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

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

A survey is provided of shape parameterization techniques formultidisciplinary optimization, and some emerging ideas are highlighted. The survey focuses on the suitability of available techniques for multidisciplinary applications of complex cone gurations using high-e delity analysis tools such as computational e uid dynamics and computational structural mechanics. The suitability criteria are based on the efe ciency, effectiveness, ease of implementation, and availability of analytical sensitivities for geometry and grids. A section on sensitivity analysis, grid regeneration, and grid deformation techniques is also provided.

Survey of Shape Parameterization Techniques for High-Fidelity Multidisciplinary Shape Optimization

A new response surface methodology for reliability-based design optimization

With the advent of powerful computers, vehicle safety issues have recently been addressed using computational methods of vehicle crashworthiness, resulting in reductions in cost and time for new vehicle development. Vehicle design demands multidisciplinary optimization coupled with a computational crashworthiness analysis. However, simulation-based optimization generates deterministic optimum designs, which are frequently pushed to the limits of design constraint boundaries, leaving little or no room for tolerances (uncertainty) in modeling, simulation uncertainties, and/or manufacturing imperfections. Consequently, deterministic optimum designs that are obtained without consideration of uncertainty may result in unreliable designs, indicating the need for Reliability-Based Design Optimization (RBDO).

Recent development in RBDO allows evaluations of probabilistic constraints in two alternative ways: using the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). The PMA using the Hybrid Mean Value (HMV) method is shown to be robust and efficient in the RBDO process, whereas RIA yields instability for some problems. This paper presents an application of PMA and HMV for RBDO for the crashworthiness of a large-scale vehicle side impact. It is shown that the proposed RBDO approach is very effective in obtaining a reliability-based optimum design.

Reliability-based design optimization for crashworthiness of vehicle side impact

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

In this paper, a mixed approach for probabilistic structural durability design of mechanical systems is proposed. In this approach, a deterministic design optimization that considers structural crack initiation and crack propagation lives at critical points of the structural component as design constraints is performed first. After an optimal design is obtained, a reliability analysis is performed to ascertain if the deterministic optimal design is reliable. If the probability of the failure of the deterministic optimal design is found to be acceptable, a reliability-based design approach that employs a set of interactive design steps, such as trade-off analysis and what-if study, is used to obtain a near-optimal design that is reliable with an affordable computational cost. A 3-D tracked vehicle roadarm is employed to demonstrate the feasibility of the proposed approach.

A mixed design approach for probabilistic structural durability

Anefe cientreliability analysis method fordurability of structural components subjected to external and inertial loads with time-dependent variable amplitudes is presented. This method is able to support reliability analysis of crack-initiation and crack-propagation lives of practical applications, considering uncertainties such as material properties, manufacturing tolerances, and initial crack size. Three techniques are employed to support the probabilistic durability prediction: 1 ) strain-based approach for multiaxial crack-initiation-life prediction and linear elastic fracture mechanics approach for crack-propagation-life prediction, 2 ) statistics-based approach for reliability analysis, and 3 ) sensitivity analysis and optimization methods for searching the most probable point (MPP) in the random variable space to compute the fatigue failure probability using the e rst-order reliability analysis method. A two-point approximation method is employed to speed up the MPP search. A tracked-vehicle roadarm is presented to demonstrate feasibility of the proposed method.

Probabilistic Structural Durability Prediction

Design Sensitivity Analysis and Optimization tool (DSO) for shape design applications

In this paper, a mixed approach for probabilistic structural durability design of mechanical systems is proposed. In this approach, a deterministic design optimization that considers structural crack initiation and crack propagation lives at critical points of the structural component as design constraints is performed first. After an optimal design is obtained, a reliability analysis is performed to determine if the deterministic optimal design is reliable. If the probability of the failure of the deterministic optimal design is found unacceptable, a reliability-based design approach that employs a set of interactive design steps, such as trade-off analysis and what-if study, is used to obtain a nearoptimal design that is reliable with an affordable computational cost. A 3-D tracked vehicle roadarm is employed to demonstrate the feasibility of the proposed approach.

Xiaoming Yu

Papers

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

A mixed design approach for probabilistic structural durability

Probabilistic Structural Durability Prediction

Design Sensitivity Analysis and Optimization tool (DSO) for shape design applications

A mixed design approach for probabilistic structural durability