P.L. Green

Energy harvesting from human motion and bridge vibrations: An evaluation of current nonlinear energy harvesting solutions:

A large quantity of recent research into the harvesting of electrical energy from ambient vibration sources has been focused on the improvement of device performance via the deliberate introduction of dynamic nonlinearities. In addition to this, the realisation that most of these kinetic energy sources are stochastic in nature has led to many studies focusing on the response of energy harvesters to random vibrations (often Gaussian white noise). This differs from early studies in which it was assumed that ambient vibration sources were sinusoidal. The aim of the present study is to take current nonlinear energy harvesting solutions and to numerically analyse their effectiveness when two real ambient vibration sources are used: human walking motion and the oscillation of the midspan of a suspension bridge. This study shows that the potential improvements that can be realised through the introduction of nonlinearities into energy harvesters are sensitive to the type of ambient excitation to which they are subjected. Additionally, the need for more research into the development of low-frequency energy harvesters is emphasised.

Bayesian and Markov chain Monte Carlo methods for identifying nonlinear systems in the presence of uncertainty

In this paper, the authors outline the general principles behind an approach to Bayesian system identification and highlight the benefits of adopting a Bayesian framework when attempting to identify models of nonlinear dynamical systems in the presence of uncertainty. It is then described how, through a summary of some key algorithms, many of the potential difficulties associated with a Bayesian approach can be overcome through the use of Markov chain Monte Carlo (MCMC) methods. The paper concludes with a case study, where an MCMC algorithm is used to facilitate the Bayesian system identification of a nonlinear dynamical system from experimentally observed acceleration time histories.

The effect of Duffing-type non-linearities and Coulomb damping on the response of an energy harvester to random excitations

Linear energy harvesters can only produce useful amounts of power when excited close to their natural frequency. Due to the uncertain nature of ambient vibrations, it has been hypothesised that such devices will perform poorly in real-world applications. To improve performance, it has been suggested that the introduction of non-linearities into such devices may extend the bandwidth over which they perform effectively. In this study, a magnetic levitation device with non-linearities similar to the Duffing oscillator is considered. The governing equations of the device are formed in which the effects of friction are considered. Analytical solutions are used to explore the effect that friction can have on the system when it is under harmonic excitations. Following this, a numerical model is formed. A differential evolution algorithm is used alongside experimental data to identify the relevant parameters of the device. The model is then validated using experimental data. Monte Carlo simulations are then used to analyse the effect of coulomb damping and Duffing-type non-linearities when the device is subjected to broadband white noise and coloured noise excitations.

Probabilistic modelling of a rotational energy harvester

Relatively recently, many researchers in the field of energy harvesting have focused on the concept of harvesting electrical energy from relatively large-amplitude, low-frequency vibrations (such as the movement caused by walking motion or ocean waves). This has led to the development of ‘rotational energy harvesters’ which, through the use of a rack-and-pinion or a ball-screw, are able to convert low-frequency translational motion into high-frequency rotational motion. A disadvantage of many rotational energy harvesters is that, as a result of friction effects in the motion transfer mechanism, they can exhibit large parasitic losses. This results in nonlinear behaviour, which can be difficult to predict using physical-law-based models. In the current article a rotational energy harvester is built and, through using experimental data in combination with a Bayesian approach to system identification, is modelled in a probabilistic manner. It is then shown that the model can be used to make predictions which are both accurate and robust against modelling uncertainties.

A short investigation of the effect of an energy harvesting backpack on the human gait

Exploiting human motion for the purpose of energy harvesting has been a popular idea for some time. Many of the approaches proposed can be uncomfortable or they impose a significant burden on the persons gait. In the current paper a hardware in-the-loop simulator of an energy harvesting backpack is employed in order to investigate the effect of a suspended-load backpack on the human gait. The idea is based on the energy produced by a suspended-load which moves vertically on a backpack while a person walks. The energy created from such a linear system can be maximised when it resonates with the walking frequency of the person. However, such a configuration can also cause great forces to be applied on the back of the user. The system which is presented here consists of a mass attached on a rucksack, which is controlled by a motor in order to simulate the suspended-load backpack. The advantage of this setup is the ability to test different settings, regarding the spring stiffness or the damping coefficient, of the backpack harvester, and study their effect on the energy harvesting potential, as well as on the human gait. The present contribution describes the preliminary results and analysis of the testing of the system with the help of nine male volunteers who carried it on a treadmill.

Energy harvesting from human motion: an evaluation of current nonlinear energy harvesting solutions

The concept of harvesting electrical energy from ambient vibration sources has been a popular topic of research in recent years. Recently, the realisation that the majority of ambient vibration sources are often stochastic in nature has led to a large body of work which has focused on the response of energy harvesters to random excitations – most of which approximate environmental excitations as being Gaussian white noise. Of particular interest here are recent findings which demonstrate the advantages that Duffing-type nonlinearities can introduce into energy harvesters. The aim of this paper is to identify how well these results can be applied to that of a real energy harvesting scenario. More specifically, the response of an energy harvester to excitation via human motion is studied using digital simulations in conjunction with acceleration data obtained from a human participant. As well as assessing whether Duffing-type nonlinearities can have a beneficial impact on device performance this paper aims to investigate whether Gaussian white noise can indeed be used as a good approximation for this particular ambient vibration source.

Predicting fatigue performance of hot mix asphalt using artificial neural networks

Developing predictive models for fatigue performance is a complex process and can depend on variables including material properties, test conditions and sample geometry. Several models have been developed in this regard; some of these are regression models and are related to mechanistic properties in addition to volumetric properties. In this work, a computational model, based on artificial neural networks (ANNs), is used to predict the fatigue performance of hot mix asphalt (HMA) tested in a dynamic shear rheometer (DSR) technique. Fatigue performance was evaluated according to three approaches: traditional, energy ratio and dissipated pseudo-strain energy. For predicting fatigue performance, two types of ANN models were developed: those dependent on test modes, that is, based on controlled test modes, and those independent of test modes, that is, irrespective of controlled test modes, using fundamental parameters, for example, stiffness modulus, phase angle and volumetric properties. In this work, limestone (L) and granite (G) aggregates were used with two binder grades (40/60 and 160/220) to prepare four mixtures with two different gradations: gap-graded hot rolled asphalt (HRA) and continuously graded dense bitumen macadam (DBM). The results revealed an excellent correlation between the predicted and experimental data. It was found that the prediction accuracy of the strain test mode was better than that of the stress test mode.

Bayesian System Identification of Dynamical Systems Using Reversible Jump Markov Chain Monte Carlo

The purpose of this contribution is to illustrate the potential of Reversible Jump Markov Chain Monte Carlo (RJMCMC) methods for nonlinear system identification. Markov Chain Monte Carlo (MCMC) sampling methods have come to be viewed as a standard tool for tackling the issue of parameter estimation using Bayesian inference. A limitation of standard MCMC approaches is that they are not suited to tackling the issue of model selection. RJMCMC offers a powerful extension to standard MCMC approaches in that it allows parameter estimation and model selection to be addressed simultaneously. This is made possible by the fact that the RJMCMC algorithm is able to “jump” between parameter spaces of varying dimension. In this paper the background theory to the RJMCMC algorithm is introduced. Comparison is made to a standard MCMC approach.

Modelling Friction in a Nonlinear Dynamic System via Bayesian Inference

This work is concerned with the system identification of a real nonlinear system with Duffing-type and friction nonlinearities. With friction being a complex nonlinear phenomenon for which a variety of models have been developed, the identification problem investigated in this paper is one of model selection as well as parameter estimation. Consequently, through the comparison of experimental results with the output of various digital simulations the parameters of several different friction models (Coulomb, hyperbolic tangent and LuGre) are estimated using Bayesian inference in conjunction with Markov Chain Monte-Carlo methods. The performance of each model is then analysed using the Deviance Information Criterion which rewards the ability of the model to replicate the experimental behavior while penalising model complexity. The potential benefits of tackling model selection and parameter estimation problems using a Bayesian framework are discussed.

Nonlinear System Identification Through Backbone Curves and Bayesian Inference

Nonlinear structures exhibit complex behaviors that can be predicted and analyzed once a mathematical model of the structure is available. Obtaining such a model is a challenge. Several works in the literature suggest different methods for the identification of nonlinear structures. Some of the methods only address the question of whether the system is linear or not, others are more suitable for localizing the source of nonlinearity in the structure, only a few suggest some quantification of the nonlinear terms. Despite the effort made in this field, there are several limits in the identification methods suggested so far, especially when the identification of a multi-degree of freedom (MDOF) nonlinear structure is required. This work presents a novel method for the identification of nonlinear structures. The method is based on estimating backbone curves and the relation between backbone curves and the response of the system in the frequency domain. Using a Bayesian framework alongside Markov chain Monte Carlo (MCMC) methods, nonlinear model parameters were inferred from the backbone curves of the response and the Second Order Nonlinear Normal Forms which gives a relationship between the model and the backbone curve. The potential advantage of this method is that it is both efficient from a computation and from an experimental point of view.