A non-separable stochastic model for pulse-like ground motions

A phenomenological non-separable non-stationary stochastic model is proposed to represent near-fault pulse-like ground motions (PLGMs) by means of a parametrically defined evolutionary power spectrum (EPSD). Numerical data pertaining to ensembles of EPSD compatible realizations and considering statistical analysis of peak elastic and inelastic spectral ordinates demonstrate the applicability of the model to capture the salient effects of PLGMs to structural responses. To this aim, the model parameters are calibrated against a field recorded PLGM. Further numerical data considering stochastic processes compatible with the response spectrum of the European aseismic code (EC8) are furnished to demonstrate the potential of the proposed model for including near-fault effects to spectrum compatible representations of the seismic action. It is foreseen that this model can be a useful tool in accounting for the low-frequency content of PLGMs in both Monte Carlo simulation-based analyses and in statistical linearization based studies

Effect of Ground Motion Characteristics on the Seismic Response of Torsionally Coupled Elastic Systems

This study presents a systematic investigation of the effects of ground motion characteristics, especially its multi-directional character, on the response of torsionally coupled elastic structural systems. The ground motion model is probabilistic and is founded on the assumption of the existence of ground motion principal directions. The structural systems considered are single-story and multi-story elastic shear beam models with stiffness eccentricity.National Science Foundation Grants ENV 77-07190 and PFR 80-0258

Introduction to Random Signals and Noise

Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired signal. With a strong mathematical grounding, this text provides a clear introduction to the fundamentals of stochastic processes and their practical applications to random signals and noise. With worked examples, problems, and detailed appendices, Introduction to Random Signals and Noise gives the reader the knowledge to design optimum systems for effectively coping with unwanted signals.\ud \ud Key features:\ud • Considers a wide range of signals and noise, including analogue, discrete-time and bandpass signals in both time and frequency domains.\ud • Analyses the basics of digital signal detection using matched filtering, signal space representation and correlation receiver.\ud • Examines optimal filtering methods and their consequences.\ud • Presents a detailed discussion of the topic of Poisson processed and shot noise.\u

A Stochastic Geometric Analysis of Device-to-Device Communications Operating over Generalized Fading Channels

Device-to-device (D2D) communications are now considered as an integral part of future 5G networks which will enable direct communication between user equipment (UE) without unnecessary routing via the network infrastructure. This architecture will result in higher throughputs than conventional cellular networks, but with the increased potential for co-channel interference induced by randomly located cellular and D2D UEs. The physical channels which constitute D2D communications can be expected to be complex in nature, experiencing both line-of-sight (LOS) and non-LOS (NLOS) conditions across closely located D2D pairs. As well as this, given the diverse range of operating environments, they may also be subject to clustering of the scattered multipath contribution, i.e., propagation characteristics which are quite dissimilar to conventional Rayeligh fading environments. To address these challenges, we consider two recently proposed generalized fading models, namely $\kappa-\mu$ and $\eta-\mu$, to characterize the fading behavior in D2D communications. Together, these models encompass many of the most widely encountered and utilized fading models in the literature such as Rayleigh, Rice (Nakagami-$n$), Nakagami-$m$, Hoyt (Nakagami-$q$) and One-Sided Gaussian. Using stochastic geometry we evaluate the rate and bit error probability of D2D networks under generalized fading conditions. Based on the analytical results, we present new insights into the trade-offs between the reliability, rate, and mode selection under realistic operating conditions. Our results suggest that D2D mode achieves higher rates over cellular link at the expense of a higher bit error probability. Through numerical evaluations, we also investigate the performance gains of D2D networks and demonstrate their superiority over traditional cellular networks.Comment: Submitted to IEEE Transactions on Wireless Communication

Efficient state-space inference of periodic latent force models

Latent force models (LFM) are principled approaches to incorporating solutions to differen-tial equations within non-parametric inference methods. Unfortunately, the developmentand application of LFMs can be inhibited by their computational cost, especially whenclosed-form solutions for the LFM are unavailable, as is the case in many real world prob-lems where these latent forces exhibit periodic behaviour. Given this, we develop a newsparse representation of LFMs which considerably improves their computational efficiency,as well as broadening their applicability, in a principled way, to domains with periodic ornear periodic latent forces. Our approach uses a linear basis model to approximate onegenerative model for each periodic force. We assume that the latent forces are generatedfrom Gaussian process priors and develop a linear basis model which fully expresses thesepriors. We apply our approach to model the thermal dynamics of domestic buildings andshow that it is effective at predicting day-ahead temperatures within the homes. We alsoapply our approach within queueing theory in which quasi-periodic arrival rates are mod-elled as latent forces. In both cases, we demonstrate that our approach can be implemented efficiently using state-space methods which encode the linear dynamic systems via LFMs.Further, we show that state estimates obtained using periodic latent force models can re-duce the root mean squared error to 17% of that from non-periodic models and 27% of thenearest rival approach which is the resonator model (S ̈arkk ̈a et al., 2012; Hartikainen et al.,2012.

The spectral analysis of nonstationary categorical time series using local spectral envelope

Most classical methods for the spectral analysis are based on the assumption that the time series is stationary. However, many time series in practical problems shows nonstationary behaviors. The data from some fields are huge and have variance and spectrum which changes over time. Sometimes,we are interested in the cyclic behavior of the categorical-valued time series such as EEG sleep state data or DNA sequence, the general method is to scale the data, that is, assign numerical values to the categories and then use the periodogram to find the cyclic behavior. But there exists numerous possible scaling. If we arbitrarily assign the numerical values to the categories and proceed with a spectral analysis, then the results will depend on the particular assignment. We would like to find the all possible scaling that bring out all of the interesting features in the data. To overcome these problems, there have been many approaches in the spectral analysis. Our goal is to develop a statistical methodology for analyzing nonstationary categorical time series in the frequency domain. In this dissertation, the spectral envelope methodology is introduced for spectral analysis of categorical time series. This provides the general framework for the spectral analysis of the categorical time series and summarizes information from the spectrum matrix. To apply this method to nonstationary process, I used the TBAS(Tree-Based Adaptive Segmentation) and local spectral envelope based on the piecewise stationary process. In this dissertation,the TBAS(Tree-Based Adpative Segmentation) using distance function based on the Kullback-Leibler divergence was proposed to find the best segmentation

Efficient State-Space Inference of Periodic Latent Force Models

Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational cost, especially when closed-form solutions for the LFM are unavailable, as is the case in many real world problems where these latent forces exhibit periodic behaviour. Given this, we develop a new sparse representation of LFMs which considerably improves their computational efficiency, as well as broadening their applicability, in a principled way, to domains with periodic or near periodic latent forces. Our approach uses a linear basis model to approximate one generative model for each periodic force. We assume that the latent forces are generated from Gaussian process priors and develop a linear basis model which fully expresses these priors. We apply our approach to model the thermal dynamics of domestic buildings and show that it is effective at predicting day-ahead temperatures within the homes. We also apply our approach within queueing theory in which quasi-periodic arrival rates are modelled as latent forces. In both cases, we demonstrate that our approach can be implemented efficiently using state-space methods which encode the linear dynamic systems via LFMs. Further, we show that state estimates obtained using periodic latent force models can reduce the root mean squared error to 17% of that from non-periodic models and 27% of the nearest rival approach which is the resonator model.Comment: 61 pages, 13 figures, accepted for publication in JMLR. Updates from earlier version occur throughout article in response to JMLR review