Adaptive Smoothing Method Based on Fuzzy Theory Study and Realization

A simple and implementable two-loop smoothing method for semi-infinite minimax problem is given with the discretization parameter and the smoothing parameter being updated adaptively. We prove the global convergence of the algorithm when the steepest descent method or a BFGS type quasi-Newton method is applied to the smooth subproblems. The strategy for updating the smoothing parameter can not only guarantee the convergence of the algorithm but also considerably reduce the ill-conditioning caused by increasing the value of the smoothing parameter. Numerical tests show that the algorithm is robust and effective.

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Adaptive Smoothing of Spectroscopic Data by a Linear Mean-Square Estimation

Applied Spectroscopy ◽

10.1366/0003702844554305 ◽

1984 ◽

Vol 38 (1) ◽

pp. 49-58 ◽

Cited By ~ 49

Author(s):

Satoshi Kawata ◽

Shigeo Minami

Keyword(s):

Spectroscopic Data ◽

Signal To Noise Ratio ◽

Computation Time ◽

Smoothing Method ◽

Window Function ◽

Mean Square ◽

Least Mean Square ◽

Adaptive Smoothing ◽

Local Statistics ◽

Convolution Algorithm

An adaptive smoothing method based on a least mean-square estimation is developed for noise filtering of spectroscopic data. The algorithm of this method is nonrecursive and shift-varying with the local statistics of data. The mean and the variance of the observed spectrum at an individual sampled point are calculated point by point from its local mean and variance. By this method, in the resultant spectrum, the signal-to-noise ratio is maximized at any local section of the entire spectrum. Experimental results for the absorption spectrum of ammonia gas demonstrate that this method distorts less amount of signal components than the conventional smoothing method based on the polynomial curve-fitting and suppresses noise components satisfactorily. The computation time of this algorithm is rather shorter than that of the convolution algorithm with seven weighting coefficients. The a priori information for the estimation of the signal by this method are: the variance of noise, which can be attainable in the experiment; and the window function which gives the local statistics. The investigation of various types of window functions shows that the selection of the window function does not directly affect the performance of adaptive smoothing.

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Adaptive Smoothing Method, Deterministically Computable Generalized Jacobians, and the Newton Method

Journal of Optimization Theory and Applications ◽

10.1023/a:1017526207997 ◽

2001 ◽

Vol 109 (1) ◽

pp. 215-224 ◽

Cited By ~ 4

Author(s):

H. Xu

Keyword(s):

Newton Method ◽

Smoothing Method ◽

Adaptive Smoothing ◽

Generalized Jacobians

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A New Smoothed Seismicity Approach to Include Aftershocks and Foreshocks in Spatial Earthquake Forecasting: Application to the Global Mw ≥ 5.5 Seismicity

Applied Sciences ◽

10.3390/app112210899 ◽

2021 ◽

Vol 11 (22) ◽

pp. 10899

Author(s):

Matteo Taroni ◽

Aybige Akinci

Keyword(s):

Seismic Hazard ◽

Smoothing Method ◽

Earthquake Forecasting ◽

Earthquake Catalog ◽

Significant Information ◽

Adaptive Smoothing ◽

Time Space ◽

Seismicity Models ◽

Seismicity Rates ◽

Smoothed Seismicity

Seismicity-based earthquake forecasting models have been primarily studied and developed over the past twenty years. These models mainly rely on seismicity catalogs as their data source and provide forecasts in time, space, and magnitude in a quantifiable manner. In this study, we presented a technique to better determine future earthquakes in space based on spatially smoothed seismicity. The improvement’s main objective is to use foreshock and aftershock events together with their mainshocks. Time-independent earthquake forecast models are often developed using declustered catalogs, where smaller-magnitude events regarding their mainshocks are removed from the catalog. Declustered catalogs are required in the probabilistic seismic hazard analysis (PSHA) to hold the Poisson assumption that the events are independent in time and space. However, as highlighted and presented by many recent studies, removing such events from seismic catalogs may lead to underestimating seismicity rates and, consequently, the final seismic hazard in terms of ground shaking. Our study also demonstrated that considering the complete catalog may improve future earthquakes’ spatial forecast. To do so, we adopted two different smoothed seismicity methods: (1) the fixed smoothing method, which uses spatially uniform smoothing parameters, and (2) the adaptive smoothing method, which relates an individual smoothing distance for each earthquake. The smoothed seismicity models are constructed by using the global earthquake catalog with Mw ≥ 5.5 events. We reported progress on comparing smoothed seismicity models developed by calculating and evaluating the joint log-likelihoods. Our resulting forecast shows a significant information gain concerning both fixed and adaptive smoothing model forecasts. Our findings indicate that complete catalogs are a notable feature for increasing the spatial variation skill of seismicity forecasts.

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