Simulation-based robust design of mass dampers for response mitigation of tension leg platforms

A robust stochastic design framework is discussed for design of mass dampers. The focus is on applications for the mitigation of the coupled heave and pitch response of Tension Leg Platforms under stochastic sea excitation. The framework presented fully addresses the complex relationship between the coupled dynamics of the platform, the stochastic excitation and the vibration of the dampers. Model parameters that have some level of uncertainty are probabilistically described. In this probabilistic setting, the system reliability is adopted as the design objective. Stochastic simulation is considered for evaluation of the system model response and the overall reliability performance. This way, all nonlinear characteristics of the structural response and environmental excitation are explicitly incorporated into their respective models. An efficient algorithm is discussed for performing the challenging stochastic design optimization. The ideas are illustrated in an application involving a tension leg platform with closely spaced frequencies for the heave and pitch degrees of freedom.     

Stochastic Subset Optimization for optimal reliability problems

Reliability-based design of a system often requires the minimization of the probability of system failure over the admissible space for the design variables. For complex systems this probability can rarely be evaluated analytically and so it is often calculated using stochastic simulation techniques, which involve an unavoidable estimation error and significant computational cost. These features make efficient reliability-based optimal design a challenging task. A new method called Stochastic Subset Optimization (SSO) is proposed here for iteratively identifying sub-regions for the optimal design variables within the original design space. An augmented reliability problem is formulated where the design variables are artificially considered as uncertain and Markov Chain Monte Carlo techniques are implemented in order to simulate samples of them that lead to system failure. In each iteration, a set with high likelihood of containing the optimal design parameters is identified using a single reliability analysis. Statistical properties for the identification and stopping criteria for the iterative approach are discussed. For problems that are characterized by small sensitivity around the optimal design choice, a combination of SSO with other optimization algorithms is proposed for enhanced overall efficiency.     

Reliability-Based Performance Objectives and Probabilistic Robustness in Structural Control Applications

A reliability-based structural control design approach is presented that optimizes a control system explicitly to minimize the probability of structural failure. Failure is interpreted as the system’s state trajectory exiting a safe region within a given time duration. This safe region is bounded by hyperplanes in the system state space, each of them corresponding to an important response quantity. An efficient approximation is discussed for the analytical evaluation of this probability, and for its optimization through feedback control. This analytical approximation facilitates theoretical discussions regarding the characteristics of reliability-optimal controllers. Versions of the controller design are described for the case using a nominal model of the system, as well as for the case with uncertain model parameters. For the latter case, knowledge about the relative plausibility of the different possible values of the uncertain parameters is quantified through the use of probability distributions on the uncertain parameter space. The influence of the excitation time duration on feedback control design is discussed and a probabilistic treatment of this time duration is suggested. The relationship to H2 (i.e., minimum variance) controller synthesis is also examined.     

Optimal probabilistic design of seismic dampers for the protection of isolated bridges against near-fault seismic excitations

A probabilistic, simulation-based framework is presented in this paper for risk assessment and optimal design of supplemental dampers for multi-span bridge systems supported on abutments and intermediate piers through isolation bearings. The adopted bridge model explicitly addresses nonlinear characteristics of the isolators and the dampers, the dynamic behavior of the abutments, and the effect of pounding between the neighboring spans against each other as well as against the abutments. Nonlinear dynamic analysis is used to evaluate the bridge performance, and a realistic stochastic ground motion model is presented for describing the time history of future near-fault ground motions and relating their characteristics to the seismic hazard for the structural site. A probabilistic foundation is used to address the various sources of structural and excitation uncertainties and ultimately characterize the seismic risk for the bridge. This risk is given by the expected value of the system response over the adopted probability models. Stochastic simulation is used for evaluating the multi-dimensional integral representing this expected value and for performing the associated optimization when searching for the most favorable damper characteristics. An efficient probabilistic sensitivity analysis is also established for identifying the importance of each of the uncertain model parameters in affecting the overall risk. An illustrative example is presented that considers the design of nonlinear viscous dampers for the protection of a two-span bridge.     

Multi-objective optimization for design under uncertainty problems through surrogate modeling in augmented input space

Multi-objective design under uncertainty problems that adopt probabilistic quantities as performance objectives and consider their estimation through stochastic simulation are examined in this paper, focusing on development of a surrogate modeling framework to reduce computational burden for the numerical optimization. The surrogate model is formulated to approximate the system response with respect to both the design variables and the uncertain model parameters, so that it can simultaneously support both the uncertainty propagation and the identification of the Pareto optimal solutions. Kriging is chosen as the metamodel, and its probabilistic nature (its ability to offer a local estimate of the prediction error) is leveraged within different aspects of the framework. To reduce the number of simulations for the expensive system model, an iterative approach is established with adaptive characteristics for controlling the metamodel accuracy. At each iteration, a new metamodel is developed utilizing all available training points. A new Pareto front is then identified utilizing this surrogate model and is compared, for assessing stopping criteria, to the front that was identified in the previous iteration. This comparison utilizes explicitly the potential error associated with the metamodel predictions. If stopping criteria are not achieved, a set of refinement experiments (new training points) is identified and process proceeds to the next iteration. A hybrid design of experiments is considered for this refinement, with a dual goal of global coverage and local exploitation of regions of interest, separately identified for the design variables and the uncertain model parameters.

     

Stochastic Subset Optimization for reliability optimization and sensitivity analysis in system design

Design problems that involve the system reliability as the objective function are discussed. In order to appropriately address the challenges of such applications when complex system models are involved, stochastic simulation is selected to evaluate the probability of failure. An innovative algorithm, called Stochastic Subset Optimization (SSO), is discussed for performing the reliability optimization as well as an efficient sensitivity analysis. The basic principle in SSO is the formulation of an augmented problem where the design variables are artificially considered as uncertain. Stochastic simulation techniques are implemented in order to simulate samples of these variables that lead to system failure. The information that these samples provide is then exploited in an iterative approach in SSO to identify a smaller subset of the design space that consists of near-optimal design variables and also that has high plausibility of containing the optimal design. At the same time, a sensitivity analysis for the influence of both the design variables and the uncertain model parameters is established.     

Life-cycle cost optimal design of passive dissipative devices

The cost-effective performance of structures under natural hazards such as earthquakes and hurricanes has long been recognized to be an important topic in the design of civil engineering systems. A realistic comprehensive treatment of such a design requires proper integration of (i) methodologies for treating the uncertainties related to natural hazards and to the structural behavior over the entire life-cycle of the building, (ii) tools for evaluating the performance using socioeconomic criteria, as well as (iii) algorithms appropriate for stochastic analysis and optimization. A systematic probabilistic framework is presented here for detailed estimation and optimization of the life-cycle cost of engineering systems. This framework is a general one but the application of interest here is the design of passive dissipative devices for seismic risk mitigation. A comprehensive methodology is initially presented for earthquake loss estimation; this methodology uses the nonlinear time-history response of the structure under a given excitation to estimate the damage in a detailed, component level. A realistic probabilistic model is then presented for describing the ground motion time history for future earthquake excitations. In this setting, the life-cycle cost is uncertain and can be quantified by its expected value over the space of the uncertain parameters for the structural and excitation models. Because of the complexity of these models, calculation of this expected value is performed using stochastic simulation techniques. This approach, though, involves an unavoidable estimation error and significant computational cost, features which make efficient design optimization challenging. A highly efficient framework, consisting of two stages, is discussed for this stochastic optimization. An illustrative example is presented that shows the efficiency of the proposed methodology; it considers the seismic retrofitting of a four-story non-ductile reinforced-concrete building with viscous dampers.