Research overview

A short note on existing structures

Once an engineering structure comes into existence, it becomes possible to measure its behavior under operating conditions. Questions on reliability models for such instrumented structures are relevant in the context of health monitoring of structures. The template for this framework consists of the following components:

1. mathematical model for the structure, typically based on FE analysis,

2. a set of noisy measurements on structural displacements, strains, applied loads, and (or) reaction transferred to the supports under operating and (or) diagnostic loads, and

3. a mathematical model which relates measured quantities to the system states in the governing mathematical model for structure.

Both the models for structural behavior and the measurements are taken to be imperfect, and this is accounted for by including appropriate random noise terms in the models. Once the structure is constructed, and measurements become available, the following newer questions can be posed:

• Dynamic state estimation: The problem here is to determine the multivariate posterior probability density function (pdf) of the states, and the associated marginal pdf, called the filtering pdf. 

• System identification: The problem here is to determine the posterior pdf of system parameters conditioned on the noisy measurements Z1:N, i.e. pΘ|Z1:N (θ|Z1:N).

• Combined problem of system identification and dynamic state estimation. 

• Reliability model updating: The problem here consists of determination of reliability of the structural system conditioned on the measurements, i.e., PS|Z1:N = 1−PF|Z1:N , where PF|Z1:N is the posterior probability of failure.

Figure 1 demonstrates broadly the phases a constructed/manufactured structural system undergoes during its lifetime (design to demolition). My research involves development of variance reduction techniques at every phase of the structure, i.e. reliability modeling, updating, and testing (see publications for details).

My research interests also include problems in statistical genetics and rare event estimation in biological systems.

Figure 1: Some of the major stages during the lifetime of a structural system (to be read from top left quadrant)

Research Projects

1. 2015-2018, Development of algorithms to efficiently identify the causal variants in Genome Wide Association Studies (GWAS), PI: Prof. Anders Dale, University of California San Diego. Funding agency: NIH, ABCD grant.

2. 2014-2015, Targeted Random Sampling for efficient Monte Carlo reliability analysis, PI: Prof. Michael Shields, Johns Hopkins University. Funding agency: NSF.

3. 2014-2015, Analysis of information content of biological images, Student project, Funding agency: NSF Center for Science of Information.

Team: M. Kayalvizhi* and R. Swetha* from Biological Science, Purdue University, Z. Yuzong* from Statistics, Purdue University, V. Priyadarshini* from Electrical and Computer Science, Texas A&M, and V. S. Sundar from Civil Engineering, Johns Hopkins University. (* - graduate student)

4. 2013-2014, Uncertainty analysis of engineering and environmental systems.Funding agency: Board of Research in Nuclear Sciences, Department of Atomic Energy, India. Project Coordinator: Professor C S Manohar.

5. 2008-2010, Fire resistance and repair of earthquake damaged structures, United Kingdom-India Education and Research Initiative (UKIERI) Collaborative Research Awards 2007, Jointly developed with University of Edinburgh, IIT Roorkee and IISc, Bangalore. Team: Professor Asif Usmani and colleagues from University of Edinburgh, C S Manohar and Ananth Ramaswamy from IISc, and Professor P Bhargava and colleagues from IIT Roorkee.