Global sensitivity analysis for the boundary control of an open channel

The goal of this paper is to solve the global sensitivity analysis for a particular control problem. More precisely, the boundary control problem of an open-water channel is considered, where the boundary conditions are defined by the position of a down stream overflow gate and an upper stream underflow gate. The dynamics of the water depth and of the water velocity are described by the Shallow Water equations, taking into account the bottom and friction slopes. Since some physical parameters are unknown, a stabilizing boundary control is first computed for their nominal values, and then a sensitivity anal-ysis is performed to measure the impact of the uncertainty in the parameters on a given to-be-controlled output. The unknown physical parameters are de-scribed by some probability distribution functions. Numerical simulations are performed to measure the first-order and total sensitivity indices

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Residual Minimizing Model Interpolation for Parameterized Nonlinear Dynamical Systems

We present a method for approximating the solution of a parameterized, nonlinear dynamical system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are computed with a nonlinear least squares procedure that minimizes the residual of the governing equations. The approximation properties of this residual minimizing scheme are comparable to existing reduced basis and POD-Galerkin model reduction methods, but its implementation requires only independent evaluations of the nonlinear forcing function. It is particularly appropriate when one wishes to approximate the states at a few points in time without time marching from the initial conditions. We prove some interesting characteristics of the scheme including an interpolatory property, and we present heuristics for mitigating the effects of the ill-conditioning and reducing the overall cost of the method. We apply the method to representative numerical examples from kinetics - a three state system with one parameter controlling the stiffness - and conductive heat transfer - a nonlinear parabolic PDE with a random field model for the thermal conductivity.Comment: 28 pages, 8 figures, 2 table

An Assessment to Benchmark the Seismic Performance of a Code-Conforming Reinforced-Concrete Moment-Frame Building

This report describes a state-of-the-art performance-based earthquake engineering methodology that is used to assess the seismic performance of a four-story reinforced concrete (RC) office building that is generally representative of low-rise office buildings constructed in highly seismic regions of California. This “benchmark” building is considered to be located at a site in the Los Angeles basin, and it was designed with a ductile RC special moment-resisting frame as its seismic lateral system that was designed according to modern building codes and standards. The building’s performance is quantified in terms of structural behavior up to collapse, structural and nonstructural damage and associated repair costs, and the risk of fatalities and their associated economic costs. To account for different building configurations that may be designed in practice to meet requirements of building size and use, eight structural design alternatives are used in the performance assessments. Our performance assessments account for important sources of uncertainty in the ground motion hazard, the structural response, structural and nonstructural damage, repair costs, and life-safety risk. The ground motion hazard characterization employs a site-specific probabilistic seismic hazard analysis and the evaluation of controlling seismic sources (through disaggregation) at seven ground motion levels (encompassing return periods ranging from 7 to 2475 years). Innovative procedures for ground motion selection and scaling are used to develop acceleration time history suites corresponding to each of the seven ground motion levels. Structural modeling utilizes both “fiber” models and “plastic hinge” models. Structural modeling uncertainties are investigated through comparison of these two modeling approaches, and through variations in structural component modeling parameters (stiffness, deformation capacity, degradation, etc.). Structural and nonstructural damage (fragility) models are based on a combination of test data, observations from post-earthquake reconnaissance, and expert opinion. Structural damage and repair costs are modeled for the RC beams, columns, and slabcolumn connections. Damage and associated repair costs are considered for some nonstructural building components, including wallboard partitions, interior paint, exterior glazing, ceilings, sprinkler systems, and elevators. The risk of casualties and the associated economic costs are evaluated based on the risk of structural collapse, combined with recent models on earthquake fatalities in collapsed buildings and accepted economic modeling guidelines for the value of human life in loss and cost-benefit studies. The principal results of this work pertain to the building collapse risk, damage and repair cost, and life-safety risk. These are discussed successively as follows. When accounting for uncertainties in structural modeling and record-to-record variability (i.e., conditional on a specified ground shaking intensity), the structural collapse probabilities of the various designs range from 2% to 7% for earthquake ground motions that have a 2% probability of exceedance in 50 years (2475 years return period). When integrated with the ground motion hazard for the southern California site, the collapse probabilities result in mean annual frequencies of collapse in the range of [0.4 to 1.4]x10 -4 for the various benchmark building designs. In the development of these results, we made the following observations that are expected to be broadly applicable: (1) The ground motions selected for performance simulations must consider spectral shape (e.g., through use of the epsilon parameter) and should appropriately account for correlations between motions in both horizontal directions; (2) Lower-bound component models, which are commonly used in performance-based assessment procedures such as FEMA 356, can significantly bias collapse analysis results; it is more appropriate to use median component behavior, including all aspects of the component model (strength, stiffness, deformation capacity, cyclic deterioration, etc.); (3) Structural modeling uncertainties related to component deformation capacity and post-peak degrading stiffness can impact the variability of calculated collapse probabilities and mean annual rates to a similar degree as record-to-record variability of ground motions. Therefore, including the effects of such structural modeling uncertainties significantly increases the mean annual collapse rates. We found this increase to be roughly four to eight times relative to rates evaluated for the median structural model; (4) Nonlinear response analyses revealed at least six distinct collapse mechanisms, the most common of which was a story mechanism in the third story (differing from the multi-story mechanism predicted by nonlinear static pushover analysis); (5) Soil-foundation-structure interaction effects did not significantly affect the structural response, which was expected given the relatively flexible superstructure and stiff soils. The potential for financial loss is considerable. Overall, the calculated expected annual losses (EAL) are in the range of $52,000 to$97,000 for the various code-conforming benchmark building designs, or roughly 1% of the replacement cost of the building ($8.8M). These losses are dominated by the expected repair costs of the wallboard partitions (including interior paint) and by the structural members. Loss estimates are sensitive to details of the structural models, especially the initial stiffness of the structural elements. Losses are also found to be sensitive to structural modeling choices, such as ignoring the tensile strength of the concrete (40 EAL) or the contribution of the gravity frames to overall building stiffness and strength (15 change in EAL). Although there are a number of factors identified in the literature as likely to affect the risk of human injury during seismic events, the casualty modeling in this study focuses on those factors (building collapse, building occupancy, and spatial location of building occupants) that directly inform the building design process. The expected annual number of fatalities is calculated for the benchmark building, assuming that an earthquake can occur at any time of any day with equal probability and using fatality probabilities conditioned on structural collapse and based on empirical data. The expected annual number of fatalities for the code-conforming buildings ranges between 0.05*10 -2 and 0.21*10 -2 , and is equal to 2.30*10 -2 for a non-code conforming design. The expected loss of life during a seismic event is perhaps the decision variable that owners and policy makers will be most interested in mitigating. The fatality estimation carried out for the benchmark building provides a methodology for comparing this important value for various building designs, and enables informed decision making during the design process. The expected annual loss associated with fatalities caused by building earthquake damage is estimated by converting the expected annual number of fatalities into economic terms. Assuming the value of a human life is$3.5M, the fatality rate translates to an EAL due to fatalities of $3,500 to$5,600 for the code-conforming designs, and $79,800 for the non-code conforming design. Compared to the EAL due to repair costs of the code-conforming designs, which are on the order of$66,000, the monetary value associated with life loss is small, suggesting that the governing factor in this respect will be the maximum permissible life-safety risk deemed by the public (or its representative government) to be appropriate for buildings. Although the focus of this report is on one specific building, it can be used as a reference for other types of structures. This report is organized in such a way that the individual core chapters (4, 5, and 6) can be read independently. Chapter 1 provides background on the performance-based earthquake engineering (PBEE) approach. Chapter 2 presents the implementation of the PBEE methodology of the PEER framework, as applied to the benchmark building. Chapter 3 sets the stage for the choices of location and basic structural design. The subsequent core chapters focus on the hazard analysis (Chapter 4), the structural analysis (Chapter 5), and the damage and loss analyses (Chapter 6). Although the report is self-contained, readers interested in additional details can find them in the appendices