Simulation and the monte carlo method

Probabilistic optimization design offers tools for making reliable decisions with the consideration of uncertainty associated with design variables/parameters and simulation models. In a probabilistic design, such as reliability-based design and robust design, the design feasibility is formulated probabilistically such that the probability of the constraint satisfaction (reliability) exceeds the desired limit. The reliability assessment for probabilistic constraints often involves an iterative procedure; therefore, two loops are involved in a probabilistic optimization. Due to the double-loop procedure, the computational demand is extremely high. To improve the efficiency of a probabilistic design, a novel method – sequential optimization and reliability assessment (SORA) is developed in this paper. The SORA method employs a single-loop strategy where a serial of cycles of optimization and reliability assessment is employed. In each cycle optimization and reliability assessment are decoupled from each other; no reliability assessment is required within optimization and the reliability assessment is only conducted after the optimization. The key concept of the proposed method is to shift the boundaries of violated deterministic constraints (with low reliability) to the feasible direction based on the reliability information obtained in the previous cycle. Hence the design is quickly improved from cycle to cycle and the computational efficiency is improved significantly. Two engineering applications, the reliability-based design for vehicle crashworthiness of side impact and the integrated reliability and robust design of a speed reducer, are presented to demonstrate the effectiveness of the SORA method.Copyright © 2002 by ASME

Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a reference manual for the commands specification for the DAKOTA software, providing input overviews, option descriptions, and example specifications. DAKOTA Version 5.0 Reference Manual generated on May 7, 2010

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DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's manual.

Reliability-Based Design Optimization (RBDO) involves evaluation of probabilistic constraints, which can be done in two different ways, the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). It has been reported in the literature that RIA yields instability for some problems but PMA is robust and efficient in identifying a probabilistic failure mode in the RBDO process. However, several examples of numerical tests of PMA have also shown instability and inefficiency in the RBDO process if the Advanced Mean Value (AMV) method, which is a numerical tool for probabilistic constraint evaluation in PMA, is used, since it behaves poorly for a concave performance function, even though it is effective for a convex performance function. To overcome difficulties of the AMV method, the Conjugate Mean Value (CMV) method is proposed in this paper for the concave performance function in PMA. However, since the CMV method exhibits the slow rate of convergence for the convex function, it is selectively used for concave-type constraints. That is, once the type of the performance function is identified, either the AMV method or the CMV method can be adaptively used for PMA during the RBDO iteration to evaluate probabilistic constraints effectively. This is referred to as the Hybrid Mean Value (HMV) method. The enhanced PMA with the HMV method is compared to RIA for effective evaluation of probabilistic constraints in the RBDO process. It is shown that PMA with a spherical equality constraint is easier to solve than RIA with a complicated equality constraint in estimating the probabilistic constraint in the RBDO process. NOMENCLATURE X

https://www.researchgate.net/profile/Kyung_Choi2/publication/237608923_Hybrid_Analysis_Method_for_Reliability-Based_Design/links/0046352a9d2fc3d1e0000000.pdf

Hybrid Analysis Method for Reliability-Based Design Optimization

Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles

This paper presents a general approach for probabilistic constraint evaluation in the reliability-based design optimization (RBDO). Different perspectives of the general approach are consistent in prescribing the probabilistic constraint, where the conventional reliability index approach (RIA) and the proposed performance measure approach (PMA) are identified as two special cases. PMA is shown to be inherently robust and more efficient in evaluating inactive probabilistic constraints, while RIA is more efficient for violated probabilistic constraints. Moreover, RBDO often yields a higher rate of convergence by using PMA, while RIA yields,singularity in some cases.

A new study on reliability-based design optimization

A novel design potential method that integrates the probabilistic constraint evaluation closely into the design optimization process is presented for robust system parameter design. From a broader perspective, it is shown that the probabilistic constraints can be evaluated using either the conventional reliability index approach or the proposed performance measure approach. The performance measure approach is inherently robust and is more effective when the prohahilistic constraint is inactive. The reliability index approach is more effective for the violated probabilistic constraint, but it could yield singularity when the probabilistic constraint is inactive. Moreover, the close coupling of performance probability analysis and design optimization is illustrated in a proposed unified system space. The design potential method, which is developed to take full advantage of the important design information obtained from the previous probabilistic constraint evaluation, can significantly accelerate the convergence of the reliability-based design optimization process.

Design Potential Method for Robust System Parameter Design

A CAD-based design parameterization for shape optimization of elastic solids

The reliability-based design optimization (RBDO) can be described by the design potential concept in a unified system space, where the probabilistic constraint is identified by the design potential surface of the reliability target that is obtained analytically from the first-order reliability method (FORM). This paper extends the design potential concept to treat nonsmooth probabilistic constraints and extreme case design in RBDO. In addition, refinement of the design potential surface, which yields better optimum design, can be obtained using more accurate second-order reliability method (SORM). By integrating performance probability analysis into the iterative design optimization process, the design potential concept leads to a very effective design potential method (DPM) for robust system parameter design. It can also be applied effectively to extreme case design (ECD) by directly representing a probabilistic constraint in terms of the system performance function.

Extensions of design potential concept for reliability-based design optimization to nonsmooth and extreme cases

This paper presents a design potential concept for reliability-based design optimization by integrating the probability analysis into the design optimization process. The reliability-based system parameter design is illustrated by the design potential concept in a unified system space, where design potential surfaces are derived from first-order reliability methods and an adaptive strategy is developed for robust and more efficient probabilistic constraint evaluation. More important, the design potential concept provides an in-depth understanding of reliability-based design optimization and leads to a design potential method that can significantly accelerate the process of robust system parameter design optimization.

Jian Tu

Papers

A new study on reliability-based design optimization

Design Potential Method for Robust System Parameter Design

A CAD-based design parameterization for shape optimization of elastic solids

Extensions of design potential concept for reliability-based design optimization to nonsmooth and extreme cases

Design potential concept for reliability-based design optimization