Area measurement method for fuzzy uncertainty structure system model confirmation
The area measurement method for confirming fuzzy uncertain structural system models solves the problems of model accuracy and reliability caused by fuzzy uncertainty, and improves the accuracy and reliability of model confirmation, which is applicable to engineering applications such as aerospace.
Patent Information
- Application Number
- CN202511461899.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-14
- Publication Date
- 2025-11-11
AI Technical Summary
Existing technologies struggle to handle real-world fuzzy uncertainties in engineering practice, leading to model parameters and measurement errors affecting the accuracy and reliability of computational models. There is a lack of model validation methods suitable for fuzzy uncertainties.
An area metric method for confirming fuzzy uncertainty structural system models is adopted. By calculating the area difference between the model's membership function and the empirical membership function of the experimental measured response, the difference between the calculated model and the experimental data is quantitatively evaluated, and a model confirmation index based on fuzzy uncertainty is established.
This paper presents a model validation method suitable for small sample data and fuzzy variables, which improves the accuracy and reliability of model validation and is applicable to practical engineering applications such as aviation and aerospace.
Smart Images
Figure CN120930386A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of model verification and validation technology, and in particular to an area measurement method for validating fuzzy uncertain structural system models. Background Technology
[0002] With the development of modern engineering technology, structural systems are becoming increasingly complex, and traditional experimental methods are difficult to meet the demands due to their high cost and long cycle. Numerical simulation technologies such as finite element analysis and computational fluid dynamics simulation provide efficient solutions for structural design optimization and reliability assessment. Although high-fidelity mathematical models can significantly improve design efficiency, the uncertainty of model parameters and the influence of measurement errors may lead to deviations between the calculated model results and the actual experimental measurement response. Therefore, before carrying out optimization design and reliability analysis, the model must be validated to ensure its computational accuracy and reliability.
[0003] While significant progress has been made in model validation and verification in academia, a unified measurement standard is still lacking. The concept of model validation and verification was first proposed in the United States, which has subsequently published multiple versions of model validation and verification standards, providing standardized guidance for engineering practice. Commonly used model verification methods in engineering mainly include four categories: classical hypothesis testing, Bayesian factors, frequency indices, and area indices. However, the first two methods can only qualitatively assess hypothesis acceptability, and frequency indices only consider expected differences; neither can comprehensively evaluate the degree of difference between the computational model and experimental measurements. In contrast, area indices and U-pooling indices comprehensively reflect uncertainty information through differences in distribution functions, making them more applicable.
[0004] However, existing methods primarily address stochastic uncertainty and struggle to handle the fuzzy uncertainty inherent in real-world engineering scenarios, stemming from imprecise data, the subjectivity of expert experience, and limitations in measurement methods. Their statistical characteristics are difficult to accurately describe using traditional probabilistic methods. Therefore, there is an urgent need to develop a model validation method suitable for fuzzy uncertainty to improve the accuracy and reliability of model calculations. Summary of the Invention
[0005] The purpose of this invention is to provide an area measurement method for confirming the model of a fuzzy uncertain structural system. It establishes a model confirmation index based on fuzzy uncertainty, specifically by calculating the area difference between the membership function of the model and the empirical membership function of the experimental measured response, and quantitatively evaluating the difference between the calculated model and the experimental data.
[0006] To achieve the above objectives, the present invention provides an area measurement method for confirming fuzzy uncertain structural system models, comprising: Step 1: In the actual engineering model verification problem, based on fuzzy set theory, fuzzy uncertainties of model parameters and measurement errors are introduced into the computational model; The input of the computational model based on fuzzy uncertainty includes deterministic variables and fuzzy uncertain variables, and the output response is a fuzzy uncertain variable. The distribution law of the uncertain variables is determined by the corresponding membership function. Step 2: Calculate the upper and lower boundary values of the output response at a given membership level using optimization methods, traverse the membership level range [0,1], and obtain the membership function curve of the calculation model; where the membership function of the calculation model is divided into a left branch and a right branch, the left branch is a monotonically increasing function, and the right branch is a monotonically decreasing function. Step 3: The empirical membership function of experimental measurement under fuzzy uncertainty is constructed in the form of a stepped line through data preprocessing, universe discretization, membership degree assignment and stepped processing. Step 4: Based on the fuzzy uncertainty area metric, the model validation method is used to obtain the area difference between the corresponding curves of the membership function of the computational model and the empirical membership function of the experimental measurement, and to quantitatively evaluate the difference between the computational model and the experimental data.
[0007] Preferably, step two includes, given a membership level, degenerating the fuzzy variables of the computational model into interval variables, and using an optimization method to calculate the upper and lower boundary values of the computational model's response at the given membership level; then, by traversing the value interval of the membership level, obtaining the membership function curve of the computational model.
[0008] Preferably, step three includes: Step 1: Based on the interquartile range method, outliers in the experimental data are removed, data points within the valid range are retained, and the measurement error caused by the error is determined. Step 2: Based on the measurement error determined in Step 1, further discretize the data in the universe of discourse to generate a discrete point sequence; Step 3: For each data point in the discrete point sequence, determine the corresponding neighborhood based on the determined measurement error, and calculate the basic membership degree; Step 4: Define the ladder nodes and construct the empirical membership function for experimental measurements.
[0009] Preferably, step 2 includes: First, define the boundary of the universe of discourse X: ; ; In the formula, , Let X be the lower and upper boundaries of the domain of discourse. The measurement error caused by the error. For the preprocessed first One experimental data point, , To obtain the minimum and maximum values; Then, choose the adaptive discrete interval. Generate discrete point series , This is the index of the data points in the discrete point column.
[0010] Preferred options for selecting adaptive discrete intervals include: ; In the formula, , These are the preprocessed numbers. The, the One experimental data point, This is a function used to return the median of a number.
[0011] Preferably, in step 3, the formula for calculating the basic membership degree is: ; in, Basic membership degree; , is a discrete point sequence Medium data points ; The determination of measurement error caused by error; The number of data points in the neighborhood; For the preprocessed first One set of experimental data; For the first The experimental measurement response data corresponding to each experimental data point.
[0012] Preferably, in step 4, the step-by-step processing includes: First, for each data point in the discrete point sequence, a ladder node is defined as the position of all experimental data in the corresponding neighborhood, and a basic membership degree is assigned. Then, sort all the ladder nodes to form an ordered node sequence, and then according to... By assigning values, we obtain a step-shaped empirical membership function curve. Indicates the first The right limit of each step node Indicates the first The left limit of each step node, Indicates the basic membership degree. This represents the processed membership degree.
[0013] Preferably, the measurement error introduced by the error is obtained through repeated experiments, and the expression is: ; in, For absolute error limit, The relative error coefficient, For the first The experimental measurement response data corresponding to each experimental data point.
[0014] Preferably, in step four, the model verification method based on fuzzy uncertainty area measurement is expressed as follows: ; In the formula, The area difference between the model membership function curve and the experimentally measured empirical membership function curve; To calculate the membership function of the model, To calculate the response of the model; For experimental measurements, the empirical membership function, This is the response measured in the experiment.
[0015] Preferably, the model validation method based on fuzzy uncertainty area measurement also includes making a judgment based on the area difference, as follows: Based on the actual accuracy requirements, determine the acceptance criteria for model deviation and calculate the difference in the true area of the two membership function curves; When the actual area difference is less than the acceptance criterion, the model is accepted and a validated model is obtained; when the actual area difference is greater than the acceptance criterion, the model is rejected and the model is modified.
[0016] Therefore, the area measurement method confirmed by the above-mentioned fuzzy uncertainty structural system model in this invention has the following technical effects: (1) This invention proposes a model validation system and implementation method based on fuzzy uncertainty area measurement. Compared with traditional probability and statistics methods, this method is applicable to small sample data, fuzzy variables and non-random uncertainty scenarios, providing a new mathematical tool for model validation.
[0017] (2) The method proposed in this invention uses a step-type membership function to construct a fuzzy set representation of experimental data when dealing with fuzzy uncertainty quantification, avoiding prior assumptions about the distribution of measurement error, and is suitable for engineering scenarios where sensor accuracy is limited or environmental interference is significant.
[0018] (3) This invention proposes a fuzzy area metric index, which quantifies the inconsistency between the two by calculating the intersection area of the membership functions of the model output and the experimental data. It is a simple and effective reliability analysis calculation method that is applicable to practical applications in aviation, aerospace and other engineering fields.
[0019] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description
[0020] Figure 1 This is a flowchart of an area measurement method for confirming a fuzzy, uncertain structural system model; Figure 2 An area measurement method for confirming a fuzzy, uncertain structural system model, using arbitrary level cuts of fuzzy numbers in an embodiment. Schematic diagram; Figure 3 It is an empirical membership function measured experimentally in an embodiment of an area measurement method confirmed by a fuzzy uncertain structural system model; Figure 4 This is a schematic diagram of an area measurement method in an embodiment of an area measurement method for confirming a fuzzy, uncertain structural system model. Detailed Implementation
[0021] The present invention will be explained in more detail through the following embodiments. The purpose of disclosing the present invention is to protect all changes and modifications within the scope of the present invention. The present invention is not limited to the following embodiments.
[0022] like Figure 1 As shown, this invention provides an area measurement method for confirming a fuzzy, uncertain structural system model, specifically including: Step 1: In the actual engineering model verification problem, consider the fuzzy uncertainty of the model parameters in the calculation model and the actual experimental measurement error.
[0023] According to fuzzy set theory, in the domain X A fuzzy set on It refers to, to , by mapping The determined set. Expressing elements Belonging to The degree of fuzziness is called a fuzzy set. The membership function (MF). Quantization of fuzzy sets elements in The membership degree is the degree of membership. A key difference between classic exact sets and fuzzy sets is that the membership degree of an exact set can only take one of two values, 0 or 1, while the membership degree of a fuzzy set can take any value between 0 and 1.
[0024] A fuzzy set can be completely characterized by its membership function. When the fuzzy number is convex, its relationship with ordinary sets can be described by the concept of cut sets, the decomposition theorem, and the extension principle. Fuzzy Sets of The level cut set can be defined by the following formula: .
[0025] If it exists ,make And for , If the interval is closed, then This is called a convex fuzzy number. The membership function is defined as: ; Among them, the left branch for A monotonically increasing function, right branch for A monotonically decreasing function. For example... Figure 2 As shown, convex fuzzy number of Horizontal cut set For a closed interval with a definite boundary, its upper bound is... Lower Boundary for: .
[0026] If a certain convex fuzzy number is known arbitrary membership level Excerpt Then this convex fuzzy number can be expressed as: .
[0027] set up For in the domain If the variable takes a value above, then the proposition " yes "The defined variables" In other words, a variable whose values are subject to fuzzy restrictions is called a fuzzy variable. The probability distribution function of a fuzzy variable is numerically equal to... The membership function is expressed as .
[0028] Since any fuzzy number can be expressed in the above interval form, any fuzzy variable defined by the fuzzy number can be expressed as: .
[0029] In practical engineering, due to limitations in cognitive level and data acquisition, computational models often contain fuzzy uncertainties. Let the expression of a computational model containing fuzzy uncertainties be: ; in, yes n A controllable input vector is a deterministic variable; yesm The model parameters are fuzzy, uncertain variables, and their values are determined by the membership function. The determination is made. Due to the fuzzy uncertainty in the model parameters, the model output response is determined through uncertainty propagation. It is also a fuzzy variable and conforms to the rules of convex fuzzy numbers; its corresponding membership function is denoted as... .
[0030] In the model validation problem, the experimental measurement results of the system can be obtained from... The experimental point where the experiment was measured is denoted as . Let the empirical membership function of the experimental measurement be . ,in yes n A controllable input vector is a deterministic variable; Let be the measurement error, and be a fuzzy uncertainty variable. The corresponding membership function can be expressed as: .
[0031] Step 2: Due to membership level and fuzzy variables It is a highly nonlinear implicit functional relationship, therefore, directly and accurately solving for the lower and upper bounds of the membership level involves a very large amount of computation. Given a membership level... Below, the computational model The fuzzy variables in the equation are degenerated into interval variables, and the membership levels are calculated using an optimization method (in this embodiment, a sequential quadratic optimization method is used). Below The upper and lower boundary values are... traversal Given the range of values for [0,1], the membership function of the computational model can be obtained, i.e., based on... Membership function curves for constructing computational models .
[0032] Step 3: In actual engineering measurements, due to limitations in the accuracy of sampling equipment, environmental interference, and cost constraints, the experimental data obtained is essentially a discrete set of points. These discrete values cannot accurately reflect the true distribution of continuous physical quantities and have the following uncertainties: random errors caused by sensor accuracy, sampling intervals caused by the lack of local information due to discontinuous sampling, and systematic errors introduced by disturbances such as temperature / vibration.
[0033] Traditional probability and statistics require a large sample size and well-defined distributions, while fuzzy set theory directly quantifies the degree of "belonging to a certain concept" through membership functions, making it more suitable for handling common engineering data. Considering the membership degrees between collected discrete points, the empirical membership function of experimentally measured responses under fuzzy uncertainty... Set it to a stepped line type, such as Figure 3As shown. This type of step-shaped membership function, without prior knowledge, does not assume any pattern of change between points, reflecting information conservation. The detailed construction steps are as follows: Step 1: Preprocess the data.
[0034] First, the Tukey fences method is used to remove outliers, with the effective range of values being [value missing]. ,in Interquartile range, , These are the first quartile and the third quartile, respectively. Data points within the valid interval are retained and denoted as... , For the preprocessed first One experimental data point, For the first The experimental measurement response data corresponding to each experimental data point To retain the number of data points.
[0035] Then, the experiment was repeated to establish the definite measurement error caused by the error. ,as follows: ; in, For absolute error limit, This is the relative error coefficient.
[0036] Step 2: Discretize the universe of discourse.
[0037] To continue discretizing within the universe of discourse, the first step is to define the boundary of the universe of discourse X: ; .
[0038] Then, choose the adaptive discrete interval. Generate discrete point series .
[0039] In this embodiment, , This function returns the median of a set of values.
[0040] Step 3: Membership assignment.
[0041] First, for each Determine its neighborhood Then, calculate the basic membership degree. ,as follows: ; In the formula, This indicates the number of experimental data in the neighborhood.
[0042] Step 4: Step-by-step processing.
[0043] For each Define a ladder node As a neighborhood All The location, and through All ladder nodes are arranged in ascending order of experimental data values to form an ordered node sequence. ,Right now .
[0044] In each interval inside, take , Indicates the right limit. Indicates the left limit, This represents the processed membership degree.
[0045] Based on the detailed steps of constructing the empirical membership function according to the above experimental measurements, it can be based on... Samples of the test measurement system response Constructing the empirical membership function curve of the experimental measurement system .
[0046] Step 4: Based on the model validation method using fuzzy uncertainty area measurement, the area difference between the membership function of the computational model and the empirical membership function of the experimental measurements is obtained to quantitatively evaluate the difference between the computational model and the experimental data, as detailed below: like Figure 4 As shown, based on the membership function of the calculation model obtained in step two... The empirical membership function of the experimental measurements obtained in step three The area difference between the membership function curve of the calculation model and the empirical membership function curve measured in experiments is calculated. The calculation formula is as follows: .
[0047] Based on area difference To make a judgment, first determine the acceptance criteria for model deviation based on the actual accuracy requirements. Then, the difference in the true area of the two membership function curves is calculated. When the actual area difference is less than the acceptance standard At this point, the model is accepted, and a validated model is obtained; when When the actual area difference is greater than the acceptance standard At this point, the model should be rejected and needs to be modified.
[0048] Therefore, the present invention adopts the above-mentioned area measurement method for confirming a fuzzy uncertainty structural system model, which comprehensively considers the uncertainties in the model and the experiment. By calculating the area difference between the model membership function curve and the experimentally measured empirical membership function curve, the difference between the calculated model and the true value is quantitatively measured, thereby improving the accuracy and reliability of model confirmation.
[0049] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.
Claims
1. An area measurement method for confirming a fuzzy, uncertain structural system model, characterized in that, include: Step 1: In the actual engineering model verification problem, based on fuzzy set theory, fuzzy uncertainties of model parameters and measurement errors are introduced into the computational model; The input of the computational model based on fuzzy uncertainty includes deterministic variables and fuzzy uncertain variables, and the output response is a fuzzy uncertain variable. The distribution law of the uncertain variables is determined by the corresponding membership function. Step 2: Calculate the upper and lower boundary values of the output response of the computational model under a given membership level using optimization methods. Traverse the value range of the membership level [0,1] to obtain the membership function curve of the computational model. The membership function of the computational model is divided into a left branch and a right branch. The left branch is a monotonically increasing function, and the right branch is a monotonically decreasing function. Step 3: The empirical membership function of experimental measurement under fuzzy uncertainty is constructed in the form of a stepped line through data preprocessing, universe discretization, membership degree assignment and stepped processing. Step 4: Based on the fuzzy uncertainty area metric, the model validation method is used to obtain the area difference between the corresponding curves of the membership function of the computational model and the empirical membership function of the experimental measurement, and to quantitatively evaluate the difference between the computational model and the experimental data.
2. The area measurement method for confirming a fuzzy uncertain structural system model according to claim 1, characterized in that, Step two includes, given a membership level, degenerating the fuzzy variables of the computational model into interval variables, and using optimization methods to calculate the upper and lower boundary values of the computational model's response at the given membership level; then, by traversing the value interval of the membership level, the membership function curve of the computational model is obtained.
3. The area measurement method for confirming a fuzzy uncertain structural system model according to claim 1, characterized in that, Step three includes: Step 1: Based on the interquartile range method, outliers in the experimental data are removed, data points within the valid range are retained, and the measurement error caused by the error is determined. Step 2: Based on the measurement error determined in Step 1, further discretize the data in the universe of discourse to generate a discrete point sequence; Step 3: For each data point in the discrete point sequence, determine the corresponding neighborhood based on the determined measurement error, and calculate the basic membership degree; Step 4: Construct the empirical membership function curve of the experimental measurement through step-wise processing.
4. The area measurement method for confirming a fuzzy uncertain structural system model according to claim 3, characterized in that, Step 2 includes: First, define the boundary of the universe of discourse X: ； ； In the formula, , For the domain The lower and upper boundaries, The measurement error caused by the error. For the preprocessed first One experimental data, , To obtain the minimum and maximum values; Then, choose the adaptive discrete interval. Generate discrete point series , This is the index of the data points in the discrete point column.
5. The area measurement method for confirming a fuzzy uncertain structural system model according to claim 4, characterized in that, The adaptive discrete interval options include: ； In the formula, , These are the preprocessed numbers. The, the One experimental data point, This is a function used to return the median of a number.
6. The area measurement method for confirming a fuzzy uncertain structural system model according to claim 5, characterized in that, In step 3, the formula for calculating the basic membership degree is: ； in, Basic membership degree; , representing a discrete point sequence Mid-data points The neighborhood; The measurement error is determined by the error itself; The number of data points in the neighborhood; For the preprocessed first One set of experimental data; For the first The experimental measurement response data corresponding to each experimental data point.
7. The area measurement method for confirming a fuzzy uncertain structural system model according to claim 6, characterized in that, Step 4, the step-by-step processing includes: First, for each data point in the discrete point sequence, a ladder node is defined as the position of all experimental data in the corresponding neighborhood, and a basic membership degree is assigned. Then, sort all the ladder nodes to form an ordered node sequence, and then according to... By assigning values, we obtain a step-shaped empirical membership function curve. Indicates the first The right limit of each step node Indicates the first The left limit of each step node, Indicates the basic membership degree. This represents the processed membership degree.
8. The area measurement method for confirming a fuzzy uncertain structural system model according to claim 4 or claim 6, characterized in that, The definite measurement error introduced by the error is obtained through repeated experiments, and its expression is: ； in, For absolute error limit, The relative error coefficient, For the first The experimental measurement response data corresponding to each experimental data point.
9. The area measurement method for confirming a fuzzy uncertain structural system model according to claim 1, characterized in that, In step four, the model validation method based on fuzzy uncertainty area measurement is expressed as follows: ； In the formula, The area difference between the model membership function curve and the experimentally measured empirical membership function curve; To calculate the membership function of the model, To calculate the response of the model; For experimental measurements, the empirical membership function, This is the response measured in the experiment.
10. The area measurement method for confirming a fuzzy uncertain structural system model according to claim 1, characterized in that, Model validation methods based on fuzzy uncertainty area measurement also include making judgments based on area differences, as follows: Based on the actual accuracy requirements, determine the acceptance criteria for model deviation and calculate the difference in the true area of the two membership function curves; When the actual area difference is less than the acceptance criterion, the model is accepted and a validated model is obtained; when the actual area difference is greater than the acceptance criterion, the model is rejected and the model is modified.