Remarks on the paper by R. Narayana Iyengar and K. T. Sundara Raja Iyengar, “A nonstationary random process model for earthquake accelerograms”

1970 ◽  
Vol 60 (2) ◽  
pp. 671-671
Author(s):  
Patricio Ruiz
Keyword(s):  
Random Process ◽  
Process Model ◽  
Nonstationary Random Process ◽  
Earthquake Accelerograms

Strongly Anisotropic Rough Surfaces

1979 ◽  
Vol 101 (1) ◽  
pp. 15-20 ◽  
Author(s):  
A. W. Bush ◽  
R. D. Gibson ◽  
G. P. Keogh
Keyword(s):  
Random Process ◽  
Rough Surface ◽  
Contact Area ◽  
Process Model ◽  
Rough Surfaces ◽  
Plasticity Index ◽  
Real Contact Area ◽  
Elastic Contact ◽  
Elastic Plastic ◽  
Real Contact

The statistics of a strongly anisotropic rough surface are briefly described. The elastic contact of rough surfaces is treated by approximating the summits of a random process model by parabolic ellipsoids and applying the Hertzian solution for their deformation. Load and real contact area are derived as functions of the separation and for all separations the load is found to be approximately proportional to the contact area. The limits of elastic/plastic contact are discussed in terms of the plasticity index.

New Metrics for Validation of Data-Driven Random Process Models in Uncertainty Quantification

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
Hongyi Xu ◽  
Zhen Jiang ◽  
Daniel W. Apley ◽  
Wei Chen
Keyword(s):  
Uncertainty Quantification ◽  
Random Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Experimental Tests ◽  
Process Models ◽  
Data Driven ◽  
Gaussian Copula ◽  
High Dimensional ◽  
Marginal Distributions

Data-driven random process models have become increasingly important for uncertainty quantification (UQ) in science and engineering applications, due to their merit of capturing both the marginal distributions and the correlations of high-dimensional responses. However, the choice of a random process model is neither unique nor straightforward. To quantitatively validate the accuracy of random process UQ models, new metrics are needed to measure their capability in capturing the statistical information of high-dimensional data collected from simulations or experimental tests. In this work, two goodness-of-fit (GOF) metrics, namely, a statistical moment-based metric (SMM) and an M-margin U-pooling metric (MUPM), are proposed for comparing different stochastic models, taking into account their capabilities of capturing the marginal distributions and the correlations in spatial/temporal domains. This work demonstrates the effectiveness of the two proposed metrics by comparing the accuracies of four random process models (Gaussian process (GP), Gaussian copula, Hermite polynomial chaos expansion (PCE), and Karhunen–Loeve (K–L) expansion) in multiple numerical examples and an engineering example of stochastic analysis of microstructural materials properties. In addition to the new metrics, this paper provides insights into the pros and cons of various data-driven random process models in UQ.

scholarly journals COMPUTER SIMULATION OF DETERMINING SILTATION VOLUMES OF WATER RESERVOIR STORAGE ON THE AKSAY RIVER

2020 ◽  
Vol 46 (4) ◽  
pp. 102-112
Author(s):  
M. R. Magomedova ◽  
Z. A. Kurbanova ◽  
B. A. Shangereeva
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Random Process ◽  
Process Model ◽  
Probabilistic Approach ◽  
Water Reservoir ◽  
Temporal Correlation ◽  
Programming System ◽  
Reservoir Storage ◽  
Hydrological System

Objectives. The development of a mathematical model for the increased turbidity zones of the Aksay river in order to determine the siltation volumes of the Aksay water reservoir storage.Method. The mathematical model is developed using the theory of probability and the theory of random process outliers. The model takes the normal distribution of the horizontal and vertical components of the instantaneous flow velocities into account, as well as the Rayleigh law of the distribution of their maxima. The proposed model is used to calculate the “turbidity tail” of the Aksay river.Result. Due to the multifactorial nature of the continuously associated processes of siltation and deposition of suspended and bottom sediments in the upper pounds of the Aksay reservoir storage hydrological system, a mathematical model of the reservoir accretion process is developed. This model provides the reliability of accretion forecasting with spatial and temporal correlation with the siltation process model, which is actually feasible on the basis of computer simulation.Conclusion. The developed model, which is based on a probabilistic approach and the theory of random process outliers, reflects the overall process of sediment transport in open channels. The development and execution of simulation programmes is carried out using the Microsoft Developer Studio (MDS) and the Fortran Power Station algorithmic language, which comprises not only a programming system, but also a set of tools for supporting large software projects integrated into MDS. 

Information Theoretic Equivalent Bandwidths of Random Processes and Their Applications

2007 ◽  
Vol 46 (02) ◽  
pp. 110-116 ◽  
Author(s):  
S. Kikkawa ◽  
H. Yoshida
Keyword(s):  
Random Process ◽  
Random Processes ◽  
Systolic Murmur ◽  
Nonstationary Random Process ◽  
Frequency Distributions ◽  
Copula Theory ◽  
Information Theoretic ◽  
Time Frequency ◽  
New Class ◽  
Stationary Random Processes

Summary Objectives : Since most of the biomedical signals, such as electroencephalogram (EEG), electromyogram (EMG) and phonocardiogram (PCG), are nonstationary random processes, the time-frequency analysis has recently been extensively applied to those signals in order to achieve precise characterization and classification. In this paper, we have first defined a new class of information theoretic equivalent bandwidths (EBWs) of stationary random processes, then instantaneous EBWs (IEBWs) using nonnegative time-frequenc distributions have been defined in order to track the change of the EBW of a nonstationary random process. Methods : The new class of EBWs which includes spectral flatness measure (SFM) for stationary random processes is defined by using generalized Burg entropy. Generalized Burg entropy is derived from the relation between Rényi entropy and Rényi information divergence of order α. In order to track the change of EBWs of a nonstationary random process, the IEBWs are defined on the nonnegative time-frequency distributions, which are constructed by the Copula theory. Results : We evaluate the IEBWs for a first order stationary auto-regressive (AR) process and three types of time-varying AR processes. The results show that the IEBWs proposed here properly represent a signal bandwidth. In practical application to PCGs, the proposed method was successful in extracting the information that the bandwidth of the innocent systolic murmur was much smaller than that of the abnormal systolic murmur. Conclusions : We have defined new information theoretic EBWs and have proposed a novel method to track the change of the IEBWs. Some computer simulation showed effectiveness of the methods. Applying the IEBWs to PCGs, we could extract some features of a systolic murmur.

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