Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-08-01
|
| Series: | Vibration |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2571-631X/4/3/36 |
| _version_ | 1797516986317537280 |
|---|---|
| author | Sina Safari Julián Londoño Monsalve |
| author_facet | Sina Safari Julián Londoño Monsalve |
| author_sort | Sina Safari |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T07:08:32Z |
| format | Article |
| id | doaj.art-4c88629d499b4207a15e77769d1917c8 |
| institution | Directory Open Access Journal |
| issn | 2571-631X |
| language | English |
| last_indexed | 2024-03-10T07:08:32Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Vibration |
| spelling | doaj.art-4c88629d499b4207a15e77769d1917c82023-11-22T15:36:10ZengMDPI AGVibration2571-631X2021-08-014364866510.3390/vibration4030036Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear SystemsSina Safari0Julián Londoño Monsalve1College of Engineering, Mathematics and Physical Sciences, Harrison Building, Streatham Campus, University of Exeter, North Park Road, Exeter EX4 4QF, UKCollege of Engineering, Mathematics and Physical Sciences, Harrison Building, Streatham Campus, University of Exeter, North Park Road, Exeter EX4 4QF, UKCharacterisation 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.https://www.mdpi.com/2571-631X/4/3/36nonlinear system identificationdata-driven modelnonlinearity characterizationnonlinear structuresnonlinear optimizationfree play nonlinearity |
| spellingShingle | Sina Safari Julián Londoño Monsalve Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems Vibration nonlinear system identification data-driven model nonlinearity characterization nonlinear structures nonlinear optimization free play nonlinearity |
| title | Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems |
| title_full | Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems |
| title_fullStr | Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems |
| title_full_unstemmed | Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems |
| title_short | Benchmarking Optimisation Methods for Model Selection and Parameter Estimation of Nonlinear Systems |
| title_sort | benchmarking optimisation methods for model selection and parameter estimation of nonlinear systems |
| topic | nonlinear system identification data-driven model nonlinearity characterization nonlinear structures nonlinear optimization free play nonlinearity |
| url | https://www.mdpi.com/2571-631X/4/3/36 |
| work_keys_str_mv | AT sinasafari benchmarkingoptimisationmethodsformodelselectionandparameterestimationofnonlinearsystems AT julianlondonomonsalve benchmarkingoptimisationmethodsformodelselectionandparameterestimationofnonlinearsystems |