Reducing the Number of Variables in a Response Surface Approximation: Application to Thermal Design

2007 ◽  
Author(s):  
Christian Gogu ◽  
Raphael T. Haftka ◽  
Satish K. Bapanapalli ◽  
Bhavani V. Sankar
Keyword(s):  
Sensitivity Analysis ◽  
Response Surface ◽  
Global Sensitivity Analysis ◽  
Thermal Design ◽  
Maximum Temperature ◽  
Fe Model ◽  
Thermal Problem ◽  
Global Sensitivity ◽  
Fe Simulations ◽  
Integrated Thermal Protection System

Response surface approximations (RSA) are a common tool in engineering, often constructed based on finite element (FE) simulations. For some design problems, the FE models can involve a high number of parameters. However it is advantageous to construct the RSA as function of a small number of variables. The purpose of this paper is to demonstrate that a significant reduction in the number of variables needed for an RSA is possible through physical reasoning, dimensional analysis and global sensitivity analysis. This approach is demonstrated for a transient thermal problem, but it is applicable to any FE based surrogate model construction. The thermal problem considered is the design of an integrated thermal protection system (ITPS) for spacecraft reentry where an RSA of the maximum bottom face temperature was needed. The FE model used to evaluate the maximum temperature depended on 15 parameters of interest for the design: 9 thermal material properties and 6 geometric parameters of the ITPS panel. A small number of assumptions simplified the thermal equations allowing easy nondimensionalization, which together with a global sensitivity analysis showed that the maximum temperature mainly depends on only two nondimensional parameters. These were selected to be the design variables of the RSA for maximum temperature. The RSA was still fitted to the original non-simplified FE simulations. Having only two variables allowed a dense design of experiments thus providing a very good quality of fit. Consequently the major error remaining in the RSA is due to the fact that the two nondimensional variables account for only part (albeit the major part) of the dependence on the original 15 variables. This error was checked and good agreement was found. The two-dimensional nature of the RSA allowed graphical representation, which was used for material selection from among hundreds of possible materials for the design optimization of an ITPS panel.

scholarly journals What do we do with model simulation crashes? Recommendations for global sensitivity analysis of earth and environmental systems models

2019 ◽  
Author(s):  
Razi Sheikholeslami ◽  
Saman Razavi ◽  
Amin Haghnegahdar
Keyword(s):  
Sensitivity Analysis ◽  
Sample Size ◽  
Response Surface ◽  
Land Surface ◽  
Global Sensitivity Analysis ◽  
Model Simulation ◽  
Surface Modelling ◽  
Global Sensitivity ◽  
Environmental Systems ◽  
Response Surface Modelling

Abstract. Complex, software-intensive, technically advanced, and computationally demanding models, presumably with ever-growing realism and fidelity, have been widely used to simulate and predict the dynamics of the Earth and environmental systems. The parameter-induced simulation crash (failure) problem is typical across most of these models, despite considerable efforts that modellers have directed at model development and implementation over the last few decades. A simulation failure mainly occurs due to the violation of the numerical stability conditions, non-robust numerical implementations, or errors in programming. However, the existing sampling-based analysis techniques such as global sensitivity analysis (GSA) methods, which require running these models under many configurations of parameter values, are ill-equipped to effectively deal with model failures. To tackle this problem, we propose a novel approach that allows users to cope with failed designs (samples) during the GSA, without knowing where they took place and without re-running the entire experiment. This approach deems model crashes as missing data and uses strategies such as median substitution, single nearest neighbour, or response surface modelling to fill in for model crashes. We test the proposed approach on a 10-paramter HBV-SASK rainfall-runoff model and a 111-parameter MESH land surface-hydrology model. Our results show that response surface modelling is a superior strategy, out of the data filling strategies tested, and can scale well to the dimensionality of the model, sample size, and the ratio of number of failures to the sample size. Further, we conduct a "failure analysis" and discuss some possible causes of the MESH model failure.

scholarly journals What should we do when a model crashes? Recommendations for global sensitivity analysis of Earth and environmental systems models

2019 ◽  
Vol 12 (10) ◽  
pp. 4275-4296 ◽  
Author(s):  
Razi Sheikholeslami ◽  
Saman Razavi ◽  
Amin Haghnegahdar
Keyword(s):  
Sensitivity Analysis ◽  
Sample Size ◽  
Response Surface ◽  
Land Surface ◽  
Nearest Neighbor ◽  
Global Sensitivity Analysis ◽  
Surface Modeling ◽  
Response Surface Modeling ◽  
Global Sensitivity ◽  
Environmental Systems

Abstract. Complex, software-intensive, technically advanced, and computationally demanding models, presumably with ever-growing realism and fidelity, have been widely used to simulate and predict the dynamics of the Earth and environmental systems. The parameter-induced simulation crash (failure) problem is typical across most of these models despite considerable efforts that modellers have directed at model development and implementation over the last few decades. A simulation failure mainly occurs due to the violation of numerical stability conditions, non-robust numerical implementations, or errors in programming. However, the existing sampling-based analysis techniques such as global sensitivity analysis (GSA) methods, which require running these models under many configurations of parameter values, are ill equipped to effectively deal with model failures. To tackle this problem, we propose a new approach that allows users to cope with failed designs (samples) when performing GSA without rerunning the entire experiment. This approach deems model crashes as missing data and uses strategies such as median substitution, single nearest-neighbor, or response surface modeling to fill in for model crashes. We test the proposed approach on a 10-parameter HBV-SASK (Hydrologiska Byråns Vattenbalansavdelning modified by the second author for educational purposes) rainfall–runoff model and a 111-parameter Modélisation Environmentale–Surface et Hydrologie (MESH) land surface–hydrology model. Our results show that response surface modeling is a superior strategy, out of the data-filling strategies tested, and can comply with the dimensionality of the model, sample size, and the ratio of the number of failures to the sample size. Further, we conduct a “failure analysis” and discuss some possible causes of the MESH model failure that can be used for future model improvement.

Thermal Design Optimization of Electric Machines Using a Global Sensitivity Analysis

2017 ◽  
Vol 53 (6) ◽  
pp. 5365-5372 ◽  
Author(s):  
Bassel Assaad ◽  
Khadija El kadri Benkara ◽  
Stephane Vivier ◽  
Guy Friedrich ◽  
Antoine Michon
Keyword(s):  
Sensitivity Analysis ◽  
Design Optimization ◽  
Global Sensitivity Analysis ◽  
Electric Machines ◽  
Thermal Design ◽  
Global Sensitivity

Multivariate Global Sensitivity Analysis for Casing String Using Neural Network

2019 ◽  
Vol 17 (05) ◽  
pp. 1940015
Author(s):  
Pan Wang ◽  
Haihe Li ◽  
Shiwang Tan ◽  
Xiaoyu Huang
Keyword(s):  
Neural Network ◽  
Sensitivity Analysis ◽  
Failure Modes ◽  
Global Sensitivity Analysis ◽  
Influential Factors ◽  
Fe Model ◽  
Complex Environment ◽  
Global Sensitivity ◽  
The Neural Network ◽  
Oil Exploitation

To evaluate the safety of casing string is an important task in the oil exploitation. In this paper, the casing string with complex environment is investigated and the global sensitivity analysis (SA) technique is employed to identify the influential factors on the safety. Since the damage of casing string is of different kinds, three failure modes are mainly considered in the analysis. Then, the multivariate global SA technique is employed to identify the influential factors for the three failure modes simultaneously. Due to the full-size FE analysis of casing string which involves contact analysis of tread, being computationally expensive, a simplified model with full constraints are constructed. Then, to compute the multivariate global sensitivity efficiently, the neural network which is used to surrogate the FE model is employed to perform SA.

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