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gaussian process regression-Based Model Error Diagnosis and Quantification Using Experimental Data of Prestressed Concrete Beams in Shear

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ASCE-ASME JOURNAL OF RISK AND UNCERTAINTY IN ENGINEERING SYSTEMS PART A-CIVIL ENGINEERING 2025年第1期11卷

作者： Liu, Jiadaren Alexander, John Li, Yong McGill Univ Dept Civil Engn Montreal PQ H3A 0C3 Canada Alberta Minist Transportat Bridge Engn Edmonton AB T6B 2X3 Canada Univ Alberta Dept Civil & Environm Engn EDMONTON AB T6G 1H9 Canada

To facilitate considering model uncertainty for rigorous reliability/probabilistic analysis, this paper proposed a gaussian process regression-based (GPR-based) model error quantification framework and applied to shear capacity prediction of prestressed concrete (PC) beams. Firstly, the model error of shear capacity models from five well-received concrete structure and bridge design codes were diagnosed based on a compiled experimental database, where systematic correlations between model error and model parameters were observed. To consider the systematic correlation, model error was then calibrated as a function of model parameters based on GPR. Different covariance functions were considered, and a model selection was conducted based on 10-fold cross validations. Then, the model error quantification performance was evaluated by investigating the residual systematic correlation between model error and model parameters, as well as by comparisons with the traditional professional factor approach. In the end, relative importance of model parameters on the model error for each design code were analyzed, indicating that the shear span-to-effective depth ratio is the most important source of model error for all considered design code models.

关键词： Model error quantification gaussian process regression Shear capacity Prestressed concrete beam

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gaussian process regression UNDER COMPUTATIONAL AND EPISTEMIC MISSPECIFICATION\ast

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SIAM JOURNAL ON NUMERICAL ANALYSIS 2025年第2期63卷 495-519页

作者： Sanz-alonso, Daniel Yang, Ruiyi Univ Chicago Dept Stat Chicago IL 60637 USA Princeton Univ Program Appl & Computat Math Princeton NJ 08544 USA

gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the effect of such kernel approximations on the interpolation error. We introduce a unified framework to analyze gaussian process regression under important classes of computational misspecification: Karhunen--Loe`\ve expansions that result in low-rank kernel approximations, multiscale wavelet expansions that induce sparsity in the covariance matrix, and finite element representations that induce sparsity in the precision matrix. Our theory also accounts for epistemic misspecification in the choice of kernel parameters.

关键词： gaussian process regression misspecification Karhunen--Loe` ve expansions multiscale wavelets finite elements

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gaussian process regression for evolutionary dynamic multiobjective optimization in complex environments

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SWARM AND EVOLUTIONARY COMPUTATION 2025年 94卷

作者： Deng, Youpeng Zheng, Yan Meng, Zhaopeng Gao, Haobo Hua, Yueyang Jin, Qiangguo Cao, Leilei Tianjin Univ Coll Intelligence & Comp 135 Yaguan Rd Tianjin 300350 Peoples R China China Acad Launch Vehicle Technol 9200 Mailbox 1 Sub Box Beijing 100076 Peoples R China Northwestern Polytech Univ Sch Software 127 West Youyi Rd Xian 710072 Shaanxi Peoples R China Zhejiang Univ Innovat Ctr Yangtze River Delta 828 Zhongxing Rd Jiaxing 314100 Zhejiang Peoples R China

Multiobjective Evolutionary Algorithms (MOEAs) face significant challenges when addressing dynamic multiobjective optimization problems, particularly those with frequent changes. The complexity of dynamic environments makes it difficult for MOEAs to accurately approximate the true Pareto-optimal solutions before subsequent changes occur. Typically, historical approximations of Pareto-optimal solutions are utilized to predict solutions in future environments. However, existing predictors often overlook the nondeterministic nature of historical solutions, potentially compromising prediction accuracy. In this paper, we propose a novel predictor based on gaussian process regression (GPR) for evolutionary dynamic multiobjective optimization. Unlike traditional deterministic predictors, our approach aims to provide a probability distribution of predicted results, thereby addressing the inherent nondeterminism of historical solutions. We employ GPR to model relationships among historical solutions across different time steps. Within the framework of the classical MOEA, MOEA/D, we introduce a new method MOEA/D-GPR for Evolutionary Dynamic Multiobjective Optimization (EDMO). Experimental results demonstrate that our method achieves state-of-the-art performance.

关键词： Multiobjective optimization Dynamic environments Evolutionary algorithms Nondeterminism gaussian process regression

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Uncertainty estimation of minimum detectable activity through sparse spectrum using kernel-based gaussian process regression

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RADIATION PHYSICS AND CHEMISTRY 2025年 233卷

作者： Park, Jaehyun Song, Gyohyeok Kim, Wonku Ki-baek, Shin Choi, Yeon Kyoung Cho, Gyuseong Korea Adv Inst Sci & Technol Dept Nucl & Quantum Engn 291 Daehak Ro Daejeon 34141 South Korea Korea Atom Energy Res Inst Daejeon 34507 South Korea

To address the growing challenge of managing the radioactive waste generated during the decommissioning of nuclear power plants, one area under focus has been liquid radioactive waste management. This area concerns the importance of adhering to clearance levels and regulations, where Minimum Detectable Activity (MDA) plays a crucial role in determining whether liquid radioactive waste can be safely released into the environment. In this study, we obtain the sparse spectrum to calculate the uncertainty by means of kernel-based gaussian process regression (GPR). After calculating the uncertainty, we applied count correction to the sparse spectrum to match the count with the long measurement spectrum. We then corrected the sparse spectrum to match that of the measurement spectrum collected over 3000 s for comparison. The results show that as the measurement time increases, the MDA converges to the true value. By applying kernel-based GPR and correcting the sparse spectrum, the uncertainty estimation of MDA achieves significantly improved accuracy, especially when the measurement time exceeds 60 s. With a measurement time of at least 60 s, a reliable MDA estimate can be obtained, allowing for more efficient and accurate MDA assessments in practical scenarios. The significance of this study lies in the fact that it offers a faster and more efficient method for estimating MDA, which can potentially enhance the management of radioactive waste and improve the monitoring of nuclear facilities.

关键词： Liquid radioactive waste Minimum detectable activity gaussian process regression Sparse spectrum

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A clustering adaptive gaussian process regression method: Response patterns based real-time prediction for nonlinear solid mechanics problems

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2025年 436卷

作者： Li, Ming-Jian Lian, Yanping Cheng, Zhanshan Li, Lehui Wang, Zhidong Gao, Ruxin Fang, Daining Beijing Inst Technol Inst Adv Struct Technol Beijing 100081 Peoples R China Beijing Key Lab Lightweight Multifunct Composite M Beijing 100081 Peoples R China

Numerical simulation is a powerful approach to study nonlinear solid mechanics problems. However, mesh-based or particle-based numerical methods suffer from the common shortcoming of being time-consuming, particularly for complex problems with real-time analysis requirements. This study presents a clustering adaptive gaussian process regression (CAG) method aiming for real-time prediction for nonlinear structural responses in solid mechanics. It is a data-driven machine learning method featuring a small sample size, high accuracy, and high efficiency, leveraging nonlinear structural response patterns. Similar to the traditional gaussian process regression (GPR) method, it operates in offline and online stages. In the offline stage, an adaptive sample generation technique is introduced to cluster datasets into distinct patterns for demand-driven sample allocation. This ensures comprehensive coverage of the critical samples for the solution space of interest. In the online stage, following the divide-and-conquer strategy, a pre-prediction classification categorizes problems into predefined patterns sequentially predicted by the trained multi-pattern gaussian process regressor. In addition, dimension reduction and restoration techniques are employed in the proposed method to enhance its efficiency. A set of problems involving material, geometric, and boundary condition nonlinearities is presented to demonstrate the CAG method's predictive abilities. The proposed method can offer predictions within a second and attain high precision with only about 20 samples within the context of this study, outperforming the traditional GPR using uniformly distributed samples for error reductions ranging from 1 to 3 orders of magnitude. The CAG method is expected to offer a powerful tool for real-time prediction of nonlinear solid mechanical problems and shed light on the complex nonlinear structural response pattern.

关键词： gaussian process regression Nonlinear problems Real-time prediction Machine learning

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Data-Driven Hierarchical Model Predictive Control for Automated Overtaking Maneuver via gaussian process regression

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2025年第1期74卷 263-278页

作者： Li, Yiqun Chen, Zong Wang, Tao Zeng, Xiangrui Yin, Zhouping Huazhong Univ Sci & Technol Sch Mech Sci & Engn State Key Lab Intelligent Mfg Equipment & Technol Wuhan 430074 Peoples R China Harbin Inst Technol Sch Mech Engn & Automat Shenzhen 518055 Peoples R China

The effectiveness of model-driven trajectory generation and control methods for an automated vehicle is closely related to the accuracy of vehicle kinematics and dynamics. However, the dynamic behavior of a vehicle is time-varying and uncertain, especially during high mobility driving. For the data-driven end-to-end trajectory generation and control approach, the transferability and robustness of the trained neural network cannot easily be guaranteed. In this paper, a combined model- and learning-based trajectory generation and control framework for automated overtaking maneuver is presented. Unlike the model-driven approach and end-to-end learning approach, the proposed framework blends the single-track vehicle model of the automated vehicle with time-series driving data to generate safe and high-quality overtaking motions. Specifically, an efficient vectorized implementation of multivariate gaussian process regression (MGPR) is applied to learn the unmodeled dynamics in hopes of shortening the deviation between the single-track dynamic model and the true vehicle dynamics. A hierarchical nonlinear model predictive control with MGPR is designed for realizing local trajectory generation and control in the overtaking maneuvers. Multi-phases automated overtaking maneuvers at different speed ranges are conducted on roads with different friction coefficients to illustrate the effectiveness of the proposed trajectory generation and control framework.

关键词： Vehicle dynamics Trajectory Tires gaussian processes Data models Wheels Optimization Automated vehicle Model predictive control Trajectory tracking gaussian process regression Overtaking maneuver

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State of health prognosis for polymer electrolyte membrane fuel cell based on principal component analysis and gaussian process regression

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INTERNATIONAL JOURNAL OF HYDROGEN ENERGY 2025年 98卷 933-943页

作者： Chen, Kui Liu, Kai Zhou, Yue Li, Yang Wu, Guangning Gao, Guoqiang Wang, Haijun Laghrouche, Salah Djerdir, Abdesslem Southwest Jiaotong Univ Sch Elect Engn Chengdu 611731 Peoples R China CNRS FEMTO ST UMR 6174 Paris France CNRS FCLAB FR 3539 Paris France Univ Bourgogne Franche Comte UTBM F-90000 Besancon France State Grid Sichuan Elect Power UHV DC Ctr Chengdu 611731 Peoples R China Power China Northwest Engn Corp Ltd Xian 710065 Peoples R China

The durability issue is the primary factor affecting the life and cost of Polymer Electrolyte Membrane Fuel Cell (PEMFC). This paper presents a novel State of health (SOH) prognosis method for PEMFC indifferent conditions using Principal Component Analysis (PCA) and gaussian process regression (GPR). Firstly, the robust locally weighted smoothing method is used to preprocess the recorded PEMFC operation data for filtering measurement errors. Then, PCA is applied to extract the principal components of the time series original multi-dimensional input variables for PEMFC, eliminating the correlation between the original variables and reducing the dimensionality of input variables. Finally, the degradation prognosis and Remaining Useful Life (RUL) prognosis are made by GPR. Two degradation experiments for PEMFC verify the proposed method indifferent conditions. The test result shows that PCA can effectively reduce the dimensionality PEMFC operating conditions. Compared with traditional methods, PCA-GPR has higher SOH prognosis accuracy. PCA-GPR provides a 462-h RUL prognosis on a life duration of 1150 h, which is sufficient for maintaining the PEMFC.

关键词： Polymer electrolyte membrane fuel cell Degradation prognosis Remaining useful life prognosis Principal component analysis gaussian process regression Robust locally weighted smoothing method

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A new approach for parameter optimization of parallel mechanisms based on Stackelberg game theory and gaussian process regression

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE 2025年

作者： Wu, Mingkun Corves, Burkhard Rhein Westfal TH Aachen Dept Inst Mech Theory Machine Dynam & Robot D-52072 Aachen Germany

Parallel mechanisms-based industrial robots have been widely applied in various industries, such as food, electronics, aerospace, etc. Undoubtedly, the performance of parallel mechanisms plays a crucial role in the working capability of robots. However, in order to achieve a comprehensive optimal performance, more and more performance indices (e.g. kinematic, rigid-body dynamic, stiffness, and elastodynamic performances) and design variables have to be considered, which results in the fact that solving such a multi-variable multi-objective optimization problem becomes an extremely challenging task. To address this problem, this paper proposes a new parameter optimization approach based on Stackelberg game theory and gaussian process regression. Firstly, the design variables and optimization objectives are categorized into two groups, that is, the leader and the follower, and parameters of each group can be optimized separately, which can effectively reduce the complexity of the optimization problem. Besides, the time-consuming performance indices are assigned to the follower to improve the efficiency of the optimization process. Without loss of generality, an integrated parameter optimization is conducted on Delta robots to verify the effectiveness of the proposed parameter optimization approach.

关键词： Stackelberg game theory gaussian process regression parameter optimization parallel mechanisms Delta robots

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A gaussian process regression Method to Nowcast Cloud-to-Ground Lightning From Remote Sensing and Numerical Weather Modeling Data

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IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING 2025年 18卷 1963-1981页

作者： La Fata, Alice Moser, Gabriele Procopio, Renato Bernardi, Marina Fiori, Elisabetta Univ Genoa Dept Elect Elect Telecommun Engn & Naval Architect I-6126 Genoa Italy Ctr Elettrotecn Sperimentale Italiano SpA I-20134 Milan Italy Agenzia Regionale Protez Ambiente Ligure I-16149 Genoa Italy

The climate change of the last decades is causing an increase in the frequency of extreme event occurrences. Numerous studies confirm the link between extreme meteorological events and lightning activity. The possibility of having short-term predictions of the intensity of lightning phenomena would allow the near-real-time monitoring of the evolution of these events. Such knowledge would help in defining operational strategies to mitigate effects on the population and the infrastructure. In this context, this article proposes a multidisciplinary approach aiming at developing a regression algorithm to nowcast the density of cloud-to-ground lightning strokes 1 h in advance. The algorithm is developed on the basis of a joint combination of remote sensing data, numerical weather prediction model outcomes, and lightning observations. The possible dependence between the meteorological data and the density of lightning is estimated using gaussian process regression models. Separate models are created for positive and negative strokes and for strokes occurrences over the land or sea. The experimental results indicate that the model quite accurately estimates low numbers of strokes, whereas larger numbers of strokes are estimated with higher errors. Nevertheless, their presence is correctly detected. This suggests the potential of the method as a processing tool to support the management of weather-related hazards.

关键词： Climate change Lightning gaussian processes Weather forecasting Infrared imaging Satellite images Precipitation Remote sensing Numerical models Predictive models nowcasting gaussian process regression numerical weather prediction satellite infrared imagery satellite precipitation radar

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A Nonintrusive Nonlinear Model Reduction Method for Thermal Cycling-Induced Viscoplastic Deformation Problems Based on Segmented gaussian process regression Machine Learning

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IEEE ACCESS 2025年 13卷 4326-4340页

作者： Lee, Jiunn-Horng Ou, Chia-Hsiu Yao, Chih-Min Lee, Ming-Hsiao Natl Appl Res Labs Natl Ctr High Performance Comp Hsinchu 300092 Taiwan Natl Taiwan Univ Dept Elect Engn Taipei City 106319 Taiwan

Numerical simulation of thermal cycling-induced viscoplastic deformation is important to design a reliable underfilled flip chip package, where the time histories of viscoplastic strains are applied to predict the fatigue life of solder joints. However, the high-fidelity full model simulations of a flip chip package under thermal cycling are time intensive tasks. Nonintrusive model order reduction combined with machine learning is increasingly being used to create efficient surrogate models for problems with high computational costs. In this paper, a segmented gaussian process regression machine learning method combined with proper orthogonal decomposition is proposed to build the reduced order models of underfilled flip chip packages for thermal cycling-induced viscoplastic displacements and strains, respectively. Simulation results show the derived reduced order models can effectively predict the viscoplastic displacements and strains induced by thermal cycling across the entire solution domain and time history for different material properties of underfills and provide better accuracy than those generated by the non-segmented gaussian process regression method.

关键词： Computational modeling Reduced order systems Mathematical models Machine learning Flip-chip devices Trajectory Strain Predictive models gaussian processes Deformation Flip chip package gaussian process regression machine learning proper orthogonal decomposition reduced order model viscoplastic

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