Reliability-based design optimization of aeroelastic structures

Aeroelastic phenomena are most often either ignored or roughly approximated when uncertainties are considered in the design optimization process of structures subject to aerodynamic loading, affecting the quality of the optimization results. Therefore, a design methodology is proposed that combines reliability-based design optimization and high-fidelity aeroelastic simulations for the analysis and design of aeroelastic structures. To account for uncertainties in design and operating conditions, a first-order reliability method (FORM) is employed to approximate the system reliability. To limit model uncertainties while accounting for the effects of given uncertainties, a high-fidelity nonlinear aeroelastic simulation method is used. The structure is modelled by a finite element method, and the aerodynamic loads are predicted by a finite volume discretization of a nonlinear Euler flow. The usefulness of the employed reliability analysis in both describing the effects of uncertainties on a particular design and as a design tool in the optimization process is illustrated. Though computationally more expensive than a deterministic optimum, due to the necessity of solving additional optimization problems for reliability analysis within each step of the broader design optimization procedure, a reliability-based optimum is shown to be an improved design. Conventional deterministic aeroelastic tailoring, which exploits the aeroelastic nature of the structure to enhance performance, is shown to often produce designs that are sensitive to variations in system or operational parameters.     

Optimum structural design via convex model superposition

A new approach is presented for implementing a multidimensional convex model for the optimal design of structures subjected to bounded but uncertain loads. This is a non-probabilistic method for including uncertainty in the design. In previous studies, a two-stage optimization process was used to predict the effect of uncertainties, modeled using convex theory, on the response constraints. Here, a superposition method is used to find the response of structures with load uncertainties. The convex model is implemented on the effect of the uncertain loads, i.e., the displacements and stresses. The advantage of the method is that one optimization process is eliminated, and the constraints do not need to be expressed explicitly as a function of the design variables.     

Robust reliability method for non-fragile guaranteed cost control of parametric uncertain systems

The problem of non-fragile guaranteed cost control of uncertain systems is studied from a new point of view of reliability against uncertainties. An efficient robust reliability method for the analysis and design of non-fragile guaranteed cost controller of parametric uncertain systems is presented systematically. By the method, a robust reliability measure of an uncertain control system satisfying required robust performance can be obtained, and the robustness bounds of uncertain parameters such that the control cost of a system is guaranteed can be provided. The optimal non-fragile guaranteed cost controller obtained in the paper may possess optimal guaranteed cost performance satisfying the precondition that the system is robustly reliable with respect to uncertainties occurring in both the controlled plant and controller gain. The presented formulations are in the framework of linear matrix inequality and thus can be carried out conveniently. The presented method provides an essential basis for the tradeoff between reliability and control cost in controller design of uncertain systems. Two numerical examples are provided to demonstrate the efficiency and feasibility of the presented method. It is shown that the coordination and simultaneous realization of the system performance, control cost, and robust reliability in control design of uncertain systems are significant.     

基于鲁棒可靠性的不确定时滞系统最优H∞控制器设计

用区间变量描述控制系统参数的不确定性,提出了不确定时滞系统鲁棒H_∞控制的鲁棒可靠性方法,基于鲁棒可靠性的不确定时滞系统最优状态反馈H_∞控制器设计方法,将系统的最优控制器设计归结为基于线性矩阵不等式(LMI)的优化问题．所设计的控制器可以在满足对所有不确定性鲁棒可靠的前提条件下,具有最优的H_∞鲁棒性能,并能在控制系统的设计中综合考虑控制性能、控制代价和鲁棒可靠性．数值算例说明了所提方法的有效性和可行性．     

Fuzzy sets in seismic inelastic analysis and design of reinforced concrete frames

In this paper, a new approach to the problem of estimating the structural response of systems with uncertain characteristics is presented. The approach is based on the theory of fuzzy sets, which allow the designers to describe the uncertain variables. The method is presented briefly in the following. First, the uncertain parameters are expressed as fuzzy numbers with specific characteristics. The concurrent effect of the various uncertainties on the structural response is obtained by applying methodologies of the theory of fuzzy sets. Then the output parameters of the design process as, e.g. the displacements or the stresses of the structure are obtained as new fuzzy numbers expressing the uncertainties of the output parameters. Finally, numerical applications on a number of relatively simple structural systems give an idea of the applicability of the proposed methodology in various aspects of the design process.     

Structural optimization under uncertain loads and nodal locations

This paper presents algorithms for solving structural topology optimization problems with uncertainty in the magnitude and location of the applied loads and with small uncertainty in the location of the structural nodes. The second type of uncertainty would typically arise from fabrication errors where the tolerances for the node locations are small in relation to the length scale of the structural elements. We first review the discrete form of the uncertain loads problem, which has been previously solved using a weighted average of multiple load patterns. With minor modifications, we extend this solution to include loads described by continuous joint probability density functions. We then proceed to the main contribution of this paper: structural optimization under uncertainty in the nodal locations. This optimization problem is computationally difficult because it involves variations of the inverse of the structural stiffness matrix. It is shown, however, that for small uncertainties the problem can be recast into a simpler but equivalent structural optimization problem with equivalent uncertain loads. By expressing these equivalent loads in terms of continuous random variables, we are able to make use of the extended form of the uncertain loads problem presented in the first part of this paper. The optimization algorithms are developed in the context of minimum compliance (maximum stiffness) design. Simple examples are presented. The results demonstrate that load and nodal uncertainties can have dramatic impact on optimal design. For structures containing thin substructures under axial loads, it is shown that these uncertainties (a) are of first-order significance, influencing the linear elastic response quantities, and (b) can affect designs by avoiding unrealistically optimistic and potentially unstable structures. The additional computational cost associated with the uncertainties scales linearly with the number of uncertainties and is insignificant compared to the cost associated with solving the deterministic structural optimization problem.     

Reliability-based design optimization for problems with interval distribution parameters

Traditional reliability-based design optimization (RBDO) generally describes uncertain variables using random distributions, while some crucial distribution parameters in practical engineering problems can only be given intervals rather than precise values due to the limited information. Then, an important probability-interval hybrid reliability problem emerged. For uncertain problems in which interval variables are included in probability distribution functions of the random parameters, this paper establishes a hybrid reliability optimization design model and the corresponding efficient decoupling algorithm, which aims to provide an effective computational tool for reliability design of many complex structures. The reliability of an inner constraint is an interval since the interval distribution parameters are involved; this paper thus establishes the probability constraint using the lower bound of the reliability degree which ensures a safety design of the structure. An approximate reliability analysis method is given to avoid the time-consuming multivariable optimization of the inner hybrid reliability analysis. By using an incremental shifting vector (ISV) technique, the nested optimization problem involved in RBDO is converted into an efficient sequential iterative process of the deterministic design optimization and the hybrid reliability analysis. Three numerical examples are presented to verify the proposed method, which include one simple problem with explicit expression and two complex practical applications.     

Linear Systems with Large Uncertainties,with Applications to Truss Structures

Linear systems whose coefficients have large uncertainties arise routinely in finite element calculations for structures with uncertain geometry, material properties, or loads. However, a true worst case analysis of the influence of such uncertainties was previously possible only for very small systems and uncertainties, or in special cases where the coefficients do not exhibit dependence. This paper presents a method for computing rigorous bounds on the solution of such systems, with a computable overestimation factor that is frequently quite small. The merits of the new approach are demonstrated by computing realistic bounds for some large, uncertain truss structures, some leading to linear systems with over 5000 variables and over 10000 interval parameters, with excellent bounds for up to about 10% input uncertainty. Also discussed are some counterexamples for the performance of traditional approximate methods for worst case uncertainty analysis.     

An efficient reliability-based optimization scheme for uncertain linear systems subject to general Gaussian excitation

A very efficient methodology to carry out reliability-based optimization of linear systems with random structural parameters and random excitation is presented. The reliability-based optimization problem is formulated as the minimization of an objective function for a specified reliability. The probability that design conditions are satisfied within a given time interval is used as a measure of the system reliability. Approximation concepts are used to construct high quality approximations of dynamic responses in terms of the design variables and uncertain structural parameters during the design process. The approximations are combined with an efficient simulation technique to generate explicit approximations of the reliability measures with respect to the design variables. In particular, an efficient importance sampling technique is used to estimate the failure probabilities. The number of dynamic analyses as well as reliability estimations required during the optimization process are reduced dramatically. Several example problems are presented to illustrate the effectiveness and feasibility of the suggested approach.     

Reliability-based structural optimization of frame structures for multiple failure criteria using topology optimization techniques

Topology optimization methods using discrete elements such as frame elements can provide useful insights into the underlying mechanics principles of products; however, the majority of such optimizations are performed under deterministic conditions. To avoid performance reductions due to later-stage environmental changes, variations of several design parameters are considered during the topology optimization. This paper concerns a reliability-based topology optimization method for frame structures that considers uncertainties in applied loads and nonstructural mass at the early conceptual design stage. The effects that multiple criteria, namely, stiffness and eigenfrequency, have upon system reliability are evaluated by regarding them as a series system, where mode reliabilities can be evaluated using first-order reliability methods. Through numerical calculations, reliability-based topology designs of typical two- or three-dimensional frames are obtained. The importance of considering uncertainties is then demonstrated by comparing the results obtained by the proposed method with deterministic optimal designs.     

A robust optimisation framework in composite generation and transmission expansion planning considering inherent uncertainties

Abstract

This paper presents a robust optimisation framework for long-term composite generation and transmission expansion planning problem which considers inherent uncertainties such as load growth, fuel cost and renewable energy output uncertainties. In this paper, a bi-level robust optimisation framework is proposed to accommodate wind output uncertainty in line with the uncertain demanded loads and uncertain fuel cost. The addressed optimisation problem is modelled as a mixed-integer optimisation framework with the objective of providing a robust expansion plan while maintaining the minimum cost expansion. In order to evaluate the robustness of each plan, an off-line Lattice Monte Carlo simulation technique is adopted in this study. The validity of the proposed method is examined on a simple six-bus and modified IEEE 118-bus test system as a large-scale case study. The simulation results show that the presented method is both satisfactory and consistent with expectation.     

不匹配不确定性系统的近似变结构输出跟踪控制

针对一类具有不匹配不确定性的非线性系统,提出一种结合变结构控制方法及自适应控制方法输出跟踪控制器。首先提出一种保证不确定性系统跟踪误差指数稳定的近似变结构控制器;进而得到一种具有不确定性范数上界估计能力的自适应近似变结构控制器,并证明了所提出的自适应近似变结构控制器使跟踪误差在时间趋于无穷时收敛于零。     

面向约束的鲁棒设计方法

提出了一种面向约束的鲁棒设计方法,该方法能够利用约束网络对并行设计中的一类不确定性参数进行有效的描述和处理。该文提出了反映协同设计需求的数学模型,设计了一个通用的一致性求解算法框架,并利用基于区间代数的一致性算法,在设计的初期就监控设计过程,使设计者在确定参数前能够通过约束网络定量地考虑下游的约束条件,并能够提早发现冲突以避免设计后期出现大的返工。文中的研究是实现并行设计中“一次成功”的技术基础。     

Adaptive synchronization on uncertain dynamics of high-order nonlinear multi-agent systems with partition of unity approach

An adaptive synchronization of uncertain chaotic system is presented using partition of unity method. First, the uncertainties of chaotic systems are approximate by the linear combination of partition of unity. Subsequently, the sliding mode adaptive controllers are proposed for synchronization of the uncertain chaotic systems. The proposed approach offers a systematic design procedure for adaptive synchronization of a class of uncertain chaotic system in the chaos research literature. We also illustrate examples of chaotic systems such as Chen and Lorenz chaotic systems to show the effectiveness of the approach.     

On Maximum Stability Margin Design of Nonlinear Uncertain Systems: Fuzzy Control Approach

This paper studies the maximum stability margin design for nonlinear uncertain systems using fuzzy control. First, the Takagi and Sugeno fuzzy model is employed to approximate a nonlinear uncertain system. Next, based on the fuzzy model, the maximum stability margin for a nonlinear uncertain system is studied to achieve as much tolerance of plant uncertainties as possible using a fuzzy control method. In the proposed fuzzy control method, the maximum stability margin design problem is parameterized in terms of a corresponding generalized eigenvalue problem (GEVP). For the case where state variables are unavailable, a fuzzy observer‐based control scheme is also proposed to deal with the maximum stability margin for nonlinear uncertain systems. Using a suboptimal approach, we characterize the maximum stability margin via fuzzy observer‐based control in terms of a linear matrix inequality problem (LMIP). The GEVP and LMIP can be solved very efficiently via convex optimization techniques. Simulation examples are given to illustrate the design procedure of the proposed method.     

A nonparametric approach to design robust controllers for uncertain systems: Application to an air flow heating system

This paper presents an approach to design robust fixed structure controllers for uncertain systems using a finite set of measurements in the frequency domain. In traditional control system design, usually, based on measurements, a model of the plant, which is only an approximation of the physical system, is first built, and then control approaches are used to design a controller based on the identified model. Errors associated with the identification process as well as the inevitable uncertainties associated with plant parameter variations, external disturbances, measurement noise, etc. are expected to all contribute to the degradation of the performance of such a scheme. In this paper, we propose a nonparametric method that uses frequency-domain data to directly design a robust controller, for a class of uncertainties, without the need for model identification. The proposed technique, which is based on interval analysis, allows us to take into account the plant uncertainties during the controller synthesis itself. The technique relies on computing the controller parameters for which the set of all possible frequency responses of the closed-loop system are included in the envelope of a desired frequency response. Such an inclusion problem can be solved using interval techniques. The main advantages of the proposed approach are: (1) the control design does not require any mathematical model, (2) the controller is robust with respect to plant uncertainties, and (3) the controller structure can be chosen a priori, which allows us to select low-order controllers. To illustrate the proposed method and demonstrate its efficacy, an application to an air flow heating system is presented.     

网络攻击下一类非线性切换多智能体系统的安全自适应控制

针对一类控制方向未知的非线性切换多智能体系统, 本文研究了在不确定网络攻击下的安全控制问题. 网 络攻击破坏传感器真实数据, 导致系统真实信息无法获取且不能直接用于控制设计. 为此, 通过受攻击状态构建一 组新颖辅助变量来消除网络攻击造成的影响. 此外, 所研究的系统包含更一般的不确定性, 即未知控制方向, 未知常 值参数以及不确定攻击. 这些不确定性在设计过程中相互耦合. 利用Nussbaum型函数并设计自适应律补偿耦合后 的不确定性, 极大降低了系统复杂性. 通过系统性地迭代构造出共同Lyapunov函数, 提出了一套安全自适应控制方 法, 保证了受攻击系统在任意切换下达到渐近输出一致性. 最后, 数值仿真验证了该方法的有效性.     

LMI‐Based Robust PID Controller Design for Voltage Control of Islanded Microgrid

This paper presents the design of a robust proportional integral derivative (PID) controller for the control of a single phase microgrid voltage. A microgrid consists of loads, distributed generation units and several power‐electronics interfaced LC filter and voltage source inverter. These loads are unknown and parameters are uncertain which produce unmodeled load dynamics. This unmodeled load dynamics reduces the voltage tracking performance of the microgrid. The proposed controller gives the robustness of the system with unmodeled load dynamics. Under different kinds of uncertainties, PID controller guarantees the stability and provides zero steady‐state error and fast transient response. The robustness and optimal performance of the controller is obtained by using linear matrix inequality approach. The performance of the controller under different uncertainties is studied. Results indicate the robustness and high voltage tracking performance of the microgrid system.