Analytical reliability calculation of linear dynamical systems in higher dimensions

The recent application of reliability analysis to controller synthesis has created the need for a computationally efficient method for the estimation of the first excursion probabilities for linear dynamical systems in higher dimensions. Simulation methods cannot provide an adequate solution to this specific application, which involves numerical optimization of the system reliability with respect to the controller parameters, because the total computational time needed is still prohibitive. Instead, an analytical approach is presented in this paper. The problem reduces to the calculation of the conditional upcrossing rate at each surface of the failure boundary. The correlation between upcrossings of the failure surface for the different failure events may be addressed by the introduction of a multi-dimensional integral. An efficient algorithm is adopted for the numerical calculation of this integral. Also, the problem of approximation of the conditional upcrossing rate is discussed. For the latter there is no known theoretical solution. Three of the semi-empirical corrections that have been proposed previously for scalar processes are compared and it is shown that the correction should be based on the bandwidth characteristics of the system. Finally, examples that verify the validity of the analytical approximations for systems in higher dimensions are discussed

Simplified PBEE to Estimate Economic Seismic Risk for Buildings

A seismic risk assessment is often performed on behalf of a buyer of large commercial buildings in seismically active regions. One outcome of the assessment is that a probable maximum loss (PML) is computed. PML is of limited use to real-estate investors as it has no place in a standard financial analysis and reflects too long a planning period for what-if scenarios. We introduce an alternative to PML called probable frequent loss (PFL), defined as the mean loss resulting from an economic-basis earthquake such as shaking with 10% exceedance probability in 5 years. PFL is approximately related to expected annualized loss (EAL) through a site economic hazard coefficient (H) introduced here. PFL and EAL offer three advantages over PML: (1) meaningful planning period; (2) applicability in financial analysis (making seismic risk a potential market force); and (3) can be estimated by a rigorous but simplified PBEE method that relies on a single linear structural analysis. We illustrate using 15 example buildings, including a 7-story nonductile reinforced-concrete moment-frame building in Van Nuys, CA and 14 buildings from the CUREE-Caltech Woodframe Project

Can Long-Range Nuclear Properties Be Influenced By Short Range Interactions? A chiral dynamics estimate

Recent experiments and many-body calculations indicate that approximately 20\% of the nucleons in medium and heavy nuclei ($A\geq12$) are part of short-range correlated (SRC) primarily neutron-proton ($np$) pairs. We find that using chiral dynamics to account for the formation of $np$ pairs due to the effects of iterated and irreducible two-pion exchange leads to values consistent with the 20\% level. We further apply chiral dynamics to study how these correlations influence the calculations of nuclear charge radii, that traditionally truncate their effect, to find that they are capable of introducing non-negligible effects.Comment: 6 pages, 0 figures. This version includes many improvement

Accounting for Seismic Risk in Financial Analysis of Property Investment

A methodology is presented for making property investment decisions using loss analysis and the principles of decision analysis. It proposes that the investor choose among competing investment alternatives on the basis of the certainty equivalent of their net asset value which depends on the uncertain discounted future net income, uncertain discounted future earthquake losses, initial equity and the investor’s risk tolerance. The earthquake losses are modelled using a seismic vulnerability function, the site seismic hazard function, and an assumption that strong shaking at a site follows a Poisson process. A building-specific vulnerability approach, called assembly-based vulnerability, or ABV, is used. ABV involves a simulation approach that includes dynamic structural analyses and damage analyses using fragility functions and probability distributions on unit repair costs and downtimes for all vulnerable structural and nonstructural components in a building. The methodology is demonstrated using some results from a seven-storey reinforced-concrete hotel in Los Angeles

Simplified Estimation of Economic Seismic Risk for Buildings

A seismic risk assessment is often performed on behalf of a buyer of commercial buildings in seismically active regions. One outcome of the assessment is that a probable maximum loss (PML) is computed. PML is of limited use to real-estate investors as it has no place in a standard financial analysis and reflects too long a planning period. We introduce an alternative to PML called probable frequent loss (PFL), defined as the mean loss resulting from shaking with 10% exceedance probability in 5 years. PFL is approximately related to expected annualized loss (EAL) through a site economic hazard coefficient (H) introduced here. PFL and EAL offer three advantages over PML: (1) meaningful planning period; (2) applicability in financial analysis (making seismic risk a potential market force); and (3) can be estimated using a single linear structural analysis, via a simplified method called linear assembly-based vulnerability (LABV) that is presented in this work. We also present a simple decision-analysis framework for real-estate investments in seismic regions, accounting for risk aversion. We show that market risk overwhelms uncertainty in seismic risk, allowing one to consider only expected consequences in seismic risk. We illustrate using 15 buildings, including a 7-story nonductile reinforced-concrete moment-frame building in Van Nuys, California, and 14 buildings from the CUREE-Caltech Woodframe Project

Uncertainty Propagation and Feature Selection for Loss Estimation in Performance-based Earthquake Engineering

This report presents a new methodology, called moment matching, of propagating the uncertainties in estimating repair costs of a building due to future earthquake excitation, which is required, for example, when assessing a design in performance-based earthquake engineering. Besides excitation uncertainties, other uncertain model variables are considered, including uncertainties in the structural model parameters and in the capacity and repair costs of structural and non-structural components. Using the first few moments of these uncertain variables, moment matching requires only a few well-chosen point estimates to propagate the uncertainties to estimate the first few moments of the repair costs with high accuracy. Furthermore, the use of moment matching to estimate the exceedance probability of the repair costs is also addressed. These examples illustrate that the moment-matching approach is quite general; for example, it can be applied to any decision variable in performance-based earthquake engineering. Two buildings are chosen as illustrative examples to demonstrate the use of moment matching, a hypothetical three-story shear building and a real seven-story hotel building. For these two examples, the assembly-based vulnerability approach is employed when calculating repair costs. It is shown that the moment-matching technique is much more accurate than the well-known First-Order-Second-Moment approach when propagating the first two moments, while the resulting computational cost is of the same order. The repair-cost moments and exceedance probability estimated by the moment-matching technique are also compared with those by Monte Carlo simulation. It is concluded that as long as the order of the moment matching is sufficient, the comparison is satisfactory. Furthermore, the amount of computation for moment matching scales only linearly with the number of uncertain input variables. Last but not least, a procedure for feature selection is presented and illustrated for the second example. The conclusion is that the most important uncertain input variables among the many influencing the uncertainty in future repair costs are, in order of importance, ground-motion spectral acceleration, component capacity, ground-motion details and unit repair costs

Horn antenna with v-shaped corrugated surface

Corrugated shape is easily machined for millimeter wave application and is better suited for folding antenna designs. Measured performance showed ""V'' corrugations and rectangular corrugations have nearly the same pattern beamwidth, gain, and impedance. Also, ""V'' corrugations have higher relative power loss

Sensitivity of Building Loss Estimates to Major Uncertain Variables

This paper examines the question of which sources of uncertainty most strongly affect the repair cost of a building in a future earthquake. Uncertainties examined here include spectral acceleration, ground-motion details, mass, damping, structural force-deformation behavior, building-component fragility, contractor costs, and the contractor's overhead and profit. We measure the variation (or swing) of the repair cost when each basic input variable except one is taken at its median value, and the remaining variable is taken at its 10th and at its 90th percentile. We perform this study using a 1960s highrise nonductile reinforced-concrete moment-frame building. Repair costs are estimated using the assembly-based vulnerability (ABV) method. We find that the top three contributors to uncertainty are assembly capacity (the structural response at which a component exceeds some damage state), shaking intensity (measured here in terms of damped elastic spectral acceleration, Sa), and details of the ground motion with a given Sa