Method for quantifying compressor uncertainty based on adaptive ensemble high-dimensional model representation
By using an adaptive ensemble high-dimensional model representation method, the compressor geometric uncertainty problem is decomposed into first-order and second-order components. Multiple surrogate models are adaptively selected to solve the problems of high computational complexity and insufficient accuracy in the quantification of high-dimensional compressor uncertainty, thus realizing efficient uncertainty propagation analysis and robust design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- XI AN JIAOTONG UNIV
- Filing Date
- 2026-05-20
- Publication Date
- 2026-07-17
Smart Images
Figure CN122413615A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of compressor technology, and in particular to a method for quantifying compressor uncertainty based on an adaptive integrated high-dimensional model representation. Background Technology
[0002] As a core component of aerospace and energy industry equipment, the performance of the compressor directly affects the overall efficiency and reliability of the system. However, in the actual production and processing of compressors, due to the influence of many factors such as processing, operation, and materials, the blade geometry inevitably deviates from the ideal design state. This causes the compressor's operating performance to deviate from the design expectations, which not only goes against the requirements of refined design, but also poses a serious threat to the efficient, stable, safe and reliable operation of the entire machine.
[0003] Uncertainty quantification (UQ) methods provide an effective tool for analyzing the aforementioned problems. However, compressor geometric uncertainties typically exhibit high dimensionality, strong nonlinearity, and multi-scale coupling characteristics. Direct Monte Carlo analysis based on high-fidelity computational fluid dynamics (CFD) is computationally extremely expensive, making it difficult to meet engineering requirements. Therefore, in fields such as turbomachinery, surrogate models have become an important alternative for high-fidelity numerical simulation, enabling rapid and reliable evaluation of aerodynamic performance characteristics. Existing surrogate model methods (such as Kriging, PCE, SVR, and ANN) perform well in low-dimensional problems, but as the dimensionality and complexity of the problem increase, the difficulty of accurately constructing a surrogate model significantly increases, with the "curse of dimensionality" being particularly prominent: to ensure approximate accuracy, the computational cost increases exponentially with the parameter dimension, severely restricting the practical application of surrogate models. Therefore, there is an urgent need to develop new surrogate modeling methods and explore efficient and high-precision solution strategies. High-Dimensional Model Representation (HDMR) is a "divide and conquer" modeling method that can effectively balance prediction accuracy and computational efficiency, alleviating the aforementioned difficulties to some extent. Its core idea is not to directly construct a proxy model in a complete high-dimensional space, but to decompose the original problem into a series of low-dimensional sub-problems, model them separately and then combine them to approximate the original response.
[0004] However, most existing HDMR methods employ a single type of surrogate model to construct low-dimensional components. This "one-size-fits-all" modeling strategy struggles to adapt to the significant differences in nonlinear characteristics, sample distribution, and complexity among different HDMR components, resulting in limited overall accuracy and generalization ability. This is especially true in compressor uncertainty quantification, where complex high-dimensional input-output relationships place higher demands on the accuracy and generalization ability of the surrogate model. Existing HDMR methods (such as RBF-HDMR, SVR-HDMR, and PCE-HDMR) decompose the high-dimensional response function into first-, second-, or even higher-order component functions, and then fit them using a single surrogate model. While these methods reduce computational complexity to some extent, they still suffer from the following shortcomings: all HDMR components use the same surrogate model, lacking specificity; they cannot adaptively select the optimal model based on the nonlinear characteristics of different components; with limited sample size, the overall surrogate accuracy and robustness are insufficient; and their adaptability to complex compressor geometric uncertainties is limited. Summary of the Invention
[0005] To address the aforementioned technical problems, this invention provides a compressor uncertainty quantification method based on adaptive integrated high-dimensional model representation, which is applicable to high-dimensional, nonlinear compressor geometric uncertainty problems.
[0006] This invention provides a method for quantifying compressor uncertainties based on an adaptive ensemble high-dimensional model representation, comprising the following steps: Define compressor uncertainty parameters and normalize them to establish a high-dimensional uncertainty input space; Samples are taken at each one-dimensional boundary of the high-dimensional uncertainty input space, the compressor aerodynamic performance response corresponding to each one-dimensional component sample is calculated, and an initial first-order high-dimensional model is constructed to represent the components. Evaluate the accuracy of all current first-order high-dimensional model representation components and identify the first-order high-dimensional model representation component with the lowest accuracy; For the first-order high-dimensional model representation component with the lowest identified accuracy, multiple different types of surrogate models are used to construct candidate sub-models using the existing sample points of this component. Within the component space, the position with the largest Euclidean distance from all existing points is selected as the new sampling point, and the prediction error at the new sampling point is calculated using each candidate sub-model. Based on the prediction error, the candidate sub-model with the smallest error is selected to update the final surrogate model of the first-order high-dimensional model representation component. Determine whether the updated first-order high-dimensional model representation component meets the preset accuracy threshold; if not, continue iterative optimization of the component; if it does, confirm that the component has been constructed. The final proxy model based on all the first-order high-dimensional model representation components is combined with the zero-order term to form a first-order high-dimensional model representation global proxy model; By using a first-order high-dimensional model to represent the global proxy model to replace computational fluid dynamics simulation, uncertainty propagation analysis is performed on the compressor uncertainty parameter samples that conform to the actual distribution, and the uncertainty quantification results of the compressor aerodynamic performance are obtained.
[0007] Specifically, after combining the components to form a first-order high-dimensional model representing the global proxy model, the process also includes determining whether there are significant second-order components: The prediction accuracy of the first-order high-dimensional model, representing the global surrogate model, is tested at the boundaries of uncertain parameter variables. If the relative error is higher than the second-order trigger threshold, a significant second-order component is determined to exist, and the following second-order component construction sub-process is executed: Identify pairs of uncertain parameters that may be correlated; For the identified parameter pairs, sample their two-dimensional boundaries to construct initial second-order components; An adaptive ensemble strategy similar to that used for modeling the first-order high-dimensional model representation components is adopted to complete the modeling of all second-order components; The first-order high-dimensional model representation components, second-order components, and zero-order terms are combined to form a complete second-order integrated high-dimensional model representation proxy model.
[0008] Specifically, the normalization process uses the following formula: , in Indicates the first One uncertain parameter, For the first Prototype design values of the center point of the space of each parameter variable. For the corresponding tolerance or disturbance range, For the normalized dimensionless variable Specifically, the method for constructing the initial first-order high-dimensional model representation components is as follows: using variables Using two sample points obtained at the upper and lower boundaries, a linear response function is established by determining a straight line from these two points. Specifically, the method for evaluating component accuracy is leave-one-out cross-validation, which quantifies component accuracy by calculating the generalized mean square error.
[0009] Specifically, the formula for calculating the generalized mean square error is as follows: in, Indicates the first The generalized cross-validation mean square error of the components represented by a first-order high-dimensional model. For this component The number of samples, Indicates that the first excluding An HDMR model constructed from individual components. For the dimension of uncertain variables.
[0010] Specifically, several different types of surrogate models are selected from the following set: linear functions, support vector regression, kriging models, multinomial chaotic expansion, radial basis function networks, and artificial neural networks.
[0011] Specifically, the selection strategy for new sampling points is as follows: among the existing sample points of the current component, select the position with the largest sum of Euclidean distances to all existing points as the new sampling point.
[0012] Specifically, methods for identifying potentially correlated pairs of uncertain parameters include: Combination and Form a new sample point The remaining variables retain their values at the center point, and the true response value at that point is calculated. ,in, Indicates the first Each variable takes the value at the upper boundary point. Indicates except the first Besides the three variables, the remaining variables are the sample center point values; similarly, That is to say, the first A first-order high-dimensional model represents components taking values at the upper boundary points. Indicates except the first Apart from one variable, the remaining variables are the sample center point values; Indicates except the first The and the first Apart from one variable, the remaining variables are the sample center point values; Calculate the second-order component values using the following formula. : , in, , The first , A first-order high-dimensional model represents the calculated component values. It is a zero-order term; If the following correlation criteria are met: , Then we consider the variable and There is no significant interaction effect between them, and they are approximately independent; otherwise, the variable is determined. and Since they are correlated, corresponding second-order components need to be constructed, where, , The first , Each variable takes the value at the lower boundary point; This is the second-order trigger threshold.
[0013] Specifically, after performing uncertainty propagation analysis using the surrogate model, the process also includes an overall performance evaluation of the constructed surrogate model. Test samples were generated using the Latin hypercube sampling method, with the number of test samples being 5-10 times the number of variable dimensions. The prediction error is evaluated using the coefficient of determination, relative mean absolute error, and relative maximum absolute error. The determination is made using a combination of criteria: the coefficient of determination is not lower than the first preset threshold, the relative average absolute error is not higher than the second preset threshold, and the relative maximum absolute error is not higher than the third preset threshold.
[0014] Compared with existing technologies, the technical solution provided by this invention has the following advantages: It decomposes high-dimensional problems into multiple first- and second-order components using the HDMR framework and introduces an adaptive iterative optimization strategy. When constructing each component, multiple candidate surrogate models are used, and the optimal model type is dynamically selected based on the prediction error of newly added sampling points. This specifically addresses the limitation of the curse of dimensionality and one-size-fits-all modeling in existing methods for high-dimensional, strongly nonlinear problems. By identifying the component with the lowest accuracy and locally refining sampling, valuable CFD computing resources are concentrated in key areas, significantly reducing the overall computational cost required for high-dimensional modeling. Through adaptive integration of different surrogate models, each component can match its own nonlinear characteristics, overcoming the problem of insufficient generalization ability of a single model and significantly improving the fitting accuracy and robustness of strongly nonlinear responses under complex compressor geometric perturbations. Finally, the constructed adaptive integrated HDMR surrogate model can approach high-fidelity simulation accuracy under limited sample conditions, achieving efficient uncertainty propagation analysis of a large number of random samples, providing a reliable basis for the robust design of compressors. Attached Figure Description
[0015] Figure 1 The flowchart illustrates an adaptive ensemble high-dimensional model representation modeling algorithm provided in this embodiment of the invention. Detailed Implementation
[0016] The following detailed description of a specific embodiment of the present invention is provided in conjunction with the accompanying drawings. However, it should be understood that the scope of protection of the present invention is not limited to the specific embodiment.
[0017] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the technical solution of this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.
[0018] The present invention will be described below through several specific embodiments. To keep the following description of the embodiments clear and concise, detailed descriptions of known functions and components may be omitted. When any component of an embodiment of the present invention appears in more than one drawing, the component may be represented by the same reference numerals in each drawing.
[0019] Figure 1 The flowchart illustrates an adaptive ensemble high-dimensional model representation modeling algorithm provided in this embodiment of the invention.
[0020] like Figure 1 As shown, this invention provides a compressor uncertainty quantification method based on adaptive integrated high-dimensional model representation, comprising the following steps: defining compressor uncertainty parameters and performing normalization processing to establish a high-dimensional uncertainty input space; sampling at each one-dimensional boundary of the high-dimensional uncertainty input space, calculating the compressor aerodynamic performance response corresponding to each one-dimensional component sample, and constructing an initial first-order high-dimensional model representation component; evaluating the accuracy of all current first-order high-dimensional model representation components, and identifying the first-order high-dimensional model representation component with the lowest accuracy; for the identified first-order high-dimensional model representation component with the lowest accuracy, employing multiple different types of surrogate models, and constructing candidate sub-models using the existing sample points of this component; within this component space, selecting the position with the largest Euclidean distance to all current existing points. The sample is designated as a new sampling point, and the prediction error at the new sampling point is calculated using each candidate sub-model. The candidate sub-model with the smallest prediction error is selected to update the final surrogate model of the first-order high-dimensional model representation component. It is determined whether the updated first-order high-dimensional model representation component meets the preset accuracy threshold. If it does not meet the threshold, the component is iteratively optimized. If it does meet the threshold, the component is confirmed to be constructed. Based on the final surrogate models of all constructed first-order high-dimensional model representation components, the zero-order term is combined to form a global surrogate model of the first-order high-dimensional model representation. The global surrogate model of the first-order high-dimensional model representation is used to replace the computational fluid dynamics simulation to perform uncertainty propagation analysis on the compressor uncertainty parameter samples that conform to the actual distribution, and obtain the uncertainty quantification results of the compressor aerodynamic performance.
[0021] Furthermore, considering the potentially complex interactions between compressor geometric parameters, using only a first-order model for approximation would make it difficult to guarantee prediction accuracy when significant coupling exists between variables. Therefore, it is necessary to further determine whether significant second-order components exist and, if necessary, construct a second-order model to more accurately describe the impact of nonlinear interactions between variables on aerodynamic performance. Based on this, embodiments of the present invention also provide the following technical solutions:
[0022] Specifically, after combining to form a first-order high-dimensional model representation global surrogate model, the process also includes a step to determine whether there are significant second-order components: checking the prediction accuracy of the first-order high-dimensional model representation global surrogate model at the boundaries of uncertain parameter variables; if the relative error is higher than the second-order trigger threshold, it is determined that there are significant second-order components, and the following second-order component construction sub-process is executed: identifying uncertain parameter pairs that may be correlated; sampling the two-dimensional boundaries of the identified parameter pairs to construct initial second-order components; using an adaptive ensemble strategy similar to that used for modeling the first-order high-dimensional model representation components to complete the modeling of all second-order components; combining the first-order high-dimensional model representation components, second-order components, and zero-order terms to form a complete second-order adaptive ensemble high-dimensional model representation surrogate model.
[0023] Furthermore, when establishing a high-dimensional uncertain input space, since different physical parameters have different dimensions and value ranges, directly using the original parameters for modeling may lead to unstable numerical calculations or the model being overly sensitive to certain parameters. The above embodiments mention normalization processing. Based on this, this embodiment of the invention provides a specific normalization calculation formula as a preferred solution, mapping the original parameters to a dimensionless standard variable space to eliminate the influence of dimensions and ensure the scientific nature and numerical stability of the modeling process.
[0024] Specifically, the normalization process uses the following formula: , in Indicates the first One uncertain parameter, For the first Prototype design values of the center point of the space of each parameter variable. For the corresponding tolerance or disturbance range, This refers to the dimensionless variable after normalization.
[0025] Furthermore, when constructing the initial first-order high-dimensional model representation components, a simple and effective initialization method is needed to quickly establish the basic mapping relationship between each one-dimensional variable and aerodynamic performance. The above embodiments mention constructing the initial first-order high-dimensional model representation components. As a preferred solution, this embodiment of the invention uses linear fitting with two sample points at the upper and lower boundaries of the variables. This allows for obtaining preliminary approximations of each component with a very small number of samples, providing a foundation for subsequent iterative optimization and adaptive selection.
[0026] Specifically, the method for constructing the initial first-order high-dimensional model representation components is as follows: using variables The linear response function is established by using two sample points obtained at the upper and lower boundaries to determine a straight line.
[0027] Specifically, it is necessary to evaluate the accuracy of each first-order high-dimensional model representation component to identify and optimize the component with the lowest current accuracy. However, it is difficult to scientifically quantify the modeling quality of each component based solely on subjective judgment or simple error comparison. Therefore, this invention provides an improved approach that introduces an objective and quantitative accuracy evaluation method to ensure the accuracy and reliability of the identification process. Leave-one-out cross-validation can fully utilize limited sample information, obtaining a reliable estimate of the model's generalization ability by eliminating samples one by one and evaluating prediction errors.
[0028] Specifically, the method for evaluating component accuracy is leave-one-out cross-validation, which quantifies component accuracy by calculating the generalized mean square error.
[0029] Furthermore, when using leave-one-out cross-validation to evaluate component accuracy, specific quantitative indicators are needed to characterize the error magnitude. Generalized mean square error (GMSE) comprehensively reflects the prediction bias of the model across different sample points and is a commonly used indicator for evaluating model accuracy. This invention, as a preferred embodiment, clarifies the calculation method of GMSE and the physical meaning of its parameters.
[0030] Specifically, the formula for calculating the generalized mean square error is as follows: in, Indicates the first The generalized cross-validation mean square error of the components represented by a first-order high-dimensional model. For this component The number of samples, Indicates that the first excluding An HDMR model constructed from individual components. For the dimension of uncertain variables.
[0031] Furthermore, when adding new sampling points, a scientific sampling strategy is needed to maximize the efficiency of sample information acquisition and avoid sampling redundancy or omissions. Inappropriate sampling point selection may lead to low sample efficiency, limited improvement in modeling accuracy, or even getting stuck in local optimization. Therefore, this embodiment of the invention, as a preferred solution, clearly defines the selection strategy for new sampling points to ensure that each new sample maximizes model accuracy.
[0032] Specifically, several different types of surrogate models are selected from the following set: linear functions, support vector regression, kriging models, multinomial chaotic expansion, radial basis function networks, and artificial neural networks.
[0033] Furthermore, when determining the existence of second-order components, it is necessary to identify which pairs of variables exhibit significant interaction effects. Relying solely on empirical judgment or simple comparisons makes it difficult to scientifically determine which pairs of variables require the construction of second-order components. Therefore, as a preferred embodiment, this invention quantifies the degree of coupling between variables by comparing the differences between the predicted and actual values of the constructed first-order model at the combined boundary points.
[0034] Specifically, the selection strategy for new sampling points is as follows: among the existing sample points of the current component, select the position with the largest sum of Euclidean distances to all existing points as the new sampling point.
[0035] Specifically, methods for identifying potentially correlated pairs of uncertain parameters include: combining and Form a new sample point The remaining variables retain their values at the center point, and the true response value at that point is calculated. Calculate the second-order component values using the following formula. ,in, Indicates the first Each variable takes the value at the upper boundary point. Indicates except the first Besides the three variables, the remaining variables are the sample center point values; similarly, That is to say, the first A first-order high-dimensional model represents components taking values at the upper boundary points. Indicates except the first Apart from one variable, the remaining variables are the sample center point values; Indicates except the first The and the first Apart from one variable, the remaining variables are the sample center point values. , in, , The first , A first-order high-dimensional model represents the calculated component values. It is a zero-order term; if the following correlation criteria are met: , Then we consider the variable and There is no significant interaction effect between them, and they are approximately independent; otherwise, the variable is determined. and Since they are correlated, corresponding second-order components need to be constructed, where, , The first , Each variable takes the value at the lower boundary point; This is the second-order trigger threshold.
[0036] Furthermore, after constructing the surrogate model, its overall predictive performance needs to be evaluated to verify whether the model meets the accuracy requirements of uncertainty quantification. Performing only uncertainty propagation analysis without evaluating the reliability of the surrogate model itself may compromise the credibility of the uncertainty quantification results. Therefore, a multi-index evaluation system needs to be introduced to comprehensively measure the model's fitting ability, average error level, and local predictive ability, and to establish joint criteria to ensure that the model meets engineering requirements across all indicators. Based on this, this invention provides an improved approach.
[0037] Specifically, after performing uncertainty propagation analysis using the surrogate model, the process also includes a step of evaluating the overall performance of the constructed surrogate model: generating test samples using the Latin hypercube sampling method, with the number of test samples being 5-10 times the number of variable dimensions; evaluating the prediction error using the coefficient of determination, relative mean absolute error, and relative maximum absolute error; and determining the prediction error using a joint criterion: the coefficient of determination is not lower than the first preset threshold, the relative mean absolute error is not higher than the second preset threshold, and the relative maximum absolute error is not higher than the third preset threshold.
[0038] In a specific implementation, the uncertainty parameters are defined and normalized by selecting key compressor parameters as uncertainty input variables and establishing a high-dimensional parameter space.
[0039] Specifically, the uncertainties mainly originate from geometric manufacturing errors and assembly deviations, as well as the randomness of actual operating parameters. These include, but are not limited to, geometric parameters such as blade installation angle, blade angle or thickness distribution, blade height, blade tip clearance, impeller inlet diameter, impeller outlet diameter, and meridional channel width; and operating parameters such as inlet total temperature, inlet total pressure, inlet flow rate, incoming flow angle, turbulence intensity, and impeller speed. Since these geometric and operating parameters exhibit a certain range of random fluctuations in actual engineering, the uncertainties are uniformly represented as a parameter vector:
[0040] in, Indicates the first One uncertain parameter, The total number of uncertain parameters is determined based on the compressor design value, manufacturing tolerance, and actual operating condition fluctuation range. The manufacturing tolerance is derived from the equipment design specifications or machining accuracy requirements, and the operating disturbance range can be obtained through historical operating data or experimental measurement results.
[0041] To eliminate the influence of different physical dimensions and value ranges on the modeling process, each uncertainty parameter is normalized and mapped to the dimensionless standard variable space. The normalized variable can be expressed as formula (1).
[0042] (1), in For the first Prototype design values of the center point of the space of each parameter variable. For the corresponding tolerance or disturbance range, This refers to the dimensionless variable after normalization.
[0043] Choose the center point of the variable space. The corresponding aerodynamic performance (such as efficiency, pressure ratio, etc.) of the compressor prototype is calculated using formula (2), that is, the response and zero-order term corresponding to the sample center point. .
[0044] (2), In each variable The upper and lower boundaries (i.e.) and Sampling, and keeping the rest fixed as the center point. Value (i.e.) and Based on existing HDMR theory, the performance of the corresponding sample is calculated using equation (3). It is easy to know .
[0045] (3), The initial first-order HDMR of each component is obtained through linear fitting. Specifically, this is achieved using variables... Two sample points were obtained at the upper and lower boundaries. and A linear response function as shown in equation (4) is established by determining a straight line from two points (this linear function is not a constant function, therefore...). (not both 0).
[0046] (4), Among them, slope and intercept Determined by equation (5): (5), The accuracy of each component is evaluated using leave-one-out cross-validation, and the generalized mean square error is calculated according to equations (6)-(7). Identify the component with the lowest precision among all components of the first-order high-dimensional model representation. As shown in equation (6), Indicates the first The generalized cross-validation mean square error of the components represented by a first-order high-dimensional model. For this component The number of samples, Indicates that the first excluding An HDMR model is constructed using individual components. The component with the lowest accuracy within the first-order term is determined according to equation (7). .
[0047] (6), (7), Multiple candidate surrogate models are pre-defined for the HDMR components, including linear functions, SVR, Kriging, PCE, RBF, and ANN. These candidate surrogate models are commonly used function approximation models in the fields of engineering uncertainty quantification and surrogate modeling, capable of describing the nonlinear mapping relationship between input variables and responses, and each represents a different type of meta-model construction method. Specifically, the linear function is a linear function, SVR is a regression model based on statistical learning theory, Kriging is an interpolation model based on stochastic processes, PCE is a surrogate model based on orthogonal polynomial expansion, RBF is an approximation model based on radial basis functions, and ANN is a nonlinear fitting model based on neural networks. Pre-defining multiple different types of candidate models provides a foundation for subsequent model accuracy evaluation and optimal model selection.
[0048] Utilizing this low-precision component (i.e., the first) In each component, a surrogate model is constructed separately for existing sample points and each meta-model of different types. New sampling points are added to this low-precision component by selecting the point with the largest Euclidean distance to an existing point. To improve the coverage of the sample space, the first-order high-dimensional model representation component response of the sampling point is calculated. ( (If the value is 0, another sampling point is selected). Simultaneously, the prediction error at that point is calculated using the different surrogate models constructed separately above. This allows for the adaptive selection of the model that minimizes prediction error and maximizes accuracy at newly added sampling points, and the corresponding components are updated accordingly. The function form.
[0049] Evaluate the updated components Does it meet the accuracy requirements? Based on the model accuracy requirements, set the prediction error threshold for newly added sample points. For example, a value of 1%-3% can be used to ensure that the construction error of each component's surrogate model is numerically much smaller than the performance change caused by the uncertainty variable. If the error in step 4... Exceeding the threshold Then continue with the component corresponding to Increase sampling and continue updating; otherwise, confirm the component. After completing the modeling, retain the current construction results of all first-order HDMR components and return to step 3. Continue to identify the component with the lowest accuracy. HDMR components that have reached the accuracy threshold will no longer participate in the accuracy evaluation and update of candidate surrogate models in subsequent rounds. Instead, their current best model results will be retained. Only components that have not met the accuracy requirements will continue to be selected and adaptively modeled until all components achieve the required accuracy, i.e., the error of all components at the last new sampling point is lower than the threshold. This completes the construction of the first-order adaptive ensemble HDMR model.
[0050] Check for the existence of second-order components. For each variable, select the upper boundary point and simultaneously obtain... exist Calculated value at (Compressor performance parameters are usually not zero), if based on The calculated error is low enough (i.e.) If the result is negative, it is considered that there is no significant second-order component. The surrogate model is constructed according to the result of step 5, and step 9 is performed directly; otherwise, continue with the following steps.
[0051] In testing compressor uncertainty parameters and The related effects. Combined with and Form a new sample point The remaining variables retain their values at the center point, and the corresponding compressor performance function values are calculated. Since accurate values of the first-order HDMR components at the boundary are already available, this combination of sampling points can effectively reflect the interaction response characteristics at the spatial boundary of the two variables, and can be used to determine whether there is a significant correlation between them. Substituting into equation (8) to calculate the second-order components :
[0052] (8), If equation (9) is satisfied: (9), Then we consider the variable and If there is no significant interaction effect between them, they can be considered approximately independent, and the correlation of other variables can be further assessed; otherwise, the variables are considered independent. and Since the second-order term is correlated, a corresponding second-order component model needs to be established. Among them, This is the second-order trigger threshold, consistent with the error threshold mentioned above.
[0053] Perform the corresponding second-order components The modeling process is similar to the first-order modeling, but the initialization uses the first-order modeling. Four sample points of the second-order component boundary , , , Calculate compressor performance, and the prediction error criterion for newly added sample points is: This continues until all second-order components are constructed. When using leave-one-out cross-validation to identify the component with the lowest accuracy among all second-order components, equations (10)-(11) are used for calculation. For this component The number of samples.
[0054] (10), (11), Construction of a proxy model for quantifying the uncertainty of the overall compressor. If there is no second-order term, the zero-order and first-order high-dimensional model representation components are combined according to Equation (12) to form a first-order HDMR model; if there is a second-order component, the zero-order, first-order and second-order components are combined according to Equation (13) to construct a complete second-order HDMR model.
[0055] (12), (13), To evaluate the predictive performance and accuracy of the constructed overall HDMR surrogate model, test samples can be generated using the Latin hypercube sampling (LHS) method, with the number of test samples approximately 5-10 times the variable dimension. The coefficient of determination (COP) is then used. The prediction error is evaluated using the relative mean absolute error (RAAE) and relative mean absolute error (RMAE). The model is used to characterize its ability to fit the overall response trend. RAAE is used to measure the average error level of the sample population, and RMAE is used to reflect the error level at the local or most unfavorable point, reflecting the model's local predictive ability. The formulas are as follows (14)-(16).
[0056] (14), (15), (16), in, This represents the number of test samples; For the first The true response of each test sample, i.e., the performance of CFD computation; To predict the performance of the surrogate model, For all The statistical average, The standard deviation is denoted as .
[0057] when When the values are close to 1.0 and RAAE and RMSE are close to 0.0, the accuracy of the metamodel is relatively high. When the RAAE or RMAE is close to 1.0 but still relatively large, it indicates that the model can well represent the overall trend of change, but the prediction error of local samples or individual regions is still relatively large; when A low RAAE or RMAE indicates a low average error level in the model, but insufficient ability to fit the overall response fluctuation characteristics. Both scenarios suggest that the model has not simultaneously met the requirements for overall fit and error control; therefore, a single indicator cannot be used to determine if the model has sufficient predictive accuracy.
[0058] Therefore, a joint criterion is used to evaluate the agency model, as shown in equations (15)-(17), only when Not lower than the preset goodness-of-fit threshold Furthermore, both RAAE and RMAE are not higher than their respective preset error thresholds. , Only when the error distribution of the validation samples is met can the constructed surrogate model be considered to meet the accuracy requirements; otherwise, training samples can be added to the parameter region with large prediction errors based on the error distribution of the validation samples, and the surrogate model can be reconstructed or updated based on the new samples until the joint accuracy criterion is met.
[0059] (17), (18), (19), The evaluation threshold can be preset according to the actual engineering requirements for prediction accuracy, or determined based on the error distribution level of the validation samples. Preferably, in some engineering applications, A value of 0.8–0.95 is acceptable. A value of 0.03–0.05 is acceptable. A value of 0.05–0.10 is acceptable.
[0060] The aerodynamic uncertainty of the compressor is quantified. A constructed HDMR surrogate model is used to replace a large number of CFD aerodynamic performance calculations. A large number of random samples conforming to the actual uncertainty distribution are input into the surrogate model to output the corresponding performance. Monte Carlo uncertainty propagation statistical analysis is then performed to ultimately obtain the impact of compressor uncertainty on aerodynamic performance.
[0061] The above inventions are merely a few specific embodiments of the present invention. However, the embodiments of the present invention are not limited thereto, and any variations that can be conceived by those skilled in the art should fall within the protection scope of the present invention.
Claims
1. A method for quantifying compressor uncertainties based on adaptive ensemble high-dimensional model representation, characterized in that, Includes the following steps: Define compressor uncertainty parameters and normalize them to establish a high-dimensional uncertainty input space; Samples are taken at each one-dimensional boundary of the high-dimensional uncertainty input space, the compressor aerodynamic performance response corresponding to each one-dimensional component sample is calculated, and an initial first-order high-dimensional model is constructed to represent the components. Evaluate the accuracy of all current first-order high-dimensional model representation components and identify the first-order high-dimensional model representation component with the lowest accuracy; For the first-order high-dimensional model representation component with the lowest identified accuracy, multiple different types of surrogate models are used to construct candidate sub-models using the existing sample points of this component. Within the component space, the position with the largest Euclidean distance from all existing points is selected as the new sampling point, and the prediction error at the new sampling point is calculated using each candidate sub-model. Based on the prediction error, the candidate sub-model with the smallest error is selected to update the final surrogate model of the first-order high-dimensional model representation component. Determine whether the updated first-order high-dimensional model representation component meets the preset accuracy threshold; if not, continue iterative optimization of the component; if it does, confirm that the component has been constructed. The final proxy model based on all the first-order high-dimensional model representation components is combined with the zero-order term to form a first-order high-dimensional model representation global proxy model; The first-order high-dimensional model is used to represent the global proxy model to replace the computational fluid dynamics simulation. Uncertainty propagation analysis is performed on the compressor uncertainty parameter samples that conform to the actual distribution to obtain the uncertainty quantification results of the compressor aerodynamic performance.
2. The compressor uncertainty quantification method based on adaptive ensemble high-dimensional model representation as described in claim 1, characterized in that, After combining the components to form a first-order high-dimensional model representing the global proxy model, the process also includes determining whether there are significant second-order components: The accuracy of the first-order high-dimensional model representing the global proxy model at the boundaries of uncertain parameter variables is verified. If the relative error is higher than the second-order trigger threshold, a significant second-order component is determined to exist, and the following second-order component construction sub-process is executed: Identify pairs of uncertain parameters that may be correlated; For the identified parameter pairs, sample their two-dimensional boundaries to construct initial second-order components; An adaptive ensemble strategy similar to that used for modeling the first-order high-dimensional model representation components is adopted to complete the modeling of all second-order components; The first-order high-dimensional model representation components, second-order components, and zero-order terms are combined to form a complete second-order integrated high-dimensional model representation proxy model.
3. The compressor uncertainty quantification method based on adaptive ensemble high-dimensional model representation as described in claim 1, characterized in that, The normalization process uses the following formula: ， in Indicates the first One uncertain parameter, For the first Prototype design values of the center point of the space of each parameter variable. For the corresponding tolerance or disturbance range, This refers to the dimensionless variable after normalization.
4. The compressor uncertainty quantification method based on adaptive ensemble high-dimensional model representation as described in claim 1, characterized in that, The method for constructing the initial first-order high-dimensional model representing the components is as follows: using variables The linear response function is established by using two sample points obtained at the upper and lower boundaries to determine a straight line.
5. The compressor uncertainty quantification method based on adaptive ensemble high-dimensional model representation as described in claim 1, characterized in that, The method for evaluating the accuracy of the components is leave-one-out cross-validation, which quantifies the accuracy of the components by calculating the generalized mean square error.
6. The compressor uncertainty quantification method based on adaptive ensemble high-dimensional model representation as described in claim 5, characterized in that, The specific formula for calculating the generalized mean square error is as follows: in, Indicates the first The generalized cross-validation mean square error of the components represented by a first-order high-dimensional model. For this component The number of samples, Indicates that the first excluding An HDMR model constructed from individual components. For the dimension of uncertain variables.
7. The compressor uncertainty quantification method based on adaptive ensemble high-dimensional model representation as described in claim 1, characterized in that, The various types of surrogate models include the following: linear functions, support vector regression, kriging models, multinomial chaotic expansion, radial basis function networks, and artificial neural networks.
8. The compressor uncertainty quantification method based on adaptive ensemble high-dimensional model representation as described in claim 1, characterized in that, The selection strategy for new sampling points is as follows: among the existing sample points of the current component, the position with the largest sum of Euclidean distances to all existing points is selected as the new sampling point.
9. The compressor uncertainty quantification method based on adaptive ensemble high-dimensional model representation as described in claim 2, characterized in that, The method for identifying potentially correlated pairs of uncertain parameters includes: Combination and Form a new sample point The remaining variables retain their values at the center point, and the true response value at that point is calculated. ,in, Indicates the first Each variable takes the value at the upper boundary point. Indicates except the first Besides the three variables, the remaining variables are the sample center point values; similarly, That is to say, the first A first-order high-dimensional model represents components taking values at the upper boundary points. Indicates except the first Apart from one variable, the remaining variables are the sample center point values; Indicates except the first The and the first Apart from one variable, the remaining variables are the sample center point values; Calculate the second-order component values using the following formula. : ， in, , The first , A first-order high-dimensional model represents the calculated component values. It is a zero-order term; If the following correlation criteria are met: ， Then we consider the variable and There is no significant interaction effect between them, and they are approximately independent; otherwise, the variable is determined. and Since they are correlated, corresponding second-order components need to be constructed, where, , The first , Each variable takes the value at the lower boundary point; This is the second-order trigger threshold.
10. The compressor uncertainty quantification method based on adaptive ensemble high-dimensional model representation as described in claim 1, characterized in that, After performing uncertainty propagation analysis using the aforementioned proxy model, the process also includes a step of evaluating the overall performance of the constructed proxy model. Test samples were generated using the Latin hypercube sampling method, with the number of test samples being 5-10 times the number of variable dimensions. The prediction error is evaluated using the coefficient of determination, relative mean absolute error, and relative maximum absolute error. The determination is made using a combination of criteria: the coefficient of determination is not lower than the first preset threshold, the relative average absolute error is not higher than the second preset threshold, and the relative maximum absolute error is not higher than the third preset threshold.