Research

The stochastic analysis and signal processing lab works on the development of numerical and computational tools for the analysis of physical and mathematical systems under uncertainties. 

Visit our GitHub page, where you can find the data and codes used in our papers: https://github.com/SASP-lab 

Machine learning for generative and predictive modeling


Machine learning (ML) has become necessary in scientific inquires due to the increasing complexity of data representation of mathematical and physical systems. The development of efficient, accurate, and reliable predictive and generative models constrained on the problem's physics is important for applications ranging from the analysis and design of chemical compounds to the monitoring of large civil infrastructure systems with digital twins. Considering the challenges faced by modern ML techniques, this line of investigation focuses on the advancement of the state-of-the-art of predictive and generative ML models on several fields of science and engineering. 

Surrogate modeling & Uncertainty quantification

The development of computationally efficient surrogates of complex and high-dimensional systems is essential for several scientific inquiries. The benefits brought by such models can be measured by the reduction of the computational cost of estimating hundreds, thousands, or even millions of response of a single model due to the large number of combinations of its parameters. Applications can be found in the design of reliable structures as well as on the optimization of complex systems. Therefore, this line of investigation focuses on the development of robust, reliable, and efficient surrogate models using advanced mathematical concepts and computational tools.

Selected publications:

Dimensionality reduction via manifold learning

High-dimensional data are becoming very common in several engineering applications either due to the  technological development of data acquisition systems that works in a very fine resolution or due to the increasing of the computational performance of modern computers that are able to estimate the solution of partial differential equations at a very small scale. However, make inference on such high-dimensional data has become a challenge that must be circumvented by manifold learning techniques (i.e., diffusion maps, Isomap, Hessian LLE). Therefore, this line of investigation focuses on the development of techniques able to identify the underlying structures of high-dimensional data aiming at the identification and classification of complex phenomena such the presence of anomalies and damage in complex structural systems.

Selected publications:

Stochastic engineering dynamics & structural reliability

Several engineering systems are modeled as nonlinear oscillators such as high-rise buildings, vibratory energy harvesters, ships, etc. They are also typically subjected to random excitation  modeled as either stationary (e.g., stationary wind excitation) or non-stationary (e.g., earthquakes) stochastic processes. However, estimating the probabilistic response of such complex systems could become intractable for high-dimensional systems whose failure modes have a low probability of occurrence. Therefore, there is a need for the development of more efficient methods capable of estimating the probabilistic response of nonlinear oscillators. This line of investigation focuses on the development of novel approximate/semi-analytical methods such as stochastic averaging, Wiener path integral, and statistical linearization for accelerating the stochastic response estimation of systems subject to random vibrations. 

Selected publications:

Signal processing techniques for system identification and data reconstruction

Signal processing techniques are powerful in the modeling and identification of systems subject to random vibrations as well as in the characterization of natural hazards. The analysis of both excitation and response of complex systems in the joint time-frequency domain has several benefits such as the evaluation of the time evolution of the frequency content of both response and/or excitation as a mean to detect anomalies in the structural response as well as to assess the non-stationary response of natural hazards such as earthquakes and wind gusts. Techniques such as wavelet analysis are typically employed in this task due to their proved performance of tracking the time-variant behavior of time-series. Moreover, in the real-world signals are typically subject to several sources of corruptions such as noise and missing data. Therefore, recovering such missing/corrupted information is necessary for tasks focused on the identification and characterization of complex systems. To this en, one can employ compressed sampling and sparse representation tools in the recovery/reconstruction of the missing information in both time series and matrices. Therefore, this research focused on the development of efficient, robust, and reliable tools used in the spectral characterization and in the system parameter identification of complex systems. Moreover, the development of advanced data-driven tools for the detection of anomalies in structural systems is also of interest.

Selected publications: