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Mathematical Analysis of Random Noise-Conclusion
About: This article is published in Bell System Technical Journal.The article was published on 1945-01-01 and is currently open access. It has received 807 citations till now.
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TL;DR: The role played by the higher-order wide-sense cyclostationarity properties in Rice's representation of a signal is investigated and it is shown that some known results relative to second-order cyclic spectra cannot be extended to higher orders.
22Â citations
TL;DR: A new multiple-point asperity model, called the n- point asperities model, is introduced in this paper, which is shown to produce remarkably good agreement with measurements from real and simulated surfaces.
Abstract: For several decades, asperities of nominally flat rough surfaces were considered to be points higher than their immediate neighbors. Recently, it has been recognized that this model is incorrect. To address the issue, a new multiple-point asperity model, called the n-point asperity model, is introduced in this paper. In the new model, asperities are composed of n neighboring sampled points with n-2 middle points being above a certain level. When the separation between two surfaces decreases, new asperities with higher number of sample points, n, will come into existence. Based on the above model, the height and curvature of n-point asperities are defined and their distributions are found. The model is developed for Gaussian surfaces and for the general case of an autocorrelation function (ACF). As a case study, the exponential ACF is applied to the new model, which is shown to produce remarkably good agreement with measurements from real and simulated surfaces.
22Â citations
TL;DR: The problem of modeling heterogeneous materials and media is a problem of fundamental importance to a wide variety of phenomena with applications to many disciplines, ranging from condensed and soft materials, fuel cells, alloys and composite media, to biological materials such as proteins, and even such large-scale structure as field-scale porous media and clusters of galaxies as mentioned in this paper.
22Â citations
TL;DR: In this article, a hybrid of analytical and empirical (or semi-analytical) formula based on moment-based Hermite polynomial model (HPM) was developed to estimate the mean of peak wind pressure and peak wind pressures at various percentiles.
22Â citations
TL;DR: Two methods based on projection outline adaptive Kriging (POK) are proposed to handle TRA and TRA with mixed interval uncertainties ( i TRA) and extended to the time-dependent reliability analysis including both random and interval variables.
Abstract: Time-dependent reliability analysis (TRA) has drawn much attention due to its ability in measuring the probability that a system or component keeps safe in the full life cycle. Since it is difficult to efficiently obtain accurate results for TRA problems with expensive simulation demand, many surrogate model-based methods have been proposed to handle this challenge. Moreover, when both random and interval uncertainties are included in these TRA problems simultaneously, the analysis process will be more complicated. In this paper, two methods based on projection outline adaptive Kriging (POK) are proposed to handle TRA and TRA with mixed interval uncertainties (iTRA), respectively. Firstly, POK-TRA method is put forward for the TRA problems with different stochastic processes. Different from current TRA methods, POK-TRA regards the time parameter as a special interval variable, which converts TRA problem into a special hybrid reliability analysis (HRA) problem with one interval variable. Based on the concept of projection outline as well as a correlation condition, an efficient sampling strategy is proposed to refine the Kriging model adaptively. Secondly, POK-TRA is extended to the time-dependent reliability analysis including both random and interval variables (POK-iTRA). By inheriting the processing strategy of time parameter and stochastic processes, the iTRA problem is converted into the HRA problem with multiple interval variables. Finally, four cases are used to show the accuracy and efficiency of the proposed method.
22Â citations