MS01.4: Reduced-Order Modeling and System Identification

A new design of power amplifier’s (PA) digital pre-distortion (DPD) model with recursive system identification algorithm based on H-infinite robust control is proposed in this study to improve the accuracy of the model without increasing the computational cost too much. With the development of hardware technology, the linearization of power amplifiers with large bandwidth and high adjacent leakage makes the traditional models need to be implemented by high order nonlinear operation, which results in a decrease in the accuracy of the model and an increase in the calculation cost of the model. Based on the framework of generalized memory polynomial model, this study uses the lower-order nonlinear piecewise function with cross-memory combination term to replace the higher-order nonlinear and implements the design of a new basis function model. In the identification of basis function model, this study designs an identification algorithm based on H-infinite robust control, which deals with the identification of PA system and limits the error to a certain disturbance range. To reduce the computational cost, a low order controller design is solved by linear matrix inequality, and the resulting increase in the disturbance range will be eliminated by the extended Kalman filter to improve the accuracy. In this study, the predistortion simulation results based on the input and output data of PA with large bandwidth and high adjacent leakage are presented to demonstrate the superiority of the model and algorithm in dealing with similar nonlinear system identification problems.

The recent theory of spectral submanifolds (SSMs) has emerged as a general, mathematically rigorous approach to reducing very high dimensional mechanical systems to very low dimensional models. Successful applications of SSM-reduction range from geometrically nonlinear finite-element models in structural dynamics through experimental fluid-structure interactions to model-predictive control in soft robotics. Open-source codes with growing libraries of worked examples are now available to carry out equation-driven SSM reduction (SSMTool) and data-driven SSM reduction (SSMLearn). As the mathematical theory of SSMs has only been developed in detail for smooth physical systems, its applicability to non-smooth systems is still the subject of ongoing research. We contribute to this development by applying data-driven SSM reduction to learn a low-dimensional reduced model for the simulated, unforced dynamics of a thin-walled jointed mechanical assembly. In this benchmark problem, frictional contact occurring at the interfaces of the assembled components is a non-smooth effect that can lead to a highly nonlinear dynamic response. Recent results by the joints research community show that predictive equation-driven reduced order modeling for this benchmark problem remains a challenge. Here, we discuss the construction of a very low dimensional, nonlinear reduced model for this problem by applying SSMLearn to numerical data obtained from a small number of unforced finite-element simulations. We then use this SSM-reduced model to make predictions for the forced response of the assembly, which we subsequently verify by direct finite-element simulations of the forced structure.

We propose a methodology to carry out nonlinear system identification based on bifurcations. The proposed approach relies on fold bifurcation curves identified experimentally through control-based continuation and an optimization framework to minimize the distance between the experimental and numerical curves computed with bifurcation tracking analyses. The approach is demonstrated on a nonlinear model of base-excited energy harvester with magnetic force nonlinearity

This work introduces the application of the Direct Parametrisation method for Invariant Manifolds to a fully coupled multiphysics problem involving nonlinear vibrations of deformable structures under an electrostatic field. The proposed formulation aims at model order reduction for electrostatically actuated resonating Micro-Electro-Mechanical Systems (MEMS). The continuous problem is rewritten in a novel mixed fully Lagrangian formulation with explicit polynomial nonlinearities for direct handling by the parametrisation method, which utilises automated asymptotic expansions. Validation is conducted on simple MEMS, comparing different formulations and reduced-order models to full-order simulations. The results demonstrate high accuracy and capture nonlinear effects, including the transition from hardening to softening behaviour and investigation of secondary resonances.

Finite element models with fine spatial discretization are required for accurate predictions of vibration-induced stresses which can cause fatigue. Dynamic analyses with these models, however, come at high computational cost. Therefore, many applications, e.g., such requiring large parameter studies, are prohibitive. Although many techniques for model order reduction have been developed, most of them are not applicable to the combination of geometric and contact nonlinearities. We present a novel dynamic substructuring approach for thin-walled jointed structures which divides the assembly into thin-walled substructures with geometric nonlinearites and geometrically linear substructures featuring contact nonlinearity. Each class of substructures is then reduced using adapted variants of Component Mode Synthesis. Moreover, interface reduction is applied to the substructure interface. The accuracy of the re-assembled reduced-order model was shown in quasi-static and transient dynamic analyses performed on a benchmark structure. Also, the importance of both types of nonlinearity was demonstrated. The method was able to reduce the computation times by orders of magnitude in the dynamic analyses.