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Bayesian shape optimisation of complex structures under stability criteria applied to brake systems

Abstract : We expose an efficient strategy to deal with shape optimization of dynamical systems exhibiting flutter-type instability induced by friction, such as the considered disc-pad system.The stability of such systems can be analysed through Complex-Eigenvalue Analysis, through which we present a squeal noise criterion to be minimized as a computationally expensive black-box function. The computational domain is discretized through Isogeometric formulation for its advantages in optimization and superior approximation properties which are well studied in structural dynamics. To be computationally efficient with the expensive black-box function, we defined the optimization based on Efficient Global Optimization scheme in the context of multi-objective optimization, with the integration of Isogeometric design-through-analysis methodology. As gradient information is hard to access for such black-box functions, in addition to the presence of constraints, we relied on meta-heuristic approach as a more generic strategy for realizing optimization of such functions in multi-objective context. As one such scheme with its own advantages was observed to provide lack of resolution to define Expected Improvement (EI) with a single reference value, we propose a multi-reference acquisition strategy which can be defined through a fast and efficient algorithm with fewer adaptation to the existing scheme. Results show the efficiency of this approach for our applicative example, which can be extended to other such applications as well. Flutter-type dynamic instability typically defines a self-excitation behaviour in the presence of non-conservative forces. In structural dynamics, this is understood as coalescence of modes, where two modes exist at a same frequency leading to self-excitation between the modes under favorable conditions in the presence of non-conservative forces. We consider shape optimization of braking system through a simple disc-pad representation, where this type of systems can exhibit flutter-type dynamic instability in the presence of friction, perceived as squeal noise. Typically, friction induced dynamic instabilities are highly nonlinear phenomena which can be computationally expensive when defined through transient analyses and hence, unrealistic to be considered for optimization. The definition of follower force model for friction makes it possible to define this type of systems as a time-independent linear dynamical system around a fixed point defined through quasi-static hypothesis, which otherwise requires satisfying non-holonomic constraints with strong time dependence. Hence, the stability of such linearized systems around a fixed point can be defined through its eigenvalues, commonly known as Complex-Eigenvalue Analysis (CEA). Through CEA, we define a black-box function {which is adversely expensive for computation, to describe a criterion for stability in shape optimization. Further, for evaluation of the expensive black-box function, we define a parallel computation strategy through dynamic model reduction. To realize an efficient generic strategy to deal with shape optimization of an arbitrary domain for computationally expensive black-box functions, we encompass Isogeometric approach for discretization and Efficient Global Optimization (EGO) approach in the context of Multi-Objective Optimization (MOO) --commonly known as Multi-Objective Bayesian Optimization (MOBO). [...]
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Submitted on : Thursday, July 28, 2022 - 4:33:11 PM
Last modification on : Tuesday, August 23, 2022 - 4:28:11 PM


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  • HAL Id : tel-03740007, version 1



Pradeep Mohanasundaram. Bayesian shape optimisation of complex structures under stability criteria applied to brake systems. Other. Université de Lyon, 2021. English. ⟨NNT : 2021LYSEC026⟩. ⟨tel-03740007⟩



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