Unconditionally Stable Central Difference Dissipative Algorithm for Multi-Directional Real-Time Hybrid Simulations of Large Nonlinear Structural Systems

Industrial structure systems may have nonlinearity, and are also sometimes exposed to the danger of random excitation. This paper proposes a method to analyze response and reliability design of a complex nonlinear structure system under random excitation. The nonlinear structure system which is subjected to random process is modeled by finite element method. The nonlinear equations are expanded sequentially using the perturbation theory. Then, the perturbed equations are solved in probabilistic methods. Several statistical properties of random process that are of interest in random vibration applications are reviewed in accordance with the nonlinear stochastic problem.

This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not necessarily for real-time testing, but rather for models that involve large-scale physical sub-structures and highly nonlinear numerical models. Four case studies are presented and discussed. In the first case study, the accuracy of integration schemes including two widely used methods, namely, modified version of the implicit Newmark with fixed-number of iteration (iterative) and the operator-splitting (non-iterative) is examined through pure numerical simulations. The second case study presents the results of 10 hybrid simulations repeated with the two aforementioned integration methods considering various time steps and fixed-number of iterations for the iterative integration method. The physical sub-structure in these tests consists of a single-degree-of-freedom (SDOF) cantilever column with replaceable steel coupons that provides repeatable highlynonlinear behavior including fracture-type strength and stiffness degradations. In case study three, the implicit Newmark with fixed-number of iterations is applied for hybrid simulations of a 1:2 scale steel moment frame that includes a relatively complex nonlinear numerical substructure. Lastly, a more complex numerical substructure is considered by constructing a nonlinear computational model of a moment frame coupled to a hybrid model of a 1:2 scale steel gravity frame. The last two case studies are conducted on the same porotype structure and the selection of time steps and fixed number of iterations are closely examined in pre-test simulations. The generated unbalance forces is used as an index to track the equilibrium error and predict the accuracy and stability of the simulations.

Conventionally modelling and simulation of complex nonlinear systems has been to construct a mathematical model and examine the system’s evolution or its control. This kind of approach can fail for many of the very large non-linear and complex systems being currently studied. With the invention of new advanced high-speed computers and the application of artificial intelligence paradigms new techniques have become available. Particularly neural networks and fuzzy logic for nonlinear modelling and genetic algorithms [Goldberg, D. (1989)] and evolutionary algorithms for optimisation methods have created new opportunities to solve complex systems [Bai, Y., Zhuang H. and Wang, D. (2006)]. This paper considers issues in design of multi-layer and hierarchical fuzzy logic systems. It proposes a decomposition technique for complex systems into hierarchical and multi-layered fuzzy logic sub-systems. The learning of fuzzy rules and internal parameters in a supervised manner is performed using genetic algorithms. The decomposition of complex nonlinear systems into hierarchical and multi-layered fuzzy logic sub-systems reduces greatly the number of fuzzy rules to be defined and improves the learning speed for such systems. In this paper a method for combining subsystems to create a hierarchical and multilayer fuzzy logic system is also described. Application areas considered are - the prediction of interest rate, unemployment rate predication and electricity usage prediction. Genetic Algorithms can be used as a tool for design and generation of fuzzy rules for a fuzzy logic system. This automatic design and generation of fuzzy rules, via genetic algorithms, can be categorised into two learning techniques namely, supervised and unsupervised. In supervised learning there are two distinct phases to the operation. In the first phase each individual is assessed based on the input signal that is propagated through the system producing output respond. The actual respond produced is then compared with a desired response, generating error signals that are then used as the fitness for the individual in the population of genetic algorithms. Supervised learning has successfully applied to solve some difficult problems. In this paper design and development of a genetic algorithm based supervised learning for fuzzy models with application to several problems is considered. A hybrid integrated architecture incorporating fuzzy logic and genetic algorithm can generate fuzzy rules that can be used in a fuzzy logic system for modelling, control and prediction

Structural system identification using Least Mean Square (LMS) adaptive technique

This article introduces a novel modular approach to the modelling of nonlinear interconnected complex systems. In the approach, a complex system is decomposed into self-contained easily identified modules to achieve easy linking of individual models. Our proposed approach to modelling differs from the traditional approaches in the following important aspects: (1) it is nonlinear, modular based, systematic, and graphical; (2) it is suitable for fault diagnosis; (3) depending on the level of complexity required, each module may be changed separately quite easily without having to change the other modules; and (4) it draws from the powerful capabilities of the widely used packages of Simulinkand Matlab. These features provide for a generic package that can simulate a complex interconnected system of any description and configuration, as well as simulating any kind of fault anywhere in the system by merely changing the input vector. Examples of two power systems are used as case studies, where it is shown that complex systems can be constructed and simulated easily by appropriately combining components together. The simulation studies show the dynamical behaviour of the two systems with and without faults being applied to them.

This article introduces a novel modular approach to the modelling of nonlinear interconnected complex systems. In the approach, a complex system is decomposed into self-contained easily identified modules to achieve easy linking of individual models. Our proposed approach to modelling differs from the traditional approaches in the following important aspects: (1) it is nonlinear, modular based, systematic, and graphical; (2) it is suitable for fault diagnosis; (3) depending on the level of complexity required, each module may be changed separately quite easily without having to change the other modules; and (4) it draws from the powerful capabilities of the widely used packages of SimulinkTM and MatlabTM . These features provide for a generic package that can simulate a complex interconnected system of any description and configuration, as well as simulating any kind of fault anywhere in the system by merely changing the input vector. Examples of two power systems are used as case studies, where it is shown that complex systems can be constructed and simulated easily by appropriately combining components together. The simulation studies show the dynamical behaviour of the two systems with and without faults being applied to them.

Symbolic computational approaches are desirable for many applications and especially for large complex and nonlinear systems. These approaches work well when (a) the user interface is "symbolized" and (b) the underlying computational algorithms are robust. This paper presents advances in both of these areas and for the specific application of numerical integration of large complex nonlinear systems. We present a method for symbolically defining complex nonlinear systems. The methodology includes a human interface for symbolic manipulations of the system model. The system model is symbolically quadratized. The quadratized model is integrated with a numerical method that belongs to the general class of collocating methods. The presented methodologies are superior to previous approaches by the authors using symbolic manipulations and trapezoidal integration. The methodology is illustrated with example systems including converters with saturable inductors, surge arresters and other complex nonlinear systems. The proposed methodology is compared to previous approaches for the purpose of quantifying the advantages

Current simulation tools for multibody dynamics are not problem dependent, they use the same modeling process to all cases regardless of their characteristics. In addition, real-time simulation of small multibody systems is achievable by existing simulation tools, however, real-time simulation of large and complex systems is not possible with existing methods. This is a challenge that needs to be addressed before further advances in mechanical simulation with hardware-in-the-loop and man-in-the-loop, as well as virtual prototyping are made possible. This paper addresses the issue of how the modeling process-dependent versus independent coordinates, and descriptor form versus state-space form of the equations of motion-affects the dynamic simulation of multibody systems and how it may be taken into account and added to the concept of intelligent simulation. With this new concept all the factors involved in the simulation process — modeling, equations, solution, etc. — are chosen and combined depending upon the characteristics of the system to be simulated. It is envisioned that this concept will lead to faster and more robust real-time simulators.

A practical and efficient coupling method for large scale soil–structure interaction problems

3R12. Nonlinearity in Structural Dynamics: Detection, Identification and Modeling. - K Worden and GR Tomlinson (Univ of Sheffield, UK). Inst Phys Publ, Bristol, UK. 2001. 659 pp. ISBN 0-7503-0356-5. $130.00.Reviewed by K Yagasaki (Dept of Mech and Syst Eng, Gifu Univ, 1-1 Yanagido, Gifu, 501-1193, Japan).This book provides backgrounds in some techniques for analyzing nonlinear structural dynamical systems and is intended for engineers and scientists in the fields of structural dynamics and nonlinear systems. It is also suitable for postgraduate and senior undergraduate students in these disciplines as a textbook and for expert structural dynamicists as a survey. Many engineering examples are given. As for the mathematics of the reader, calculation of vectors and matrices, and basic knowledge of linear differential equations and Fourier analysis are almost sufficient. The most enthusiastic topics in modern nonlinear dynamics are chaos and bifurcation. There have also been remarkable advances in the field of nonlinear control. However, these subjects are not treated in this book at all. Instead, it explains useful techniques, which include the frequency response functions (FRFs) and Hilbert transformations, for detection of nonlinearity and system identification (ie, estimation of the governing equations) when the systems do not exhibit very different motions, like chaos, from ones of linear systems. The techniques are especially important from a point of view of structural engineering because really nonlinear behavior like chaos is thought to be rather uncommon in the problems of that field. The book begins by describing the relevant backgrounds including the frequency response functions (FRFs) in linear dynamics for discrete- and continuous-time systems in Chapter 1. The discussion is first given for single-degree-of-freedom (SDOF) systems and finally generalized to multi-degree-of-freedom (MDOF) systems with an outline of modal analysis. Chapter 2 gives fundamental results and classical approaches to nonlinear systems in structural dynamics. An idea of FRF distortion is also stated there. Chapter 3 discusses FRFs for nonlinear systems in detail and describes how they are used to obtain information about nonlinearity.In Chapters 4 and 5, the Hilbert transformation, which can not only detect nonlinearity but also solve system identification problems, is explained. A mathematical exposition of the method by complex analysis is also presented. In Chapters 6 and 7, several techniques of system identification for discrete- and continuous-time equations are discussed. In Chapter 8, the concept of FRFs is generalized to higher-order FRFs with the assistance of the Volterra series. The generalization presents a method of system identification for MDOF systems. Finally, three experimental examples of a built-in beam rig, automotive shock absorber, and bilinear beam rig (the last of which is motivated from constructing a system with localized damage in the benchmark of fault detection algorithms) are given, and the techniques of the earlier chapters are applied to demonstrate their effectiveness in Chapter 9. This chapter is especially interesting for the reader from a practical point of view. A substantial set of appendices is also valuable for not only the beginners, but also ordinary researchers in the field. In summary, this reviewer recommends Nonlinearity in Structural Dynamics: Detection, Identification and Modeling for students and researchers in structural dynamics who want to study techniques for detection of nonlinearity and system identification in realistic problems.

Response evolutionary power spectrum determination of chain-like MDOF non-linear structural systems via harmonic wavelets

Inference of hidden common driver dynamics by anisotropic self-organizing neural networks.

Fine-Grained Parallel and Distributed Spatial Stochastic Simulation of Biological Reactions

An Efficient and Flexible Out‐of‐Core Equation Solver

In this paper, nonlinear dynamic system identification by using multiobjectively selected RBF network is considered. RBF networks are widely used as a model structure for nonlinear systems. The determination of its structure that is the number of basis functions is prior important step in system identification, and the tradeoff between model complexity and accuracy exists in this problem. By using multiobjective evolutionary algorithms, the candidates of the RBF network structure are obtained in the sense of Pareto optimality. We discuss an application to system identification by using such RBF networks having Pareto optimal structures. Some numerical simulations for nonlinear dynamic systems are carried out to show the applicability of the proposed approach.