Non-Gradient Based Parameter Sensitivity Estimation for Robust Design Optimization

2003 ◽  
Author(s):  
S. Gunawan ◽  
S. Azarm
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Parameter Sensitivity ◽  
Robust Design Optimization ◽  
Optimization Approach ◽  
Case Scenario ◽  
Worst Case ◽  
Design Alternative ◽  
Sensitivity Estimation ◽  
Gradient Based

We present a method for estimating the parameter sensitivity of a design alternative for use in robust design optimization. The method is non-gradient based: it is applicable even when the objective function of an optimization problem is non-differentiable and/or discontinuous with respect to the parameters. Also, the method does not require a presumed probability distribution for parameters, and is still valid when parameter variations are large. The sensitivity estimate is developed based on the concept that associated with each design alternative there is a region in the parameter variation space whose properties can be used to predict that design’s sensitivity. Our method estimates such a region using a worst-case scenario analysis and uses that estimate in a bi-level robust optimization approach. We present a numerical and an engineering example to demonstrate the applications of our method.

Non-Gradient Based Parameter Sensitivity Estimation for Single Objective Robust Design Optimization

2003 ◽  
Vol 126 (3) ◽  
pp. 395-402 ◽  
Author(s):  
S. Gunawan ◽  
S. Azarm
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Parameter Sensitivity ◽  
Robust Design Optimization ◽  
Optimization Approach ◽  
Case Scenario ◽  
Worst Case ◽  
Design Alternative ◽  
Gradient Based ◽  
Single Objective

We present a method for estimating the parameter sensitivity of a design alternative for use in single objective robust design optimization. The method is non-gradient based: it is applicable even when the objective function of an optimization problem is non-differentiable and/or discontinuous with respect to the parameters. Also, the method does not require a presumed probability distribution for parameters, and is still valid when parameter variations are large. The sensitivity estimate is developed based on the concept that associated with each design alternative there is a region in the parameter variation space whose properties can be used to predict that design’s sensitivity. Our method estimates such a region using a worst-case scenario analysis and uses that estimate in a bi-level robust optimization approach. We present a numerical and an engineering example to demonstrate the applications of our method.

scholarly journals Efficient Robust Design Optimization of Optical Systems

2019 ◽  
Vol 215 ◽  
pp. 02001
Author(s):  
Stephanie Kunath
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Optical Design ◽  
Simulation Software ◽  
Robust Design Optimization ◽  
Optical Systems ◽  
Optical Simulation ◽  
Optimization Approach ◽  
Trade Off ◽  
Virtual Product Development

To accelerate the virtual product development of using optical simulation software, the Robust Design Optimization approach is very promising. Optical designs can be explored thoroughly by means of sensitivity analysis. This includes the identification of relevant input parameters and the modelling of inputs vs. outputs to understand their dependencies and interactions. Furthermore, the intelligent definition of objective functions for an efficient subsequent optimization is of high importance for multi-objective optimization tasks. To find the best trade-off between two or more merit functions, a Pareto optimization is the best choice. As a result, not only one design, but a front of best designs is obtained and the most appropriate design can be selected by the decision maker. Additionally, the best trade-off between output variation of the robustness (tolerance) and optimization targets can be found to secure the manufacturability of the optical design by several advanced approaches. The benefit of this Robust Design Optimization approach will be demonstrated.

Gradient-based design robustness measure for robust geotechnical design

2014 ◽  
Vol 51 (11) ◽  
pp. 1331-1342 ◽  
Author(s):  
Wenping Gong ◽  
Sara Khoshnevisan ◽  
C. Hsein Juang
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Cost Efficiency ◽  
Robust Design Optimization ◽  
System Response ◽  
Robustness Measure ◽  
Gradient Based ◽  
Geotechnical Design ◽  
Safety Constraint ◽  
Noise Factors

This paper presents a gradient-based robustness measure for robust geotechnical design (RGD) that considers safety, design robustness, and cost efficiency simultaneously. In the context of robust design, a design is deemed robust if the system response of concern is insensitive, to a certain degree, to the variation of noise factors (i.e., uncertain geotechnical parameters, loading parameters, construction variation, and model biases or errors). The key to a robust design is a quantifiable robustness measure with which the robust design optimization can be effectively and efficiently implemented. Based on the developed gradient-based robustness measure, a robust design optimization framework is proposed. In this framework, the design (safety) constraint is analyzed using advanced first-order second-moment (AFOSM) method, considering the variation in the noise factors. The design robustness, in terms of sensitivity index (SI), is evaluated using the normalized gradient of the system response to the noise factors, which can be efficiently computed from the by-product of AFOSM analysis. Within the proposed framework, robust design optimization is performed with two objectives, design robustness and cost efficiency, while the design (safety) constraint is satisfied by meeting a target reliability index. Generally, cost efficiency and design robustness are conflicting objectives and the robust design optimization yields a Pareto front, which reveals a tradeoff between the two objectives. Through an illustrative example of a shallow foundation design, the effectiveness and significance of this new robust design approach is demonstrated.

scholarly journals How to compare performance of robust design optimization algorithms, including a novel method

2017 ◽  
Vol 31 (3) ◽  
pp. 286-297 ◽  
Author(s):  
Johan A. Persson ◽  
Johan Ölvander
Keyword(s):  
Robust Optimization ◽  
Design Optimization ◽  
Robust Design ◽  
Performance Metrics ◽  
Computational Cost ◽  
Optimization Method ◽  
Engineering Problem ◽  
Robust Design Optimization ◽  
Optimization Approach ◽  
Novel Method

AbstractThis paper proposes a method to compare the performances of different methods for robust design optimization of computationally demanding models. Its intended usage is to help the engineer to choose the optimization approach when faced with a robust optimization problem. This paper demonstrates the usage of the method to find the most appropriate robust design optimization method to solve an engineering problem. Five robust design optimization methods, including a novel method, are compared in the demonstration of the comparison method. Four of the five compared methods involve surrogate models to reduce the computational cost of performing robust design optimization. The five methods are used to optimize several mathematical functions that should be similar to the engineering problem. The methods are then used to optimize the engineering problem to confirm that the most suitable optimization method was identified. The performance metrics used are the mean value and standard deviation of the robust optimum as well as an index that combines the required number of simulations of the original model with the accuracy of the obtained solution. These measures represent the accuracy, robustness, and efficiency of the compared methods. The results of the comparison show that sequential robust optimization is the method with the best balance between accuracy and number of function evaluations. This is confirmed by the optimizations of the engineering problem. The comparison also shows that the novel method is better than its predecessor is.

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