Vibration Analysis of Driving-Point System with Uncertainties Using Polynomial Chaos Expansion by Bin Xiao, Yu-long Zhou, Chao Gao, Shuang-Xia Shi, Ze-Xi Sun, Zong-biao Song

“…A vibration transfer analysis method based on polynomial chaos expansion (PCE) is proposed in this study and is used to analyze the stochastic dynamic compliance of uncertain systems with the Gaussian distribution. …”
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Time-Dependent Reliability-Based Design Optimization Utilizing Nonintrusive Polynomial Chaos by Yao Wang, Shengkui Zeng, Jianbin Guo

“…This paper proposes a time-dependent RBDO method considering both of the time-dependent kinematic reliability and the time-dependent structural reliability as constrains. Polynomial chaos combined with the moving least squares (PCMLS) is presented as a nonintrusive time-dependent surrogate model to conduct uncertainty quantification. …”
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Nonlinear Dynamic Behaviour Analysis of a Clutch System with Uncertainties Using Polynomial Chaos and the Constrained Harmonic Balance Method by M.-H. Trinh, S. Berger, E. Aubry

“…This article aims to study the ability of robust approaches based on developments in nonintrusive generalized polynomial chaos and a constrained harmonic balance method to estimate the vibration levels through the limit cycles of a clutch system in the presence of uncertainty. …”
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Analysis of inductive power transfer systems by metamodeling techniques by Pei, Yao, Pichon, Lionel, Bensetti, Mohamed, Le Bihan, Yann

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A New Uncertain Analysis Method for the Prediction of Acoustic Field with Random and Interval Parameters by Mingjie Wang, Zhimin Wan, Qibai Huang

“…For the frequency response analysis of acoustic field with random and interval parameters, a nonintrusive uncertain analysis method named Polynomial Chaos Response Surface (PCRS) method is proposed. …”
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Bifurcation Analysis with Aerodynamic-Structure Uncertainties by the Nonintrusive PCE Method by Linpeng Wang, Yuting Dai, Chao Yang

“…The nonintrusive polynomial chaos expansion (PCE) based on tensor product is applied to quantify the uncertainty of aerodynamic and structure parameters on the aerodynamic force and aeroelastic behavior. …”
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Uncertainty Quantification of GEKO Model Coefficients on Compressible Flows by Yeong-Ki Jung, Kyoungsik Chang, Jae Hyun Bae

“…A metamodel is constructed based on general polynomial chaos expansion (gPCE) using ordinary least squares (OLS). …”
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A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters by Rugao Gao, Keping Zhou, Yun Lin

“…The generalized Polynomial Chaos Expansion Method (gPCEM), which is a random uncertainty analysis method by employing the orthogonal polynomial bases from the Askey scheme to represent the random space, has been widely used in engineering applications due to its good performance in both computational efficiency and accuracy. …”
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Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation by Mohamed A. El-Beltagy, Mohamed I. Wafa

“…The vorticity-stream function formulation is considered. The polynomial chaos expansion was integrated with an unstructured node-centered finite-volume solver. …”
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Stochastic Behaviour of Mistuned Stator Vane Sectors: An Industrial Application by A.C. Sall, F. Thouverez, L. Blanc, P. Jean

“…The methodology has been developed first on a simplified model and then applied to an industrial case. Polynomial chaos based results are in good agreement with reference Monte Carlo simulations.…”
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Nonlinear Augmented Proportional Navigation for Midrange Rendezvous Guidance and Performance Assessment by Weilin Wang, Xumin Song

“…This paper builds on previous efforts in polynomial chaos expansion (PCE) to develop an efficient analysis technique for guidance algorithms. …”
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Smolyak-Grid-Based Flutter Analysis with the Stochastic Aerodynamic Uncertainty by Yuting Dai, Chao Yang

“…Afterwards, the methodology for flutter uncertainty quantification due to aerodynamic perturbation was developed, based on the nonintrusive polynomial chaos expansion theory. In order to enhance the computational efficiency, the integration algorithm, namely, Smolyak sparse grids, was employed to calculate the coefficients of the stochastic polynomial basis. …”
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Bayesian Approach for Sequential Probabilistic Back Analysis of Uncertain Geomechanical Parameters and Reliability Updating of Tunneling-Induced Ground Settlements by Cong Li, Shui-Hua Jiang, Jinhui Li, Jinsong Huang

“…Within the framework of the proposed approach, a complex Bayesian back analysis problem is transformed into an equivalent structural reliability problem based on subset simulation. Hermite polynomial chaos expansion-based surrogate models are constructed to improve the computational efficiency of probabilistic back analysis. …”
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Hypersonic Vehicle Aerodynamic Optimization Using Field Metamodel-Enhanced Sequential Approximate Optimization by Wenjie Wang, Zeping Wu, Donghui Wang, Jiawei Yang, Pengyu Wang, Weihua Zhang

“…A hybrid metamodel combing radial basis functions and polynomial chaos expansion is applied to construct the field metamodel with good approximate performance. …”
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Uncertainty and Sensitivity Analysis of Significant Parameters for Superlarge Diameter Shield Excavation by Elton J. Chen, Yang-Yang Chen, Lin-Chun Wei, Han-Bin Luo

“…In this paper, we (i) utilize a BIM-based big data platform (BIM-BDP) to manage the essential construction data of tunnel project in digital format; (ii) adopt the global sensitivity analysis (SA) to recognize significant parameters for shield excavation based on polynomial chaos expansion (PCE)–extended Fourier amplitude sensitivity test (eFAST) model; and (iii) employ the uncertainty analysis (UA) to discover the correlation between significant parameters from the data of the BIM-BDP. …”
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Prediction of Adhesively Bonded Polyurethane-to-Steel Double Butt Joint Failure Using Uncertainty Analysis by Xiaofu Li, Chuanpeng Ji, Zhi Zhang, Shiwei Zhang, Hongqin Liu, Shulin Wang

“…Then, uncertainty analysis using polynomial chaos expansion (PCE) is applied to examine if it can enhance the prediction of the joint failure. …”
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Neurovascular bundle sparing in hypofractionated radiotherapy maintained with realistic treatment uncertainties by Roel C. Kwakernaak, Victor J. Brand, Jesús Rojo-Santiago, Femke E. Froklage, Mischa S. Hoogeman, Steven J.M. Habraken, Maaike T.W. Milder

“…Materials and methods: Non-sparing and sparing NVB treatment plans, delivered in 5 × 7.25 Gy, were automatically generated for 20 patients. Polynomial Chaos Expansion (PCE) was used to fast and accurately model the dose against treatment errors. …”
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