Adaptive anisotropic response surface method based on univariate dimension-reduction model and its high-order revision

2020 ◽  
Vol 37 (9) ◽  
pp. 3097-3125
Author(s):  
Wenliang Fan ◽  
Wentong Zhang ◽  
Min Li ◽  
Alfredo H.-S. Ang ◽  
Zhengliang Li
Keyword(s):  
Dimension Reduction ◽  
Response Surface ◽  
Response Surface Method ◽  
High Order ◽  
Practical Implementation ◽  
Content Type ◽  
Reduction Model ◽  
Surface Method ◽  
Univariate Function ◽  
Improving Accuracy

Purpose Based on univariate dimension-reduction model, this study aims to propose an adaptive anisotropic response surface method (ARSM) and its high-order revision (HARSM) to balance the accuracy and efficiency for response surface method (RSM). Design/methodology/approach First, judgment criteria for the constitution of a univariate function are derived mathematically, together with the practical implementation. Second, by combining separate polynomial approximation of each component function of univariate dimension-reduction model with its constitution analysis, the anisotropic ARSM is proposed. Third, the high-order revision for component functions is introduced to improve the accuracy of ARSM, namely, HARSM, in which the revision is also anisotropic. Finally, several examples are investigated to verify the accuracy, efficiency and convergence of the proposed methods, and the influence of parameters on the proposed methods is also performed. Findings The criteria for constitution analysis are appropriate and practical. Obtaining the undetermined coefficients for every component functions is easier than the existing RSMs. The existence of special component functions is useful to improve the efficiency of the ARSM. HARSM is helpful for improving accuracy significantly and it is more robust than ARSM and the existing quadratic polynomial RSMs and linear RSM. ARSM and HARSM can achieve appropriate balance between precision and efficiency. Originality/value The constitution of univariate function can be determined adaptively and the nonlinearity of different variables in the response surface can be treated in an anisotropic way.

A new response surface method based on the adaptive bivariate cut-HDMR

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wenliang Fan ◽  
Wei Shen ◽  
Qingbin Zhang ◽  
Alfredo H.-S. Ang
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Limit State ◽  
Sampling Technique ◽  
Content Type ◽  
Surface Method ◽  
Wide Range ◽  
Cross Terms ◽  
Order Polynomial ◽  
Component Function

Purpose The purpose of this study is to improve the efficiency and accuracy of response surface method (RSM), as well as its robustness. Design/methodology/approach By introducing cut-high-dimensional representation model (HDMR), the delineation of cross terms and the constitution analysis of component function, a new adaptive RSM is presented for reliability calculation, where a sampling scheme is also proposed to help constructing response surface close to limit-state. Findings The proposed method has a more feasible process of evaluating undetermined coefficients of each component function than traditional RSM, and performs well in terms of balancing the efficiency and accuracy when compared to the traditional second-order polynomial RSM. Moreover, the proposed method is robust on the parameter in a wide range, indicating that it is able to obtain convergent result in a wide feasible domain of sample points. Originality/value This study constructed an adaptive bivariate cut-HDMR by introducing delineation of cross-terms and constitution of univariate component function; and a new sampling technique is proposed.

Application of a new local effective constrained response surface method in structural reliability optimization design

2019 ◽  
Vol 36 (3) ◽  
pp. 1055-1078 ◽  
Author(s):  
Hailiang Su ◽  
Fengchong Lan ◽  
Yuyan He ◽  
Jiqing Chen
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Optimization Design ◽  
Structural Reliability ◽  
Reliability Optimization ◽  
Content Type ◽  
Meta Model ◽  
Proxy Model ◽  
Surface Method ◽  
Sampling Points

Purpose Meta-model method has been widely used in structural reliability optimization design. The main limitation of this method is that it is difficult to quantify the error caused by the meta-model approximation, which leads to the inaccuracy of the optimization results of the reliability evaluation. Taking the local high efficiency of the proxy model, this paper aims to propose a local effective constrained response surface method (LEC-RSM) based on a meta-model. Design/methodology/approach The operating mechanisms of LEC-RSM is to calculate the index of the local relative importance based on numerical theory and capture the most effective area in the entire design space, as well as selecting important analysis domains for sample changes. To improve the efficiency of the algorithm, the constrained efficient set algorithm (ESA) is introduced, in which the sample point validity is identified based on the reliability information obtained in the previous cycle and then the boundary sampling points that violate the constraint conditions are ignored or eliminated. Findings The computational power of the proposed method is demonstrated by solving two mathematical problems and the actual engineering optimization problem of a car collision. LEC-RSM makes it easier to achieve the optimal performance, less feature evaluation and fewer algorithm iterations. Originality/value This paper proposes a new RSM technology based on proxy model to complete the reliability design. The originality of this paper is to increase the sampling points by identifying the local importance of the analysis domain and introduce the constrained ESA to improve the efficiency of the algorithm.

scholarly journals A nonlinear modelling-based high-order response surface method for predicting monthly pan evaporations

2016 ◽  
Author(s):  
Behrooz Keshtegar ◽  
Ozgur Kisi
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
High Order ◽  
Climatic Data ◽  
Pan Evaporation ◽  
Surface Method ◽  
Neuro Fuzzy ◽  
Comparison Results ◽  
Fuzzy Genetic ◽  
Better Than

Abstract. Accurate modelling of pan evaporation has a vital importance in the planning and management of water resources. In this paper, the response surface method (RSM) is extended for estimation of monthly pan evaporations using high-order response surface (HORS) function. A HORS function is proposed to improve the accurate predictions with various climatic data, which are solar radiation, air temperature, relative humidity and wind speed from two stations, Antalya and Mersin, in Mediterranean Region of Turkey. The HORS predictions were compared to artificial neural networks (ANNs), neuro-fuzzy (ANFIS) and fuzzy genetic (FG) methods in these stations. Finally, the pan evaporation of Mersin station was estimated using input data of Antalya station in terms of HORS, FG, ANNs, and ANFIS modelling. Comparison results indicated that HORS models performed slightly better than FG, ANN and ANFIS models. The HORS approach could be successfully and simply applied to estimate the monthly pan evaporations.

An adaptive order response surface method for structural reliability analysis

2019 ◽  
Vol 36 (5) ◽  
pp. 1626-1655
Author(s):  
Wentong Zhang ◽  
Yiqing Xiao
Keyword(s):  
Response Surface ◽  
Failure Mode ◽  
Response Surface Method ◽  
Structural Engineering ◽  
Goodness Of Fit ◽  
Structural Reliability ◽  
Content Type ◽  
Original Response ◽  
Surface Method ◽  
Curve Fit

Purpose Balancing accuracy and efficiency is an important evaluation index of response surface method. The purpose of this paper is to propose an adaptive order response surface method (AORSM) based on univariate decomposition model (UDM). Design/methodology/approach First, the nonlinearity of the univariate function can be judged by evaluating the goodness of fit and the error of curve fit rationally. Second, combining UDM with the order analysis of separate component polynomial, an easy-to-implement AORSM is proposed. Finally, several examples involving mathematical functions and structural engineering problems are studied in detail. Findings With the proposed AORSM, the orders of component functions in the original response surface can be determined adaptively and the results of those cases in this paper indicate that the proposed method performs good accuracy, efficiency and robustness. Research limitations/implications Because just the cases with single failure mode and single MPP are studied in this paper, the application in multi-failure mode and multi-MPP cases need to be investigated in the coming work. Originality/value The nonlinearity of the univariate in the response surface can be determined adaptively and the undetermined coefficients of each component function are obtained separately, which reduces the computation dramatically.

scholarly journals Reliability Analysis for Bypass Seepage Stability of Complex Reinforced Earth-Rockfill Dam with High-Order Practical Stochastic Response Surface Method

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Jinwen He ◽  
Ping Zhang ◽  
Xiaona Li
Keyword(s):  
Water Level ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
High Order ◽  
Stochastic Response ◽  
Rockfill Dam ◽  
Surface Method ◽  
Reinforced Earth

Practical stochastic response surface method (SRSM) using ordinary high-order polynomials with mixed terms to approximate the true limit state function (LSF) is proposed to analyze the reliability of bypass seepage stability of earth-rockfill dam. Firstly, the orders of random variable are determined with a univariate fitting. Secondly, nonessential variables are excluded to identify possible mixed terms. Thirdly, orthogonal table is used to arrange additional samples, and stepwise regression is conducted to achieve a specific high-order response surface polynomial (RSP). Fourthly, Monte Carlo simulation (MCS) is used to calculate the failure probability, and RSP is updated by arranging several additional samplings around the design point. At last, the Bantou complex reinforced earth-rockfill dam was taken as an example. There are 6 random variables, that is, the upper water level and 5 hydraulic conductivities (HCs). The result shows that a third-order RSP can ensure good precision, and the failure probability of bypass seepage stability is 3.680×10−5 within an acceptable risk range. The HC of concrete cut-off wall and the HC of rockfill are unimportant random variables. Maximum failure probability at the bank slope has positive correlation with the HC of curtain and the upper water level, negative correlation with the HC of alluvial deposits, and less significance with the HC of filled soil. With the increase of coefficient of variation (Cov) of the HC of curtain, the bypass seepage failure probability increases dramatically. Practical SRSM adopts a nonintrusive form. The reliability analysis and the bypass seepage analysis were conducted separately; therefore, it has a high computational efficiency. Compared with the existing SRSM, the RSP of practical SRSM is simpler and the procedure of the reliability analysis is easier. This paper provides a further evidence for readily application of the high-order practical SRSM to engineering.

Optimized River Stream-Flow Forecasting Model Utilizing High-Order Response Surface Method

2016 ◽  
Vol 30 (11) ◽  
pp. 3899-3914 ◽  
Author(s):  
Behrooz Keshtegar ◽  
Mohammed Falah Allawi ◽  
Haitham Abdulmohsin Afan ◽  
Ahmed El-Shafie
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Stream Flow ◽  
High Order ◽  
Forecasting Model ◽  
Surface Method
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