Product design parameter determination method based on reliability quantitative analysis and related equipment

Abstract

The invention provides a product design parameter determination method based on reliability quantitative analysis and related equipment, and relates to the technical field of product design and manufacturing, and the method comprises the steps: obtaining physical fault mode data associated with each node in a product structure tree of a target product; constructing a performance function model comprising a plurality of random variables in each different physical fault mode; substituting a preset target reliability index and the to-be-solved design variable into the corresponding performance function model for reverse solving to obtain candidate design parameters; substituting the candidate design parameters into the performance function model, and performing forward checking calculation by adopting a preset numerical value reliability algorithm to obtain a checking calculation reliability index; and determining the candidate design parameters of which the checking reliability indexes meet the target reliability indexes as target design parameters. By implementing the method, the efficiency and accuracy of design parameter determination can be improved.

Description

Technical Field

[0001] This application relates to the field of product design and manufacturing technology, and in particular to a method and related equipment for determining product design parameters based on quantitative reliability analysis. Background Technology

[0002] In today's globalized market competition, product reliability has become a key indicator of core competitiveness. Whether in aerospace, automotive manufacturing, or high-end electronic equipment, users are placing unprecedented demands on the stability and durability of products throughout their entire lifecycle. To stand out in the fierce market competition, companies not only need to ensure product functionality but also need to proactively consider reliability during the design phase. They must strive to prevent potential failure risks through scientific design methods, thereby reducing costly repairs, recall losses, and damage to brand reputation later on. Therefore, how to conduct quantitative reliability analysis and optimization of various design parameters in the early stages of product design to ensure that the final product meets the preset reliability targets has become a core issue of widespread concern in modern manufacturing.

[0003] In related technologies, reliability analysis methods based on forward simulation are commonly used to assist product design. Designers first establish a physical or mathematical model of the product based on its structure and working principle. Then, drawing on engineering experience or industry standards, they preset a set of initial design parameters, such as component dimensions, material strength properties, and workload range. After determining these initial parameters, numerical calculation methods such as Monte Carlo simulation and finite element analysis are used to perform extensive simulations of the product's performance under various random factors. Finally, the reliability index of the product under the current combination of design parameters is statistically calculated. Designers compare the reliability obtained from the simulation with the preset reliability target to determine whether the current design meets the requirements.

[0004] However, the relevant technologies rely on forward simulation and iterative trial-and-error methods for determining design parameters. When faced with increasingly complex product structures and multiple design variables, the initial selection and subsequent adjustments of design parameters depend heavily on the designer's experience, lacking clear quantitative guidance and exhibiting significant uncertainty. When simulation results fail to meet target reliability, designers struggle to determine which parameter to adjust and by how much to most effectively improve reliability. This leads to repeated cycles of "adjusting parameters - running simulation - verifying results," each potentially involving enormous computational loads, especially with complex models and numerous variables, where a single simulation can take hours or even days. This inefficient iterative process not only significantly extends the product development cycle and increases costs, but also, due to time and resource constraints, design teams often stop optimizing after finding an "acceptable" solution, meaning the final combination of design parameters may not be the optimal solution. Summary of the Invention

[0005] This application provides a method and related equipment for determining product design parameters based on quantitative reliability analysis, which addresses the problem that the determination of product design parameters in related technologies relies on iterative trial and error through forward simulation, resulting in low efficiency in the parameter optimization process.

[0006] In a first aspect, this application provides a method for determining product design parameters based on quantitative reliability analysis, applied to a product design parameter quantitative analysis system, the method comprising: Obtain product structure tree data of the target product and physical failure mode data associated with each node in the product structure tree data. The product structure tree data includes digital data of the components of the target product and the physical hierarchical relationships between the components. The failure mode data is data on the predictable failure modes of the target product under specific physical stress. Based on the physical failure mode data, a functional function model including multiple random variables is constructed for each different physical failure mode. The functional function model is an expression used to describe the mathematical relationship between product strength and stress. The random variables include the design dimensions, material properties and load conditions of the target product. The preset target reliability index and the design variable to be solved are substituted into the function model corresponding to the design variable to be solved for inverse solution to obtain candidate design parameters. The design variable to be solved is a combination of one or more variables among the random variables. The candidate design parameters are substituted into the function model, and a preset numerical reliability algorithm is used for positive verification to obtain the verification reliability index. Candidate design parameters that satisfy the target reliability index are determined as target design parameters.

[0007] By adopting the above technical solution, the system acquires product structure tree data and associated physical failure mode data. For each failure mode, a functional function model is constructed, incorporating random variables such as design dimensions, material properties, and load conditions, thus realizing a mathematical expression of the relationship between product strength and stress. A reverse-engineering strategy is employed, directly substituting the target reliability index into the functional function model to calculate candidate design parameters, rather than the traditional forward trial-and-error iteration. This is combined with forward verification to validate the reliability of the candidate parameters, ensuring improved accuracy. This two-way mechanism of "reverse-engineering-forward verification" fundamentally changes the traditional parameter determination model that relies on experience and repeated iterations. It transforms the original process of blindly trying and failing dozens or even hundreds of times into a goal-oriented, precise solution process, improving the efficiency and accuracy of design parameter determination.

[0008] In some embodiments, the step of constructing a functional model including multiple random variables under each different physical fault mode based on the physical fault mode data specifically includes: When the physical failure mode is a time-dependent degradation failure mode, a time-dependent function model containing time variables is constructed. Obtain the target task time used to specify the reliability assessment time in the time-dependent function model; Substitute the target task time into the time-dependent function model to generate the function model.

[0009] By employing the aforementioned technical solutions, the system identifies time-related degradation failure modes in products, such as material fatigue, corrosion, and wear—failures that accumulate over time. The system constructs a time-dependent function model, incorporating time variables into the reliability analysis framework to accurately describe the degradation patterns of product performance over time. By introducing target task time parameters, the system can assess the product's reliability status at specific service moments, transforming the time-varying degradation process into a static reliability problem at a specific moment. This precise time-dimensional modeling enables the system not only to analyze the reliability of the product in its initial state but also to predict its reliability level at any point throughout its entire lifecycle, ensuring that design parameters still meet long-term service requirements even after considering time-related degradation factors.

[0010] In some embodiments, after the step of substituting the candidate design parameters into the function model and performing a forward verification using a preset numerical reliability algorithm to obtain the verification reliability index, the method further includes: Substituting the target task time and the verification reliability index into the preset exponential distribution conversion formula, the mean time between failures (MTBF) is calculated. When the verified reliability index meets the target reliability index and the mean time between failures (MTBF) meets the preset target MTBF, the candidate design parameter is determined as the target design parameter.

[0011] By adopting the above technical solution, after obtaining the reliability index, the system further uses the exponential distribution conversion formula to convert the reliability index into the more intuitive Mean Time Between Failures (MTBF) index in engineering practice. The system establishes a dual evaluation system of reliability and MTBF, requiring not only that candidate design parameters meet instantaneous reliability requirements but also that they meet long-term MTBF targets. This dual-index constraint mechanism ensures that the product possesses both high instantaneous reliability and good long-term stability. Simultaneously, by converting the probabilistic reliability index into the time-scale MTBF index, designers can more intuitively understand the product's expected lifespan and maintenance cycle.

[0012] In some embodiments, the step of substituting the preset target reliability index and the design variable to be solved into the function model corresponding to the design variable to be solved for inverse solution to obtain candidate design parameters specifically includes: generating training sample points in the design space of the design variable to be solved using a preset experimental design method, and calling the function model to calculate the performance response value corresponding to each training sample point to obtain a training sample set, wherein the training sample set includes a data set of multiple sets of design variable values ​​and corresponding performance response values; The preset machine learning model is trained based on the training sample set to obtain a proxy model that represents the mapping relationship between the design variable to be solved and the reliability index. Using the target reliability index as the optimization objective, a preset intelligent optimization algorithm is used to perform optimization calculations on the surrogate model to solve for the variable combination that satisfies the target reliability index, and this combination is determined as the candidate design parameters.

[0013] By adopting the above technical solutions, the system scientifically arranges training sample points within the design space using a design-of-experiments approach, ensuring the representativeness and coverage of the samples. The system obtains the training sample set through function model calculations and establishes a mapping database between design variables and performance responses. Machine learning techniques are used to train a surrogate model, transforming the complex physical model into an efficient mathematical mapping relationship, reducing computational complexity. The system employs an intelligent optimization algorithm to quickly find the optimal solution on the surrogate model, avoiding repeated calls to the original complex model. This three-stage strategy of "design of experiments - surrogate modeling - intelligent optimization" transforms the optimization process, which originally required thousands of complex simulations, into a highly efficient process of calculating a small number of samples plus rapid surrogate optimization, significantly improving computational efficiency while ensuring solution accuracy.

[0014] In some embodiments, after the step of substituting the candidate design parameters into the function model and performing a forward verification using a preset numerical reliability algorithm to obtain the verification reliability index, the method further includes: Identify target component nodes in the product structure tree data that contain multiple physical failure modes; Obtain the verification reliability index corresponding to each physical failure mode in the target component node to obtain a set of reliability indices; perform a product operation on all verification reliability indices in the set of reliability indices to obtain the comprehensive reliability index of the target component node.

[0015] By adopting the above technical solution, the system automatically identifies key component nodes in the product structure tree that exhibit multiple failure modes, achieving intelligent identification of complex failure scenarios. The system acquires reliability indices for all failure modes of this node, forming a complete reliability evaluation set. By performing a product operation on all reliability indices, the overall reliability of the component is calculated based on the reliability theory of series systems. This multi-failure mode comprehensive analysis method overcomes the limitations of traditional methods that only consider a single dominant failure mode, comprehensively evaluating the true reliability level of components under the combined effects of multiple failure mechanisms. The system achieves system integration from local failure modes to overall reliability, ensuring that the design parameters of key components simultaneously meet the reliability requirements of all potential failure modes, avoiding design defects caused by neglecting secondary failure modes.

[0016] In some embodiments, the step of performing a product operation on all verified reliability indices in the reliability index set to obtain a comprehensive reliability index for the target component node specifically includes: Based on the correlation strength between each reliability index in the reliability index set, a correlation coefficient matrix is ​​generated, wherein the correlation strength is determined by engineering mechanism analysis or statistical quantification of historical data. Based on the correlation coefficient matrix, a connection function model is constructed to describe the joint probability distribution among multiple verification reliability indicators in the reliability index set; The reliability index set is substituted into the connection function model for calculation to obtain the comprehensive reliability index of the target component node.

[0017] By employing the above technical solutions, the system constructs a correlation coefficient matrix based on engineering mechanism analysis or historical data, accurately quantifying the correlation strength between different failure modes. The system uses a connection function model to describe the joint probability distribution of multiple reliability indices, overcoming the limitations of traditional independence assumptions. By considering the correlations between failure modes, such as complex coupling relationships like common-cause failure and cascading failure, the system can more accurately assess the true comprehensive reliability of components. This comprehensive reliability calculation method based on correlation analysis avoids overly conservative or overly optimistic evaluation results that may result from simple multiplication operations, providing reliability quantification indicators that better reflect actual engineering conditions. This makes the determination of design parameters more scientific and reasonable, improving the accuracy of reliability assessment for complex systems.

[0018] In some embodiments, after the step of substituting the candidate design parameters into the function model and performing a forward verification using a preset numerical reliability algorithm to obtain the verification reliability index, the method further includes: When the verified reliability index does not meet the target reliability index, a new target reliability index is generated based on a preset adjustment strategy; The new target reliability index and the design variables to be solved are substituted back into the function model for inverse solution to obtain new candidate design parameters; The new candidate design parameters that satisfy the target reliability index are determined as the target design parameters.

[0019] By adopting the above technical solution, when the initial reliability calculation fails to meet the requirements, the system automatically initiates a parameter adjustment mechanism, intelligently generating a new target reliability index based on a preset strategy. The system then re-substitutes the adjusted target into the function model for iterative solving, forming an adaptive parameter optimization closed loop. This iterative optimization strategy searches for feasible solutions in the design space by gradually adjusting the target reliability, avoiding situations where no solution is found due to excessively high initial target settings. The system achieves an automatic optimization process from ideal target to feasible solution, ensuring that design parameters that meet the requirements are found while also identifying the reliability limits under current design constraints. This provides comprehensive reference information for design decisions and improves the success rate and practicality of determining design parameters under complex constraints.

[0020] Secondly, this application provides a quantitative analysis system for product design parameters, the system comprising: one or more processors and a memory; The memory is coupled to the one or more processors. The memory is used to store computer program code, which includes computer instructions. The one or more processors call the computer instructions so that the system can implement the product design parameter determination method based on quantitative reliability analysis provided in the above embodiments, which will not be described in detail here.

[0021] Thirdly, this application provides a computer-readable storage medium including instructions that, when executed on a product design parameter quantitative analysis system, enable the system to implement a product design parameter determination method based on reliability quantitative analysis provided in the above embodiments, which will not be elaborated further here.

[0022] Fourthly, this application provides a computer program product that, when running on a product design parameter quantitative analysis system, enables the system to implement a product design parameter determination method based on reliability quantitative analysis provided in the above embodiments, which will not be elaborated here.

[0023] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages: 1. The system directly substitutes the preset target reliability index as known conditions into the functional function model, and calculates the required combination of design parameters through mathematical inverse solving. Then, it verifies the results through forward verification to ensure accuracy. This two-way mechanism of "inverse solving-forward verification," combined with machine learning-based surrogate models and intelligent optimization algorithms, transforms the traditional iterative process requiring dozens or even hundreds of blind trial-and-error iterations into a goal-oriented, precise solution process. When the initial solution fails to meet the requirements, the system can automatically adjust the target and iteratively optimize, forming an adaptive parameter determination closed loop. This method fundamentally solves the core pain points of traditional methods—reliance on experience and low efficiency—significantly improving the efficiency of product design parameter determination.

[0024] 2. In the time dimension, the system constructs a time-dependent function model for degradation-type failures, accurately describing the law of product performance degradation over time and enabling reliability assessment at any service point. In the spatial dimension, the system achieves reliability transfer analysis from components to the whole based on the hierarchical relationship of the product structure tree. In the mode dimension, the system not only considers single failure modes but also accurately describes the coupling effect of multiple failure modes through correlation coefficient matrices and connection function models. The system also establishes a dual-index evaluation system of reliability and mean time between failures (MTBF), realizing an effective conversion from probability statistics to engineering applications. This multi-dimensional, multi-index systematic modeling method ensures the reliability performance of design parameters under various complex operating conditions.

[0025] 3. The system first employs a scientific experimental design method to rationally arrange sample points within the design space, ensuring the maximum information is obtained with minimal computational resources. Then, it uses machine learning technology to train a surrogate model, transforming the complex physical simulation model into an efficient mathematical mapping relationship. Finally, an intelligent optimization algorithm is used to quickly find the optimal solution on the surrogate model, avoiding repeated calls to the original complex model. For critical components with multiple failure modes, the system can automatically identify and comprehensively analyze all failure modes, providing a more accurate comprehensive reliability assessment by considering the correlation between failure modes. This intelligent architecture transforms the optimization process, which originally required thousands of complex simulations, into a highly efficient process of a small number of sample calculations plus rapid surrogate optimization, greatly improving computational efficiency while ensuring solution accuracy. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating a method for determining product design parameters based on quantitative reliability analysis in an embodiment of this application. Figure 2 This is another flowchart illustrating a method for determining product design parameters based on quantitative reliability analysis in an embodiment of this application; Figure 3 This is a schematic diagram of the physical device structure of a product design parameter quantitative analysis system in the embodiments of this application. Detailed Implementation

[0027] The terminology used in the following embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application. As used in the specification and appended claims of this application, the singular expressions “a,” “an,” “the,” “the,” “the,” and “this” are intended to include the plural expressions as well, unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in this application refers to any or all possible combinations including one or more of the listed items.

[0028] Hereinafter, the terms "first" and "second" are used for descriptive purposes only and should not be construed as implying or suggesting relative importance or implicitly indicating the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature, and in the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more.

[0029] For ease of understanding, the method provided in this implementation is described in process below. Please refer to [link / reference]. Figure 1 This is a flowchart illustrating a method for determining product design parameters based on quantitative reliability analysis in an embodiment of this application.

[0030] S101. Obtain the product structure tree data of the target product and the physical fault mode data associated with each node in the product structure tree data.

[0031] The target product refers to a specific product that requires quantitative reliability analysis and design parameter determination, such as mechanical equipment, electronic products, or aerospace equipment. The product structure tree data represents the hierarchical decomposition structure of the target product from the whole to its components, including information such as product name, component number, hierarchical relationship, material properties, and geometric dimensions. The nodes in the product structure tree represent the various levels of the product's constituent units, such as system-level nodes, subsystem-level nodes, and component-level nodes. The physical failure mode data refers to the failure modes that a product or component may experience under specific operating conditions, such as fatigue fracture, corrosion failure, wear degradation, and short circuits in electronic components. The correlation indicates that there is a clear correspondence between the failure mode of each node and the position of that node in the product structure tree.

[0032] Specifically, the product design parameter quantitative analysis system first synchronously obtains the complete structure tree data of the target product from the enterprise's product data management system or hardware BOM system via a data interface. This data is organized in a tree topology, clearly defining the parent-child relationships and assembly relationships of each level of the product's components. The system then extracts failure mode information corresponding to each node from the hardware FMECA (Failure Mode, Effects, and Criticality Analysis) module or failure database. This failure mode data includes attributes such as the physical mechanism of the failure, its probability of occurrence, severity, and detection difficulty. The system uses node identifiers to associate and map the product structure tree data with the failure mode data, establishing a complete correspondence between the product structure and potential failures.

[0033] In some embodiments, product structure tree data and failure mode data can be acquired in multiple ways: Optionally, the system establishes a connection with the enterprise PDM system through a standardized data interface protocol (such as OPC UA or REST API); the system sends a data synchronization request, specifying the product model and version information to be acquired; the PDM system returns product structure tree data in XML or JSON format; the system parses the data format and constructs a tree-like data structure in memory; the system then sends a query request to the FMECA database to obtain the failure mode list for each node; the system establishes a mapping table between node IDs and failure modes to complete the data association. Optionally, the system provides a graphical BOM import interface, allowing users to upload local BOM files; the system parses the BOM file format (such as Excel, CSV, etc.) and extracts product structure information; the system automatically generates a visual display of the product structure tree; users select the nodes to be analyzed through the interface; the system matches the corresponding failure type from the built-in failure mode library based on the selected node; the system allows users to manually supplement or correct failure mode information. It is understood that other methods can also be used to acquire and associate product structure and failure mode data, which are not limited here.

[0034] S102. Based on physical fault mode data, construct a functional model including multiple random variables for each different physical fault mode.

[0035] Among them, the function model represents the mathematical relationship between the performance state of a product or component and various influencing factors, usually expressed as a function relationship between strength and stress; random variables refer to parameters with uncertainty in the function, whose values ​​follow a specific probability distribution; design dimensions are used to represent the geometric parameters of the product, such as length, width, thickness, diameter, etc.; material properties refer to the physical and mechanical performance parameters of the material, such as elastic modulus, yield strength, fatigue limit, etc.; load conditions represent the external forces, temperature, pressure and other environmental factors that the product is subjected to during operation.

[0036] Specifically, for each identified physical failure mode, the system establishes a corresponding functional model based on its failure mechanism. The system first analyzes the physical nature of the failure mode to identify the key influencing factors leading to the failure. These factors include structural design parameters, material performance parameters, and operating environment parameters. The system defines these influencing factors as random variables in the functional function and determines the probability distribution type and distribution parameters of each variable based on engineering experience or historical data. For different failure modes, the system constructs different forms of functional functions; for example, it uses a stress-strength interference model for strength failure, a fatigue cumulative damage model for fatigue failure, and a corrosion rate model for corrosion failure. The system allows users to define custom functional function expressions through a function editor, supporting basic mathematical operations, trigonometric functions, logarithmic functions, etc., and can automatically identify the variable types in the expressions.

[0037] In some embodiments, the construction of functional function models can be implemented in multiple ways: Optionally, the system provides a predefined model template library containing standard functional functions for common fault modes; the user selects a template matching the current fault mode; the system automatically loads the function expressions and default parameters in the template; the user adjusts variable names and value ranges according to actual conditions; the system verifies the mathematical validity of the functions and the completeness of the variables; the system saves the constructed functional function model to the project model library. Optionally, the system provides a visual function construction interface, where the user selects variables and operators by dragging and dropping; the system suggests recommended function forms based on the physical mechanism of the fault; the user inputs a custom function expression, and the system checks the syntax correctness in real time; the system automatically identifies variables in the expression and prompts for setting variable attributes; the user specifies the distribution type (such as normal distribution, Weibull distribution, etc.) and distribution parameters for each variable; the system generates a complete functional function model and provides a visual preview. It is understood that other methods can also be used to implement the construction of fault mode-based functional function models, which are not limited here.

[0038] The core formula of the reliability design analytical theory based on the generalized stress-strength interference model is: Where R is the preset target reliability index, Φ(·) is the inverse function of the standard normal distribution function (i.e., the quantile function corresponding to reliability), μS is the generalized strength mean, and σ S Let μL be the generalized strength standard deviation, μL be the generalized stress mean, and σ be the stress mean. L This represents the generalized stress standard deviation.

[0039] If the design variables include normally distributed random variables with unknown mean but known standard deviation (or coefficient of variation, tolerance range) (e.g., the mean of the design dimensions is unknown, but the tolerance range is known), then an equation about the unknown mean can be established using the above formula. For example, if the generalized strength mean μS is an unknown design variable, and other parameters are known, it can be transformed into: Where, Φ -1 (R) is the inverse function value of the standard normal distribution function at the reliability R (i.e., the reliability index β).

[0040] If the tolerance range (or limit deviation) Δ of the design variable is given, the standard deviation of the variable is taken as σ = Δ / 3 (based on the 3σ principle of normal distribution). Substituting it into the above formula, the mean value μS (or μL) of the design variable can be obtained. Finally, the mean and standard deviation of the design parameters of the non-degenerate unit, or the mean and standard deviation of the design parameters of the degenerate unit at a given time point, are output.

[0041] S103. Substitute the preset target reliability index and the design variables to be solved into the functional model corresponding to the design variables to be solved for inverse solution to obtain candidate design parameters.

[0042] Among them, the target reliability index represents the required level of reliability that the product or component needs to achieve, usually expressed as a probability value, such as 0.95, 0.99, etc.; the design variables to be solved refer to the design parameters whose values ​​need to be determined in the function model, which can be a single variable or a combination of multiple variables; the reverse solution is used to represent the calculation process of deriving the design parameters from the known reliability target, which is the opposite of the traditional forward process of calculating reliability from parameters; the candidate design parameters represent the preliminary design parameter values ​​obtained through the reverse solution, which need to be further verified for their effectiveness.

[0043] The system employs a reverse-engineering strategy to determine design parameters that meet reliability requirements. Specifically, the system first obtains the target reliability index from the reliability allocation module or user input. This index represents the probability requirement that the product will not fail under specific operating conditions. The system identifies the design variables to be solved in the function function model. These variables are parameters that designers can control and adjust, such as part dimensions or material selection parameters. The system uses the target reliability index as constraints, transforming the function function into an equation or optimization problem concerning the design variables to be solved. For simple linear function functions, the system can solve them directly using analytical methods; for complex nonlinear function functions, the system uses numerical optimization methods for iterative solutions. During the solution process, the system considers engineering constraints on the design variables, such as dimensional processing limitations and material availability, to ensure the engineering feasibility of the solution results.

[0044] In some embodiments, the inverse solution of the target reliability index and the design variables to be solved can be achieved in various ways: Optionally, the system adopts an analytical solution method based on stress-strength interference theory; the system converts the target reliability into a reliability index β value; the system establishes a system of equations about the mean and standard deviation of the design variables based on the function; the system solves the system of equations through algebraic operations to obtain the mean of the design variables; the system calculates the standard deviation of the design variables according to preset coefficient of variation or tolerance requirements; the system outputs the mean and tolerance range of the candidate design parameters. Optionally, the system adopts a numerical solution method based on optimization algorithms; the system defines an optimization function with the goal of minimizing reliability deviation; the system sets the initial guess value and search range of the design variables; the system calls gradient descent, genetic algorithm, or particle swarm optimization algorithm for iterative optimization; the system calculates the reliability corresponding to the current design parameter in each iteration; the system judges the convergence condition, and stops iterating when the reliability deviation is less than a threshold; the system outputs the optimized candidate design parameters. It is understood that other methods can also be used to achieve the inverse solution of design parameters based on the target reliability, which are not limited here.

[0045] S104. Substitute the candidate design parameters into the function model and perform forward verification using a preset numerical reliability algorithm to obtain the verification reliability index.

[0046] Among them, forward verification refers to the traditional analysis process of calculating reliability from design parameters, which is used to verify the correctness of the reverse solution results; numerical reliability algorithm refers to numerical methods used to calculate the reliability of complex function functions, such as the first second moment method, Monte Carlo simulation method, etc.; verification reliability index is used to represent the actual reliability value obtained through forward calculation, which is used to compare and verify with the target reliability.

[0047] Specifically, the product design parameter quantitative analysis system verifies the validity of candidate design parameters through forward verification. The system substitutes the candidate design parameter values ​​obtained from the inverse solution into the original function model. These parameters include the mean, standard deviation, or other distribution parameters of the design variables. The system selects an appropriate numerical reliability algorithm for calculation. For linear or weakly nonlinear function models, the system uses the first second moment method (FORM) or the improved mean method (AMV), which are computationally efficient and suitable for rapid verification. For strongly nonlinear or multi-failure-mode cases, the system uses Monte Carlo simulation or importance sampling, obtaining more accurate reliability estimates through extensive random sampling. During the calculation process, the system considers the probability distribution characteristics and correlations of all random variables, calculating the probability of the function model being greater than zero, i.e., the reliability of the product not failing, through numerical integration or simulation methods. The system records the reliability index values ​​obtained from the verification and calculates their deviation from the target reliability.

[0048] In some embodiments, positive verification of candidate design parameters can be achieved in multiple ways: Optionally, the system uses the first second-order moment method (FORM) for rapid verification; the system inputs the distribution parameters of candidate design parameters and other random variables into the FORM algorithm; the system performs a Taylor expansion of the function at the mean point to obtain a linear approximation; the system calculates the mean and variance of the linearized function; the system calculates the reliability index β based on the normal distribution theory; the system converts the β value into a reliability probability value; the system outputs the verified reliability and compares it with the target value. Optionally, the system uses Monte Carlo simulation for precise verification; the system generates a large number of random samples (e.g., 100,000) based on the distribution of each random variable; the system substitutes each group of samples into the function to calculate the function value; the system counts the number of samples with a function value greater than zero; the system calculates the reliability as the ratio of the number of successful samples to the total number of samples; the system evaluates the simulation accuracy and increases the number of samples if necessary; the system outputs a high-precision verified reliability index.

[0049] The FORM method involves linearly expanding the limit state equations and using the first moment (mean) and second moment (standard deviation) of the basic random variables to calculate the probability—reliability—that the performance function is greater than zero. When the limit state equations are nonlinear, the performance function is linearly expanded at the mean point, and β can be approximated by the distance from the origin of the standardized normal space to the tangent plane passing through the mean point on the failure surface. Specific formula: Where, x * To determine the mean point on the preset failure surface, the function Z = g(X) is applied at x. * The expression is expanded linearly into a series, where n is the number of random variables and x is the number of variables. i Let i be the actual value of the i-th random variable. Let be the value of the i-th random variable at the mean point. Let be the partial derivative of the function with respect to the i-th random variable at the mean point.

[0050] Based on the sum (difference) property of normal random variables, the mean μZ and variance of the linearized function Z are... The formula is: μZ=g(x * ) in, Let be the standard deviation of the i-th random variable. Let p be the standard deviation of the j-th random variable. ij Let be the correlation coefficient between the i-th and j-th random variables.

[0051] The formula for calculating the reliability index β (the distance from the origin of the coordinate system in the normalized normal space to the tangent plane of the failure surface) is as follows: The reliability index is converted into reliability R (the probability that the function function is greater than zero) using the standard normal distribution function Φ(·), as shown in the formula: R = Φ(β) Finally, the mean and standard deviation of the random variables corresponding to the candidate design parameters are substituted into the above formula to calculate the reliability index for verification.

[0052] In addition to the FORM method, the Improved Mean Value (AMV) method can also be used for positive verification. The AMV method improves the calculation accuracy of the nonlinear function by correcting the position of the mean point. The specific formula is as follows: First, assume an initial mean point x0 (usually the mean of the random variable), then calculate the initial function value g(x0) and its partial derivatives. The initial reliability index β0 is calculated using the FORM method formula.

[0053] Based on the initial reliability index β0 and the coordinates of the corrected mean point x k+1 Perform iterative calculations, the formula is: Where k is the number of iterations. Let β be the coordinates of the verification point of the i-th random variable after the (k+1)-th iteration. k This is the reliability index obtained in the k-th iteration.

[0054] Repeat the iterative calculation until the reliability index difference between two adjacent iterations is |β. k+1 -β k |≤ε (ε is a preset precision threshold, usually taken as 0.001), at this time β k+1 This is the final reliability index, and the verification reliability index is obtained by calculating R = Φ(β) using the formula R = Φ(β).

[0055] S105. The candidate design parameters that meet the target reliability index after verification are determined as the target design parameters.

[0056] Among them, the target design parameters refer to the final determined design parameter values ​​that can ensure the product meets the predetermined reliability requirements, and can be directly used for product design and manufacturing.

[0057] Specifically, the system determines the validity of candidate design parameters by comparing the verified reliability with the target reliability. First, the system calculates the difference between the verified reliability index and the target reliability index. When the verified reliability is greater than or equal to the target reliability, it indicates that the candidate design parameter meets the reliability requirements. The system considers an engineering safety factor, typically requiring the verified reliability to be slightly higher than the target value to provide a certain design margin. The system evaluates the engineering feasibility of the candidate design parameters, including the feasibility of the manufacturing process, the economic efficiency of material costs, and compatibility with other components. For candidate design parameters that meet all conditions, the system designates them as the final target design parameters and generates a design parameter report containing information such as the parameter's nominal value, tolerance range, and reliability verification results. The system saves the target design parameters to the product database and can export them in a standard format for use by CAD software or manufacturing systems.

[0058] Optionally, the system can also establish a design parameter evaluation system, setting multiple evaluation dimensions such as reliability satisfaction, cost indicators, and processing difficulty; the system comprehensively scores each candidate parameter that meets the reliability requirements; the system selects the optimal combination of design parameters based on the score ranking; the system generates a detailed design parameter specification document, including parameter values, tolerances, material specifications, etc.; the system exports the parameters in XML or JSON format for easy integration with other systems; the system automatically updates the relevant parameter information in the product BOM.

[0059] Optionally, the system can also provide parameter sensitivity analysis to assess the impact of each design parameter on reliability; the system can identify critical and non-critical design parameters; the system can set stricter tolerance requirements for critical parameters; the system can generate parameter control charts to visually display the allowable range of parameter variation; the system can establish a parameter change tracking mechanism to record the modification history of design parameters; and the system can output the final list of target design parameters and its verification report. It is understood that other methods can also be used to determine the target design parameters that meet reliability requirements, and these are not limited here.

[0060] S106. If the verified reliability index does not meet the target reliability index, a new target reliability index is generated based on the preset adjustment strategy.

[0061] The adjustment strategy refers to the rules and methods by which the system automatically adjusts the target or parameters when the initial target cannot be achieved; the new target reliability index represents the adjusted, more reasonable or achievable reliability target value.

[0062] Specifically, the product design parameter quantitative analysis system activates an adaptive adjustment mechanism when the verified reliability fails to meet requirements. The system first analyzes the gap between the verified reliability and the target reliability to determine whether the infeasibility is due to an excessively high target or overly stringent design constraints. The system generates a new target reliability based on preset adjustment strategies, which may include: a gradual reduction strategy (gradually decreasing the target value in fixed steps); an adaptive adjustment strategy (dynamically adjusting the target based on the highest achievable reliability); and a tiered adjustment strategy (setting different reliability targets based on the product's importance level). While adjusting the target, the system may need to relax certain design constraints, such as expanding the range of material choices or relaxing size restrictions. The system then re-introduces the new target reliability index into the reverse solution process, forming an iterative optimization loop until feasible design parameters are found or the maximum number of iterations is reached. The system records the results of each iteration, providing complete optimization path information for design decisions.

[0063] Optionally, the system may employ a gradient-based adaptive adjustment method; the system calculates the maximum achievable reliability within the current design space; the system evaluates the marginal cost curve of reliability improvement; the system determines a new target value at the reliability-cost balance point; the system compares the new target value with the minimum acceptable standard; the system generates an adjustment suggestion report explaining the reasons and impacts of the target adjustment; and the system updates the target reliability index after obtaining user confirmation.

[0064] Optionally, the system can also employ a multi-objective trade-off adjustment strategy; the system identifies the main constraints affecting reliability; the system evaluates the reliability improvement effect of relaxing different constraints; the system determines the optimal constraint relaxation scheme through Pareto analysis; the system adjusts the target reliability accordingly to an achievable level; the system generates multiple alternative schemes for decision-makers to choose from; the system updates the target based on the selected scheme and restarts the solution process. It is understood that other methods can also be used to achieve dynamic adjustment and optimization of target reliability, which are not limited here.

[0065] In the above embodiments, the system acquires product structure tree data and associated physical failure mode data. For each failure mode, it constructs a functional function model containing random variables such as design dimensions, material properties, and load conditions, thus realizing a mathematical expression of the relationship between product strength and stress. A reverse solution strategy is adopted, directly substituting the target reliability index into the functional function model to calculate candidate design parameters, rather than the traditional forward trial-and-error iteration. This is combined with forward verification to validate the reliability of the candidate parameters, ensuring improved accuracy. This two-way mechanism of "reverse solution-forward verification" fundamentally changes the traditional parameter determination mode that relies on experience and repeated iterations. It transforms the original process of blindly trying and failing dozens or even hundreds of times into a goal-oriented, precise solution process, improving the efficiency and accuracy of design parameter determination.

[0066] The following provides a more detailed description of the process of the method provided in this implementation. Please refer to [link / reference]. Figure 2 This is another flowchart illustrating a method for determining product design parameters based on quantitative reliability analysis in an embodiment of this application.

[0067] S201. When the physical failure mode is a time-dependent degradation failure mode, construct a time-dependent function model that includes time variables.

[0068] Among them, time-related degradation failure modes refer to failure types in which the degree of failure gradually intensifies with the passage of time, and the probability of failure increases with time. Examples include the decrease in precision of bearings due to long-term wear and the capacity decay of batteries due to the increase in the number of charge and discharge cycles. Time variables refer to parameters used in the functional function model to characterize the product's usage time or service life, usually measured in time units such as hours, days, and years, which can reflect the product's performance status at different time points. Time-dependent functional function models refer to mathematical expressions that include time variables and can describe the law of product performance degradation over time. They can be used to quantitatively analyze the reliability level of products at different time points, and their core is to establish the correlation between strength, stress, and time.

[0069] This step is executed after the system completes the identification of physical failure modes of the target product and determines that a time-related degradation failure mode exists. Specifically, the system first classifies and filters the acquired physical failure mode data. Through failure mechanism analysis (such as checking whether the failure is related to time-related parameters such as usage time and cycle count), it identifies the type of degradation failure mode. For cases determined to be degradation failure modes, the system initiates the time-dependent function model construction process: first, it clarifies the core influencing factors of the degradation failure. In addition to conventional random variables such as design dimensions, material properties, and load conditions, it focuses on adding a time variable. This time variable needs to cover key time nodes within the product's expected service life (such as the initial break-in stage, stable operation stage, and aging failure stage). Next, the system determines the basic form of the function model based on failure physics theories (such as fatigue damage accumulation theory and corrosion kinetics theory). For example, for fatigue degradation failures, the model needs to reflect the correlation between "time-cycle count-damage degree"; for corrosion degradation failures, the model needs to include the calculation logic of "time-environmental corrosion rate-material thickness loss". At the same time, the system will combine historical failure data (such as life test data of similar products) to determine the initial value range of each parameter in the model (such as degradation rate coefficient and initial performance parameters), to ensure that the model can accurately reflect the degradation trend of product performance over time, and finally form a time-dependent function model containing time variables.

[0070] Optionally, the system is built based on a predefined degradation model template library: The system matches the corresponding standard time-dependent model template (e.g., Miner linear cumulative damage model template for fatigue degradation, linear corrosion rate model template for corrosion degradation) from the template library based on the identified degradation fault type (e.g., fatigue degradation corresponds to the Miner linear cumulative damage model template, and corrosion degradation corresponds to the linear corrosion rate model template) from the template library; the system automatically loads the function expression in the template, which has preset time variables and related parameter positions; the user adjusts the parameters in the template (e.g., fatigue limit value, corrosion rate coefficient) under system guidance according to the specific characteristics of the target product (e.g., material type, working environment); the system verifies the mathematical rationality of the adjusted model (e.g., ensuring that the function does not fluctuate abnormally within the range of time variable values); the system saves the adjusted time-dependent function model and associates it with the corresponding fault mode.

[0071] S202. Obtain the target task time used to specify the reliability assessment time in the time-dependent function model, and substitute it into the time-dependent function model to generate the function model.

[0072] In this context, the target mission time refers to a specific point in time or time interval used in the time-dependent function model to evaluate the reliability of a product. This point in time must correspond to the key mission nodes in the actual working scenario of the product (such as the duration of a single mission, the interval of regular maintenance, and the end of the design life). For example, if the duration of a single flight mission of a spacecraft is 24 hours, then 24 hours is the target mission time.

[0073] Specifically, the system first clarifies the source of the target task time, mainly through two methods: one is extraction from the product requirements specification. The system connects to the product requirements management system through a data interface to automatically extract the explicit task time requirements (e.g., "The product must guarantee continuous operation for 1000 hours without failure," then 1000 hours is the target task time); the other is manual input by the user based on the actual application scenario. If the task time is not explicitly stated in the requirements document, the system will pop up an input interface, prompting the user to input the target task time and the corresponding task scenario description (e.g., "Task scenario: high-speed driving stage, target task time: 500 hours"). At the same time, the system will perform a reasonableness check on the input time value (e.g., ensuring that the time value does not exceed the product's expected design life and is greater than 0). After obtaining the target task time, the system locates the constructed time-dependent function model and replaces the time variable with the specific value of the target task time. At this time, the time dimension in the model is fixed, and the performance parameters that originally changed with time (e.g., material strength, structural stiffness) are transformed into fixed parameter values ​​at this specific time point. The system will further calculate the specific values ​​of each parameter in the model at that time point (such as calculating the fatigue damage and corrosion loss of materials based on the time variable value) to ensure that the model can accurately reflect the actual performance state of the product under the target task time, and finally generate a functional function model that can be used for reliability analysis at that time point.

[0074] S203. Substitute the target task time and the reliability index into the preset exponential distribution conversion formula to calculate the mean time between failures.

[0075] The preset exponential distribution conversion formula is a mathematical formula based on the exponential distribution theory (the exponential distribution is often used to describe the probability distribution of a product's fault-free operating time and has the characteristic of "memorylessness"), which establishes the conversion relationship between reliability, target task time, and mean time between failures (MTBF). This formula is pre-stored in the system and does not require users to derive it again. Mean time between failures (MTBF) refers to the average operating time between two consecutive failures under specified operating conditions. It is an important indicator for measuring product reliability and is usually expressed in hours. For example, an MTBF of 5000 hours means that the product may fail once every 5000 hours of operation on average.

[0076] Specifically, the system first confirms the key data acquired: one is the reliability index obtained through positive verification (this index must be a valid value, such as between 0 and 1), and the other is the target task time previously substituted into the time-dependent function model (this time point must be consistent with the time point corresponding to the reliability index). Next, the system calls a pre-stored exponential distribution conversion formula. The core logic of this formula is based on the reliability function of the exponential distribution: reliability R(t) = e^(-t / MTBF) (where t is the target task time and MTBF is the mean time between failures). The system transforms this into the MTBF calculation formula: MTBF = -t / ln(R(t)). Subsequently, the system substitutes the target task time t and the reliability index R(t) into this formula for numerical calculation: first, it calculates ln(R(t)) (note that when R(t) is close to 1, ln(R(t)) is a negative number close to 0), then it divides the negative value of the target task time t by the logarithm to obtain the mean time between failures. During the calculation process, the system will verify the reasonableness of the calculation results. For example, if the reliability index is verified to be 0.95 and the target task time is 1000 hours, the calculated MTBF is approximately 19500 hours. The system will determine whether this value is within the reasonable range of MTBF for similar products (such as the MTBF of similar equipment, which is usually between 10000-30000 hours, and the verification passes). If the calculation result is abnormal (such as a negative MTBF or far exceeding the reasonable range), the user will be prompted to check the correctness of the verified reliability index or the target task time to ensure that the final mean time between failures is accurate and effective.

[0077] S204. When the reliability index meets the target reliability index and the mean time between failures (MTBF) meets the preset target MTBF, the candidate design parameters are determined as the target design parameters.

[0078] The preset target mean time between failures (MTBF) refers to the benchmark value of the mean time between failures set in advance based on factors such as product application scenarios, customer needs, and operation and maintenance costs. It is an important indicator for judging whether the reliability of a product meets the standards from the perspective of engineering practice. For example, the preset target MTBF for a certain industrial robot is 8,000 hours.

[0079] Specifically, the system first initiates a dual-index comparison verification process: Step 1: Compare the calculated reliability index with the target reliability index to determine if the calculated reliability index is greater than or equal to the target reliability index (considering errors in actual engineering, the system usually allows the calculated reliability index to be slightly higher than the target value; for example, if the target value is 0.98, a calculated value of 0.985 is considered acceptable). If the calculated value is lower than the target value, the candidate design parameter is deemed not to meet the requirements. Step 2: Based on the calculated reliability meeting the requirements, compare the mean time between failures (MTBF) with the preset target MTBF to determine if the MTBF is greater than or equal to the target value (for example, if the target value is 8000 hours, a calculated MTBF of 8500 hours is considered acceptable). If the MTBF is lower than the target value, the candidate design parameter is also deemed not to meet the requirements. When both indicators meet the standards, the system further verifies the engineering feasibility of the candidate design parameters: checking whether the parameters meet the processing requirements (e.g., whether the design dimensions are within the accuracy range of existing processing equipment); assessing whether the material and manufacturing costs corresponding to the parameters are within the budget (e.g., whether the cost of the selected high-strength materials is too high); and verifying the compatibility of the parameters with other components (e.g., whether the design dimensions of a certain part match the interface of the assembly component). If the engineering feasibility verification passes, the system officially determines the candidate design parameter as the target design parameter and generates a target design parameter report. The report includes the specific values ​​of the parameter, tolerance requirements, reliability verification results (reliability calculation, MTBF), applicable scenarios, and other information. At the same time, the report is synchronized to the product design database for subsequent CAD design, production process formulation, and other stages.

[0080] S205. Using a pre-defined experimental design method, training sample points are generated in the design space of the design variables to be solved, and the performance response value corresponding to each training sample point is calculated by calling the functional model to obtain the training sample set.

[0081] Among them, the preset experimental design method refers to the standardized method that the system pre-stores for scientifically selecting sample points within the design space. It aims to cover key areas with fewer samples and reduce the amount of computation. Common methods include orthogonal experimental design, Latin hypercube sampling, and central composite design. The design space refers to the range of values ​​of the design variables to be solved, which is determined by engineering constraints (such as machining accuracy and material performance limits) and design requirements. For example, the design space for the diameter of a certain shaft part is 20-30mm. The training sample points refer to the specific combination of variables selected within the design space through the experimental design method for training the model. Each sample point contains a set of values ​​of the design variables to be solved. The performance response value refers to the numerical value reflecting the product performance, such as reliability, stress value, and strength value, calculated after substituting the training sample points into the function model. Specifically, the system first clarifies the details of the design variables to be solved: first, the number of variables (e.g., two variables: diameter and length); second, the design space for each variable (e.g., diameter 20-30mm, length 50-80mm); and third, the constraints on the variables (e.g., the ratio of diameter to length must be between 1:2 and 1:4). Next, the system selects a preset experimental design method based on the number of variables and the model complexity: if there are few variables (2-3) and the central region needs to be covered, a central composite design is selected; if there are many variables (4 or more) and the entire design space needs to be covered evenly, Latin hypercube sampling is selected; if orthogonality and computational efficiency need to be balanced, an orthogonal experimental design is selected. After determining the method, the system generates training sample points within the design space: during the generation process, it automatically avoids combinations that violate the constraints (e.g., if the diameter is 25mm, a length of 60mm conforms to the 1:2.4 ratio and is retained; if it is 40mm, it does not conform to the ratio and is discarded), ensuring the engineering feasibility of the sample points. Subsequently, the system batch calls the functional model, substituting the variable values ​​of each training sample point into the model to calculate the corresponding performance response value (e.g., a reliability of 0.95 and a stress value of 200 MPa are obtained after substitution). After the calculation is completed, the system verifies the sample data: first, it checks for outliers (e.g., performance response values ​​exceeding a reasonable range may indicate a calculation error); second, it confirms the uniformity of the sample point distribution within the design space (if samples are sparse in a certain area, additional samples are generated), ultimately forming a training sample set containing a one-to-one correspondence between "sample point and response value".

[0082] Optionally, the system generates data based on orthogonal experimental design: The system determines the design variables to be solved and the number of levels (e.g., two variables: width (level 1: 15mm, level 2: 20mm, level 3: 25mm), hardness (level 1: 200HV, level 2: 250HV, level 3: 300HV)); the system selects the corresponding orthogonal array (e.g., L9(3^2), which can cover 9 sample points); the system automatically generates 9 sets of training sample points based on the orthogonal array (e.g., (15mm, 200HV), (15mm, 250HV)...(25mm, 300HV)); the system checks whether the sample points meet the engineering constraints (e.g., when the width is 25mm, whether the hardness of 300HV is within the material's achievable range, if so, it is retained); the system calls the functional model to calculate the performance response values ​​(e.g., strength values) of the 9 sample points, and organizes them into a training sample set in the format of "sample point - response value".

[0083] It is understandable that other methods can be used to generate training sample sets, such as combining response surface methodology to design sample points, which is not limited here.

[0084] S206. Train the preset machine learning model based on the training sample set to obtain a surrogate model that represents the mapping relationship between the design variables to be solved and the reliability index.

[0085] Among them, the pre-set machine learning model refers to the algorithm model that is pre-integrated into the system to learn the mapping relationship between variables and responses. Common types include support vector machines, neural networks, gradient boosting trees, kriging models, etc. Different models are suitable for different data characteristics (such as linear, nonlinear, small sample, large sample). The surrogate model refers to a simplified model that is trained by machine learning and can replace the complex functional function model to quickly calculate the reliability index corresponding to the design variable to be solved. Its core is to establish a fast mapping between "design variable and reliability index" to reduce computational complexity. Specifically, the system first preprocesses the training sample set, including but not limited to data standardization and partitioning the training and validation sets. Next, the system selects a pre-defined machine learning model based on sample set characteristics (such as sample size and the degree of variable nonlinearity): a Kriging model is selected if the sample size is small (less than 50 samples) and highly nonlinear; a neural network is selected if the sample size is large (more than 100 samples) and there is high variable coupling; and a gradient boosting tree is selected if both interpretability and accuracy are required. After determining the model, the system initiates the training process: the training set is input into the model, and the model parameters (such as the weights of the neural network and the kernel function parameters of the support vector machine) are adjusted iteratively through the algorithm to optimize the model with the goal of minimizing the error between the predicted reliability index and the actual sample response value. During training, the system evaluates the model performance in real time using the validation set, employing common metrics (such as the coefficient of determination R). 2The closer the value is to 1, the higher the accuracy; the smaller the root mean square error (RMSE), the higher the accuracy. This is used to determine whether the model meets the standards (e.g., preset R²). 2 (≥0.95, RMSE≤0.02). If performance is not up to standard, the system automatically adjusts model parameters (e.g., increasing the number of neural network layers) or supplements training samples (e.g., adding sample points in regions with large errors) and retrains. If performance is up to standard, the system stops training, saves the final model parameters, and forms a surrogate model. Finally, the system performs a generalization test on the surrogate model: new sample points within the design space that were not used in training are selected, the reliability index is calculated using the surrogate model, and compared with the calculation results of the function model. If the error is within the allowable range (e.g., ≤5%), the surrogate model is officially usable.

[0086] S207. Using the target reliability index as the optimization objective, a preset intelligent optimization algorithm is used to perform optimization calculations on the proxy model to solve for the combination of variables that meet the target reliability index, and these combinations are determined as candidate design parameters.

[0087] Among them, intelligent optimization algorithm refers to the algorithm preset by the system to search for the optimal combination of variables in the design space. Common types include genetic algorithm, particle swarm optimization algorithm, simulated annealing algorithm, ant colony algorithm, etc. These algorithms can efficiently handle multi-constraint and nonlinear optimization problems. Optimization calculation refers to the process of continuously searching for variable combinations in the design space of the design variables to be solved through intelligent optimization algorithm with the support of surrogate model until a combination that meets the target reliability index is found. Variable combination refers to the specific value combination of multiple design variables to be solved, such as "diameter 25mm + length 60mm + hardness 280HV", each combination corresponds to a reliability index.

[0088] Specifically, the system first clarifies the core elements of the optimization task: First, the optimization objective (centered on the target reliability index, such as "reliability ≥ 0.98"; other objectives can be weighted, such as "reliability ≥ 0.98 and cost ≤ 500 yuan"); second, the optimization variables (the design variables to be solved and their design space, such as "diameter 20-30mm, length 50-80mm"); and third, the constraints (such as "diameter to length ratio 1:2-1:4" and "material strength ≥ 300MPa"). Next, the system selects a preset intelligent optimization algorithm based on the characteristics of the optimization task: if there are many variables and complex constraints, a genetic algorithm (excelling in global search) is selected; if rapid convergence to a local optimum is required, a particle swarm optimization algorithm is selected; and if avoiding getting trapped in local optima is required, a simulated annealing algorithm is selected. After determining the algorithm, the system sets the algorithm parameters (e.g., population size of 50, number of iterations of 100, crossover probability of 0.8, and mutation probability of 0.05 for the genetic algorithm) and integrates the surrogate model as an "evaluator" into the optimization process (i.e., after the algorithm generates variable combinations, it calls the surrogate model to quickly calculate the reliability index and determine whether the target is met). During the optimization process, the system iteratively searches according to the algorithm logic: taking the genetic algorithm as an example, it first randomly generates an initial population (50 sets of variable combinations), evaluates the reliability index of each group through the surrogate model, and selects individuals that meet the target; then, it generates a new population through crossover (e.g., exchanging some values ​​between two sets of variable combinations) and mutation (e.g., randomly fine-tuning the value of a variable), and repeats the evaluation and selection; until the number of iterations reaches 100, or the best individual in the population no longer changes after 10 consecutive generations, the optimization stops. Finally, the system selects all variable combinations that meet the target reliability index from the final population, eliminates combinations that violate engineering constraints (e.g., cost overruns), and selects 1-3 combinations with the best overall performance (e.g., lowest cost and lightest weight) as candidate design parameters.

[0089] S208. After determining the verification reliability index corresponding to the candidate design parameters, identify the target component nodes in the product structure tree data that contain multiple physical failure modes.

[0090] Specifically, the system first retrieves the complete product structure tree data, which is associated with the physical failure mode information of each component node (synchronized from the hardware FMECA module). Next, the system initiates node traversal analysis: starting from the root node of the product structure tree, it traverses downwards layer by layer through child nodes and leaf nodes, counting the number of associated physical failure modes for each component corresponding to each node. During the traversal, the system identifies target component nodes according to the following rules: the number of failure modes is ≥2 (i.e., it contains multiple physical failure modes); the component is a critical component (judged by preset criticality evaluation criteria, such as whether it affects the overall function of the machine, and whether the severity of the failure consequence is ≥8 levels); the candidate design parameters of the component have been verified under a single failure mode (ensuring that reliability data is available for subsequent comprehensive analysis). For nodes that meet the above rules, the system marks them as target component nodes and extracts their key information, including basic component attributes (name, model, and hierarchy in the structure tree), a list of all associated physical failure modes (e.g., "Failure 1: Fatigue Fracture, Failure 2: Corrosion Failure"), and the verification reliability index corresponding to each failure mode (e.g., fatigue fracture reliability 0.98, corrosion failure reliability 0.97). Simultaneously, the system excludes nodes that do not meet the conditions (e.g., ordinary parts with only one failure mode, nodes that have not completed verification), ensuring the accuracy and validity of the target component nodes.

[0091] S209. Obtain the verification reliability index corresponding to each physical failure mode in the target component node, and obtain the reliability index set.

[0092] Specifically, the system first locates the identified target component node and retrieves the "failure mode-reliability" association record of that node from the product structure tree database. This record is automatically stored after the verification of a single failure mode is completed and includes information such as "failure mode name", "verification reliability index", "verification time" and "verification algorithm".

[0093] Next, the system filters and organizes the related records: First, it filters out valid records (such as those with a verification time within 3 months to ensure data timeliness; and those with verification algorithms that are standard methods, such as FORM or Monte Carlo methods, to ensure data accuracy); second, it sorts the records from highest to lowest severity of the failure modes (such as "fatigue fracture" having the highest severity and being ranked first; and "minor wear" having the lowest severity and being ranked last), which facilitates subsequent analysis of the impact of key failure modes.

[0094] Subsequently, the system extracts the "reliability verification index" from each valid record and binds it with the corresponding failure mode name to form a "failure mode-reliability" key-value pair (e.g., "fatigue fracture": 0.98, "corrosion failure": 0.97). Finally, the system integrates these key-value pairs into a reliability index set. The set format must be consistent (e.g., list or dictionary format), and metadata (e.g., the number of failure modes included, data source, and generation time) is appended to ensure the set's integrity and traceability. If a failure mode's reliability verification index is missing (e.g., verification incomplete), the system will prompt the user to complete the verification, and the reliability index set will be generated again once the data is complete.

[0095] S210. Generate a correlation coefficient matrix based on the correlation strength between each reliability index in the reliability index set.

[0096] Specifically, the system first clarifies the number of verifiable reliability indicators included in the reliability index set (e.g., 3 indicators corresponding to 3 failure modes) and determines the dimension of the correlation coefficient matrix (e.g., a 3×3 matrix). Next, the system initiates the correlation strength analysis process: First, it identifies common factors affecting the reliability of each failure mode by consulting failure mechanism data (e.g., material handbooks, failure reports of similar products) to determine variables that may lead to index correlation (e.g., ambient temperature, load frequency, material purity). Second, it collects historical data to support the correlation analysis, including multi-failure mode reliability data of similar products under different operating conditions (e.g., reliability change curves of "fatigue fracture" and "corrosion" at different temperatures). If historical data is insufficient, the system will base its analysis on engineering mechanisms (e.g., increased temperature simultaneously accelerates fatigue and corrosion processes). The system first provides an initial correlation assessment; then, it quantifies the correlation strength by using statistical methods (such as Pearson correlation coefficient and Spearman rank correlation coefficient) to calculate the correlation coefficient between each pair of reliability indicators (e.g., the correlation coefficient between "fatigue fracture reliability" and "corrosion reliability" is 0.6, indicating a moderate positive correlation). Finally, the system arranges all correlation coefficients in a matrix format to generate a correlation coefficient matrix. The elements on the main diagonal of the matrix are always 1 (indicators are perfectly correlated with themselves), and the elements off the main diagonal are the correlation coefficients between the corresponding pairs of indicators. S211. Construct a connection function model based on the correlation coefficient matrix to describe the joint probability distribution among multiple verification reliability indicators in the reliability index set.

[0097] Specifically, the system first obtains the basic data for constructing the copula function model: one is the marginal distributions of the respective verification reliability indices in the reliability index set (such as normal distribution, Weibull distribution, determined by fitting historical data or engineering standards), and the other is the generated correlation coefficient matrix. Next, the system selects an appropriate copula function type according to the data characteristics: if the correlation coefficient matrix shows weak correlations between the indices and the same distribution type (such as all being normal distributions), the Gaussian copula function is selected (which is computationally simple and suitable for normal distributions); if the correlations are strong or the distribution types are diverse (such as some being normal distributions and some being uniform distributions), the t-copula function is selected (which is more adaptable to changes in correlations); if there are extreme value effects (such as a sudden drop in reliability under a few working conditions), the Gumbel copula function is selected (which is good at describing scenarios related to extreme values). After determining the type, the system starts the model parameter calibration process: taking the correlation coefficients in the correlation coefficient matrix as constraint conditions, substituting them into the parameter equations of the copula function (such as the covariance matrix equation of the Gaussian copula function), and solving the model parameters (such as the elements of the covariance matrix of the Gaussian copula function) through a numerical optimization algorithm (such as the Newton-Raphson method) to ensure that the joint distribution generated by the model meets the preset correlation requirements. After calibration, the system verifies the model: selecting a small number of multi-index value combinations from the historical data, substituting them into the copula function model to calculate the joint probability, and comparing it with the actual occurrence frequency. If the error ≤ 5%, the model is qualified; if the error exceeds the standard, readjust the copula function type or optimize the parameters until the model accuracy meets the standard, and finally form a copula function model that can accurately describe the joint probability distribution of multiple verification reliability indices.

[0098] S212. Substitute the reliability index set into the copula function model for calculation to obtain the comprehensive reliability index of the target component node.

[0099] Specifically, the system first confirms the completeness and accuracy of the input data: first, a set of reliability indicators for the target component nodes (which must include the verified reliability of all failure modes, with no missing values); and second, a calibrated connection function model (ensuring that the model parameters match the current analysis scenario). Next, the system initiates the comprehensive reliability calculation process: First, each verified reliability indicator in the reliability indicator set is converted to a standardized value according to its corresponding marginal distribution (e.g., converting a normally distributed reliability into a standard normally distributed variable to eliminate dimensional differences); second, the standardized value is substituted into the connection function model, which calculates the joint probability that all failure modes will not fail simultaneously (i.e., the core content of comprehensive reliability) based on the preset joint probability distribution logic; third, the system performs error control during the calculation process. If numerical integration is used to calculate the joint probability, accuracy is improved by adjusting the integration step size (e.g., reducing the step size to 0.01); if Monte Carlo simulation is used, random error is reduced by increasing the sample size (e.g., 100,000 simulations). After the calculation is completed, the system outputs a comprehensive reliability index along with calculation instructions, including the set of input reliability indices, the type of connection function, the calculation method, and the error range (e.g., comprehensive reliability 0.95 ± 0.02). Simultaneously, the system compares the comprehensive reliability index with a preset target comprehensive reliability (e.g., 0.95) to determine if the current design parameters meet the requirements. If they do, the system records the result; otherwise, it prompts the user to adjust the design parameters (e.g., optimize material properties, adjust geometric dimensions) and re-execute the reliability analysis process.

[0100] When substituting the set of reliability indices into the connection function model, the comprehensive reliability is calculated using the failure mode synthesis method for multiple failure modes of the target component node. The core formula is: Among them, R S (t) represents the overall reliability of the target component node after integrating failure modes (at time t), where n is the number of failure modes included in the reliability index set, and R i (t) represents the reliability index of the i-th failure mode at time t.

[0101] If the reliability index set contains reliability indices corresponding to degradation failure modes with time variables, the reliability value R of each degradation failure mode at the critical time point (such as the target task time) must be extracted first. S (t0) (t0 is the target task time), then substitute it into the above formula to calculate, that is: This formula, combined with the connection function model, corrects the correlation between failure modes (e.g., adjusting each R based on the correlation coefficient matrix). iThe weights of (t) are used to obtain the comprehensive reliability index of the target component node.

[0102] The product design parameter quantitative analysis system of this invention is applied to electronic devices. Figure 3 A schematic diagram of the architecture of an electronic device suitable for implementing embodiments of the present invention is shown.

[0103] It should be noted that, Figure 3 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0104] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by instructions (computer programs), or by instructions (computer programs) controlling related hardware. These instructions can be stored in a computer-readable storage medium and loaded and executed by a processor. The electronic device of this embodiment includes a storage medium and a processor, wherein the storage medium stores multiple instructions that can be loaded by the processor to execute any step of the method provided in the embodiments of the present invention.

[0105] Specifically, the storage medium and the processor are electrically connected directly or indirectly to enable data transmission or interaction. For example, these components can be electrically connected to each other via one or more signal lines. The storage medium stores computer-executable instructions that implement data access control methods, including at least one software functional module that can be stored in the storage medium in the form of software or firmware. The processor executes various functional applications and data processing by running the software program and module stored in the storage medium. The storage medium can be, but is not limited to, Random Access Memory (RAM), Read-Only Memory (ROM), Programmable Read-Only Memory (PROM), Erasable Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), etc. The storage medium stores the program, and the processor executes the program after receiving the execution instructions.

[0106] Furthermore, the software programs and modules within the aforementioned storage medium may also include an operating system, which may include various software components and / or drivers for managing system tasks (e.g., memory management, storage device control, power management, etc.) and can communicate with various hardware or software components to provide an operating environment for other software components. The processor may be an integrated circuit chip with signal processing capabilities. The aforementioned processor may be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc., which can implement or execute the methods, steps, and logic flowcharts disclosed in this embodiment. The general-purpose processor may be a microprocessor or any conventional processor.

[0107] Since the instructions stored in the storage medium can execute the steps in any of the methods provided in the embodiments of the present invention, the beneficial effects of any of the methods provided in the embodiments of the present invention can be achieved, as detailed in the preceding embodiments, and will not be repeated here.

[0108] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for determining product design parameters based on quantitative reliability analysis, applied to a quantitative analysis system for product design parameters, characterized in that, The method includes: Obtain product structure tree data of the target product and physical failure mode data associated with each node in the product structure tree data. The product structure tree data includes digital data of the components of the target product and the physical hierarchical relationships between the components. The failure mode data is data on the predictable failure modes of the target product under specific physical stress. Based on the physical failure mode data, a functional function model including multiple random variables is constructed for each different physical failure mode. The functional function model is an expression used to describe the mathematical relationship between product strength and stress. The random variables include the design dimensions, material properties and load conditions of the target product. The preset target reliability index and the design variable to be solved are substituted into the function model corresponding to the design variable to be solved for inverse solution to obtain candidate design parameters. The design variable to be solved is a combination of one or more variables among the random variables. The candidate design parameters are substituted into the function model, and a preset numerical reliability algorithm is used for positive verification to obtain the verification reliability index. Candidate design parameters that satisfy the target reliability index are determined as target design parameters.

2. The method according to claim 1, characterized in that, The step of constructing a functional model including multiple random variables under each different physical fault mode based on the physical fault mode data specifically includes: When the physical failure mode is a time-dependent degradation failure mode, a time-dependent function model containing time variables is constructed. Obtain the target task time used to specify the reliability assessment time in the time-dependent function model; Substitute the target task time into the time-dependent function model to generate the function model.

3. The method according to claim 2, characterized in that, After the step of substituting the candidate design parameters into the function model and performing a forward verification using a preset numerical reliability algorithm to obtain the verification reliability index, the method further includes: Substituting the target task time and the verification reliability index into the preset exponential distribution conversion formula, the mean time between failures (MTBF) is calculated. When the verified reliability index meets the target reliability index and the mean time between failures (MTBF) meets the preset target MTBF, the candidate design parameter is determined as the target design parameter.

4. The method according to claim 1, characterized in that, The step of substituting the preset target reliability index and the design variables to be solved into the function model corresponding to the design variables to be solved for reverse solution to obtain candidate design parameters specifically includes: A training sample point is generated in the design space of the design variable to be solved using a preset experimental design method, and the performance response value corresponding to each training sample point is calculated by calling the function model to obtain a training sample set. The training sample set includes a data set of multiple sets of design variable values ​​and corresponding performance response values. The preset machine learning model is trained based on the training sample set to obtain a proxy model that represents the mapping relationship between the design variable to be solved and the reliability index. Using the target reliability index as the optimization objective, a preset intelligent optimization algorithm is used to perform optimization calculations on the surrogate model to solve for the variable combination that satisfies the target reliability index, and this combination is determined as the candidate design parameters.

5. The method according to claim 1, characterized in that, After the step of substituting the candidate design parameters into the function model and performing a forward verification using a preset numerical reliability algorithm to obtain the verification reliability index, the method further includes: Identify target component nodes in the product structure tree data that contain multiple physical failure modes; Obtain the verification reliability index corresponding to each physical failure mode in the target component node to obtain a set of reliability indices; Perform a product operation on all the verified reliability indices in the set of reliability indices to obtain the comprehensive reliability index of the target component node.

6. The method according to claim 5, characterized in that, The step of performing a product operation on all verified reliability indices in the reliability index set to obtain the comprehensive reliability index of the target component node specifically includes: Based on the correlation strength between each reliability index in the reliability index set, a correlation coefficient matrix is ​​generated, wherein the correlation strength is determined by engineering mechanism analysis or statistical quantification of historical data. Based on the correlation coefficient matrix, a connection function model is constructed to describe the joint probability distribution among multiple verification reliability indicators in the reliability index set; The reliability index set is substituted into the connection function model for calculation to obtain the comprehensive reliability index of the target component node.

7. The method according to claim 1, characterized in that, After the step of substituting the candidate design parameters into the function model and performing a forward verification using a preset numerical reliability algorithm to obtain the verification reliability index, the method further includes: When the verified reliability index does not meet the target reliability index, a new target reliability index is generated based on a preset adjustment strategy; The new target reliability index and the design variables to be solved are substituted back into the function model for inverse solution to obtain new candidate design parameters; The new candidate design parameters that satisfy the target reliability index are determined as the target design parameters.

8. A quantitative analysis system for product design parameters, characterized in that, The system includes: one or more processors and memory; The memory is coupled to the one or more processors, the memory being used to store computer program code, the computer program code including computer instructions, the one or more processors invoking the computer instructions to cause the system to perform the method as described in any one of claims 1-7.

9. A computer-readable storage medium comprising instructions, characterized in that, When the instructions are run on the product design parameter quantitative analysis system, the system performs the method as described in any one of claims 1-7.

10. A computer program product, characterized in that, When the computer program product is run on the product design parameter quantitative analysis system, the system performs the method as described in any one of claims 1-7.

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