Industrial equipment parameter sensitivity analysis method based on white box and black box mixed driving

Abstract

The application provides an industrial equipment parameter sensitivity analysis method based on a white box and a black box mixed driving, comprising the following steps: inputting current working condition data of an industrial equipment into a pre-constructed white box and a black box model to obtain corresponding prediction values; calculating local data density of the working condition data in a historical training set; dynamically generating a fusion weight according to the density and weighting and fusing double model outputs to obtain a mixed prediction result; finally, introducing a black box model prediction variance as an uncertainty correction factor, performing global sensitivity analysis on the mixed prediction result, and calculating the uncertainty weighted sensitivity index of each parameter. The method realizes adaptive fusion of the white box and the black box, effectively filters out false sensitivity caused by "black box pollution", improves the robustness of data sparse area analysis, can accurately identify key physical parameters of the industrial equipment, and meets the real-time and safety requirements of online optimization in the industrial field.

Description

Technical Field

[0001] This invention relates to the field of industrial equipment modeling and parameter analysis technology, and in particular to a method for sensitivity analysis of industrial equipment parameters based on a hybrid white-box and black-box approach. Background Technology

[0002] In the field of industrial process control and equipment health management, accurate modeling of key equipment and analysis of its parameter sensitivity are fundamental to achieving optimized equipment control, fault diagnosis, and life prediction. Currently, mainstream modeling methods are divided into white-box models based on physical laws and black-box models based on data-driven approaches. To combine the advantages of both, parallel hybrid models (grey-box models) have emerged. These models typically use black-box models to compensate for the prediction residuals of white-box models, thereby achieving higher overall prediction accuracy.

[0003] However, existing sensitivity analysis methods based on parallel hybrid models have significant drawbacks. These methods typically statically and linearly superimpose the outputs of the white-box and black-box models, directly treating this mixed output as a deterministic function for global sensitivity analysis (e.g., the Sobol exponent method). This leads to a core problem: during sensitivity analysis, it's impossible to effectively distinguish whether fluctuations in the model output are caused by actual changes in physical parameters or by overfitting the black-box model to training data noise or blind predictions in sparse regions of the data. This uncertainty introduced by the black-box model "contaminates" the sensitivity analysis results, distorting the calculated parameter sensitivity index and incorrectly attributing data noise or model defects to the importance of physical parameters, thus misleading engineers in identifying key parameters and making subsequent optimization decisions.

[0004] Therefore, how to achieve adaptive fusion of white-box and black-box models, effectively filter out false sensitivity caused by "black-box contamination," improve the robustness of data sparse region analysis, accurately identify key physical parameters of industrial equipment, and meet the real-time and security requirements of online optimization in industrial sites are technical problems that urgently need to be solved by those skilled in the art. Summary of the Invention

[0005] This invention provides a method for sensitivity analysis of industrial equipment parameters based on a hybrid white-box and black-box approach, which improves the robustness of data sparse region analysis, accurately identifies key physical parameters of industrial equipment, and meets the real-time and safety requirements of online optimization in industrial settings.

[0006] On one hand, this invention provides a method for sensitivity analysis of industrial equipment parameters based on a hybrid white-box and black-box driving mechanism, comprising: The current operating condition data of the industrial equipment is input into the pre-built white-box model and the pre-built black-box model respectively to obtain the white-box residual prediction value and the black-box residual prediction value. Calculate the local data density of the current operating condition data in the historical training dataset; The fusion weights are dynamically generated based on the local data density, and the white-box prediction values ​​and the black-box residual prediction values ​​are weighted and fused to obtain a hybrid prediction output. A global sensitivity analysis is performed on the hybrid prediction output, and the prediction variance of the black-box model is introduced as an uncertainty correction factor to calculate the uncertainty weighted sensitivity index of each industrial equipment parameter.

[0007] This invention provides a method for sensitivity analysis of industrial equipment parameters based on a hybrid white-box and black-box approach. By pre-constructing physically constrained white-box and black-box models, the current operating data of the industrial equipment is input into both models to obtain corresponding predicted values. The local data density of the current operating data is calculated, and fusion weights are dynamically generated, achieving adaptive weighted fusion of white-box and black-box outputs. Furthermore, the prediction variance of the black-box model is introduced as an uncertainty correction factor to conduct global sensitivity analysis on the hybrid prediction output and calculate the uncertainty-weighted sensitivity index of each parameter. This achieves accurate, dynamic, and robust analysis of industrial equipment parameter sensitivity, effectively solving the problems of sensitivity index distortion, unreliable predictions in sparse data regions, and lack of physical consistency in analysis results caused by "black-box contamination." It filters out false sensitivity caused by data noise and model overfitting, improving the accuracy and industrial applicability of sensitivity analysis results while meeting the real-time and security requirements of online optimization in industrial settings. Attached Figure Description

[0008] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0009] Figure 1 This is a flowchart illustrating the sensitivity analysis method for industrial equipment parameters based on a hybrid white-box and black-box driving mechanism provided in this embodiment of the invention. Figure 2 This is a schematic diagram of the structure of an industrial equipment parameter sensitivity analysis system based on a hybrid white-box and black-box driving method provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the structure of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0010] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0011] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0012] The following are explanations of some key technical terms used in this invention: White-box models (mechanistic models): These are built upon fundamental scientific laws such as physics and thermodynamics (e.g., Newton's laws, Navier-Stokes equations). Their advantages lie in their clear physical interpretability and good extrapolation capabilities. However, in order to make the solution feasible, idealized assumptions are often introduced, leading to "model bias" and making it difficult to accurately describe complex nonlinear and time-varying characteristics.

[0013] Black-box models (data-driven models): These are built upon machine learning (such as neural networks and support vector machines) and learn the input-output mapping relationship from historical data. They have high prediction accuracy when there is sufficient data, but lack physical interpretability and have extremely poor generalization ability in areas not covered by training data (OOD areas), easily producing predictions that violate physical common sense.

[0014] Hybrid models (grey box models): These attempt to combine the strengths of the two approaches mentioned above. Common forms include serial, parallel (residual compensation), and embedded (such as physical information neural networks PINNs).

[0015] Sensitivity analysis (SA) is used to quantitatively assess how the uncertainty of a model's output is distributed among the input parameters. Global sensitivity analysis (GSA) (such as the Sobol index method) is considered the most rigorous method to date, as it can evaluate the importance of parameters and their interactions across the entire parameter space.

[0016] Local Data Density (LDD): Characterizes the density of the distribution of current operating condition data of industrial equipment in the historical training dataset, reflecting the model's "familiarity" with the current operating condition. High density indicates common operating conditions, while low density indicates sparse operating conditions such as extreme / fault conditions. Cognitive uncertainty: Prediction uncertainty caused by the inherent defects of the black-box model (such as overfitting and data sparsity), which is quantified by the prediction variance of the black-box model; Uncertainty Weighted Sensitivity Index (UWSI): This parameter sensitivity index is obtained by introducing the prediction variance of the black-box model as a correction factor. It can filter out spurious sensitivity and truly reflect the degree of influence of physical parameters on the output of industrial equipment. Physically constrained residual learning: This training method introduces physical laws such as mass conservation, energy conservation, and nonnegativity constraints into black-box model training, ensuring that the residual compensation value output by the black-box model always remains within the physically permissible boundaries.

[0017] Figure 1 This is a flowchart illustrating the sensitivity analysis method for industrial equipment parameters based on a hybrid white-box and black-box driving approach provided in this embodiment of the invention.

[0018] like Figure 1 As shown, the industrial equipment parameter sensitivity analysis method based on hybrid white-box and black-box driving provided in this embodiment of the invention mainly includes the following steps: 101. Input the current operating condition data of the industrial equipment into the pre-built white-box model and the pre-built black-box model respectively to obtain the white-box residual prediction value and the black-box residual prediction value; 102. Calculate the local data density of the current operating condition data in the historical training dataset; 103. Dynamically generate fusion weights based on the local data density, and perform weighted fusion of the white-box prediction value and the black-box residual prediction value to obtain a hybrid prediction output; 104. Perform a global sensitivity analysis on the hybrid prediction output, introduce the prediction variance of the black box model as an uncertainty correction factor, and calculate the uncertainty weighted sensitivity index of each industrial equipment parameter.

[0019] This embodiment uses the sensitivity analysis of load parameters of large wind turbine blades as an application scenario, and the specific implementation process is as follows: Step 1: Pre-construction of dual models: First, construct an aeroelastic white-box model of the wind turbine based on blade element momentum theory, and calibrate the physical parameters of the model (blade lift and drag coefficients, structural stiffness, etc.) using wind field benchmark operating data; then, using the residual between the predicted values ​​of the white-box model and the actual load values ​​as the training target, construct an LSTM black-box residual model with aerodynamic conservation constraints, and complete the training and deployment of dual models.

[0020] In a specific implementation, the construction process of the white-box model includes: An initial white-box model is constructed based on physical laws; baseline operating data of industrial equipment is obtained, and the physical parameters in the initial white-box model are calibrated using the baseline operating data to obtain the white-box model.

[0021] Specifically, taking large wind turbines as an application scenario, the construction of the white-box model is implemented as follows: Initial white-box model construction: Based on blade element momentum theory (aerodynamic physical law) and beam theory (structural mechanics physical law), an initial white-box model of wind turbine blade load is constructed. The model inputs are manipulated variables such as wind speed, pitch angle, and generator speed, and the outputs are physical quantities such as blade root bending moment and blade load. The model contains physical parameters to be calibrated (blade lift-drag coefficient, structural stiffness EI, structural damping ratio, etc.).

[0022] Baseline operating condition data acquisition: Long-term operating data of wind turbines under nominal operating conditions (stable wind speed of 3-15 m / s, no extreme turbulence) are collected. This type of data is high-confidence baseline operating data. After cleaning and denoising, a calibration dataset is obtained. The data includes input operating variables and corresponding actual output observations.

[0023] Physical parameter calibration: Using the mean square error between the predicted values ​​of the initial white-box model and the actual observed values ​​under the baseline operating conditions as the objective function, the particle swarm optimization algorithm is used to globally optimize and calibrate the physical parameters in the model to obtain the calibrated physical parameter values. The calibrated parameters are then substituted into the initial white-box model to complete the model correction and obtain the final white-box model. This model can accurately characterize the physical operation law of the wind turbine under the baseline operating conditions.

[0024] In a specific implementation process, the construction process of the black box model includes: inputting the benchmark operating data into the white box model to obtain the difference between the predicted value and the actual observed value of the white box model under the benchmark operating conditions, which is used as the original residual; training the initial black box model by introducing physical constraints to learn and fit the original residual to obtain the black box model.

[0025] Specifically, continuing with the application scenario of large wind turbines, the construction of the black box model is carried out as follows: Raw residual calculation: The obtained wind turbine baseline operating data is input into the calibrated white-box model to obtain the model's baseline operating prediction value; the difference between the actual observation value and the white-box prediction value is calculated to obtain the raw residual. This residual contains high-order dynamic characteristics (such as complex turbulence and blade surface friction) and random noise that the white-box model did not capture, and serves as the training target for the black-box model.

[0026] Initial black-box model construction: LSTM (Long Short-Term Memory) network was selected as the initial black-box model. The model input consisted of the operating variables of the wind turbine and environmental disturbances (wind speed, turbulence intensity, wind shear index, etc.). The model output was the residual prediction value. The network structure was set to 3 hidden layers, and the number of neurons was adaptively adjusted according to the scale of the residual data.

[0027] Physical constraints are introduced and the model is trained: During the training of the initial black-box model, aerodynamic conservation physical constraints (such as non-negative constraints on blade loads and matching constraints between aerodynamic torque and rotational speed) are introduced. The original residuals are used as the training target, and the gradient descent algorithm is used to train the model so that the model learns and fits the residual rules of the white-box model. If the model output violates the physical constraints during the training process, the model parameters are forcibly corrected through the penalty term of the loss function, and finally the trained black-box model is obtained.

[0028] Specifically, a deep neural network can be constructed as the initial black-box model, with the operating variables of the industrial equipment and environmental disturbances as inputs, and the original residuals as the training target. During training, a loss function containing a physical penalty term is constructed, which is determined based on whether the sum of the predicted values ​​of the white-box model and the predicted values ​​of the black-box residuals satisfies a preset physical conservation law or non-negativity constraint. The parameters of the initial black-box model are optimized through a backpropagation algorithm so that the residual compensation value output is constrained within the physically allowed boundaries, thus obtaining the black-box model.

[0029] In detail, the deep neural network is constructed as follows: an LSTM deep neural network is constructed as the initial black box model. The input layer consists of the wind turbine's operating variables (pitch angle, speed) and environmental disturbances (turbulence intensity, wind shear index). There are 3 hidden layers (with 64, 32, and 16 neurons respectively). The output layer is the residual prediction value of the blade load. The input and output of the model are normalized.

[0030] Construction of the loss function with physical penalty: The loss function is composed of a weighted mean squared error (MSE) term and a physical penalty term. The MSE term is used to measure the fit between the model residual predictions and the original residuals. The physical penalty term is determined based on whether the mixed prediction output (white-box predictions + black-box residual predictions) satisfies the physical constraints: If the mixed output satisfies the aerodynamic conservation law and the non-negativity constraint of the blade load, the physical penalty term is 0; if the mixed output violates the physical constraints, a penalty coefficient is set according to the degree of violation (the more severe the violation, the larger the coefficient), and the physical penalty term is the product of the penalty coefficient and the violation value.

[0031] Model parameter optimization and training: Using the original residuals as the training target, the Adam backpropagation algorithm is used to iteratively optimize the parameters of the initial black-box model. In each iteration, the mixed prediction output is calculated and the physical constraints are verified. The loss function value is updated according to the constraint satisfaction and the loss function is minimized by gradient descent. When the model converges and the mixed prediction outputs all satisfy the physical constraints, the training stops, and the final black-box model is obtained. The residual compensation value of its output is always within the physically allowed boundary.

[0032] The second step is dual-model prediction output: real-time acquisition of the current operating data of the wind turbine (wind speed, pitch angle, turbulence intensity, etc.), input into the pre-built white-box model and black-box model respectively, and the white-box prediction value and black-box residual prediction value of the blade load are obtained through model inference calculation.

[0033] Step 3, Local Data Density Calculation: Using the current operating condition data as the query point and the historical training dataset as the reference distribution, the kernel density estimation algorithm is used to estimate the probability density value of the query point under the reference distribution, which is then used as the local data density; or, the average distance from the query point to a preset number of nearest neighbor samples in the historical training dataset is calculated, and the local data density is determined based on the reciprocal of the average distance or the negative correlation value; or, a Gaussian mixture model is used to fit the historical training dataset, and the probability value of the query point under the Gaussian mixture model is calculated, which is then used as the local data density.

[0034] Specifically, the three methods for calculating local data density are implemented, and all calculation results are normalized to the [0,1] interval for dimensionless processing, as follows: Kernel density estimation method: Using the operating condition features such as wind speed and turbulence intensity in the historical training dataset as the sample set, the Gaussian kernel function is used as the basis function for kernel density estimation. An appropriate kernel bandwidth is set (adaptively selected according to the number of samples). The kernel density probability value of the current operating condition query point is calculated. The ratio of this value to the maximum probability value in the sample set is processed to obtain the normalized local data density.

[0035] K-Nearest Neighbors: The preset number of nearest neighbor samples K=20 (can be adjusted according to the scale of industrial equipment operating data). The Euclidean distance is used to calculate the distance from the current operating condition query point to the 20 nearest neighbor samples in the historical training dataset, and the average distance is calculated. The reciprocal of this average value is used as the original density value, and then it is normalized to the [0,1] interval to obtain the local data density (the smaller the average distance, the larger the density value).

[0036] Gaussian Mixture Model Method: The expectation-maximization (EM) algorithm is used to fit a Gaussian mixture model to the historical training dataset to determine the number of Gaussian components, mean, covariance and other parameters of the model; the current working condition query point is input into the fitted Gaussian mixture model, and its joint probability value in the model is calculated. The probability value is normalized to the interval [0,1] to obtain the local data density.

[0037] All three methods can independently calculate local data density, and the calculation results can effectively characterize the distribution density of current operating data in the historical training set. They can be flexibly selected according to the type of industrial equipment operating data (continuous / discrete) and the data scale.

[0038] Step 4, Adaptive Weighted Fusion: The local data density is input into a preset nonlinear mapping function to calculate the fusion weight. The nonlinear mapping function is a monotonically increasing S-shaped function. The function value of the S-shaped function increases with the increase of local data density. When the local data density is lower than a first density threshold, the function value is close to zero. When the local data density is higher than a second density threshold, the function value is close to 1. When the local data density is between the first and second density thresholds, the function value changes smoothly. The fusion weight is used to weight the black-box residual prediction value, and the weight of the white-box prediction value is 1 minus the fusion weight.

[0039] Specifically, the dynamic generation of fusion weights is achieved through the following process: Threshold and mapping function settings: Set the first density threshold of local data density to 0.2 and the second density threshold to 0.8 (both are dimensionless quantities, which can be adjusted according to the risk level of the industrial equipment); select the Sigmoid variant as the nonlinear mapping function. This function is a monotonically increasing S-shaped curve, the domain is the normalized local data density [0,1], and the value range is the fusion weight [0,1].

[0040] Fusion weight calculation: The local data density of the chemical reactor (such as the density value corresponding to the reaction temperature and feed rate) obtained by any method in claim 2 is input into the above S-shaped mapping function, and the fusion weight is obtained by function calculation: When the density value < 0.2, the function value approaches 0, and the weight of the black box model is almost 0; when the density value > 0.8, the function value approaches 1, and the black box model fully exerts the residual compensation function; when the density value is between 0.2 and 0.8, the function value increases smoothly with the increase of the density value, realizing the gradual adjustment of the weight of the black box model.

[0041] Dual-model weight allocation: The fusion weight is the exclusive weight of the black-box residual prediction value, and the weight of the white-box model is fixed at 1 minus the fusion weight, so as to achieve dynamic complementarity of the weights of the two models, and the sum of the weights of the two models is always 1, ensuring the consistency of the dimensions of the mixed prediction output.

[0042] This embodiment achieves smooth and dynamic generation of fusion weights by setting an S-shaped nonlinear mapping function and a density threshold, avoiding oscillations in the mixed prediction output caused by sudden weight changes and improving the stability of model fusion. At the same time, the threshold limitation implements an "adaptive backoff mechanism," which automatically reduces the weights of the black-box model in sparse data regions, forcing the mixed output to approach the reliable white-box prediction value. This effectively avoids erroneous predictions by the black-box model under extreme conditions and improves the robustness and safety of the technical solution under all operating conditions. The complementary allocation of weights between the two models ensures the consistency of the dimensions of the mixed prediction output, laying a reliable data foundation for subsequent sensitivity analysis.

[0043] The fifth step, the process of uncertainty-weighted sensitivity analysis, may include: a1. Quantify the cognitive uncertainty of the black box model to obtain the prediction variance of the black box model under the current working condition data; The Dropout layer of the black-box model can be enabled, and 50 random forward propagations can be performed on the current working condition data to obtain 50 sets of black-box residual prediction values. The variance of these prediction values ​​is calculated as the original prediction variance of the black-box model. All original prediction variances of the full parameter space sampling area are normalized to obtain the uncertainty correction factor corresponding to each sampling area. The correction factor is negatively correlated with the prediction variance (the larger the prediction variance, the smaller the correction factor, with a value range of [0,1]).

[0044] It should be noted that the above methods are only illustrative examples, and other methods, such as deep integration technology, can also be used, which will not be illustrated here.

[0045] a2. The variance-based global sensitivity analysis method is used to sample the full-parameter spatial perturbation of the parameters of industrial equipment, generate multiple sets of parameter perturbation samples, and construct the corresponding dataset of the parameter perturbation samples and the hybrid prediction output; The Sobol sequence sampling method (variance basis global sensitivity analysis method) can be used to perform full-parameter spatial perturbation sampling of industrial equipment parameters (geometric error elements, spindle temperature coefficient, etc.) to generate 1000 sets of parameter perturbation samples; each set of samples is input into the hybrid model after adaptive fusion according to claim 3 to obtain the corresponding hybrid prediction output (tool tip position deviation), and a one-to-one correspondence dataset between parameter perturbation samples and hybrid prediction output is constructed.

[0046] a3. Normalize the black-box model prediction variance corresponding to each parameter perturbation sample to obtain the uncertainty correction factor corresponding to each sampling region; wherein, the value of the correction factor is negatively correlated with the prediction variance. a4. Calculate the basic contribution of each industrial equipment parameter to the total variance of the hybrid prediction output based on the corresponding dataset; the total variance is used to characterize the overall fluctuation of the hybrid model output under full parameter space perturbation; Based on the corresponding datasets mentioned above, the variance decomposition method is used to calculate the total variance of the mixed prediction output (characterizing the overall fluctuation of the output under full parameter perturbation); then the total variance is decomposed into each physical parameter to obtain the basic contribution of each parameter to the total variance, which reflects the original sensitivity of the parameter before correction.

[0047] Specifically, this step can be performed as follows: The total variance is decomposed, and the output fluctuation caused by the individual change of each industrial equipment parameter is calculated as the main effect contribution of each industrial equipment parameter. The portion of the joint output fluctuation caused by the simultaneous change of all industrial equipment parameters in each parameter combination that exceeds the sum of the main effect contributions generated by the individual changes of each industrial equipment parameter is calculated as the interaction effect contribution of each parameter combination. The main effect contribution of each industrial equipment parameter is added to the interaction effect contributions in which each industrial equipment parameter participates to obtain the basic contribution of each industrial equipment parameter. This basic contribution comprehensively reflects the total sensitivity of the individual effect and the coupling effect of the parameter.

[0048] The calculation of the output fluctuation caused by individual changes in each industrial equipment parameter, as the main effect contribution of each industrial equipment parameter, includes: fixing the values ​​of all other industrial equipment parameters except the current industrial equipment parameter, calculating the conditional expectation of the mixed prediction output with respect to the current industrial equipment parameter; obtaining the variance of the conditional expectation as the main effect contribution of the current industrial equipment parameter, which is used to quantify the direct impact of individual changes in the current industrial equipment parameter on the total variance of the mixed prediction output; and iterating through all industrial equipment parameters to obtain the main effect contribution of each industrial equipment parameter.

[0049] In detail, taking a chemical reactor as an example, the target physical parameter (reaction rate constant) of the chemical reactor is selected, and all other physical parameters (activation energy, feed concentration, stirring rate, etc.) are fixed to industrial nominal values. The reaction rate constant is perturbed at equal steps within its feasible region to obtain multiple sets of single-parameter perturbation samples. Each set of samples is input into a mixing model to obtain the corresponding mixing prediction output (reaction conversion rate). Based on this set of output values, the conditional expectation of the mixing prediction output with respect to the reaction rate constant is calculated, representing the average level of the output when this parameter changes alone. The variance of the above conditional expectation is calculated and normalized to the [0,1] interval to obtain the main effect contribution of the reaction rate constant. This value quantifies the direct impact of the individual change of this parameter on the fluctuation of the reaction conversion rate. Following the above steps, each physical parameter of the chemical reactor is sequentially taken as the target parameter, the other parameters are fixed, and their conditional expectations and variances are calculated. After traversing all physical parameters, the main effect contribution of each parameter is obtained. All results are dimensionless values ​​and are comparable.

[0050] In a specific implementation process, the portion of the joint output fluctuation caused by the simultaneous change of all industrial equipment parameters in each parameter combination that exceeds the sum of the main effect contributions generated by the individual changes of each industrial equipment parameter is taken as the interaction effect contribution of each parameter combination. This includes: simultaneously perturbing all industrial equipment parameters in the current parameter combination to obtain the joint fluctuation of the mixed predicted output; subtracting the sum of the main effect contributions generated by the individual changes of each industrial equipment parameter in the current parameter combination from the joint fluctuation, and taking the difference as the interaction effect contribution of the current parameter combination; wherein, the interaction effect contribution is used to measure the additional impact of the synergistic or coupling effect between multiple parameters on the output fluctuation; and traversing all parameter combinations to obtain the interaction effect contribution of each current parameter combination.

[0051] In detail, a parameter combination (reaction rate constant + stirring rate) of the chemical reactor is selected. The two parameters within this combination are simultaneously subjected to joint perturbation within their respective feasible domains, generating multiple sets of two-parameter perturbation samples. These samples are input into a mixing model to obtain the corresponding mixing prediction output (reaction conversion rate). The variance of this set of output values ​​is calculated and normalized to [0,1], yielding the joint fluctuation of the parameter combination, which characterizes the total fluctuation of the output when parameters change synergistically. The main effect contributions of the reaction rate constant and stirring rate within this combination are extracted, and their sum is calculated. The combined fluctuation is subtracted from this sum of main effect contributions; the difference is the interaction effect contribution of the parameter combination. This value is dimensionless; a positive value indicates a synergistic enhancement effect between parameters, while a negative value indicates a coupling inhibition effect. Following these steps, all non-empty parameter combinations (two-parameter, three-parameter, and above) of the chemical reactor are selected sequentially. The joint perturbation, joint fluctuation calculation, and interaction effect contribution solution for each parameter group are completed, ultimately yielding the interaction effect contribution of all parameter combinations.

[0052] This embodiment decomposes the basic contribution of a parameter into main effect contribution and interaction effect contribution, achieving a refined quantification of the sensitivity of industrial equipment parameters. It can not only identify the independent influence of a single parameter, but also capture the synergistic / coupling effects between parameters, making up for the shortcomings of traditional sensitivity analysis that only considers the influence of a single parameter. The summation of main effect and interaction effect can comprehensively reflect the total contribution of the parameter to the output fluctuation, providing comprehensive and accurate raw sensitivity data for subsequent uncertainty weighting correction. This variance decomposition method has rigorous mathematical theoretical support, ensuring the reliability of the basic contribution calculation results.

[0053] a5. The basic contribution of each industrial equipment parameter in each sampling area is weighted and fused with the uncertainty correction factor of the corresponding area to obtain the preliminary weighted sensitivity index of each industrial equipment parameter. Specifically, the basic contribution of each industrial equipment parameter in each sampling region can be multiplied by the uncertainty correction factor of the corresponding region, and then the product results over all sampling regions can be summed to obtain the preliminary weighted sensitivity index of each parameter; the preliminary weighted sensitivity index is then normalized to the [0,1] interval to obtain the uncertainty weighted sensitivity index. a6. Normalize the preliminary weighted sensitivity index to obtain the uncertainty weighted sensitivity index of each industrial equipment parameter, sort the uncertainty weighted sensitivity index of each industrial equipment parameter, and verify the physical consistency of the sorting result in combination with the physical laws and operating rules of the industrial equipment. Finally, output the verified uncertainty weighted sensitivity index and parameter sorting result.

[0054] Specifically, the uncertainty weighted sensitivity indices of various industrial equipment parameters can be sorted from high to low. The physical consistency of the sorting results can be verified by combining the kinematics theory of multibody systems (the physical laws of CNC machine tools) (e.g., the sensitivity of the spindle temperature coefficient should be higher than that of minor geometric error parameters). Abnormal results that violate physical common sense are eliminated, and finally the verified sensitivity indices and parameter sorting are output.

[0055] This embodiment achieves dynamic adaptive fusion of white-box and black-box models, effectively avoiding the blind prediction problem of black-box models in sparse data areas. At the same time, by introducing the prediction variance of the black-box model as an uncertainty correction factor, it solves the problem of sensitivity index distortion caused by "black-box contamination". Compared with the existing static fusion hybrid model analysis method, this solution can accurately identify the key physical parameters of industrial equipment, improve the accuracy and reliability of sensitivity analysis results, and the analysis process is based on real-time operating data, meeting the real-time requirements of online optimization in industrial sites.

[0056] It should be noted that, for those skilled in the art, the aforementioned calculation process involving local data density, black-box model prediction variance, uncertainty correction factor, parameter sensitivity index, etc., can be normalized or not, depending on actual needs, in order to complete the acquisition process of each parameter.

[0057] Based on the same general inventive concept, this invention also protects an industrial equipment parameter sensitivity analysis system based on a hybrid white-box and black-box driving method. The industrial equipment parameter sensitivity analysis system based on a hybrid white-box and black-box driving method provided by this invention will be described below. The industrial equipment parameter sensitivity analysis system based on a hybrid white-box and black-box driving method described below can be referred to in correspondence with the industrial equipment parameter sensitivity analysis method based on a hybrid white-box and black-box driving method described above.

[0058] Figure 2This is a schematic diagram of the structure of the industrial equipment parameter sensitivity analysis system based on a hybrid white-box and black-box driving method provided in an embodiment of the present invention, as shown below. Figure 2 As shown, the industrial equipment parameter sensitivity analysis system based on white-box and black-box hybrid driving in this embodiment includes a prediction module 21, a calculation module 22, a fusion module 23, and an analysis module 24.

[0059] Among them, the prediction module 21 is used to input the current operating condition data of the industrial equipment into the pre-built white-box model and the pre-built black-box model respectively to obtain the white-box residual prediction value and the black-box residual prediction value. Calculation module 22 is used to calculate the local data density of the current working condition data in the historical training dataset; The fusion module 23 is used to dynamically generate fusion weights based on the local data density, and to perform weighted fusion of the white-box prediction values ​​and the black-box residual prediction values ​​to obtain a mixed prediction output; Analysis module 24 is used to perform global sensitivity analysis on the hybrid prediction output, introduce the prediction variance of the black box model as an uncertainty correction factor, and calculate the uncertainty weighted sensitivity index of each industrial equipment parameter.

[0060] Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. The electronic device may include: a processor 310, a communication interface 320, a memory 330, and a communication bus 340. The processor 310, communication interface 320, and memory 330 communicate with each other via the communication bus 340. The processor 310 can call logical instructions in the memory 330 to execute a sensitivity analysis method for industrial equipment parameters based on a hybrid white-box and black-box driving mechanism.

[0061] Furthermore, the logical instructions in the aforementioned memory 330 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0062] It should be noted that all relevant information that may be involved in the various embodiments of the present invention is processed in strict accordance with the requirements of laws and regulations, following the principles of legality, legitimacy, and necessity, based on the reasonable purpose of the business scenario, and is information that users actively provide or generate during the use of the product / service, as well as information obtained with user authorization.

[0063] The information processed by this invention may vary depending on the specific product / service scenario and should be based on the specific scenario in which the user uses the product / service. This may involve user account information, device information, or other related information. This invention will treat the relevant information and its processing with the utmost diligence.

[0064] This invention places great emphasis on the security of relevant information and has adopted reasonable and feasible security protection measures that comply with industry standards to protect user information and prevent unauthorized access, public disclosure, use, modification, damage or loss of relevant information.

[0065] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0066] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0067] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for sensitivity analysis of industrial equipment parameters based on a hybrid white-box and black-box driving mechanism, characterized in that, include: The current operating condition data of the industrial equipment is input into the pre-built white-box model and the pre-built black-box model respectively to obtain the white-box residual prediction value and the black-box residual prediction value. Calculate the local data density of the current operating condition data in the historical training dataset; The fusion weights are dynamically generated based on the local data density, and the white-box prediction values ​​and the black-box residual prediction values ​​are weighted and fused to obtain a hybrid prediction output. A global sensitivity analysis is performed on the hybrid prediction output, and the prediction variance of the black-box model is introduced as an uncertainty correction factor to calculate the uncertainty weighted sensitivity index of each industrial equipment parameter.

2. The method for sensitivity analysis of industrial equipment parameters based on hybrid white-box and black-box driving according to claim 1, characterized in that, Calculating the local data density of the current operating condition data in the historical training dataset includes: Using the current working condition data as the query point and the historical training dataset as the reference distribution, the kernel density estimation algorithm is used to estimate the probability density value of the query point under the reference distribution, which is then used as the local data density. Alternatively, calculate the average distance from the query point to a preset number of nearest neighbor samples in the historical training dataset, and determine the local data density based on the reciprocal of the average distance or the negative correlation value; Alternatively, a Gaussian mixture model can be used to fit the historical training dataset, and the probability value of the query point under the Gaussian mixture model can be calculated as the local data density.

3. The method for sensitivity analysis of industrial equipment parameters based on hybrid white-box and black-box driving according to claim 1, characterized in that, Dynamically generate fusion weights based on the local data density, including: The local data density is input into a preset nonlinear mapping function to calculate the fusion weight. The nonlinear mapping function is a monotonically increasing S-shaped function. The function value of the S-shaped function increases with the increase of local data density. When the local data density is lower than a first density threshold, the function value is close to zero. When the local data density is higher than a second density threshold, the function value is close to 1. When the local data density is between the first and second density thresholds, the function value changes smoothly. The fusion weight is used to weight the black-box residual prediction value, and the weight of the white-box prediction value is 1 minus the fusion weight.

4. The method for sensitivity analysis of industrial equipment parameters based on hybrid white-box and black-box driving according to claim 1, characterized in that, A global sensitivity analysis is performed on the hybrid prediction output. The prediction variance of the black-box model is introduced as a cognitive uncertainty correction factor, and the uncertainty-weighted sensitivity index of each industrial equipment parameter is calculated, including: The cognitive uncertainty of the black-box model is quantified to obtain the prediction variance of the black-box model under the current working condition data. The variance-based global sensitivity analysis method is used to sample the full-parameter spatial perturbation of industrial equipment parameters, generating multiple sets of parameter perturbation samples, and constructing a corresponding dataset of the parameter perturbation samples and the hybrid prediction output; The black-box model prediction variance corresponding to each parameter perturbation sample is normalized to obtain an uncertainty correction factor corresponding to each sampling region; wherein the value of the correction factor is negatively correlated with the prediction variance. Calculate the basic contribution of each industrial equipment parameter to the total variance of the hybrid prediction output based on the corresponding dataset; The basic contribution of each industrial equipment parameter in each sampling area is weighted and fused with the uncertainty correction factor of the corresponding area to obtain the preliminary weighted sensitivity index of each industrial equipment parameter. The preliminary weighted sensitivity index is normalized to obtain the uncertainty weighted sensitivity index of each industrial equipment parameter.

5. The method for sensitivity analysis of industrial equipment parameters based on hybrid white-box and black-box driving according to claim 1, characterized in that, The basic contribution of each industrial equipment parameter to the total variance of the hybrid prediction output is calculated based on the corresponding dataset, including: The total variance is decomposed, and the output fluctuation caused by the individual change of each industrial equipment parameter is calculated as the main effect contribution of each industrial equipment parameter. The portion of the joint output fluctuation caused by the simultaneous change of all industrial equipment parameters in each parameter combination that exceeds the sum of the main effects contributions generated by the individual changes of each industrial equipment parameter is calculated as the interaction effect contribution of each parameter combination. The base contribution of each industrial equipment parameter is obtained by summing the main effect contribution of each industrial equipment parameter with the contribution of all interaction effects in which each industrial equipment parameter participates.

6. The method for sensitivity analysis of industrial equipment parameters based on hybrid white-box and black-box driving according to claim 5, characterized in that, Calculate the output fluctuation caused by individual changes in each industrial equipment parameter, as the main effect contribution of each industrial equipment parameter, including: Fix the values ​​of all other industrial equipment parameters except the current industrial equipment parameters, and calculate the conditional expectation of the hybrid prediction output with respect to the current industrial equipment parameters; The variance of the conditional expectation is taken as the main effect contribution of the current industrial equipment parameters, which is used to quantify the direct impact of individual changes in the current industrial equipment parameters on the total variance of the mixed prediction output. By iterating through all industrial equipment parameters, the main effect contribution of each industrial equipment parameter is obtained.

7. The method for sensitivity analysis of industrial equipment parameters based on hybrid white-box and black-box driving according to claim 5, characterized in that, The portion of the joint output fluctuation caused by the simultaneous change of all industrial equipment parameters in each parameter combination that exceeds the sum of the main effects contributions generated by the individual changes of each industrial equipment parameter is calculated as the interaction effect contribution of each parameter combination, including: The parameters of all industrial equipment within the current parameter combination are simultaneously perturbed to obtain the joint fluctuation of the mixed prediction output; The sum of the main effects contributions generated when each industrial equipment parameter in the current parameter combination changes individually is subtracted from the joint fluctuation amount, and the difference is taken as the interaction effect contribution of the current parameter combination; wherein, the interaction effect contribution is used to measure the additional impact of the synergistic or coupling effect between multiple parameters on the output fluctuation. By iterating through all parameter combinations, we can calculate the interaction effect contribution for each current parameter combination.

8. The method for sensitivity analysis of industrial equipment parameters based on hybrid white-box and black-box driving according to claim 1, characterized in that, The process of constructing the white-box model includes: Construct an initial white-box model based on physical laws; Obtain baseline operating data of industrial equipment, and use the baseline operating data to calibrate the physical parameters in the initial white-box model to obtain the white-box model.

9. The method for sensitivity analysis of industrial equipment parameters based on hybrid white-box and black-box driving according to claim 8, characterized in that, The construction process of the black-box model includes: The baseline operating data is input into the white-box model to obtain the difference between the predicted value and the actual observed value of the white-box model under the baseline operating conditions, which is used as the original residual. The initial black-box model is trained by introducing physical constraints to learn and fit the original residuals, thus obtaining the black-box model.

10. The method for sensitivity analysis of industrial equipment parameters based on hybrid white-box and black-box driving according to claim 9, characterized in that, The black-box model is obtained by training an initial black-box model with physical constraints to learn and fit the original residuals, including: A deep neural network is constructed as the initial black-box model, with the operating variables of the industrial equipment and the amount of environmental disturbance as inputs, and the original residual as the training target; During training, a loss function containing a physical penalty term is constructed. The physical penalty term is determined based on whether the sum of the white-box model prediction value and the black-box residual prediction value satisfies a preset physical conservation law or non-negativity constraint. The parameters of the initial black-box model are optimized by backpropagation algorithm so that the residual compensation value of its output is constrained within the physically allowed boundary, thus obtaining the black-box model.

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