Balancing reduction of linear systems having multiple delays

Abstract

In this paper we apply the balancing reduction method to derive reduced‐order models for linear systems having multiple delays. The time‐domain balanced realization is achieved through computing the controllability and observability gramians in the frequency domain. With the variable transformation s = i tan(θ/2), the gramians of linear multi‐delay systems can be accurately evaluated by solving first‐order differential equations over a finite domain. The proposed approach is computationally superior to that of using the two‐dimensional realization of delay differential systems.     

Aeroelastic forces and dynamic response of long‐span bridges

In this paper a time domain approach for predicting the non‐linear dynamic response of long‐span bridges is presented. In particular the method that leads to the formulation of aeroelastic and buffeting forces in the time domain is illustrated in detail, where a recursive algorithm for the memory term's integration is properly developed. Moreover in such an approach the forces' expressions, usually formulated according to quasi‐static theory, have been substituted by expressions including the frequency‐dependent characteristics. Such expressions of aeroelastic and buffeting forces are made explicit in the time domain by means of the convolution integral that involves the impulse functions and the structural motion or the fluctuating velocities. A finite element model (FEM) has been developed within the framework of geometrically non linear analysis, by using 3‐d degenerated finite element. The proposed procedure can be used to analyze both the flutter instability phenomenon and buffeting response. Moreover, working in the geometrically non‐linearity range, it verifies the possibility of strongly flexible structures of actively resisting the wind loading. Copyright © 2004 John Wiley & Sons, Ltd.     

Nonlinear gas turbine modeling using NARMAX structures

The estimation of a nonlinear autoregressive moving average with exogenous inputs (NARMAX) model of an aircraft gas turbine is presented. A method is proposed whereby periodic signals with certain harmonic content are used to qualify the nature of the nonlinearity of the engine in the frequency domain. The static behavior of the engine is investigated in the time domain to approximate the order of nonlinearity and this information is used a priori to restrict the search space of the potential NARMAX models. A forward-regression orthogonal estimation algorithm is then employed to select the model terms using the error reduction ratio. The performance of the estimated NARMAX model is illustrated against a range of small- and large-signal engine tests     

Selective mass scaling for explicit finite element analyses

Due to their inherent lack of convergence problems explicit finite element techniques are widely used for analysing non‐linear mechanical processes. In many such processes the energy content in the high frequency domain is small. By focusing an artificial mass scaling on this domain, the critical time step may be increased substantially without significantly affecting the low frequency behaviour. This is what we refer to as selective mass scaling. Two methods for selective mass scaling are introduced in this work. The proposed methods are based on non‐diagonal mass matrices that scale down the eigenfrequencies of the system. The applicability of the methods is illustrated in two example models where the critical time step is increased by up to 30 times its original size. Copyright © 2005 John Wiley & Sons, Ltd.     

LQG optimal controller synthesis with robust optimization in multivariable systems

Abstract

This paper presents an algorithm to synthesize a controller for treating the problem of robustness optimization in an LQG (linear‐quadratic‐Gaussian) control system. The controller not only maximizes the excess stability margin in perturbed system but also minimizes the cost functional J in LQG problems by specifying two frequency dependent weighting matrices Q(s) and R(s) in the cost functional.

Our approach is based on Wiener‐Hopf's technique (frequency domain approach), and two weighting matrices in cost functional are shaped by inverse LQG method. The feature of this paper is that the plant of the system has no stable, proper, square, and minimum phase constraints.     

Simultaneous Optimization of Robust Parameter and Tolerance Design Based on Generalized Linear Models

Robust parameter design (RPD) and tolerance design (TD) are two important stages in design process for quality improvement. Simultaneous optimization of RPD and TD is well established on the basis of linear models with constant variance assumption. However, little attention has been paid to RPD and TD with non‐constant variance of residuals or non‐normal responses. In order to obtain further quality improvement and cost reduction, a hybrid approach for simultaneous optimization of RPD and TD with non‐constant variance or non‐normal responses is proposed from generalized linear models (GLMs). First, the mathematical relationship among the process mean, process variance and control factors, noise factors and tolerances is derived from a dual‐response approach based on GLMs, and the quality loss function integrating with tolerance is developed. Second, the total cost model for RPD‐TD concurrent optimization based on GLMs is proposed to determine the best control factors settings and the optimal tolerance values synchronously, which is solved by genetic algorithm in detail. Finally, the proposed approach is applied into an example of electronic circuit design with non‐constant variance, and the results show that the proposed approach performs better on quality improvement and cost reduction. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic analysis of arch dams—a continuum damage mechanics approach

In this paper, the non‐linear seismic response of arch dams is presented using the concept of Continuum Damage Mechanics (CDM). The analysis is performed using the finite element technique and appropriate non‐linear material and damage models in conjunction with the α‐algorithm for time marching. Because of the non‐linear nature of the discretizied equations of motion, modified Newton–Raphson approach has been used at each time step. Damage evolution based on tensile principal strain using mesh‐dependent hardening modulus technique is adopted to ensure the mesh objectivity and to calculate the accumulated damage. The methodology employed is shown to be computationally efficient and consistent in its treatment of both damage growth and damage propagation. As an application of the proposed formulation, a double curvature arch dam has been analysed and the results are compared with the solutions from linear analysis and it is shown that the structural response of arch dams varies significantly in terms of damage evolution. Copyright © 1999 John Wiley & Sons, Ltd.     

Selective damping method for the weak‐Arlequin coupling of molecular dynamics and finite element method

An artificial damping force is introduced in the weak coupling between the molecular dynamics (MD) and finite element (FE) models, to reduce the reflection of the high‐frequency motion that cannot be transmitted from the MD domain to the FE domain. We take advantage of the orthogonal property of the decomposed velocity in the weak coupling method and apply the damping force only to the high‐frequency part, therefore minimizing its effect on the low‐frequency part, which can be transmitted into the FE domain. The effectiveness of the damping method will be demonstrated by 1D numerical examples with linear force field applied to the atomistic model. In addition, we emphasize the importance of using the Arlequin energy interpolation, which is usually ignored in the weak coupling literature. Non‐uniform rational basis spline functions have been used to interpolate the MD data for the weak coupling method, and the influence of changing the number and order of basis functions on the interpolation accuracy has been investigated numerically. For this work, we restrict our discussion to mechanical problems only, involving only mechanical energy terms (e.g., strain potential and kinetic energy). Copyright © 2013 John Wiley & Sons, Ltd.     

A parallel computational method in steady power‐law creep

A new approach to parallelization of materially non‐linear problems in solid mechanics is developed. It is based on approximating generalized models of subdomains. The procedure does not retain the same substructuring technique used in a linear version. The convergence proof of the single‐ and multilevel‐domain decomposition algorithms uses the principle of minimum potential energy dissipation and investigated properties of the substructural models. The high efficiency of the approach introduced is shown through the study of several examples. The method developed in this paper for steady creep can be used without modification to solve non‐linear elasticity problems and, at active loading, plasticity problems for bodies of the power‐law strain–stress diagrams. Copyright © 2001 John Wiley & Sons, Ltd.     

基于Hammerstein模型的柴油机隔振非线性系统振动分析

针对柴油机隔振非线性系统,提出基于Hammerstein模型的曲线拟合方法,研究系统非线性对其振动特性的影响,并在模态试验基础上获得线性结构动力特征。基于Hammerstein模型建立广义频响函数,考虑基频谐振广义频响函数对基频响应的作用,提取系统（1阶广义）频响函数。曲线拟合技术对（1阶广义）频响函数进行频域估计,识别出线性结构动力特征。模态参数辨识试验结果表明,提出的方法对于柴油机隔振非线性系统的线性模态参数估计是合理、有效的。基于Hammerstein模型的曲线拟合,能够消除系统非线性对振动特性影响,并能够获得系统的线性结构动力特征。     

Perfectly matched layers for transient elastodynamics of unbounded domains

One approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outward from the bounded domain. A perfectly matched layer (PML) is an unphysical absorbing layer model for linear wave equations that absorbs, almost perfectly, outgoing waves of all non‐tangential angles‐of‐incidence and of all non‐zero frequencies. In a recent work [Computer Methods in Applied Mechanics and Engineering 2003; 192: 1337–1375], the authors presented, inter alia, time‐harmonic governing equations of PMLs for anti‐plane and for plane‐strain motion of (visco‐) elastic media. This paper presents (a) corresponding time‐domain, displacement‐based governing equations of these PMLs and (b) displacement‐based finite element implementations of these equations, suitable for direct transient analysis. The finite element implementation of the anti‐plane PML is found to be symmetric, whereas that of the plane‐strain PML is not. Numerical results are presented for the anti‐plane motion of a semi‐infinite layer on a rigid base, and for the classical soil–structure interaction problems of a rigid strip‐footing on (i) a half‐plane, (ii) a layer on a half‐plane, and (iii) a layer on a rigid base. These results demonstrate the high accuracy achievable by PML models even with small bounded domains. Copyright © 2004 John Wiley & Sons, Ltd.     

Remarks on the efficiency of POD for model reduction in non‐linear dynamics of continuous elastic systems

The first objective of this paper is to analyse the efficiency of the reduced models constructed using the proper orthogonal decomposition (POD)‐basis and the LIN‐basis in non‐linear dynamics for continuous elastic systems. The POD‐basis is the Hilbertian basis constructed with the POD method while the LIN‐basis is the Hilbertian basis derived from the generalized continuous eigenvalue problem associated with the underlying conservative part of the continuous elastic system and usually called the eigenmodes of vibration. The efficiency of the POD‐basis or the LIN‐basis is related to the rate of convergence in the frequency domain of the solution constructed with the reduced model with respect to its dimension. A basis will be more efficient than another if the reduced‐order solution of the Galerkin projection converges to the solution of the dynamical system more rapidly than the reduced‐order solution of the other. As a second objective of this paper, we present the usual results concerning the POD method using a continuous formulation, with respect to both time and space variables, and then deriving the numerical approximations. Such a presentation allows convergence discussions to be treated. Six examples in non‐linear elastodynamics problems are presented in order to analyse the efficiency of the POD‐basis and the LIN‐basis. It is concluded that the POD‐basis is not more efficient than the LIN‐basis for the examples treated in non‐linear elastodynamics. Copyright © 2007 John Wiley & Sons, Ltd.     

Energy‐momentum consistent algorithms for dynamic thermomechanical problems—Application to mortar domain decomposition problems

An energy‐momentum consistent integrator for non‐linear thermoelastodynamics is newly developed and extended to domain decomposition problems. The energy‐momentum scheme is based on the first law of thermodynamics for strongly coupled, non‐linear thermoelastic problems. In contrast to staggered algorithms, a monolithic approach, which solves the mechanical as well as the thermal part simultaneously, is introduced. The approach is thermodynamically consistent in the sense that the first law of thermodynamics is fulfilled. Furthermore, a domain decomposition method for the thermoelastic system is developed based on previous developments in the context of the mortar method. The excellent performance of the new approach is illustrated in representative numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.     

Slenderness effects of Biaxially loaded reinforced concrete columns

Abstract

An analysis on the strength of reinforced concrete slender columns subjected to biaxial loads is presented. The behavior of pin‐ended square and rectangular columns under a braced condition was studied. Lateral deflections and secondary moments were evaluated iteratively using non‐linear moment‐thrust‐curvature (M‐P‐F) relationships. Results have been verified with published data. The moment magnification factors were also compared to those calculated using ACI Code approximate method and the agreement is good for most practical cases. Parametric studies reveal that under the same steel ratio, gross cross sectional area and length, square columns lead to better capacities than rectangular columns for M_x/M_y < 2.0. The advantage of using a rectangular long column could only be achieved when M_x/M_y > 2.0     

A hierarchical finite element for geometrically non‐linear vibration of doubly curved,moderately thick isotropic shallow shells

A p‐version, hierarchical finite element for doubly curved, moderately thick, isotropic shallow shells is derived and geometrically non‐linear free vibrations of panels with rectangular planform are investigated. The geometrical non‐linearity is due to large displacements, and the effects of the rotatory inertia and transverse shear are considered. The time domain equations of motion are obtained by applying the principle of virtual work and the d'Alembert's principle. These equations are mapped to the frequency domain by the harmonic balance method, and are finally solved by a predictor–corrector method. The convergence properties of the element proposed and the influence of several parameters on the dynamic response are studied. These parameters are the shell's thickness, the width‐to‐length ratio, the curvature‐to‐width ratio and the ratio between curvature radii. The first and higher order modes are analysed. Some results are compared with results published or calculated using a commercial finite element package. It is demonstrated that with the proposed element low‐dimensional, accurate models are obtained. Copyright © 2002 John Wiley & Sons, Ltd.     

Design of low sensitivity controllers: Frequency domain technique

Abstract

The reduction of response deviation due to plant parameter changes is investigated. The algorithms are developed based on the frequency domain design technique of optimal theory. The obtained controllers are in transfer‐function matrix form. The approach for obtaining the low sensitivity controller gain is different from the methods presented in the literature since the types of controller gain were prespecified and the design were carried out in the time domain. From the example, it shows that the trajectory sensitivity has been reduced significantly.     

An accelerated surface discretization‐based BEM approach for non‐homogeneous linear problems in 3‐D complex domains

For non‐homogeneous or non‐linear problems, a major difficulty in applying the boundary element method (BEM) is the treatment of the volume integrals that arise. An accurate scheme that requires no volume discretization is highly desirable. In this paper, we describe an efficient approach, based on the precorrected‐FFT technique, for the evaluation of volume integrals resulting from non‐homogeneous linear problems. In this approach, the 3‐D uniform grid constructed initially to accelerate surface integration is used as the baseline mesh for the evaluation of volume integrals. As such, no volume discretization of the interior problem domain is necessary. Moreover, with the uniform 3‐D grid, the matrix sparsification techniques (such as the precorrected‐FFT technique used in this work) can be extended to accelerate volume integration in addition to surface integration, thus greatly reducing the computational time. The accuracy and efficiency of our approach are demonstrated through several examples. A 3‐D accelerated BEM solver for Poisson equations has been developed and has been applied to a 3‐D multiply‐connected problem with complex geometries. Good agreement between simulation results and analytical solutions has been obtained. Copyright © 2005 John Wiley & Sons, Ltd.     

Suppression of smeared spectrum ECM signal

Abstract

Three electronic counter‐countermeasures (ECCM) techniques for suppressing smeared spectrum (SMSP) jamming, a new electronic counter measures (ECM) technique, are presented. The analytical representations of the SMSP ECM signal in the time domain and the frequency domain are first derived, and then the differences between the SMSP jamming signal and the radar linear frequency modulation (LFM) signal are analyzed. Based on the differences, a jamming suppression system specifically for SMSP jamming interference excision is designed, which applies three different signal processing tools, i.e. fractional Fourier transform (FRFT), Fourier transform (FT) and atomic decomposition (AD). The jamming suppression performance of the presented methods is evaluated through simulations. The simulation results show that the presented methods can successfully suppress SMSP jamming.