Direct optimisation based model selection and parameter estimation using time-domain data for identifying localised nonlinearities

Safari, Sina; Monsalve, Julián Mauricio Londoño

doi:10.1016/j.jsv.2021.116056

Cited by 13 publications

(12 citation statements)

References 37 publications

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“…In this section, the most relevant parts of optimisation based model selection and parameter estimation strategies, which are developed in [26], are reproduced for completeness. The optimisation problem considers the dynamics of mechanical systems with nonlinear stiffness that can be described by the following differential equation:…”

Section: Nonlinear Model Selection For Dynamic Equations Of Engineeri...mentioning

confidence: 99%

“…Only the nonlinear model ( f nl ) and its parameters are unknown and need to be identified. For more information on the quantification of linear parameters and their uncertainties on the nonlinear identification, one can refer to [26]. To identify the nonlinear model ( f nl ), harmonic excitation is used as an input force (F) at high vibration level, which can excite the structure near resonance frequencies where it is more likely that certain nonlinear effects (e.g., opening and closing a joint) are activated.…”

Section: Nonlinear Model Selection For Dynamic Equations Of Engineeri...mentioning

confidence: 99%

“…In addition, the application of machine learning [23], approximate Bayesian computation [24] and an optimisation based framework using experimental data from stepped sine results [25] have been considered for nonlinear model selection. More recently, the authors have proposed new optimisation based model selection algorithms for structures with localised stiffness nonlinearities [26]. Modal equations of motions were used and nonlinear modal couplings related to the presence of local nonlinear elements were taken into account.…”

Section: Introductionmentioning

confidence: 99%

“…The main contribution of this paper is the performance evaluation and comparison of ten powerful optimization algorithms (detailed in Section 2.3) when used in the task of selecting the best nonlinear model to describe the dynamic behaviour of a nonlinear mechanical system from its vibration response data. The search of models and their parameters are performed following the data-driven nonlinear system identification approaches already proposed by the authors in [26]. Therefore, the scope of this paper is limited to the comparison of optimisation methods as such, with the purpose of providing evidence to facilitate the selection of the most suitable optimisation algorithm for the nonlinear system identification of mechanical systems from vibration time-series data.…”

Section: Introductionmentioning

confidence: 99%

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Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems

Safari

Monsalve

2021

Vibration

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Characterisation and quantification of nonlinearities in the engineering structures include selecting and fitting a good mathematical model to a set of experimental vibration data with significant nonlinear features. These tasks involve solving an optimisation problem where it is difficult to choose a priori the best optimisation technique. This paper presents a systematic comparison of ten optimisation methods used to select the best nonlinear model and estimate its parameters through nonlinear system identification. The model selection framework fits the structure’s equation of motions using time-domain dynamic response data and takes into account couplings due to the presence of the nonlinearities. Three benchmark problems are used to evaluate the performance of two families of optimisation methods: (i) deterministic local searches and (ii) global optimisation metaheuristics. Furthermore, hybrid local–global optimisation methods are examined. All benchmark problems include a free play nonlinearity commonly found in mechanical structures. Multiple performance criteria are considered based on computational efficiency and robustness, that is, finding the best nonlinear model. Results show that hybrid methods, that is, the multi-start strategy with local gradient-based Levenberg–Marquardt method and the particle swarm with Levenberg–Marquardt method, lead to a successful selection of nonlinear models and an accurate estimation of their parameters within acceptable computational times.

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Section: Nonlinear Model Selection For Dynamic Equations Of Engineeri...mentioning

confidence: 99%

Section: Nonlinear Model Selection For Dynamic Equations Of Engineeri...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems

Safari

Monsalve

2021

Vibration

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“…In another type of classification, nonlinear identification methods can be categorized into two main classes: non-parametric ([134]- [135]) and parametric ([136]- [149]). The latter group can be divided into two sub-classes: methods with a model selection stage ([136]- [145]) and methods using an assumed model for the nonlinear system ([146]- [149]). Despite the efforts in developing nonlinear identification methods, there is not yet any identification method that can be generally applied to an extensive range of nonlinear systems.…”

Section: Parametric Vs Non-parametric Identificationmentioning

confidence: 99%

Nonlinear Model Updating in Structural Dynamics

Taghipour¹

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Identification of nonlinear structural dynamics has received a significant attention during last decades. Yet, there are many aspects of the identification methods of nonlinear structural models to be improved. The main objective of this study is to introduce novel identification approaches for nonlinear structures. The first step in identifying nonlinear structural elements is to detect their exact location. Hence, the first section of this study focuses on the localization of nonlinear elements in structural dynamics utilizing base excitation measured data. To this end, a localization approach is used to find the location of nonlinear electromagnetic restoring force applied to the tip of a cantilever beam.Inferring the exact location of nonlinear elements, identification methods are utilized to identify and characterize the mathematical model of nonlinear structures. However, various sources of noise and error may affect the accuracy of the identified model. Therefore, in the second part of the thesis, the effect of various sources of inaccuracy on the results of nonlinear model identification is investigated. It is shown that measurement noise, expansion error, modelling error, and neglecting the effect of higher harmonics may lead to an erroneously identified model.An optimization-based framework for the identification of nonlinear systems is proposed in this work in order to avoid the bottlenecks mentioned above. The introduced method is applied to a test rig composed of a base-excited cantilever beam subjected to an electromagnetic force at the tip. According to the nonlinear response of the system, four different functions are assumed as candidate models for the unknown nonlinear electromagnetic force. The measured response is compared with the reconstructed response using various models and the most appropriate mathematical model is selected.Utilizing optimization-based identification method to characterize complex mathematical models with large number of unknown parameters would be computationally expensive. Therefore, this study introduces a harmonic-balance-based parameter estimation method for the identification of nonlinear structures in the presence of multi-harmonic response and force. For this purpose, a method with two different approaches are introduced: Analytical Harmonic-Balance-based (AHB) approach and the Alternating Frequency/Time approach using Harmonic Balance (AFTHB). The method is applied to five simulated examples of nonlinear systems to highlight different features of the method. The method can be applied to all forms of both smooth and non-smooth nonlinear functions. The computational cost is relatively low since a dictionary of candidate basis functions is avoided. The results illustrate that neglecting higher harmonics, particularly in systems with multi-harmonic response and force, may lead to an inaccurate identified model. The AFTHB approach benefits from including significant harmonics of the response and force. Applying this method leads to accurate algebraic equations for each harmonic, including the effect of higher harmonics without truncated error. In the last part of this study, the AFTHB method is applied to two experimental case studies and identifies the nonlinear mathematical model of the structures. The first case is composed of a cantilever beam with a nonlinear electromagnetic restoring force applied to the tip which is excited by a multi-harmonic external force. In the second experimental case study, a configuration of linear springs applies a geometric nonlinear restoring force to the tip of a cantilever beam resulting in internal resonance in the dynamics of the system. The good performance of the AFTHB approach in estimating the unknown parameters of the structure is illustrated by the results of identification.

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Experimental Parameter Identification of Nonlinear Mechanical Systems via Meta-heuristic Optimisation Methods

Martinelli,

Coraddu,

Cammarano

2023

Conference Proceedings of the Society for Experimental Mechanics Series

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Meta-heuristic optimisation algorithms are high-level procedures designed to discover near-optimal solutions to optimisation problems. These strategies can efficiently explore the design space of the problems; therefore, they perform well even when incomplete and scarce information is available. Such characteristics make them the ideal approach for solving nonlinear parameter identification problems from experimental data. Nonetheless, selecting the meta-heuristic optimisation algorithm remains a challenging task that can dramatically affect the required time, accuracy, and computational burden to solve such identification problems. To this end, we propose investigating how different meta-heuristic optimisation algorithms can influence the identification process of nonlinear parameters in mechanical systems. Two mature meta-heuristic optimisation methods, i.e. particle swarm optimisation (PSO) method and genetic algorithm (GA), are used to identify the nonlinear parameters of an experimental two-degrees-of-freedom system with cubic stiffness. These naturally inspired algorithms are based on the definition of an initial population: this advantageously increases the chances of identifying the global minimum of the optimisation problem as the design space is searched simultaneously in multiple locations. The results show that the PSO method drastically increases the accuracy and robustness of the solution, but it requires a quite expensive computational burden. On the contrary, the GA requires similar computational effort but does not provide accurate solutions.

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Direct optimisation based model selection and parameter estimation using time-domain data for identifying localised nonlinearities

Cited by 13 publications

References 37 publications

Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems

Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems

Nonlinear Model Updating in Structural Dynamics

Experimental Parameter Identification of Nonlinear Mechanical Systems via Meta-heuristic Optimisation Methods

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