Research theme three of five
Uncertainty quantification and stochastic mechanics
Propagating uncertainty through a dynamic model is a different problem from propagating it through a static one, because the quantities of interest are spectra and resonances.
The problem
General-purpose uncertainty quantification is well served by existing tools. The gap is the dynamic case, where the map from parameters to response is rough: eigenvalues cross and veer, resonances move through the observation band, and a small parameter change can reorder the modes. Polynomial approximations built for smooth maps degrade badly there.
The response of this theme is to work with the operators themselves: random eigenvalue problems, random matrix models of the system matrices themselves, and closed-form ensemble quantities wherever they can be obtained.
Why it matters
A safety case is an argument about probability, and for a dynamic structure the quantity it turns on is the location of a resonance or the chance of exceeding a limit. Both live in the tails, and both move discontinuously as parameters change, which is where the general-purpose surrogate machinery loses its guarantees. Composite aerospace structures are the sharpest case: the layup process produces scatter that the design has to absorb, and the aeroelastic response is exactly the quantity that scatter moves. Getting this right lets a manufacturer set a probabilistic margin from the process data it already collects, and the same argument sets the variance on the ten-year yield that finances a wind farm.
Current frontier
- stochastic structural dynamics and random operators
- random eigenvalue problems and random spectra
- random matrix and Wishart system models
- random fields and Karhunen-Loeve representations
- stochastic Green functions and ensemble response
- rare events and reliability in dynamic systems
- stochastic metamaterials and stochastic localisation
- surrogate modelling and operator learning
Signature concepts
- random operators
- ensemble response
- rare events
- stochastic localisation
- measure transport
Open problems
- Which ensemble of random matrices is the right model for a given class of manufactured structure?
- How should a surrogate be trained when the quantity of interest is a failure probability?
- What closed-form ensemble results exist beyond the Gaussian case?
Selected papers
- Uncertainty quantification in inerter-based quasiperiodic lattices
T. Chatterjee, D. Karličić, M. Cajić, S. Adhikari, M. I. Friswell · International Journal of Mechanical Sciences 249, 108258 · 2023 - A comparative analysis of intrusive and non-intrusive PCE methods for random mode computation
E. Jacquelin, S. Adhikari, D. Brizard · Probabilistic Engineering Mechanics 81, 103792 · 2025 - Enhanced multi-fidelity modeling for digital twin and uncertainty quantification
A. S. Desai, N. Navaneeth, S. Adhikari, S. Chakraborty · Probabilistic Engineering Mechanics 74, 103525 · 2023 - Seismic reliability analysis of nonlinear structures by active learning-based adaptive sparse Bayesian regressions
A. Roy, S. Chakraborty, S. Adhikari · International Journal of Non-Linear Mechanics 165, 104817 · 2024 - Dynamic analysis of wind turbine towers on flexible foundations
S. Adhikari, S. Bhattacharya · Shock and Vibration · 2012
Foundations
Random vibration, Karhunen-Loeve expansions, stochastic finite elements, polynomial chaos, structural reliability, uncertainty propagation and stochastic model reduction, developed from 2001 onward and applied with Embraer to composite aerospace structures.