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

Abstract

The application discloses a method for mathematical modeling of main equipment of pumped storage power station based on dynamic simulation, which comprises the following steps: S1, collecting 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 variational autoencoder model, and initializing through a dynamic latent space control factor; S3, using a meerkat optimization algorithm to dynamically optimize the time sequence variational autoencoder model hyperparameters; S4, using a differential evolution algorithm to globally optimize the time sequence variational autoencoder model weight parameters; S5, using the time sequence variational autoencoder model to make a prediction, and introducing a nonlinear time decay mechanism to correct the prediction result; and S6, comparing the prediction result with actual equipment operation data to assist power station operation and maintenance personnel in formulating an equipment operation optimization strategy. The application realizes high-precision prediction and dynamic simulation of the operation state of the main equipment of the pumped storage power station, and improves the safety and maintenance efficiency of equipment operation.

Description

Technical Field

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

[0002] During the operation of the main equipment in a pumped-storage power station, the safety, stability, and efficiency of the equipment are crucial to the overall operation of the station. The main equipment of a pumped-storage power station (such as pumps, turbines, generators, and transformers) exhibits significant nonlinear and dynamic characteristics during long-term operation due to complex operating conditions, environmental factors, and load fluctuations. To ensure the safe and stable operation of the equipment, real-time monitoring and prediction of its operating status are typically required to promptly identify potential faults or anomalies and assist maintenance personnel in developing effective maintenance and optimization strategies. Therefore, developing 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 lifespan, and ensuring the overall operational safety of the power station.

[0003] Currently, in the field of mathematical modeling of pumped storage power station main equipment, commonly used methods mainly include physical mechanism-based modeling methods and data-driven modeling methods. Physical mechanism-based modeling methods typically rely on equipment structure, physical characteristics, and operating conditions, simulating equipment behavior by establishing differential equations or mechanistic models. However, these methods are highly dependent on the internal mechanisms of the equipment, and the accuracy and applicability of the model are limited when the equipment operating environment is complex or comprehensive data is difficult to obtain. Furthermore, due to various uncertainties in actual equipment operation (such as environmental changes and operating condition disturbances), physical mechanism models are difficult to dynamically adjust and adaptively learn, resulting in large prediction errors in long-term predictions or under dynamic operating conditions.

[0004] Data-driven modeling methods have developed rapidly in recent years, primarily utilizing machine learning and deep learning to analyze and model equipment operation data. These methods can uncover implicit patterns in equipment operation from historical data without requiring explicit knowledge of the equipment's internal physical mechanisms. Common models in this category include Long Short-Term Memory (LSTM) networks, Autoregressive Integral Moving Average (ARIMA) models, and Variational Autoencoders (VAEs). These models have demonstrated certain advantages in equipment state prediction, especially in handling nonlinear and time-series data. However, traditional data-driven methods still have some shortcomings in practical applications. For example, LSTM models may suffer from the vanishing gradient problem when dealing with long-term dependencies, leading to decreased prediction accuracy; ARIMA models have limited capabilities in 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 pumped storage power stations based on dynamic simulation is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] One objective of this invention is to propose a mathematical modeling method for the main equipment of pumped-storage power stations based on dynamic simulation. This invention achieves high-precision prediction of equipment operating status through an improved temporal variational autoencoder model. It introduces a dynamic latent space adjustment factor and an adaptive compensation mechanism to dynamically adjust the latent space dimension and the adaptability of the predicted data during model encoding and decoding. Simultaneously, an improved honey badger optimization algorithm dynamically fine-tunes the model's hyperparameters, including the latent space dimension, the number of hidden layer nodes, and the learning rate, enabling adaptive adjustment of the model under different dynamic operating conditions. This invention also incorporates a differential evolutionary algorithm (DE) for global weight parameter optimization. Through an innovative fitness function, based on the Pearson correlation coefficient and dynamic range deviation between the predicted equipment operating status data and the time-series dataset, it ensures the global optimality of the model weights. During the prediction process, a nonlinear time decay mechanism is employed to dynamically correct the prediction results based on the prediction confidence factor, ensuring data stability in long-term series predictions. This invention features high prediction accuracy, strong model stability, good dynamic adaptability, and excellent generalization ability in complex dynamic environments, effectively improving the operational safety and maintenance efficiency of the main equipment of pumped-storage power stations.

[0007] The mathematical modeling method for main equipment of pumped-storage power stations based on dynamic simulation according to embodiments 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, and preprocess the multi-source time-series data to generate a time-series dataset;

[0009] S2. Construct a temporal variational autoencoder model. Input the temporal dataset into the temporal variational autoencoder model for training. The encoder maps the temporal data to the dynamic latent space, and the decoder reconstructs the latent variables into device operating status prediction data.

[0010] S3. The honey badger optimization algorithm is introduced 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, the number of hidden layer nodes and the 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 on the basis of global search.

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

[0013] S6. Compare and analyze the prediction results with the actual equipment operation data in the time series dataset. When the prediction error exceeds the set threshold, trigger the anomaly detection and early warning mechanism. Through equipment operation status prediction and anomaly early warning, assist power plant operation and maintenance personnel in formulating equipment operation optimization strategies.

[0014] Optionally, S2 specifically includes:

[0015] S21. Construct encoder E, and convert the time series dataset X∈R. T×n Mapped to latent variables z∈R in the dynamic latent space d R is the 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 decoder D to reconstruct the latent variable z into predicted device operating state data.

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

[0018]

[0019] Where, d t+1 d represents the potential spatial dimension of the next iteration. t Let η represent the latent space dimension of the current iteration, η be the regulation coefficient, tanh() be the hyperbolic tangent function, and H(z) be the Shannon entropy of the latent variable. max The preset maximum entropy value;

[0020] S24. In the process of constructing the temporal variational autoencoder model, a multimodal adaptive mapping mechanism is introduced to dynamically set the hidden layer size h and the 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] Where h0 and α0 are the initial hidden layer size and learning rate, respectively, β and λ are the regulation factors, δ is the weight coefficient, and H targetLet exp() be the target entropy value, exp() be the exponential function, and C(X) be 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 dataset X, and log2 is the logarithmic function;

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

[0027] Optionally, S3 specifically includes:

[0028] S31. Initialize the population for the honey badger optimization algorithm, forming 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 Let h be the latent space dimension of the temporal variational autoencoder model for the i-th individual. i Let α be the number of hidden nodes for the i-th individual. i Let be the learning rate of the i-th individual;

[0031] S32. Define the fitness function and use an evaluation metric that combines the prediction performance of the temporal variational autoencoder model with the characteristics of multimodal data:

[0032]

[0033] in, For equipment operating status data The Pearson correlation coefficient between the dataset X and the time series dataset X. The coefficient of variation is 1. and These are the standard deviation and the mean, respectively, and the CV. ref The coefficient of variation is used as a reference, and ω1, ω2, and ω3 are preset weighting coefficients. For Shannon entropy, H ref As the reference entropy value, F(Θ) hp ) is the fitness function;

[0034] S33. By introducing historical best-in-class memory, the behavior of honey badgers searching simultaneously in multiple independent search areas is simulated, and historical best-in-class hyperparameters are recorded:

[0035]

[0036] Where t is the current iteration number, T max τ is the maximum number of iterations, φ is the decay constant, ρ is the balance coefficient, and φ is the equilibrium coefficient. t With 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 a honey badger simultaneously searching within multiple independent search regions, an adaptive balancing mechanism is introduced. The ratio of global to local search is dynamically adjusted based on the fitness change rate during the search process, and each hyperparameter P∈{d,h,α} is dynamically optimized.

[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 P is the current hyperparameter value. * The historical optimal hyperparameter value is given by ζ, which is the control coefficient, and ΔP is the value of ΔP. g and ΔP l These are adjustment terms for global search and local development, respectively, where ω is the balance coefficient between global and local search, and P... t+1 This represents the updated value of the hyperparameter P during the (t+1)th iteration.

[0040] S35. Apply the updated hyperparameter vector to the temporal variational autoencoder model to dynamically fine-tune the hyperparameters.

[0041] Optionally, S4 specifically includes:

[0042] S41. Construct a population of weight parameters. The weight parameter matrix of the temporal variational autoencoder model is as follows: Where m is the number of layers in the neural network, n w Let R be the dimension of the weight parameters for each layer, and R be the set of real numbers. Initialize the candidate population as follows:

[0043] {W i |i=1,2,…,NP};

[0044] Where NP is the population size, Wi This represents the vector of the i-th candidate weight parameters;

[0045] S42, For each candidate solution W i The mutation vector V is calculated using a mutation strategy. i :

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

[0047] Where r1, r2, and r3 are randomly selected and distinct indices in the population, F is the scaling factor, γ is the momentum factor, and W... prev W represents the value of the candidate solution in the previous iteration. r1 W r2 and W r3 ;

[0048] S43, regarding candidate solutions W i With the mutation vector V i Perform a binomial crossover operation to generate the test vector U. i :

[0049]

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

[0051] S44. Define the 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, This represents the Pearson correlation coefficient. The dynamic range of the predicted data for the device operating status is represented by DR(X), the dynamic range of the time series dataset is represented by ln(), the logarithmic function is represented by ||W||2, the L2 norm of the weight matrix W is represented by ||W||2, and ω3, ω4 and ω5 are preset weight coefficients.

[0054] S45. Perform a selection operation for each candidate solution W. i If F DE (U i ) <F DE (W i If so, then update the candidate solution W. i =U i Otherwise, keep the candidate solutions unchanged.

[0055] S46. Repeat steps S42 to S45 until the preset number of iterations or convergence criteria are reached, and obtain the globally optimal weight parameter W. * The globally optimal weight parameters are applied to the temporal variational autoencoder model to minimize the prediction error.

[0056] Optionally, S5 specifically includes:

[0057] S51. Obtain real-time device 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 the set of real numbers;

[0058] S52, Transfer real-time device operation data X t Inputting a temporal variational autoencoder model, encoder E yields a 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 ) represents the dynamic latent space control factor, ⊙ represents element-wise multiplication, φ represents the encoder parameter, and E(X) is the dynamic latent space control factor. t ) represents the encoder's mapping to real-time device operation data, and ρ is a random noise vector. It follows a standard normal distribution;

[0061] S53. Using the variational autoencoder model decoder D to process the latent vector z t Decode the data to generate real-time predicted device operating status data.

[0062]

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

[0064] S54. Introduce a nonlinear time decay mechanism to calculate the prediction confidence factor γ. t :

[0065]

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

[0067] S55, Based on the predicted confidence factor γ t The real-time predicted equipment operating status data is corrected to obtain the final predicted equipment operating status data.

[0068]

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

[0070] The beneficial effects of this invention are:

[0071] This invention achieves high-precision prediction of the operating status of pumped-storage power station main equipment in complex dynamic environments by introducing an improved temporal variational autoencoder model, an innovative honey badger optimization algorithm, and a differential evolution algorithm. This effectively solves the problems of existing mathematical modeling methods, such as difficulty in adapting to complex operating conditions, low prediction accuracy, and poor dynamic adaptability. In terms of model structure, a dynamic latent space adjustment factor enables the temporal variational autoencoder model to dynamically adjust the latent space dimension according to changes in input data, thereby improving the model's learning ability under nonlinear dynamic data. Simultaneously, an adaptive compensation mechanism ensures dynamic correction of predicted data during model decoding, enabling the model to not only focus on historical data patterns but also quickly respond to changes in real-time input data, improving the accuracy and robustness of prediction results. Regarding model hyperparameter optimization, this invention achieves dynamic tuning of hyperparameters through an improved honey badger optimization algorithm. An adaptive memory factor is introduced in both global search and local development, breaking the limitation of traditional optimization algorithms that only make decisions based on the current environment, effectively improving the efficiency and effectiveness of hyperparameter search. Furthermore, during the optimization of model weight parameters, the global search capability of the differential evolution algorithm is utilized to introduce the Pearson correlation coefficient and dynamic range deviation between the predicted equipment operating status data and the time-series dataset into the fitness function. This allows the model to maintain prediction accuracy while improving the stability of prediction results under complex dynamic operating conditions. During the prediction process, the nonlinear time decay mechanism introduced in this invention automatically corrects the prediction data in long-term series predictions through dynamic adjustment of the prediction confidence factor, preventing the prediction error from accumulating and expanding over time. Combining the above technical means, this invention possesses significant advantages such as high prediction accuracy, strong model stability, good dynamic adaptability, and excellent generalization ability. It can effectively improve the accuracy and real-time performance of monitoring the operating status of pumped-storage power station main equipment, providing important technical support for the safe operation, intelligent operation and maintenance, and optimization of operation and maintenance strategies for power station equipment. Attached Figure Description

[0072] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0073] Figure 1 This is a flowchart of the mathematical modeling method for the main equipment of pumped storage power stations based on dynamic simulation proposed in this invention;

[0074] Figure 2 This is a schematic diagram illustrating the practical application of the mathematical modeling method for pumped storage power station main equipment based on dynamic simulation proposed in this invention in predicting the operating status of pumped storage power station main equipment. Detailed Implementation

[0075] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0076] refer to Figure 1 and Figure 2 The mathematical modeling method for main equipment of pumped storage power stations 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, and preprocess the multi-source time-series data to generate a time-series dataset;

[0078] S2. Construct a temporal variational autoencoder model. Input the temporal dataset into the temporal variational autoencoder model for training. The encoder maps the temporal data to the dynamic latent space, and the decoder reconstructs the latent variables into device operating status prediction data.

[0079] S3. The honey badger optimization algorithm is introduced 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, the number of hidden layer nodes and the 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 on the basis of global search.

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

[0082] S6. Compare and analyze the prediction results with the actual equipment operation data in the time series dataset. When the prediction error exceeds the set threshold, trigger the anomaly detection and early warning mechanism. Through equipment operation status prediction and anomaly early warning, assist power plant operation and maintenance personnel in formulating equipment operation optimization strategies.

[0083] In this embodiment, S2 specifically includes:

[0084] S21. Construct encoder E, and convert the time series dataset X∈R. T×n Mapped to latent variables z∈R in the dynamic latent space d R is the 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 decoder D to reconstruct the latent variable z into predicted device operating state data.

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

[0087]

[0088] Where, d t+1 d represents the potential spatial dimension of the next iteration. t Let η represent the latent space dimension of the current iteration, η be the regulation coefficient, tanh() be the hyperbolic tangent function, and H(z) be the Shannon entropy of the latent variable. max The preset maximum entropy value;

[0089] S24. In the process of constructing the temporal variational autoencoder model, a multimodal adaptive mapping mechanism is introduced to dynamically set the hidden layer size h and the 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] Where h0 and α0 are the initial hidden layer size and learning rate, respectively, β and λ are the regulation factors, δ is the weight coefficient, and H target Let exp() be the target entropy value, exp() be the exponential function, and C(X) be 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 dataset X, and log2 is the logarithmic function;

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

[0096] In this embodiment, S3 specifically includes:

[0097] S31. Initialize the population for the honey badger optimization algorithm, forming 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 Let h be the latent space dimension of the temporal variational autoencoder model for the i-th individual. i Let α be the number of hidden nodes for the i-th individual. i Let be the learning rate of the i-th individual;

[0100] S32. Define the fitness function and use an evaluation metric that combines the prediction performance of the temporal variational autoencoder model with the characteristics of multimodal data:

[0101]

[0102] in, For equipment operating status data The Pearson correlation coefficient between the dataset X and the time series dataset X. The coefficient of variation is 1. and These are the standard deviation and the mean, respectively, and the CV. ref The coefficient of variation is used as a reference, and ω1, ω2, and ω3 are preset weighting coefficients. For Shannon entropy, H ref As the reference entropy value, F(Θ) hp ) is the fitness function;

[0103] S33. By introducing historical best-in-class memory, the behavior of honey badgers searching simultaneously in multiple independent search areas is simulated, and historical best-in-class hyperparameters are recorded:

[0104]

[0105] Where t is the current iteration number, T max τ is the maximum number of iterations, φ is the decay constant, ρ is the balance coefficient, and φ is the equilibrium coefficient. t With 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 a honey badger simultaneously searching within multiple independent search regions, an adaptive balancing mechanism is introduced. The ratio of global to local search is dynamically adjusted based on the fitness change rate during the search process, and each hyperparameter P∈{d,h,α} is dynamically optimized.

[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 P is the current hyperparameter value. * The historical optimal hyperparameter value is given by ζ, which is the control coefficient, and ΔP is the value of ΔP. g and ΔP l These are adjustment terms for global search and local development, respectively, where ω is the balance coefficient between global and local search, and P... t+1 This represents the updated value of the hyperparameter P during the (t+1)th iteration.

[0109] S35. Apply the updated hyperparameter vector to the temporal variational autoencoder model to dynamically fine-tune the hyperparameters.

[0110] In this embodiment, S4 specifically includes:

[0111] S41. Construct a population of weight parameters. The weight parameter matrix of the temporal variational autoencoder model is as follows: Where m is the number of layers in the neural network, n w Let R be the dimension of the weight parameters for each layer, and R be the set of real numbers. Initialize the candidate population as follows:

[0112] {W i |i=1,2,…,NP};

[0113] Where NP is the population size, W i This represents the vector of the i-th candidate weight parameters;

[0114] S42, For each candidate solution W i The mutation vector V is calculated using a mutation strategy. i :

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

[0116] Where r1, r2, and r3 are randomly selected and distinct indices in the population, F is the scaling factor, γ is the momentum factor, and W... prev W represents the value of the candidate solution in the previous iteration. r1 W r2 and W r3 ;

[0117] S43, regarding candidate solutions W i With the mutation vector V iPerform a binomial crossover operation to generate the test vector U. i :

[0118]

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

[0120] S44. Define the 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, This represents the Pearson correlation coefficient. The dynamic range of the predicted data for the device operating status is represented by DR(X), the dynamic range of the time series dataset is represented by ln(), the logarithmic function is represented by ||W||2, the L2 norm of the weight matrix W is represented by ||W||2, and ω3, ω4 and ω5 are preset weight coefficients.

[0123] S45. Perform a selection operation for each candidate solution W. i If F DE (U i ) <F DE (W i If so, then update the candidate solution W. i =U i Otherwise, keep the candidate solutions unchanged.

[0124] S46. Repeat steps S42 to S45 until the preset number of iterations or convergence criteria are reached, and obtain the globally optimal weight parameter W. * The globally optimal weight parameters are applied to the temporal variational autoencoder model to minimize the prediction error.

[0125] In this embodiment, S5 specifically includes:

[0126] S51. Obtain real-time device 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 the set of real numbers;

[0127] S52, Transfer real-time device operation data Xt Inputting a temporal variational autoencoder model, encoder E yields a 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 ) represents the dynamic latent space control factor, ⊙ represents element-wise multiplication, φ represents the encoder parameter, and E(X) is the dynamic latent space control factor. t ) represents the encoder's mapping to real-time device operation data, and ρ is a random noise vector. It follows a standard normal distribution;

[0130] S53. Using the variational autoencoder model decoder D to process the latent vector z t Decode the data to generate real-time predicted device operating status data.

[0131]

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

[0133] S54. Introduce a nonlinear time decay mechanism to calculate the prediction confidence factor γ. t :

[0134]

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

[0136] S55, Based on the predicted confidence factor γ t The real-time predicted equipment operating status data is corrected to obtain the final predicted equipment operating status data.

[0137]

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

[0139] Example 1:

[0140] To verify the feasibility of this invention in practice, it was applied to the actual operation of a large pumped-storage power station. Under frequent start-ups and shutdowns, load changes, and seasonal operating condition switching, the main equipment of the power station (including pumps, turbines, generators, transformers, etc.) exhibited complex nonlinear and dynamic characteristics. To ensure the safe and stable operation of the equipment, real-time prediction of its operating status is necessary to promptly identify potential faults or anomalies and assist maintenance personnel in formulating maintenance and optimization strategies. However, traditional modeling methods often suffer from low prediction accuracy and poor model generalization ability when dealing with dynamic operating condition changes. Especially in long-term series prediction, prediction errors tend to accumulate and amplify, leading to reduced reliability of the prediction results.

[0141] The "Mathematical Modeling Method for Main Equipment of Pumped Storage Power Station Based on Dynamic Simulation" proposed in this invention has been practically applied in the operation of the main equipment of this power station. The method of this invention employs an improved temporal variational autoencoder model, which demonstrates excellent performance in predicting equipment operating status through dynamic latent space adjustment factors and adaptive compensation mechanisms. Regarding 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, achieving automatic adaptation of the model under different operating conditions. Furthermore, a differential evolution algorithm (DE) is used for global optimization of weight parameters to ensure that the model maintains high accuracy throughout the prediction process. In the prediction stage, a nonlinear time decay mechanism is used to dynamically adjust the prediction confidence, effectively solving the problem of unstable prediction results in long-term series prediction.

[0142] In practical applications, taking the prediction of the operating status of a power station's pump turbine as an example, equipment operation data for 12 months from May 2023 to May 2024 was collected. The data included multi-dimensional time-series data such as equipment power, speed, vibration, temperature, and flow rate, collected every minute, totaling 52,560 data points. During data processing, these data were divided into a training set (60%), a validation set (20%), and a test set (20%), and a temporal variational autoencoder model was used for training and prediction. During the model training phase, 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 hyperparameter tuning. After 50 iterations, the prediction error of the model hyperparameters on the validation set reached its optimal level. 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 the actual data through the fitness function, and realizes dynamic optimization of weight parameters in the global search, which ultimately greatly improves the prediction accuracy of the model.

[0143] In the actual prediction process, vibration data of the water pump turbine was selected as the key prediction object, and the prediction performance of the method of this invention was compared with that of traditional models (LSTM and ARIMA models). The mean absolute error (MAE%) of different models was recorded at prediction durations of 30 minutes, 60 minutes, 120 minutes, and 240 minutes. The results show that the prediction error of the method of this invention is significantly lower than that of the traditional models, especially exhibiting higher prediction stability in long-term predictions. In practical applications, the system successfully predicted three turbine vibration exceeding-standard events, enabling maintenance personnel to carry out effective preventative maintenance before failures occurred, avoiding unplanned equipment downtime and saving approximately 300,000 yuan in maintenance costs.

[0144] Table 1 Comparison of errors of different models in predicting equipment operating status.

[0145] Predicted 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 shown in Table 1, the method of this invention exhibits significant advantages in prediction accuracy at different prediction timeframes. When predicting for 30 minutes, the average absolute error of the method of this invention is only 3.1%, compared to 5.4% for the Long Short-Term Memory network model and 6.7% for the Autoregressive Integral Moving Average model. The prediction error is reduced by approximately 42.6% and 53.7% respectively, demonstrating its high accuracy in short-term time series prediction.

[0147] Although the prediction error of the method of this invention increases with the extension of the prediction time, the rate of increase is significantly lower than that of traditional models. For example, when predicting for 120 minutes, the error of the method of this invention is 6.2%, while the errors of the Long Short-Term Memory Network model and the Autoregressive Integral Moving Average model reach 10.5% and 12.1%, respectively. The error of the method of this invention is still 41% lower than that of the Long Short-Term Memory Network model and 48.8% lower than that of the Autoregressive Integral Moving Average model. This indicates that the method of this invention has stronger stability in medium- and long-term prediction, and the model can effectively cope with dynamic changes in operating conditions and maintain high prediction accuracy.

[0148] The advantages of the method of this invention are even more significant over longer prediction periods (240 minutes and above). When the prediction duration is 240 minutes, the error of the method of this invention is 8.8%, while that of the Long Short-Term Memory (LSTM) network model is 13.2%, and the Autoregressive Integral Moving Average (AMI) model is as high as 15.7%. Particularly in predictions lasting up to 720 minutes (12 hours), the prediction error of the method of this invention is 14.2%, while the prediction errors of the LSM network model and the AMI model are 22.1% and 26.3%, respectively. Compared with the LSM network model, the prediction error of the method of this invention is reduced by 35.7%; compared with the AMI model, it is reduced by 45.9%. This data demonstrates the significant advantage of the method of this invention in long-term series prediction, not only maintaining the accuracy of the prediction results but also effectively reducing the cumulative effect of errors.

[0149] Overall, the method of this invention exhibits significant characteristics of high accuracy and low error in predicting equipment operating conditions from short to long periods. Compared with traditional methods, this invention, through dynamic latent space regulation, adaptive compensation mechanisms, and nonlinear time decay mechanisms, can better capture long-term dependencies in data when facing complex dynamic changes in equipment operation, and automatically adjust the confidence level of the prediction model, ensuring that the prediction results remain stable and reliable under dynamically changing operating conditions. This capability is particularly suitable for monitoring the operating status of large 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 embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A mathematical modeling method for main equipment of pumped-storage power stations based on dynamic simulation, characterized in that, Includes the following steps: S1. Collect multi-source time-series data of the main equipment of the pumped storage power station, and preprocess the multi-source time-series data to generate a time-series dataset. The main equipment of the pumped storage power station includes the power station's water pumps and turbines, and the multi-source time-series data includes power, speed, vibration, temperature, and flow data. S2. Construct a temporal variational autoencoder model. Input the temporal dataset into the temporal variational autoencoder model for training. The encoder maps the temporal data to the dynamic latent space, and the decoder reconstructs the latent variables into device operating status prediction data. S3. The honey badger optimization algorithm is introduced 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, the number of hidden layer nodes and the 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 on the basis of global search. S5. Use a time-series variational autoencoder model to predict real-time input device operation data and generate prediction data for the future state of the device. In the prediction process, a nonlinear time decay mechanism is introduced. By setting a nonlinear time decay factor, the prediction confidence is automatically adjusted when predicting long-term series. S6. Compare and analyze the prediction results with the actual equipment operation data in the time series dataset. When the prediction error exceeds the set threshold, trigger the anomaly detection and early warning mechanism. Through equipment operation status prediction and anomaly early warning, assist power plant operation and maintenance personnel in formulating equipment operation optimization strategies. S3 specifically includes: S31. Initialize the population of the honey badger optimization algorithm to form a set of hyperparameter vectors. : ； in, For population size, For the first The latent space dimension of the temporal variational autoencoder model for each individual. For the first The number of hidden nodes for each individual. For the first The learning rate of each individual; S32. Define the fitness function and use an evaluation metric that combines the prediction performance of the temporal variational autoencoder model with the characteristics of multimodal data: ； in, For equipment operating status data With time series datasets The Pearson correlation coefficient between them The coefficient of variation is 1. For reference coefficient of variation, and For preset weighting coefficients, For Shannon entropy, For reference entropy value, The fitness function; S33. By introducing historical best-in-class memory, the behavior of honey badgers searching simultaneously in multiple independent search areas is simulated, and historical best-in-class hyperparameters are recorded: ； in, This represents the current iteration number. The maximum number of iterations, The attenuation constant is For balance coefficient, and The Pearson correlation coefficient is used. To prevent small constants from being divided by zero, As an adaptive memory factor, ( ) is an exponential function. It is the hyperbolic tangent function; S34. By simulating a honey badger simultaneously searching within multiple independent search areas, an adaptive balancing mechanism is introduced. This mechanism dynamically adjusts the ratio of global to local searches based on the fitness change rate during the search process, and applies this mechanism to each hyperparameter. Perform dynamic optimization: ； in, This is the current hyperparameter value. These are the best hyperparameter values ​​in history. For the control coefficient, and These are adjustments for global search and local development, respectively. This is a balance coefficient between global and local searches. This represents the updated value of the hyperparameter P during the (t+1)th iteration. S35. Apply the updated hyperparameter vector to the temporal variational autoencoder model to dynamically optimize the hyperparameters. S4 specifically includes: S41. Construct a population of weight parameters. The weight parameter matrix of the temporal variational autoencoder model is as follows: in The number of layers in the neural network. The dimension of the weight parameters for each layer. Given the set of real numbers, initialize the candidate population: ； in, For population size, This represents the vector of the i-th candidate weight parameters; S42. For each candidate solution Calculate the mutation vector using a mutation strategy : ； in, and To select distinct indices randomly from the population, Scaling factor Momentum factor This represents the value of the candidate solution in the previous iteration. and ; S43. On candidate solutions With the mutation vector Perform a binomial crossover operation to generate test vectors. ; ； in, The dimension index representing the weight parameter. Uniformly distributed random numbers, For crossover probability, For randomly selected mandatory dimension indexes, Let i be the value of the i-th mutation vector in the j-th dimension. Let be the value of the i-th individual in the j-th dimension; S44. Define the fitness function Based on equipment operating status prediction data With time series datasets Pearson correlation coefficient between the data and dynamic range matching and weight regularization: ； in, This represents the Pearson correlation coefficient. This indicates the dynamic range of the equipment operating status prediction data. This represents the dynamic range of a time-series dataset. ( ) is a logarithmic function. Represents the weight matrix L2 norm, , and Preset weighting coefficients; S45. Perform a selection operation for each candidate solution. ,like Then update the candidate solutions. Otherwise, keep the candidate solutions unchanged. S46. Repeat steps S42 to S45 until the preset number of iterations or convergence criteria are reached to obtain the globally optimal weight parameters. The globally optimal weight parameters are applied to the temporal variational autoencoder model to minimize the prediction error. S5 specifically includes: S51. Obtain real-time device operation data ,in For timing length, For the input feature dimension, Indicates the current time step. It is the set of real numbers; S52, Real-time device operation data Input-time variational autoencoder model encoder Obtain the dynamic latent vector ; ； in, Represents the mean function, Represents the standard deviation function. As a dynamic potential spatial regulatory factor, This represents element-wise multiplication. For encoder parameters, This represents the encoder's mapping to real-time device operation data. It is a random noise vector. It follows a standard normal distribution; S53, Decoder using a variational autoencoder model For latent vectors Decode the data to generate real-time predicted device operating status data. : ； in, For the predicted time step, This is the decoder weight matrix. For bias vectors, It is a non-linear activation function. For adaptive compensation terms, These are decoder parameters; S54. Introduce a nonlinear time decay mechanism to calculate the prediction confidence factor. : ； in, The time decay coefficient, The preset maximum prediction time length, The Pearson correlation coefficient is used. For rate control coefficient, Standard deviation To prevent small constants from being divided by zero, It is the hyperbolic tangent function. It is an exponential function; S55. Based on the prediction confidence factor The real-time predicted equipment operating status data is corrected to obtain the final predicted equipment operating status data. : ； S56. Output the corrected final equipment operating status prediction data as the final prediction result, and use it for equipment status monitoring and dynamic updating of variational autoencoder model parameters.

2. The mathematical modeling method for main equipment of pumped-storage power stations based on dynamic simulation according to claim 1, characterized in that, S2 specifically includes: S21, Constructing the encoder Time series dataset Mapped to latent variables in the dynamic latent space , For the set of real numbers, The time step of the time series data. The number of data features at each time step. For the dimensions of the dynamic potential space; S22, Constructing a decoder latent variables Reconstructed into predicted device operating status data ; S23. Set up the dynamic potential space module By introducing a dynamic entropy regulation mechanism, the potential spatial dimension is dynamically adjusted: ； in, Indicates the potential spatial dimension for the next iteration. Represents the potential spatial dimension of the current iteration. For the control coefficient, It is the hyperbolic tangent function. Shannon entropy for latent variables, The preset maximum entropy value; S24. In the process of constructing the temporal variational autoencoder model, a multimodal adaptive mapping mechanism is introduced to dynamically set the hidden layer size. and learning rate : ； ； in, and These represent the initial hidden layer size and the learning rate, respectively. and As a regulatory factor, These are the weighting coefficients. For the target entropy value, ( ) is an exponential function. For input time series dataset Complexity metric: ； in, Representing time series datasets variance It is a logarithmic function; S25. Initialize the hyperparameters of the model, including encoder parameters, decoder parameters, initial latent space dimension, hidden layer size, and learning rate. Integrate the encoder, decoder, and dynamic latent space module to construct the improved temporal variational autoencoder model.

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