Limiting performance of dynamic systems subject to random inputs

The problem of determining the limiting performance characteristics of mechanical systems subject to random input is studied. A review is presented of the classical work in the optimal design of stochastic systems. Some recent results of stochastic optimal control theory are employed. The solution to the limiting performance problem is formulated in both the frequency and time domains. Both formulations require substantial, burdensome computations when applied to large scale systems

Stochastic urban pluvial flood hazard maps based upon a spatial-temporal rainfall generator

It is a common practice to assign the return period of a given storm event to the urban pluvial flood event that such storm generates. However, this approach may be inappropriate as rainfall events with the same return period can produce different urban pluvial flooding events, i.e., with different associated flood extent, water levels and return periods. This depends on the characteristics of the rainfall events, such as spatial variability, and on other characteristics of the sewer system and the catchment. To address this, the paper presents an innovative contribution to produce stochastic urban pluvial flood hazard maps. A stochastic rainfall generator for urban-scale applications was employed to generate an ensemble of spatially—and temporally—variable design storms with similar return period. These were used as input to the urban drainage model of a pilot urban catchment (~9 km2) located in London, UK. Stochastic flood hazard maps were generated through a frequency analysis of the flooding generated by the various storm events. The stochastic flood hazard maps obtained show that rainfall spatial-temporal variability is an important factor in the estimation of flood likelihood in urban areas. Moreover, as compared to the flood hazard maps obtained by using a single spatially-uniform storm event, the stochastic maps generated in this study provide a more comprehensive assessment of flood hazard which enables better informed flood risk management decisions

Identification of nonlinear phenomena in a stochastically excited beam system with impact

The response of strongly nonlinear dynamic systems to stochastic excitation exhibits many interesting characteristics. In this paper, an impacting beam system under broad and small banded, Gaussian noise excitation is investigated numerically as well as experimentally. The emphasis lies on frequency domain characteristics. Phenomena like multiple resonance frequencies and stochastic equivalents of harmonic and subharmonic solutions are found. A better understanding of such stochastic response characteristics is obtained by a comparison with nonlinear periodic response features. It is shown that these stochastic response phenomena can provide valuable information on periodic response characteristics of the system

Identification of nonlinear phenomena in a stochastically excited beam system with impact

The response of strongly nonlinear dynamic systems to stochastic excitation exhibits many interesting characteristics. In this paper, an impacting beam system under broad and small banded, Gaussian noise excitation is investigated numerically as well as experimentally. The emphasis lies on frequency domain characteristics. Phenomena like multiple resonance frequencies and stochastic equivalents of harmonic and subharmonic solutions are found. A better understanding of such stochastic response characteristics is obtained by a comparison with nonlinear periodic response features. It is shown that these stochastic response phenomena can provide valuable information on periodic response characteristics of the system

Fisher-Wright model with deterministic seed bank and selection

Seed banks are a common characteristics to many plant species, which allow storage of genetic diversity in the soil as dormant seeds for various periods of time. We investigate an above-ground population following a Fisher-Wright model with selection coupled with a deterministic seed bank assuming the length of the seed bank is kept constant and the number of seeds is large. To assess the combined impact of seed banks and selection on genetic diversity, we derive a general diffusion model. The applied techniques outline a path of approximating a stochastic delay differential equation by an appropriately rescaled stochastic differential equation, which is a common issue in statistical physics. We compute the equilibrium solution of the site-frequency spectrum and derive the times to fixation of an allele with and without selection. Finally, it is demonstrated that seed banks enhance the effect of selection onto the site-frequency spectrum while slowing down the time until the mutation-selection equilibrium is reached

Measuring and forecasting financial variability using realised variance with and without a model

We use high frequency financial data to proxy, via the realised variance, each day's financial variability. Based on a semiparametric stochastic volatility process, a limit theory shows you can represent the proxy as a true underlying variability plus some measurement noise with known characteristics. Hence filtering, smoothing and forecasting ideas can be used to improve our estimates of variability by exploiting the time series structure of the realised variances. This can be carried out based on a model or without a model. A comparison is made between these two methods.Kalman filter; Mixed Gaussian limit; OU process; Quadratic variation; Realised variance; Realised volatility; Square root process; Stochastic volatility.