dynamically adjust the latent space dimension, learning rate and number of hidden layer nodes, thereby realizing automatic adaptation of the model under different working conditions. In addition, the global optimization of weight parameters is performed by the differential evolution algorithm (DE) to ensure that the model always maintains high accuracy during the prediction process. In the prediction stage, the nonlinear time decay mechanism is used to dynamically adjust the prediction confidence, which effectively solves the problem of unstable prediction results in long time series prediction.

[0142] In practical applications, taking the operating status prediction of power station pump turbines as an example, equipment operation data for 12 months from May 2023 to May 2024 were collected. The data included multi-dimensional time series data such as equipment power, speed, vibration, temperature, flow, etc. The data was collected once per minute, totaling 52,560 data. During the data processing process, these data were divided into training set (60%), validation set (20%) and test set (20%), and the time series variational autoencoder model was used for training and prediction. During the model training stage, the Honey Badger optimization algorithm dynamically adjusted the latent space dimension from 16 to 64, the number of hidden layer nodes from 128 to 512, and the learning rate from 0.001 to 0.01 during the model hyperparameter tuning process. After 50 iterations, the prediction error of the model hyperparameters on the validation set reached the optimal value. In the model weight parameter optimization stage, the differential evolution algorithm evaluates the Pearson correlation coefficient and dynamic range deviation between the model's predicted data and actual data through the fitness function, realizes dynamic optimization of the weight parameters in the global search, and ultimately greatly improves the prediction accuracy of the model.

[0143] In the actual prediction process, the vibration data of the pump turbine was selected as the key prediction object, and the prediction effects of the method of the present invention and traditional models (LSTM and ARIMA models) were compared. The mean absolute error (MAE%) of different models was recorded at prediction times of 30 minutes, 60 minutes, 120 minutes, and 240 minutes. The results show that the prediction error of the method of the present invention is significantly lower than that of the traditional model, especially in long-term predictions, showing higher prediction stability. In actual application, the system successfully predicted three turbine vibration exceeding the standard event, enabling the operation and maintenance personnel to carry out effective preventive maintenance before the failure occurred, avoiding unplanned equipment downtime and saving approximately 300,000 yuan in maintenance costs.

[0144] Table 1 Error comparison of different models in equipment operation status prediction

[0145] Prediction time (minutes) Method of the present invention LSTM model ARIMA model 30 3.1 5.4 6.7 60 4.5 7.9 9.8 120 6.2 10.5 12.1 240 8.8 13.2 15.7 360 10.1 15.0 18.4 480 11.5 17.3 21.0 600 13.0 19.8 23.6 720 14.2 22.1 26.3

[0146] As can be seen in Table 1, the proposed method exhibits significant advantages in forecast accuracy at various forecast times. When forecasting for 30 minutes, the proposed method achieves a mean absolute error of only 3.1%, compared to 5.4% for the long short-term memory network model and 6.7% for the autoregressive integrated moving average model. These reductions represent approximately 42.6% and 53.7% reductions, respectively, demonstrating its high accuracy in short-term time series forecasting.

[0147] While the prediction error of the proposed method increases with longer forecast time, the rate of increase is significantly lower than that of traditional models. For example, when forecasting for 120 minutes, the proposed method's error is 6.2%, while the errors of the long-short-term memory network model and the autoregressive integrated moving average model reach 10.5% and 12.1%, respectively. The proposed method's error is still 41% lower than that of the long-short-term memory network model and 48.8% lower than that of the autoregressive integrated moving average model. This demonstrates that the proposed method is more stable in medium- and long-term forecasts, and the model can effectively respond to dynamic operating conditions and maintain high forecast accuracy.

[0148] In longer prediction times (240 minutes and above), the advantages of the method of the present invention are even more significant. When the prediction time is 240 minutes, the error of the method of the present invention is 8.8%, while the long short-term memory network model is 13.2%, and the autoregressive integral moving average model is as high as 15.7%. In particular, in predictions up to 720 minutes (12 hours), the prediction error of the method of the present invention is 14.2%, while the prediction errors of the long short-term memory network model and the autoregressive integral moving average model are 22.1% and 26.3%, respectively. Compared with the long short-term memory network model, the prediction error of the method of the present invention is reduced by 35.7%; compared with the autoregressive integral moving average model, it is reduced by 45.9%. This data demonstrates the significant advantages of the method of the present invention in long time series prediction. It not only maintains the accuracy of the prediction results, but also effectively reduces the cumulative effect of errors.

[0149] Overall, the method of the present invention exhibits significant characteristics of high precision and low error when predicting the operating status of equipment for both short and long periods of time. Compared to traditional methods, the present invention, through dynamic latent space regulation, adaptive compensation mechanism, and nonlinear time attenuation mechanism, can better capture the long-term dependencies of data when faced with complex dynamic changes in equipment operation, and automatically adjust the confidence level of the prediction model, so that the prediction results remain stable and reliable under dynamically changing working conditions. This capability is particularly suitable for operating status monitoring scenarios of large-scale industrial equipment such as pumped storage power stations, helping to improve the safety of equipment operation and the predictability of maintenance, ultimately improving the operating efficiency and economic benefits of the equipment.

[0150] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A mathematical modeling method for main equipment of a pumped storage power station based on dynamic simulation, characterized in that: The steps include: S1. Collect multi-source time series data of the main equipment of the pumped storage power station, pre-process the multi-source time series data, and generate a time series data set; S2. Build a time series variational autoencoder model, input the time series dataset into the time series variational autoencoder model for training, map the time series data into a dynamic latent space through the encoder, and reconstruct the latent variables into device operation status prediction data through the decoder; S3. Introducing the Honey Badger optimization algorithm to dynamically tune the hyperparameters of the temporal variational autoencoder model. Through the global exploration and local development strategies of the Honey Badger optimization algorithm, the latent space dimension, number of hidden layer nodes, and learning rate of the variational autoencoder model are dynamically adjusted. S4. Based on the Pearson correlation coefficient between the equipment operation status prediction data and the time series dataset, the weight parameters of the time series variational autoencoder model are globally optimized using the differential evolution algorithm to minimize the prediction error based on a global search. S5. Use the time series variational autoencoder model to predict the real-time input equipment operation data and generate predicted data of the equipment's future state. In the prediction process, a nonlinear time decay mechanism is introduced. By setting the nonlinear time decay factor, the prediction confidence is automatically adjusted during long time series prediction. S6. Compare and analyze the prediction results with the actual data of equipment operation in the time series data set. When the prediction error exceeds the set threshold, the anomaly detection and early warning mechanism is triggered. Through equipment operation status prediction and anomaly early warning, the power station operation and maintenance personnel are assisted in formulating equipment operation optimization strategies.

2. The mathematical modeling method for main equipment of a pumped storage power station based on dynamic simulation according to claim 1 is characterized in that: The S2 specifically includes: S21, build encoder E, and transform the time series dataset X∈R T×n Mapped to a latent variable z∈R in a dynamic latent space d , R is a set of real numbers, R is the time step of the time series data, n is the number of data features at each time step, and d is the dimension of the dynamic latent space; S22. Construct a decoder D to reconstruct the latent variable z into the predicted device operating status data S23. Set up a dynamic latent space module L and dynamically adjust the latent space dimension by introducing a dynamic entropy control mechanism: Among them, d t+1 represents the potential space dimension of the next iteration, d t represents the potential space dimension of the current iteration, η is the control coefficient, tanh() is the hyperbolic tangent function, H(z) is the Shannon entropy of the latent variable, H max is the preset maximum entropy value; S24. In the process of building the temporal variational autoencoder model, a multimodal adaptive mapping mechanism is introduced to dynamically set the hidden layer size h and learning rate α: h=h0+β·tanh(δ·H(z)+(1-δ)·C(X)-H target ); α=α0·exp(-λ·[δ·H(z)+(1-δ)·C(X)]); Among them, h0 and α0 are the initial hidden layer size and learning rate, β and λ are control factors, δ is the weight coefficient, and H target is the target entropy value, exp() is the exponential function, and C(X) is the complexity measure of the input time series dataset X: C(X)=log2(1+Var(X)); Where Var(X) represents the variance of the time series data set X, and log2 is the logarithmic function; S25. Initialize the model's hyperparameters, including encoder parameters, decoder parameters, initial latent space dimension, hidden layer size, and learning rate. Integrate the encoder, decoder, and dynamic latent space modules to construct an improved temporal variational autoencoder model.

3. The mathematical modeling method for main equipment of a pumped storage power station based on dynamic simulation according to claim 1 is characterized in that: The S3 specifically includes: S31. Initialize the population of the honey badger optimization algorithm to form a set of hyperparameter vectors Θ hp : I hp ={[d i ,h i ,a i ]∣i=1,2,…,N}; Where N is the population size, d i is the potential space dimension of the temporal variational autoencoder model of the i-th individual, h i is the number of hidden nodes of the i-th individual, α i is the learning rate of the i-th individual; S32. Define the fitness function and use the evaluation index that combines the prediction effect of the time series variational autoencoder model with the characteristics of multimodal data: in, Equipment operating status data The Pearson correlation coefficient between the time series data set X, is the coefficient of variation, and are standard deviation and mean, CV ref is the reference variation coefficient, ω1, ω2 and ω3 are the preset weight coefficients, is the Shannon entropy, H ref is the reference entropy value, F(Θ hp ) is the fitness function; S33. By introducing historical optimal memory, we simulate the behavior of honey badgers searching simultaneously in multiple independent search areas and record the historical optimal hyperparameters: Among them, t is the current iteration number, T max is the maximum number of iterations, τ is the decay constant, φ is the balance coefficient, ρ t and ρ t-1 is the Pearson correlation coefficient, ∈ is a small constant to prevent division by zero, M is the adaptive memory factor, exp() is the exponential function, and tanh() is the hyperbolic tangent function; S34. By simulating the honey badger to search simultaneously in multiple independent search areas, an adaptive balancing mechanism is introduced to dynamically adjust the ratio of global and local searches according to the fitness change rate during the search process, and dynamically tune each hyperparameter P∈{d,h,α}: P t+1 =P t +ζ·[M·(P * -P t )+(1-M)·(ω·ΔP g +(1-ω)·ΔP l )]; Among them, P t is the current hyperparameter value, P * is the historical optimal hyperparameter value, ζ is the control coefficient, ΔP g and ΔP l are the adjustment items for global search and local development respectively, ω is the balance coefficient between global and local search, P t+1 Represents the updated value of the hyperparameter P during the t+1th iteration; S35. Apply the updated hyperparameter vector to the time series variational autoencoder model to dynamically tune the hyperparameters.

4. The mathematical modeling method for main equipment of a pumped storage power station based on dynamic simulation according to claim 1 is characterized in that: The S4 specifically includes: S41. Construct a weight parameter population. The weight parameter matrix of the time series variational autoencoder model is: Where m is the number of neural network layers, n w is the dimension of the weight parameters of each layer, R is a real number set, and the candidate population is initialized: {W i ∣i=1,2,…,NP}; Where NP is the population size, W i represents the i-th candidate weight parameter vector; S42, for each candidate solution W i Use mutation strategy to calculate mutation vector V i : V i =W r1 +F·(W r2 -W r3 )+γ·(W i -W prev ); Among them, r1, r2 and r3 are randomly selected and different indexes in the population, F is the scaling factor, γ is the momentum factor, and W prev represents the value of the candidate solution in the previous iteration, W r1 、W r2 and W r3 ; S43, for candidate solution W i With the mutation vector V i Perform binomial crossover operation to generate the test vector U i : Among them, j represents the dimension index of the weight parameter, rand j is a uniformly distributed random number, CR is the crossover probability, j rand is the randomly selected variable dimension index, V i,j is the value of the i-th mutation vector in the j-th dimension, W i,j is the value of the i-th population individual in the j-th dimension; S44. Define fitness function F DE (W), based on equipment operating status prediction data Pearson correlation coefficient with time series dataset X, data dynamic range matching and weight regularization: in, represents the Pearson correlation coefficient, represents the dynamic range of the equipment operation status prediction data, DR(X) represents the dynamic range of the time series data set, ln() is the logarithmic function, ||W||2 represents the L2 norm of the weight matrix W, ω3, ω4 and ω5 are the preset weight coefficients; S45, perform selection operation, for each candidate solution W i , if F DE (U i ) <F DE (W i ), then update the candidate solution W i =U i ; Otherwise, keep the candidate solution unchanged; S46, repeat steps S42 to S45 until the preset number of iterations or convergence standard is reached, and the global optimal weight parameter W is obtained. * , the globally optimal weight parameters are applied to the time series variational autoencoder model to minimize the prediction error.

5. The mathematical modeling method for main equipment of a pumped storage power station based on dynamic simulation according to claim 1 is characterized in that: The S5 specifically includes: S51, obtain real-time equipment operation data X t ∈R T×n , where T is the time series length, n is the input feature dimension, t represents the current time step, and R is a set of real numbers; S52, real-time equipment operation data X t Input the temporal variational autoencoder model encoder E to obtain the dynamic latent vector z t : Among them, f μ (X t ;φ) represents the mean function, σ(X t ;φ) represents the standard deviation function, δ(X t ) is the dynamic latent space regulation factor, ⊙ represents element-by-element multiplication, φ is the encoder parameter, E(X t ) represents the encoder's mapping of real-time device operation data, ρ is a random noise vector, is a standard normal distribution; S53, use the variational autoencoder model decoder D to the potential vector z t Decode and generate real-time predicted equipment operating status data Where Δ is the predicted time step, W o is the decoder weight matrix, b is the bias vector, f θ () is a nonlinear activation function, γ(z t ,X t ) is the adaptive compensation term, θ is the decoder parameter; S54, introduce nonlinear time decay mechanism and calculate prediction confidence factor γ t : Where λ is the time decay coefficient, T max is the preset maximum prediction time length, is the Pearson correlation coefficient, κ is the rate control coefficient, σ(X t ) is the standard deviation, ∈ is a small constant to prevent division by zero, tanh() is the hyperbolic tangent function, and exp() is the exponential function; S55, according to the prediction confidence factor γ t Correct the real-time predicted equipment operation status data to obtain the final equipment operation status prediction data S56. Output the corrected final equipment operation status prediction data as the final prediction result, and use it for equipment status monitoring and dynamic update of variational autoencoder model parameters.

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