Numerical Approach to Identifiability Test of Parametric Models in Nonlinear Mechanical Systems

The present paper develops an enhanced response sensitivity approach for parameter identification of nonlinear time-delay systems from the time-domain data. Accurate and rapid identification of the time-delay system’s parameters is the key to achieve effective control and synchronization, especially for the delay parameters. The work of this paper is mainly threefold. Firstly, taking a general nonlinear time-delay system as the investigated object, the characteristics of the nonlinear time-delay system are introduced, and the response sensitivity analysis with respect to the system parameters is derived. Then, the problem of parameter identification is modeled as a nonlinear least-squares optimization function. To this end, a novel iteration-based approach is developed to solve such problem, and the ill-posed situation is tackled by Tikhonov regularization. Besides, the trust-region constraint is implemented to enhance the convergence of the algorithm. Finally, the feasibility of the proposed approach is verified by two numerical examples and a real electronic circuit experiment. The results proved that the proposed approach can identify parameters of nonlinear time-delay systems accurately, robustly and effectively.

A global design methodology for supersonic air intakes is proposed. It is strongly based on numerical computations. The emphasis is especially put on the optimization of the links between the various stages of the design so as to rationalize the process and insure a good communication between the designer, the numerical computation engineer and the configuration manager. WHY IS IT IMPORTANT TO MASTER THE AIR INTAKE DESIGN IN A HIGH SPEED AEROBIC MISSILE DEVELOPPEMENT ? The design of a high-speed air-breathing vehicle is a long and delicate operation requiring the optimization of numerous design compromises interacting with each other and conditioning very widely the definition of the various constituents. The realization of these compromises is all the more difficult as we are more and more confronted with the imperative need to reduce the costs and the duration of the global cycle of development. One of the key elements of the global optimization of the aeropropulsive balance of high speed aerobic vehicles is the air intake which: Determines both the quantity and the quality of the air taken from the atmosphere (which influences directly all the tuning of the combustion chamber) Constitutes an important part of the global drag (which directly influences the fuel tank sizing) COPYRIGHT © 2001 EADS AEROSPATIALE MATRA MISSILES. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. Contributes strongly to the global lift (that participates to the global aerodynamic formula) Can be a major contributor to the radar signature (RCS) Participates substantially to the mass estimate Represents a significant part of the production cost. It is thus advisable to master and to rationalize the iterative design process of the air intake aerodynamics to be capable of: Minimizing the cost by limiting as much as possible the expensive experimental iterations; Reducing the cycle times to favour the flexibility and the reactivity of the global optimization; Estimating quickly the feasibility of beneficial shape evolutions or minimizing development and production costs or reducing the RCS. WHAT KIND OF APPROACHES ARE CLASSICALLY USED TODAY ? To establish the definition of an air intake, two approaches are possible: The experimental approach, which consists in realizing, reduced scale models and testing them in a wind tunnel; The numerical approach which consists in realizing a computation of the flow upstream and in the air intake by means of a two-, then threedimensional using, depending on the development, more and more accurate modeling of the fluid mechanics laws (Euler then NavierStokes). 1 American Institute of Aeronautics and Astronautics (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. THE EXPERIMENTAL APPROACH Led with skill, the experimental approach gives the surest results in terms of accessible global performances (performance curve). Even if the computation times have been reduced formidably, it remains today the most effective means to characterize an air intake in a wide flight domain in order to establish a performance serviceable for the propulsive system design, the global flight simulations, or the embarked regulation software. On the other hand, it requires heavy seed money, which consists in: Defining and realizing a model (modular able to receive various elements which allow to study configuration variants, the manufacture of which should be of very good quality precision, repeatability of the configurations, surface roughness...); Endow the of a detailed enough and precise instrumentation; Realize tests campaigns, the preparation of which being long and expensive. Besides, this experimental approach is too long if it is the only mean for the selection of the optimal air intake shape (model kit never perfectly adapted from the first tests campaign, time consuming configuration changes increasing the tests costs...). THE NUMERICAL APPROACH The numerical approach presents actually the inverse advantages and drawbacks of the experimental approach. In spite of the considerable progress realized these last ten years in the validation of the computation codes, and in spite of the precision presently obtained (of the same order as that of the tests), it will always be necessary to characterize in tests the shapes elaborated by computations, in order to definitively raise any doubt on the performances of the air intakes. Furthermore, the cost (in terms of duration) can turn out high if one wishes to perform a fine characterization requiring the computation of numerous running points. On the contrary, the numerical approach, although one endows it with effective meshing means, allows estimating in a reliable way and with a limited investment different configurations on a few flight points. Furthermore, it gives access to the detailed flow structure so yielding to understand better the physical phenomena that govern the functioning and favoring therefore the configuration desing. THE COUPLING OF THE EXPERIMENTAL AND NUMERICAL APPROACHES ALLOWS TO OPTIMIZE THE DESIGN To drive quoted rationalization process and answer more effectively the needs of the projects, we defines as objective: To establish an air intakes design methodology involving intimately both approaches to benefit of their advantages while minimizing (even eliminating) their drawbacks To obtain, thanks to this methodology, a sensitive reduction of the cost and the duration of the design cycle of an air intake To operate it according to its implementation on concrete industrial cases. GLOBAL DESIGN METHODOLOGY OF AIR INTAKES The development and the validation of internal aerodynamics computation codes being acquired, we focused on building a general design methodology for supersonic air intakes which strongly integrates the numerical approach into the traditional process based on wind-tunnel tests. Given the advantages and drawbacks described above for both experimental and numerical approaches, the best complementarity is obtained through the process described in the following scheme: American Institute of Aeronautics and Astronautics (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. Figure 1: coupling of numerical and experimental approaches A few of key points was identified as determining the efficiency of the process: Configuration management Simplification of the CAD / meshing interface

We introduce a consecutive identification of ANFIS-based fuzzy systems with the aid of genetic data granulation to carry out the model identification of complex and nonlinear systems. The proposed model implements system structure and parameter identification with the aid of information granulation and genetic algorithms. The design methodology emerges as a hybrid structural optimization and parametric optimization. Information granulation realized with HCM clustering algorithm help determine the initial parameters of fuzzy model such as the initial apexes of the membership functions in the premise and the initial values of polynomial functions in the consequence. And the structure and the parameters of fuzzy model are identified by GAs and the membership parameters are tuned by GAs. In this case we exploit a consecutive identification. The numerical example is included to evaluate the performance of the proposed model.

The time finite element method (TFM) is employed for parametric identification of nonlinear structural dynamic systems. An advantage of TFM is the ease with which one can calculate the sensitivity of the transient response with respect to various design parameters, a key requirement for gradient-based parameter identification schemes. The method is simple, because one obtains the sensitivities of the response to system parameters by differentiating the algebraic equations, not original differential equations. These sensitivities are used in the Levenberg-Marquardt iterative direct method to identify parameters for nonlinear single- and two-degree-of-freedom systems. The measured response was simulated by integrating the example nonlinear systems using the given values of the system parameters. The accuracy and the efficiency of the present method are compared to a previously available approach that employs a multistep method to integrate nonlinear differential equations. It is seen, for the same accuracy, that the present approach requires fewer data points.

Identification of nonlinear systems is one of the important problems in engineering. Chaotic systems are among those nonlinear systems that have been in the center of attention of many researchers because of their complex and unpredictable behaviors. This paper proposes an algorithm for optimally estimating the parameters of system by minimizing the mean of squared errors (MSE) index. In this paper, Teaching Learning Based Optimization (TLBO) algorithm is used for solving both offline and online parameter estimation problems for chaotic systems. The validity of this algorithm in terms of convergence speed and parameter accuracy in comparison to other popular optimization algorithms such as Standard PSO (PSO), Differential Evolution (DE), Adaptive Particle Swarm Optimization (APSO) and Genetic Algorithm (GA) is shown through an illustrative example for the modeling of chaotic systems. Furthermore, in order to demonstrate the feasibility of this algorithm, it is applied to the problem of parameter identification of a well-known nonlinear Lorenz chaotic system. According to simulation results, the proposed algorithm is a very suitable algorithm for online parameter identification for a class of nonlinear chaotic systems.

A new algorithm for the identification of continuous time nonlinear systems from sampled data records is derived based on state variable filters coupled with an orthogonal least squares estimator. Delayed filtered inputs, outputs and associated higher order derivatives collected from the state variable filters are used for the identification of the unknown system parameters using an orthogonal least squares estimator. Because of the high dimensionality of general nonlinear systems the error reduction ratio derived from the orthogonal least squares estimator is used to detect the model structure. Plots of the unmodelled estimation errors against the state variables is also proposed as a means of investigating the nonlinear system characteristics. Simulation studies are included to illustrate the concepts.

A low-cost experimental averaging method for fast–slow mechanical systems via long-exposure video: Application to the Kapitza pendulum

The efficacy of the multimodel framework (MMF) in modeling and identification of complex, nonlinear, and uncertain systems has been widely recognized in the literature owing to its simplicity, transparency, and mathematical tractability, allowing the use of well-known modeling analysis and control design techniques. The approach proved to be effective in addressing some of the shortcomings of other modeling techniques such as those based on a single nonlinear autoregressive network with exogenous inputs model or neural networks. A great number of researchers have contributed to this active field. Due to the significant amount of contributions and the lack of a recent survey, the review of recent developments in this field is vital. In this two-part paper, we attempt to provide a comprehensive coverage of the multimodel approach for modeling and identification of complex systems. The study contains a classification of different methods, the challenges encountered, as well as recent applications of MMF in various fields. Part 1 of this paper presents an overview of MMF for modeling and identification of nonlinear systems as well as the review of recent developments in the partitioning strategies employed.

Time–frequency characterization of nonlinear normal modes and challenges in nonlinearity identification of dynamical systems

In this paper, a novel numerical approach is proposed for workspace determination of parallel mechanisms. Compared with the classical numerical approaches, this presented approach discretizes both location and orientation of the mechanism simultaneously, not only one of the two. This technique makes the presented numerical approach applicable in determining almost all types of workspaces, while traditional numerical approaches are only applicable in determining the constant orientation workspace and orientation workspace. The presented approach and its steps to determine the inclusive orientation workspace and total orientation workspace are described in detail. A lower-mobility parallel mechanism and a six-degrees-of-freedom Stewart platform are set as examples, the workspaces of these mechanisms are estimated and visualized by the proposed numerical approach. Furthermore, the efficiency of the presented approach is discussed. The examples show that the presented approach is applicable in determining the inclusive orientation workspace and total orientation workspace of parallel mechanisms with high efficiency.

Numerical and empirical approach in predicting the penetration of a concrete target by an ogive-nosed projectile

Many classes of nonlinear systems can be represented by Volterra kernels. The authors have recently developed a method for identification of Volterra kennels of nonlinear systems by using M-sequence and correlation technique. In this paper, the authors propose a new method for identification of nonlinear mechanical systems by use of Volterra kernels. The nonlinear mechanical systems are approximated to a nonlinear vibrating system which consists of a mass, a dumper, a linear spring and a nonlinear spring. Then, the parameters, which represent the nonlinear springs are calculated by use of the Volterra kernels. From the results of computer simulation and experiment, the parameters that represent the nonlinear characteristics of the nonlinear mechanical systems can be identified by the proposed method.

Accurate and timely identification of modal parameters of long-span bridges is important for bridge health monitoring and wind tunnel tests. Wavelet analysis is one of the most advantageous methods for identification because of its good localization characteristics in both time and frequency domain. In recent years, the wavelet method has been applied more frequently in parameter identification of linear and nonlinear systems. In this article, based on wavelet ridges and wavelet skeleton, the improved modal parameter identification method was studied. To find the appropriate time-frequency resolution, an optimal wavelet basis design principle based on minimum Shannon entropy was proposed. Aiming at endpoint effect in wavelet transform, a prediction continuation method based on support vector machine (SVM) was proposed, which can effectively suppress the endpoint effect of the extended samples. In view of the fact that the ridges of metric matrices obtained by the traditional crazy climber algorithm cannot fully reflect the distribution of ridges of modulus value matrices of wavelet coefficients, an improved high-precision crazy climber algorithm was put forward to accurately identify the position of the ridge of wavelet coefficients. Finally, taking a long-span cable-stayed bridge and a long-span suspension bridge as the engineering background, improved continuous wavelet transform (CWT) was applied to modal parameter identification of bridge under ambient excitation. The modal parameters such as modal frequency, damping ratio, and mode shape were obtained. Compared with the calculation value of the numerical simulation of long-span cable-stayed bridge and wind tunnel test of long-span suspension bridge, the reliability of CWT for modal parameter identification of long-span bridges under ambient excitation was verified.

Teaching Aids for Modeling and Control of Hybrid Systems (CAMCHS)

Identification of continuous-time nonlinear systems: The nonlinear difference equation with moving average noise (NDEMA) framework