ACADEMIC Projects

In many areas of engineering and applied science, differential equations are used to analyze the behavior of dynamical systems. In forward analyses, these equations are known to the user. However, in reality, very little is known about the true equations. Naturally, a question arises that: can we discover equations from measured data? In a pioneering research in 2016, Prof. Kutz and his collaborators at University of Washington demonstrated that the task of equation discovery can indeed be solved as a variable selection problem using sparse linear regression techniques.

In this research, I have focused on discovering equations of motion of nonlinear structural dynamical systems from measured data. Instead of following a deterministic framework, which requires cross-validation and mostly relies on convex optimization, I have followed a Bayesian framework which does not have these drawbacks. For inducing sparsity, I have employed two different sparse priors: the Student's-t prior and the spike-and-slab prior. Equation discovery with the spike-and-slab prior provides excellent results with accurate variable selection consistency and low false discovery rate compared to the Student's-t prior.

Structural identification and health monitoring strategies typically rely on data collected using networks of static sensors (i.e., sensors that remain fixed at certain locations on the structure) which are prone to poor spatial resolution when only using a few sensors. To circumvent this issue, a large, dense network is required which has negative cost and implementation implications. An appealing alternative to large static sensor networks is the use of a much smaller network of mobile sensors. Mobile sensors are sensors mounted on carrier vehicles (such as robots or cars) that can be sequentially conveyed to various locations on a structure, thereby achieving dense spatial resolution with relatively few sensors.

In my PhD, I worked on developing a unifying Bayesian inference framework for state-space models using mobile sensor measurements. State-space models are commonly employed in estimation with static-sensor networks. In my PhD work, I modified two Bayesian computational algorithms (the Gibbs sampler and the variational Bayes) to allow posterior inference of modal parameters of a bridge structure using measurements from moving vehicles.

In this study, a new methodology for joint input-state estimation is proposed for linear systems using Gaussian process latent force models. Gaussian process latent force models (GPLFMs) are hybrid models that combine differential equations representing a physical system with data-driven non-parametric Gaussian process models.

In this work, the unknown input forces acting on a structure are modelled as Gaussian processes which are combined with the mechanistic differential equation representing the structure to construct a GPLFM. The GPLFM is then conveniently formulated as an augmented stochastic state-space model with additional states representing the latent force components, and the joint input and state inference of the resulting model is implemented using Kalman filter. The augmented state-space model of GPLFM is shown as a generalization of the class of input-augmented state-space models, is proven observable, and is robust against drift in force estimation compared to conventional augmented formulations.

The study aimed at developing a random vibration testing protocol wherein reliability of engineering systems with active/semi-active control could be accomplished without the knowledge of the mathematical model of the controlled system. For the development of the theoretical background of the testing method, both analytical and simulation-based studies have been undertaken on a simple actively controlled system. Based on the analytical and numerical results for the actively controlled system a random vibration testing procedure for systems with active control elements had been propounded. Experimental studies were carried out using a 3-storey laboratory scale building frame affixed with a MR damper device at the base to validate the results.