This work is concerned with the performance of a single degree of freedom electromagnetic energy harvester when subjected to a broadband white noise base acceleration. Firstly, using the Fokker-Planck-Kolmogorov equation, it is shown that Duffing-type nonlinearities can be used to reduce the size of energy harvesting devices without affecting their power output. This is then verified using the technique of Equivalent Linearisation. Secondly, it is shown analytically that the optimum load resistance of the device is different to that which is dictated by the principle of impedance matching. This result is then verified experimentally.

a b s t r a c tThis work details the Bayesian identification of a nonlinear dynamical system using a novel MCMC algorithm: 'Data Annealing'. Data Annealing is similar to Simulated Annealing in that it allows the Markov chain to easily clear 'local traps' in the target distribution. To achieve this, training data is fed into the likelihood such that its influence over the posterior is introduced gradually -this allows the annealing procedure to be conducted with reduced computational expense. Additionally, Data Annealing uses a proposal distribution which allows it to conduct a local search accompanied by occasional long jumps, reducing the chance that it will become stuck in local traps. Here it is used to identify an experimental nonlinear system. The resulting Markov chains are used to approximate the covariance matrices of the parameters in a set of competing models before the issue of model selection is tackled using the Deviance Information Criterion.

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