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

Model selection and parameter estimation of dynamical systems using a novel variant of approximate Bayesian computation

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 likely 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 which is based essentially on the evaluation of a likelihood function is one of the most popular approach to deal with model selection and parameter estimation issues. However, in some circumstances, the likelihood function is either intractable or not available even in a closed form. To overcome this issue, the likelihood-free or approximate Bayesian computation (ABC) algorithm has been introduced in the literature, which relaxes the need for an explicit likelihood function to measure the level of agreement between model predictions and measurements. However, ABC algorithms suffer from a low acceptance rate of samples 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 (NS) technique is introduced in this paper; it has been called ABC-NS. Through this paper, it will be shown how the new algorithm is a promising alternative to deal with parameter estimation and model selection issues. It promises drastic speedups and provides a good approximation of the posterior distributions. To demonstrate its robust computational efficiency, four illustrative examples are given. Firstly, the efficiency of the algorithm is demonstrated to deal with parameter estimation. Secondly, two examples based on simulated and real data are given to demonstrate the efficiency of the algorithm to deal with model selection in structural dynamics

Optimal Design For Injection Molding

Peer reviewed: YesNRC publication: Ye

Identification of piecewise-linear mechanical oscillators via Bayesian model selection and parameter estimation

The problem of identifying single degree-of-freedom (SDOF) nonlinear mechanical oscillators with piecewise-linear (PWL) restoring forces is considered. PWL nonlinear systems are a class of models that specify or approximate nonlinear systems via a set of locally-linear maps, each defined over different operating regions. They are useful in modelling hybrid phenomena common in practical situations, such as, systems with different modes of operation, or systems whose dynamics change because of physical limits or thresholds. However, identifying PWL models can be a challenging task when the number of operating regions and their partitions are unknown. This paper formulates the identification of oscillators with PWL restoring forces as a task of concurrent model selection and parameter estimation, where the selection of the number of linear regions is treated as a model selection task and identifying the associated system parameters as a task of parameter estimation. In this study, PWL maps in restoring forces with up to four regions are considered, and the task of model selection and parameter estimation task is addressed in a Bayesian framework. A likelihood-free Approximate Bayesian Computation (ABC) scheme is followed, which is easy to implement and provides a simplified way of doing model selection. The proposed approach has been demonstrated using two numerical examples and an experimental study, where ABC has been used to select models and identify parameters from among four SDOF PWL systems with different number of PWL regions. The results demonstrate the flexibility of using the proposed Bayesian approach for identifying the correct model and parameters of PWL systems, in addition to furnishing uncertainty estimates of the identified parameters

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

Maternal Antibody Transmission in Relation to Mother Fluctuating Asymmetry in a Long-Lived Colonial Seabird: The Yellow-Legged Gull Larus michahellis

Female birds transfer antibodies to their offspring via the egg yolk, thus possibly providing passive immunity against infectious diseases to which hatchlings may be exposed, thereby affecting their fitness. It is nonetheless unclear whether the amount of maternal antibodies transmitted into egg yolks varies with female quality and egg laying order. In this paper, we investigated the transfer of maternal antibodies against type A influenza viruses (anti-AIV antibodies) by a long-lived colonial seabird, the yellow-legged gull (Larus michahellis), in relation to fluctuating asymmetry in females, i.e. the random deviation from perfect symmetry in bilaterally symmetric morphological and anatomical traits. In particular, we tested whether females with greater asymmetry transmitted fewer antibodies to their eggs, and whether within-clutch variation in yolk antibodies varied according to the maternal level of fluctuating asymmetry. We found that asymmetric females were in worse physical condition, produced fewer antibodies, and transmitted lower amounts of antibodies to their eggs. We also found that, within a given clutch, yolk antibody level decreased with egg laying order, but this laying order effect was more pronounced in clutches laid by the more asymmetric females. Overall, our results support the hypothesis that maternal quality interacts with egg laying order in determining the amount of maternal antibodies transmitted to the yolks. They also highlight the usefulness of fluctuating asymmetry as a sensitive indicator of female quality and immunocompetence in birds

Annealing study and thermal investigation on bismuth sulfide thin films prepared by chemical bath deposition in basic medium

This is a post-peer-review, pre-copyedit version of an article published in Applied Physics A 124.2 (2018): 166. The final authenticated version is available online at: http://doi.org/10.1007/s00339-018-1584-7Bismuth sulfide thin films were prepared by chemical bath deposition using thiourea as sulfide ion source in basic medium. First, the effects of both the deposition parameters on films growth as well as the annealing effect under argon and sulfur atmosphere on as-deposited thin films were studied. The parameters were found to be influential using the Doehlert matrix experimental design methodology. Ranges for a maximum surface mass of films (3 mg cm-2) were determined. A well crystallized major phase of bismuth sulfide with stoichiometric composition was achieved at 190°C for 3 hours. The prepared thin films were characterized using Grazing Incidence X-ray diffraction (GIXRD), Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray analysis (EDX). Second, the band gap energy value was found to be 1.5 eV. Finally, the thermal properties have been studied for the first time by means of the electropyroelectric (EPE) technique. Indeed, the thermal conductivity varied in the range of 1.20 - 0.60 W m-1 K-1 while the thermal diffusivity values increased in terms of the annealing effect ranging from 1.8 to 3.5 10-7 m2s-1This work was financially supported by the Tunisian Ministry of Higher Education and Scientific Research and by the WINCOST (ENE2016-80788-C5-2-R) project funded by the Spanish Ministry of Economy and Competitivenes

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

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