An adaptive PCE-HDMR metamodeling approach for high-dimensional problems

Yue, Xinxin; Zhang, Jian; Gong, Wenping; Luo, Min; Duan, Libin

doi:10.1007/s00158-021-02866-7

Cited by 27 publications

(6 citation statements)

References 56 publications

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“…In this paper, we use the coefficient of determination R 2 , relative average absolute error (RAAE), relative maximum absolute error (RMAE) and root mean square error (RMSE) as evaluation criteria for prediction performance, and these metrics are widely used in the accuracy assessment of surrogate models [ 68 , 69 , 70 ], the variance accounted factor (VAF), performance index (PI), A 10 −index and uncertainty analysis (U 95 ), which are defined as follows:

where

and

are the observed and simulated values, respectively,

is the mean of the observed values and

is the number of samples. Additionally,

is the number of records with a ratio of measured to predicted value between 0.9 and 1.1.…”

Section: Numerical and Experimental Validationsmentioning

confidence: 99%

“…In this paper, we use the coefficient of determination R 2 , relative average absolute error (RAAE), relative maximum absolute error (RMAE) and root mean square error (RMSE) as evaluation criteria for prediction performance, and these metrics are widely used in the accuracy assessment of surrogate models [68][69][70], the variance accounted factor (VAF), performance index (PI), A 10 −index and uncertainty analysis (U 95 ), which are defined as follows:…”

Section: Predictive Accuracy Measuresmentioning

confidence: 99%

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Prediction and Global Sensitivity Analysis of Long-Term Deflections in Reinforced Concrete Flexural Structures Using Surrogate Models

Dan

Yue

et al. 2023

Materials

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Reinforced concrete (RC) is the result of a combination of steel reinforcing rods (which have high tensile) and concrete (which has high compressive strength). Additionally, the prediction of long-term deformations of RC flexural structures and the magnitude of the influence of the relevant material and geometric parameters are important for evaluating their serviceability and safety throughout their life cycles. Empirical methods for predicting the long-term deformation of RC structures are limited due to the difficulty of considering all the influencing factors. In this study, four popular surrogate models, i.e., polynomial chaos expansion (PCE), support vector regression (SVR), Kriging, and radial basis function (RBF), are used to predict the long-term deformation of RC structures. The surrogate models were developed and evaluated using RC simply supported beam examples, and experimental datasets were collected for comparison with common machine learning models (back propagation neural network (BP), multilayer perceptron (MLP), decision tree (DT) and linear regression (LR)). The models were tested using the statistical metrics R2, RAAE, RMAE, RMSE, VAF, PI, A10−index and U95. The results show that all four proposed models can effectively predict the deformation of RC structures, with PCE and SVR having the best accuracy, followed by the Kriging model and RBF. Moreover, the prediction accuracy of the surrogate model is much lower than that of the empirical method and the machine learning model in terms of the RMSE. Furthermore, a global sensitivity analysis of the material and geometric parameters affecting structural deflection using PCE is proposed. It was found that the geometric parameters are more influential than the material parameters. Additionally, there is a coupling effect between material and geometric parameters that works together to influence the long-term deflection of RC structures.

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where

and

are the observed and simulated values, respectively,

is the mean of the observed values and

is the number of samples. Additionally,

is the number of records with a ratio of measured to predicted value between 0.9 and 1.1.…”

Section: Numerical and Experimental Validationsmentioning

confidence: 99%

“…In this paper, we use the coefficient of determination R 2 , relative average absolute error (RAAE), relative maximum absolute error (RMAE) and root mean square error (RMSE) as evaluation criteria for prediction performance, and these metrics are widely used in the accuracy assessment of surrogate models [68][69][70], the variance accounted factor (VAF), performance index (PI), A 10 −index and uncertainty analysis (U 95 ), which are defined as follows:…”

Section: Predictive Accuracy Measuresmentioning

confidence: 99%

Prediction and Global Sensitivity Analysis of Long-Term Deflections in Reinforced Concrete Flexural Structures Using Surrogate Models

Dan

Yue

et al. 2023

Materials

Self Cite

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show abstract

“…Since then, many scholars invested in the research on probabilistic small-disturbance stability, and the SDFs taken into account have been expanded from load fluctuations and generator damping coefficients at the beginning to probabilistic models of node injected power levels and component parameters (e.g., line impedance, controller parameters, etc.) [48].…”

Section: Probabilistic Small-disturbance Stabilitymentioning

confidence: 99%

Classification Study of New Power System Stability Considering Stochastic Disturbance Factors

Li,

Duan,

Gao

et al. 2023

Sustainability

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Power system instability causes many local or large-scale power outage accidents. To maintain sustainable development, a new power system construction aimed at maximizing new energy consumption is being put on the agenda. However, with a large increase in stochastic disturbance factors (SDFs), the system gradually shows strong stochasticity, and the stability presents greater complexity. It is necessary to analyze the impact on the system based on different processing methods of SDFs to maintain system stability. This paper delves into the impact of SDFs on system stability by analyzing and summarizing both stochastic variables and processes. Initially, the SDFs in the power system are meticulously analyzed and categorized. When the SDFs are treated as stochastic variables, the probabilistic stability is classified and evaluated based on a probability analysis method, which includes the probabilistic small-disturbance stability, the probabilistic transient stability, and the probabilistic voltage stability. When the SDFs are treated as stochastic processes, the stochastic stability is classified and evaluated by using a stochastic analysis method, including the stochastic small-disturbance stability, the stochastic transient stability, and the stochastic voltage stability. Finally, the research perspectives on SDFs and system stability are discussed and prospected.

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“…Figure 3c schematically shows the two-dimensional plane of this term. When using PCE-HDMR, metamodels of these component functions within the Cut-HDMR are simultaneously approximated through PCEs [15]: The summation of these terms yields the PCE-HDMR approximation of the response:…”

Section: Pce-hdmrmentioning

confidence: 99%

“…A further advanced UQ methodology, which involves the combination of PCE and KLE, was applied for the analysis of uncertainties of a turbulent round jet by Jivani et al [14]. One promising metamodeling approach was also developed by Yue et al [15] and involves the approximation of a response function with PCE-HDMR. The methodology has been successfully tested with mathematical functions and several engineering examples.…”

Section: Introductionmentioning

confidence: 99%

CFD Uncertainty Quantification using PCE-HDMR – Exemplary Application to a Buoyancy-Driven Mixing Process

Wenig

Kelm

Klein

2023

Preprint

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For the investigation of uncertainties in high dimensional spaces of computationally expensive engineering applications, reliable Uncertainty Quantification (UQ) methods are needed. These methods should provide accurate and efficient High-Dimensional Model Representations (HDMR) of stochastic results using a reasonable number of calculations. Therefore, the PCE-HDMR approach is utilized to qualify appropriate UQ methods for large-scale computations in the field of Computational Fluid Dynamics (CFD). This technique is a combination of Cut-HDMR, a hierarchical decomposition modeling approach, with Polynomial Chaos Expansion (PCE). To demonstrate its effectiveness, the PCE-HDMR methodology in conjunction with complementary modeling techniques is applied for the UQ analysis of a buoyancy-driven mixing process between two miscible fluids within the Differentially Heated Cavity (DHC) of aspect ratio 4. The results include a thorough probabilistic representation of time-dependent response quantities that comprehensively describe the mixing process. The stochastic models are derived from Large Eddy Simulations (LES) using PCE HDMR and the Sparse Grid Method (SGM), which serves as a reference for the results from PCE-HDMR. The results show that PCE-HDMR provides accurate statistics of the modeled time-dependent stochastic processes and shows good agreement with the SGM reference. Thus, PCE-HDMR indicates great potential for UQ of technical-scale computations due to its efficiency and flexibility in the construction of stochastic models.

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An adaptive PCE-HDMR metamodeling approach for high-dimensional problems

Cited by 27 publications

References 56 publications

Prediction and Global Sensitivity Analysis of Long-Term Deflections in Reinforced Concrete Flexural Structures Using Surrogate Models

Prediction and Global Sensitivity Analysis of Long-Term Deflections in Reinforced Concrete Flexural Structures Using Surrogate Models

Classification Study of New Power System Stability Considering Stochastic Disturbance Factors

CFD Uncertainty Quantification using PCE-HDMR – Exemplary Application to a Buoyancy-Driven Mixing Process

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