Bayesian System Identification using auxiliary stochastic dynamical systems
| Autor: | Thomas A. Catanach, James L. Beck |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Mathematical optimization
Stationary distribution Dynamical systems theory Applied Mathematics Mechanical Engineering Bayesian probability Posterior probability System identification 020101 civil engineering Markov chain Monte Carlo 02 engineering and technology Statistics::Computation 0201 civil engineering symbols.namesake Stochastic differential equation 020303 mechanical engineering & transports 0203 mechanical engineering Mechanics of Materials symbols Statistical inference Statistics::Methodology Algorithm Mathematics |
| Zdroj: | International Journal of Non-Linear Mechanics. 94:72-83 |
| ISSN: | 0020-7462 |
| DOI: | 10.1016/j.ijnonlinmec.2017.03.012 |
| Popis: | Bayesian approaches to statistical inference and system identification became practical with the development of effective sampling methods like Markov Chain Monte Carlo (MCMC). However, because the size and complexity of inference problems has dramatically increased, improved MCMC methods are required. Dynamical systems based samplers are an effective extension of traditional MCMC methods. These samplers treat the posterior probability distribution as the potential energy function of a dynamical system, enabling them to better exploit the structure of the inference problem. We present an algorithm, Second-Order Langevin MCMC (SOL-MC), a stochastic dynamical system based MCMC algorithm, which uses the damped second-order Langevin stochastic differential equation (SDE) to sample a posterior distribution. We design the SDE such that the desired posterior probability distribution is its stationary distribution. Since this method is based upon an underlying dynamical system, we can utilize existing work to develop, implement, and optimize the sampler's performance. As such, we can choose parameters which speed up the convergence to the stationary distribution and reduce temporal state and energy correlations in the samples. We then apply this sampler to a system identification problem for a non-linear hysteretic structure model to investigate this method under globally identifiable and unidentifiable conditions. |
| Databáze: | OpenAIRE |
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