A self-adaptive modified chaos control method for reliability-based design optimization

In the reliability-based design optimization (RBDO), the Advanced mean value (AMV) method sometimes yields unstable results such as chaotic and periodic solutions for highly nonlinear probabilistic constraints. The chaos control (CC), modified chaos control (MCC) and adaptive chaos control (ACC) methods are more robust than the AMV but inefficient for some moderately nonlinear performance functions. In this paper, a self-adaptive modified chaos control (SMCC) method is developed based on a dynamical control factor to improve the efficiency of MCC for reliability analysis and RBDO. The self-adaptive control factor is dynamically computed based on the new and previous results. The efficiency and robustness of the proposed SMCC are compared with the AMV, CC, MCC and ACC methods using several nonlinear structural/mathematical performance functions and RBDO problems. The results illustrate that the SMCC is more efficient than CC, MCC, and ACC methods, and also more robust than AMV method for highly nonlinear problems.     

Relaxed performance measure approach for reliability-based design optimization

The efficiency and robustness of reliability analysis methods are important factors to evaluate the probabilistic constraints in reliability-based design optimization (RBDO). In this paper, a relaxed mean value (RMV) approach is proposed in order to evaluate probabilistic constraints including convex and concave functions in RBDO using the performance measure approach (PMA). A relaxed factor is adaptively determined in the range from 0 to 2 using an inequality criterion to improve the efficiency and robustness of the inverse first-order reliability methods. The performance of the proposed RMV is compared with six existing reliability methods, including the advanced mean value (AMV), conjugate mean value (CMV), hybrid mean value (HMV), chaos control (CC), modified chaos control (MCC), and conjugate gradient analysis (CGA) methods, through four nonlinear concave and convex performance functions and three RBDO problems. The results demonstrate that the proposed RMV is more robust than the AMV, CMV, and HMV for highly concave problems, and slightly more efficient than the CC, MCC, and CGA methods. Furthermore, the proposed relaxed mean value guarantees robust and efficient convergence for RBDO problems with highly nonlinear performance functions.     

Reliability-based structural design optimization: hybridized conjugate mean value approach

The efficiency and robustness of reliability techniques are important in reliability-based design optimization (RBDO). Commonly, advanced mean value (AMV) is utilized in reliability loop of RBDO but unstable solutions using AMV may be obtained for highly concave performance functions. Owing to the challenges of commonly reliability methods, the conjugate gradient analysis (CGA) is proposed as a robust methodology but it shows inefficient results for convex constraints. In this research, hybrid conjugate mean value (HCMV) method is proposed using sufficient condition for the enhancement of efficiency and robustness of RBDO. The CGA and AMV are dynamically utilized for simple solution of convex/concave constraints using sufficient descent criterion in HCMV. The HCMV is used to evaluate the convergence performances and is compared with numerous existing reliability methods through three reliability problems (two concave/convex mathematical examples and one applicable structure) and four RBDO problems. From the numerical results, the HCMV exhibited the better efficiency, and robustness compared to other studied formulations in reliability and RBDO problems.

     

Chaos control of performance measure approach for evaluation of probabilistic constraints

Performance measure approach (PMA) is a recently proposed method for evaluation of probabilistic constraints in reliability-based design optimization of structure. The advanced mean-value (AMV) method is well suitable for PMA due to its simplicity and efficiency. However, when the AMV iterative scheme is applied to search for the minimum performance target point for some nonlinear performance functions, the iterative sequences could fall into the periodic oscillation and even chaos. In the present paper, the phenomena of numerical instabilities of AMV iterative solutions are illustrated firstly. And the chaotic dynamics analysis on the iterative procedure of AMV method is performed. Then, the stability transformation method of chaos feedback control is suggested for the convergence control of AMV procedure in the parameter interval in which the iterative scheme fails. Numerical results of several nonlinear performance functions demonstrate that the control of periodic oscillation, bifurcation and chaos for AMV iterative procedure is achieved, and the stable convergence solutions are obtained.     

An adaptive hybrid single-loop method for reliability-based design optimization using iterative control strategy

Single-loop approach (SLA) is one of the most promising methods for solving linear and weakly nonlinear reliability-based design optimization (RBDO) problems. However, since SLA locates the current approximate most probable point (MPP) by using the gradient information of the previous one to reduce the computational cost, it may lead to inaccuracy when the nonlinearity of probabilistic constraints becomes relatively high. To overcome this limitation, a new adaptive hybrid single-loop method (AH-SLM) that can automatically choose to search for the approximate MPP or accurate MPP is proposed in this paper. Moreover, to get the accurate MPP more efficiently and alleviate the oscillation in the search process, an iterative control strategy (ICS) with two iterative control criteria is developed. In each iterative step, the KKT-condition of performance measure approach (PMA) is introduced to check the validity of the approximate MPP. If the approximate MPP is infeasible, ICS will be further carried out to search for the accurate MPP. The two iterative control criteria are used to update the oscillation control step length, then ICS can converge fast for both weakly and highly nonlinear performance functions. Besides, numerical examples are presented to verify the efficiency and robustness of our proposed method.     

Limited descent-based mean value method for inverse reliability analysis

Engineering with Computers - The robustness and efficiency of inverse reliability methods are important issues in reliability-based design optimization (RBDO) using performance measure approach...     

Convergence control of single loop approach for reliability-based design optimization

For solution of reliability-based design optimization (RBDO) problems, single loop approach (SLA) shows high efficiency. Thus SLA is extensively used in RBDO. However, the iteration solution procedure by SLA is often oscillatory and non-convergent for RBDO with nonlinear performance function. This prevents the application of SLA to engineering design problems. In this paper, the chaotic single loop approach (CLSA) is proposed to achieve the convergence control of original iterative algorithm in SLA. The modification involves automated selection of the chaos control factor by solving a novel one-dimensional optimization model. Additionally, a new oscillation-checking method is constructed to detect the oscillation of iterative process of design variables. The computational capability of CLSA is demonstrated through five benchmark examples and one stiffened shell application. The comparison of numerical results indicates that CSLA is more efficient than the double loop approach and the decoupled approach. CSLA also solves the RBDO problems with highly nonlinear performance function and non-normal random variables stably.     

An inverse analysis method for design optimization with both statistical and fuzzy uncertainties

If the statistical data for the input uncertainties are sufficient to construct the distribution function, the input uncertainties can be treated as random variables to use the reliability-based design optimization (RBDO) method; otherwise, the input uncertainties can be treated as fuzzy variables to use the possibility-based design optimization (PBDO) method. However, many structural design problems include both input uncertainties with sufficient and insufficient data. This paper proposes a new mixed-variable design optimization (MVDO) method using the performance measure approach (PMA) for such design problems. For the inverse analysis, this paper proposes a new most probable/possible point (MPPP) search method called maximal failure search (MFS), which is an integration of the enhanced hybrid mean value method (HMV+) and maximal possibility search (MPS) method. This paper also improves the HMV+ method using an angle-based interpolation. Mathematical and physical examples are used to demonstrate the proposed inverse analysis method and MVDO method.     

Single loop single vector approach using the conjugate gradient in reliability based design optimization

Conventional reliability-based design optimization (RBDO) approaches require high computing costs. Among the existing RBDO methods, the single loop single vector approach (SLSV) converts the RBDO problem into a single loop deterministic optimization. Hence, it can efficiently reduce the design cost compared to other methods. However, this method has a weakness in that instability or inaccuracy in convergence can be increased according to the problem characteristics. It often happens when the performance function is highly nonlinear or concave. In this study, a novel method is proposed to overcome the problems. It is an SLSV method using the conjugate gradient that is calculated with the gradient directions at the most probable points (MPP) of the previous cycles. Mathematical examples and structural applications are solved to verify the proposed method. The numerical performances of the proposed method are compared with other RBDO methods such as the RIA, PMA, SORA and SLSV approaches. It is shown that the SLSV method using the conjugate gradient (SLSVCG) is not greatly influenced by problem characteristics and the convergence capability is quite superior. Also, the computational cost of the proposed method is significantly reduced and an excellent solution satisfying the specified reliability is obtained.     

Reliability-based design optimization for crashworthiness of vehicle side impact

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

一种基于LTE-A的联合自适应传输方法

LTE-A上行每帧数据在自适应传输时,不能实时切换为分簇的DFT-S-OFDM和N×SC-FDMA系统。为此,提出一种联合自适应调制编码方法。该方法依据接收端的信干噪比,分别预测下一帧在采用分簇的DFT-S-OFDM和N×SC-FDMA进行自适应传输时的吞吐量,选择吞吐量大的系统及相应的调制编码方式在下一帧使用,可获得分簇的DFT-S-OFDM和N×SC-FDMA系统在自适应传输时频谱效率的联合性能。仿真结果表明,与单一自适应系统相比,该方法在多径信道下的吞吐量性能能够取得1 dB增益。     

模糊神经网络的混沌优化算法设计

提出了一种基于混沌变量的多层模糊神经网络优化算法设计.离线优化部分采用混沌算法,将混沌变量引入到模糊神经网络结构和参数的优化搜索中,使整个网络处于动态混沌状态,根据性能指标在动态模糊神经网络中寻找较优的网络结构和参数.在线优化部分采用梯度下降法,把混沌搜索后得到的参数全局次优值作为梯度下降搜索的初始值,进一步调整模糊神经网络的参数,实现混沌粗搜索和梯度下降细搜索相结合的优化目的,能较快地找到全局最优解.最后对二阶延迟系统进行仿真,结果表明混沌优化方法控制精度高、超调小、响应快和鲁棒性强.     

A local adaptive sampling method for reliability-based design optimization using Kriging model

Reliability-based design optimization (RBDO) in practical applications is hindered by its huge computational cost during structure reliability evaluating process. Kriging-model-based RBDO is an effective method to overcome this difficulty. However, the accuracy of Kriging model depends directly on how to select the sample points. In this paper, the local adaptive sampling (LAS) is proposed to enhance the efficiency of constructing Kriging models for RBDO problems. In LAS, after initialization, new samples for probabilistic constraints are mainly selected within the local region around the current design point from each optimization iteration, and in the local sampling region, sample points are first considered to be located on the limit state constraint boundaries. The size of the LAS region is adaptively defined according to the nonlinearity of the performance functions. The computation capability of the proposed method is demonstrated using three mathematical RBDO problems and a honeycomb crash-worthiness design application. The comparison results show that the proposed method is very efficient.     

Sampling-based RBDO using the stochastic sensitivity analysis and Dynamic Kriging method

This paper presents a sampling-based RBDO method using surrogate models. The Dynamic Kriging (D-Kriging) method is used for surrogate models, and a stochastic sensitivity analysis is introduced to compute the sensitivities of probabilistic constraints with respect to independent or correlated random variables. For the sampling-based RBDO, which requires Monte Carlo simulation (MCS) to evaluate the probabilistic constraints and stochastic sensitivities, this paper proposes new efficiency and accuracy strategies such as a hyper-spherical local window for surrogate model generation, sample reuse, local window enlargement, filtering of constraints, and an adaptive initial point for the pattern search. To further improve computational efficiency of the sampling-based RBDO method for large-scale engineering problems, parallel computing is proposed as well. Once the D-Kriging accurately approximates the responses, there is no further approximation in the estimation of the probabilistic constraints and stochastic sensitivities, and thus the sampling-based RBDO can yield very accurate optimum design. In addition, newly proposed efficiency strategies as well as parallel computing help find the optimum design very efficiently. Numerical examples verify that the proposed sampling-based RBDO can find the optimum design more accurately than some existing methods. Also, the proposed method can find the optimum design more efficiently than some existing methods for low dimensional problems, and as efficient as some existing methods for high dimensional problems when the parallel computing is utilized.     

一种基于混沌优化的混合人口迁移算法

针对人口迁移算法存在着收敛速度慢,易陷入局部最优和精度低等缺点,根据混沌运动具有随机性、遍历性和内在规律性的特点,利用混沌方法对人口迁移算法进行改进,提出了一种基于混沌优化机制的混合人口迁移算法。通过8个典型函数测试,测试结果表明,所提出的算法对初始值不敏感,收敛速度快,计算精度高,其性能远优于人口迁移算法。     

Adaptive probability analysis using an enhanced hybrid mean value method

This paper proposes an adaptive probability analysis method that can effectively generate the probability distribution of the output performance function by identifying the propagation of input uncertainty to output uncertainty. The method is based on an enhanced hybrid mean value (HMV+) analysis in the performance measure approach (PMA) for numerical stability and efficiency in search of the most probable point (MPP). The HMV+ method improves numerical stability and efficiency especially for highly nonlinear output performance functions by providing steady convergent behavior in the MPP search. The proposed adaptive probability analysis method approximates the MPP locus, and then adaptively refines this locus using an a posteriori error estimator. Using the fact that probability levels can be easily set a priori in PMA, the MPP locus is approximated using the interpolated moving least-squares method. For refinement of the approximated MPP locus, additional probability levels are adaptively determined through an a posteriori error estimator. The adaptive probability analysis method will determine the minimum number of necessary probability levels, while ensuring accuracy of the approximated MPP locus. Several examples are used to show the effectiveness of the proposed adaptive probability analysis method using the enhanced HMV+ method.     

基于混沌理论的差异演化算法研究

差异演化算法（Differential Evolution,DE）足一种基于群体个体间差异的进化计算方法,可以对高维复杂空间进行有效搜索。利用混沌（Chaos）信号的遍历性与随机性,结合DE算法,提出了一种基于混沌的DE优化算法（CDE）。与DE相比,CDE减少了控制参数。通过典型高维非线性测试函数的验证,测试结果显示该方法在优化速度、搜索效率和避免陷入局部极值点方面,大大提高DE算法的性能,在不同情兜下几乎具有最佳的函数优化性能,从而具有一定的鲁棒性。     

Optimisation of tensile membrane structures under uncertain wind loads using PCE and kriging based metamodels

Tensile membrane structures (TMS) are light-weight flexible structures that are designed to span long distances with structural efficiency. The stability of a TMS is jeopardised under heavy wind forces due to its inherent flexibility and inability to carry out-of-plane moment and shear. A stable TMS under uncertain wind loads (without any tearing failure) can only be achieved by a proper choice of the initial prestress. In this work, a double-loop reliability-based design optimisation (RBDO) of TMS under uncertain wind load is proposed. Using a sequential polynomial chaos expansion (PCE) and kriging based metamodel, this RBDO reduces the cost of inner-loop reliability analysis involving an intensive finite element solver. The proposed general approach is applied to the RBDO of two benchmark TMS and its computational efficiency is demonstrated through these case studies. The method developed here is suggested for RBDO of large and complex engineering systems requiring costly numerical solution.     

An enhanced simulation-based design method coupled with meta-heuristic search algorithm for accurate reliability-based design optimization

The enhanced weighted simulation-based design method in conjunction with particle swarm optimization (PSO) is developed as a pseudo double-loop algorithm for accurate reliability-based design optimization (RBDO). According to this hybrid method, generated samples of weighed simulation method (WSM) are considered as initial population of the PSO. The proposed population is then employed to evaluate the safety level of each PSO swarm (design candidates) during movement. Using this strategy, there is no required to conduct new sampling for reliability assessment of design candidates (PSO swarms). Employing PSO as the search engine of RBDO and WSM as the reliability analyzer provide more accurate results with few samples and also increase the application range of traditional WSM. Besides, a shift strategy is also introduced to increase the capability of the WSM to investigate general RBDO problems including both deterministic and random design variables. Several examples are investigated to demonstrate the accuracy and robustness of the method. Results demonstrate the computational efficiency and superiority of the proposed method for practical engineering problems with highly nonlinear and implicit probabilistic constrains.     

Hybrid probabilistic adaptation mode controller for generalized sidelobe cancellers applied to multi-microphone speech enhancement

In this paper, we propose a new adaptation mode controller (AMC) for a generalized sidelobe canceller (GSC)-based speech enhancement system. Here, a likelihood ratio for target speech presence was first estimated and then utilized to estimate both the local target speech presence probability (SPP) and global SPP. Next, the estimated SPPs were applied to the design of an AMC that controlled the parameters of adaptive filters for an adaptive blocking matrix (ABM) and noise canceller (NC). In particular, the combination of local and global SPPs was applied to the AMC in the ABM, whereas only global SPPs were used for the NC. Finally, a multiple-microphone speech enhancement system was constructed on the basis of a GSC having the proposed AMC. The performance of the speech enhancement system was subsequently evaluated in terms of the perceptual evaluation of speech quality (PESQ) and the cepstral distortion (CD) for car noise conditions. It was shown from this evaluation that a speech enhancement system using the proposed AMC method provided better performance than conventional AMC methods using power ratios between the target and non-target directional signals, the inter-channel normalized cross-correlation, and the local SPPs only.