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In this paper, we derive a system identification framework for continuous-time nonlinear systems, for the first time using a simulation-focused computational Bayesian approach. Simulation approaches to nonlinear system identification have been shown to outperform regression methods under certain conditions, such as non-persistently exciting inputs and fast-sampling. We use the approximate Bayesian computation (ABC) algorithm to perform simulation-based inference of model parameters. The framework has the following main advantages: (1) parameter distributions are intrinsically generated, giving the user a clear description of uncertainty, (2) the simulation approach avoids the difficult problem of estimating signal derivatives as is common with other continuous-time methods, and (3) as noted above, the simulation approach improves identification under conditions of non-persistently exciting inputs and fast-sampling. Term selection is performed by judging parameter significance using parameter distributions that are intrinsically generated as part of the ABC procedure. The results from a numerical example demonstrate that the method performs well in noisy scenarios, especially in comparison to competing techniques that rely on signal derivative estimation. [ABSTRACT FROM AUTHOR]

This paper proposes a procedure of synthetic detection for the location of a change point and outliers in bilinear time series models with a change after an unknown time point. Based on Bayesian framework, we first derive the conditional posterior distribution of the change point and from that distribution estimate the position of the change point. Then we use these results to detect the outliers in the time series before and after that change point via Gibbs sampler algorithm. Our simulation studies show that the proposed procedure is effective. [ABSTRACT FROM PUBLISHER]

The inertial stabilisation of the line of sight of an imager fixed on a mobile carrier is considered in order to acquire good quality images despite the disturbances generated by the carrier. A double stage mechanical stabilisation architecture is proposed, where a second stabilisation stage, based on a piezoelectric actuator, is added to the usual structure. The piezoelectric actuator transfer function and hysteresis are characterised through experiments. In order to design the controllers of both stages, a high-level image quality criterion (the modulation transfer function (MTF)) is considered, together with design constraints on the main variables of interest. The criterion and the constraints are evaluated by realistic simulations based on some input and noise profiles measured on a real-life system. The MTF evaluation being time-consuming, a Bayesian optimisation method specially dedicated to expensive-to-evaluate functions is used to obtain the parameters of the controllers. The obtain experimental results are displayed and their performances discussed. [ABSTRACT FROM AUTHOR]

Many real world optimisation problems have opposing objective functions which are subjected to the influence of noise. Noise in the objective functions can adversely affect the stability, performance and convergence of evolutionary optimisers. This article proposes a Bayesian frequent data mining (DM) approach to identify optimal regions to guide the population amidst the presence of noise. The aggregated information provided by all the solutions helped to average out the effects of noise. This article proposes a DM crossover operator to make use of the rules mined. After implementation of this operator, a better convergence to the true Pareto front is achieved at the expense of the diversity of the solution. Consequently, an ExtremalExploration operator will be proposed in the later part of this article to help curb the loss in diversity caused by the DM operator. The result is a more directive search with a faster convergence rate. The search is effective in decision space where the Pareto set is in a tight cluster. A further investigation of the performance of the proposed algorithm in noisy and noiseless environment will also be studied with respect to non-convexity, discontinuity, multi-modality and uniformity. The proposed algorithm is evaluated on ZDT and other benchmarks problems. The results of the simulations indicate that the proposed method is effective in handling noise and is competitive against the other noise tolerant algorithms. [ABSTRACT FROM PUBLISHER]

A Bayesian system identification approach to modelling stochastic linear dynamical systems involving multiple scales is proposed, where multiscale means that the output of the system is observed at one (coarse) resolution whilst the input of the system can only be observed at another (fine) resolution. The proposed method identifies linear models at different levels of resolution, where the link between the two resolutions is realised via a non-overlapping averaging process. The averaged data at the coarse level of resolution is assumed to be a set of observations from an implied process so that the implied process and the output of the system result in an errors-in-variables model at the coarse level of resolution. By using a Bayesian inference and Markov chain Monte Carlo method, such a modelling framework results in different dynamical models at different levels of resolution at the same time. The new method is also shown to have the ability to combine information across different levels of resolution. Simulation examples are provided to show the efficiency of the new method. Furthermore, an application to the analysis of the relativistic electron intensity at the geosynchronous orbit is also included. [ABSTRACT FROM AUTHOR]