Inversion of fracture density from field seismic velocities using artificial neural networks

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 534-545 ◽  
Author(s):  
Fred K. Boadu
Keyword(s):  
Neural Network ◽  
Least Squares ◽  
Displacement Discontinuity ◽  
Fracture Model ◽  
Seismic Velocities ◽  
Fracture Density ◽  
S Wave ◽  
Least Squares Fitting ◽  
The Neural Network ◽  
Fitting In

The inversion of fracture density from field measured P- and S-wave seismic velocities is performed using a neural network trained with an output from the modified displacement discontinuity fracture model. The basic idea is to use input‐output pairs generated by the fracture model to train the neural network. Once the neural network is trained, inversion of fracture density from field‐measured seismic velocities is performed very quickly. The overall performance of the neural network in the inversion process is assessed by means of a loss function. The results indicate that both sources of field information (P- and S-wave velocities) predict the field fracture density with reasonable accuracy. The performance of the neural network was compared to the prediction from least‐squares fitting. It is shown that the neural network out performs the least‐squares fitting in predicting the field‐fracture density values.

Fitting Weighted Total Least-Squares Planes and Parallel Planes to Support Tolerancing Standards

2012 ◽  
Author(s):  
Craig M. Shakarji ◽  
Vijay Srinivasan
Keyword(s):  
Least Squares ◽  
Point Contact ◽  
Coordinate Measuring Machine ◽  
Total Least Squares ◽  
Point Sampling ◽  
Least Squares Fitting ◽  
Weighted Total Least Squares ◽  
Measuring Machine ◽  
Fitting In ◽  
Value Decomposition

We present elegant algorithms for fitting a plane, two parallel planes (corresponding to a slot or a slab) or many parallel planes in a total (orthogonal) least-squares sense to coordinate data that is weighted. Each of these problems is reduced to a simple 3×3 matrix eigenvalue/eigenvector problem or an equivalent singular value decomposition problem, which can be solved using reliable and readily available commercial software. These methods were numerically verified by comparing them with brute-force minimization searches. We demonstrate the need for such weighted total least-squares fitting in coordinate metrology to support new and emerging tolerancing standards, for instance, ISO 14405-1:2010. The widespread practice of unweighted fitting works well enough when point sampling is controlled and can be made uniform (e.g., using a discrete point contact Coordinate Measuring Machine). However, we demonstrate that nonuniformly sampled points (arising from many new measurement technologies) coupled with unweighted least-squares fitting can lead to erroneous results. When needed, the algorithms presented also solve the unweighted cases simply by assigning the value one to each weight. We additionally prove convergence from the discrete to continuous cases of least-squares fitting as the point sampling becomes dense.

On the Enduring Appeal of Least-Squares Fitting in Computational Coordinate Metrology

2011 ◽  
Vol 12 (1) ◽  
Author(s):  
Vijay Srinivasan ◽  
Craig M. Shakarji ◽  
Edward P. Morse
Keyword(s):  
Least Squares ◽  
Geometric Features ◽  
Coordinate Measuring Machines ◽  
Historical Survey ◽  
Least Squares Fitting ◽  
Coordinate Metrology ◽  
International Standardization ◽  
Manufacturing Applications ◽  
Fitting In ◽  
Current Practices

The vast majority of points collected with coordinate measuring machines are not used in isolation; rather, collections of these points are associated with geometric features through fitting routines. In manufacturing applications, there are two fundamental questions that persist about the efficacy of this fitting—first, do the points collected adequately represent the surface under inspection; and second, does the association of substitute (fitted) geometry with the points meet criteria consistent with the standardized geometric specification of the product. This paper addresses the second question for least-squares fitting both as a historical survey of past and current practices, and as a harbinger of the influence of new specification criteria under consideration for international standardization. It also touches upon a set of new issues posed by the international standardization on the first question as related to sampling and least-squares fitting.

scholarly journals Polynomial least squares fitting in the Bernstein basis

2010 ◽  
Vol 433 (7) ◽  
pp. 1254-1264 ◽  
Author(s):  
Ana Marco ◽  
José-Javier Martı´nez
Keyword(s):  
Least Squares ◽  
Bernstein Basis ◽  
Least Squares Fitting ◽  
Fitting In

Research of Oilfield Production Forecast Based on Least Squares Fitting and Improved BP Neural Network

2013 ◽  
Vol 333-335 ◽  
pp. 1456-1460 ◽  
Author(s):  
Wen Bo Na ◽  
Zhi Wei Su ◽  
Ping Zhang
Keyword(s):  
Neural Network ◽  
Least Squares ◽  
Curve Fitting ◽  
Bp Neural Network ◽  
Least Squares Method ◽  
Forecast Error ◽  
Production Forecast ◽  
Least Squares Fitting ◽  
Weak Points ◽  
Lm Algorithm

A new method which is least squares fitting combined with improved BP neural network based on LM algorithm was put forward. In order to overcome the weak points that easy to fall into local minimum, slow convergence of traditional BP neural network, we use LM algorithm to improve it. Least-squares curve fitting can be used to reflect the overall trend of the data changes, so we adopted least squares method firstly to make curve fitting for sample data firstly. Then, we corrected the fitting error by the improved BP Neural Network which has the advantages that reflecting external factors. Finally, the fitted values and error correction values were added to get oilfield production forecast. The results show that the oilfield production forecast error is significantly lower than the single curve fitting, BP Neural Network or LMBP.

A Hybrid Modeling Technique for Partially-Known Systems Using Linear Regression and Neural Network

2009 ◽  
Author(s):  
Andrew J. Joslin ◽  
Chengying Xu
Keyword(s):  
Neural Network ◽  
Linear Regression ◽  
Least Squares ◽  
Process Model ◽  
Modeling Method ◽  
Hybrid Modeling ◽  
Model Description ◽  
Least Squares Regression ◽  
The Neural Network ◽  
Macro Scale

In this paper a hybrid modeling and system identification method, combining linear least squares regression and artificial neural network techniques, is presented to model a type of dynamic systems which have an incomplete analytical model description. This approach in modeling nonlinear, partially-understood systems is particularly useful to the study of manufacturing processes, where the linear regression portion of the hybrid model is established using a known mathematical model for the process and the neural network is constructed using the residuals from the least squares regression, therefore ensuring a more precise process model for the specific machining setup, tooling selection, workpiece properties, etc. In this paper the method is mathematically proven to give regression coefficients close to those which would be found if only a regression had been performed. The modeling method is then simulated for a macro-scale hard turning process, and the result proves the effectiveness of the proposed hybrid modeling method.

Incorporation of Neural Network State Estimator for GPS Attitude Determination

2004 ◽  
Vol 57 (1) ◽  
pp. 117-134 ◽  
Author(s):  
Dah-Jing Jwo ◽  
Chun-Fan Pai
Keyword(s):  
Neural Network ◽  
Kalman Filter ◽  
Least Squares ◽  
Kalman Filtering ◽  
Attitude Determination ◽  
Least Squares Method ◽  
State Estimator ◽  
Estimation Errors ◽  
Network State ◽  
The Neural Network

The Global Positioning System (GPS) can be employed as a free attitude determination interferometer when carrier phase measurements are utilized. Conventional approaches for the baseline vectors are essentially based on the least-squares or Kalman filtering methods. The raw attitude solutions are inherently noisy if the solutions of baseline vectors are obtained based on the least-squares method. The Kalman filter attempts to minimize the error variance of the estimation errors and will provide the optimal result while it is required that the complete a priori knowledge of both the process noise and measurement noise covariance matrices are available. In this article, a neural network state estimator, which replaces the Kalman filter, will be incorporated into the attitude determination mechanism for estimating the attitude angles from the noisy raw attitude solutions. Employing the neural network estimator improves robustness compared to the Kalman filtering method when uncertainty in noise statistical knowledge exists. Simulation is conducted and a comparative evaluation based on the neural network estimator and Kalman filter is provided.

scholarly journals A Recursive Bifurcation Model for Predicting the Peak of COVID-19 Virus Spread in United States and Germany

2020 ◽  
Author(s):  
Julia Shen
Keyword(s):  
United States ◽  
Decision Making ◽  
South Korea ◽  
Least Squares ◽  
Nonlinear Least Squares ◽  
Peak Time ◽  
Virus Spread ◽  
Linear Least Squares ◽  
Least Squares Fitting ◽  
Fitting In

AbstractPrediction on the peak time of COVID-19 virus spread is crucial to decision making on lockdown or closure of cities and states. In this paper we design a recursive bifurcation model for analyzing COVID-19 virus spread in different countries. The bifurcation facilitates a recursive processing of infected population through linear least-squares fitting. In addition, a nonlinear least-squares fitting is utilized to predict the future values of infected populations. Numerical results on the data from three countries (South Korea, United States and Germany) indicate the effectiveness of our approach.

scholarly journals A recursive bifurcation model for early forecasting of COVID-19 virus spread in South Korea and Germany

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Julia Shen
Keyword(s):  
South Korea ◽  
Least Squares ◽  
Nonlinear Least Squares ◽  
Future Research ◽  
Logistic Growth ◽  
Virus Spread ◽  
Least Squares Fitting ◽  
Fitting Procedure ◽  
Logistic Growth Model ◽  
Fitting In

AbstractEarly forecasting of COVID-19 virus spread is crucial to decision making on lockdown or closure of cities, states or countries. In this paper we design a recursive bifurcation model for analyzing COVID-19 virus spread in different countries. The bifurcation facilitates recursive processing of infected population through linear least-squares fitting. In addition, a nonlinear least-squares fitting procedure is utilized to predict the future values of infected populations. Numerical results on the data from two countries (South Korea and Germany) indicate the effectiveness of our approach, compared to a logistic growth model and a Richards model in the context of early forecast. The limitation of our approach and future research are also mentioned at the end of this paper.

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