Reliability-Based Design Optimization Using Response Surface Method With Prediction Interval Estimation

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Chwail Kim ◽  
K. K. Choi
Keyword(s):  
Design Optimization ◽  
Response Surface ◽  
Response Surface Method ◽  
Prediction Interval ◽  
Upper And Lower Bounds ◽  
Computational Time ◽  
Engineering System ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Surface Method

Since variances in the input variables of the engineering system cause subsequent variances in the product output performance, reliability-based design optimization (RBDO) is getting much attention recently. However, RBDO requires expensive computational time. Therefore, the response surface method is often used for computational efficiency in solving RBDO problems. A method to estimate the effect of the response surface error on the RBDO result is developed in this paper. The effect of the error is expressed in terms of the prediction interval, which is utilized as the error metric for the response surface used for RBDO. The prediction interval provides upper and lower bounds for the confidence level that the design engineer specified. Using the prediction interval of the response surface, the upper and lower limits of the reliability are computed. The lower limit of reliability is compared with the target reliability to obtain a conservative optimum design and thus safeguard against the inaccuracy of the response surface. On the other hand, in order to avoid obtaining a design that is too conservative, the developed method also constrains the upper limit of the reliability in the design optimization process. The proposed procedure is combined with an adaptive sampling strategy to refine the response surface. Numerical examples show the usefulness and the efficiency of the proposed method.

RELIABILITY DESIGN EVALUATION AND OPTIMIZATION OF A NITROGEN GAS BOTTLE USING RESPONSE SURFACE METHOD

2010 ◽  
Vol 17 (02) ◽  
pp. 119-132 ◽  
Author(s):  
P. BHATTACHARJEE ◽  
K. RAMESH KUMAR ◽  
T. A. JANARDHAN REDDY
Keyword(s):  
Design Optimization ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Operating Conditions ◽  
Optimization Under Uncertainty ◽  
Reliability Based Design Optimization ◽  
Nitrogen Gas ◽  
Reliability Based Design ◽  
Surface Method

Optimization of any aerospace product results in increasing payload capacity of space vehicles. Essentially weight, volume and cost are the main constraints. Design optimization studies for aerospace system are increasingly gaining importance. The problem of optimum design under uncertainty has been formulated as reliability-based design optimization. The reliability based optimization, which includes robustness requirements leads to multi-objective optimization under uncertainty. In this paper Reliability, based design optimization study is carried out under linear constraint optimization to minimize the weight of a nitrogen gas bottle with specified target reliability. Response surface method considering full factorial experiment is used to establish multiple regression equation for induced hoop stress and maximum strain. Necessary data pertaining to design, manufacturing and operating conditions are collected systematically for variability study. Structural reliability is evaluated using Advanced First-Order Second-Moment Method (AFOSM). Finally, optimization formulation established and it has been discussed in this paper.

scholarly journals Fuzzy Multi-SVR Learning Model for Reliability-Based Design Optimization of Turbine Blades

Materials ◽  
2019 ◽  
Vol 12 (15) ◽  
pp. 2341 ◽  
Author(s):  
Chun-Yi Zhang ◽  
Ze Wang ◽  
Cheng-Wei Fei ◽  
Zhe-Shan Yuan ◽  
Jing-Shan Wei ◽  
...  
Keyword(s):  
Machine Learning ◽  
Response Surface ◽  
Turbine Blade ◽  
Response Surface Method ◽  
Fuzzy Theory ◽  
Turbine Blades ◽  
Learning Method ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Surface Method

The effectiveness of a model is the key factor of influencing the reliability-based design optimization (RBDO) of multi-failure turbine blades in the power system. A machine learning-based RBDO approach, called fuzzy multi-SVR learning method, was proposed by absorbing the strengths of fuzzy theory, support vector machine of regression (SVR), and multi-response surface method. The model of fuzzy multi-SVR learning method was established by adopting artificial bee colony algorithm to optimize the parameters of SVR models and considering the fuzziness of constraints based on fuzzy theory, in respect of the basic thought of multi-response surface method. The RBDO model and procedure with fuzzy multi-SVR learning method were then resolved and designed by multi-objective genetic algorithm. Lastly, the fuzzy RBDO of a turbine blade with multi-failure modes was performed regarding the design parameters of rotor speed, temperature, and aerodynamic pressure, and the design objectives of blade stress, strain, and deformation, and the fuzzy constraints of reliability degree and boundary conditions, as well. It is revealed (1) the stress and deformation of turbine blade are reduced by 92.38 MPa and 0.09838 mm, respectively. (2) The comprehensive reliability degree of the blade was improved by 3.45% from 95.4% to 98.85%. (3) It is verified that the fuzzy multi-SVR learning method is workable for the fuzzy RBDO of complex structures just like a multi-failure blade with high modeling precision, as well as high optimization, efficiency, and accuracy. The efforts of this study open a new research way, i.e., machine learning-based RBDO, for the RBDO of multi-failure structures, which expands the application of machine learning methods, and enriches the mechanical reliability design method and theory as well.

Response Surface Method Using Sequential Sampling for Reliability-Based Design Optimization

2009 ◽  
Author(s):  
Liang Zhao ◽  
K. K. Choi ◽  
Ikjin Lee ◽  
Liu Du
Keyword(s):  
Design Optimization ◽  
Response Surface ◽  
Response Surface Method ◽  
Sampling Method ◽  
Prediction Interval ◽  
Sequential Sampling ◽  
Kriging Method ◽  
Point Of Interest ◽  
Surface Method ◽  
Current Point

Traditional RBDO requires the sensitivity for both the most probable point (MPP) search in inverse reliability analysis and design optimization. However, the sensitivity is often unavailable or difficult to compute in complex multi-physics or multidisciplinary engineering applications. Hence, the response surface method (RSM) is often used to calculate both function evaluations and sensitivity effectively. Researchers have been developing the RSM for decades, and yet are still searching for an approach with an efficient sampling method for fast convergence while meeting the accuracy criteria. This paper proposes a new adaptive sequential sampling method to be integrated with the Kriging method for RBDO. By using the bandwidth of the prediction interval from the Kriging method, a new sampling strategy and a new local response surface accuracy criteria are proposed. In this sequential sampling method, the response surface is initiated using very few samples. An additional sampling point will then be determined by finding the point that has the largest absolute ratio between the bandwidth of the prediction interval and the predicted response within a neighboring area of current point of interest. The insertion of additional sampling will continue until the accuracy criterion of the response surface in the neighborhood of the current point of interest is achieved. Case studies show this proposed adaptive sequential sampling technique yields better result in terms of convergence speed compared with other sampling methods, such as the Latin hypercube sampling and the grid sampling, when the same sample size is used. Both a highly nonlinear mathematical example and a vehicle durability engineering example show that the proposed RSM yields accurate RBDO results that are comparable to the sensitivity-based RBDO results, as well as significant savings in computational time for function evaluation and sensitivity computation.

scholarly journals Inverse Response Surface Method in Reliability-Based Design

2017 ◽  
Vol 17 (2) ◽  
pp. 37-42 ◽  
Author(s):  
David Lehký ◽  
Martina Šomodíková
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Limit State ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Surface Method ◽  
Reliability Method ◽  
Adaptive Response Surface Method ◽  
Inverse Response ◽  
State Functions

Abstract The paper introduces an inverse response surface method utilized when performing reliability-based design optimization of time-consuming problems. Proposed procedure is based on a coupling of the adaptive response surface method and the artificial neural network-based inverse reliability method. The validity and accuracy of the method is tested using examples with explicit nonlinear limit state functions. Obtained results as well as important aspects of the method are discussed.

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