Intelligent initial point selection for MPP search in reliability-based design optimization

Buckling failure mainly occurs in slender rod structure under pressure, which incurs great concern and should be addressed in topology optimization (TO). However, due to the internal defects of material and the external environment interference of engineering system, the practical engineering structure inevitably produces many uncertain factors in the manufacturing and service stages. Therefore, a reliability-based topology optimization (RBTO) model under buckling and compliance constraints is established to operate the structural lightweight design considering reliability and stability requirements. To reduce the number of probabilistic constraints, the Kreisselmeier-Steinhauser aggregation function is adopted for combining the multiple constraints into a single smooth and differentiable constraint. Then, a single-loop approach combining modified chaos control strategy is applied to guarantee the robustness, effectiveness, and computational efficiency of RBTO. In addition, the sensitivities of the probabilistic constraint with respect to design and random variables are deduced, and the accuracy of sensitivities is verified by finite difference method. Finally, the validity of the RBTO method is verified by comparing with deterministic TO, in which three numerical examples are employed to demonstrate the robustness and computational accuracy.

show abstract

“…

\hat{\mathbf{n}}\left({\mathbf{x}}_{\mathbf{u}}^{\left(k+1\right)}\right)

represents the descent direction of

{\mathbf{x}}_{\mathbf{u}}^{\left(k+1\right)}

{\mathbf{x}}_{\mathbf{u}\_\mathrm{AMV}}^{(k)}

are the random variables at the k th iteration computed by the advanced mean value method 45 .

\zeta

is the control factor, which is set to 0.5.…”

Section: Rbto Formula Under Buckling and Compliance Constraintsmentioning

confidence: 99%

“…x (k) u_AMV are the random variables at the kth iteration computed by the advanced mean value method. 45 𝜁 is the control factor, which is set to 0.5. Subscript j denotes the random variable number.…”

Section: Rbto Modelmentioning

confidence: 99%

Reliability‐based topology optimization of continuum structure under buckling and compliance constraints

Guo

Wang

Meng

et al. 2022

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“… d U and d L denote the upper and lower limit of design variable vector. The probability of failure is defined by a multi-dimensional integration in the failure domain, which can be expressed as (Jung et al, 2020)…”

Section: Reliability-based Topology Optimizationmentioning

confidence: 99%

“…Because of its high efficiency and stability, the FORM has a extensive application in the evaluation of the probabilistic constraint in RBDO problem. In FORM, the random variable vector X in original space should be transformed to the random variable vector Y in standard normal space by using the Rosenblatt transformation (Jung et al, 2020). The reliability index β is defined as the shortest distance from the origin to the limit state surface in the standard normal space.…”

Section: Reliability-based Topology Optimizationmentioning

confidence: 99%

Reliability-based topology optimization of piezoelectric smart structures with voltage uncertainty

Yang

Cheng

Wang

et al. 2022

Journal of Intelligent Material Systems and Structures

View full text Add to dashboard Cite

Currently, most of the piezoelectric structures are designed under deterministic conditions, where the influence of uncertain factors on the output motion accuracy is ignored. In this work, a probabilistic reliability-based topology optimization method for piezoelectric structure is proposed to deal with the working voltage uncertainty. A nested double-loop optimization algorithm of minimizing the total volume while satisfying the reliability requirement of the displacement performance is established, where the PEMAP-P (piezoelectric material with penalization and polarization) model is used for parameterization of stiffness matrix, piezoelectric coupling matrix, and polarization direction. This strategy consists of an inner loop for reliability analysis and an outer loop for topology optimization. The reliability index approach based on most probable point (MPP) is used for realizing the evaluation of reliability constraint in reliability analysis. The sensitivities of reliability constraint with respect to the random variables and design variables are detailed using the adjoint variable method. Typical examples are performed to illustrate the effectiveness of the proposed RBTO method. A comparison of the optimization results for different reliability indexes, standard deviations of the voltage, spring stiffnesses, and displacement limits are conducted, as well as the deterministic topology optimization results.

show abstract

“…which promotes PMA as a more efficient and robust choice to wisely deal with RBDO problems. 24,25 Ting Lin et al 26 proposed the modified reliability index approach (MRIA) to overcome the disadvantage of RIA by a new definition of reliability index. Although MRIA could converge the optimal solution efficiently and stably in assessing the active probabilistic constraints, it also inherits the low efficiency of searching for the most probability point (MPP); hence, the hybrid reliability method is presented.…”

Section: Introductionmentioning

confidence: 99%

A novel reliability index approach and applied it to cushioning packaging design

Huang

Shi

2022

Advances in Mechanical Engineering

View full text Add to dashboard Cite

This paper is aimed at proposing a new approach to Reliability-based Design Optimization (RBDO) and applying it to cushioning packaging design with a highly nonlinear system. The problem is formulated as an RBDO problem, which is included a minimizing cost function and probabilistic constraints. Here, the thickness of the cushion material is dealt with uncertainty and uncontrolled parameters. The traditional reliability index approach (RIA) has evolved as a powerful tool to solve the RBDO problem; however, due to its convergence problem, the modified reliability index approach (MRIA) is proposed. Although the MRIA method solves the problems of the traditional RIA, it inherits the low efficiency of searching for the most probability point (MPP). Thus, we developed a novel RIA based on MRIA to improve the efficiency and robustness during the RBDO process. The innovation active set strategy is developed in reliability assessment, which is a strict inequality to determine whether the current constraint is active or inactive. An application example is presented, and the results are compared with MRIA to assess cost-effectiveness and efficiency. Results indicate the proposed method is feasible to solve the uncertainty problem of packaging materials in the processing process and is also an efficient RBDO method.

show abstract

Intelligent initial point selection for MPP search in reliability-based design optimization

Cited by 16 publications

References 33 publications

Reliability‐based topology optimization of continuum structure under buckling and compliance constraints

Reliability‐based topology optimization of continuum structure under buckling and compliance constraints

Reliability-based topology optimization of piezoelectric smart structures with voltage uncertainty

A novel reliability index approach and applied it to cushioning packaging design

Contact Info

Product

Resources

About