Mechanical and Civil Engineering Seminar

In Recent years we have seen a growing interest in the development of on‐line system identification methods, which make use of measurements from a system to learn the equations and parameters characterizing it, possibly in real‐time. These methods find a wide variety of applications, including but not restricted to, damage  detection  and  structural  health  monitoring  in  civil  engineering,  control  and  diagnostics  of  mechanical systems, state estimation of chemical processes, improved modelling of biomechanical systems. 
 In  particular,  Bayesian  inference  methods  are  very  attractive  due  to  their  ability  to  take  into  account  uncertainties in the system and measurements, as well as stochastic input excitations, and yield results in a probabilistic format thus enabling more accurate performance assessment of the systems of interest. The Bayesian framework is also well‐suited to address ill‐conditioned problems, where not all parameters can be  learnt from the available noisy data, a problem which will surely arise when  considering large  dimensional systems. 
 A major challenge regarding on‐line Bayesian filtering algorithms lies in achieving good accuracy for large dimensional systems and complex nonlinear non‐Gaussian systems, where non‐Gaussianity can arise for instance  in  systems  which  are  not  globally  identifiable.  In using  algorithmic  enhancements  of  filtering  techniques, mainly based on innovative ways to reduce the dimensionality of the problem at hand, one can obtain a good trade‐off between accuracy and computational complexity of the learning algorithms. For instance, for particle filtering techniques (sampling‐based algorithms) subjected to the so‐called curse of dimensionality, the concept of Rao‐Blackwellisation can be used to greatly reduce the dimension of the sampling space. On the other hand, one can also build upon nonlinear Kalman filtering techniques, which are very computationally efficient, and expand their capabilities to non‐Gaussian distributions. 
 Thus, using some prior knowledge of the system, one can derive efficient Bayesian inference techniques, potentially  enabling  real‐time  monitoring,  or  improved  modelling  capabilities,  for  a  wide  variety  of  nonlinear dynamical systems. *This lecture is part of the Young Investigators Lecture Series sponsored by the Caltech Division of Engineering & Applied Science.