Under random and interval hybrid uncertainties, solving hybrid reliability based design optimization (HRBDO) can acquire an optimal balance between structural performance and reliability. Since solving HRBDO includes ...
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Under random and interval hybrid uncertainties, solving hybrid reliability based design optimization (HRBDO) can acquire an optimal balance between structural performance and reliability. Since solving HRBDO includes a triple nested framework involving minimum analysis of performance function (PF), failure probability constraint analysis and design parameter optimization, the computational complexity of HRBDO is high, especially for dealing with complex structures. Therefore, a quantile-based sequential optimization and reliability assessment method (QSORA) is proposed for reducing the computational complexity of HRBDO. In the proposed QSORA for HRBDO, failure probability constraint is firstly transformed into minimum PF (MPF) quantile one corresponding to target failure probability. Then, approximating the difference between PF and its target quantile at current iteration by that at previous one, the failure probability constraint analysis is decoupled from the design parameter optimization. Moreover, by approximating the minimum point of the PF with respect to the interval input in the current iteration by that in the previous one, the minimum analysis of PF is separated from the design parameter optimization. By the separation of minimum analysis and failure probability constraint analysis from the design parameter optimization in the proposed QSORA, the triple nested framework of HRBDO is decoupled sequentially as the deterministic design optimization, the minimum analysis of the PF and the target MPF quantile estimation, and this way of reconstructing the HRBDO from the triple nested framework to three singleloop frameworks can significantly enhance the efficiency of solving HRBDO. Furthermore, the MPF quantile at the current design parameter is estimated by stochastic collocation based statistical moment method, in which the stochastic collocation method is employed to efficiently estimate the MPF moment to approximate the probability density function of MPF.
Uncertainty is inevitable in the real physical world, and it is necessary to take into account its effects on the structural design and optimization processes. In this study a reliability-based shape and topology opti...
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Uncertainty is inevitable in the real physical world, and it is necessary to take into account its effects on the structural design and optimization processes. In this study a reliability-based shape and topology optimization method is proposed for plane frames. The reliability constraint is expressed in terms of quantile which is estimated by using the maximum entropy method subject to constraints on the sample linear moments (L-moments) with small sample size. An iterative scheme of sequential optimization and reliability assessment is employed to solve a series of deterministic optimization problems with shifted boundaries on the constraints. Derivative of the quantile function is obtained by solving a convex optimization problem, instead of solving a system of nonlinear equations. Force density method is applied to an auxiliary truss model for simultaneous shape and topology optimization of plane frames to alleviate the difficulties caused by melting nodes. It is demonstrated by the benchmark and numerical examples that the quantile function can be appropriately estimated by the proposed method, and the solution satisfying the required reliability constraint can also be achieved..
In reliability-Based design optimization (RBDO), the aim is to develop an optimal design characterized by high reliability through fulfilling design requirements at the targeted probability threshold. The goal of reli...
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In reliability-Based design optimization (RBDO), the aim is to develop an optimal design characterized by high reliability through fulfilling design requirements at the targeted probability threshold. The goal of reliabilityoptimization is to obtain excellent algorithms by focusing on evaluation and optimization. In RBDO, due to the selection of evaluation methods and the problem of updating reliable point methods, it is often impossible to obtain accurate failure probability results with less computation, and the results are inaccurate, or the computation amount is increased. The integral-based reliability analysis method: Hyperspherical cap area integral method (HCAIM) can achieve an accuracy close to that of the MCS method while having a very low computational load, thus enabling the efficient and precise calculation of failure probabilities. Therefore, by introducing a reliability evaluation method based on Integral Method for reliabilityoptimization (IMRO), as a decoupling method, high accuracy failure probability calculation results can be obtained with relatively small calculation amount, and then optimization results can be obtained by IMRO and sequence optimization methods. First, a reliability analysis example is utilized to demonstrate the accuracy of the reliability analysis part of IMRO. Then, a set of nonlinear challenges and diverse engineering case studies were utilized to assess the algorithm's performance. The calculation results after comparison prove that IMRO is more accurate in dealing with nonlinear problems and engineering examples, and can better meet the requirements.
reliability assessment (RA) is pivotal to enhancing the efficiency and robustness of reliability-based optimization. Classical RA algorithms suffer from inefficiency and non-convergence problems such as bifurcation, p...
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reliability assessment (RA) is pivotal to enhancing the efficiency and robustness of reliability-based optimization. Classical RA algorithms suffer from inefficiency and non-convergence problems such as bifurcation, periodic oscillations, and chaos. In this paper, a bi-directional adaptive conjugate gradient (BACG) algorithm incorporating a newly developed concave vs. convex decision criterion (CCDC) is suggested. The BACG technique is harmoniously fused with the sequential optimization and reliability assessment (SORA) to expedite design timelines while simultaneously enhancing precision. Within the BACG, an adaptive acceleration factor is presented to dynamically activate the positive and negative acceleration of the most probable point (MPP) search, specifically tailored for convex and concave performance functions. The concavity/convexity of the performance function is adjudicated via the CCDC using two adjoining MPPs. The validation of the convergence of BACG is established through rigorous mathematical formulation. A comprehensive study is conducted to assess the robustness, stability, and efficiency of BACG via matching with eight prominent inverse RA methods. The study encompasses six inverse reliability problems, one reliability-based design optimization (RBDO), and two reliability-based topology optimization (RBTO) projects involving a simply supported beam and a submarine pressure hull. Lastly, the BACG is utilized to perform the RBTO design for a jacket offshore platform.
The uncertainty and extremity of ocean conditions make the design of marine structures a challenging process. reliability-based optimization is a powerful approach to enhance material utilization and ensure system sur...
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The uncertainty and extremity of ocean conditions make the design of marine structures a challenging process. reliability-based optimization is a powerful approach to enhance material utilization and ensure system survivability. In this paper, a novel reliability-based design optimization (RBDO) method that combines topology, shape, and size optimization is proposed to achieve the design of marine structures. Within the framework of decoupled sequence optimization and reliability assessment, the developed method employs an innovative multitechnology combined optimization Scheme and a new reliability assessment algorithm. The combined optimization Scheme is established by simultaneously incorporating topology, shape, and size optimization technologies to further improve the lightweighting effect. The advanced arc interpolation algorithm is developed, which dynamically selects the advanced mean value method or arc interpolation method based on the trend judgment criterion to accelerate the calculation for the most probable point in reliability assessments. The RBDO examples of the wind turbine jacket and platform stiffened plate are utilized to verify the proposed method's applicability and validity, and the results are compared with those of other approaches. The findings prove that this RBDO method can effectively address reliability-based design problems of marine structures and is superior in providing lightweighting structures compared with others.
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