Stochastic System Design and Applications to Stochastically Robust Structural Control

The knowledge about a planned system in engineering design applications is never complete. Often, a probabilistic quantification of the uncertainty arising from this missing information is warranted in order to efficiently incorporate our partial knowledge about the system and its environment into their respective models. In this framework, the design objective is typically related to the expected value of a system performance measure, such as reliability or expected life-cycle cost. This system design process is called stochastic system design and the associated design optimization problem stochastic optimization. In this thesis general stochastic system design problems are discussed. Application of this design approach to the specific field of structural control is considered for developing a robust-to-uncertainties nonlinear controller synthesis methodology. Initially problems that involve relatively simple models are discussed. Analytical approximations, motivated by the simplicity of the models adopted, are discussed for evaluating the system performance and efficiently performing the stochastic optimization. Special focus is given in this setting on the design of control laws for linear structural systems with probabilistic model uncertainty, under stationary stochastic excitation. The analysis then shifts to complex systems, involving nonlinear models with high-dimensional uncertainties. To address this complexity in the model description stochastic simulation is suggested for evaluating the performance objectives. This simulation-based approach addresses adequately all important characteristics of the system but makes the associated design optimization challenging. A novel algorithm, called Stochastic Subset Optimization (SSO), is developed for efficiently exploring the sensitivity of the objective function to the design variables and iteratively identifying a subset of the original design space that has v i high plausibility of containing the optimal design variables. An efficient two-stage framework for the stochastic optimization is then discussed combining SSO with some other stochastic search algorithm. Topics related to the combination of the two different stages for overall enhanced efficiency of the optimization process are discussed. Applications to general structural design problems as well as structural control problems are finally considered. The design objectives in these problems are the reliability of the system and the life-cycle cost. For the latter case, instead of approximating the damages from future earthquakes in terms of the reliability of the structure, as typically performed in past research efforts, an accurate methodology is presented for estimating this cost; this methodology uses the nonlinear response of the structure under a given excitation to estimate the damages in a detailed, component level

Nonlinear stochastic controllers for semiactive and regenerative structural systems, with guaranteed quadratic performance margins

In many applications of vibration control, the circumstances of the application impose constraints on the energy available for the actuation of control forces. Semiactive dampers (i.e., viscous dampers with controllable coefficients) constitute the simplest example of such actuation in structural control applications. Regenerative Force Actuation (RFA) networks are an extension of semiactive devices, in which mechanical energy is first converted to electrical energy, which is then dissipated in a controllable resistive network. A fairly general class of semiactive and regenerative systems can be characterized by a differential equation which is bilinear (i.e., linear in state, linear in control input, but nonlinear in both). This paper presents a general approach to bilinear feedback control system design for semiactive and regenerative systems, which is analytically guaranteed to out-perform optimal linear viscous damping in stationary stochastic response, under the familiar Quadratic Gaussian performance measure. The design for full-state feedback and for the more practical case of noise-corrupted and incomplete measurements (i.e., output feedback) are separately discussed. Variants of the theory are shown to exist for other quadratic performance measures, including risk-sensitive and multi-objective frameworks. An illustrative application to civil engineering is presented

Robust Stochastic Design of Linear Controlled Systems for Performance Optimization

This study discusses a robust controller synthesis methodology for linear, time invariant systems, under probabilistic parameter uncertainty. Optimization of probabilistic performance robustness for [script H]_2 and multi-objective [script H]_2 measures is investigated, as well as for performance measures based on first-passage system reliability. The control optimization approaches proposed here exploit recent advances in stochastic simulation techniques. The approach is illustrated for vibration response suppression of a civil structure. The results illustrate that, for problems with probabilistic uncertainty, the explicit optimization of probabilistic performance robustness can result in markedly different optimal feedback laws, as well as enhanced performance robustness, when compared to traditional “worst-case” notions of robust optimal control

Reduced order modelling of hysteretic structural response in seismic risk assessment

Modern seismic risk/loss estimation practices require simulation of structural behavior for different levels of earthquake shaking through time-history analysis. This behavior can be strongly inelastic/hysteretic and evaluating it through high-fidelity finite element models introduces a significant computational burden. A reduced order modeling approach is discussed here to alleviate this burden. The reduced order model is developed using data from the original high-fidelity finite element model (FEM). Static condensation is first used to obtain the stiffness matrix and linear equations of motion for the dynamic degrees of freedom. The restoring forces prescribed by the linear stiffness matrix are then substituted with hysteretic ones, calibrated by comparing the reduced order model time-history to the time-history of the initial FEM for a range of different excitations. This is posed as a least squares optimization problem and its efficient solution is facilitated through a sequential approach. The accuracy and the computational savings of the reduced order model are then examined for seismic risk assessment applications by comparing to the FEM predictions. A stochastic ground motion model is used to describe the seismic hazard and the accuracy for different levels of intensity is separately examined.Authors would like to thank Dr. Papakonstantinou for prodiving the codes for generation of synthetic acceleration time-histories using the (Vlachos, et al. 2018) model

Probabilistically-robust nonlinear control of offshore structures

A controller design for offshore structures is discussed in this study. Stochastic simulation is considered for evaluation of the system's performance in the design stage. This way, nonlinear characteristics of the structural response and excitation are explicitly incorporated into the model assumed for the system. Model parameters that have some level of uncertainty are probabilistically described. In this context, the controller is designed for optimal reliability, quantified as the probability, based on the available information, that the performance will not exceed some acceptable bounds. This treatment leads to a robust-to-uncertainty design. The methodology is illustrated in an example involving the control of a Tension Leg Platform in a random sea environment. Multifold nonlinearities are taken into account for the evaluation of the platform's dynamic response and a probabilistic description is adopted for characterizing the random sea environment

A New Normative Workflow for Integrated Life-Cycle Assessment

In order to curtail energy use by the building sector, consideration of how a sustainable building is constructed is paramount, in many respects, to how efficiently it operates over its lifetime. A typical building must be in use for decades before the energy expended in its daily operations surpasses the energy embodied within its initial construction, as a result of the materials used. More vitally: every building has specific vulnerabilities, particularly to hazards (e.g., earthquakes, wind, flooding) whose effects on sustainability are not explicitly considered alongside other aspects of sustainability in the design process – despite the significant environmental impact of damage and repairs after a disaster. Unfortunately, the joint consideration of resilience and sustainability in design is far from trivial, requiring various interdisciplinary perspectives involved in the delivery of building projects. These perspectives each contribute the models and data necessary for integrated evaluation, leading to the notorious challenges of BIM and data interoperability. In response, this paper presents a new end-to-end workflow for life-cycle assessment (LCA) of buildings that captures the dependencies between multi-hazard resilience and sustainability, across multiple dimensions of environmental impact. An illustrative example reveals how consideration of hazards during design and material selection influence embodied energy, ultimately revealing design choices that best achieve joint resiliency and sustainability

Innovation clubs: Mobilizing local creativity for sustainable development and pedagogy

Two months after the 2010 Haiti earthquake devastated Port-au-Prince, a reconnaissance team of structural engineering researchers from the University of Notre Dame travelled to Léogâne to assess the damage. As their research revealed the underlying problems plaguing the residential construction industry in Léogâne, they realized that recommending externally-devised engineering solutions alone would not bring about significant change. In order to discover more holistic and implementable solutions, they turned to the affected community. By hosting open innovation challenges throughout Léogâne, the research team identified local innovators who demonstrated leadership, problem-solving skills, and creativity. These local innovators, forty-two men and women of various professions representing each of the six zones of Léogâne, were then trained and certified in the Pwosesis pou Innovasyon (Innovation Process) - a Creole-adapted form of Human-Centered Design. These individuals subsequently engaged their neighbors to form six Innovation Clubs. For seven years, undergraduate and graduate engineering students have worked with these Innovation Clubs to facilitate sustainable development research initiatives. This paper describes the framework used to establish these Innovation Clubs, case studies of cooperative projects, the observed benefits of this collaboration, and recommendations for future implementation

Integrated workflow for evaluating sustainability and resiliency of building systems

This study describes the development of a workflow for integrated life-cycle assessment (iLCA) of buildings that is capable of capturing the dependencies between multi-hazard resilience and sustainability using tools native to professional practice. Modules dedicated to hazard characterization, structural response, damage, repair/loss, and environmental impact (embodied and operating energy) are developed using Application Programming Interfaces (APIs) and semantic data perspectives from computer science. A unifying probabilistic framework is utilized to quantify life-cycle performance and a common, versatile, simulation-based approach is adopted for estimation of performance. This approach supports various resilience/sustainability metrics, including monetary losses, downtime, total embodied energy (initial construction and repairs), and operating energy. A case study executed in the Revit environment evaluates the performance of a special reinforced concrete frame located near Los Angeles International Airport (LAX). Two design alternatives are considered to illustrate the impact of design and material decisions, ultimately revealing design choices which best achieve joint resiliency and sustainability.The authors gratefully acknowledge the support of NSF (CMMI-1537652). The first author also recognizes the support of her NSF Graduate Research Fellowship (DGE-1313583) and Deans Fellowship from the University of Notre Dame. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of NSF