A new philosophy for stochastic equivalent linearization

An extension, to the time-dependent situation, of what is known in static structural reliability as the ‘normal tail approximation’ is presented. This is pursued within the classical stochastic equivalent linearization scheme. Duffing and hysteretic oscillators are studied in detail.     

Optimal control of sprinklers in compartment fires

There is no doubt that increased application of sprinkler protection through a building can significantly reduce fire losses. In many compartment fires, the water damage is far more extensive than the flame damage. This paper examines the possibility of controlling the flow of water from sprinklers in an optimal way so as to minimize the water damage and the overall property damage. Two cases are considered. The first when the water damage is proportional to the total amount of water and the second when it is proportional to the integral of the square of the water flow rate. © 1997 John Wiley & Sons, Ltd.     

A statistical theory of the brittle fracture of steel

A statistical model for the brittle fracture of steel is formulated and analyzed. Fracture is assumed to occur by coalescence of a number of arrested cracks initiated at different points. The upper tail of the distribution of maximum stress is shown, to be given by the formula 1-(x/(σ_o)^θ, where σ_o and θ are functions of the microstructural constants of the material. It is further shown that the size effect in this model is much less marked than in the case of weakest-link models. Finally, some experimental results from a pilot program are presented and suggestions for further experimental work given.     

Response surface modelling of monte carlo fire data

The results of a large-scale Monte-Carlo simulation of a computer fire model are summarised in the form of a simple response surface for each of a number of subranges of the input parameters. The subranges are automatically determined through the use of a powerful modern regression methodology. A brief summary of the first-order second moment reliability index method is given. It is shown that the particular form of the obtained response surface allows the reliability index to be easily calculated. The reliability index and corresponding probability of failure are obtained for a particular example and the result confirmed by Monte-Carlo simulation.     

Estimating the transmission rate for a highly infectious disease

It is pointed out that estimates of disease transmission parameters based on the final size of an epidemic are unsatisfactory when all susceptibles are infected and that this is an event with a substantial probability for communities of practical interest. We propose a method for estimating the transmission rate for such highly infectious diseases under the assumptions that the removal process of the disease is fully observed and that the mean duration of the infectious period is known. The method uses smoothed differentiation of the removal process. A simulation study shows that the method performs satisfactorily.     

Vector outcrossing probabilities by Monte Carlo

An exact method for calculating the probability that a vector-valued Gaussian stationary process will cross out of a safe set in a given time, is presented. It is based on representing the process by a random trigonometric polynomial and then calculating the probability by directional simulation. Exact bounds for the error can be calculated, giving a predetermined accuracy. A numerical example relating to the response of a structure to wind excitation is given.     

Statistical analysis of response to fire cues

A statistical analysis of data on recognition of fire cues during sleep was carried out to determine the influence of the type of cue, sex and age on response. Four cues were used: crackling, shuffling, a flickering light and smell. The analysis was carried out on the observed data as well as on the corresponding parameters of a stochastic model of response previously developed. Linear models and, where required, a generalized linear model were used. At the low intensity levels used the most effective cues were auditory (crackle, followed by shuffle) while the two least effective were light and smell. Females had a waking up probability consistently higher than males, as well as a shorter response time. The influence of age was borderline for all cues. An important practical conclusion of the study is that a low level flickering light and fire smells are unlikely on their own to arouse sleeping people.     

Modern sensitivity analysis of the CESARE-Risk computer fire model

This paper introduces two new modern methods of global sensitivity analysis for computer models: Fourier Amplitude and Sobol, as well as a modern factor screening method: the Morris method. The methods are applied to the sensitivity analysis of the apartment fire module of the CESARE-Risk building fire computer model with eight input factors and door and window open. Two output variables are considered: the maximum temperature reached and the time of onset of untenable conditions. Response surfaces previously derived for the model [Jianguo Qu, Response surface modelling of Monte Carlo fire data, Ph.D. Thesis, Victoria University, Melbourne, Australia, 2003, http://eprints.vu.edu.au/archive/00000260/01/Qu,_Jianguo.pdf] are used to speed up the computations. For the maximum temperature all three methods agree that the most sensitive factors are the window height and width factors, followed by the fuel area factor. The largest interaction was between the length of room and the fuel area factor. For the time of untenable conditions the Fourier Amplitude and Sobol methods agreed that one factor, the flame spread rate, had overwhelming significance. The only significant Sobol interaction was between the width of room and the flame spread rate.     

On the Slepian process of a random Gaussian trigonometricpolynomial

It is proved that the Slepian process of a stationary trigonometric polynomial with Gaussian coefficients has a Karhunen-Loeve expansion consisting of a finite number of terms, and that each eigenfunction is itself a finite trigonometric polynomial. Upper bounds for the error which results when replacing the Slepian process corresponding to a general Gaussian stationary process by the Slepian process corresponding to its finite trigonometric approximation are obtained. A numerical example is given and the results are used to estimate by simulation the distribution of the excursion time above a level of a particular Gaussian stationary process