GR_EST: An OCTAVE/MATLAB Toolbox to Estimate Gutenberg–Richter Law Parameters and Their Uncertainties

2020 ◽  
Vol 92 (1) ◽  
pp. 508-516
Author(s):  
Matteo Taroni ◽  
Jacopo Selva
Keyword(s):  
Parameter Estimation ◽  
Seismic Hazard ◽  
Source Code ◽  
Time Varying ◽  
Relative Uncertainty ◽  
Matlab Toolbox ◽  
Distribution Parameters ◽  
Earthquake Size ◽  
Functional Forms ◽  
Seismic Catalogs

Abstract The estimation of the earthquake size distribution parameters is one of the most important parts in any seismic hazard study. GR_EST toolbox is a source code written for OCTAVE/MATLAB (Eaton et al., 2019; MATLAB, 2019) that allows estimating these parameters in a proper way, including the estimation of the associated uncertainties. The toolbox contains functions to make the parameter estimation both for instrumental and historical seismic catalogs, also considering time-varying completeness for magnitudes. Different functional forms for the magnitude–frequency distribution and different strategies for the estimation of its parameters and relative uncertainty are included. To guide the seismologists into the use of this toolbox, a set of complete examples is provided, to be used as “how to” use cases.

scholarly journals Wavelet multi-resolution approximation of time-varying frame structure

2018 ◽  
Vol 10 (8) ◽  
pp. 168781401879559 ◽  
Author(s):  
Min Xiang ◽  
Feng Xiong ◽  
Yuanfeng Shi ◽  
Kaoshan Dai ◽  
Zhibin Ding
Keyword(s):  
Parameter Estimation ◽  
Degrees Of Freedom ◽  
Structural Parameters ◽  
Identification Problem ◽  
Frame Structure ◽  
Structural Parameter ◽  
Time Varying ◽  
Engineering Structures ◽  
Time Frequency ◽  
Non Parametric

Engineering structures usually exhibit time-varying behavior when subjected to strong excitation or due to material deterioration. This behavior is one of the key properties affecting the structural performance. Hence, reasonable description and timely tracking of time-varying characteristics of engineering structures are necessary for their safety assessment and life-cycle management. Due to its powerful ability of approximating functions in the time–frequency domain, wavelet multi-resolution approximation has been widely applied in the field of parameter estimation. Considering that the damage levels of beams and columns are usually different, identification of time-varying structural parameters of frame structure under seismic excitation using wavelet multi-resolution approximation is studied in this article. A time-varying dynamical model including both the translational and rotational degrees of freedom is established so as to estimate the stiffness coefficients of beams and columns separately. By decomposing each time-varying structural parameter using one wavelet multi-resolution approximation, the time-varying parametric identification problem is transformed into a time-invariant non-parametric one. In solving the high number of regressors in the non-parametric regression program, the modified orthogonal forward regression algorithm is proposed for significant term selection and parameter estimation. This work is demonstrated through numerical examples which consider both gradual variation and abrupt changes in the structural parameters.

scholarly journals Methods for Parameter Estimation of the Lorenz Functional Forms and Compare Them Based on Household Expenses Data

2008 ◽  
Vol 5 (1) ◽  
pp. 57-74
Author(s):  
A. Mojiri ◽  
R. Mohtashami Borzadaran ◽  
Y. Waghei ◽  
◽  
◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Functional Forms

scholarly journals Asymmetric Dependence Analysis of International Crude Oil Spot and Futures Based on the Time Varying Copula-GARCH

2015 ◽  
Vol 8 (1) ◽  
pp. 463-467
Author(s):  
He Xin ◽  
Zhang Jun
Keyword(s):  
Parameter Estimation ◽  
Crude Oil ◽  
Significant Influence ◽  
Tail Dependence ◽  
Sliding Window ◽  
Dependence Structure ◽  
Dependence Analysis ◽  
Time Varying ◽  
Daily Return ◽  
Asymmetric Dependence

Taking daily return of international crude oil spot and futures as sample, this paper analyzed the time varying and asymmetric dependence structure of them by time varying Copula-GARCH model based on sliding window and semi parameter estimation. This paper analyzed the regular changing between dependence structure of crude oil spot and futures and the return fluctuation, and confirmed that there is significant time varying asymmetric tail dependence. This paper found that the size of the sliding window had no significant influence on the conclusion, and the data of weekly return is more suitable for analysis of the trend of dependence structure of spot.

scholarly journals Flowtrace: simple visualization of coherent structures in biological fluid flows

2016 ◽  
Author(s):  
William Gilpin ◽  
Vivek N. Prakash ◽  
Manu Prakash
Keyword(s):  
Coherent Structures ◽  
Collective Motion ◽  
Biological Fluid ◽  
Source Code ◽  
Fluid Flows ◽  
Flow Structures ◽  
Time Varying ◽  
Middle Ground ◽  
Complex Flow ◽  
User Intervention

1AbstractWe present a simple, intuitive algorithm for visualizing time-varying flow fields that can reveal complex flow structures with minimal user intervention. We apply this technique to a variety of biological systems, including the swimming currents of invertebrates and the collective motion of swarms of insects. We compare our results to more experimentally-diffcult and mathematically-sophisticated techniques for identifying patterns in fluid flows, and suggest that our tool represents an essential “middle ground” allowing experimentalists to easily determine whether a system exhibits interesting flow patterns and coherent structures without the need to resort to more intensive techniques. In addition to being informative, the visualizations generated by our tool are often striking and elegant, illustrating coherent structures directly from videos without the need for computational overlays. Our tool is available as fully-documented open-source code available for MATLAB, Python, or ImageJ at www.flowtrace.org.

scholarly journals Neglect Of Parameter Estimation Uncertainty Can Significantly Overestimate Structural Reliability

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Árpád Rózsás ◽  
Miroslav Sýkora
Keyword(s):  
Parameter Estimation ◽  
Bayesian Statistics ◽  
Failure Probability ◽  
Structural Reliability ◽  
Probabilistic Models ◽  
Estimation Uncertainty ◽  
Point Estimates ◽  
Distribution Parameters ◽  
Order Of Magnitude ◽  
Parameter Estimation Uncertainty

Abstract Parameter estimation uncertainty is often neglected in reliability studies, i.e. point estimates of distribution parameters are used for representative fractiles, and in probabilistic models. A numerical example examines the effect of this uncertainty on structural reliability using Bayesian statistics. The study reveals that the neglect of parameter estimation uncertainty might lead to an order of magnitude underestimation of failure probability.

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