An Approach to Reliability Analysis Using the Response Surface Method and Monte Carlo Simulation

1999 ◽  
Author(s):  
Irfan Kaymaz ◽  
Chris A. McMahon
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Actual Performance ◽  
Surface Method ◽  
Analysis System ◽  
Different Response ◽  
Response Surface Function

Abstract It is important in reliability evaluation to take an approach in which the required calculations can be performed efficiently in terms of time and cost. In this study, an approach is proposed whereby reliability analysis is carried out by means of Monte Carlo simulation in which the actual performance function is replaced by a function obtained using the response surface method (RSM). The common approach in the conventional RSM is to use a second-degree polynomial for the response surface function, but in many reliability problems this may not be the best choice. This paper first reviews the approaches and limitations of reliability methods, and then goes on to discuss a method of modelling error when using the response surface method for reliability analysis. It shows the errors obtained for different response functions under different circumstances, and then describes the application of a network-based analysis system to reliability problems.

Comparison of Monte Carlo Simulation and Response Surface Method by Using ANSYS PDS

2014 ◽  
Vol 578-579 ◽  
pp. 1449-1453
Author(s):  
Chun Xue Song ◽  
Yi Zhang ◽  
Ying Yi Cao
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Probabilistic Analysis ◽  
Limit State ◽  
Design System ◽  
State Function ◽  
Surface Method

Monte Carlo Simulation and Response Surface Method are two very powerful reliability analysis methods. Normally, in the reliability analysis of complex structures, the limit state function often can not be expressed in a closed-form. Usually, the codes for probabilistic analysis need to be combined with finite element models. ANSYS Probabilistic Design System (PDS) has provided a package to conduct probabilistic analysis automatically. This paper is going to compare the performance of these methods through an easy engineering problem in ANSYS. The results are going to be derived to show the feature of applying the corresponding reliability methods.

Robust Thermal Design for Power Device Package Using Response Surface Method and Monte Carlo Simulation

2007 ◽  
Author(s):  
Yasuyuki Yokono ◽  
Katsumi Hisano ◽  
Kenji Hirohata
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Thermal Resistance ◽  
Response Surface ◽  
Response Surface Method ◽  
Thermal Conduction ◽  
Thermal Design ◽  
Power Device ◽  
Design Parameters ◽  
Surface Method

In the present study, the robust thermal design of a power device package was accomplished using thermal conduction calculation, design of experiment, response surface method and Monte Carlo simulation. Initially, the effects of the design parameters on the solder strain were examined in terms of the thermal expansion difference as a result of unsteady thermal conduction simulation. From the factorial effects of design parameters, the design proposals were screened. Then, robustness of the thermal resistance was evaluated for the three design proposals obtained. The thermal resistances were calculated by solving the steady thermal conduction equation under the design of experiment conditions. The solder thickness, the substrate thickness, and the cooling fin performance were considered as the fluctuation factors, assuming the error associated with manufacturing process. Using a response surface method, the values of thermal resistance were expressed as a function of the design variables. The variances of the thermal resistance were examined based on Monte Carlo simulations. Related to the cooling fin design, the Pareto line showing the trade-off relation between the fin dimension and the fan velocity was obtained. By repeating the Monte Carlo simulations, the Pareto solution was calculated so that the thermal resistances satisfy the criteria in the position of 95 percrntile of the thermal resistance variation. Under the same flow velocity conditions, the fin dimensions become about 10% higher compared to the case where the manufacturing error was not taken into account. By carrying out the thermal design following this Pareto line, even if the manufacturing error was taken into consideration, the thermal resistance could satisfy the desired value.

scholarly journals Creep-Based Reliability Evaluation of Turbine Blade-Tip Clearance with Novel Neural Network Regression

Materials ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 3552 ◽  
Author(s):  
Chun-Yi Zhang ◽  
Jing-Shan Wei ◽  
Ze Wang ◽  
Zhe-Shan Yuan ◽  
Cheng-Wei Fei ◽  
...  
Keyword(s):  
Neural Network ◽  
High Pressure ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Tip Clearance ◽  
Strong Nonlinearity ◽  
Surface Method ◽  
Blade Tip ◽  
Blade Tip Clearance

To reveal the effect of high-temperature creep on the blade-tip radial running clearance of aeroengine high-pressure turbines, a distributed collaborative generalized regression extremum neural network is proposed by absorbing the heuristic thoughts of distributed collaborative response surface method and the generalized extremum neural network, in order to improve the reliability analysis of blade-tip clearance with creep behavior in terms of modeling precision and simulation efficiency. In this method, the generalized extremum neural network was used to handle the transients by simplifying the response process as one extremum and to address the strong nonlinearity by means of its nonlinear mapping ability. The distributed collaborative response surface method was applied to handle multi-object multi-discipline analysis, by decomposing one “big” model with hyperparameters and high nonlinearity into a series of “small” sub-models with few parameters and low nonlinearity. Based on the developed method, the blade-tip clearance reliability analysis of an aeroengine high-pressure turbine was performed subject to the creep behaviors of structural materials, by considering the randomness of influencing parameters such as gas temperature, rotational speed, material parameters, convective heat transfer coefficient, and so forth. It was found that the reliability degree of the clearance is 0.9909 when the allowable value is 2.2 mm, and the creep deformation of the clearance presents a normal distribution with a mean of 1.9829 mm and a standard deviation of 0.07539 mm. Based on a comparison of the methods, it is demonstrated that the proposed method requires a computing time of 1.201 s and has a computational accuracy of 99.929% over 104 simulations, which are improvements of 70.5% and 1.23%, respectively, relative to the distributed collaborative response surface method. Meanwhile, the high efficiency and high precision of the presented approach become more obvious with the increasing simulations. The efforts of this study provide a promising approach to improve the dynamic reliability analysis of complex structures.

scholarly journals Reliability-Based Topology Optimization Using Stochastic Response Surface Method with Sparse Grid Design

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Qinghai Zhao ◽  
Xiaokai Chen ◽  
Zheng-Dong Ma ◽  
Yi Lin
Keyword(s):  
Topology Optimization ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Computational Efficiency ◽  
Sparse Grid ◽  
Stochastic Response ◽  
Stochastic Response Surface Method ◽  
Surface Method ◽  
Grid Design

A mathematical framework is developed which integrates the reliability concept into topology optimization to solve reliability-based topology optimization (RBTO) problems under uncertainty. Two typical methodologies have been presented and implemented, including the performance measure approach (PMA) and the sequential optimization and reliability assessment (SORA). To enhance the computational efficiency of reliability analysis, stochastic response surface method (SRSM) is applied to approximate the true limit state function with respect to the normalized random variables, combined with the reasonable design of experiments generated by sparse grid design, which was proven to be an effective and special discretization technique. The uncertainties such as material property and external loads are considered on three numerical examples: a cantilever beam, a loaded knee structure, and a heat conduction problem. Monte-Carlo simulations are also performed to verify the accuracy of the failure probabilities computed by the proposed approach. Based on the results, it is demonstrated that application of SRSM with SGD can produce an efficient reliability analysis in RBTO which enables a more reliable design than that obtained by DTO. It is also found that, under identical accuracy, SORA is superior to PMA in view of computational efficiency.

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