INVERSE PROBLEMS

If you could measure vibrations and waves generated by a solid; what can you infer about such a solid? The answer to that question, at various length scales, is at the heart of many important problems in physics, biology, engineering,  and medicine.  My students and I are currently exploring fundamental aspects of this question and their potential applications to complex systems found in structural engineering. We are interested in using measured vibrations and waves on a structure to infer geometrical, mechanical and electro-magnetic properties, applied loads, internal stress fields and hidden defects or damage. Difficulties arise because measurements are contaminated by noise, the number of measurements is typically small in comparison with the size of the structure and measurements can only be obtained at the surface.  In addition, due to the inevitable assumptions and simplifications, models used for inversion have multiple types of errors and uncertainties. One of the most significant challenges when attempting to solve an inverse problem is to characterize the uncertainty in the estimate given all aforementioned sources of uncertainty.

RELIABILITY OF ENGINEERING SYSTEMS

I am interested in Bayesian Reliability of Engineering Systems, which seeks to continuously assess the reliability of a system by combining prior knowledge (typically in the form of a model) with component failure data and real-time performance monitoring. In this context the term Reliability is defined as the probability of not failing and the manner in which it is updated gives rise to the term Bayesian. This is an exciting concept that eventually seeks to minimize catastrophic failures of engineering systems during operation. As our society grows increasingly dependent on the reliable operation of very complex infrastructure systems, Bayesian Reliability becomes an essential computational paradigm.

UNINTENDED CONSEQUENCES

Finally, and in a slightly different direction, I am interested in studying unintended consequences of technological and scientific developments. I became interested in this topic after reading Edward Tenner’s book “Why Things Bite Back: Technology and the Revenge of Unintended Consequences“. In an age of unprecedented and unfettered technological development, I believe this is an important and sobering concept to consider. Some unintended consequences are good but some can be devastating. Many lessons can be learned from studying the history of technological developments with their associated triumphs and downfalls.

To learn more, please click on the following links for a complete list and description of Funded Research Projects and Publications.