Model selection and parameter estimation in structural dynamics using approximate Bayesian computation

This paper will introduce the use of the approximate Bayesian computation (ABC) algorithm for model selection and parameter estimation in structural dynamics. ABC is a likelihood-free method typically used when the likelihood function is either intractable or cannot be approached in a closed form. To circumvent the evaluation of the likelihood function, simulation from a forward model is at the core of the ABC algorithm. The algorithm offers the possibility to use different metrics and summary statistics representative of the data to carry out Bayesian inference. The efficacy of the algorithm in structural dynamics is demonstrated through three different illustrative examples of nonlinear system identification: cubic and cubic-quintic models, the Bouc-Wen model and the Duffing oscillator. The obtained results suggest that ABC is a promising alternative to deal with model selection and parameter estimation issues, specifically for systems with complex behaviours

An efficient likelihood-free Bayesian computation for model selection and parameter estimation applied to structural dynamics

Model selection is a challenging problem that is of importance in many branches of the sciences and engineering, particularly in structural dynamics. By definition, it is intended to select the most plausible model among a set of competing models, that best matches the dynamic behaviour of a real structure and better predicts the measured data. The Bayesian approach is based essentially on the evaluation of a likelihood function and is arguably the most popular approach. However, in some circumstances, the likelihood function is intractable or not available even in a closed form. To overcome this issue, likelihood-free or approximate Bayesian computation (ABC) algorithms have been introduced in the literature, which relax the need of an explicit likelihood function to measure the degree of similarity between model prediction and measurements. One major issue with the ABC algorithms in general is the low acceptance rate which is actually a common problem with the traditional Bayesian methods. To overcome this shortcoming and alleviate the computational burden, a new variant of the ABC algorithm based on an ellipsoidal nested sampling technique is introduced in this paper. It has been called ABC-NS. This paper will demonstrate how the new algorithm promises drastic speedups and provides good estimates of the unknown parameters. To demonstrate its practical applicability, two illustrative examples are considered. Firstly, the efficiency of the novel algorithm to deal with parameter estimation is demonstrated using a moving average process based on synthetic measurements. Secondly, a real structure called the VTT benchmark, which consists of a wire rope isolators mounted between a load mass and a base mass, is used to further assess the performance of the algorithm in solving the model selection issue

ABC-NS: a new computational inference method applied to parameter estimation and model selection in structural dynamics

The inference of dynamical systems is a challenging issue, particularly when the dynamics include complex phenomena such as the existence of bifurcations and/or chaos. In this situation, the likelihood function formulated based on time-series data may be complex with several local minima and as a result not suitable for parameter inference. In the most challenging scenarios, the likelihood function may not be available in an analytical form, so a standard statistical inference is impossible to carry out. To overcome this problem, the inclusion of new features/invariants less sensitive to small variations from either the time or frequency domains seems to be potentially a very useful way to make Bayesian inference. The use of approximate Bayesian computation (ABC) or likelihood-free algorithms is an appropriate option as they offer the flexibility to use different metrics for parameter inference. However, most variants of the ABC algorithm are inefficient due to the low acceptance rate. In this contribution, a new ABC algorithm based on an ellipsoidal nested sampling technique is proposed to overcome this issue. It will be shown that the new algorithm performs perfectly well and maintains a relatively high acceptance rate through the iterative inference process. In addition to parameter estimation, the new algorithm allows one to deal with the model selection issue. To demonstrate its efficiency and robustness, a numerical example is presented

ABC-NS: a new computational inference method applied to parameter estimation and model selection in structural dynamics

The inference of dynamical systems is a challenging issue, particularly when the dynamics include complex phenomena such as the existence of bifurcations and/or chaos. In this situation, the likelihood function formulated based on time-series data may be complex with several local minima and as a result not suitable for parameter inference. In the most challenging scenarios, the likelihood function may not be available in an analytical form, so a standard statistical inference is impossible to carry out. To overcome this problem, the inclusion of new features/invariants less sensitive to small variations from either the time or frequency domains seems to be potentially a very useful way to make Bayesian inference. The use of approximate Bayesian computation (ABC) or likelihood-free algorithms is an appropriate option as they offer the flexibility to use different metrics for parameter inference. However, most variants of the ABC algorithm are inefficient due to the low acceptance rate. In this contribution, a new ABC algorithm based on an ellipsoidal nested sampling technique is proposed to overcome this issue. It will be shown that the new algorithm performs perfectly well and maintains a relatively high acceptance rate through the iterative inference process. In addition to parameter estimation, the new algorithm allows one to deal with the model selection issue. To demonstrate its efficiency and robustness, a numerical example is presented

Effects of barium deficiency on structural, magnetic and magnetocaloric properties of La 0.6

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Identification of nonlinear dynamical systems using approximate Bayesian computation based on a sequential Monte Carlo sampler

The Bayesian approach is well recognised in the structural dynamics community as an attractive approach to deal with parameter estimation and model selection in nonlinear dynamical systems. In the present paper, one investigates the potential of approximate Bayesian computation employing sequential Monte Carlo (ABC-SMC) sampling [1] to solve this challenging problem. In contrast to the classical Bayesian inference algorithms which are based essentially on the evaluation of a likelihood function, the ABC-SMC uses different metrics based mainly on the level of agreement between observed and simulated data. This alternative is very attractive especially when the likelihood function is complex and cannot be approximated in a closed form. Moreover, this flexibility allows one to use new features from either the temporal or the frequency domains for system identification. To demonstrate the practical applicability of the ABC-SMC algorithm, two illustrative examples are considered in this paper

Effects of music therapy on occupational stress and burn-out risk of operating room staff

The operating theatre staff is exposed to various constraints such as excessive working hours, severe medical conditions and dreadful consequences in case of malpractice. These working conditions may lead to high and chronic levels of stress, which can interfere with medical staff well-being and patients quality of care. The aim of this study is to assess the impact of music therapy on stress levels and burn-out risk on the operating room staff. This is a pre-experimental study including the operating rooms staff of urology and maxillofacial surgery in the academic hospital of Sahloul Sousse (Tunisia) over a period of six weeks. The study consisted of three phases. The first was an initial assessment of stress level with a predefined survey. The second included three music therapy sessions per day over one month. The third was an immediate stress level reassessment following the intervention. Stress levels were evaluated using the Perceived Stress Scale version PSS-10 and the Maslach Burnout Inventory. The overall response rate was 73.9%.The average age of the study population was 37.8 ± 7.7 years with a female predominance (64.7%). After the music therapy program, Perceived Stress Scale average score decreased from 22 ± 8.9 to 16 ± 7.9 (p = 0.006). Concerning the burnout, only the average score of emotional exhaustion decreased signifi- cantly from 27 ± 10.8 to 19.2 ± 9.5 (p = 0.004). Music therapy is an innovative approach that seems to reduce operating theatre staff stress. It must be considered as a non pharmacological, simple, economic and non invasive preventive tool