Integrated topology optimization and optimal control for vibration suppression in structural design

This paper presents a topology design methodology for structures with active vibration control. The methodology takes into account the structural effect of the control forces and includes the modal control design. Location points for the actuation forces are chosen a priori. Structural topology optimization is used for distributing material on a fixed domain, using continuum finite element discretization for the static and free vibration analyses. Optimal control for transient response in modal space is used to derive the control force. The cost function for the optimization combines the strain energy and the control energy. Results of the numerical simulations validates the proposed methodology.     

Multi-objective optimal design of fuzzy controller for structural vibration control using Hedge-algebras approach

In this paper, the problem of multi-objective optimal design of hedge-algebras-based fuzzy controller (HAC) for structural vibration control with actuator saturation is presented. The main advantages of HAC are: (i) inherent order relationships among linguistic values of each linguistic variable are always ensured; (ii) instead of using any fuzzy sets, linguistic values of linguistic variables are determined by an isomorphism mapping called semantically quantifying mapping (SQM) based on a few fuzziness parameters of each linguistic variable and hence, the process of fuzzy inference is very simple due to SQM values occurring in the fuzzy rule base and (iii) when optimizing HAC, only a few design variables which are above fuzziness parameters are needed. As a case study, a HAC and optimal HACs (opHACs) based on multi-objective optimization view point have been designed to active control of a benchmark structure with active bracing system subjected to earthquake excitation. Control performance of controllers is also discussed in order to shown advantages of the proposed method.     

Isoperimetric inequalities in optimal structural design

Isoperimetric inequalities arising in exactly solvable structural optimization problems are discussed in this article.Most isoperimetric inequalities of mechanical problems have been proved using one of three known methods. The first tool is the variational method, which is a powerful way to prove inequalities for systems described by ordinary differential equations. For the systems described by equations with partial derivatives, the symmetrization method can be applied. Methods based on positivity properties of operators, for example, Hopf's maximum principle, are used to prove the inequalities for local functionals. Using these algorithms, the new isoperimetric inequalities for engineering problems were investigated.Classical examples, namely the St. Venant-Pólya inequality rigidity, the Faber-Krahn inequality for vibrating membranes, the Banichuk-Wheeler inequality for maximum stress in a perforated plane and the Keller-Ting inequality for static moments of a bar are treated. The inequalities for the maximum stress in twisted isotropic and orthotropic elastic bars are proved. For the perfectly-plastic solid, the inequalities for collapse load are considered. The other class of inequalities, associated with eigenvalue problems, arises in vibration, conservative and non-conservative stability problems. The new inequalities for the bimodal critical axial compression load for bars with clamped ends, a generalized Pfluger column and a circular ring under hydrostatic pressure are stated.Extended version a paper presented at NATO ASI Optimization of Large Structural Systems, Berchtesgaden, Germany, Sept. 23 — Oct. 4, 1991     

Discrete-variable optimal structural design using tabu search

Tabu search is a discrete-variable optimization algorithm with the ability to avoid entrapment by local optima and hence continue searching for a global optimum. In this paper tabu search is applied to the optimal structural design, in terms of weight minimization, of two standard (test) structural configurations; a 10-bar planar truss and a 25-bar space truss. The design variables are the cross-sectional areas of the bars, which take discrete values.An implementation of tabu search in a structural design context is presented which features-depth neighbourhoods and a search back-track facility. Investigations show that tabu search may readily cope with problem formulations that include buckling, gravity effects and design variables with realistic values. Furthermore, compared to previous research, superior (i.e. lower) minimum weights may be obtained.It is shown that tabu search is a technically viable technique for use in optimal structural design, although, for practical use, current (significant) execution times may inhibit its utilisation.     

Integrated optimization of 3D structural topology and actuator configuration for vibration control in ultra-precision motion systems

Structural and Multidisciplinary Optimization - Ever-increasing demands for precision and efficiency in ultra-precision motion systems will result in a lightweight and flexible motion system with...     

Active optimal vibration control for a lumped system

A dynamic absorber with active torque generating DC motors has been studied as an actively suppressing vibration system. A typical two-level spring-lumped mass system with slider undergoing internal excitation vibrations has been considered. Both the main mass and the secondary absorber mass have DC servo motors planned to suppress the amplitude of vibration. State variable techniques are used to formulate the complete system and three optimal control schemes are used to control such a system. First, the discrete time optimal disturbance rejection control for a system with known disturbance is considered, in the second approach a digital optimal control for a linear quadratic regulator problem is studied and in the last approach a discrete optimal control with selected system characteristic matrix is investigated. The response of the system obtained from these optimal control approaches are compared with the response without control action first. The performance of these optimal control approaches are also compared and the availability of implementations of them are evaluated.     

An optimal control approach to robust control design

We propose an optimal control approach to robust control design. Our goal is to design a state feedback to stabilize a system under uncertainty. We translate this robust control problem into an optimal control problem of minimizing a cost. Because the uncertainty bound is reflected in the cost, the solution to the optimal control problem is a solution to the robust control problem. Our approach can deal with both linear and non-linear systems. Furthermore it can handle both matched and unmatched uncertainties. It can also handle uncertainty in the control input matrix.     

A mutual energy formulation for optimal structural design

This paper presents a variational formulation for the design of elastic structures where the function to be minimized by the optimal design, i.e. the objective, is expressed in abstract form. The resulting statement of necessary conditions is uniformly applicable for all admissible objectives. Both state and adjoint state variables appear directly in the problem statement, and all objectives and the arguments of constraints are scalars. The adjoint pair of state variables appear in symmetric roles via the expression termed “mutual energy". Application of the generalized formulation is demonstrated by treatment of the following examples: design to minimize the maximum value of displacement or to minimize a global measure of stress, design for generalized compliance, design where self-weight is taken into account, and multicriterion design. Received April 28, 2000     

On a game approach to optimal structural design

A game problem of structural design is formulated as a problem of playing against external circumstances. The compliance plays the role of the pay-off function. Two players — the designer and nature — try to respectively minimize or maximize it, possessing limited resources. Discrete and continual optimization problems are considered.It is proved that the essential game characteristic, the upper game value, is expressed in terms of the minimal eigenvalue of the inverse operator of the system (continual case), or the response matrix (discrete case). For a special case of convex game, this eigenvalue is equal to the value of the game, and the optimal strategies of the designer and nature are uniquely determined.     

Integrated optimal topology design and shape optimization using neural networks

In this paper, neural network- and feature-based approaches are introduced to overcome current shortcomings in the automated integration of topology design and shape optimization. The topology optimization results are reconstructed in terms of features, which consist of attributes required for automation and integration in subsequent applications. Features are defined as cost-efficient simple shapes for manufacturing. A neural network-based image-processing technique is presented to match the arbitrarily shaped holes inside the structure with predefined features. The effectiveness of the proposed approach in integrating topology design and shape optimization is demonstrated with several experimental examples.     

无抖振滑模控制在结构振动中的应用研究

考虑传统滑模控制的趋近律方法应用于建筑结构振动控制中存在高频抖振,且控制效果过分依赖于参数的选取。利用双曲正切函数,设计了一种新的趋近律方法。新的方法能加快趋近速度,从理论上消除抖振,并有效减小趋近律设计过程中参数选取的复杂度。最后,以一个三层Benchmark结构模型为例进行了仿真数值分析,结果表明,该方法对结构的地震峰值响应抑制效果明显。     

An efficient method for optimal structural design by substructuring

An optimal structural design technique incorporating the concept of substructuring in its formulation is presented. The method is developed using functional analysis techniques and the state space formulation of the optimal design problem. Design sensitivity analysis for the problem is discussed and an integrated computational algorithm for optimal design is presented. As an application of the method, optimal design of general trusses is presented. Numerical results for two standard truss structures of 25 and 200 members are obtained, using substructuring, and are compared with results obtained without substructuring. It is shown that the algorithm with substructuring is up to 66% more efficient.     

飞机座舱减振降噪优化设计方法

采用结构拓扑优化的变密度法和形貌优化法,对模拟飞机座舱的四角固支声音箱体,进行了减振降噪的研究.比较优化前后结构固有频率的变化和对声压的影响,得出了结构拓扑优化对减振降噪作用的高效性.     

A separable augmented Lagrangian algorithm for optimal structural design

Structural and Multidisciplinary Optimization - We propose an iterative separable augmented Lagrangian algorithm (SALA) for optimal structural design, with SALA being a subset of the alternating...     

An optimal crusher control: Its design

A particular complex static system, viz., a partial positive feedback static system (closed cycle) for crushing mineral ores and other materials, is studied. Its structure is assumed to be known. Mathematical models for two representations of a closed cycle, called the ideal and real systems, are described. The optimal design of the real complex system (whose nature is stochastic) is determined from a mathematic model of an ideal complex system. Optimal problems are formulated as simple nonlinear programming and vector optimization problems. Examples on their solution are given.     

半车非线性悬架的非平稳随机振动及控制

研究了1/2车非线性悬架模型在路面随机激励下的非平稳振动响应,并基于随机最优控制理论对其进行主动控制.首先利用等效线性化方法将具有非线性阻尼及迟滞刚度的非线性悬架模型线性化,然后将主动、被动悬架非平稳随机响应进行比较,结果表明非线性主动悬架的性能要优于被动悬架.最后,通过Monte-Carlo数值模拟验证了理论结果.     

On some simplified models for optimal design of structural systems

Some simplified models for optimal design of large structural systems are reviewed. The design variables represent the members' cross-sections and the constraints are related to stress, displacement and design considerations. Using displacement analysis formulation, several explicit behavior models which do not involve multiple implicit analyses are presented. It is shown that approximations of the displacements, often used in optimization of large systems, essentially lead to solutions which do not satisfy equilibrium.Approximations along a line in the design variables space are developed, and simplifications based on the virtual load method and inverse design variables formulations are presented. The relationships between the various models are derived; it is shown that, under the usual assumption of linear relationship between the stiffness matrix elements and the design variables, some of the approximations become equivalent.