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1
Chiralaksanakul, Anukal, and Sankaran Mahadevan. "First-Order Approximation Methods in Reliability-Based Design Optimization." Journal of Mechanical Design 127, no. 5 (October 8, 2004): 851–57. http://dx.doi.org/10.1115/1.1899691.
Анотація:
Efficiency of reliability-based design optimization (RBDO) methods is a critical criterion as to whether they are viable for real-world problems. Early RBDO methods are thus based primarily on the first-order reliability method (FORM) due to its efficiency. Recently, several first-order RBDO methods have been proposed, and their efficiency is significantly improved through problem reformulation and/or the use of inverse FORM. Our goal is to present these RBDO methods from a mathematical optimization perspective by formalizing FORM, inverse FORM, and associated RBDO reformulations. Through the formalization, their relationships are revealed. Using reported numerical studies, we discuss their numerical efficiency, convergence, and accuracy.
2
Li, Xiaoke, Qingyu Yang, Yang Wang, Xinyu Han, Yang Cao, Lei Fan, and Jun Ma. "Development of surrogate models in reliability-based design optimization: A review." Mathematical Biosciences and Engineering 18, no. 5 (2021): 6386–409. http://dx.doi.org/10.3934/mbe.2021317.
Анотація:
<abstract> <p>Reliability-based design optimization (RBDO) is applied to handle the unavoidable uncertainties in engineering applications. To alleviate the huge computational burden in reliability analysis and design optimization, surrogate models are introduced to replace the implicit objective and performance functions. In this paper, the commonly used surrogate modeling methods and surrogate-assisted RBDO methods are reviewed and discussed. First, the existing reliability analysis methods, RBDO methods, commonly used surrogate models in RBDO, sample selection methods and accuracy evaluation methods of surrogate models are summarized and compared. Then the surrogate-assisted RBDO methods are classified into global modeling methods and local modeling methods. A classic two-dimensional RBDO numerical example are used to demonstrate the performance of representative global modeling method (Constraint Boundary Sampling, CBS) and local modeling method (Local Adaptive Sampling, LAS). The advantages and disadvantages of these two kinds of modeling methods are summarized and compared. Finally, summary and prospect of the surrogate–assisted RBDO methods are drown.</p> </abstract>
3
Deng, Siyang, Stéphane Brisset, and Stephane Clénet. "Comparative study of methods for optimization of electromagnetic devices with uncertainty." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 2 (March 5, 2018): 704–17. http://dx.doi.org/10.1108/compel-11-2016-0502.
Анотація:
PurposeThis paper compares six reliability-based design optimization (RBDO) approaches dealing with uncertainties for a simple mathematical model and a multidisciplinary optimization problem of a safety transformer to highlight the most effective. Design/methodology/approachThe RBDO and various approaches to calculate the probability of failure are is presented. They are compared in terms of precision and number of evaluations on mathematical and electromagnetic design problems. FindingsThe mathematical example shows that the six RBDO approaches have almost the same results except the approximate moment approach that is less accurate. The optimization of the safety transformer highlights that not all the methods can converge to the global solution. Performance measure approach, single-loop approach and sequential optimization and reliability assessment (SORA) method appear to be more stable. Considering both numerical examples, SORA is the most effective method among all RBDO approaches. Originality/valueThe comparison of six RBDO methods on the optimization problem of a safety transformer is achieved for the first time. The comparison in terms of precision and number of evaluations highlights the most effective ones.
4
Zou, T., and S. Mahadevan. "Versatile Formulation for Multiobjective Reliability-Based Design Optimization." Journal of Mechanical Design 128, no. 6 (November 22, 2005): 1217–26. http://dx.doi.org/10.1115/1.2218884.
Анотація:
This paper develops a multiobjective optimization methodology for system design under uncertainty. Model-based reliability analysis methods are used to compute the probabilities of unsatisfactory performance at both component and system levels. Combined with several multiobjective optimization formulations, a versatile reliability-based design optimization (RBDO) approach is used to achieve a tradeoff between two objectives and to generate the Pareto frontier for decision making. The proposed RBDO approach uses direct reliability analysis to decouple the reliability and optimization iterations, instead of inverse first-order reliability analysis as other existing decoupled approaches. This helps to solve a wide variety of RBDO problems with competing objectives, especially when system-level reliability constraints need to be considered. The approach also allows more accurate methods to be used for reliability analysis, and reliability terms to be included in the objective function. Two important automotive quality objectives, related to the door closing effort (evaluated using component reliability analysis) and the wind noise (evaluated using system reliability analysis), are used to illustrate the proposed method.
5
Zhang, Li-Xiang, Xin-Jia Meng, and He Zhang. "Reliability-Based Design Optimization for Design Problems with Random Fuzzy and Interval Uncertainties." International Journal of Computational Methods 17, no. 06 (April 4, 2019): 1950018. http://dx.doi.org/10.1142/s021987621950018x.
Анотація:
Reliability-based design optimization (RBDO) has been widely used in mechanical design. However, the treatment of various uncertainties and associated computational burden are still the main obstacle of its application. A methodology of RBDO under random fuzzy and interval uncertainties (RFI-RBDO) is proposed in this paper. In the proposed methodology, two reliability analysis approaches, respectively named as FORM-[Formula: see text]-URA and interpolation-based sequential performance measurement approach (ISPMA), are developed for the mixed uncertainties assessment, and a parallel-computing-based SOMUA (PCSOMUA) method is proposed to reduce the computational cost of RFI-RBDO. Finally, two examples are provided to verify the validity of the methods.
6
Albuquerque, Carla Simone de, and Mauro de Vasconcelos Real. "Comparative analysis of deterministic and reliability-based structural optimization methods." Ciência e Natura 45, esp. 3 (December 1, 2023): e74335. http://dx.doi.org/10.5902/2179460x74335.
Анотація:
Optimization is the act of obtaining the best possible result under established conditions. Usually, the optimization of a structural design is done considering the structure's dimensions, the materials' properties, and the loads as deterministic values. This way, the optimization process can lead to a more economical design without guaranteeing that this structure is safe. In practice, there are always uncertainties about the final dimensions of the built structure, material properties, and loads. Then, the need arises to use design optimization techniques based on reliability to guarantee a project that is both economical and safe. This objective is achieved by including uncertainties in the optimization process. This article evaluates the parameters that determine the global minimum of the optimization methods DDO (Deterministic Design Optimization) and RBDO (Reliability-Based Design Optimization). This work aims to compare the structural optimization methods of DDO and RBDO through an example. The results are obtained through the codes of the methods implemented in the Python language and show that when comparing the two optimization methods, the presence of uncertainties alters the optimal solution.
7
El Hami, A., and Bouchaib Radi. "Comparison Study of Different Reliability-Based Design Optimization Approaches." Advanced Materials Research 274 (July 2011): 113–21. http://dx.doi.org/10.4028/www.scientific.net/amr.274.113.
Анотація:
In this paper, we present a new method based on Optimal Safety Factors (OSF) in the context of the Reliability-Based Design Optimization (RBDO) analysis of ultrasonic motors with traveling wave taking into account the contact between the different components (stator and rotor). We will underline also the different methods of the RBDO analysis and we highlight the advantage of our approach based on OSF. Numerical results are given to illustrate the proposed method.
8
Chen, Zhen Zhong, Hao Bo Qiu, Hong Yan Hao, and Hua Di Xiong. "A Reliability Index Based Decoupling Method for Reliability-Based Design Optimization." Advanced Materials Research 544 (June 2012): 223–28. http://dx.doi.org/10.4028/www.scientific.net/amr.544.223.
Анотація:
Reliability-based design optimization (RBDO) evaluates variation of output induced by uncertainties of design variables and results in an optimal design while satisfying the reliability requirements. However, its use in practical applications is hindered by the huge computational cost during the evaluation of structure reliability. In this paper, the reliability index based decoupling method is developed to improve the efficiency of probabilistic optimization. The reliability index is used to calculate the shifting vector in the decoupling process, due to its efficiency in evaluating violated probabilistic constraints. The computation capability of the proposed method is demonstrated using two examples, which are widely used to test RBDO methods. The comparison results show that the proposed method has the same accuracy as the existing methods, and it is also very efficient.
9
Chun, Junho. "Reliability-Based Design Optimization of Structures Using Complex-Step Approximation with Sensitivity Analysis." Applied Sciences 11, no. 10 (May 20, 2021): 4708. http://dx.doi.org/10.3390/app11104708.
Анотація:
Structural optimization aims to achieve a structural design that provides the best performance while satisfying the given design constraints. When uncertainties in design and conditions are taken into account, reliability-based design optimization (RBDO) is adopted to identify solutions with acceptable failure probabilities. This paper outlines a method for sensitivity analysis, reliability assessment, and RBDO for structures. Complex-step (CS) approximation and the first-order reliability method (FORM) are unified in the sensitivity analysis of a probabilistic constraint, which streamlines the setup of optimization problems and enhances their implementation in RBDO. Complex-step approximation utilizes an imaginary number as a step size to compute the first derivative without subtractive cancellations in the formula, which have been observed to significantly affect the accuracy of calculations in finite difference methods. Thus, the proposed method can select a very small step size for the first derivative to minimize truncation errors, while achieving accuracy within the machine precision. This approach integrates complex-step approximation into the FORM to compute sensitivity and assess reliability. The proposed method of RBDO is tested on structural optimization problems across a range of statistical variations, demonstrating that performance benefits can be achieved while satisfying precise probabilistic constraints.
10
Zhang, Chun-Yi, Ze Wang, Cheng-Wei Fei, Zhe-Shan Yuan, Jing-Shan Wei, and Wen-Zhong Tang. "Fuzzy Multi-SVR Learning Model for Reliability-Based Design Optimization of Turbine Blades." Materials 12, no. 15 (July 24, 2019): 2341. http://dx.doi.org/10.3390/ma12152341.
Анотація:
The effectiveness of a model is the key factor of influencing the reliability-based design optimization (RBDO) of multi-failure turbine blades in the power system. A machine learning-based RBDO approach, called fuzzy multi-SVR learning method, was proposed by absorbing the strengths of fuzzy theory, support vector machine of regression (SVR), and multi-response surface method. The model of fuzzy multi-SVR learning method was established by adopting artificial bee colony algorithm to optimize the parameters of SVR models and considering the fuzziness of constraints based on fuzzy theory, in respect of the basic thought of multi-response surface method. The RBDO model and procedure with fuzzy multi-SVR learning method were then resolved and designed by multi-objective genetic algorithm. Lastly, the fuzzy RBDO of a turbine blade with multi-failure modes was performed regarding the design parameters of rotor speed, temperature, and aerodynamic pressure, and the design objectives of blade stress, strain, and deformation, and the fuzzy constraints of reliability degree and boundary conditions, as well. It is revealed (1) the stress and deformation of turbine blade are reduced by 92.38 MPa and 0.09838 mm, respectively. (2) The comprehensive reliability degree of the blade was improved by 3.45% from 95.4% to 98.85%. (3) It is verified that the fuzzy multi-SVR learning method is workable for the fuzzy RBDO of complex structures just like a multi-failure blade with high modeling precision, as well as high optimization, efficiency, and accuracy. The efforts of this study open a new research way, i.e., machine learning-based RBDO, for the RBDO of multi-failure structures, which expands the application of machine learning methods, and enriches the mechanical reliability design method and theory as well.
11
Sokołowski, Damian, and Marcin Kamiński. "Stochastic Reliability-Based Design Optimization Framework for the Steel Plate Girder with Corrugated Web Subjected to Corrosion." Materials 15, no. 20 (October 14, 2022): 7170. http://dx.doi.org/10.3390/ma15207170.
Анотація:
This paper proposes the framework for reliability-based design optimization (RBDO) of structural elements with an example based on the corrugated web I-girder. It tackles the problem of topological optimization of corroding structures with uncertainties. Engineering restrictions follow a concept of the limit states (LS) and extend it for stability and eigenfrequency assessment. The reliability constraints include all the LS; they are computed according to first- and second-order reliability methods. The RBDO example minimizes the bridge girder cross-section while satisfying the structural reliability level for the ultimate and the serviceability limit states, stability, and eigenfrequency. It takes into consideration two uncorrelated random effects, i.e., manufacturing imperfection and corrosion. They are both Gaussian; the first of them is applied at assembly time, while the second is applied according to the time series. The example confronts three independent FEM models with an increasing level of detailing, and compares RBDO results for three concurrent probabilistic methods, i.e., the iterative stochastic perturbation technique (ISPT), the semi-analytical method, and the Monte Carlo simulation. This study proves that the RBDO analysis is feasible even for computationally demanding structures, can support automation of structural design, and that the level of detailing in the FEM models influences its results. Finally, it exemplifies that reliability restrictions for LS are much more rigorous than for their deterministic counterparts, and that the fastest ISPT method is sufficiently accurate for probabilistic calculations in this RBDO.
12
Mahadevan, Sankaran, and Ramesh Rebba. "Inclusion of Model Errors in Reliability-Based Optimization." Journal of Mechanical Design 128, no. 4 (January 8, 2006): 936–44. http://dx.doi.org/10.1115/1.2204973.
Анотація:
This paper proposes a methodology to estimate errors in computational models and to include them in reliability-based design optimization (RBDO). Various sources of uncertainties, errors, and approximations in model form selection and numerical solution are considered. The solution approximation error is quantified based on the model itself, using the Richardson extrapolation method. The model form error is quantified based on the comparison of model prediction with physical observations using an interpolated resampling approach. The error in reliability analysis is also quantified and included in the RBDO formulation. The proposed methods are illustrated through numerical examples.
13
Sleesongsom, Suwin, and Sujin Bureerat. "Multi-Objective, Reliability-Based Design Optimization of a Steering Linkage." Applied Sciences 10, no. 17 (August 20, 2020): 5748. http://dx.doi.org/10.3390/app10175748.
Анотація:
Reliability-based design optimization (RBDO) of a mechanism is normally based on the non-probabilistic model, which is viewed as failure possibility constraints in each optimization loop. It leads to a double-loop nested problem that causes a computationally expensive evaluation. Several methods have been developed to solve the problem, which are expected to increase the realization of optimum results and computational efficiency. The purpose of this paper was to develop a new technique of RBDO that can reduce the complexity of the double-loop nested problem to a single-loop. This involves using a multi-objective evolutionary technique combined with the worst-case scenario and fuzzy sets, known as a multi-objective, reliability-based design optimization (MORBDO). The optimization test problem and a steering linkage design were used to validate the performance of the proposed technique. The proposed technique can reduce the complexity of the design problem, producing results that are more conservative and realizable.
14
Kharmanda, Gh, and I. R. Antypas. "RELIABILITY-BASED DESIGN OPTIMIZATION USING OPTIMUM SAFETY FACTORS FOR LARGE-SCALE PROBLEMS." Vestnik of Don State Technical University 18, no. 3 (September 29, 2018): 271–79. http://dx.doi.org/10.23947/1992-5980-2018-18-3-271-279.
Анотація:
Introduction. Reliability-Based Design Optimization (RBDO) model reduces the structural weight in uncritical regions, does not only provide an improved design but also a higher level of confidence in the design.Materials and Methods. The classical RBDO approach can be carried out in two separate spaces: the physical space and the normalized space. Since very many repeated researches are needed in the above two spaces, the computational time for such an optimization is a big problem. An efficient method called Optimum Safety Factor (OSF) method is developed and successfully put to use in several engineering applications. Research Results. A numerical application on a large scale problem under fatigue loading shows the efficiency of the developed RBDO method relative to the Deterministic Design Optimization (DDO). The efficiency of the OSF method is also extended to multiple failure modes to control several out-put parameters, such as structural volume and damage criterion.Discussion and Conclusions. The simplified implementation framework of the OSF strategy consists of a single optimization problem to evaluate the design point, and a direct evaluation of the optimum solution considering OSF formulations. It provides designers with efficient solutions that should be economic, satisfying a required reliability level with a reduced computing time.
15
Savage, Gordon J., and Young Kap Son. "Efficient Reliability-Based Design Optimization of Degrading Systems Using a Meta-Model of the System Reliability." International Journal of Reliability, Quality and Safety Engineering 27, no. 06 (June 19, 2020): 2050019. http://dx.doi.org/10.1142/s0218539320500199.
Анотація:
The application of reliability-based design optimization (RBDO) to degrading systems is challenging because of the continual interplay between calculating time-variant reliability (to ensure reliability policies are met) and moving the design point to optimize various objectives, such as cost, weight, size and so forth. The time needed for Monte Carlo Simulation (MCS) is lengthy when reliability calculations are required for each iteration of the design point. The common methods used to date to improve efficiency have some shortcomings: First, most approaches approximate probability via a method that invokes the most-likely failure point (MLFP), and second, tolerances are almost always excluded from the list of design parameters (hence only so-called parameter design is performed), and, without tolerances, true monetary costs cannot be determined, especially in manufactured systems. Herein, the efficiency of RBDO for degrading systems is greatly improved by essentially uncoupling the time-variant reliability problem from the optimization problem. First, a meta-model is built to relate time-variant reliability to the design space. Design of experiment techniques helps to select a few judicious training sets. Second, the meta-model is accessed to quickly evaluate objectives and reliability constraints in the optimization process. The set-theory approach (with MCS) is invoked to find the system reliability accurately and efficiently for multiple competing performance measures. For a case study, the seminal roller clutch with degradation due to wear is examined. The meta-model method, using both moving least-squares and kriging (using DACE in Matlab), is compared to the traditional approach whereby reliability is determined by MCS at each optimization iteration. The case study shows that both means and tolerances are found that correctly minimize a monetary cost objective and yet ensure that reliability policies are met. The meta-model approach is simple, accurate and very fast, suggesting an attractive means for RBDO of time-variant systems.
16
Kharmanda, Gh, and I. R. Antypas. "Efficient optimum safety factor approach for system reliability-based design optimization with application to composite yarns." Vestnik of Don State Technical University 19, no. 3 (October 4, 2019): 221–30. http://dx.doi.org/10.23947/1992-5980-2019-19-3-221-230.
Анотація:
Introduction. The integration of reliability and optimization concepts seeks to design structures that should be both economic and reliable. This model is called Reliability-Based Design Optimization (RBDO). In fact, the coupling between the mechanical modelling, the reliability analyses and the optimization methods leads to very high computational cost and weak convergence stability. Materials andMethods. Several methods have been developed to overcome these difficulties. The methods called Reliability Index Approach (RIA) and Performance Measure Approach (PMA) are two alternative methods. RIA describes the probabilistic constraint as a reliability index while PMA was proposed by converting the probability measure to a performance measure. An Optimum Safety Factor (OSF) method is proposed to compute safety factors satisfying a required reliability level without demanding additional computing cost for the reliability evaluation. The OSF equations are formulated considering RIA and PMA and extended to multiple failure case.Research Results. Several linear and nonlinear distribution laws are applied to composite yarns studies and then extended to multiple failure modes. It has been shown that the idea of the OSF method is to avoid the reliability constraint evaluation with a particular optimization process.Discussion and Conclusions. The simplified implementation framework of the OSF strategy consists of decoupling the optimization and the reliability analyses. It provides designers with efficient solutions that should be economic satisfying a required reliability level. It is demonstrated that the RBDO compared to OSF has several advantages: small number of optimization variables, good convergence stability, small computing time, satisfaction of the required reliability levels.
17
Ren, Xuchun, and Sharif Rahman. "Stochastic design optimization accounting for structural and distributional design variables." Engineering Computations 35, no. 8 (November 5, 2018): 2654–95. http://dx.doi.org/10.1108/ec-10-2017-0409.
Анотація:
Purpose This paper aims to present a new method, named as augmented polynomial dimensional decomposition (PDD) method, for robust design optimization (RDO) and reliability-based design optimization (RBDO) subject to mixed design variables comprising both distributional and structural design variables. Design/methodology/approach The method involves a new augmented PDD of a high-dimensional stochastic response for statistical moments and reliability analyses; an integration of the augmented PDD, score functions, and finite-difference approximation for calculating the sensitivities of the first two moments and the failure probability with respect to distributional and structural design variables; and standard gradient-based optimization algorithms. Findings New closed-form formulae are presented for the design sensitivities of moments that are simultaneously determined along with the moments. A finite-difference approximation integrated with the embedded Monte Carlo simulation of the augmented PDD is put forward for design sensitivities of the failure probability. Originality/value In conjunction with the multi-point, single-step design process, the new method provides an efficient means to solve a general stochastic design problem entailing mixed design variables with a large design space. Numerical results, including a three-hole bracket design, indicate that the proposed methods provide accurate and computationally efficient sensitivity estimates and optimal solutions for RDO and RBDO problems.
18
An, Xue, and Dongyan Shi. "Active set strategy-based sequential approximate programming for reliability-based design optimization." Advances in Mechanical Engineering 14, no. 8 (August 2022): 168781322211152. http://dx.doi.org/10.1177/16878132221115281.
Анотація:
To improve the evaluation efficiency of failure probability in RBDO models with uncertainty, many RIA-based, PMA-based methods have evolved as a powerful procedure, including the modified reliability index approach (MRIA), PMA two-level, PMA with sequential approximate programming (SAP). However, MRIA may encounter inefficiency and instability when applied to complex concave performance functions, and so does PMA two-level, not for PMA with SAP. The active set strategy-based SAP (ASS-based SAP) for PMA is proposed to accelerate computational efficiency through establishing an active set strategy and a deciding factor. The active set strategy defined by using inequality is to identify the feasible most probable target point (MPTP) in the inner loop. The decision factor integrates the reliability index and the active set strategy to quickly renew the active constraints in the outer loop. The reliability assessment and outer optimization are driven simultaneously, thereby the computational efficiency is strengthened. Numerical examples are compared with other reliability methods to demonstrate the excellent performance of the proposed method in efficiency and robustness. Results also show that the proposed method has the ability to solve complex RBDO problems.
19
Bala Subramaniyan, Arun Bala, Rong Pan, and Xiaoping Du. "Reliability-Based Design Optimization of Load Sharing Systems Using SSI-Markov Models." Designs 3, no. 3 (July 6, 2019): 34. http://dx.doi.org/10.3390/designs3030034.
Анотація:
This paper presents a novel single loop approach to design the components of the load sharing systems by optimally allocating the failure probabilities to each component, thereby satisfying the overall system reliability requirement. The Reliability–Based Design Optimization (RBDO) of load sharing systems is computationally intensive due to the dynamic nature of component failure probabilities, since the failure of one component will vary the failure probabilities of other working components. Many RBDO methods have been successfully utilized to design individual components, however using these methods for handling system level reliability constraints is still a challenging task. This is because of a drop in accuracy and computational efficiency, especially when considering a load sharing system, where there is dependency in failure probabilities of components. The key idea is to integrate Stress–Strength Interference (SSI) theory with discrete (or) continuous time-discrete state Markov model for the reliability assessment of system, with the states being the condition of components (working/failed). This method takes advantage of the state transition probability matrix to represent the dynamic nature of the system performance. A numerical example of a simple load sharing system with two I-Beams is presented to illustrate and evaluate the performance of the proposed methodology.
20
Du, Liu, K. K. Choi, Byeng D. Youn, and David Gorsich. "Possibility-Based Design Optimization Method for Design Problems With Both Statistical and Fuzzy Input Data." Journal of Mechanical Design 128, no. 4 (November 23, 2005): 928–35. http://dx.doi.org/10.1115/1.2204972.
Анотація:
The reliability based design optimization (RBDO) method is prevailing in stochastic structural design optimization by assuming the amount of input data is sufficient enough to create accurate input statistical distribution. If the sufficient input data cannot be generated due to limitations in technical and/or facility resources, the possibility-based design optimization (PBDO) method can be used to obtain reliable designs by utilizing membership functions for epistemic uncertainties. For RBDO, the performance measure approach (PMA) is well established and accepted by many investigators. It is found that the same PMA is a very much desirable approach also for the PBDO problems. In many industry design problems, we have to deal with uncertainties with sufficient data and uncertainties with insufficient data simultaneously. For these design problems, it is not desirable to use RBDO since it could lead to an unreliable optimum design. This paper proposes to use PBDO for design optimization for such problems. In order to treat uncertainties as fuzzy variables, several methods for membership function generation are proposed. As less detailed information is available for the input data, the membership function that provides more conservative optimum design should be selected. For uncertainties with sufficient data, the membership function that yields the least conservative optimum design is proposed by using the possibility-probability consistency theory and the least conservative condition. The proposed approach for design problems with mixed type input uncertainties is applied to some example problems to demonstrate feasibility of the approach. It is shown that the proposed approach provides conservative optimum design.
21
Xiao, Yanjie, Feng Yue, Xinwei Wang, and Xun’an Zhang. "Reliability-Based Design Optimization of Structures Considering Uncertainties of Earthquakes Based on Efficient Gaussian Process Regression Metamodeling." Axioms 11, no. 2 (February 20, 2022): 81. http://dx.doi.org/10.3390/axioms11020081.
Анотація:
The complexity of earthquakes and the nonlinearity of structures tend to increase the calculation cost of reliability-based design optimization (RBDO). To reduce computational burden and to effectively consider the uncertainties of ground motions and structural parameters, an efficient RBDO method for structures under stochastic earthquakes based on adaptive Gaussian process regression (GPR) metamodeling is proposed in this study. In this method, the uncertainties of ground motions are described by the record-to-record variation and the randomness of intensity measure (IM). A GPR model is constructed to obtain the approximations of the engineering demand parameter (EDP), and an active learning (AL) strategy is presented to adaptively update the design of experiments (DoE) of this metamodel. Based on the reliability of design variables calculated by Monte Carlo simulation (MCS), an optimal solution can be obtained by an efficient global optimization (EGO) algorithm. To validate the effectiveness and efficiency of the developed method, it is applied to the optimization problems of a steel frame and a reinforced concrete frame and compared with the existing methods. The results show that this method can provide accurate reliability information for seismic design and can deal with the problems of minimizing costs under the probabilistic constraint and problems of improving the seismic reliability under limited costs.
22
El-Hami, Khalil, and Abdelkhalak El Hami. "Safety and Reliability of Carbon Nanotubes in Nanoactuator Application." Applied Mechanics and Materials 146 (December 2011): 130–36. http://dx.doi.org/10.4028/www.scientific.net/amm.146.130.
Анотація:
This paper presents a nanoactuator device as new model of the nanocomposite application. The carbon nanotube was incorporated in the polyvinylidne fluoride and trifluoroethylene P(VDF-TrFE) copolymer matrix. The P(VDF-TrFE) was chosen for its three characteristics which is ferroelectric, piezoelectric and pyroelectric to convert directly the electrical excitation to the mechanical motion (deflection). The SWCNT/P(VDF-TrFE) nanocomposite nanostructure is proposed as nanomaterial challenge to build a nanoactuator and drive systems in nanometer scale size. A deflection the SWCNT of about 10 picometer was found using the atomic force microscopy technique combined with lock-in-amplifier. And in this paper, we present a new method based on Optimal Safety Factors (OSF) in the context of the Reliability-Based Design Optimization (RBDO) analysis of of Carbon Nanotubes in Nanoactuator. We will underline also the different methods of the RBDO analysis and we highlight the advantage of our approach. Numerical results are given to illustrate the proposed method.
23
Yaich, A., G. Kharmanda, A. El Hami, L. Walha, and M. Haddar. "Reliability Based Design Optimization for Multiaxial Fatigue Damage Analysis Using Robust Hybrid Method." Journal of Mechanics 34, no. 5 (July 6, 2017): 551–66. http://dx.doi.org/10.1017/jmech.2017.44.
Анотація:
AbstractThe purpose of the Reliability-Based Design Optimization (RBDO) is to find the best compromise between safety and cost. Therefore, several methods, such as the Hybrid Method (HM) and the Optimum Safety Factor (OSF) method, are developed to achieve this purpose. However, these methods have been applied only on static cases and some special dynamic ones. But, in real mechanical applications, structures are subject to random vibrations and these vibrations can cause a fatigue damage. So, in this paper, we propose an extension of these methods in the case of structures under random vibrations and then demonstrate their efficiency. Also, a Robust Hybrid Method (RHM) is then developed to overcome the difficulties of the classical one. A numerical application is then used to present the advantages of the modified hybrid method for treating problem of structures subject to random vibration considering fatigue damage.
24
Xu, Huanwei, Xin Wang, Wei Li, Mufeng Li, Suichuan Zhang, and Cong Hu. "Reliability-Based Multidisciplinary Design Optimization under Correlated Uncertainties." Mathematical Problems in Engineering 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/7360615.
Анотація:
Complex mechanical system is usually composed of several subsystems, which are often coupled with each other. Reliability-based multidisciplinary design optimization (RBMDO) is an efficient method to design such complex system under uncertainties. However, the present RBMDO methods ignored the correlations between uncertainties. In this paper, through combining the ellipsoidal set theory and first-order reliability method (FORM) for multidisciplinary design optimization (MDO), characteristics of correlated uncertainties are investigated. Furthermore, to improve computational efficiency, the sequential optimization and reliability assessment (SORA) strategy is utilized to obtain the optimization result. Both a mathematical example and a case study of an engineering system are provided to illustrate the feasibility and validity of the proposed method.
25
Yuan, Chao, Hao Zhang, Yong Sun, Yunhan Ling, Lidong Pan, Yue Sun, Dianyu Fu, and Zhengguo Hu. "A Reliability-Based Multidisciplinary Design Optimization Strategy considering Interval Uncertainty Based on the Point-Infilled Kriging Model." Mathematical Problems in Engineering 2022 (November 17, 2022): 1–23. http://dx.doi.org/10.1155/2022/8582511.
Анотація:
Generally, traditional uncertainty design optimization (UDO) methods are based on probability density distribution function or fuzzy membership function. In this situation, a large amount of uncertain information is necessary to construct the UDO model accurately. While, the interval UDO methods require less design information. Only the upper and lower bounds of interval uncertainty are utilized to construct the optimization model. In this study, to enhance the efficiency and accuracy of UBDO considering interval uncertainty, a reliability-based multidisciplinary design optimization (RBMDO) strategy using the point-infilled Kriging model is proposed. In the given method, a double-nested RBMDO model considering interval uncertainty is established. The collaborative optimization is utilized to deal with coupling relationships among complex systems. Then, the point-infilled Kriging response surface strategy is introduced to approximate the RBMDO model. The procedure of the interval multidisciplinary collaborative optimization method based on the Kriging model is discussed. Two examples are given to illustrate the application of the proposed method.
26
Youn, Byeng D., and Kyung K. Choi. "An Investigation of Nonlinearity of Reliability-Based Design Optimization Approaches." Journal of Mechanical Design 126, no. 3 (October 1, 2003): 403–11. http://dx.doi.org/10.1115/1.1701880.
Анотація:
Because deterministic optimum designs obtained without taking uncertainty into account could lead to unreliable designs, a reliability-based approach to design optimization is preferable using a Reliability-Based Design Optimization (RBDO) method. A typical RBDO process iteratively carries out a design optimization in an original random space (X-space) and a reliability analysis in an independent and standard normal random space (U-space). This process requires numerous nonlinear mappings between X- and U-spaces for various probability distributions. Therefore, the nonlinearity of the RBDO problem will depend on the type of distribution of random parameters, since a transformation between X- and U-spaces introduces additional nonlinearity into the reliability-based performance measures evaluated during the RBDO process. The evaluation of probabilistic constraints in RBDO can be carried out in two ways: using either the Reliability Index Approach (RIA), or the Performance Measure Approach (PMA). Different reliability analysis approaches employed in RIA and PMA result in different behaviors of nonlinearity for RIA and PMA in the RBDO process. In this paper, it is shown that RIA becomes much more difficult to solve for non-normally distributed random parameters because of the highly nonlinear transformations that are involved. However, PMA is rather independent of probability distributions because it only has a small involvement with a nonlinear transformation.
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Youn, Byeng D., Kyung K. Choi, and Young H. Park. "Hybrid Analysis Method for Reliability-Based Design Optimization." Journal of Mechanical Design 125, no. 2 (June 1, 2003): 221–32. http://dx.doi.org/10.1115/1.1561042.
Анотація:
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 optimization 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.
28
Elhami, Norelislam, Mhamed Itmi, and Rachid Ellaia. "Reliability-Based Design and Heuristic Optimization MPSO-SA of Structures." Advanced Materials Research 274 (July 2011): 91–100. http://dx.doi.org/10.4028/www.scientific.net/amr.274.91.
Анотація:
In this paper, we present a probability study about spring of clutch structure. In the structure problems, the randomness and the uncertainties of the distribution of the structural parameters are a crucial problem. In the case of Reliability Based Design Optimization (RBDO), it is the objective is to play a dominant role in the structural optimization problem introducing the reliability concept. The RBDO problem is often formulated as a minimization of the initial structural cost under constraints imposed on the values of elemental reliability indices corresponding to various limit states. This paper proposes a new method for a modified particle swarm optimization algorithm (MPSO) combined with a simulated annealing algorithm (SA) and RBDO. MPSO is known as an efficient approach with a high performance of solving optimization problems in many research fields. It is a population intelligence algorithm inspired by social behavior simulations of bird flocking. Numerical results show the robustness of the MPSO-SA algorithm and RBDO.
29
Tu, J., K. K. Choi, and Y. H. Park. "A New Study on Reliability-Based Design Optimization." Journal of Mechanical Design 121, no. 4 (December 1, 1999): 557–64. http://dx.doi.org/10.1115/1.2829499.
Анотація:
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.
30
Yang, Shiyuan, Hongtao Wang, Yihe Xu, Yongqiang Guo, Lidong Pan, Jiaming Zhang, Xinkai Guo, Debiao Meng, and Jiapeng Wang. "A Coupled Simulated Annealing and Particle Swarm Optimization Reliability-Based Design Optimization Strategy under Hybrid Uncertainties." Mathematics 11, no. 23 (November 27, 2023): 4790. http://dx.doi.org/10.3390/math11234790.
Анотація:
As engineering systems become increasingly complex, reliability-based design optimization (RBDO) has been extensively studied in recent years and has made great progress. In order to achieve better optimization results, the mathematical model used needs to consider a large number of uncertain factors. Especially when considering mixed uncertainty factors, the contradiction between the large computational cost and the efficiency of the optimization algorithm becomes increasingly fierce. How to quickly find the optimal most probable point (MPP) will be an important research direction of RBDO. To solve this problem, this paper constructs a new RBDO method framework by combining an improved particle swarm algorithm (PSO) with excellent global optimization capabilities and a decoupling strategy using a simulated annealing algorithm (SA). This study improves the efficiency of the RBDO solution by quickly solving MPP points and decoupling optimization strategies. At the same time, the accuracy of RBDO results is ensured by enhancing global optimization capabilities. Finally, this article illustrates the superiority and feasibility of this method through three calculation examples.
31
Doan, Bao Quoc, Guiping Liu, Can Xu, and Minh Quang Chau. "An Efficient Approach for Reliability-Based Design Optimization Combined Sequential Optimization with Approximate Models." International Journal of Computational Methods 15, no. 04 (May 24, 2018): 1850018. http://dx.doi.org/10.1142/s0219876218500184.
Анотація:
Reliability-based design optimization (RBDO) involves evaluation of probabilistic constraints which can be time-consuming in engineering structural design problems. In this paper, an efficient approach combined sequential optimization with approximate models is suggested for RBDO. The radial basis functions and Latin hypercube sampling are used to construct approximate models of the probabilistic constraints. Then, a sequential optimization with approximate models is carried out by the sequential optimization and reliability assessment method which includes a serial of cycles of deterministic optimization and reliability assessment. Three numerical examples are presented to demonstrate the efficiency of the proposed approach.
32
Yoo, Donghyeon, Jinhwan Park, Jaemin Moon, and Changwan Kim. "Reliability-Based Design Optimization for Reducing the Performance Failure and Maximizing the Specific Energy of Lithium-Ion Batteries Considering Manufacturing Uncertainty of Porous Electrodes." Energies 14, no. 19 (September 24, 2021): 6100. http://dx.doi.org/10.3390/en14196100.
Анотація:
Uncertainty quantification in LIB manufacturing has received interest in order to improve the reliability of LIB. The uncertainty generated during the manufacturing causes variations in the performance of LIBs, thereby increasing capacity degradation and leading to failure. In this study, a reliability-based design optimization (RBDO) of LIBs is conducted to reduce performance failure while maximizing the specific energy. The design variables with uncertainty are the thickness, porosity, and particle size of the anode and cathode. The specific energy is defined as the objective function in the optimization design problem. To maintain the specific power in the initial design of the LIB, it is defined as the constraint function. Reliability is evaluated as the probability that the battery satisfies the performance of the required design. The results indicate that the design optimized through RBDO increases the specific energy by 42.4% in comparison with that of the initial design while reducing the failure rate to 1.53%. Unlike the conventional deterministic design optimization method (DDO), which exhibits 55.09% reliability, the proposed RBDO method ensures 98.47% reliability. It is shown that the proposed RBDO approach is an effective design method to reduce the failure rate while maximizing the specific energy.
33
Ren, Ziyan, Dianhai Zhang, and Chang Seop Koh. "Multi-objective optimization approach to reliability-based robust global optimization of electromagnetic device." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 33, no. 1/2 (December 20, 2013): 191–200. http://dx.doi.org/10.1108/compel-11-2012-0341.
Анотація:
Purpose – The purpose of this paper is to propose a multi-objective optimization algorithm, which can improve both the performance robustness and the constraint feasibility when the uncertainty in design variables is considered. Design/methodology/approach – Multi-objective robust optimization by gradient index combined with the reliability-based design optimization (RBDO). Findings – It is shown that searching for the optimal design of the TEAM problem 22, which can minimize the magnetic stray field by keeping the target system energy (180 MJ) and improve the feasibility of superconductivity constraint (quenching condition), is possible by using the proposed method. Originality/value – RBDO method applied to the electromagnetic problem cooperated with the design sensitivity analysis by the finite element method.
34
Lu, Li, Yizhong Wu, Qi Zhang, and Ping Qiao. "A Transformation-Based Improved Kriging Method for the Black Box Problem in Reliability-Based Design Optimization." Mathematics 11, no. 1 (January 1, 2023): 218. http://dx.doi.org/10.3390/math11010218.
Анотація:
In order to overcome the drawbacks of expensive function evaluation in the practical reliability-based design optimization (RBDO) problem, researchers have proposed the black box-based RBDO method. The algorithm flow of the commonly employed RBDO method for the black box problem consists of the outer construction loop of the surrogate model of the constraint function and the inner surrogate model-based solving loop. To improve the solving ability of the black box RBDO problem, this paper proposes a transformation-based improved kriging method to increase the effectiveness of the two loops identified above. For the outer loop, a sample distribution-based learning function is suggested to improve the construction efficiency of the surrogate model of the constraint function. For the inner loop, a paired incremental sample-based limit reliability boundary construction approach is suggested to transform the RBDO problem into an equivalent deterministic design optimization problem that can be efficiently solved by classical optimization algorithms. The test results of five cases demonstrate that the proposed method can accurately construct the surrogate model of the constraint function and efficiently solve the black box RBDO problem.
35
Yi, Ping, Dongchi Xie, and Zuo Zhu. "Reliability-Based Design Optimization Using Step Length Adjustment Algorithm and Sequential Optimization and Reliability Assessment Method." International Journal of Computational Methods 16, no. 07 (July 26, 2019): 1850109. http://dx.doi.org/10.1142/s0219876218501098.
Анотація:
A step length adjustment (SLA) iterative algorithm was proposed for locating the minimum performance target point (MPTP) in the inverse reliability analysis. This paper elaborates SLA and two deliberately designed numerical examples are used to compare SLA with other algorithms appearing in recent literatures for locating MPTP. The results show that SLA is much more robust and efficient. Then SLA and sequential optimization and reliability assessment (SORA) are combined to solve reliability-based design optimization (RBDO) problems. In the reliability assessment of SORA, with the design obtained from the previous cycle, SLA is used to locate MPTP. Then in the deterministic optimization, the boundaries of violated constraints are shifted to the feasible direction according to the MPTP obtained in the reliability assessment. Several examples frequently cited in similar studies are used to compare SORA-SLA with other RBDO algorithms. The results indicate the effectiveness and robustness of SORA-SLA.
36
Bowling, Alan P., John E. Renaud, Jeremy T. Newkirk, Neal M. Patel, and Harish Agarwal. "Reliability-Based Design Optimization of Robotic System Dynamic Performance." Journal of Mechanical Design 129, no. 4 (April 7, 2006): 449–54. http://dx.doi.org/10.1115/1.2437804.
Анотація:
In this investigation a robotic system’s dynamic performance is optimized for high reliability under uncertainty. The dynamic capability equations (DCE) allow designers to predict the dynamic performance of a robotic system for a particular configuration and reference point on the end effector (i.e., point design). Here the DCE are used in conjunction with a reliability-based design optimization (RBDO) strategy in order to obtain designs with robust dynamic performance with respect to the end-effector reference point. In this work a unilevel performance measure approach is used to perform RBDO. This is important for the reliable design of robotic systems in which a solution to the DCE is required for each constraint call. The method is illustrated on a robot design problem.
37
Sutha, Arnut, Thu Huynh Van, and Sawekchai Tangaramvong. "Combined Subset Simulation and Comprehensive Learning Particle Swarm Optimization in Reliability-Based Structural Optimization." IOP Conference Series: Materials Science and Engineering 1222, no. 1 (January 1, 2022): 012001. http://dx.doi.org/10.1088/1757-899x/1222/1/012001.
Анотація:
Abstract Reliability-based design optimization (RBDO) addresses the cost-effective integrity design of structures in the presence of inherent uncertain parameters. Processing this class of problem is challenging from the computational burden to determine the failure probability of structures violating the limit-state function. This paper proposes an efficient decoupling RBDO method that advantageously couples a comprehensive learning particle swarm optimization (CLPSO) algorithm with a subset simulation (SS), termed as SS-CLPSO approach. In essence, the proposed method iteratively performs the CLPSO assuming deterministic parameters based on the most probable point underpinning limit-state functions updated within the reliability evaluation process. Based on the CLPSO design data, the SS approximates the spectrum of limit-state functions under uncertain parameters, and hence enables the significant reduction of Monte-Carlo simulations for the failure probability prediction. The SS map outs the failure probability from the conditional samples constructed at each intermediate event. The proposed SS-CLPSO terminates the optimal solution to the RBDO problem as when the resulting failure probability converges to the permissible threshold. The applications of the present approach are illustrated through the steel truss design under probabilistic uncertain parameters and constraints.
38
Chun, Junho. "Reliability-Based Design Optimization of Structures Using the Second-Order Reliability Method and Complex-Step Derivative Approximation." Applied Sciences 11, no. 11 (June 7, 2021): 5312. http://dx.doi.org/10.3390/app11115312.
Анотація:
This paper proposes a reliability-based design optimization (RBDO) approach that adopts the second-order reliability method (SORM) and complex-step (CS) derivative approximation. The failure probabilities are estimated using the SORM, with Breitung’s formula and the technique established by Hohenbichler and Rackwitz, and their sensitivities are analytically derived. The CS derivative approximation is used to perform the sensitivity analysis based on derivations. Given that an imaginary number is used as a step size to compute the first derivative in the CS derivative method, the calculation stability and accuracy are enhanced with elimination of the subtractive cancellation error, which is commonly encountered when using the traditional finite difference method. The proposed approach unifies the CS approximation and SORM to enhance the estimation of the probability and its sensitivity. The sensitivity analysis facilitates the use of gradient-based optimization algorithms in the RBDO framework. The proposed RBDO/CS–SORM method is tested on structural optimization problems with a range of statistical variations. The results demonstrate that the performance can be enhanced while satisfying precisely probabilistic constraints, thereby increasing the efficiency and efficacy of the optimal design identification. The numerical optimization results obtained using different optimization approaches are compared to validate this enhancement.
39
Pei, Pei, Ser Tong Quek, and Yongbo Peng. "Multiobjective Reliability-Based Design Optimization of the Fuzzy Logic Controller for MR Damper-Based Structures." Structural Control and Health Monitoring 2023 (August 14, 2023): 1–26. http://dx.doi.org/10.1155/2023/4009397.
Анотація:
To devise an optimum and robust fuzzy logic controller for MR damper-based structures subjected to earthquake ground motions, the multiobjective reliability-based design optimization (RBDO) using the adaptive Kriging model is performed to determine the parameters of the fuzzy logic controller. The optimization problem is formulated with two objective functions, namely, the minimization of interstory drift and average control force of the concerned structure, and subjected to a probability constraint on structural dynamic responses under the effects of random structural stiffness and stochastic earthquake loadings. To reduce the computational cost of reliability assessment, a global Kriging model is constructed in an augmented space as a surrogate for computational evaluations. Subsequently, the trained metamodel combined with the nondominated sorting genetic algorithm (NSGA-II) is integrated into the framework of RBDO for solving the fuzzy logic control (FLC) optimization problem. The feasibility and effectiveness of the multiobjective RBDO in the FLC design are finally validated by conducting numerical simulations on both linear and nonlinear structures. As demonstrated in the linear case, the fuzzy logic controllers obtained from the multiobjective RBDO show more robustness than those derived from the multiobjective deterministic design optimization (DDO). In the nonlinear case, using the multiobjective DDO to prelocate a coarse safety domain can significantly reduce the number of samples for training the metamodel and facilitate the implementation of the multiobjective RBDO; in addition, the controlled structural performance with a specified fuzzy logic controller can be further improved by considering MR damper distribution optimization.
40
Wang, Yao, Shengkui Zeng, and Jianbin Guo. "Time-Dependent Reliability-Based Design Optimization Utilizing Nonintrusive Polynomial Chaos." Journal of Applied Mathematics 2013 (2013): 1–16. http://dx.doi.org/10.1155/2013/513261.
Анотація:
Time-dependent reliability-based design optimization (RBDO) has been acknowledged as an advance optimization methodology since it accounts for time-varying stochastic nature of systems. This paper proposes a time-dependent RBDO method considering both of the time-dependent kinematic reliability and the time-dependent structural reliability as constrains. Polynomial chaos combined with the moving least squares (PCMLS) is presented as a nonintrusive time-dependent surrogate model to conduct uncertainty quantification. Wear is considered to be a critical failure that deteriorates the kinematic reliability and the structural reliability through the changing kinematics. According to Archard’s wear law, a multidiscipline reliability model including the kinematics model and the structural finite element (FE) model is constructed to generate the stochastic processes of system responses. These disciplines are closely coupled and uncertainty impacts are cross-propagated to account for the correlationship between the wear process and loads. The new method is applied to an airborne retractable mechanism. The optimization goal is to minimize the mean and the variance of the total weight under both of the time-dependent and the time-independent reliability constraints.
41
An, Xue, Bowen Huang, and Dongyan Shi. "A novel reliability index approach and applied it to cushioning packaging design." Advances in Mechanical Engineering 14, no. 11 (November 2022): 168781322211359. http://dx.doi.org/10.1177/16878132221135992.
Анотація:
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.
42
Mourelatos, Zissimos P., and Jinghong Liang. "A Methodology for Trading-Off Performance and Robustness Under Uncertainty." Journal of Mechanical Design 128, no. 4 (December 28, 2005): 856–63. http://dx.doi.org/10.1115/1.2202883.
Анотація:
Mathematical optimization plays an important role in engineering design, leading to greatly improved performance. Deterministic optimization, however, may result in undesired choices because it neglects uncertainty. Reliability-based design optimization (RBDO) and robust design can improve optimization by considering uncertainty. This paper proposes an efficient design optimization method under uncertainty, which simultaneously considers reliability and robustness. A mean performance is traded-off against robustness for a given reliability level of all performance targets. This results in a probabilistic multiobjective optimization problem. Variation is expressed in terms of a percentile difference, which is efficiently computed using the advanced mean value method. A preference aggregation method converts the multiobjective problem to a single-objective problem, which is then solved using an RBDO approach. Indifference points are used to select the best solution without calculating the entire Pareto frontier. Examples illustrate the concepts and demonstrate their applicability.
43
Dey, Shibshankar, and Kais Zaman. "Dimension Reduction Method-Based RBDO for Dependent Interval Variables." International Journal of Computational Methods 17, no. 10 (June 20, 2020): 2050017. http://dx.doi.org/10.1142/s0219876220500176.
Анотація:
Reliability-based design optimization (RBDO) under epistemic uncertainty (i.e., imprecise probabilistic information), especially in the presence of dependency of input variables, is a challenging problem. In this paper, we propose a dimension reduction-based RBDO framework considering dependent interval variables, which is pursued in a purely probabilistic manner. Most probable point (MPP) based dimension reduction method (DRM) is used for reliability evaluation due to its ability to circumvent the shortcomings of poor approximation by first order reliability method (FORM) and pronounced computational complexity by second order reliability method (SORM). For modeling correlation of input variables, copula is used instead of true joint cumulative density function (CDF). A flexible Johnson family of distributions is used to handle the stochastic but poorly known epistemic uncertainty. In order to handle the uncertainty in correlation measures, arisen due to interval data, expert suggested bounds of correlation measures have been recommended. For the overall RBDO problem, a decoupled approach to optimization is explored. Two numerical examples — one mathematical problem and one engineering problem — have been solved to properly explicate the proposed RBDO process. It is demonstrated that correlations in input variables have significant impact on the optimal design solutions.
44
Mourelatos, Zissimos P., and Jun Zhou. "A Design Optimization Method Using Evidence Theory." Journal of Mechanical Design 128, no. 4 (December 28, 2005): 901–8. http://dx.doi.org/10.1115/1.2204970.
Анотація:
Early in the engineering design cycle, it is difficult to quantify product reliability or compliance to performance targets due to insufficient data or information to model uncertainties. Probability theory cannot be, therefore, used. Design decisions are usually based on fuzzy information that is vague, imprecise qualitative, linguistic or incomplete. Recently, evidence theory has been proposed to handle uncertainty with limited information as an alternative to probability theory. In this paper, a computationally efficient design optimization method is proposed based on evidence theory, which can handle a mixture of epistemic and random uncertainties. It quickly identifies the vicinity of the optimal point and the active constraints by moving a hyperellipse in the original design space, using a reliability-based design optimization (RBDO) algorithm. Subsequently, a derivative-free optimizer calculates the evidence-based optimum, starting from the close-by RBDO optimum, considering only the identified active constraints. The computational cost is kept low by first moving to the vicinity of the optimum quickly and subsequently using local surrogate models of the active constraints only. Two examples demonstrate the proposed evidence-based design optimization method.
45
El Hami, A., B. Radi, and A. Cherouat. "Reliability-based design optimization analysis of tube hydroforming process." SIMULATION 88, no. 9 (June 7, 2012): 1129–37. http://dx.doi.org/10.1177/0037549712441986.
Анотація:
In this paper, we are interested particularly in the tube hydroforming process (THP). This process consists of applying an inner pressure combined with an axial displacement to manufacture the part. During the manufacturing phase, inappropriate choice of the load paths can lead to failure. Deterministic approaches are unable to optimize the process by taking into account the uncertainty. So we introduce the reliability-based design optimization (RBDO) to optimize the process under probabilistic constraints to ensure a high reliability level and stability during the manufacturing phase and avoid the occurrence of such plastic instability. Taking some uncertainties into account the process is very stable and associated with a low failure probability. The definition of the objective function and the probabilistic constraints take advantage of the forming limit diagram (FLD) and the forming limit stress diagram (FLSD) used as a failure criterion to detect the occurrence of wrinkling, severe thinning and necking. To validate the proposed approach, the THP is then introduced as an example. The numerical results show the robustness and efficiency of the RBDO to improve thickness distribution and minimize the risk of potential failure modes.
46
Safaeian Hamzehkolaei, Naser, Mahmoud Miri, and Mohsen Rashki. "An improved binary bat flexible sampling algorithm for reliability-based design optimization of truss structures with discrete-continuous variables." Engineering Computations 35, no. 2 (April 16, 2018): 641–71. http://dx.doi.org/10.1108/ec-06-2016-0207.
Анотація:
Purpose Reliability-based design optimizations (RBDOs) of engineering structures involve complex non-linear/non-differentiable performance functions, including both continuous and discrete variables. The gradient-based RBDO algorithms are less than satisfactory for these cases. The simulation-based approaches could also be computationally inefficient, especially when the double-loop strategy is used. This paper aims to present a pseudo-double loop flexible RBDO, which is efficient for solving problems, including both discrete/continuous variables. Design/methodology/approach The method is based on the hybrid improved binary bat algorithm (BBA) and weighed simulation method (WSM). According to this method, each BBA’s movement generates proper candidate solutions, and subsequently, WSM evaluates the reliability levels for design candidates to conduct swarm in a low-cost safe-region. Findings The accuracy of the proposed enhanced BBA and also the hybrid WSM-BBA are examined for ten benchmark deterministic optimizations and also four RBDO problems of truss structures, respectively. The solved examples reveal computational efficiency and superiority of the method to conventional RBDO approaches for solving complex problems including discrete variables. Originality/value Unlike other RBDO approaches, the proposed method is such organized that only one simulation run suffices during the optimization process. The flexibility future of the proposed RBDO framework enables a designer to present multi-level design solutions for different arrangements of the problem by using the results of the only one simulation for WSM, which is very helpful to decrease computational burden of the RBDO. In addition, a new suitable transfer function that enhanced convergence rate and search ability of the original BBA is introduced.
47
Wang, Yu, Xiongqing Yu, and Xiaoping Du. "Improved Reliability-Based Optimization with Support Vector Machines and Its Application in Aircraft Wing Design." Mathematical Problems in Engineering 2015 (2015): 1–14. http://dx.doi.org/10.1155/2015/569016.
Анотація:
A new reliability-based design optimization (RBDO) method based on support vector machines (SVM) and the Most Probable Point (MPP) is proposed in this work. SVM is used to create a surrogate model of the limit-state function at the MPP with the gradient information in the reliability analysis. This guarantees that the surrogate model not only passes through the MPP but also is tangent to the limit-state function at the MPP. Then, importance sampling (IS) is used to calculate the probability of failure based on the surrogate model. This treatment significantly improves the accuracy of reliability analysis. For RBDO, the Sequential Optimization and Reliability Assessment (SORA) is employed as well, which decouples deterministic optimization from the reliability analysis. The improved SVM-based reliability analysis is used to amend the error from linear approximation for limit-state function in SORA. A mathematical example and a simplified aircraft wing design demonstrate that the improved SVM-based reliability analysis is more accurate than FORM and needs less training points than the Monte Carlo simulation and that the proposed optimization strategy is efficient.
48
Papadrakakis, M., N. D. Lagaros, and V. Plevris. "Structural optimization considering the probabilistic system response." Theoretical and Applied Mechanics 31, no. 3-4 (2004): 361–94. http://dx.doi.org/10.2298/tam0404361p.
Анотація:
In engineering problems, the randomness and uncertainties are inherent and the scatter of structural parameters from their nominal ideal values is unavoidable. In Reliability Based Design Optimization (RBDO) and Robust Design Optimization (RDO) the uncertainties play a dominant role in the formulation of the structural optimization problem. In an RBDO problem additional non deterministic constraint functions are considered while an RDO formulation leads to designs with a state of robustness, so that their performance is the least sensitive to the variability of the uncertain variables. In the first part of this study a metamodel assisted RBDO methodology is examined for large scale structural systems. In the second part an RDO structural problem is considered. The task of robust design optimization of structures is formulated as a multi-criteria optimization problem, in which the design variables of the optimization problem, together with other design parameters such as the modulus of elasticity and the yield stress are considered as random variables with a mean value equal to their nominal value. .
49
Yi, Ping. "Discussion of Mathematical Models of Probabilistic Constraints Calculation in Reliability-Based Design Optimization." Advanced Materials Research 243-249 (May 2011): 5717–26. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.5717.
Анотація:
In a reliability-based design optimization (RBDO) problem, most of the computations are used for probabilistic constraints assessment, i.e., reliability analysis. Therefore, the effectiveness, especially the correctness of the reliability analysis is very important. If the probabilistic constraint is misjudged, the optimization iteration would have convergence problems or arrive at erratic solutions. The probabilistic constraint assessment can be carried out using either the conventional reliability index approach (RIA) or the performance measure approach (PMA). In this paper, the mathematical models to calculate the reliability index in RIA and to calculate the probabilistic performance measure (PPM) in PMA are discussed. In RIA, through estimating whether the mean-value point in safe domain or not, we should use a positive or negative reliability index respectively. In PMA, one should always minimize the performance measure to compute PPM whether the performance measure at the mean-value point is positive or negative, which puts right the wrong mathematical model in some literatures and makes it possible to produce effective and efficient approach for RBDO.
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Gomes, Herbert M., and Leandro L. Corso. "A Hybrid Method for Truss Mass Minimization considering Uncertainties." Mathematical Problems in Engineering 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/2324316.
Анотація:
In real-world structural problems, a number of factors may cause geometric imperfections, load variability, or even uncertainties in material properties. Therefore, a deterministic optimization procedure may fail to account such uncertainties present in the actual system leading to optimum designs that are not reliable; the designed system may show excessive safety or sometimes not sufficient reliability to carry applied load due to uncertainties. In this paper, we introduce a hybrid reliability-based design optimization (RBDO) algorithm based on the genetic operations of Genetic Algorithm, the position and velocity update of the Particle Swarm Algorithm (for global exploration), and the sequential quadratic programming, for local search. The First-Order Reliability Method is used to account uncertainty in design and parameter variables and to evaluate the associated reliability. The hybrid method is analyzed based on RBDO benchmark examples that range from simple to complex truss parametric sizing optimizations with stress, displacements, and frequency deterministic and probabilistic constraints. The proposed final problem, which cannot be handled by single loop RBDO algorithms, highlights the importance of the proposed approach in cases where the discrete design variables are also random variables.