Simulated annealing wavelet estimation via fourth‐order cumulant matching

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1939-1948 ◽  
Author(s):  
Danilo R. Velis ◽  
Tadeusz J. Ulrych
Keyword(s):  
Simulated Annealing ◽  
Fourth Order ◽  
Simulated Annealing Algorithm ◽  
Numerical Solutions ◽  
Mean Squared Error ◽  
Real Data ◽  
Hybrid Strategy ◽  
Minimum Mean Squared Error ◽  
Highly Nonlinear ◽  
Fourth Order Cumulant

The fourth‐order cumulant matching method has been developed recently for estimating a mixed‐phase wavelet from a convolutional process. Matching between the trace cumulant and the wavelet moment is done in a minimum mean‐squared error sense under the assumption of a non‐Gaussian, stationary, and statistically independent reflectivity series. This leads to a highly nonlinear optimization problem, usually solved by techniques that require a certain degree of linearization, and that invariably converge to the minimum closest to the initial model. Alternatively, we propose a hybrid strategy that makes use of a simulated annealing algorithm to provide reliability of the numerical solutions by reducing the risk of being trapped in local minima. Beyond the numerical aspect, the reliability of the derived wavelets depends strongly on the amount of data available. However, by using a multidimensional taper to smooth the trace cumulant, we show that the method can be used even in a trace‐by‐trace implementation, which is very important from the point of view of stationarity and consistency. We demonstrate the viability of the method under several reflectivity models. Finally, we illustrate the hybrid strategy using marine and field real data examples. The consistency of the results is very encouraging because the improved cumulant matching strategy we describe can be effectively used with a limited amount of data.

Mixed‐phase wavelet estimation using fourth‐order cumulants

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 1042-1051 ◽  
Author(s):  
Gregory D. Lazear
Keyword(s):  
Fourth Order ◽  
Mean Squared Error ◽  
Moving Average ◽  
High Order ◽  
Mixed Phase ◽  
Order Moment ◽  
Covariance Functions ◽  
Minimum Mean Squared Error ◽  
Air Gun ◽  
Fourth Order Cumulant

In recent years methods have been developed in the field of high‐order statistics that can reliably estimate a mixed‐phase wavelet from the noisy output of a convolutional process. These methods use high‐order covariance functions of the data called cumulants, which retain phase information and allow recovery of the wavelet. The assumption is that the reflection coefficient series is a non‐Gaussian, stationary, and statistically independent random process. The method described in this paper uses the fourth‐order cumulant of the data, and a moving‐average, noncausal parametric model for the wavelet. The fourth‐order moment function of this wavelet matches the fourth‐order cumulant of the data in a minimum mean‐squared error sense. Numerical simulations demonstrate that the method can accurately estimate mixed‐phase wavelets, even when the reflectivity has a distribution close to Gaussian. Three seismic data examples demonstrate possible uses of the method. In the first two, an average source wavelet is estimated from marine shot records acquired with air gun and water gun sources, respectively. These wavelets compare favorably with recorded far‐field signatures modified for receiver ghosting. In the third example, a wavelet estimate from marine stacked data is used to correct the phase of the stacked section, resulting in zero‐phase water bottom and salt top reflections.

scholarly journals Joint influence of measurement errors and randomized response technique on mean estimation under stratified double sampling

2021 ◽  
Vol 5 (1) ◽  
pp. 192-199
Author(s):  
Ronald Onyango ◽  
◽  
Brian Oduor ◽  
Francis Odundo ◽  
◽  
...  
Keyword(s):  
Measurement Errors ◽  
Mean Squared Error ◽  
Numerical Study ◽  
Real Data ◽  
Auxiliary Variable ◽  
Randomized Response Technique ◽  
Randomized Response ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Joint Influence

The present study proposes a generalized mean estimator for a sensitive variable using a non-sensitive auxiliary variable in the presence of measurement errors based on the Randomized Response Technique (RRT). Expressions for the bias and mean squared error for the proposed estimator are correctly derived up to the first order of approximation. Furthermore, the optimum conditions and minimum mean squared error for the proposed estimator are determined. The efficiency of the proposed estimator is studied both theoretically and numerically using simulated and real data sets. The numerical study reveals that the use of the Randomized Response Technique (RRT) in a survey contaminated with measurement errors increases the variances and mean squared errors of estimators of the finite population mean.

scholarly journals Multiple-Try Simulated Annealing Algorithm for Global Optimization

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Wei Shao ◽  
Guangbao Guo
Keyword(s):  
Global Optimization ◽  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Optimization Problems ◽  
Real Data ◽  
Global Optimum ◽  
Stochastic Optimization Algorithm ◽  
Multiple Try Metropolis Algorithm ◽  
Quasi Newton ◽  
Cooling Schedule

Simulated annealing is a widely used algorithm for the computation of global optimization problems in computational chemistry and industrial engineering. However, global optimum values cannot always be reached by simulated annealing without a logarithmic cooling schedule. In this study, we propose a new stochastic optimization algorithm, i.e., simulated annealing based on the multiple-try Metropolis method, which combines simulated annealing and the multiple-try Metropolis algorithm. The proposed algorithm functions with a rapidly decreasing schedule, while guaranteeing global optimum values. Simulated and real data experiments including a mixture normal model and nonlinear Bayesian model indicate that the proposed algorithm can significantly outperform other approximated algorithms, including simulated annealing and the quasi-Newton method.

scholarly journals An Improved HotSpot Algorithm and Its Application to Sandstorm Data in Inner Mongolia

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Ren Qing-dao-er-ji ◽  
Rui Pang ◽  
Yue Chang
Keyword(s):  
Simulated Annealing ◽  
Association Rules ◽  
Inner Mongolia ◽  
Simulated Annealing Algorithm ◽  
Solution Space ◽  
Real Data ◽  
Wine Quality ◽  
Minimum Support ◽  
Support Threshold ◽  
Annealing Algorithm

HotSpot is an algorithm that can directly mine association rules from real data. Aiming at the problem that the support threshold in the algorithm cannot be set accurately according to the actual scale of the dataset and needs to be set artificially according to experience, this paper proposes a dynamic optimization algorithm with minimum support threshold setting: S_HotSpot algorithm. The algorithm combines simulated annealing algorithm with HotSpot algorithm and uses the global search ability of simulated annealing algorithm to dynamically optimize the minimum support in the solution space. Finally, the Inner Mongolia sandstorm dataset is used for experiment while the wine quality dataset is used for verification, and the association rules screening indicators are set for the mining results. The results show that S_HotSpot algorithm can not only dynamically optimize the selection of support but also improve the quality of association rules as it is mining reasonable number of rules.

Design of Spring Coupling for High Q, High Frequency MEMS Filters

2006 ◽  
Author(s):  
Mohammed Shalaby ◽  
Mohammed Abdelmoneum ◽  
Kazuhiro Saitou
Keyword(s):  
Simulated Annealing ◽  
Simulated Annealing Algorithm ◽  
Beam Width ◽  
Center Frequency ◽  
Coupling Beam ◽  
Flexural Mode ◽  
Resonance Modes ◽  
Highly Nonlinear ◽  
Wine Glass ◽  
Annealing Algorithm

This paper presents the design optimization of the coupling beam of wine glass (WG) mode micromechanical disk filters using the simulated annealing algorithm. The filter under consideration consists of two identical wine-glass mode disk resonators, mechanically coupled by a flexural mode beam. Such coupled two-resonator system exhibits two mechanical resonance modes with closely spaced frequencies that define the filter passband. The frequencies of the constituent resonators determine the center frequency of the filter, while the bandwidth is determined by the stiffness and location of attachment of the coupling beam. The goal is to design a filter with a commonly used bandwidth, namely 100 kHz. The design variables that control the bandwidth value are the beam length, the beam width, and the location of attachment of the coupling beam from the center. The simulated annealing algorithm is used to solve the optimization problem, since the governing dynamic equations of the resonator-coupling system are highly nonlinear. The resulting optimum design is simulated using the finite element method, which confirms the achievement of the desired center frequency and bandwidth.

scholarly journals Spatial Warped Gaussian Processes: Estimation and Efficient Field Reconstruction

2021 ◽  
Author(s):  
Gareth William Peters ◽  
Ido Nevat ◽  
Sai Ganesh Nagarajan ◽  
Tomoko Matsui
Keyword(s):  
Gaussian Processes ◽  
Random Fields ◽  
Mean Squared Error ◽  
Real Data ◽  
Statistical Properties ◽  
Process Models ◽  
Multiple Point ◽  
Field Reconstruction ◽  
Minimum Mean Squared Error ◽  
Non Gaussian

A class of models for non-Gaussian spatial random fields is explored for spatial field reconstruction in environmental and sensor network monitoring. The family of models explored utilises a class of transformation functions known as the Tukey g-and-h transformations to create a family of warped spatial Gaussian process models which can support various desirable features such as flexible marginal distributions, which can be skewed, leptokurtic and/or heavy-tailed. The resulting model is widely applicable in a range of spatial field reconstruction applications. To utilise the model in applications in practice, it is important to carefully characterise the statistical properties of the Tukey g-and-h random fields. In this work, we both study the properties of the resulting warped Gaussian processes as well as using the characterising statistical properties of the warped processes to obtain flexible spatial field reconstructions. In this regard, we derive five different estimators for various important quantities often considered in spatial field reconstruction problems. These include the multi-point Minimum Mean Squared Error (MMSE) estimators; the multiple point Maximum A-Posteriori (MAP) estimators; an efficient class of multiple-point linear estimators based on the Spatial-Best Linear Unbiased (S-BLUE) estimators; and two multi-point threshold exceedance based estimators, namely the Spatial Regional and Level Exceedance estimators. Simulation results and real data examples show the benefits of using the Tukey g-and-h transformation as opposed to standard Gaussian spatial random fields in a real data application for environmental monitoring.

scholarly journals A Novel Bottom-Up/Top-Down Hybrid Strategy-Based Fast Sequential Fault Diagnosis Method

Electronics ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 1441
Author(s):  
Jingyuan Wang ◽  
Zhen Liu ◽  
Xiaowu Chen ◽  
Bing Long ◽  
Chenglin Yang ◽  
...  
Keyword(s):  
Simulated Annealing ◽  
Fault Diagnosis ◽  
Simulated Annealing Algorithm ◽  
Heuristic Algorithms ◽  
Optimal Decision ◽  
Bottom Up ◽  
Hybrid Strategy ◽  
Diagnosis Method ◽  
Annealing Algorithm ◽  
Karnaugh Map

Sequential fault diagnosis is a kind of important fault diagnosis method for large scale complex systems, and generating an excellent fault diagnosis strategy is critical to ensuring the performance of sequential diagnosis. However, with the system complexity increasing, the complexity of fault diagnosis tree increases sharply, which makes it extremely difficult to generate an optimal diagnosis strategy. Especially, because the existing methods need massive redundancy iteration and repeated calculation for the state parameters of nodes, the resulting diagnosis strategy is often inefficient. To address this issue, a novel fast sequential fault diagnosis method is proposed. In this method, we present a new bottom-up search idea based on Karnaugh map, SVM and simulated annealing algorithm. It combines failure sources to generate states and a Karnaugh map is used to judge the logic of every state. Eigenvalues of SVM are obtained quickly through the simulated annealing algorithm, then SVM is used to eliminate the less useful state. At the same time, the bottom-up method and cost heuristic algorithms are combined to generate the optimal decision tree. The experiments show that the calculation time of the method is shorter than the time of previous algorithms, and a smaller test cost can be obtained when the number of samples is sufficient.

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