Concept

Uncertainties play an important role in the prediction of the performance and safety of mechanical and structural systems. Uncertainties arise in the process of simulating the behavior of the systems. The simulation process begins with the development of mathematical models, constituting a collection of equations (usually algebraic and partial differential equations) for the description of a mechanical system based on mechanics principles. It then continues with the development of computational models (e.g. finite element models) by appropriate discretization of the model equations, aiming at performing the analysis of the system in high-speed computers. Uncertainties arise mainly from the assumptions and compromises that enter into the development of mathematical models of mechanical systems as well as the applied loads. Such uncertainties lead to significant uncertainties in the predictions made using simulations. Since simulations constitute the basis for design and maintenance decisions in order to meet desirable system performance and safety requirements, uncertainties affect these decisions and they have to be accounted for in simulations.

Uncertainties in engineering simulations arise from several sources.

Stochastic/probabilistic models offer suitable mathematical tools for quantifying and propagating loading uncertainties in engineering simulations. Specifically, stochastic processes or random fields are widely used to quantify the temporal and spatial uncertain variability in dynamic loads exerted on structural and mechanical systems.
Random vibration methods are used to propagate these uncertainties in simulations and analyze their impact on the system performance. Probability models and probability density functions are used to quantify uncertainties associated with the values of the parameters of mathematical models of mechanical systems and the characteristics of excitations (e.g. spectral-related parameters).

When parameter uncertainties are taken into account in simulations together with any uncertainties in random loads, they yield “robust predictions” of the system performance that is not sensitive to uncertainties. Approximate semi-analytical methods (e.g. perturbation, response surface methods, asymptotic approximations, first passage expressions, FORM, SORM, sparse grid and polynomial chaos techniques), as well as accurate but computationally very demanding stochastic simulation algorithms [Schueller 2009, “Efficient Monte Carlo Simulation Procedures in Structural Uncertainty & Reliability Analysis-Recent Advances”, Struct. Eng. & Mech.] have been developed to propagate system model and loading uncertainties in simulations and investigate the effects of uncertainties on the performance of the mechanical system.

However, the performance predictions from the aforementioned methods are conditioned on the system models, the load models and the uncertainty models assumed. These models are often selected among alternative competitive models and uncertainties are subjectively postulated, based on engineering judgement or user preference. Such simulations under modeling and loading uncertainties results in “prior robust predictions” that are adequate in the initial design phase of a mechanical system where model validation is not possible due to lack of knowledge of the actual conditions prevailing during normal and/or extreme operation of the system.

During system operation, however, one can deploy a sensor network on the system to collect monitoring or test data in order to accomplish three important tasks. (A) Select, calibrate and improve the mathematical models and the probability models of uncertainties of both the system and loads used to perform simulations, thus resulting in improved and accurate “posterior robust predictions” of the system performance, reliability and safety. (B) Provide invaluable information for tracing the health of the structure, identifying significant structural changes, damage or long-term deterioration (e.g. due to fatigue and corrosion) that may have a serious impact on system performance and safety. (C) Infer the characteristics of the unknown loads that are applied on the mechanical system during various operational conditions (normal, unusual, severe), thus contributing to more reliable load modeling processes that, combining with the computational models of the systems, can help to evaluate the system condition (sudden loss of integrity or long-term deterioration due to fatigue and corrosion) or even prognose its remaining lifetime.

Project Objectives

The major objective (A) of the proposed research is to develop a comprehensive, fast and accurate Bayesian probabilistic framework for treating uncertainties in engineering simulations for complex mechanical systems based on monitored data, effectively addressing both conceptual and computational challenges.

During system operation, the condition of a structure and, as a result, its performance and reliability against various modes of structural failure may deteriorate due to damage induced by normal or sudden severe loading events or due to long-term deterioration (fatigue and corrosion) induced by normal operational loads. Monitoring data from sensor systems deployed within the structure, combined with the theoretical information build in complex mechanical models of the structure, can be used within the Bayesian UQ&P framework, offering the tools to better manage uncertainties, to continually track structural integrity and identify structural changes. The diagnosed degradation state and the identified uncertainties can subsequently be incorporated in simulations for updating predictions of system performance, residual lifetime and safety against various failure modes, taking into account stochastic models of future loading characteristics.

Relying on the progress made on the UQ&P framework, the objective of the proposed research is also to impact developments in the high priority research areas of (B) structural health monitoring (SHM), focusing in continually tracking the health of the structure and rapidly predicting, identifying and locating the onset of structural damage, and (C) residual lifetime prognosis of structures based on the healthy or deteriorated states identified from the monitoring system. Items (B) and (C) are recognized worldwide as issues of great urgency and importance for planning cost-effective maintenance strategies.

Novelties & Impact

This project constitutes a novel and ambitious effort towards developing a comprehensive generic Bayesian framework, integrating fast and reliable algorithms, for UQ&P in simulations of complex physical systems, based on monitoring data. The research findings are anticipated to impact developments in the emerging area of UQ&P in structural dynamics and engineering science simulations based on test/monitoring data. The framework can be adopted to manage uncertainties in simulations for a number of related engineering science disciplines: civil, mechanical, aerospace, naval, air & ground vehicle, multi-scale & multi-physics problems, and molecular dynamics. The damage identification and the robust reliability prediction methodologies will certainly impact cost-effective robust design and maintenance decisions under uncertainty, aiming at reducing lifecycle cost for a large number of important structures (e.g. air and ground vehicles, civil infrastructure, wind turbines, naval, aerospace), while maintaining performance and comfort requirements, as well as safety against various modes of failure, including fatigue and corrosion.