Method and device for predicting the results of interference fit checking of ball bearings

Abstract

The application relates to the technical field of mechanical engineering, in particular to a method and device for predicting interference fit checking results of ball bearings, which comprises the following steps: inputting interference fit data of a target ball bearing obtained into a pre-trained interference fit checking prediction model of the target ball bearing, repeatedly performing model reasoning according to a preset sampling number, and obtaining multiple sets of interference fit checking results of ball bearings; calculating at least one uncertainty index by using the multiple sets of interference fit checking results of ball bearings; and outputting a final prediction result of the target ball bearing based on the multiple sets of interference fit checking results of ball bearings and the corresponding at least one uncertainty index. Therefore, the problems of the related art, such as a complicated and inefficient interference fit checking process of ball bearings, low checking accuracy depending on manual experience and inability to evaluate potential risks of prediction errors, are solved, and the efficiency and reliability of the whole process of ball bearing design are improved.

Description

Technical Field

[0001] This application relates to the field of mechanical engineering technology, and in particular to a method and apparatus for predicting the verification results of ball bearing interference fit. Background Technology

[0002] With the increasing demands for operational precision, reliability, and service life in the high-end equipment manufacturing sector, interference fit verification of ball bearings has become a core design step in key industries such as aerospace, precision machine tools, and new energy vehicles. To meet the design requirements of high precision and high stability, related technologies are gradually developing towards simulation and intelligence. The industry generally adopts finite element simulation combined with manual parameter adjustment to conduct interference fit verification, and relies on traditional predictive models and specialized software for auxiliary analysis.

[0003] However, the interference fit verification method for ball bearings in related technologies is cumbersome and inefficient, and the verification accuracy depends on human experience, making it impossible to assess the potential risks of prediction errors. This reduces the efficiency and reliability of the entire ball bearing design process and fails to provide more comprehensive reliability support for engineering decisions, which urgently needs to be addressed. Summary of the Invention

[0004] This application provides a method and apparatus for predicting the verification results of ball bearing interference fit, in order to solve the problems of cumbersome process, low efficiency and reliance on manual experience for verification accuracy of ball bearing interference fit in related technologies, which cannot assess the potential risks of prediction errors and reduce the efficiency and reliability of the entire ball bearing design process.

[0005] The first aspect of this application provides a method for predicting the interference fit verification result of a ball bearing, comprising the following steps: acquiring interference fit data of a target ball bearing; inputting the interference fit data of the target ball bearing into a pre-trained target ball bearing interference fit verification prediction model, repeatedly executing model inference according to a preset number of samplings to obtain multiple sets of ball bearing interference fit verification results; calculating at least one uncertainty index using the multiple sets of ball bearing interference fit verification results, and outputting the final prediction result of the target ball bearing based on the multiple sets of ball bearing interference fit verification results and the corresponding at least one uncertainty index.

[0006] Based on the above technical means, the embodiments of this application can obtain multiple sets of verification results and calculate uncertainty indicators by performing multiple model inferences based on a pre-constructed target ball bearing interference fit verification prediction model. This can quantify the dispersion and credibility range of the prediction results, thereby determining the final prediction result of the ball bearing and improving the reliability and decision robustness of the ball bearing interference fit verification results.

[0007] Optionally, in one embodiment of this application, before inputting the interference fit data of the target ball bearing into the pre-trained target ball bearing interference fit verification prediction model, the method further includes: constructing an initial ball bearing interference fit verification prediction model based on at least one set of ball bearing interference fit sample data; performing network hyperparameter optimization on the initial ball bearing interference fit verification prediction model to obtain an optimized model; and embedding a Monte Carlo Dropout structure into the optimized model to construct the target ball bearing interference fit verification prediction model.

[0008] Based on the above technical means, the embodiments of this application can first construct an initial ball bearing interference fit verification prediction model, and then optimize the initial model through a dual optimization strategy of "Bayesian optimization + MC Dropout" to improve the model's generalization ability and ensure the accuracy and stability of subsequent verification results.

[0009] Optionally, in one embodiment of this application, the step of optimizing the network hyperparameters of the initial ball bearing interference fit verification prediction model to obtain an optimized model includes: determining the hyperparameter optimization range of the initial ball bearing interference fit verification prediction model, wherein the hyperparameters include the number of network layers, the number of neurons per layer, the learning rate, and the regularization coefficient; setting an optimization objective function and iteratively searching for a target hyperparameter combination; and stopping the optimization of the initial ball bearing interference fit verification prediction model in response to the objective function value reaching a preset threshold or the number of iterations exceeding a preset number, and outputting the target hyperparameter combination and the corresponding optimized model.

[0010] Based on the above technical means, the embodiments of this application can automatically iteratively search for hyperparameter combinations of the target network by optimizing the hyperparameter range and setting the optimization objective function, which can effectively improve the fitting accuracy and generalization ability of the model, reduce the cost of manual parameter tuning, and ensure stable and reliable prediction results.

[0011] Optionally, in one embodiment of this application, the at least one uncertainty indicator includes at least one of standard deviation, coefficient of variation, and confidence interval.

[0012] Based on the above technical means, the embodiments of this application can use standard deviation, coefficient of variation, and confidence interval as uncertainty indicators, which can quantify and predict risks from multiple dimensions such as dispersion, relative size, and confidence interval, thereby improving the comprehensiveness and accuracy of the verification result evaluation.

[0013] Optionally, in one embodiment of this application, the step of outputting the final prediction result of the target ball bearing includes: performing statistical analysis on the multiple sets of ball bearing interference fit verification results to obtain the statistical mean of the multiple sets of ball bearing interference fit verification results; and combining the at least one uncertainty index with the statistical mean to output the final prediction result.

[0014] Based on the above technical means, the embodiments of this application can combine statistical mean and uncertainty index to output the final result, which not only provides a stable and reliable core prediction value, but also intuitively reflects the prediction credibility range, thereby improving the guidance and decision robustness of engineering applications.

[0015] A second aspect of this application provides an apparatus for predicting the interference fit verification results of a ball bearing, comprising: an acquisition module for acquiring interference fit data of a target ball bearing; a processing module for inputting the interference fit data of the target ball bearing into a pre-trained target ball bearing interference fit verification prediction model, repeatedly executing model inference according to a preset number of samplings to obtain multiple sets of ball bearing interference fit verification results; and a prediction module for calculating at least one uncertainty index using the multiple sets of ball bearing interference fit verification results, and outputting the final prediction result of the target ball bearing based on the multiple sets of ball bearing interference fit verification results and the corresponding at least one uncertainty index.

[0016] Optionally, in one embodiment of this application, the apparatus further includes: a first construction module, configured to construct an initial ball bearing interference fit verification prediction model based on at least one set of ball bearing interference fit sample data; an optimization module, configured to perform network hyperparameter optimization on the initial ball bearing interference fit verification prediction model to obtain an optimized model; and a second construction module, configured to embed a Monte Carlo Dropout structure into the optimized model to construct the target ball bearing interference fit verification prediction model.

[0017] Optionally, in one embodiment of this application, the optimization module includes: a determining unit, configured to determine the hyperparameter optimization range of the initial ball bearing interference fit verification prediction model, wherein the hyperparameters include the number of network layers, the number of neurons per layer, the learning rate, and the regularization coefficient; a setting unit, configured to set the optimization objective function and iteratively search for the target hyperparameter combination; and an optimization unit, configured to stop optimizing the initial ball bearing interference fit verification prediction model in response to the objective function value reaching a preset threshold or the number of iterations exceeding a preset number, and output the target hyperparameter combination and the corresponding optimized model.

[0018] Optionally, in one embodiment of this application, the at least one uncertainty indicator includes at least one of standard deviation, coefficient of variation, and confidence interval.

[0019] Optionally, in one embodiment of this application, the prediction module includes: an acquisition unit, configured to perform statistical analysis on the multiple sets of ball bearing interference fit verification results to obtain the statistical mean of the multiple sets of ball bearing interference fit verification results; and an output unit, configured to combine the at least one uncertainty index with the statistical mean to output the final prediction result.

[0020] A third aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method for predicting the interference fit verification result of a ball bearing as described in the above embodiments.

[0021] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for predicting the interference fit verification results of ball bearings.

[0022] A fifth aspect of this application provides a computer program product, including a computer program that, when executed, is used to implement the method described above for predicting the interference fit verification results of ball bearings.

[0023] This application embodiment can input the obtained interference fit data of the target ball bearing into a pre-trained target ball bearing interference fit verification prediction model to calculate multiple sets of ball bearing interference fit verification results. Using these multiple sets of ball bearing interference fit verification results, at least one uncertainty index is calculated. Based on these multiple sets of ball bearing interference fit verification results and the corresponding at least one uncertainty index, the final prediction result of the target ball bearing is output, effectively improving the efficiency and reliability of the entire ball bearing design process. Therefore, it solves the problems of cumbersome and inefficient ball bearing interference fit verification methods in related technologies, where verification accuracy relies on manual experience, making it impossible to assess the potential risks of prediction errors and reducing the efficiency and reliability of the entire ball bearing design process.

[0024] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0025] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart illustrating a method for predicting the verification results of ball bearing interference fits according to an embodiment of this application. Figure 2 This is a predicted structural diagram of an interference fit ball bearing according to a specific embodiment of this application; Figure 3 This is a schematic diagram of a fully connected neural network structure according to a specific embodiment of this application; Figure 4 This is a diagram illustrating the neural network training process of a specific embodiment of this application; Figure 5This is a diagram showing the neural network prediction result of a specific embodiment of this application; Figure 6 This is a diagram illustrating the neural network hyperparameter optimization search process according to a specific embodiment of this application; Figure 7 This is a diagram showing the neural network uncertainty prediction results of a specific embodiment of this application; Figure 8 This is a schematic diagram of the application interface of a specific embodiment of this application; Figure 9 This is a schematic diagram of a device for predicting the verification results of ball bearing interference fit according to an embodiment of this application; Figure 10 This is a schematic diagram of the structure of an electronic device provided according to an embodiment of this application. Detailed Implementation

[0026] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0027] The following describes a method and apparatus for predicting the interference fit verification results of ball bearings according to embodiments of this application, with reference to the accompanying drawings. Addressing the problems mentioned in the background art regarding the cumbersome and inefficient interference fit verification methods for ball bearings, where verification accuracy relies on manual experience and cannot assess the potential risks of prediction errors, thus reducing the efficiency and reliability of the entire ball bearing design process, this application provides a method for predicting the interference fit verification results of ball bearings. In this method, the obtained interference fit data of the target ball bearing is input into a pre-trained target ball bearing interference fit verification prediction model to calculate multiple sets of ball bearing interference fit verification results. At least one uncertainty index is calculated using these multiple sets of ball bearing interference fit verification results. Based on these multiple sets of ball bearing interference fit verification results and the corresponding at least one uncertainty index, the final prediction result of the target ball bearing is output, effectively improving the efficiency and reliability of the entire ball bearing design process. Therefore, this solves the problems of cumbersome and inefficient ball bearing interference fit verification methods in related technologies, where verification accuracy relies on manual experience and cannot assess the potential risks of prediction errors, thus reducing the efficiency and reliability of the entire ball bearing design process.

[0028] Specifically, Figure 1 This is a flowchart illustrating a method for predicting the verification results of ball bearing interference fits, as provided in an embodiment of this application.

[0029] like Figure 1As shown, the method for predicting the interference fit verification result of the ball bearing includes the following steps: In step S101, the interference fit data of the target ball bearing is obtained.

[0030] It is understood that the embodiments of this application can obtain interference fit data of the target ball bearing. For example, the core parameters such as bearing model, shaft / bore fit tolerance, load condition, operating temperature, speed, and material properties manually input by the user are obtained from the input feature area of ​​the graphical user interface in the following steps. At the same time, combined with the built-in standard library and bearing manufacturer sample data, the interference range, fit tolerance zone, and boundary constraint conditions are integrated and extracted to form a complete interference fit input dataset. Thus, by obtaining interference fit data through multi-source data fusion, the integrity and standardization of input parameters can be guaranteed, laying a reliable data foundation for subsequent high-precision prediction calculations.

[0031] For example, in this embodiment of the application, the data can be obtained through user interface input. That is, the user manually inputs parameters such as the model of the target ball bearing (e.g., 6205), shaft fit grade (e.g., k6), and operating temperature (e.g., 80°C) on the visual interface, and the program directly reads and parses them into structured data.

[0032] For example, it can also be obtained through standard library matching. That is, based on the input bearing model and operating conditions, it can automatically match the corresponding bearing inner / outer diameter tolerance zone, recommended interference range and allowable load threshold from the built-in standard library.

[0033] For example, the actual effective interference fit and safety boundary conditions can also be calculated based on the operating conditions. That is, based on the input material thermal expansion coefficient, rotational speed, and load, the actual effective interference fit and safety boundary conditions can be calculated through mechanical and thermal models. It should be noted that the specific method for obtaining the interference fit data of the target ball bearing is set by those skilled in the art, and is not specifically limited here.

[0034] Optionally, in one embodiment of this application, before inputting the interference fit data of the target ball bearing into the pre-trained target ball bearing interference fit verification prediction model, the method further includes: constructing an initial ball bearing interference fit verification prediction model based on at least one set of ball bearing interference fit sample data; optimizing the network hyperparameters of the initial ball bearing interference fit verification prediction model to obtain an optimized model; and embedding a Monte Carlo Dropout structure into the optimized model to construct the target ball bearing interference fit verification prediction model.

[0035] In actual implementation, the embodiments of this application can first build an initial ball bearing interference fit verification prediction model. Firstly, the input ball bearing interference fit dataset is preprocessed. This dataset comes from finite element simulation and includes input parameters characterizing the bearing interference fit and output parameters characterizing the verification results. The preprocessing mainly includes dividing the ball bearing interference fit dataset and data normalization. The dataset partitioning for ball bearing interference fit refers to randomly dividing the obtained dataset into training set, validation set, and test set according to a certain proportion. Data normalization refers to the use of the Min-Max normalization method to normalize the input parameters and output variables, as shown in formula (1). (1) in, The standardized data is mapped to the [0,1] interval; The minimum value of the original data. The maximum value of the original data. This is the original input data.

[0036] Next, the network structure is designed. To meet the prediction requirements of the output parameters, a fully connected neural network is used to achieve the prediction. The network consists of three parts: an input layer, a hidden layer, and an output layer. The input layer has 8 neurons to accommodate the 8-dimensional input feature vector and is connected to the first fully connected layer of the hidden layer. There are 3 hidden layers, each containing variables such as a configurable number of neurons, an optional batch normalization layer, a configurable DropOut layer, and an activation function. The output layer has 3 neurons and no activation function to adapt to regression tasks; Secondly, model training is performed, with the goal of minimizing the loss function. The backpropagation algorithm is used to achieve precise iterative updates of the model parameters. First, the weights and biases of the neural network are initialized. The predicted values ​​of the output are obtained through forward propagation. Then, the deviation between the predicted values ​​and the true values ​​of the finite element method is quantified by the loss function. Subsequently, the backpropagation algorithm backtracks from the output layer to the input layer, calculates the gradient of the loss function with respect to the parameters of each layer (i.e., the contribution of the parameters to the error), and dynamically adjusts the weights and biases based on the gradient direction to reduce the error. Finally, the model accurately learns the nonlinear mapping law between the input parameters and the output physical quantity, while avoiding overfitting. The model training process mainly includes the loss function, training parameters, training strategy, and training process monitoring. In this application, the loss function refers to the mean squared error (MSE) between the predicted value and the actual output value, as shown in formula (2). (2) in, The total number of samples, For the first i The true value of each sample For the first i The predicted value for each sample.

[0037] Training parameter settings mainly include optimizer, learning rate, number of iterations, batch size, etc. The core function of the optimizer is to dynamically adjust the learnable parameters of the neural network through iterative calculation to minimize the loss function. Optimizer types include Adam and RMSprop. The learning rate is the "step size coefficient" when the optimizer updates the model parameters. It is a core hyperparameter that controls the adjustment magnitude each time the parameters are adjusted based on the gradient calculated by backpropagation. The number of iterations refers to the maximum number of training epochs, controlling the total number of times the model learns and avoiding undertraining or overtraining. The batch size is the number of samples used for each parameter update, affecting training stability and efficiency. Training strategies include early stopping and learning rate decay. Early stopping involves monitoring the validation set loss during training and automatically terminating training when the validation set loss stops decreasing after several consecutive rounds. The model weights with the lowest validation set loss during training are then restored, which can prevent overfitting and improve training efficiency. Learning rate decay involves decaying the learning rate by a specified factor and limiting it to a minimum when the validation set loss stagnates. This can solve the training stagnation problem and balance convergence speed and accuracy. Training process monitoring refers to recording key metrics for each round of training, including training set loss, training set mean absolute error, validation set loss, validation set mean absolute error, and learning rate changes. This provides data support for judging the model training status and records training duration to evaluate model training efficiency.

[0038] Furthermore, the prediction results can be evaluated, and multi-dimensional assessments can be achieved through evaluation functions, including dimensional and dimensionless indicators. Among them, the dimensional indicators include mean squared error (MSE) and root mean squared error (RMSE), as detailed in formulas (2) to (3): (3) Dimensionless indicators include Symmetric Mean Absolute Percentage Error (SMAPE), Normalized Root Mean Squared Error (NRMSE), and Coefficient of Determination (R²). 2 For details, see formulas (4) to (6). (4) (5) (6) in, This is the mean of the true values.

[0039] Furthermore, embodiments of this application can perform hyperparameter optimization on the initial ball bearing interference fit verification prediction model. For example, Bayesian optimization methods can be used to optimize network hyperparameters. The core objective is to efficiently search for the optimal balance of "accuracy-stability-complexity" among a massive number of hyperparameter combinations by minimizing the objective function. This replaces inefficient methods such as traditional manual tuning and grid search, solving the problem that neural network hyperparameters (such as network structure and training strategy parameters) are difficult to accurately match the characteristics of the dataset, thereby improving prediction accuracy, generalization ability, and model efficiency, and thus obtaining an optimized model. The specific optimization process will be described in detail in the following steps.

[0040] Next, this application embodiment can quantify the uncertainty of the optimized model. Specifically, in the practical application of neural network models, the accuracy index of the prediction result alone cannot fully reflect the reliability of the model. Especially in key areas such as engineering decision-making and risk assessment, the uncertainty information of the prediction result (i.e., the credibility of the prediction value) is as important as the prediction accuracy. Traditional neural network models usually only output single-point prediction results, lacking effective quantification of prediction uncertainty, making it difficult for decision-makers to assess the potential risks of prediction errors. Therefore, to address the above problems, this application proposes a neural network uncertainty quantification method based on Monte Carlo Dropout (MC Dropout). By introducing a probabilistic inference mechanism into the trained neural network, the uncertainty of the prediction result can be measured. This method does not require modification of the basic architecture of the neural network. It can efficiently calculate the uncertainty index simply by keeping the Dropout layer active and performing multiple samplings during the prediction phase. It is suitable for complex prediction scenarios with multiple output variables and has the characteristics of simple implementation, high computational efficiency, and intuitive quantification results. The specific process of constructing the neural network model for uncertainty quantification is as follows: Constructing a neural network model for uncertainty quantification refers to building the neural network model based on the optimal combination of hyperparameters obtained through optimization. This optimized model ensures the inclusion of Dropout layers within the neural network structure. Dropout layers prevent overfitting during training and maintain activation during prediction to achieve probabilistic sampling. Specifically, the model includes: an input layer that receives multidimensional feature data; hidden layers containing multiple fully connected layers, each followed by a LeakyReLU activation function and a Dropout layer; an output layer that outputs multidimensional prediction results according to task requirements; and model compilation using the RMSprop optimizer with mean squared error (MSE) as the loss function to ensure the model converges to a stable state.

[0041] Further, preprocessing and model training are performed, with the following specific steps: Data loading and splitting: Read the input feature and output variable data, and split them into training and test sets according to a preset ratio; Standardization: MinMaxScaler is used to normalize the input features and output variables respectively, mapping the data to the [0,1] interval to avoid the impact of differences in scale on model training and uncertainty calculation; Model training: The training process is optimized through early stopping and learning rate decay to ensure optimal model performance on the validation set, while training time is recorded to evaluate computational efficiency.

[0042] In summary, this application embodiment constructs a target ball bearing interference fit verification prediction model that supports Monte Carlo Dropout sampling through standardized data preprocessing and efficient model training, laying a core foundation for the generation of multiple sets of verification results and the calculation of uncertainty indicators in the following steps.

[0043] Optionally, in one embodiment of this application, the network hyperparameters of the initial ball bearing interference fit verification prediction model are optimized to obtain an optimized model. This includes: determining the hyperparameter optimization range of the initial ball bearing interference fit verification prediction model, whereby the hyperparameters include the number of network layers, the number of neurons per layer, the learning rate, and the regularization coefficient; setting an optimization objective function and iteratively searching for a target hyperparameter combination; and stopping the optimization of the initial ball bearing interference fit verification prediction model in response to the objective function value reaching a preset threshold or the number of iterations exceeding a preset number, and outputting the target hyperparameter combination and the corresponding optimized model.

[0044] As one possible implementation method, this application embodiment can adopt the Bayesian optimization core logic of "surrogate model + acquisition function" to iteratively realize hyperparameter search, and the specific process is as follows: First, the objective function is defined. In this embodiment, the objective function refers to a composite objective function to optimize the accuracy, stability, and complexity performance of the network, avoiding the problem of excessive model complexity and poor generalization ability caused by solely pursuing accuracy. See formula (7) for details: (7) in, The mean of SMAPE values ​​from multiple experiments represents the average prediction error. The standard deviation of SMAPE over multiple experiments represents the predictive stability. This represents the number of neurons in each hidden layer of the average neural network.

[0045] Next, the hyperparameters and search space are determined. The types of hyperparameters to be optimized include network structure parameters, training parameters, and algorithm selection parameters (activation function type, optimizer type). Network structure parameters include the number of neurons in the three layers, DropOut parameter, and BatchNorm parameter; the number of neurons in the three layers is a discrete value; the DropOut parameter refers to the DropOut rate of the three DropOut layers; the BatchNorm parameter indicates whether to enable the BatchNorm layer; training parameters include learning rate, batch size, maximum number of iterations, and early stopping tolerance value; algorithm selection parameters include activation function parameters and optimizer parameters; activation function parameters refer to the types of activation functions in each layer; optimizer parameters refer to the types of optimizers; the search space is determined by the specific instance.

[0046] Secondly, an optimization search is performed, and the specific optimization search process is as follows: determine the number of hyperparameter combinations; in the initial stage, randomly sample a small number of hyperparameter combinations and calculate the target value; subsequently, based on the experimental "hyperparameter-target value" mapping relationship, predict the hyperparameter combination that is "most likely to reduce the target value" through a Bayesian probability model (such as a Gaussian process) and sample it first; record and output the evaluation index of each experiment result.

[0047] Finally, the optimization results are processed. After optimization, the results are analyzed, saved, and verified to ensure the validity of the optimal hyperparameters. This includes outputting core results, saving optimization records, and verifying the optimal parameters. Specifically, outputting core results means outputting the best integrated objective function value and its corresponding mean and variance. Saving optimization records means saving all hyperparameter combinations and their target values ​​during the optimization process, and generating visualization charts of relevant variables, including optimization history, parameter importance, parallel coordinates, and SMAPE mean-standard deviation scatter plots. Verifying the optimal parameters means performing five independent evaluations using the optimal hyperparameters to verify the accuracy and stability on the test set, and saving the final model, hyperparameter file, and test set prediction results.

[0048] In step S102, the interference fit data of the target ball bearing is input into the pre-trained target ball bearing interference fit verification prediction model. The model inference is repeatedly executed according to the preset number of samplings to obtain multiple sets of ball bearing interference fit verification results.

[0049] It is understood that the embodiments of this application can input the obtained interference fit data of the ball bearing, such as bearing model, shaft / bore fit tolerance, load conditions, operating temperature, speed, and material properties, into the pre-trained target ball bearing interference fit verification prediction model; during the model inference phase, all Dropout layers are kept active, converting the model into a probabilistic inference mode; based on the sampling number N preset by the user in the visualization interface, the target ball bearing interference fit data is repeatedly subjected to N independent forward propagation, generating N sets of ball bearing interference fit verification results, forming a three-dimensional tensor containing the sampling number, sample dimension, and output dimension, providing original data support for subsequent uncertainty quantification analysis. Thus, the embodiments of this application, through repeated inference with a certain number of samplings, can obtain multiple sets of verification results while ensuring prediction accuracy, providing a reliable data foundation for the uncertainty quantification (such as mean, standard deviation, confidence interval, etc.) of ball bearing interference fit verification, and improving the reliability and robustness of engineering decisions.

[0050] For example, embodiments of this application can perform Monte Carlo Dropout sampling prediction. Based on the trained target ball bearing interference fit verification prediction model, uncertainty quantification is achieved through the following steps: (1) Enable Dropout layers: Keep all Dropout layers active during the prediction phase to make the model a probabilistic model; (2) Multiple sampling: Perform N independent forward propagation on the test set data to generate N sets of prediction results, forming a three-dimensional tensor (number of samplings × number of samples × output dimension). (3) Destandardization: All sampling results are transformed to the original data scale through the output variable standardizer (scaler_y) to ensure that the uncertainty index is interpretable in the actual physical space.

[0051] In summary, the embodiments of this application can use Monte Carlo Dropout sampling to predict, introduce model randomness and sample multiple times during the inference stage, and combine it with destandardization processing to quantify the uncertainty of the ball bearing interference fit verification results, thereby improving the reliability and engineering applicability of the interference fit verification results.

[0052] In step S103, at least one uncertainty index is calculated using the interference fit verification results of multiple sets of ball bearings, so as to output the final prediction result of the target ball bearing based on the interference fit verification results of multiple sets of ball bearings and the corresponding at least one uncertainty index.

[0053] It is understood that the embodiments of this application can use multiple sets of ball bearing interference fit verification results to calculate at least one uncertainty index, wherein the at least one uncertainty index includes at least one of standard deviation, coefficient of variation, and confidence interval, so as to output the final prediction result of the target ball bearing based on multiple sets of ball bearing interference fit verification results and the corresponding at least one uncertainty index.

[0054] It is understood that the embodiments of this application can perform statistical analysis on the predicted data of each group based on multiple sets of ball bearing interference fit verification results, and calculate at least one uncertainty index, including the predicted mean, standard deviation, confidence interval (such as 95% confidence level), and coefficient of variation. The predicted mean represents the central trend of the interference fit verification results, the standard deviation reflects the dispersion of the predicted results, the confidence interval characterizes the reliable range of the results, and the coefficient of variation measures the relative uncertainty. Subsequently, the multiple sets of ball bearing interference fit verification results are integrated with the above uncertainty indexes, and the final predicted result of the target ball bearing interference fit is output through tables, bar charts, and error bars in a visual interface, providing an intuitive basis for engineering design and reliability assessment. Therefore, this application obtains uncertainty indexes through statistical analysis of multiple sets of prediction results, which can quantitatively assess the reliability and risk of the prediction results while providing the predicted value of the interference fit verification, providing more comprehensive and robust decision support for ball bearing interference fit design.

[0055] For example, based on the sampling results, i.e., the N sets of prediction results generated in the above steps, the three-dimensional tensor (number of samplings × number of samples × output dimension) can be used to calculate the following core indicators to quantify uncertainty: Predicted mean: The average of the N sampling results is taken as the final predicted value, reflecting the central trend of the model; Prediction standard deviation: Calculates the standard deviation of N sampling results to measure the dispersion of the predicted values; Coefficient of variation (CV): Calculated by the formula (standard deviation / |mean|)×100%. The standard deviation is normalized into a dimensionless index to eliminate the influence of dimensions and make the uncertainty between different output variables comparable. Confidence interval: Based on the predicted mean and standard deviation, calculate the confidence interval (mean ± 1.96 × standard deviation) at a preset confidence level (e.g., 95%), which intuitively reflects the possible range of the predicted value.

[0056] Therefore, the embodiments of this application can calculate the prediction mean, standard deviation, coefficient of variation and confidence interval based on multiple sets of prediction results obtained by Monte Carlo Dropout sampling, realize the uncertainty quantification of ball bearing interference fit verification results, and provide a reliable risk assessment basis for engineering decision-making.

[0057] Furthermore, embodiments of this application can evaluate and visualize the prediction results, as detailed below: Accuracy metrics: Calculate the mean square error (MSE), root mean square error (RMSE), symmetric mean absolute percentage error (SMAPE), normalized root mean square error (NRMSE), and coefficient of determination (R²) between the predicted mean and the actual value to evaluate the prediction accuracy of the model. Uncertainty assessment: Quantifying the level of uncertainty of the whole and each output variable through uncertainty indicators; Visualization: The relationship between prediction accuracy and uncertainty is presented intuitively through scatter plots (actual values ​​vs. predicted mean, with color mapping of the coefficient of variation) and trend plots (predicted sequences with confidence intervals).

[0058] Thus, by quantifying accuracy with precision indicators, quantifying risk with uncertainty indicators, and presenting the results visually, a comprehensive evaluation of the interference fit verification prediction results of ball bearings is achieved, thereby improving the robustness of engineering decisions and the pertinence of model optimization.

[0059] Optionally, in one embodiment of this application, outputting the final prediction result of the target ball bearing includes: performing statistical analysis on multiple sets of ball bearing interference fit verification results to obtain the statistical mean of the multiple sets of ball bearing interference fit verification results; and combining at least one uncertainty index with the statistical mean to output the final prediction result.

[0060] In some embodiments, the present application embodiments can perform statistical analysis on the multiple sets of ball bearing interference fit verification results after de-standardization processing in the above steps, take the arithmetic mean of the N sampled prediction values, and obtain the statistical mean that characterizes the central trend of the interference fit verification results, which is used as the core prediction value.

[0061] Next, by combining at least one uncertainty indicator (including prediction standard deviation, coefficient of variation, confidence interval at a pre-set confidence level, etc.), the statistical mean and uncertainty indicator are integrated and encapsulated to form a complete structure containing "predicted value ± error range".

[0062] Finally, the statistical mean, standard deviation, coefficient of variation, and confidence interval are displayed in a table through a visualization interface, and the predicted values ​​and reliability ranges of each output indicator are presented intuitively in the form of bar charts and error bars, ultimately outputting the final prediction result of the target ball bearing.

[0063] Thus, by integrating statistical mean and uncertainty indicators, the completeness and reliability of the prediction results are improved. While providing core prediction values, the risk of the results is quantified, providing a more robust decision-making basis for engineering design.

[0064] In this embodiment, the encapsulation and deployment of neural networks can be achieved by designing a graphical user interface-based application. The specific process is as follows: 1. The application architecture is designed using object-oriented programming principles, integrating UI components, model management, data processing, prediction calculation, and result display modules to achieve modular coupling of various functions.

[0065] 2. Graphical user interface design, based on the Tkinter framework, including the following core areas: (1) Model Status Area: Displays the model loading status in real time and provides feedback on the initialization results; (2) Input feature area: Input boxes displaying input parameters in a grid layout, supporting manual input by the user; (3) Input diagram area: Load the diagram corresponding to the physical parameters to help users understand the meaning of the parameters; (4) Prediction parameter setting area: Provides configuration controls for the number of samples and confidence level; (5) Results display area: The predicted mean, standard deviation, confidence interval, coefficient of variation and other statistical measures are displayed in tables; (6) Visualization area: The predicted values ​​and confidence intervals of each output indicator are visualized in the form of bar charts and error bars; (7) Log area: records key information about model loading and prediction process, which is convenient for troubleshooting.

[0066] 3. Model loading and management: Multi-threading technology is used to asynchronously load neural network models and normalizers to avoid interface lag; during the loading process, progress is fed back in real time through logs and status labels, and the error reason (such as missing files) is automatically indicated when loading fails.

[0067] 4. Input validation and processing: This includes validating the input parameters, such as: (1) Non-empty check: Ensure that all input parameters are filled in; (2) Type validation: Validate that the input is a valid number (integer or floating-point number); (3) Range verification: Limit the number of samplings to a fixed range to avoid wasting computational resources.

[0068] 5. Prediction calculation process: Based on the Monte Carlo dropout method, uncertainty prediction is achieved. The steps are as follows: (1) Standardize the user input parameters (using the preloaded scaler_X); (2) Repeat the model prediction according to the configured number of samplings (enable training=True mode to simulate dropout randomness); (3) Denormalize the multiple prediction results (using scaler_y) to restore the physical dimensions; (4) Calculate statistical indicators: mean (predicted value), standard deviation (uncertainty), coefficient of variation ((standard deviation / mean)×100%), confidence interval (confidence coefficient×standard deviation, the coefficient is dynamically adjusted with the confidence level).

[0069] 6. Results presentation and visualization: Results are presented using tables and charts. Table display: The statistical results of each output parameter are displayed in a tree view control, categorized by indicator; Chart visualization: Three subplots (corresponding to three output metrics) are drawn using Matplotlib, with the mean represented by a bar chart, the confidence interval represented by error bars, and the axis range is automatically adjusted to optimize readability.

[0070] In summary, the embodiments of this application quantify uncertainty by calculating the mean, standard deviation, coefficient of variation, and confidence interval, and intuitively and clearly display the predicted results and reliability range of the ball bearing interference fit verification in a tree table, bar chart, and error bar visualization.

[0071] For example, the working principle of the embodiments of this application will be described in detail below with a specific example.

[0072] like Figure 2 As shown, the embodiments of this application can be used to build neural network models: First, data preprocessing was performed. 400 datasets were generated using the automated finite element method and divided into 320 training sets, 40 validation sets, and 40 test sets in an 8:1:1 ratio. Min-Max normalization was then used to map all input and output data to the [0,1] interval.

[0073] Next, network architecture design is carried out, such as... Figure 3 The diagram shows the fully connected neural network structure designed in this application: 8 neurons in the input layer, 3 hidden layers (with 128, 64, and 32 neurons respectively), LeakyReLU activation function, BatchNorm layer enabled, DropOut rate 0.2; and 3 neurons in the output layer. Secondly, model training is performed. In this embodiment, the training parameters are set as follows: the loss function is MSE, the optimizer is RMSprop, the learning rate is 0.001, the batch size is 32, the maximum number of iterations is 500, the early stopping patience value is 30, the validation set loss is monitored, and if there is no decrease for 30 consecutive rounds, training is terminated and the optimal weights are restored. The learning rate decay strategy is enabled, and if the validation set loss stagnates for 5 consecutive rounds, the learning rate is halved, down to a minimum of 1e-6. Figure 4The diagram shows the neural network training process of this application. Figure 5 The image shows the prediction results of the neural network for the three outputs in this application.

[0074] Furthermore, multi-dimensional evaluation is achieved through evaluation functions, as shown in Table 1, which is a table of evaluation indicators for neural network prediction results. These indicators represent the evaluation metrics for neural network prediction results in this application. Among them, MSE and RMSE are dimensional indicators; the smaller their values, the lower the model prediction error. SMAPE, NRMSE, and R... 2 Dimensionless indices: smaller values ​​for SMAPE and NRMSE indicate lower prediction errors. R 2 The closer the value is to 1, the better the model fit. See Table 1 below for details: Table 1

[0075] Furthermore, the embodiments of this application can perform model hyperparameter optimization. This application uses the Bayesian optimization method to optimize network hyperparameters. Its core objective is to efficiently search for the optimal balance of "accuracy-stability-complexity" among a massive number of hyperparameter combinations by minimizing the objective function. This replaces inefficient methods such as traditional manual tuning and grid search, and solves the problem that neural network hyperparameters (such as network structure and training strategy parameters) are difficult to accurately match the characteristics of the dataset, thereby improving prediction accuracy, generalization ability, and model efficiency.

[0076] The core logic of Bayesian optimization, which uses a "surrogate model + acquisition function", is adopted to iteratively perform hyperparameter search. The specific process is as follows: First, the objective function is defined, namely the composite objective function proposed in this application embodiment, to optimize the accuracy, stability, and complexity performance of the network, avoiding the problem of excessive model complexity and poor generalization ability caused by solely pursuing accuracy. See formula (7) for details: (7) Next, the hyperparameters and search space are determined. The types of hyperparameters to be optimized include network structure parameters, training parameters, and algorithm selection parameters (activation function type, optimizer type). The network structure parameters include the number of neurons in the three layers, the DropOut parameter, and the BatchNorm parameter. The number of neurons in the three layers takes discrete values, with a search space of (8 / 16 / 32 / 64 / 128 / 256 / 512). The DropOut parameter refers to the DropOut rate of the three DropOut layers, with a search space of (0~0.3, step size 0.01). The BatchNorm parameter indicates whether the BatchNorm layer is enabled, with a search space of (True / False). Training parameters include learning rate, batch size, maximum number of iterations, and early stopping patience value; the search space for learning rate is (1e-4~1e-2, logarithmic search); the search space for batch size is (4 / 8 / 16 / 32 / 64); the search space for maximum number of iterations is (300 / 400 / 500 / 600); and the search space for early stopping patience value is (20 / 25 / 30 / 40 / 50). The algorithm selection parameters include activation function parameters and optimizer parameters; activation function parameters refer to the types of activation function layers, and their search space is (relu / tanh / leakyrelu); optimizer parameters refer to the types of optimizers, and their search space is (adam / rmsprop). Secondly, an optimization search is performed. The optimization search process is as follows: determine the number of hyperparameter combinations; in the initial stage, randomly sample a small number of hyperparameter combinations and calculate the target value; subsequently, based on the experimental "hyperparameter-target value" mapping relationship, predict the hyperparameter combinations that are "most likely to reduce the target value" using a Bayesian probability model (such as a Gaussian process), and prioritize sampling these combinations; record and output the evaluation index of each experiment result; such as... Figure 6 The diagram shows the optimized search process in this application.

[0077] Finally, the optimization results are processed. After optimization, the results are analyzed, saved, and verified to ensure the validity of the optimal hyperparameters. This includes outputting the core results, saving the optimization record, and verifying the optimal parameters. The optimal parameter combination after optimization is as follows: units1: 256; units2: 512; units3: 64 dropout1: 0.0; dropout2: 0.2; dropout3: 0.03 use_batchnorm: False learning_rate: 0.0036591482519118075 batch_size: 8 epochs: 400 patience: 50 activation: leakyrelu optimizer: rmsprop; Table 2 shows the evaluation index table for the optimized neural network prediction results in this application. The specific table is as follows: Table 2

[0078] As can be seen from Table 2, the optimized model has improved its predictive performance on all indicators, proving the effectiveness of this optimization method.

[0079] Furthermore, embodiments of this application can construct a neural network model with uncertainty quantification, that is, construct a neural network model based on the optimal combination of hyperparameters obtained through optimization, ensuring that a Dropout layer is embedded in the neural network structure. The Dropout layer is used to prevent overfitting during the model training phase and remains active during the prediction phase to achieve probabilistic sampling. The model structure remains the same as the optimal model parameters obtained above.

[0080] Next, this embodiment can perform preprocessing and model training, the specific steps of which are as follows: Data loading and splitting: Read the input feature and output variable data, and split them into training and test sets according to a preset ratio; Standardization: MinMaxScaler is used to normalize the input features and output variables respectively, mapping the data to the [0,1] interval to avoid the impact of differences in scale on model training and uncertainty calculation; Model training: The training process is optimized through early stopping strategy and learning rate decay to ensure optimal model performance on the validation set, while the training time is recorded to evaluate computational efficiency.

[0081] Furthermore, embodiments of this application can perform Monte Carlo Dropout sampling prediction, that is, based on the trained neural network, uncertainty quantification is achieved through the following steps: (1) Enable Dropout layers: Keep all Dropout layers active during the prediction phase to make the model a probabilistic model; (2) Multiple sampling: Perform N independent forward propagation on the test set data to generate N sets of prediction results, forming a three-dimensional tensor (number of samplings × number of samples × output dimension). (3) Destandardization: All sampling results are transformed to the original data scale through the output variable standardizer (scaler_y) to ensure that the uncertainty index is interpretable in the actual physical space.

[0082] Next, based on the sampling results, the following core indicators are calculated to quantify the uncertainty: Predicted mean: The average of the N sampling results is taken as the final predicted value, reflecting the central trend of the model; Prediction standard deviation: Calculates the standard deviation of N sampling results to measure the dispersion of the predicted values; Coefficient of variation (CV): Calculated by the formula (standard deviation / |mean|)×100%. The standard deviation is normalized into a dimensionless index to eliminate the influence of dimensions and make the uncertainty between different output variables comparable. Confidence interval: Based on the predicted mean and standard deviation, calculate the confidence interval (mean ± 1.96 × standard deviation) at a preset confidence level (e.g., 95%), which intuitively reflects the possible range of the predicted value.

[0083] Finally, the results are evaluated and visualized as follows: Accuracy metrics: Calculate the mean square error (MSE), root mean square error (RMSE), symmetric mean absolute percentage error (SMAPE), normalized root mean square error (NRMSE), and coefficient of determination (R²) between the predicted mean and the actual value to evaluate the prediction accuracy of the model. Uncertainty assessment: The uncertainty level of the whole and each output variable is quantified using the uncertainty indicators mentioned above; Visualization: Scatter plots (actual values ​​vs. predicted mean, color mapping to coefficient of variation) and trend charts (predicted sequences with confidence intervals) visually demonstrate the relationship between prediction accuracy and uncertainty; for example... Figure 7 The following shows the uncertainty prediction results of this model: Table 3 shows the evaluation index table for neural network prediction results considering uncertainty. The specific table is as follows: Table 3

[0084] In addition, the embodiments of this application can perform application design and encapsulation, that is, by designing a graphical user interface-based application, the neural network can be encapsulated and deployed. The specific process is as follows: 1. Application Architecture Design It adopts object-oriented programming concepts and integrates interface components, model management, data processing, prediction calculation and result display modules to achieve modular coupling of various functions.

[0085] 2. Graphical User Interface Design The interface is built using the Tkinter framework and includes the following core areas: (1) Prediction button: Enables the software prediction function; (2) Input feature area: Input boxes displaying input parameters in a grid layout, supporting manual input by the user; (3) Input diagram area: Load the diagram corresponding to the physical parameters to help users understand the meaning of the parameters; (4) Interval prediction parameter setting area: provides configuration controls for the number of samples and confidence level; (5) Results display area: The predicted mean, standard deviation, confidence interval, coefficient of variation and other statistical measures are displayed in tables; (6) Visualization area: The predicted values ​​and confidence intervals of each output indicator are visualized in the form of bar charts and error bars; (7) Log area: records key information about model loading and prediction process, which is convenient for troubleshooting.

[0086] 3. Model Loading and Management Multi-threading technology is used to load neural network models and normalizers asynchronously to avoid interface lag; during the loading process, progress is fed back in real time through logs and status labels, and the error reason (such as missing files) is automatically indicated when loading fails.

[0087] 4. Input Validation and Processing Implement input parameter validity validation, including: (1) Non-empty check: Ensure that all input parameters are filled in; (2) Type validation: Validate that the input is a valid number (integer or floating-point number); (3) Range verification: Limit the number of samplings to a fixed range to avoid wasting computational resources.

[0088] 5. Prediction Calculation Process Uncertainty prediction based on the Monte Carlo dropout method is achieved through the following steps: (1) Standardize the user input parameters (using the preloaded scaler_X); (2) Repeat the model prediction according to the configured number of samplings (enable training=True mode to simulate dropout randomness); (3) Denormalize the multiple prediction results (using scaler_y) to restore the physical dimensions; (4) Calculate statistical indicators: mean (predicted value), standard deviation (uncertainty), coefficient of variation ((standard deviation / mean)×100%), confidence interval (confidence coefficient×standard deviation, the coefficient is dynamically adjusted with the confidence level).

[0089] 6. Results Display and Visualization The results are presented using tables and charts for visualization. Table display: The statistical results of each output parameter are displayed in a tree view control, categorized by indicator; Chart visualization: Three subplots (corresponding to three output metrics) are plotted using Matplotlib, with the mean represented by a bar chart, the confidence interval represented by error bars, and the axis range automatically adjusted to optimize readability.

[0090] like Figure 8 The image shows the application interface developed in this embodiment and its running results.

[0091] In summary, the fully connected neural network structure for ball bearing interference fit verification in this application can adapt to the nonlinear prediction requirements of clamping force and radial deformation, with the total number of parameters controlled within 12,000, balancing accuracy and deployment efficiency. Furthermore, the composite objective function that balances accuracy, stability, and complexity, and the efficient hyperparameter search method based on Bayesian optimization, address the problems of low efficiency and unbalanced model performance in traditional tuning methods. Secondly, the multi-output variable uncertainty quantification method based on MCDropout in this application can output uncertainty-related indicators without modifying the model architecture, filling the gap in risk assessment in traditional models. The evaluation gap is filled; moreover, it integrates functions such as multi-threaded model asynchronous loading, three-layer input verification, uncertainty prediction, and multi-format result display (table + chart), realizing real-time collaboration between design and verification; the standardized and easy-to-use GUI design in the embodiments of this application, including parameter annotation, range limitation, physical diagram to aid understanding, and installation-free features, lowers the usage threshold for ordinary designers, allowing operation without professional finite element knowledge; finally, through the adaptation design of neural network models and ordinary computer hardware, second-level prediction can be achieved without high-end CPUs / GPUs, and the overall application cost of the software is reduced by more than 95% compared with the existing technology.

[0092] The method for predicting the interference fit verification results of ball bearings proposed in this application involves inputting the obtained interference fit data of the target ball bearing into a pre-trained target ball bearing interference fit verification prediction model to calculate multiple sets of ball bearing interference fit verification results. At least one uncertainty index is calculated using these multiple sets of ball bearing interference fit verification results. Based on these multiple sets of ball bearing interference fit verification results and the corresponding at least one uncertainty index, the final prediction result of the target ball bearing is output, effectively improving the efficiency and reliability of the entire ball bearing design process. This solves the problems of cumbersome and inefficient ball bearing interference fit verification methods in related technologies, where verification accuracy relies on manual experience, making it impossible to assess the potential risks of prediction errors and reducing the efficiency and reliability of the entire ball bearing design process.

[0093] Next, referring to the accompanying drawings, a device for predicting the interference fit verification results of ball bearings according to an embodiment of this application is described.

[0094] Figure 9 This is a block diagram of a device for predicting the interference fit verification results of ball bearings according to an embodiment of this application.

[0095] like Figure 9 As shown, the device 10 for predicting the interference fit verification result of the ball bearing includes: an acquisition module 100, a processing module 200, and a prediction module 300.

[0096] Specifically, module 100 is used to acquire the interference fit data of the target ball bearing.

[0097] The processing module 200 is used to input the interference fit data of the target ball bearing into the pre-trained target ball bearing interference fit verification prediction model, and repeatedly execute the model inference according to the preset number of samplings to obtain multiple sets of ball bearing interference fit verification results.

[0098] The prediction module 300 is used to calculate at least one uncertainty index using the interference fit verification results of multiple sets of ball bearings, and to output the final prediction result of the target ball bearing based on the interference fit verification results of multiple sets of ball bearings and the corresponding at least one uncertainty index.

[0099] Optionally, in one embodiment of this application, the apparatus 10 of this application embodiment further includes: a first construction module and an optimization module.

[0100] The first construction module is used to construct an initial ball bearing interference fit verification and prediction model based on at least one set of ball bearing interference fit sample data.

[0101] The optimization module is used to optimize the network hyperparameters of the initial ball bearing interference fit verification prediction model to obtain the optimized model.

[0102] The second building module is used to embed the Monte Carlo Dropout structure into the optimized model to construct a target ball bearing interference fit verification prediction model.

[0103] Optionally, in one embodiment of this application, the optimization module includes: a determining unit, a setting unit, and an optimization unit.

[0104] The determining unit is used to determine the hyperparameter optimization range of the initial ball bearing interference fit verification prediction model. The hyperparameters include the number of network layers, the number of neurons per layer, the learning rate, and the regularization coefficient.

[0105] The setting unit is used to set the optimization objective function and iteratively search for the target hyperparameter combination.

[0106] The optimization unit is used to stop optimizing the initial ball bearing interference fit verification prediction model in response to the objective function value reaching a preset threshold or the number of iterations exceeding a preset number, and outputs the target hyperparameter combination and the corresponding optimized model.

[0107] Optionally, in one embodiment of this application, at least one uncertainty indicator includes at least one of standard deviation, coefficient of variation, and confidence interval.

[0108] Optionally, in one embodiment of this application, the prediction module 300 includes an acquisition unit and an output unit.

[0109] The acquisition unit is used to perform statistical analysis on the interference fit verification results of multiple sets of ball bearings and obtain the statistical mean of the interference fit verification results of multiple sets of ball bearings.

[0110] The output unit combines at least one uncertainty indicator with the statistical mean to output the final prediction result.

[0111] It should be noted that the explanation of the aforementioned method embodiment for predicting the interference fit verification result of ball bearings also applies to the device for predicting the interference fit verification result of ball bearings in this embodiment, and will not be repeated here.

[0112] The apparatus for predicting the interference fit verification results of ball bearings according to the embodiments of this application can input the obtained interference fit data of the target ball bearing into a pre-trained target ball bearing interference fit verification prediction model to calculate multiple sets of ball bearing interference fit verification results. At least one uncertainty index is calculated using these multiple sets of ball bearing interference fit verification results. Based on these multiple sets of ball bearing interference fit verification results and the corresponding at least one uncertainty index, the final prediction result of the target ball bearing is output, effectively improving the efficiency and reliability of the entire ball bearing design process. This solves the problems of cumbersome and inefficient ball bearing interference fit verification methods in related technologies, where verification accuracy relies on manual experience and cannot assess the potential risks of prediction errors, thus reducing the efficiency and reliability of the entire ball bearing design process.

[0113] Figure 10 A schematic diagram of the structure of an electronic device provided in an embodiment of this application. The electronic device may include: The memory 1001, the processor 1002, and the computer program stored on the memory 1001 and capable of running on the processor 1002.

[0114] When the processor 1002 executes the program, it implements the method for predicting the interference fit verification result of the ball bearing provided in the above embodiments.

[0115] Furthermore, electronic devices also include: Communication interface 1003 is used for communication between memory 1001 and processor 1002.

[0116] The memory 1001 is used to store computer programs that can run on the processor 1002.

[0117] The memory 1001 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0118] If the memory 1001, processor 1002, and communication interface 1003 are implemented independently, then the communication interface 1003, memory 1001, and processor 1002 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized into address buses, data buses, control buses, etc. For ease of representation, Figure 10 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0119] Optionally, in a specific implementation, if the memory 1001, processor 1002, and communication interface 1003 are integrated on a single chip, then the memory 1001, processor 1002, and communication interface 1003 can communicate with each other through an internal interface.

[0120] The processor 1002 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0121] This embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for predicting the interference fit verification results of ball bearings.

[0122] This embodiment also provides a computer program product, including a computer program, which, when executed, is used to implement the above-mentioned method for predicting the interference fit verification results of ball bearings.

[0123] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0124] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0125] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0126] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0127] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0128] Those skilled in the art will understand that all or part of the steps of the methods described in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it includes one or a combination of the steps of the method embodiments.

[0129] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0130] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

Claims

1. A method for predicting the verification results of ball bearing interference fit, characterized in that, Includes the following steps: Obtain the interference fit data of the target ball bearing; The interference fit data of the target ball bearing is input into the pre-trained target ball bearing interference fit verification prediction model. The model inference is repeatedly executed according to the preset number of sampling times to obtain multiple sets of ball bearing interference fit verification results. At least one uncertainty index is calculated using the multiple sets of ball bearing interference fit verification results, and the final prediction result of the target ball bearing is output based on the multiple sets of ball bearing interference fit verification results and the corresponding at least one uncertainty index.

2. The method according to claim 1, characterized in that, Before inputting the interference fit data of the target ball bearing into the pre-trained target ball bearing interference fit verification and prediction model, the following steps are also included: Based on at least one set of ball bearing interference fit sample data, an initial ball bearing interference fit verification and prediction model is constructed. The network hyperparameters of the initial ball bearing interference fit verification prediction model are optimized to obtain the optimized model; The Monte Carlo Dropout structure is embedded into the optimized model to construct the target ball bearing interference fit verification prediction model.

3. The method according to claim 2, characterized in that, The process of optimizing the network hyperparameters of the initial ball bearing interference fit verification prediction model to obtain the optimized model includes: The hyperparameter optimization range of the initial ball bearing interference fit verification prediction model is determined. The hyperparameters include the number of network layers, the number of neurons per layer, the learning rate, and the regularization coefficient. Define the objective function and iteratively search for combinations of objective hyperparameters; In response to the objective function value reaching a preset threshold or the number of iterations exceeding a preset number, the optimization of the initial ball bearing interference fit verification prediction model is stopped, and the objective hyperparameter combination and the corresponding optimized model are output.

4. The method according to claim 1, characterized in that, The at least one uncertainty indicator includes at least one of standard deviation, coefficient of variation, and confidence interval.

5. The method according to claim 4, characterized in that, The final prediction result of the target ball bearing is output, including: Statistical analysis was performed on the multiple sets of ball bearing interference fit verification results to obtain the statistical mean of the multiple sets of ball bearing interference fit verification results; The final prediction result is output by combining the at least one uncertainty indicator with the statistical mean.

6. A device for predicting the verification results of ball bearing interference fit, characterized in that, include: The acquisition module is used to acquire the interference fit data of the target ball bearing; The processing module is used to input the interference fit data of the target ball bearing into the pre-trained target ball bearing interference fit verification prediction model, and repeatedly execute the model inference according to the preset number of samplings to obtain multiple sets of ball bearing interference fit verification results; The prediction module is used to calculate at least one uncertainty index using the multiple sets of ball bearing interference fit verification results, and to output the final prediction result of the target ball bearing based on the multiple sets of ball bearing interference fit verification results and the corresponding at least one uncertainty index.

7. The apparatus according to claim 6, characterized in that, Also includes: The first construction module is used to construct an initial ball bearing interference fit verification and prediction model based on at least one set of ball bearing interference fit sample data. The optimization module is used to optimize the network hyperparameters of the initial ball bearing interference fit verification prediction model to obtain the optimized model. The second building module is used to embed the Monte Carlo Dropout structure into the optimized model to construct the target ball bearing interference fit verification prediction model.

8. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and capable of running on the processor, the processor executing the program to implement the method for predicting the interference fit verification results of ball bearings as described in any one of claims 1-5.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement the method for predicting the verification results of ball bearing interference fit as described in any one of claims 1-5.

10. A computer program product, comprising a computer program, characterized in that, The computer program is executed by a processor to implement the method for predicting the verification results of ball bearing interference fit as described in any one of claims 1-5.

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