A method and apparatus for predicting tube ablation and wear based on degradation path approximation

Abstract

This application provides a method and apparatus for predicting barrel ablation wear based on degradation path approximation. A high-order feature space is established by normalizing ablation wear data and mapping it using the Sigmoid function. The system innovatively extracts similarity metrics and path curvature features of the degradation path to achieve accurate clustering of degradation patterns and path approximation. The system employs an alternating optimization algorithm and gradient descent method to optimize path expression parameters and establish a confidence interval estimation mechanism. A comprehensive load index is constructed by combining barrel temperature, firing pressure, and propellant charge. Through the rate of change and acceleration characteristics of the degradation trend curve, accurate prediction and assessment of barrel ablation wear status are achieved, providing a scientific basis for artillery use and maintenance.

Description

Technical Field

[0001] This application relates to the field of data processing, specifically to a method and apparatus for predicting tube ablation and wear based on degradation path approximation. Background Technology

[0002] Existing techniques for predicting tube ablation wear have significant limitations. Traditional prediction methods often employ a single model for analysis, failing to fully consider the path differences under different degradation modes, resulting in prediction results lacking universality. Furthermore, existing methods have limitations when processing high-dimensional nonlinear degradation data, making it difficult to accurately capture complex degradation evolution patterns.

[0003] Furthermore, existing technologies also face bottlenecks in quantifying prediction uncertainty and optimizing parameters. Most methods lack reliable confidence interval estimation mechanisms, making it impossible to effectively assess the credibility of prediction results. The geometric features and similarity information of degenerate paths are not fully utilized during model parameter optimization, affecting prediction accuracy.

[0004] Existing systems have technical shortcomings in comprehensive load assessment and condition judgment. They lack a unified consideration of multiple factors such as barrel temperature, firing pressure, and propellant charge, making it difficult to accurately reflect the ablation and wear process under actual operating conditions. Solving these problems is of great significance for improving the scientific basis of artillery life prediction and maintenance decisions. Summary of the Invention

[0005] To address the problems in the existing technology, this application provides a method and device for predicting barrel ablation and wear based on degradation path approximation, which can accurately predict and assess the state of barrel ablation and wear, providing a scientific basis for the use and maintenance of artillery.

[0006] To solve at least one of the above problems, this application provides the following technical solution:

[0007] In a first aspect, this application provides a method for predicting tube ablation wear based on degradation path approximation, including:

[0008] The collected data on ablation and wear of the artillery barrel are normalized. Based on the normalized ablation and wear data, a multidimensional degradation path sample space is established. The Sigmoid function is used to map the sample space to a higher-order feature space. Similarity measurement features and path curvature features of the degradation paths are extracted in the higher-order feature space. The degradation paths are clustered into multiple degradation pattern clusters according to the similarity measurement features. A curve fitting algorithm is used to fit the path curvature features of each degradation pattern cluster to obtain approximate expressions of the paths under different degradation patterns.

[0009] The parameters in the path approximation expression are iteratively optimized by an alternating optimization algorithm. An optimization objective function is established based on the least squares criterion. The optimal parameter combination is obtained by solving the optimization objective function using the gradient descent method. The optimal parameter combination is substituted into the path approximation expression to generate a tube ablation and degradation prediction model. The confidence interval of the output result of the tube ablation and degradation prediction model is estimated to construct an ablation and wear prediction interval with prediction uncertainty.

[0010] The real-time firing data of the artillery to be predicted is read, and a comprehensive load index is calculated based on the barrel temperature, firing pressure, and propellant loading amount contained in the firing data. The comprehensive load index is input into the barrel ablation degradation prediction model to obtain the predicted value of barrel ablation wear and its prediction range under different firing numbers. Based on the predicted value, a degradation trend curve of barrel ablation wear is established. The rate of change and acceleration characteristics of barrel ablation wear are calculated based on the degradation trend curve. The ablation wear state of the artillery barrel is judged in combination with the prediction range.

[0011] Furthermore, the collected data on the ablation and wear of the artillery barrel is normalized. Based on the normalized ablation and wear data, a multidimensional degradation path sample space is established. The Sigmoid function is used to map the sample space to a higher-order feature space, and similarity measurement features and path curvature features of the degradation paths are extracted in the higher-order feature space, including:

[0012] Data on ablation and wear depth, barrel pressure, and barrel temperature of the artillery barrel under different firing counts are collected. The ablation and wear depth data are normalized to their maximum and minimum values. A comprehensive load coefficient is calculated by combining the barrel pressure and barrel temperature data. A multidimensional feature vector is constructed by combining the comprehensive load coefficient with the normalized ablation and wear depth data.

[0013] A degenerate path sample space is established based on the multidimensional feature vectors. A high-dimensional feature representation is obtained by nonlinearly mapping the degenerate path sample space using the Sigmoid function. The Mahalanobis distance between degenerate paths is calculated in the high-dimensional feature representation to obtain the similarity measurement feature. The curvature change of the degenerate path is calculated using differential geometry to obtain the path curvature feature.

[0014] Further, the process of clustering the degraded paths into multiple degradation pattern clusters based on similarity measurement features, and then using a curve fitting algorithm to fit the path curvature features of each degradation pattern cluster to obtain approximate path expressions under different degradation patterns, includes:

[0015] Based on the similarity measurement features, a distance matrix of the degradation path is constructed. A hierarchical clustering algorithm is used to perform cluster analysis on the distance matrix. According to the cluster analysis results, the degradation path is divided into multiple degradation pattern clusters. The cluster center of each degradation pattern cluster is calculated. Feature decomposition is performed on the cluster center to obtain the main degradation features.

[0016] The path curvature features in each degradation mode cluster are normalized, and a polynomial fitting algorithm is used to fit the normalized path curvature features. The coefficient matrix of the fitted curve is calculated, and an approximate expression of the degradation path is established based on the coefficient matrix. The approximate expression is combined with the main degradation features to construct a complete path approximation model.

[0017] Further, the step of iteratively optimizing the parameters in the path approximation expression using an alternating optimization algorithm, establishing an optimization objective function based on the least squares criterion, and solving the optimization objective function using the gradient descent method to obtain the optimal parameter combination includes:

[0018] In the path approximation expression, the parameter vector to be optimized is set, and the objective function for parameter optimization is constructed based on the least squares criterion. The objective function includes a path approximation error term and a parameter regularization term. The partial derivative of the objective function with respect to the parameter vector is used to obtain the gradient expression. The parameter update direction and step size are calculated based on the gradient expression.

[0019] An alternating iterative strategy is used to optimize the parameter vector in blocks. In each iteration, some parameters are fixed and others are updated. The objective function value after each parameter update is calculated. The iteration stops when the relative change of the objective function value is less than a preset convergence threshold. The finally converged parameter vector is taken as the optimal parameter combination.

[0020] Further, the step of substituting the optimal parameter combination into the path approximation expression to generate a tube ablation degradation prediction model, estimating the confidence interval of the output of the tube ablation degradation prediction model, and constructing an ablation wear prediction interval with prediction uncertainty includes:

[0021] The optimal parameter combination is substituted into the parameter vector in the path approximation expression, and the path approximation expression is mapped to the prediction space using a kernel function. A nonlinear prediction model is constructed by combining the main degradation characteristics of the degradation path. The parameters of the nonlinear prediction model are calibrated based on the training samples to generate a tube ablation degradation prediction model.

[0022] The probability distribution characteristics of the output results of the tube ablation degradation prediction model are calculated, the variance of the predicted values ​​is estimated using the delta method, the standard error of the prediction results is calculated based on the variance, the confidence coefficient is determined according to the preset confidence level, the confidence coefficient is multiplied by the standard error to obtain the half-width of the prediction interval, and the half-width of the prediction interval is superimposed on the predicted values ​​to construct the ablation wear prediction interval.

[0023] Furthermore, the real-time firing data of the artillery to be predicted is read, and a comprehensive load index is calculated based on the barrel temperature, firing pressure, and propellant charge included in the firing data. This comprehensive load index is then input into the barrel ablation and degradation prediction model to obtain predicted barrel ablation and wear values ​​and their prediction ranges for different firing counts, including:

[0024] The firing data of the artillery to be predicted is obtained, and barrel temperature data, firing pressure data and propellant loading data are extracted from the firing data. The barrel temperature data, firing pressure data and propellant loading data are normalized, and the comprehensive load index is calculated by weighted superposition. The weight coefficients of each index are determined based on historical data.

[0025] The comprehensive load index is input into the barrel ablation and degradation prediction model according to the firing sequence. Based on the prediction model, the ablation wear prediction value corresponding to each firing sequence is calculated. The upper and lower confidence limits of each prediction value are calculated in combination with the pre-constructed prediction interval. The prediction value and its upper and lower confidence limits constitute a complete ablation wear prediction result.

[0026] Further, the step of establishing a degradation trend curve for barrel erosion and wear based on the predicted value, calculating the rate of change and acceleration characteristics of barrel erosion and wear based on the degradation trend curve, and determining the erosion and wear state of the gun barrel in conjunction with the predicted interval includes:

[0027] The predicted values ​​are numerically smoothed, and a continuous degradation trend curve is constructed using a piecewise polynomial interpolation method. The first derivative of the degradation trend curve is used to obtain the rate of change characteristics of ablation wear, and the second derivative is used to obtain the acceleration characteristics of ablation wear. The key feature points of the degradation process are calculated based on the rate of change characteristics and acceleration characteristics.

[0028] Based on the key feature points, the degradation process is divided into multiple stages. The reliability index of each stage is calculated by combining the upper and lower confidence limits of the prediction interval. The ablation and wear state of the gun barrel is quantitatively evaluated according to the preset state evaluation criteria, and the barrel state evaluation result is generated.

[0029] Secondly, this application provides a tube ablation wear prediction device based on degradation path approximation, comprising:

[0030] The path expression construction module is used to normalize the collected data of gun barrel ablation and wear. Based on the normalized ablation and wear data, a multidimensional degradation path sample space is established. The Sigmoid function is used to map the sample space to a higher-order feature space. The similarity measurement features and path curvature features of the degradation paths are extracted in the higher-order feature space. The degradation paths are clustered into multiple degradation pattern clusters according to the similarity measurement features. The path curvature features of each degradation pattern cluster are fitted using a curve fitting algorithm to obtain approximate path expressions under different degradation patterns.

[0031] The wear interval prediction module is used to iteratively optimize the parameters in the path approximation expression using an alternating optimization algorithm, establish an optimization objective function based on the least squares criterion, solve the optimization objective function using the gradient descent method to obtain the optimal parameter combination, substitute the optimal parameter combination into the path approximation expression to generate a tube ablation degradation prediction model, estimate the confidence interval of the output of the tube ablation degradation prediction model, and construct an ablation wear prediction interval with prediction uncertainty.

[0032] The wear state prediction module is used to read the real-time firing data of the artillery to be predicted, calculate the comprehensive load index based on the barrel temperature, firing pressure and propellant loading amount contained in the firing data, input the comprehensive load index into the barrel ablation degradation prediction model, obtain the barrel ablation wear prediction value and its prediction range under different firing numbers, establish the barrel ablation wear degradation trend curve based on the prediction value, calculate the change rate and acceleration characteristics of barrel ablation wear based on the degradation trend curve, and determine the ablation wear state of the artillery barrel in combination with the prediction range.

[0033] Thirdly, 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 steps of the tube ablation wear prediction method based on degradation path approximation.

[0034] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the tube ablation and wear prediction method based on degradation path approximation.

[0035] Fifthly, this application provides a computer program product, including a computer program / instructions, which, when executed by a processor, implement the steps of the tube ablation and wear prediction method based on degradation path approximation.

[0036] As described above, this application provides a method and apparatus for predicting barrel ablation wear based on degradation path approximation. A high-order feature space is established through normalization processing of ablation wear data and Sigmoid function mapping. The system innovatively extracts similarity measurement features and path curvature features of the degradation path, achieving accurate clustering of degradation patterns and path approximation. The system employs an alternating optimization algorithm and gradient descent method to optimize path expression parameters and establish a confidence interval estimation mechanism. A comprehensive load index is constructed by combining barrel temperature, firing pressure, and propellant charge. Through the rate of change and acceleration characteristics of the degradation trend curve, accurate prediction and evaluation of barrel ablation wear status are achieved, providing a scientific basis for artillery use and maintenance. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of this application 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 application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is one of the flowcharts illustrating the tube ablation and wear prediction method based on degradation path approximation in the embodiments of this application;

[0039] Figure 2 This is the second flowchart illustrating the tube ablation and wear prediction method based on degradation path approximation in the embodiments of this application.

[0040] Figure 3 This is the third flowchart illustrating the tube ablation and wear prediction method based on degradation path approximation in the embodiments of this application.

[0041] Figure 4 This is the fourth flowchart illustrating the tube ablation and wear prediction method based on degradation path approximation in the embodiments of this application.

[0042] Figure 5 This is the fifth flowchart illustrating the tube ablation and wear prediction method based on degradation path approximation in the embodiments of this application.

[0043] Figure 6 This is the sixth flowchart illustrating the tube ablation and wear prediction method based on degradation path approximation in the embodiments of this application.

[0044] Figure 7 This is the seventh flowchart illustrating the tube ablation and wear prediction method based on degradation path approximation in the embodiments of this application.

[0045] Figure 8This is a structural diagram of the tube ablation and wear prediction device based on degradation path approximation in the embodiments of this application;

[0046] Figure 9 This is a schematic diagram of the structure of the electronic device in the embodiments of this application.

[0047] Figure label:

[0048] Electronic device 9600, central processing unit 9100, memory 9140, communication module 9110, input unit 9120, audio processor 9130, display 9160, power supply 9170, buffer memory 9141, application / function storage unit 9142, data storage unit 9143, driver storage unit 9144, antenna 9111, speaker 9131, microphone 9132. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0050] The acquisition, storage, use, and processing of data in this application all comply with the relevant provisions of national laws and regulations.

[0051] To address the problems existing in the prior art, this application provides a method and apparatus for predicting barrel ablation wear based on degradation path approximation. A high-order feature space is established by normalizing ablation wear data and mapping it using the Sigmoid function. The system innovatively extracts similarity measurement features and path curvature features of the degradation path, achieving accurate clustering of degradation patterns and path approximation. The system employs an alternating optimization algorithm and gradient descent method to optimize the path expression parameters and establish a confidence interval estimation mechanism. A comprehensive load index is constructed by combining barrel temperature, firing pressure, and propellant charge. Through the rate of change and acceleration characteristics of the degradation trend curve, accurate prediction and assessment of the barrel ablation wear state are achieved, providing a scientific basis for artillery use and maintenance.

[0052] To achieve accurate prediction and assessment of barrel ablation and wear, and to provide a scientific basis for artillery use and maintenance, this application provides an embodiment of a barrel ablation and wear prediction method based on degradation path approximation. See [link to relevant documentation]. Figure 1 The tube ablation wear prediction method based on degradation path approximation specifically includes the following:

[0053] Step S101: Normalize the collected data of gun barrel ablation and wear, establish a multidimensional degradation path sample space based on the normalized ablation and wear data, map the sample space to a higher-order feature space using the Sigmoid function, and extract the similarity measurement features and path curvature features of the degradation paths in the higher-order feature space. Based on the similarity measurement features, cluster the degradation paths into multiple degradation pattern clusters, and use a curve fitting algorithm to fit the path curvature features of each degradation pattern cluster to obtain approximate expressions for paths under different degradation patterns.

[0054] Optionally, this embodiment employs a multi-level normalization strategy in the data preprocessing stage. For the depth data of gun barrel ablation and wear, an adaptive data window is first constructed, with the window size determined by the data fluctuation characteristics. Within each window, robust scaling is used for normalization, eliminating the influence of outliers through the median and interquartile range. For temperature data, considering its periodic variation characteristics, a segmented normalization strategy is adopted, dividing the firing process into three stages: preheating, stabilization, and cooling, which are processed separately. Pressure data normalization uses the Z-score method, combined with exponentially weighted moving average filtering to eliminate instantaneous fluctuations.

[0055] This embodiment implements an innovative dynamic feature fusion mechanism during feature space construction. By constructing a feature vector matrix, each vector contains 15 key parameters: ablation depth, radial strain, axial strain, surface temperature gradient, internal temperature distribution, maximum pressure, pressure rise rate, pressure duration, propellant loading density, and barrel vibration frequency. To improve feature representation capabilities, a dimensionality reduction framework based on principal component analysis is designed. The number of principal components is determined through contribution rate analysis, achieving data dimensionality reduction while retaining key information.

[0056] This embodiment employs an improved Sigmoid mapping function to achieve nonlinear feature transformation. The mapping function adopts an improved hyperbolic tangent form, introducing adjustable shape and scale parameters. Parameter optimization uses a grid search strategy, with optimization objectives including inter-class separation and intra-class clustering. To enhance the adaptability of the mapping, a multi-kernel fusion mechanism is designed, combining radial basis kernel functions and polynomial kernel functions, and achieving effective extraction of features at different scales through weighted combination. L1 / L2 hybrid regularization constraints are introduced during the mapping process to control model complexity.

[0057] This embodiment implements a robust similarity measurement framework in a high-order feature space. The feature extraction uses an improved Mahalanobis distance, and the feature weights are dynamically adjusted through adaptive covariance estimation. To improve the stability of the measurement, a local structure preservation mechanism is designed, using a K-nearest neighbor graph model to describe the topological relationships between samples. In the graph model construction, edge weights are calculated using a Gaussian kernel function, and the kernel width is determined through cross-validation. Temporal constraints are considered during the measurement calculation process, and time window constraints ensure the temporal consistency of similarity evaluation.

[0058] This embodiment innovatively implements a path curvature feature extraction mechanism. Curvature calculation is based on differential geometry theory, using parametric curves to represent degenerate paths. An improved three-point method is employed for curvature calculation, with Richardson extrapolation enhancing computational accuracy. To improve computational stability, an adaptive step-size selection strategy is designed, dynamically adjusting the step size based on the local rate of curvature change. Wavelet multiresolution analysis is introduced during curvature feature extraction, using continuous wavelet transform to identify and extract curvature features at different scales.

[0059] This embodiment employs an improved hierarchical clustering algorithm to achieve degenerate pattern recognition. A distance matrix is ​​constructed based on similarity metrics, and the cluster merging strategy is determined using Ward's minimum variance method. The number of clusters is determined jointly through contour analysis and gap statistics to ensure the reliability of the clustering results. To improve clustering stability, an adaptive merging threshold is designed, and the threshold value is dynamically adjusted based on the inter-cluster distance distribution. Constraints are introduced during the clustering process to ensure that sample points from the same time series belong to the same cluster.

[0060] This embodiment implements a precise curve fitting strategy in the path fitting stage. The fitting algorithm employs an improved B-spline basis function, achieving precise control of the curve shape through control point optimization. Node selection is based on curvature extremum analysis, increasing node density in regions of drastic curvature changes. To improve fitting accuracy, an adaptive weighting mechanism is designed, with weights dynamically adjusted through residual analysis. Monotonicity and smoothness constraints are introduced during the fitting process to ensure the physical rationality of the fitted curve.

[0061] This embodiment innovatively constructs a complete path approximation expression. The expression design is based on an ablation physics model, including an Arrhenius-type exponential term describing the temperature effect, a power function term describing the pressure effect, and an interaction term describing the coupling effect. Coefficients are determined through multi-objective optimization, with optimization objectives including fitting accuracy, model complexity, and satisfaction of physical constraints. The optimization solution employs an improved NSGA-II algorithm, and the optimal solution is determined through Pareto front analysis.

[0062] This embodiment establishes a reliable degradation path modeling framework through systematic data processing and feature extraction. While ensuring modeling accuracy, this scheme improves the model's adaptability through multi-level optimization. The overall design fully considers the characteristics of artillery ablation, achieving end-to-end optimization from data preprocessing to path approximation. Experimental verification shows that this scheme can effectively capture the dynamic characteristics of the ablation process, providing a reliable basis for lifetime prediction.

[0063] The modeling results in this embodiment demonstrate excellent physical consistency and predictive capability, achieving a precise characterization of the ablation degradation process through multi-level analysis. This scheme exhibits powerful analytical capabilities in practical applications, providing a scientific basis for equipment maintenance decisions and enabling accurate assessment and prediction of equipment condition. The model's adaptive characteristics allow it to adapt to the ablation prediction needs under different operating conditions, demonstrating good versatility and scalability.

[0064] Step S102: Iteratively optimize the parameters in the path approximation expression using an alternating optimization algorithm, establish an optimization objective function based on the least squares criterion, solve the optimization objective function using the gradient descent method to obtain the optimal parameter combination, substitute the optimal parameter combination into the path approximation expression to generate a tube ablation degradation prediction model, estimate the confidence interval of the output result of the tube ablation degradation prediction model, and construct an ablation wear prediction interval with prediction uncertainty.

[0065] Optionally, this embodiment implements an innovative alternating iterative strategy in the parameter optimization stage. The parameter vector is divided into three sub-blocks: physical parameter block, shape parameter block, and weight parameter block. The physical parameter block includes temperature sensitivity coefficient, pressure influence factor, and material degradation coefficient; the shape parameter block includes curve fitting coefficient and nonlinear mapping parameter; and the weight parameter block describes the relative importance of each factor. During the optimization process, two parameter blocks are fixed at a time, and the other parameter block is optimized, achieving the global optimum through iterative iteration.

[0066] This embodiment designs a complete framework for constructing the objective function. Based on the least squares criterion, the objective function consists of three parts: a fitting error term, a physical constraint term, and a regularization term. The fitting error uses a weighted Euclidean distance metric, with weights determined by data reliability. The physical constraint term introduces monotonicity and boundary conditions to ensure that the prediction results conform to the physical laws of ablation wear. The regularization term adopts an elastic network form, combining L1 and L2 norms to achieve parameter selection and convergence control.

[0067] This embodiment employs an improved gradient descent algorithm for optimization. To enhance convergence speed and stability, an adaptive learning rate adjustment mechanism is designed, with the learning rate dynamically determined using the Armijo criterion. To avoid local optima, a momentum term and random perturbations are introduced, and simulated annealing is used to fully explore the parameter space. An early stopping strategy is implemented during optimization, and the training process is monitored using validation set performance to prevent overfitting.

[0068] This embodiment implements an innovative parameter update strategy. The update process employs a block coordinate descent method, with the update direction of each parameter block calculated using the proximal operator. To improve update efficiency, a parameter preconditioning mechanism is designed, approximating the Hessian matrix using the Fisher information matrix to accelerate optimization convergence. Adaptive step size control is introduced during parameter update, with the step size dynamically adjusted using Wolfe conditions.

[0069] This embodiment constructs a reliable predictive model generation framework. The optimal parameter combination is determined through cross-validation, and the validation process employs a time-series segmentation strategy to ensure the model's temporal predictive capability. Ensemble learning is introduced during model construction, improving prediction stability through a weighted combination of multiple sub-models. Weight determination is achieved through stacked generalization, effectively reducing prediction variance.

[0070] This embodiment designs a complete confidence interval estimation scheme. The interval estimation is based on the Delta method, approximating the probability distribution of the predicted values ​​through a first-order Taylor expansion. To improve estimation accuracy, a bootstrap resampling strategy is designed, constructing an empirical distribution of the predicted values ​​through multiple resampling operations. The construction of the confidence intervals considers parameter uncertainty and model structure uncertainty, and the interval width is determined through error propagation analysis.

[0071] This embodiment implements an innovative method for constructing prediction intervals. Interval construction is based on quantile regression theory, determining the prediction interval by simultaneously estimating the upper and lower quantiles of the conditional distribution. To improve interval reliability, an adaptive coverage adjustment mechanism is designed, dynamically adjusting the confidence level through historical data validation. Heteroscedasticity is considered during interval construction, and the interval width is dynamically adjusted through local variance estimation.

[0072] This embodiment employs a systematic verification and evaluation strategy. The verification process includes point prediction accuracy evaluation, interval coverage evaluation, and interval width evaluation. Accuracy evaluation uses a multi-index system, including indicators such as RMSE, MAE, and MAPE. Coverage evaluation is achieved by comparing empirical coverage with nominal coverage. Interval width evaluation considers the practicality of the prediction interval and constrains the interval width through engineering limits.

[0073] This embodiment establishes a reliable ablation prediction framework through precise parameter optimization and systematic model construction. While ensuring prediction accuracy, this scheme improves prediction reliability through multi-level optimization. The overall design fully considers the characteristics of artillery ablation, achieving end-to-end optimization from parameter optimization to interval prediction.

[0074] The prediction results of this embodiment demonstrate excellent accuracy and reliability, achieving precise prediction of the ablation process through multi-level analysis. This scheme exhibits strong predictive capabilities in practical applications, providing a reliable quantitative basis for equipment maintenance decisions. The construction of the prediction interval quantifies uncertainty in decision-making, improving the practicality and credibility of the prediction results.

[0075] The optimization strategy and prediction framework in this embodiment have good adaptability and scalability, and can meet the ablation prediction needs under different operating conditions. Through parameter adaptation and interval dynamic adjustment, accurate modeling and reliable prediction of complex ablation processes are achieved, providing a scientific basis for equipment condition assessment.

[0076] Step S103: Read the real-time firing data of the artillery to be predicted, calculate the comprehensive load index based on the barrel temperature, firing pressure and propellant loading amount contained in the firing data, input the comprehensive load index into the barrel ablation degradation prediction model, obtain the predicted value of barrel ablation wear and its prediction range under different firing numbers, establish the degradation trend curve of barrel ablation wear based on the predicted value, calculate the rate of change and acceleration characteristics of barrel ablation wear based on the degradation trend curve, and determine the ablation wear state of the artillery barrel in combination with the prediction range.

[0077] Optionally, this embodiment employs a multi-channel real-time monitoring system to acquire artillery firing data during the data acquisition phase. Temperature monitoring utilizes a distributed thermocouple array, with 12 measuring points arranged along the barrel axis and 3 layers radially, forming a three-dimensional temperature field distribution monitoring network. Each measuring point uses a K-type thermocouple, covering a measurement range of -200℃ to 1200℃, and high-precision temperature acquisition is achieved through signal conditioning circuitry. Pressure data is collected using a piezoelectric pressure sensor installed at the bottom of the barrel, with a sampling frequency set to 100kHz to ensure accurate capture of transient pressure characteristics. Propellant charge is measured using a high-precision weighing device with gram-level accuracy, and environmental temperature and humidity compensation is incorporated to improve measurement reliability.

[0078] This embodiment presents an innovative method for calculating comprehensive load indices. Temperature data processing begins with spatial interpolation, constructing a continuous temperature field distribution using a three-dimensional spline function. Considering the influence of temperature gradients on ablation, radial and axial temperature gradients are calculated and weighted to reflect thermal stress intensity. Pressure data analysis focuses on several key parameters: peak pressure, pressure rise rate, pressure duration, and pressure pulsation characteristics. Wavelet analysis is used to extract the time-frequency features of the pressure signal, evaluating the dynamic characteristics of the pressure load.

[0079] This embodiment achieves dynamic fusion of multi-source information during the construction of load indices. A thermo-mechanical coupling model is established to analyze the interaction between temperature and pressure fields. The model considers the temperature dependence of materials and describes the coupling relationship between load factors through nonlinear mapping. Loading volume data is combined with an internal ballistic model to evaluate its modulating effect on ablation intensity. The final form of the load indices adopts a weighted sum form, with weighting coefficients determined through sensitivity analysis.

[0080] This embodiment innovatively implements a dynamic update mechanism for predicted values. The prediction model adopts a recursive structure and achieves real-time updates of predicted values ​​through a sliding time window. The timeliness of historical data is considered during the prediction process, and the influence of long-term data is reduced through exponential weighting. To improve prediction stability, a predicted value smoothing strategy is designed, eliminating random fluctuations through local polynomial fitting.

[0081] This embodiment employs an improved trend curve construction method. Curve fitting utilizes piecewise spline functions, with the segmentation points determined through curvature analysis. Monotonicity and smoothness constraints are introduced during the fitting process to ensure the physical validity of the trend curve. The uncertainty of the prediction interval is considered during curve construction, and the fitting parameters are dynamically adjusted based on the interval width.

[0082] This embodiment achieves reliable state feature extraction. The rate of change is calculated using an adaptive difference scheme, with the step size dynamically determined by local curvature. Acceleration feature extraction considers noise effects and achieves stable differentiation through Savitzky-Golay filtering. Scale analysis is incorporated into the feature extraction process, identifying change features at different time scales through multi-scale decomposition.

[0083] This embodiment innovatively constructs a state judgment framework. The judgment process is based on a fuzzy inference system, and the input variables include ablation depth, rate of change, and acceleration characteristics. The design of fuzzy rules is based on expert experience and historical data analysis, and the rule parameters are optimized through machine learning methods. The judgment result takes into account the uncertainty of the prediction interval, and the reliability is quantified by a credibility score.

[0084] This embodiment designs a complete prediction interval utilization strategy. Interval analysis first assesses the time-varying characteristics of the interval width, and determines the changing trend of prediction uncertainty through local variance estimation. Interval information is combined with state judgment results, and the reliability of the judgment results is adjusted through Bayesian updates. Engineering limit constraints are considered during interval utilization, and alarm thresholds are determined through risk assessment.

[0085] This embodiment implements a visual representation of the state assessment results. The visualization interface includes multiple views: the trend curve view displays the prediction results and uncertainty range; the feature analysis view displays the time-series changes in the rate of change and acceleration characteristics; and the state assessment view intuitively displays the current state level in a dashboard format. The views are interactive and interconnected, supporting comprehensive analysis of multi-dimensional data.

[0086] This embodiment establishes a reliable condition assessment framework through systematic data analysis and feature extraction. While ensuring assessment accuracy, this scheme improves assessment reliability through multi-level analysis. The overall design fully considers the erosion characteristics of artillery, achieving end-to-end optimization from data acquisition to condition assessment.

[0087] The prediction and evaluation results of this embodiment demonstrate excellent accuracy and reliability, achieving precise assessment of the ablation state through multi-level analysis. This scheme exhibits powerful analytical capabilities in practical applications, providing reliable quantitative basis for equipment maintenance decisions. The visualization of the evaluation results improves analytical efficiency, enabling maintenance personnel to intuitively grasp the equipment status.

[0088] The analytical framework in this embodiment has good adaptability and scalability, and can meet the condition assessment needs under different operating conditions. Through parameter adaptation and judgment rule optimization, it achieves accurate characterization and reliable assessment of complex ablation processes, providing a scientific basis for equipment maintenance and support.

[0089] As described above, the barrel ablation wear prediction method based on degradation path approximation provided in this application can establish a high-order feature space through normalization processing of ablation wear data and Sigmoid function mapping. It innovatively extracts similarity measurement features and path curvature features of degradation paths to achieve accurate clustering of degradation patterns and path approximation. The system uses an alternating optimization algorithm and gradient descent method to optimize path expression parameters and establish a confidence interval estimation mechanism. A comprehensive load index is constructed by combining barrel temperature, firing pressure, and propellant charge. Through the rate of change and acceleration characteristics of the degradation trend curve, accurate prediction and evaluation of barrel ablation wear status are achieved, providing a scientific basis for artillery use and maintenance.

[0090] In one embodiment of the tube ablation wear prediction method based on degradation path approximation in this application, see [link to relevant documentation]. Figure 2It can also specifically include the following:

[0091] Step S201: Collect ablation wear depth data, barrel pressure data, and barrel temperature data of the gun barrel under different firing counts. Perform maximum and minimum value normalization processing on the ablation wear depth data. Calculate the comprehensive load coefficient by combining the barrel pressure data and barrel temperature data. Construct a multi-dimensional feature vector by combining the comprehensive load coefficient with the normalized ablation wear depth data.

[0092] Step S202: Based on the multidimensional feature vector, establish a degenerate path sample space, use the Sigmoid function to perform nonlinear mapping on the degenerate path sample space to obtain a high-dimensional feature expression, calculate the Mahalanobis distance between degenerate paths in the high-dimensional feature expression to obtain a similarity measurement feature, and use differential geometry to calculate the curvature change of the degenerate path to obtain a path curvature feature.

[0093] Optionally, this embodiment employs a multi-dimensional data acquisition strategy to obtain the gun barrel's condition information. The ablation wear depth is measured using a high-resolution endoscope system, with 36 measuring points evenly distributed axially along the inner wall of the barrel. Each measuring point measures eight positions circumferentially, forming a complete three-dimensional description of the ablation morphology. The measurement process utilizes autofocus technology, achieving sub-pixel precision positioning through image processing algorithms. The barrel pressure is acquired using a piezoelectric sensor array, with multiple measuring points arranged at the bottom and middle of the barrel, and a sampling frequency reaching 100kHz to accurately capture pressure fluctuations. The barrel temperature is monitored using a distributed fiber optic sensing system, with optical fibers embedded along the barrel wall for continuous temperature field monitoring.

[0094] This embodiment implements an innovative normalization strategy in the data preprocessing stage. For ablation depth data, outlier detection is first performed, identifying and correcting abnormal measurement points through local statistical characteristics. The normalization process considers the data distribution characteristics, employing a piecewise linear mapping method with different mapping coefficients for different depth intervals to improve the normalization effect. To preserve the physical meaning of the data, the normalization parameters are determined through theoretical limits, ensuring the interpretability of the processed data.

[0095] This embodiment designs a framework for calculating the load factor of the system. Temperature load analysis considers thermal cycling effects, extracting temperature fluctuation characteristics through Fourier transform to assess thermal stress intensity. Pressure load assessment focuses on multiple characteristic quantities: peak pressure, pressure rise rate, pressure duration, and pressure pulsation characteristics. Wavelet analysis is used to achieve time-frequency decomposition of the pressure signal, extracting load characteristics at different scales. The load factor is calculated using a nonlinear combination form, employing a neural network model to achieve coupled analysis of the temperature and pressure fields.

[0096] This embodiment implements an innovative feature vector construction method. The vector design adopts a hierarchical structure, comprising three layers: a basic feature layer describing the original measurement data, a derived feature layer containing various statistical and physical features, and a combined feature layer forming a higher-order representation through feature fusion. Temporal dependencies are considered during feature extraction, and a sliding window strategy is used to capture dynamic features. The Lasso algorithm is employed for feature selection to achieve dimensionality reduction optimization of the feature space.

[0097] This embodiment employs an innovative mapping mechanism during the construction of the path sample space. A modified sigmoid function is used to achieve nonlinear feature transformation, with the function form including adjustable shape and scale parameters. Parameter optimization employs a cross-validation strategy, determining the optimal parameter combination through grid search. To enhance the expressive power of the mapping, a multi-kernel fusion mechanism is designed, combining radial basis function kernels and polynomial kernels to effectively extract features at different scales.

[0098] This embodiment innovatively implements similarity metric feature extraction. Mahalanobis distance calculation employs adaptive covariance estimation, determining the covariance matrix through local data structures. To improve the stability of the metric, a robust estimation strategy is designed, using a weighted method to reduce the impact of outliers. Temporal constraints are considered during feature extraction, ensuring temporal consistency in similarity evaluation through time window constraints.

[0099] This embodiment employs a systematic curvature feature extraction method. Based on differential geometry theory, the degradation path is represented by a parameterized curve. Curvature calculation uses an improved three-point method, incorporating Richardson extrapolation to enhance computational accuracy. To enhance the expressive power of the features, a multi-scale analysis framework is designed, using continuous wavelet transform to identify and extract curvature features at different scales.

[0100] This embodiment implements an innovative feature fusion strategy. The fusion process employs an attention mechanism, dynamically combining different features through adaptive weights. Weight calculation considers the local importance of features, and weight parameters are determined through correlation analysis. The fusion result is then dimensionality-reduced using an autoencoder to extract the most representative feature combinations.

[0101] This embodiment establishes a reliable framework for degenerate feature extraction through systematic feature engineering and data analysis. While ensuring feature expressive power, this scheme improves feature interpretability through multi-level optimization. The overall design fully considers the characteristics of artillery ablation, achieving end-to-end optimization from data acquisition to feature extraction.

[0102] The feature extraction results of this embodiment demonstrate excellent expressive power and discriminative ability, achieving a precise characterization of the ablation process through multi-level analysis. This scheme exhibits strong feature representation capabilities in practical applications, providing a reliable feature foundation for subsequent modeling and analysis. The multi-dimensional representation of features offers a new analytical perspective for the study of degradation mechanisms.

[0103] The feature extraction framework in this embodiment has good adaptability and scalability, and can meet the feature extraction needs under different operating conditions. Through parameter adaptation and feature optimization, it achieves accurate feature representation of complex ablation processes, providing reliable feature support for equipment condition assessment.

[0104] In one embodiment of the tube ablation wear prediction method based on degradation path approximation in this application, see [link to relevant documentation]. Figure 3 It can also specifically include the following:

[0105] Step S301: Construct a distance matrix of the degradation path based on the similarity measurement features, perform cluster analysis on the distance matrix using a hierarchical clustering algorithm, divide the degradation path into multiple degradation pattern clusters according to the cluster analysis results, calculate the cluster center of each degradation pattern cluster, and perform feature decomposition on the cluster center to obtain the main degradation features.

[0106] Step S302: Normalize the path curvature features in each degradation mode cluster, use a polynomial fitting algorithm to fit the normalized path curvature features, calculate the coefficient matrix of the fitted curve, establish an approximate expression for the degradation path based on the coefficient matrix, and combine the approximate expression with the main degradation features to construct a complete path approximation model.

[0107] Optionally, this embodiment employs an innovative distance matrix construction method. Based on similarity measurement features, an adaptive weight calculation strategy is designed, determining the importance weights of sample points through local density estimation. Distance calculation uses an improved Mahalanobis distance formula: D(i,j) = sqrt((xi-xj)^TW (xi-xj)), where W is the weight matrix, determined through iterative optimization. To improve computational efficiency, a sparse representation technique is used, retaining only the key elements of the distance matrix.

[0108] This embodiment implements an optimization strategy for hierarchical clustering. The clustering process adopts the Ward minimum variance criterion, achieving optimal grouping by minimizing the sum of squares within each cluster. To determine the optimal number of clusters, a multi-index evaluation system is designed, combining the silhouette coefficient, CH index, and Gap statistic for comprehensive evaluation. Constraints are introduced during the clustering process to ensure that samples with similar time sequences are more likely to cluster together, improving the physical rationality of the clustering results.

[0109] This embodiment innovatively achieves optimized extraction of cluster centers. A weighted average method is used for center calculation, with weights determined by the distance between the sample and the cluster center. To improve the representativeness of the centers, an anomaly detection mechanism is designed, identifying and processing abnormal samples using Mahalanobis distance. Temporal characteristics are considered during center extraction, and dynamic time warping ensures the temporal consistency of the center trajectories.

[0110] This embodiment designs a feature decomposition method for the system. Singular value decomposition (SVD) is employed, and orthogonal transformations are used to convert cluster centers into principal component space. Feature selection is based on cumulative contribution rate, retaining principal components whose explained variance exceeds a threshold. To enhance the physical interpretability of the features, a variational autoencoder is used to achieve nonlinear feature extraction, capturing complex degradation pattern features.

[0111] This embodiment implements an innovative curvature feature processing scheme. The normalization process employs piecewise linear mapping, determining the mapping parameters through local statistical properties. To preserve the local structure of the features, a conformal mapping strategy is designed, using Laplacian feature mapping to maintain the local relationships between samples. The normalization results are evaluated through cross-validation to ensure the effectiveness of the processed features.

[0112] This embodiment employs an improved polynomial fitting algorithm. The fitting process uses weighted least squares, with weights determined by data reliability. To avoid overfitting, regularization constraints are introduced, and parameter selection and smoothing control are achieved through a combination of L1 and L2 norms. The fitting order is determined using the AIC criterion, striking a balance between fitting accuracy and model complexity.

[0113] This embodiment innovatively constructs a coefficient matrix analysis framework. Matrix analysis employs Tucker decomposition, extracting high-order feature relationships through tensor decomposition. To improve decomposition efficiency, an incremental computation strategy is designed, updating the decomposition results through a recursive method. Spatiotemporal correlations are considered during matrix feature extraction, capturing complex feature patterns through a spatiotemporal convolutional network.

[0114] This embodiment achieves an innovative path approximation expression. The expression is constructed using a hybrid basis function approach, combining polynomial and radial basis functions to achieve flexible modeling. Parameter optimization is achieved through the alternating direction multiplier method, enabling efficient solution of constrained optimization problems. To improve the generalization ability of the expression, an adaptive basis function selection mechanism is designed, determining the optimal combination of basis functions through sparse learning.

[0115] This embodiment employs a systematic model fusion strategy. An attention mechanism is used to dynamically fuse path expressions and degenerate features, with weight coefficients optimized through end-to-end learning. The fusion process considers the multi-scale characteristics of features, achieving effective integration of information at different scales through multi-resolution analysis.

[0116] This embodiment establishes a reliable path approximation framework through systematic feature analysis and model construction. While ensuring model accuracy, this scheme improves model interpretability through multi-level optimization. The overall design fully considers the characteristics of artillery ablation, achieving end-to-end optimization from feature extraction to model construction.

[0117] The analysis results of this embodiment demonstrate excellent modeling performance and predictive capabilities, achieving a precise characterization of the ablation process through multi-level analysis. This approach exhibits strong adaptability in practical applications, providing a reliable analytical tool for equipment condition assessment. The model's interpretability offers a new analytical perspective for the study of degradation mechanisms.

[0118] The analysis framework in this embodiment has good scalability and adaptability, and can meet the modeling needs under different operating conditions. Through parameter adaptation and model optimization, accurate modeling of complex ablation processes is achieved, providing reliable theoretical support for equipment condition assessment.

[0119] In one embodiment of the tube ablation wear prediction method based on degradation path approximation in this application, see [link to relevant documentation]. Figure 4 It can also specifically include the following:

[0120] Step S401: Set the parameter vector to be optimized in the path approximation expression, construct the objective function for parameter optimization based on the least squares criterion, the objective function includes a path approximation error term and a parameter regularization term, take the partial derivative of the objective function with respect to the parameter vector to obtain the gradient expression, and calculate the parameter update direction and step size according to the gradient expression;

[0121] Step S402: The parameter vector is optimized by using an alternating iteration strategy. In each iteration, some parameters are fixed and other parameters are updated. The objective function value after each parameter update is calculated. The iteration stops when the relative change of the objective function value is less than the preset convergence threshold. The finally converged parameter vector is taken as the optimal parameter combination.

[0122] Optionally, this embodiment designs an innovative parameter vector optimization framework. The parameter vector comprises two main categories: path shape parameters and scale parameters. Shape parameters control the geometric features of the path, while scale parameters adjust the weight distribution of these features. Vector initialization is guided by prior knowledge, and reasonable value ranges for the parameters are determined through historical data analysis. To improve optimization efficiency, a hierarchical structure is adopted for the parameter vector design, with different levels of parameters having different update frequencies.

[0123] This embodiment constructs a complete optimization objective function. The path approximation error term adopts a weighted L2 norm form: E = Σwi||yi - f(xi,θ)||², where wi is the sample weight, determined through reliability analysis. The regularization term includes a combination of L1 and L2 norms: R(θ) = λ1||θ||1 + λ2||θ||², achieving dual constraints on parameter sparsity and smoothness. The regularization coefficients are determined through cross-validation, achieving a balance between model complexity and generalization ability.

[0124] This embodiment implements an efficient gradient calculation strategy. The gradient expression is derived using automatic differentiation, avoiding the complexity of manual derivation. To improve computational efficiency, a gradient sparsity scheme is designed, calculating only the gradients of parameters that significantly affect the objective function. Numerical stability is considered during gradient calculation, and gradient pruning is used to avoid the gradient explosion problem.

[0125] This embodiment innovatively implements a parameter update mechanism. The update direction is determined using the momentum method, and historical gradient information is combined to improve the convergence speed. An adaptive strategy is adopted for step size selection, and the Armijo criterion is used to ensure sufficient descent of the objective function. To avoid getting trapped in local optima, a random perturbation mechanism is designed to introduce appropriate randomness into the update process.

[0126] This embodiment employs an improved block optimization strategy. Parameter block partitioning is based on sensitivity analysis, grouping strongly correlated parameters into the same block. Inter-block updates utilize the Gauss-Seidel iterative approach, achieving efficient optimization through coordinate descent. To improve optimization stability, an intra-block preprocessing mechanism is designed, improving the condition number through parameter scale normalization.

[0127] This embodiment implements an innovative iterative control mechanism. Convergence is determined using a multi-criteria strategy, comprehensively evaluating the objective function value, gradient norm, and parameter changes. To improve iteration efficiency, an adaptive learning rate adjustment scheme is designed, dynamically adjusting the update step size based on the objective function curvature information. An early stopping strategy is employed during iteration to avoid overfitting.

[0128] This embodiment designs a parameter evaluation scheme for the system. The evaluation metrics include three dimensions: fitting accuracy, model complexity, and computational efficiency. Accuracy evaluation employs cross-validation, estimating the model's generalization error using leave-one-out method. Complexity evaluation is based on parameter sparsity, measuring the model's simplicity through the number of effective parameters. Efficiency evaluation focuses on computation time and storage requirements to ensure the model's usability.

[0129] This embodiment innovatively constructs a visualization framework for parameter optimization. The optimization process visualization includes the objective function convergence curve, parameter change trajectory, and error distribution plot. The visualization results support interactive exploration, facilitating the analysis of key features in the optimization process. To enhance interpretability, a parameter importance analysis module is designed to identify key parameters through sensitivity analysis.

[0130] This embodiment establishes a reliable model tuning framework through systematic parameter optimization and evaluation. While ensuring optimization effectiveness, this scheme improves optimization efficiency through multi-level analysis. The overall design fully considers the characteristics of artillery ablation, achieving full-process optimization from parameter initialization to optimization.

[0131] The optimization results of this embodiment demonstrate excellent convergence and stability, achieving precise adjustment of model parameters through multi-level analysis. This scheme exhibits powerful optimization capabilities in practical applications, providing a reliable optimization tool for model refinement. The interpretability of the parameters offers a new analytical perspective for model improvement.

[0132] The optimization framework in this embodiment has good adaptability and scalability, and can adapt to the parameter optimization needs under different operating conditions. Through parameter adaptation and optimization strategy improvement, accurate tuning of complex models is achieved, providing reliable model support for equipment condition assessment.

[0133] The optimization scheme in this embodiment demonstrates excellent performance and reliability through theoretical analysis and practical verification. The stability and repeatability of the optimization results provide a solid foundation for model application and are of great significance for improving the accuracy of equipment condition assessment.

[0134] In one embodiment of the tube ablation wear prediction method based on degradation path approximation in this application, see [link to relevant documentation]. Figure 5 It can also specifically include the following:

[0135] Step S501: Substitute the optimal parameter combination into the parameter vector in the path approximation expression, use a kernel function to map the path approximation expression to the prediction space, construct a nonlinear prediction model by combining the main degradation features of the degradation path, calibrate the parameters of the nonlinear prediction model based on the training samples, and generate a tube ablation degradation prediction model.

[0136] Step S502: Calculate the probability distribution characteristics of the output results of the tube ablation degradation prediction model, estimate the variance of the predicted values ​​using the delta method, calculate the standard error of the prediction results based on the variance, determine the confidence coefficient according to the preset confidence level, multiply the confidence coefficient by the standard error to obtain the half-width of the prediction interval, and construct the ablation wear prediction interval by superimposing the half-width of the prediction interval on the predicted values.

[0137] Optionally, this embodiment designs an innovative kernel function mapping scheme. An adaptive strategy is adopted for kernel function selection, combining Gaussian and polynomial kernels to achieve nonlinear transformation of the feature space. Kernel function parameters are optimized through grid search, and the optimal parameter combination is determined through cross-validation. To enhance the expressive power of the mapping, a multi-kernel fusion mechanism is designed, achieving effective extraction of features at different scales through weighted combination.

[0138] This embodiment implements a method for constructing a predictive model for the system. The model structure adopts a deep neural network framework, comprising three modules: feature extraction, nonlinear mapping, and prediction output. The feature extraction layer employs an attention mechanism to adaptively select important features. The nonlinear mapping layer improves gradient propagation through residual connections, thereby enhancing model training efficiency. The prediction output layer uses a probabilistic output format to quantify uncertainty.

[0139] This embodiment innovatively implements a parameter calibration strategy. The calibration process employs a Bayesian optimization method, modeling the relationship between parameters and performance through a Gaussian process. To improve calibration efficiency, an active learning strategy is designed, prioritizing parameter combinations with high uncertainty for evaluation. An early stopping mechanism is introduced during the calibration process to avoid overfitting.

[0140] This embodiment employs an improved model training scheme. The loss function design combines mean squared error and negative log-likelihood to achieve dual optimization of prediction accuracy and uncertainty estimation. Batch normalization is used during training to improve model convergence speed. To enhance model robustness, dropout regularization is introduced to reduce the risk of overfitting.

[0141] This embodiment implements an innovative method for extracting probability distribution features. The distribution features include the mean, variance, and higher-order moments, estimated through Monte Carlo sampling. To improve sampling efficiency, an importance sampling strategy is designed to reduce computational overhead. Temporal correlations are considered during the distribution feature extraction process, and temporal dependencies are captured through conditional probability modeling.

[0142] This embodiment designs a variance estimation framework for the system. The Delta method is implemented based on a first-order Taylor expansion, approximating the variance of the predicted value through gradient information. To improve estimation accuracy, a second-order correction term is introduced to account for the influence of nonlinear effects. Parameter uncertainty is considered during variance estimation, and this uncertainty is propagated through the posterior distribution of the parameters.

[0143] This embodiment innovatively constructs a standard error calculation scheme. The error calculation considers multi-source uncertainties, including model parameter uncertainties, data noise, and prediction errors. Uncertainty propagation employs the error propagation law, using the covariance matrix to describe the correlation between errors from different sources. To improve computational stability, a numerical optimization strategy is designed.

[0144] This embodiment implements a reliable confidence interval construction method. The confidence level is selected based on application requirements, and a reasonable value is determined through risk analysis. The confidence coefficient is calculated using the Student-t distribution, taking into account the influence of degrees of freedom. During the interval construction process, the time-varying characteristics of the predicted values ​​are considered, and the interval width is adjusted through a dynamic update mechanism.

[0145] This embodiment employs a systematic interval evaluation scheme. Evaluation metrics include interval coverage, average interval width, and interval uncertainty. Coverage evaluation is validated using historical data to ensure interval reliability. Width evaluation focuses on the compactness of the interval, avoiding overly conservative estimates. Uncertainty evaluation uses information entropy quantification to analyze the information content of the interval.

[0146] This embodiment establishes a reliable prediction framework through systematic model building and uncertainty analysis. While ensuring prediction accuracy, the scheme provides reliable uncertainty quantification through multi-level analysis. The overall design fully considers the characteristics of artillery ablation, achieving optimization of the entire process from model building to uncertainty assessment.

[0147] The prediction results of this embodiment demonstrate excellent accuracy and reliability, achieving precise prediction of the ablation process through multi-level analysis. This scheme exhibits strong predictive capabilities in practical applications, providing a reliable quantitative basis for equipment maintenance decisions. The quantification of prediction uncertainty provides a scientific foundation for risk assessment.

[0148] The prediction framework in this embodiment has good adaptability and scalability, and can adapt to prediction needs under different operating conditions. Through parameter adaptation and uncertainty propagation, it achieves accurate prediction of complex ablation processes, providing reliable decision support for equipment condition assessment.

[0149] The prediction scheme in this embodiment demonstrates excellent performance and reliability through theoretical analysis and practical verification. The accuracy and interpretability of the prediction results provide a scientific basis for equipment maintenance and support, which is of great significance for improving equipment reliability.

[0150] In one embodiment of the tube ablation wear prediction method based on degradation path approximation in this application, see [link to relevant documentation]. Figure 6 It can also specifically include the following:

[0151] Step S601: Obtain the firing data of the artillery to be predicted, extract barrel temperature data, firing pressure data and propellant loading data from the firing data, normalize the barrel temperature data, firing pressure data and propellant loading data, calculate the comprehensive load index by weighted superposition, and determine the weight coefficient of each index based on historical data.

[0152] Step S602: Input the comprehensive load index into the barrel ablation degradation prediction model according to the firing sequence, calculate the ablation wear prediction value corresponding to each firing sequence based on the prediction model, and calculate the upper and lower confidence limits of each prediction value in combination with the pre-constructed prediction interval. The prediction value and its upper and lower confidence limits constitute a complete ablation wear prediction result.

[0153] Optionally, this embodiment employs a multi-channel data acquisition system to acquire artillery firing data. Barrel temperature is measured using a distributed thermocouple array, with 16 measuring points arranged axially and 4 layers of measuring points radially to achieve precise temperature field monitoring. Each measuring point uses a K-type thermocouple, covering a measurement range from -50℃ to 1100℃. Firing pressure is acquired using piezoelectric sensors installed at the bottom and middle of the barrel, with a sampling frequency set to 200kHz to capture transient pressure characteristics. Propellant charge is measured using a high-precision weighing system, combined with temperature and humidity compensation to improve measurement reliability.

[0154] This embodiment employs an innovative data preprocessing scheme. Temperature data processing begins with spatial interpolation, constructing a continuous temperature field distribution using a three-dimensional spline function. A sliding window method is used to eliminate measurement noise, with the window length determined through signal-to-noise ratio analysis. Normalization utilizes an improved min-max method: T_norm = (T-T_min) / (T_max-T_min), where T is the original temperature value, and T_min and T_max are the minimum and maximum values ​​of the historical data, respectively.

[0155] This embodiment implements a systematic method for processing pressure data. The pressure signal is first denoised using wavelet denoising, and then multi-scale decomposition is performed using the db4 wavelet. Feature extraction focuses on several key parameters: maximum pressure value Pmax, pressure rise rate dP / dt, pressure duration τ, and pressure fluctuation amplitude ΔP. The normalization process considers the physical meaning of the parameters and employs piecewise linear mapping to ensure a reasonable data distribution.

[0156] This embodiment innovatively implements loading volume data processing. Data preprocessing includes outlier detection and temperature compensation, identifying outliers through local statistical characteristics. The compensation model considers the effects of ambient temperature and chamber volume to ensure the consistency of loading volume data. Normalization uses the Z-score method: M_norm = (M-μ) / σ, where M is the loading volume, and μ and σ are the mean and standard deviation of historical data, respectively.

[0157] This embodiment designs a method for constructing the system's load index. The comprehensive load index adopts a weighted sum form: L = w1·T_norm + w2·P_norm + w3·M_norm, where w1 is the weight coefficient. The weights are determined using the analytic hierarchy process (AHP), constructing a judgment matrix through expert scoring and calculating the eigenvectors to obtain the initial weights. Weight optimization is achieved through sensitivity analysis to assess the influence of each factor on the ablation process.

[0158] This embodiment employs an innovative model input construction strategy. The input sequence uses a sliding window approach, with the window length determined through autocorrelation analysis. To capture temporal features, a data augmentation scheme is designed to increase the input dimension through temporal embedding. Data organization considers causal relationships to ensure the physical plausibility of the prediction model.

[0159] This embodiment implements a reliable prediction computation framework. The prediction process adopts a recursive structure, using historical prediction results to guide subsequent predictions. Prediction calculations consider model uncertainties, and ensemble learning methods are used to improve prediction stability. Constraints are introduced during the prediction process to ensure that the prediction results conform to physical laws.

[0160] This embodiment innovatively constructs a prediction interval calculation scheme. The interval calculation is based on error propagation theory, considering the uncertainty of model parameters and the impact of data noise. The upper and lower confidence limits are determined through the normal distribution assumption: CI = Y ± k·σ, where Y is the predicted value, k is the confidence coefficient, and σ is the prediction standard deviation. Interval optimization uses the empirical Bayesian method to dynamically adjust the confidence level.

[0161] This embodiment designs a complete evaluation system for prediction results. The evaluation indicators include two dimensions: point prediction accuracy and interval reliability. Accuracy evaluation adopts a multi-indicator system, including RMSE, MAE, and MAPE. Interval evaluation focuses on coverage and interval width, and verifies interval effectiveness through historical data.

[0162] This embodiment establishes a reliable ablation prediction framework through systematic data processing and predictive analysis. While ensuring prediction accuracy, this scheme provides reliable uncertainty quantification through multi-level analysis. The overall design fully considers the characteristics of artillery ablation, achieving end-to-end optimization from data processing to prediction output.

[0163] The prediction results of this embodiment demonstrate excellent accuracy and reliability, achieving precise prediction of the ablation process through multi-level analysis. This scheme exhibits strong predictive capabilities in practical applications, providing a reliable quantitative basis for equipment maintenance decisions. The quantification of prediction uncertainty provides a scientific foundation for risk assessment.

[0164] The prediction framework in this embodiment has good adaptability and scalability, and can adapt to prediction needs under different operating conditions. Through parameter adaptation and uncertainty propagation, it achieves accurate prediction of complex ablation processes, providing reliable decision support for equipment condition assessment.

[0165] In one embodiment of the tube ablation wear prediction method based on degradation path approximation in this application, see [link to relevant documentation]. Figure 7 It can also specifically include the following:

[0166] Step S701: Perform numerical smoothing on the predicted value, construct a continuous degradation trend curve using piecewise polynomial interpolation, obtain the rate of change characteristic of ablation wear by taking the first derivative of the degradation trend curve, obtain the acceleration characteristic of ablation wear by taking the second derivative, and calculate the key feature points of the degradation process based on the rate of change characteristic and acceleration characteristic.

[0167] Step S702: Based on the key feature points, the degradation process is divided into multiple stages. The reliability index of each stage is calculated by combining the upper and lower confidence limits of the prediction interval. The ablation and wear state of the gun barrel is quantitatively evaluated according to the preset state evaluation criteria, and the barrel state evaluation result is generated.

[0168] Optionally, this embodiment employs an innovative numerical smoothing strategy. The smoothing process uses a local weighted regression method, achieving smooth fitting of local data through a cubic weighting function. The weighting function W(x) = (1-|x / h|³)³, where x is the distance between data points and h is the bandwidth parameter. The bandwidth is optimized using a generalized cross-validation criterion, achieving a balance between smoothness and fidelity. To prevent endpoint effects, mirror extension techniques are used to process boundary data.

[0169] This embodiment implements the system's interpolation modeling scheme. The piecewise polynomial adopts a cubic B-spline form, ensuring the continuity of the first and second derivatives at the nodes. An adaptive strategy is used for node placement, dynamically adjusting the node density based on data variation characteristics. The interpolation function expression is: S(x) = Σai·Bi,k(x), where ai are control point parameters, and Bi,k(x) are k-order B-spline basis functions. Parameter optimization is achieved through the least squares method, considering data reliability weights.

[0170] This embodiment designs an innovative method for calculating derivatives. The first derivative uses an improved central difference scheme: v(t) = [S(t+h)-S(th)] / 2h, where v(t) is the rate of change and h is the step size parameter. The second derivative is calculated using a four-point scheme: a(t) = [S(th)-2S(t)+S(t+h)] / h², where a(t) is the acceleration characteristic. The step size is determined through error analysis, balancing computational accuracy and numerical stability.

[0171] In this embodiment, an innovative feature point recognition strategy is realized. The key feature points include inflection points, extreme points, and acceleration mutation points. Inflection points are determined by the zeros of the second derivative, representing the critical moments of the degradation rate change. Extreme points are identified by the zeros of the first derivative, reflecting the local maximum or minimum of the degradation degree. Mutation points are detected by the acceleration threshold to capture the drastic changes in the degradation process.

[0172] This embodiment adopts a systematic stage division method. The stage boundaries are determined based on the key feature points, and the intervals with similar features are merged through clustering analysis. The stage feature extraction uses multi-dimensional analysis, including the average degradation rate, degradation acceleration, and fluctuation degree. The stage division results are verified by physical meaning to ensure the rationality of the division. <0,

[0173] This embodiment designs a complete reliability evaluation framework. The reliability index R(t) = P[D(t)<Dc], where D(t) is the degradation amount and Dc is the critical threshold. The index calculation considers the uncertainty of the prediction interval, and the reliability is evaluated through probability integration. The influence of the confidence interval is analyzed by the Monte Carlo method to evaluate the impact of uncertainty on reliability.

[0174] This embodiment realizes an innovative state evaluation scheme. The evaluation criteria adopt a multi-level structure, including three dimensions: safety, reliability, and economy. The safety evaluation focuses on the margin between the degradation amount and the critical value, and the safety level is determined through fuzzy reasoning. The reliability evaluation is based on the analysis of the failure probability, considering the randomness of the usage environment. The economic evaluation combines the maintenance cost and the usage benefit to optimize the decision-making suggestions.

[0175] This embodiment innovatively constructs an evaluation result generation framework. The result expression adopts a multi-dimensional form, including quantitative indicators and qualitative descriptions. The quantitative indicators include remaining life prediction, reliability evaluation, and risk level. The qualitative description is based on the expert rule base, and the maintenance suggestions are generated through fuzzy reasoning. The result visualization adopts a multi-level display to support interactive exploration.

[0176] Through systematic analysis and evaluation, this embodiment establishes a reliable state evaluation framework. While ensuring the evaluation accuracy, this scheme provides a comprehensive state description through multi-level analysis. The overall design fully considers the usage characteristics of the artillery, achieving the full-process optimization from data analysis to decision support.

[0177] The evaluation results of this embodiment demonstrate excellent reliability and practicality, and achieve the accurate evaluation of the equipment state through multi-level analysis. This scheme shows strong evaluation capabilities in practical applications, providing a reliable theoretical basis for equipment maintenance decision-making. The multi-dimensional characteristics of the evaluation provide a scientific basis for the optimization of maintenance strategies.

[0178] To achieve accurate prediction and assessment of barrel ablation and wear conditions, and to provide a scientific basis for artillery use and maintenance, this application provides an embodiment of a barrel ablation and wear prediction device based on degradation path approximation, which implements all or part of the aforementioned barrel ablation and wear prediction method. See [link to embodiment]. Figure 8 The tube ablation and wear prediction device based on degradation path approximation specifically includes the following components:

[0179] The path expression construction module 10 is used to normalize the collected data of gun barrel ablation and wear. Based on the normalized ablation and wear data, a multidimensional degradation path sample space is established. The Sigmoid function is used to map the sample space to a higher-order feature space. The similarity measurement features and path curvature features of the degradation paths are extracted in the higher-order feature space. The degradation paths are clustered into multiple degradation pattern clusters according to the similarity measurement features. The path curvature features of each degradation pattern cluster are fitted using a curve fitting algorithm to obtain approximate path expressions under different degradation patterns.

[0180] Wear interval prediction module 20 is used to iteratively optimize the parameters in the path approximation expression through an alternating optimization algorithm, establish an optimization objective function based on the least squares criterion, solve the optimization objective function using the gradient descent method to obtain the optimal parameter combination, substitute the optimal parameter combination into the path approximation expression to generate a tube ablation degradation prediction model, estimate the confidence interval of the output result of the tube ablation degradation prediction model, and construct an ablation wear prediction interval with prediction uncertainty.

[0181] The wear state prediction module 30 is used to read the real-time firing data of the artillery to be predicted, calculate the comprehensive load index based on the barrel temperature, firing pressure and propellant loading amount contained in the firing data, input the comprehensive load index into the barrel ablation degradation prediction model, obtain the barrel ablation wear prediction value and its prediction range under different firing numbers, establish the barrel ablation wear degradation trend curve based on the prediction value, calculate the change rate and acceleration characteristics of barrel ablation wear based on the degradation trend curve, and judge the ablation wear state of the artillery barrel in combination with the prediction range.

[0182] As described above, the barrel ablation and wear prediction device based on degradation path approximation provided in this application can establish a high-order feature space through normalization processing of ablation and wear data and Sigmoid function mapping. It innovatively extracts similarity measurement features and path curvature features of degradation paths to achieve accurate clustering of degradation patterns and path approximation. The system uses an alternating optimization algorithm and gradient descent method to optimize path expression parameters and establish a confidence interval estimation mechanism. By combining barrel temperature, firing pressure, and propellant charge, a comprehensive load index is constructed. Through the rate of change and acceleration characteristics of the degradation trend curve, accurate prediction and evaluation of barrel ablation and wear status are achieved, providing a scientific basis for artillery use and maintenance.

[0183] From a hardware perspective, in order to achieve accurate prediction and assessment of barrel ablation and wear conditions and provide a scientific basis for artillery use and maintenance, this application provides an embodiment of an electronic device for implementing all or part of the aforementioned barrel ablation and wear prediction method based on degradation path approximation. The electronic device specifically includes the following components:

[0184] The system comprises a processor, memory, a communications interface, and a bus; wherein the processor, memory, and communications interface communicate with each other via the bus; the communications interface is used to realize information transmission between the tube ablation and wear prediction device based on degradation path approximation and core business systems, user terminals, and related databases and other related devices; the logic controller can be a desktop computer, tablet computer, or mobile terminal, etc., and this embodiment is not limited to these. In this embodiment, the logic controller can be implemented with reference to the embodiments of the tube ablation and wear prediction method based on degradation path approximation and the embodiments of the tube ablation and wear prediction device based on degradation path approximation in the embodiments, the contents of which are incorporated herein, and repeated details will not be described again.

[0185] It is understood that the user terminal may include smartphones, tablet computers, network set-top boxes, portable computers, desktop computers, personal digital assistants (PDAs), in-vehicle devices, smart wearable devices, etc. Among these, the smart wearable devices may include smart glasses, smartwatches, smart bracelets, etc.

[0186] In practical applications, the tube ablation and wear prediction method based on degradation path approximation can be partially executed on the electronic device side as described above, or all operations can be completed in the client device. The specific choice depends on the processing power of the client device and the limitations of the user's usage scenario. This application does not impose any limitations on this. If all operations are completed in the client device, the client device may further include a processor.

[0187] The aforementioned client device may have a communication module (i.e., a communication unit) that can communicate with a remote server to achieve data transmission with the server. The server may include a server on the task scheduling center side; in other implementation scenarios, it may also include a server on an intermediate platform, such as a server on a third-party server platform that has a communication link with the task scheduling center server. The server may include a single computer device, a server cluster consisting of multiple servers, or a distributed server structure.

[0188] Figure 9 This is a schematic block diagram illustrating the system configuration of the electronic device 9600 according to an embodiment of this application. Figure 9 As shown, the electronic device 9600 may include a central processing unit 9100 and a memory 9140; the memory 9140 is coupled to the central processing unit 9100. It is worth noting that... Figure 9 This is an example; other types of structures can also be used to supplement or replace this structure to achieve telecommunications functions or other functions.

[0189] In one embodiment, the tube ablation wear prediction method based on degradation path approximation can be integrated into the central processing unit 9100. The central processing unit 9100 can be configured to perform the following control:

[0190] Step S101: Normalize the collected data of gun barrel ablation and wear, establish a multidimensional degradation path sample space based on the normalized ablation and wear data, map the sample space to a higher-order feature space using the Sigmoid function, and extract the similarity measurement features and path curvature features of the degradation paths in the higher-order feature space. Based on the similarity measurement features, cluster the degradation paths into multiple degradation pattern clusters, and use a curve fitting algorithm to fit the path curvature features of each degradation pattern cluster to obtain approximate expressions for paths under different degradation patterns.

[0191] Step S102: Iteratively optimize the parameters in the path approximation expression using an alternating optimization algorithm, establish an optimization objective function based on the least squares criterion, solve the optimization objective function using the gradient descent method to obtain the optimal parameter combination, substitute the optimal parameter combination into the path approximation expression to generate a tube ablation degradation prediction model, estimate the confidence interval of the output result of the tube ablation degradation prediction model, and construct an ablation wear prediction interval with prediction uncertainty.

[0192] Step S103: Read the real-time firing data of the artillery to be predicted, calculate the comprehensive load index based on the barrel temperature, firing pressure and propellant loading amount contained in the firing data, input the comprehensive load index into the barrel ablation degradation prediction model, obtain the predicted value of barrel ablation wear and its prediction range under different firing numbers, establish the degradation trend curve of barrel ablation wear based on the predicted value, calculate the rate of change and acceleration characteristics of barrel ablation wear based on the degradation trend curve, and determine the ablation wear state of the artillery barrel in combination with the prediction range.

[0193] As described above, the electronic device provided in this application establishes a high-order feature space by normalizing ablation wear data and mapping it using the Sigmoid function. It innovatively extracts similarity measurement features and path curvature features of degradation paths to achieve accurate clustering of degradation patterns and path approximation. The system employs an alternating optimization algorithm and gradient descent method to optimize path expression parameters and establish a confidence interval estimation mechanism. By combining barrel temperature, firing pressure, and propellant charge, a comprehensive load index is constructed. Through the rate of change and acceleration characteristics of the degradation trend curve, accurate prediction and evaluation of barrel ablation wear state are achieved, providing a scientific basis for artillery use and maintenance.

[0194] In another embodiment, the tube ablation and wear prediction device based on degradation path approximation can be configured separately from the central processing unit 9100. For example, the tube ablation and wear prediction device based on degradation path approximation can be configured as a chip connected to the central processing unit 9100, and the tube ablation and wear prediction method based on degradation path approximation can be implemented through the control of the central processing unit.

[0195] like Figure 9 As shown, the electronic device 9600 may further include: a communication module 9110, an input unit 9120, an audio processor 9130, a display 9160, and a power supply 9170. It is worth noting that the electronic device 9600 does not necessarily need to include these components. Figure 9 All components shown; in addition, the electronic device 9600 may also include Figure 9 For components not shown, please refer to existing technologies.

[0196] like Figure 9 As shown, the central processing unit 9100, sometimes also referred to as a controller or operating control, may include a microprocessor or other processor device and / or logic device, which receives inputs and controls the operation of various components of the electronic device 9600.

[0197] The memory 9140 may be, for example, one or more of a cache, flash memory, hard drive, removable media, volatile memory, non-volatile memory, or other suitable devices. It may store the aforementioned failure-related information, and also store a program for executing that information. The central processing unit 9100 may execute the program stored in the memory 9140 to perform information storage or processing, etc.

[0198] Input unit 9120 provides input to central processing unit 9100. Input unit 9120 may be, for example, a keypad or touch input device. Power supply 9170 provides power to electronic device 9600. Display 9160 displays images and text. Display may be, for example, an LCD display, but is not limited thereto.

[0199] The memory 9140 can be a solid-state memory, such as a read-only memory (ROM), random access memory (RAM), a SIM card, etc. It can also be a memory that retains information even when power is off, can be selectively erased, and contains more data; examples of this type of memory are sometimes referred to as EPROMs. The memory 9140 can also be some other type of device. The memory 9140 includes a buffer memory 9141 (sometimes referred to as a buffer). The memory 9140 may include an application / function storage unit 9142 for storing application programs and function programs or processes for executing the operation of the electronic device 9600 via the central processing unit 9100.

[0200] The memory 9140 may also include a data storage unit 9143 for storing data, such as contacts, digital data, pictures, sounds, and / or any other data used by the electronic device. The driver storage unit 9144 of the memory 9140 may include various drivers for the electronic device for communication functions and / or for performing other functions of the electronic device (such as messaging applications, address book applications, etc.).

[0201] The communication module 9110 is a transmitter / receiver that sends and receives signals via the antenna 9111. The communication module 9110 (transmitter / receiver) is coupled to the central processing unit 9100 to provide input signals and receive output signals, which is the same as in a conventional mobile communication terminal.

[0202] Based on different communication technologies, multiple communication modules 9110 can be configured in the same electronic device, such as cellular network modules, Bluetooth modules, and / or wireless LAN modules. The communication module 9110 (transmitter / receiver) is also coupled to a speaker 9131 and a microphone 9132 via an audio processor 9130 to provide audio output via the speaker 9131 and receive audio input from the microphone 9132, thereby realizing typical telecommunications functions. The audio processor 9130 may include any suitable buffer, decoder, amplifier, etc. Additionally, the audio processor 9130 is coupled to a central processing unit 9100, enabling on-device recording via the microphone 9132 and on-device playback of stored audio via the speaker 9131.

[0203] Embodiments of this application also provide a computer-readable storage medium capable of implementing all steps of the tube ablation and wear prediction method based on degradation path approximation, where the execution subject is a server or client, as described in the above embodiments. The computer-readable storage medium stores a computer program that, when executed by a processor, implements all steps of the tube ablation and wear prediction method based on degradation path approximation, where the execution subject is a server or client, as described in the above embodiments. For example, when the processor executes the computer program, it implements the following steps:

[0204] Step S101: Normalize the collected data of gun barrel ablation and wear, establish a multidimensional degradation path sample space based on the normalized ablation and wear data, map the sample space to a higher-order feature space using the Sigmoid function, and extract the similarity measurement features and path curvature features of the degradation paths in the higher-order feature space. Based on the similarity measurement features, cluster the degradation paths into multiple degradation pattern clusters, and use a curve fitting algorithm to fit the path curvature features of each degradation pattern cluster to obtain approximate expressions for paths under different degradation patterns.

[0205] Step S102: Iteratively optimize the parameters in the path approximation expression using an alternating optimization algorithm, establish an optimization objective function based on the least squares criterion, solve the optimization objective function using the gradient descent method to obtain the optimal parameter combination, substitute the optimal parameter combination into the path approximation expression to generate a tube ablation degradation prediction model, estimate the confidence interval of the output result of the tube ablation degradation prediction model, and construct an ablation wear prediction interval with prediction uncertainty.

[0206] Step S103: Read the real-time firing data of the artillery to be predicted, calculate the comprehensive load index based on the barrel temperature, firing pressure and propellant loading amount contained in the firing data, input the comprehensive load index into the barrel ablation degradation prediction model, obtain the predicted value of barrel ablation wear and its prediction range under different firing numbers, establish the degradation trend curve of barrel ablation wear based on the predicted value, calculate the rate of change and acceleration characteristics of barrel ablation wear based on the degradation trend curve, and determine the ablation wear state of the artillery barrel in combination with the prediction range.

[0207] As described above, the computer-readable storage medium provided in this application establishes a high-order feature space through normalization processing and Sigmoid function mapping of ablation wear data. It innovatively extracts similarity measurement features and path curvature features of degradation paths to achieve accurate clustering of degradation patterns and path approximation. The system employs an alternating optimization algorithm and gradient descent method to optimize path expression parameters and establish a confidence interval estimation mechanism. By combining barrel temperature, firing pressure, and propellant charge, a comprehensive load index is constructed. Through the rate of change and acceleration characteristics of the degradation trend curve, accurate prediction and evaluation of barrel ablation wear state are achieved, providing a scientific basis for artillery use and maintenance.

[0208] Embodiments of this application also provide a computer program product capable of implementing all steps in the tube ablation wear prediction method based on degradation path approximation, where the execution subject is a server or client, as described in the above embodiments. When executed by a processor, this computer program / instruction implements the steps of the tube ablation wear prediction method based on degradation path approximation. For example, the computer program / instruction implements the following steps:

[0209] Step S101: Normalize the collected data of gun barrel ablation and wear, establish a multidimensional degradation path sample space based on the normalized ablation and wear data, map the sample space to a higher-order feature space using the Sigmoid function, and extract the similarity measurement features and path curvature features of the degradation paths in the higher-order feature space. Based on the similarity measurement features, cluster the degradation paths into multiple degradation pattern clusters, and use a curve fitting algorithm to fit the path curvature features of each degradation pattern cluster to obtain approximate expressions for paths under different degradation patterns.

[0210] Step S102: Iteratively optimize the parameters in the path approximation expression using an alternating optimization algorithm, establish an optimization objective function based on the least squares criterion, solve the optimization objective function using the gradient descent method to obtain the optimal parameter combination, substitute the optimal parameter combination into the path approximation expression to generate a tube ablation degradation prediction model, estimate the confidence interval of the output result of the tube ablation degradation prediction model, and construct an ablation wear prediction interval with prediction uncertainty.

[0211] Step S103: Read the real-time firing data of the artillery to be predicted, calculate the comprehensive load index based on the barrel temperature, firing pressure and propellant loading amount contained in the firing data, input the comprehensive load index into the barrel ablation degradation prediction model, obtain the predicted value of barrel ablation wear and its prediction range under different firing numbers, establish the degradation trend curve of barrel ablation wear based on the predicted value, calculate the rate of change and acceleration characteristics of barrel ablation wear based on the degradation trend curve, and determine the ablation wear state of the artillery barrel in combination with the prediction range.

[0212] As described above, the computer program product provided in this application establishes a high-order feature space through normalization processing and Sigmoid function mapping of ablation wear data. It innovatively extracts similarity measurement features and path curvature features of degradation paths, achieving accurate clustering of degradation patterns and path approximation. The system employs an alternating optimization algorithm and gradient descent method to optimize path expression parameters and establish a confidence interval estimation mechanism. By combining barrel temperature, firing pressure, and propellant charge, a comprehensive load index is constructed. Through the rate of change and acceleration characteristics of the degradation trend curve, accurate prediction and evaluation of barrel ablation wear state are achieved, providing a scientific basis for artillery use and maintenance.

[0213] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0214] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (devices), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0215] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0216] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0217] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for barrel erosion wear prediction based on deteriorated path approximation, characterized in that, The method includes: Data on ablation wear depth, bore pressure, and barrel temperature of the artillery barrel were collected under different firing counts. The collected data on ablation wear of the artillery barrel were normalized. For temperature data, a segmented normalization strategy was adopted, dividing the firing process into three stages: preheating, stabilization, and cooling, and processing them separately. A multidimensional degradation path sample space was established based on the normalized ablation wear data. The sample space was mapped to a higher-order feature space through a nonlinear mapping using the Sigmoid function. Similarity measurement features and path curvature features of the degradation paths were extracted in the higher-order feature space. Based on the similarity measurement features, the degradation paths were clustered into multiple degradation pattern clusters. A curve fitting algorithm was used to fit the path curvature features of each degradation pattern cluster to obtain approximate expressions for the paths under different degradation patterns. The parameters in the path approximation expression are iteratively optimized by an alternating optimization algorithm. An optimization objective function is established based on the least squares criterion. The optimal parameter combination is obtained by solving the optimization objective function using the gradient descent method. The optimal parameter combination is substituted into the path approximation expression to generate a tube ablation and degradation prediction model. The confidence interval of the output result of the tube ablation and degradation prediction model is estimated to construct an ablation and wear prediction interval with prediction uncertainty. The real-time firing data of the artillery to be predicted is read, and a comprehensive load index is calculated based on the barrel temperature, firing pressure, and propellant loading amount contained in the firing data. The comprehensive load index is input into the barrel ablation degradation prediction model to obtain the predicted value of barrel ablation wear and its prediction range under different firing numbers. Based on the predicted value, a degradation trend curve of barrel ablation wear is established. The rate of change and acceleration characteristics of barrel ablation wear are calculated based on the degradation trend curve. The ablation wear state of the artillery barrel is judged in combination with the prediction range.

2. The bore erosion wear prediction method based on the deteriorated path approximation according to claim 1, characterized in that, The collected data on the ablation and wear of the artillery barrel are normalized. Based on the normalized ablation and wear data, a multidimensional degradation path sample space is established. The Sigmoid function is used to map the sample space to a higher-order feature space, and similarity measurement features and path curvature features of the degradation paths are extracted in the higher-order feature space, including: Data on ablation and wear depth, barrel pressure, and barrel temperature of the artillery barrel under different firing counts are collected. The ablation and wear depth data are normalized to their maximum and minimum values. A comprehensive load coefficient is calculated by combining the barrel pressure and barrel temperature data. A multidimensional feature vector is constructed by combining the comprehensive load coefficient with the normalized ablation and wear depth data. A degenerate path sample space is established based on the multidimensional feature vectors. A high-dimensional feature representation is obtained by nonlinearly mapping the degenerate path sample space using the Sigmoid function. The Mahalanobis distance between degenerate paths is calculated in the high-dimensional feature representation to obtain the similarity measurement feature. The curvature change of the degenerate path is calculated using differential geometry to obtain the path curvature feature.

3. The bore erosion wear prediction method based on the deteriorating path approximation according to claim 1, characterized in that, The degradation path is clustered into multiple degradation mode clusters according to the similarity measurement feature, a curve fitting algorithm is used to fit the path curvature feature of each degradation mode cluster, and a path approximate expression under different degradation modes is obtained, including: A distance matrix of the degradation path is constructed based on the similarity measurement feature, a hierarchical clustering algorithm is used for clustering analysis of the distance matrix, and the degradation path is divided into multiple degradation mode clusters according to the clustering analysis result, and the cluster center of each degradation mode cluster is calculated, and the main degradation feature is obtained by feature decomposition of the cluster center. The path curvature feature in each degradation mode cluster is normalized, a polynomial fitting algorithm is used to fit the normalized path curvature feature, the coefficient matrix of the fitting curve is calculated, and an approximate expression of the degradation path is established based on the coefficient matrix. The approximate expression is combined with the main degradation feature to construct a complete path approximation model.

4. The bore erosion wear prediction method based on the deteriorating path approximation according to claim 1, characterized in that, The parameters in the path approximate expression are iteratively optimized by an alternating optimization algorithm, an optimization objective function is established based on the least squares criterion, and the optimal parameter combination is obtained by solving the optimization objective function using the gradient descent method, including: The parameter vector to be optimized is set in the path approximate expression, and an objective function for parameter optimization is constructed based on the least squares criterion. The objective function includes a path approximation error term and a parameter regularization term. The gradient expression is obtained by taking the partial derivative of the objective function with respect to the parameter vector. The parameter update direction and step size are calculated according to the gradient expression; The parameter vector is optimized in blocks using an alternating iteration strategy. In each iteration, part of the parameters are fixed and the other parameters are updated. The objective function value after each parameter update is calculated. When the relative change of the objective function value is less than a preset convergence threshold, the iteration is stopped. The final converged parameter vector is used as the optimal parameter combination.

5. The bore erosion wear prediction method based on the deteriorating path approximation according to claim 1, characterized in that, The optimal parameter combination is substituted into the path approximate expression to generate a barrel ablation degradation prediction model. The output result of the barrel ablation degradation prediction model is confidence interval estimation, and an ablation wear prediction interval with prediction uncertainty is constructed, including: The optimal parameter combination is substituted into the parameter vector in the path approximate expression. The path approximate expression is mapped to the prediction space using a kernel function. A nonlinear prediction model is constructed by combining the main degradation features of the degradation path. The nonlinear prediction model is parameter calibrated based on the training samples to generate a barrel ablation degradation prediction model. The probability distribution characteristics of the output result of the barrel ablation degradation prediction model are calculated. The variance of the prediction value is estimated using the delta method. The standard error of the prediction result is calculated based on the variance. The confidence coefficient is determined according to the preset confidence level. The confidence coefficient is multiplied by the standard error to obtain the half-width of the prediction interval. The ablation wear prediction interval is constructed by adding the half-width of the prediction interval to the prediction value.

6. The bore erosion wear prediction method based on the deteriorating path approximation of claim 1, wherein, The real-time firing data of the artillery to be predicted is read, a comprehensive load index is calculated according to a barrel temperature, a firing pressure and a propellant charge amount contained in the firing data, the comprehensive load index is input into the barrel ablation degradation prediction model, and barrel ablation wear prediction values and prediction intervals at different firing rounds are obtained, including: The firing data of the artillery to be predicted is acquired, barrel temperature data, firing pressure data and propellant charge amount data are extracted from the firing data, the barrel temperature data, the firing pressure data and the propellant charge amount data are normalized, a comprehensive load index is calculated in a weighted superposition manner, and the weight coefficients of each index are determined according to historical data; The comprehensive load index is input into the barrel ablation degradation prediction model according to a firing round sequence, the ablation wear prediction value corresponding to each firing round is calculated based on the prediction model, the confidence upper limit and the confidence lower limit of each prediction value are calculated in combination with a prediction interval constructed in advance, and the prediction value and the confidence upper and lower limits thereof constitute a complete ablation wear prediction result.

7. The tube ablation wear prediction method based on degradation path approximation according to claim 1, characterized in that, A degradation trend curve of barrel ablation wear is established based on the prediction value, a change rate and an acceleration feature of barrel ablation wear are calculated according to the degradation trend curve, and the ablation wear state of the artillery barrel is judged in combination with the prediction interval, including: The prediction value is subjected to numerical smoothing processing, a continuous degradation trend curve is constructed by using a piecewise polynomial interpolation method, a change rate feature of ablation wear is obtained by taking the first derivative of the degradation trend curve, an acceleration feature of ablation wear is obtained by taking the second derivative of the degradation trend curve, and key feature points of the degradation process are calculated according to the change rate feature and the acceleration feature; The degradation process is divided into multiple stages based on the key feature points, a reliability index of each stage is calculated in combination with the confidence upper limit and the confidence lower limit of the prediction interval, the ablation wear state of the artillery barrel is quantitatively evaluated according to a preset state evaluation criterion, and a barrel state evaluation result is generated.

8. A barrel erosion wear prediction device based on a deteriorating path approximation, characterized by, The device comprises: A path expression construction module is configured to perform normalization processing on collected data of artillery barrel ablation wear, establish a multi-dimensional degradation path sample space based on the normalized ablation wear data, map the sample space to a high-order feature space by using a Sigmoid function, extract similarity measurement features and path curvature features of the degradation path in the high-order feature space, cluster the degradation path into multiple degradation mode clusters according to the similarity measurement features, and fit the path curvature features of each degradation mode cluster by using a curve fitting algorithm to obtain path approximate expressions under different degradation modes. A wear interval prediction module is configured to perform iterative optimization on parameters in the path approximate expressions by using an alternating optimization algorithm, establish an optimization objective function based on a least square criterion, solve the optimization objective function by using a gradient descent method to obtain an optimal parameter combination, substitute the optimal parameter combination into the path approximate expressions to generate a barrel ablation degradation prediction model, perform confidence interval estimation on an output result of the barrel ablation degradation prediction model, and construct an ablation wear prediction interval of prediction uncertainty. The wear state prediction module is configured to read real-time firing data of the artillery to be predicted, calculate a comprehensive load index according to a barrel temperature, a firing pressure and a propellant charge amount contained in the firing data, input the comprehensive load index into the barrel ablation degradation prediction model to obtain a barrel ablation wear prediction value and a prediction interval thereof at different firing numbers, establish a degradation trend curve of barrel ablation wear based on the prediction value, calculate a change rate and an acceleration characteristic of the barrel ablation wear according to the degradation trend curve, and determine a barrel ablation wear state of the artillery in combination with the prediction interval.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the steps of the barrel ablation wear prediction method based on the degradation path approximation according to any one of claims 1 to 7 when executing the program.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program implements the steps of the barrel ablation wear prediction method based on the degradation path approximation according to any one of claims 1 to 7 when executed by the processor.

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