Reduced order model-inspired system identification of geometrically nonlinear structures

Author:

Ahmadi M. Wasi1ORCID,Hill Thomas L.1,Jiang Jason Zheng1,Neild Simon A.1

Affiliation:

1. University of Bristol

Abstract

AbstractIn the field of structural dynamics, system identification usually refers to building mathematical models from an experimentally-obtained data set. To build reliable models using the measurement data, the mathematical model must be representative of the structure. In this work, attention is given to robust identification of nonlinear structures. We draw inspiration from reduced order modelling to determine a suitable model for the system identification. There are large similarities between reduced order modelling and system identification fields, i.e. both are used to replicate the dynamics of a system using a mathematical model with low complexity. Reduced Order Models (ROMs) can accurately capture the physics of a system with a low number of degrees of freedom; thus, in system identification, a model based on the form of a ROM is potentially more robust. Nonlinear system identification of a structure is presented, where inspiration is taken from a novel ROM to form the model. A finite-element model of the structure is built to simulate an experiment and the identification is performed. It is shown how the ROM-inspired model in the system identification improves the accuracy of the predicted response, in comparison to a standard nonlinear model. As the data is gathered from simulations, system identification is first demonstrated on the high fidelity data, then the fidelity of data is reduced to represent a more realistic experiment. A good response agreement is achieved when using the ROM-inspired model, which accounts for the kinetic energy of unmodelled modes. The estimated parameters of this model are also demonstrated to be more robust and rely on the underlying physics of the system.

Publisher

Research Square Platform LLC

Reference71 articles.

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2. Gordon, Robert W. and Hollkamp, Joseph J. (2011) {Reduced-order models for acoustic response prediction of a curved panel}. Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference (April): 1--14 https://doi.org/10.2514/6.2011-2081, 02734508, 9781600869518, ::, Predicting the response of stiffened shell structures subjected to extreme acoustic loading and aerodynamic heating is a challenging computational task. The acoustic loading induces nonlinear, stochastic vibratory response. The aerodynamic heating results in significant quasi-static thermal stresses which can significantly alter the dynamic response. Curvature effects in stiffened skin structures exposed to these loadings can further complicate numerical analysis. Reduced-order nonlinear models have been shown to be accurate and computationally efficient in simulating the time response of simple beams and plates with acoustic and thermal loading. The next step in the development and verification of reduced-order methods for acoustic response prediction of real structures is their application to curved panels. This paper presents the results of a numerical study of reduced-order models using "cold" and "hot" modes applied to a curved panel with static thermal and acoustic loading. The cold modes approach uses normal modes of the structure at ambient temperature while the hot modes approach uses modes from the thermally loaded state. In general, results from both approaches agree closely with full-order finite element simulations of a curved panel example problem. However, both approaches suffered from stability problems at very high sound pressure levels. While the cold modes models are more desirable for analysis at multiple temperatures, more modes are generally required to achieve results equivalent to a hot modes model.

3. Li, Wenlong and Chen, Yanmao and Lu, Zhong Rong and Liu, Jike and Wang, Li (2021) {Parameter identification of nonlinear structural systems through frequency response sensitivity analysis}. Nonlinear Dynamics 104(4): 3975--3990 https://doi.org/10.1007/s11071-021-06481-5, https://doi.org/10.1007/s11071-021-06481-5, Springer Netherlands, Frequency response sensitivity analysis,Harmonic balance method,Nonlinear structural system,Parameter identification,Trust-region constraint, 1573269X, :C$$\backslash$$:/Users/ql20488/OneDrive - University of Bristol/Papers/Li2021{\_}Article{\_}ParameterIdentificationOfNonli.pdf:pdf, Nonlinearity is ubiquitously encountered in structural systems, and it may have a great and complicated influence on the dynamic behaviours, including bifurcation, internal resonance, load history dependence, etc. Identifying the nonlinear system parameters is essential for analysis and design of the structure. To this end, a new approach is developed in this paper for nonlinear system parameter identification from frequency response sensitivity analysis. At first, the harmonic balance equation is established to govern the frequency response of the nonlinear system, upon which the frequency response and sensitivity analysis can be conducted. A remarkable feature is that the harmonic balance equation is algebraic so that the sensitivity analysis, pertaining to a linearized equation, is rather simple and straightforward. Then, parameter identification is modelled as a nonlinear least-squares problem, and the sensitivity approach is adopted in conjunction with the trust-region constraint for convergent solution. Numerical examples are conducted to demonstrate the feasibility and performance of the proposed approach.

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5. Neild, Simon A. (2012) Approximate Methods for Analysing Nonlinear Structures. Springer Vienna, Vienna, https://doi.org/10.1007/978-3-7091-1187-1_2, 10.1007/978-3-7091-1187-1_2, 978-3-7091-1187-1, The dynamics of the majority of nonlinear structures cannot be solved exactly. In this chapter, approximate methods for solving the equations of motion of weakly nonlinear structures are presented. Common types of nonlinear response behaviour are identified using an example structure. Perturbation techniques and the method of secondorder normal forms are then discussed and used to analyse three applications in which the nonlinear behaviour is exploited., 53--109, Exploiting Nonlinear Behavior in Structural Dynamics, Wagg, David J. and Virgin, Lawrence

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