A multi-source uncertainty robust quantization method, system and application

Abstract

The application discloses a multi-source uncertainty robust quantification method, system and application, belongs to the technical field of uncertainty quantification, and comprises the following steps: S1, acquiring a multi-source uncertainty original input object; S2, preprocessing the multi-source uncertainty original input object; S3, performing key parameter estimation based on a preprocessing result and performing abnormal sample processing in combination with a Mahalanobis distance; S4, constructing a robust hyperellipsoid submodel and a multi-hyperellipsoid combination structure according to the acquired key parameters; S5, adopting a hierarchical solving strategy of outer shape parameter searching and inner scale optimization to obtain optimal shape parameters, optimal scale parameters and a final model; and S6, outputting the final result generated in the above steps to a downstream system through a local interface, a remote interface or a software module calling mode. The application provides a multi-source uncertainty robust quantification method, system and application, and realizes robust modeling, stable solving and unified parameter output.

Description

Technical Field

[0001] This invention relates to the field of uncertainty quantification technology, and in particular to a robust quantification method, system and application for multi-source uncertainty. Background Technology

[0002] With the development of complex engineering equipment, structural systems, digital prototypes, and multidisciplinary design tasks, the demand for modeling, analysis, and decision-making for multi-source uncertainties is constantly increasing. In existing engineering scenarios, input variables typically come from experimental samples, simulation samples, historical operating samples, and experience samples. These different sources often share characteristics such as limited sample size, a small number of outliers, complex variable correlations, and distinct working condition segments.

[0003] In existing technologies, ellipsoidal domain modeling based on sample mean and sample covariance, nonlinear fitting based on geometric envelope, and hyperellipsoidal modeling for a single set of uncertainties are commonly used to process related objects. These methods can meet basic requirements in scenarios with few normal, single-source, and outlier samples and weak variable coupling. However, when faced with target scenarios involving multiple source samples, a small number of outliers, and multiple related structures, these methods still struggle to simultaneously achieve robustness, numerical stability, and multi-source expansion capability. Therefore, it is necessary to propose a technical solution that can achieve robust modeling, stable solution, and unified parameter output. Summary of the Invention

[0004] The purpose of this invention is to provide a robust quantification method, system, and application for multi-source uncertainty, in order to solve the problems of outlier sensitivity, severe coupling of model parameters, difficulty in scaling to complex multi-source scenarios, and difficulty in directly serving engineering software deployment in the prior art.

[0005] To achieve the above objectives, this invention provides a robust quantification method for multi-source uncertainty, comprising the following steps: S1. Obtain the original input objects of multi-source uncertainty, including sample data, source labels, operating condition labels, or variable grouping information; S2. Perform preprocessing, grouping, cleaning, and structuring operations on the original input objects with multi-source uncertainties; S3. Estimate key parameters based on preprocessing results and process outlier samples using Mahalanobis distance; S4. Construct a robust hyperellipsoidal sub-model and a multi-hyperellipsoidal combination structure based on the obtained key parameters; S5. A hierarchical solution strategy of searching for outer shape parameters and optimizing inner scale is adopted to obtain the optimal shape parameters, optimal scale parameters and final model. S6. Output the final results generated in the above steps to the downstream system through local interface, remote interface or software module call.

[0006] Preferably, step S2 specifically includes: reading and formatting the original input objects with multi-source uncertainty, identifying and processing abnormal missing items, and grouping samples or variables according to variable source, variable correlation, operating condition mode, or physical attributes, thereby generating a standardized data structure for subsequent modeling. The key function of the above steps is that instead of treating all samples as a single whole for direct modeling, a structured entry point of "sample group / variable group / operating condition group" is pre-established for subsequent multi-hyperellipsoidal combination modeling.

[0007] Preferably, step S3 specifically includes: S31, for a given data point of the sample The robust center is obtained by using the minimum covariance determinant. and robust covariance ;in, For the first One sample, for 3D variable space, For sample serial number, The total number of samples; S32, regarding the obtained robust covariance Perform eigenvalue decomposition: ; in, It is a diagonal matrix. For eigenvalues, The eigenvector matrix is ​​used as the principal axis direction of the main distribution. S33. Based on Mahalanobis distance and threshold judgment, abnormal samples are removed, downweighted or marked, and the samples are divided into in-points and out-points according to the chi-square distribution quantile threshold. S34. Estimate the rotation matrix of the hyperellipsoid model based on the principal axis direction. and center coordinates , represented as: .

[0008] Preferably, the formula for dividing the interior and exterior points in step S33 is as follows: ; Conversely, it is an exterior point; among which, For the sample Mahalanobis distance to all samples Let be the chi-square distribution bit function. Quantities.

[0009] Preferably, step S4 specifically includes: S41. Based on the center parameters and direction parameters output in step S3, establish the principal axis coordinate representation: ; in, For the original space variables, For the corresponding number Scale parameters in each dimension; S42. Establish a single robust hyperellipsoidal sub-model based on the scattering parameters, scale parameters, and shape parameters; S43. When the object is a multi-source uncertainty scenario, construct multiple sub-models based on variable grouping, source grouping, or related structure grouping. ; S44. The uncertainty domain of the overall multi-hyperellipsoid is formed by combining blocks.

[0010] Preferably, the hyperellipsoidal sub-model in step S42 is expressed parametrically in principal axis coordinates: ; in, For shape parameters, when When it is a classical ellipsoid; when As time progresses, the model boundary gradually approaches an axis-aligned hyperrectangle; this expression naturally extends the modeling of a single hyperellipsoid to the modeling of multiple hyperellipsoid combinations.

[0011] Preferably, step S5 specifically includes: S51. Use a grid search to search for the outer shape parameters; S52. Given the outer shape parameters, the volume calculation of the hyperellipsoid model is related to the scale parameter. Define the convex optimization model as the optimal hyperellipsoid model: ; in, For the first The first standard space sample Dimensional variables; S53. A double-layer nested optimization strategy is adopted, with the outer layer focusing on shape parameters. Perform a grid search , The inner layer represents the mesh search range for each candidate shape parameter. The globally optimal scale is obtained from the convex optimization model in step S52 through an optimization algorithm. Finally, the outermost layer is chosen to minimize the overall volume. Finally, the outer shape parameters are obtained. With the inner optimal scale parameter ; S54. Based on the solution results, output the final parameterized uncertainty quantification model.

[0012] This invention also provides a robust quantization system for multi-source uncertainty, comprising: The data acquisition module is used to acquire raw input object data from multiple sources with uncertainties. The preprocessing module is used to preprocess the original input object data with multi-source uncertainty. The parameter estimation module is used to estimate the center parameter, orientation parameter, and scattering parameter, and to identify anomalous samples; The model building module is used to build a single hyperellipsoid model or a combination of multiple hyperellipsoid models. The solution and optimization module is used to perform hierarchical solution and optimization on the constructed model; The results output module is used to generate parameter results, graphical results, and interface results. The application interface module provides an entry point for downstream analysis, optimization, or decision-making systems.

[0013] This invention also provides an application of a robust quantification method for multi-source uncertainty, which can be applied to reliability analysis, optimization design, uncertainty propagation, and digital prototype scenarios.

[0014] Therefore, the present invention employs the above-mentioned robust quantification method, system, and application for multi-source uncertainty, and has the following beneficial effects: (1) It has stronger robustness and can suppress the interference of a small number of outliers on center, pose and scale estimation; (2) It has better numerical stability and reduces parameter coupling through the hierarchical structure of outer search and inner solution; (3) It has higher interpretability and can output clear center, orientation, scale and shape parameters; (4) It has stronger multi-source extension capability and supports the extension from a single model to a multi-hyperellipsoid combination model; (5) It has better system implementation capabilities and can generate structured results that can be directly called by engineering software, analysis platforms and interface services.

[0015] 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

[0016] Figure 1 This is a flowchart of a robust quantification method for multi-source uncertainty according to the present invention; Figure 2 This is a schematic diagram of the two-dimensional optimal model of Embodiment 1 of the present invention; Figure 3 This is a two-dimensional optimization process diagram of Embodiment 1 of the present invention; Figure 4This is a schematic diagram of the first-view three-dimensional optimal model of Embodiment 2 of the present invention; Figure 5 This is a schematic diagram of the second-view three-dimensional optimal model of Embodiment 2 of the present invention; Figure 6 This is a diagram illustrating the three-dimensional optimization process of Embodiment 2 of the present invention. Detailed Implementation

[0017] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0018] Please see Figure 1 A robust quantification method for multi-source uncertainty includes the following steps: S1. Obtain the original input objects of multi-source uncertainty, including sample data, source labels, operating condition labels, or variable grouping information.

[0019] S2. Preprocessing, grouping, cleaning, and structuring the original input objects with multi-source uncertainty: This involves reading and standardizing the format of the original input objects with multi-source uncertainty, identifying and handling abnormal missing items, and grouping samples or variables according to variable source, variable correlation, operating condition mode, or physical attributes to generate a standardized data structure for subsequent modeling. The key function of the above steps is that instead of treating all samples as a single whole for direct modeling, it pre-establishes a structured entry point of "sample group / variable group / operating condition group" for subsequent multi-hyperellipsoidal combination modeling.

[0020] S3. Estimate key parameters based on the preprocessing results, and handle outlier samples using Mahalanobis distance; specifically: S31. Perform center parameter estimation on the sample, preferably using the minimum covariance determinant method to obtain robust centers; S32. Perform scatter parameter estimation on the sample and obtain the robust covariance matrix. S33. Based on the robust covariance matrix, perform eigenvalue decomposition to extract the main distribution axis direction; S34. Based on Mahalanobis distance and threshold criteria, abnormal samples are removed, downweighted, or labeled. S35. Output the key parameters required for subsequent model construction.

[0021] When the present invention employs a robust estimation method, it is preferable to obtain the center of the main sample through robust position estimation, suppress the influence of a small number of outliers through robust dispersion estimation, obtain the principal axis direction through feature decomposition, and remove outliers through Mahalanobis distance. In this embodiment, the specific implementation method is as follows: S31, for a given data point of the sample The robust center is obtained by using the minimum covariance determinant (MCD). and robust covariance ;in, For the first One sample, for 3D variable space, For sample serial number, The total number of samples; S32, regarding the obtained robust covariance Perform eigenvalue decomposition: ; in, It is a diagonal matrix. For eigenvalues, The eigenvector matrix is ​​used as the principal axis direction of the main distribution. S33. Based on Mahalanobis distance and threshold judgment, outlier samples are removed, downweighted, or marked, and the samples are divided into inliers and outliers according to the chi-square distribution quantile threshold: ; Conversely, it is an exterior point; among which, For the sample Mahalanobis distance to all samples Let be the chi-square distribution bit function. Quantities.

[0022] S34. Estimate the rotation matrix of the hyperellipsoid model based on the principal axis direction. and center coordinates , represented as: .

[0023] S4. Construct a robust hyperellipsoidal sub-model and a multi-hyperellipsoidal combination structure based on the obtained key parameters; specifically including: S41. Based on the center parameters and direction parameters output in step S3, establish the principal axis coordinate representation: ; in, For the original space variables, For the corresponding number Scale parameters in each dimension; S42. A single robust hyperellipsoidal sub-model is established based on the scattering parameters, scale parameters, and shape parameters, and expressed parametrically in principal axis coordinates: ; in, For shape parameters, when When it is a classical ellipsoid; when As time progresses, the model boundary gradually approaches an axis-aligned hyperrectangle; this expression naturally extends the modeling of a single hyperellipsoid to the modeling of multiple hyperellipsoid combinations.

[0024] S43. When the object is a multi-source uncertainty scenario, construct multiple sub-models based on variable grouping, source grouping, or related structure grouping. ; S44. The uncertainty domain of the overall multi-hyperellipsoid is formed by combining blocks.

[0025] S5. A hierarchical solution strategy of searching for outer shape parameters and optimizing inner scale is adopted to obtain the optimal shape parameters, optimal scale parameters, and final model; specifically including: S51. Use a grid search to search for the outer shape parameters; S52. Given the outer shape parameters, the volume calculation of the hyperellipsoid model is related to the scale parameter. Define the convex optimization model as the optimal hyperellipsoid model: ; in, For the first The first standard space sample Dimensional variables; S53. A double-layer nested optimization strategy is adopted, with the outer layer focusing on shape parameters. Perform a grid search , The mesh search range for the shape parameters is typically between 2 and 8, with a search step of 0.1. The inner layer searches for each candidate shape parameter. The globally optimal scale is obtained from the convex optimization model in step S52 through an optimization algorithm (such as sequential quadratic programming SQP). Finally, the outermost layer is chosen to minimize the overall volume. Finally, the outer shape parameters are obtained. With the inner optimal scale parameter ; S54. Based on the solution results, output the final parameterized uncertainty quantification model. By decomposing the originally highly coupled, nonlinear, and difficult-to-solve problem into a two-level structure of outer search and inner solution, the numerical stability, interpretability, and engineering reproducibility can be significantly improved.

[0026] S6. The generated final results are structurally encapsulated, producing parameter tables, configuration files, visualizations, or model description files. These final results are then output to downstream systems via local interfaces, remote interfaces, or software module calls. This step emphasizes structured output, rather than simply providing a single evaluation value. For multi-hyperellipsoidal scenarios, the preferred unified output content includes: the center of each sub-model, the principal axis direction of each sub-model, the scale parameters of each sub-model, the shape parameters of each sub-model, outlier handling markers, and sub-model combination relationship parameters.

[0027] Based on the above method, the present invention also provides a robust quantification system for multi-source uncertainty, comprising: The data acquisition module is used to acquire raw input object data from multiple sources with uncertainties. The preprocessing module is used to preprocess the original input object data with multi-source uncertainty. The parameter estimation module is used to estimate the center parameter, orientation parameter, and scattering parameter, and to identify anomalous samples; The model building module is used to build a single hyperellipsoid model or a combination of multiple hyperellipsoid models. The solution and optimization module is used to perform hierarchical solution and optimization on the constructed model; The results output module is used to generate parameter results, graphical results, and interface results. The application interface module provides an entry point for downstream analysis, optimization, or decision-making systems.

[0028] The system described above can be deployed as a local software system, a functional module within an analysis platform, a cloud service program, or a computer program product. Modules can be executed sequentially or in parallel by sub-sample groups or sub-models.

[0029] The methods or systems provided above can be applied to, but are not limited to, the following scenarios: 1. Reliability Analysis Scenario: The uncertainty quantification model output by this invention is used to evaluate the reliability of structures, systems or equipment.

[0030] 2. Optimize design scenarios: The parameterized uncertainty model output by this invention provides input boundaries for robust design, robust optimization, or constrained design.

[0031] 3. Uncertainty propagation scenario: The model output by this invention is used as upstream input for simulation analysis, proxy modeling, risk assessment or digital prototype modules to call.

[0032] 4. Digital Prototype Scenario: The multi-hyperellipsoidal combination model output by this invention is used as the whole-machine level or subsystem level parameter domain for multi-source, multi-condition digital prototype modeling.

[0033] The above method is verified through two examples: a two-dimensional sample modeling example and a three-dimensional sample modeling example.

[0034] Example 1 The input is two-dimensional sample data, as shown in Table 1. First, the samples are read, cleaned, and structured; second, robust center estimation, robust scatter estimation, and outlier identification are performed based on MCD; then, a two-dimensional robust hyperellipsoidal model is established; next, the final optimal parameter set is obtained; finally, the model parameters and visualization results are output.

[0035] Table 1 Two-dimensional uncertainty samples

[0036] Robust hyperellipsoid quantization is performed on the above two-dimensional uncertain samples using this method, and the resulting two-dimensional hyperellipsoid model is as follows: Figure 2 and Figure 3 As shown, the relevant model parameters are as follows: ; in, , , Center coordinates Scale parameters and rotation matrix The estimated value.

[0037] The results show that the present invention can stably obtain the envelope model of the main sample under the condition of a small number of noisy samples, while taking into account both robustness and interpretability. As can be seen from the optimization process diagram, the logarithmic ellipsoidal volume has a clear optimum near the candidate shape parameters; as can be seen from the optimal model diagram, outlier samples are effectively identified, and the final model mainly encloses the main sample rather than being abnormally stretched by outliers.

[0038] Example 3 The input is three-dimensional sample data, as shown in Table 2. The processing flow is similar to Example 1, except that the model dimension is increased to three dimensions, and three-dimensional structural features are modeled. First, the samples are structured to complete robust estimation and outlier identification, a three-dimensional robust hyperellipsoid model is established, the optimal parameter set is obtained, and the three-dimensional model results are output.

[0039] Table 2 Three-dimensional uncertainty samples

[0040] Robust hyperellipsoid quantization was performed on the above-mentioned three-dimensional uncertain samples using this method, and the resulting three-dimensional hyperellipsoid model is as follows: Figures 4-6 As shown, the relevant model parameters are as follows: ; The results show that the present invention can stably generate a hyperellipsoidal model containing center, pose, scale, and shape parameters in a 3D scene, and can effectively distinguish a small number of anomalous samples from the main samples. The 3D optimization process diagram shows that the logarithmic ellipsoidal volume also has a clear optimal value as the candidate shape parameters change, proving that the double-layer nested optimization structure is applicable to higher-dimensional cases.

[0041] Therefore, this invention adopts the above-mentioned robust quantification method, system and application for multi-source uncertainty. Through the collaborative design of multi-source sample preprocessing and grouping mechanism, robust key parameter estimation and abnormal sample processing mechanism based on MCD, and hierarchical solution mechanism based on outer shape parameter search and inner scale optimization, a robust multi-hyperellipsoid modeling scheme for multi-source uncertainty sample scenarios is constructed.

[0042] 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. A multi-source uncertainty robust quantization method, characterized in that, Includes the following steps: S1. Obtain the original input objects of multi-source uncertainty, including sample data, source labels, operating condition labels, or variable grouping information; S2. Perform preprocessing, grouping, cleaning, and structuring operations on the original input objects with multi-source uncertainties; S3. Estimate key parameters based on preprocessing results and process outlier samples using Mahalanobis distance; S4. Construct a robust hyperellipsoidal sub-model and a multi-hyperellipsoidal combination structure based on the obtained key parameters; S5. A hierarchical solution strategy of searching for outer shape parameters and optimizing inner scale is adopted to obtain the optimal shape parameters, optimal scale parameters and final model. S6. Output the final results generated in the above steps to the downstream system through local interface, remote interface or software module call method; Step S2 specifically includes: reading and formatting the original input objects of multi-source uncertainty, identifying and processing abnormal missing items, and grouping samples or variables according to variable source, variable correlation, working condition mode or physical attributes, thereby generating a standardized data structure for subsequent modeling. Step S3 specifically includes: S31, for a given data point of a sample , employing minimum covariance determinant to obtain robust center and robust covariance ; wherein, is the th sample, is the dimensional variable space, is the sample sequence number, is the total number of samples; S32, regarding the obtained robust covariance Perform eigenvalue decomposition: ； in, It is a diagonal matrix. For eigenvalues, The eigenvector matrix is ​​used as the principal axis direction of the main distribution. S33. Based on Mahalanobis distance and threshold judgment, abnormal samples are removed, downweighted or marked, and the samples are divided into in-points and out-points according to the chi-square distribution quantile threshold. S34. Estimate the rotation matrix of the hyperellipsoid model based on the principal axis direction. and center coordinates , is represented as: 。 2. The robust quantification method for multi-source uncertainty according to claim 1, characterized in that, The formula for dividing interior and exterior points in step S33 is as follows: ； Conversely, it is an exterior point; among which, For the sample Mahalanobis distance to all samples Let be the chi-square distribution bit function. It represents the quantile.

3. The robust quantification method for multi-source uncertainty according to claim 1, characterized in that, Step S4 specifically includes: S41. Based on the center parameters and direction parameters output in step S3, establish the principal axis coordinate representation: ； in, For the original space variables, For the corresponding number Scale parameters in each dimension; S42. Establish a single robust hyperellipsoidal sub-model based on the scattering parameters, scale parameters, and shape parameters; S43. When the object is a multi-source uncertainty scenario, construct multiple sub-models based on variable grouping, source grouping, or related structure grouping. ; S44. The uncertainty domain of the overall multi-hyperellipsoid is formed by combining blocks.

4. The robust quantification method for multi-source uncertainty according to claim 3, characterized in that, The hyperellipsoidal sub-model in step S42 is expressed parametrically in principal axis coordinates: ； in, For shape parameters, when When it is a classical ellipsoid; when As time progresses, the model boundary gradually approaches an axis-aligned hyperrectangle; this expression naturally extends the modeling of a single hyperellipsoid to the modeling of multiple hyperellipsoid combinations.

5. A robust quantification method for multi-source uncertainty according to claim 3, characterized in that, Step S5 specifically includes: S51. Use a grid search to search for the outer shape parameters; S52. Given the outer shape parameters, the volume calculation of the hyperellipsoid model is related to the scale parameter. Define the convex optimization model as the optimal hyperellipsoid model: ； in, For the first The first standard space sample Dimensional variables; S53. A double-layer nested optimization strategy is adopted, with the outer layer focusing on shape parameters. Perform a grid search , The inner layer represents the mesh search range for each candidate shape parameter. The globally optimal scale is obtained from the convex optimization model in step S52 through an optimization algorithm. Finally, the outermost layer is chosen to minimize the overall volume. Finally, the outer shape parameters are obtained. With the inner optimal scale parameter ; S54. Based on the solution results, output the final parameterized uncertainty quantification model.

6. A robust quantization system for multi-source uncertainty, applied to the robust quantization method for multi-source uncertainty as described in any one of claims 1-5, characterized in that, include: The data acquisition module is used to acquire raw input object data from multiple sources with uncertainties. The preprocessing module is used to preprocess the original input object data with multi-source uncertainty. The parameter estimation module is used to estimate the center parameter, orientation parameter, and scattering parameter, and to identify anomalous samples; The model building module is used to build a single hyperellipsoid model or a combination of multiple hyperellipsoid models. The solution and optimization module is used to perform hierarchical solution and optimization on the constructed model; The results output module is used to generate parameter results, graphical results, and interface results. The application interface module provides an entry point for downstream analysis, optimization, or decision-making systems.

7. An application method of the robust quantification method for multi-source uncertainty as described in any one of claims 1-5, characterized in that: This method can be applied to reliability analysis, optimization design, uncertainty propagation, and digital prototype scenarios.

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