scholarly journals Correlation effect of transformed or corrected data inversion

2021 ◽  
Author(s):  
László Balázs
Keyword(s):  
Likelihood Function ◽  
Measurement Data ◽  
Least Square Method ◽  
Estimation Procedure ◽  
Correlation Effect ◽  
Least Square ◽  
Inversion Method ◽  
Data Set ◽  
Data Inversion ◽  
Fitting Procedure

AbstractBefore performing the inversion process, the original measured data set is often transformed (corrected, smoothed, Fourier-transformed, interpolated etc.). These preliminary transformations may make the original (statistically independent) noisy measurement data correlated. The noise correlation on transformed data must be taken into account in the parameter fitting procedure (inversion) by proper derivation of likelihood function. The covariance matrix of transformed data system is no longer diagonal, so the likelihood based metrics, which determines the fitting process is also changed as well as the results of inversion. In the practice, these changes are often neglected using the “customary” estimation procedure (simple least square method) resulting wrong uncertainty estimation and sometimes biased results. In this article the consequence of neglected correlation is studied and discussed by decomposing the inversion functional to “customary” and additional part which represents the effect of correlation. The ratio of two components demonstrates the importance and justification of the inversion method modification.

Model-based control of the substrate concentration in an aeration basin using the wastewater level

1998 ◽  
Vol 37 (12) ◽  
pp. 335-342 ◽  
Author(s):  
Jacek Czeczot
Keyword(s):  
Substrate Concentration ◽  
Consumption Rate ◽  
Least Square Method ◽  
Estimation Procedure ◽  
Adaptive Controller ◽  
Open Loop ◽  
Least Square ◽  
Substrate Consumption ◽  
Model Based ◽  
Effluent Flow Rate

This paper deals with the minimal-cost control of the modified activated sludge process with varying level of wastewater in the aerator tank. The model-based adaptive controller of the effluent substrate concentration, basing on the substrate consumption rate and manipulating the effluent flow rate outcoming from the aerator tank, is proposed and its performance is compared with conventional PI controller and open loop behavior. Since the substrate consumption rate is not measurable on-line, the estimation procedure on the basis of the least-square method is suggested. Finally, it is proved that cooperation of the DO concentration controller with the adaptive controller of the effluent substrate concentration allows the process to be operated at minimum costs (low consumption of aeration energy).

scholarly journals Data approximation using Lotka-Volterra models and a software minimization function

2019 ◽  
Vol 15 (2) ◽  
pp. 5-14
Author(s):  
M. Fečkan ◽  
J. Pačuta
Keyword(s):  
Mathematical Models ◽  
Historical Data ◽  
Least Square Method ◽  
Least Square ◽  
Data Set ◽  
Data Approximation ◽  
Standard Methods ◽  
Volterra Models ◽  
Coefficient Estimation

Abstract In recent years, a lot of effort has been put into finding suitable mathematical models that fit historical data set. Such models often include coefficients and the accuracy of data approximation depends on them. So the goal is to choose the unknown coefficients to achieve the best possible approximation of data by the corresponding solution of the model. One of the standard methods for coefficient estimation is the least square method. This can provide us data approximation but it can also serve as a starting method for further minimizations such as Matlab function fminsearch.

A rapid four-dimensional resistivity data inversion method using temporal segmentation

2020 ◽  
Vol 221 (1) ◽  
pp. 586-602 ◽  
Author(s):  
Bin Liu ◽  
Yonghao Pang ◽  
Deqiang Mao ◽  
Jing Wang ◽  
Zhengyu Liu ◽  
...  
Keyword(s):  
Current Data ◽  
Inversion Method ◽  
Data Sets ◽  
Temporal Segmentation ◽  
Data Set ◽  
Subsurface Structures ◽  
Data Inversion ◽  
Rapid Changes ◽  
High Level ◽  
Acquisition Cycle

SUMMARY 4-D electrical resistivity tomography (ERT), an important geophysical method, is widely used to observe dynamic processes within static subsurface structures. However, because data acquisition and inversion consume large amounts of time, rapid changes that occur in the medium during a single acquisition cycle are difficult to detect in a timely manner via 4-D inversion. To address this issue, a scheme is proposed in this paper for restructuring continuously measured data sets and performing GPU-parallelized inversion. In this scheme, multiple reference time points are selected in an acquisition cycle, which allows all of the acquired data to be sequentially utilized in a 4-D inversion. In addition, the response of the 4-D inversion to changes in the medium has been enhanced by increasing the weight of new data being added dynamically to the inversion process. To improve the reliability of the inversion, our scheme uses actively varied time-regularization coefficients, which are adjusted according to the range of the changes in model resistivity; this range is predicted by taking the ratio between the independent inversion of the current data set and historical 4-D inversion model. Numerical simulations and experiments show that this new 4-D inversion method is able to locate and depict rapid changes in medium resistivity with a high level of accuracy.

Automatic Reverse Engineering Based on Reconstructing Measurement Data in 3D-Lattice

2012 ◽  
Vol 523-524 ◽  
pp. 414-419
Author(s):  
Kiyomoto Tsushima ◽  
Hideki Aoyama
Keyword(s):  
Reverse Engineering ◽  
Mathematical Models ◽  
Measurement Data ◽  
Least Square Method ◽  
Lattice Points ◽  
Least Square ◽  
Physical Models ◽  
Engineering System ◽  
Surface Data ◽  
Data Density

Reverse engineering systems are used to construct mathematical models of physical models such as clay model based on measurement data. In this study, we proposed a reverse engineering method which can construct high quality surface data automatically. This method consists of the following steps; The first globally and regionally smooths measured data based on the target shape by fitting quadric surface to measurement data. The second defines quadric surfaces and converts measurement points into 3D lattice points to obtain uniform measurement data density. As the positions of measurement data are converted from coordinate values into 3D lattice points, it is easier to find neighboring points and clarify neighboring relations between surfaces. The third acquires segment measurement data based on maximum curvatures and normals at each point. The last defines NURBS surfaces for each segment using the least square method to average positional errors. In order to validate the effectiveness of the proposed method, we developed a reverse engineering system and constructed mathematical models through basic experiments using clay car model measurement data.

Gaussian envelope for 3D geomagnetic data inversion

Geophysics ◽  
2003 ◽  
Vol 68 (3) ◽  
pp. 996-1007 ◽  
Author(s):  
Fabio Caratori Tontini ◽  
Osvaldo Faggioni ◽  
Nicolò Beverini ◽  
Cosmo Carmisciano
Keyword(s):  
Synthetic Data ◽  
Iteration Scheme ◽  
Source Distribution ◽  
Magnetic Data ◽  
Real Field ◽  
Inversion Method ◽  
Data Set ◽  
Data Inversion ◽  
Geomagnetic Data ◽  
Subjective Input

We describe an inversion method for 3D geomagnetic data based on approximation of the source distribution by means of positive constrained Gaussian functions. In this way, smoothness and positivity are automatically imposed on the source without any subjective input from the user apart from selecting the number of functions to use. The algorithm has been tested with synthetic data in order to resolve sources at very different depths, using data from one measurement plane only. The forward modeling is based on prismatic cell parameterization, but the algebraic nonuniqueness is reduced because a relationship among the cells, expressed by the Gaussian envelope, is assumed to describe the spatial variation of the source distribution. We assume that there is no remanent magnetization and that the magnetic data are produced by induced magnetization only, neglecting any demagnetization effects. The algorithm proceeds by minimization of a χ2 misfit function between real and predicted data using a nonlinear Levenberg‐Marquardt iteration scheme, easily implemented on a desktop PC, without any additional regularization. We demonstrate the robustness and utility of the method using synthetic data corrupted by pseudorandom generated noise and a real field data set.

scholarly journals Estimation of Informal Sector of the Nigerian Construction Industry

2020 ◽  
pp. 203-208
Author(s):  
Ojo O. J. ◽  
Yusuf B. A. ◽  
Aremu J. A.
Keyword(s):  
Construction Industry ◽  
Informal Sector ◽  
Instrumental Variable ◽  
Value Added ◽  
Least Square Method ◽  
Cement Industry ◽  
Least Square ◽  
Pool Data ◽  
Time Series Regression ◽  
Data Set

The study estimated the output of informal sector of the Nigerian Cement Industry through the consumption of cement by the Nigerian Construction industry. The research was conducted using secondary data. The study adopted the statistical model of informal sector estimation, Nigeria construction industry being cement intensive, cement consumption approach was used for the estimation of the informal sector of the industry by using annual cement consumption as an independent variable against the annual construction output in a time series regression analysis, treating the informal sector output as an omitted variable in the ordinary least square method of estimation. Annual value added tax (VAT) pool data set was chosen as an instrumental variable. Using the instrumental variable method of estimation, the informal sector proportion of the Nigeria construction industry was therefore estimated. The study concluded that the informal sector of the Nigerian construction industry is 4.07 percent of the industry's output.

scholarly journals Local magnitude scale in Slovenia

2013 ◽  
Vol 34 ◽  
pp. 23-28 ◽  
Author(s):  
J. Bajc ◽  
Ž. Zaplotnik ◽  
M. Živčić ◽  
M. Čarman
Keyword(s):  
Vertical Component ◽  
Large Data ◽  
Least Square Method ◽  
Least Square ◽  
Magnitude Scale ◽  
Local Magnitude ◽  
Data Set ◽  
Seismic Stations ◽  
Short Period ◽  
Environment Agency

Abstract. In the paper a calibration study of the local magnitude scale in Slovenia is presented. The Seismology and Geology Office of the Slovenian Environment Agency routinely reports the magnitudes MLV of the earthquakes recorded by the Slovenian seismic stations. The magnitudes are computed from the maximum vertical component of the ground velocity with the magnitude equation that was derived some thirty years ago by regression analysis of the magnitudes recorded by a Wood-Anderson seismograph in Trieste and a short period seismograph in Ljubljana. In the study the present single magnitude MLV equation is replaced by a general form of the Richter local magnitude MWA equation. The attenuation function and station-component corrections that compensate the local effects near seismic stations are determined from the synthetic Wood-Anderson seismograms of a large data set by iterative least-square method. The data set used consists of approximately 18 000 earthquakes during a period of 14 yr, each digitally recorded on up to 29 stations. The derived magnitude equation is used to make the final comparison between the new MWA magnitudes and the routinely calculated MLV magnitudes. The results show good overall accordance between both magnitude equations. The main advantage of the introduction of station-component corrections is the reduced uncertainty of the local magnitude that is assigned to a certain earthquake.

scholarly journals 3D induced-polarization data inversion for complex resistivity

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. F157-F171 ◽  
Author(s):  
Michael Commer ◽  
Gregory A. Newman ◽  
Kenneth H. Williams ◽  
Susan S. Hubbard
Keyword(s):  
Environmental Remediation ◽  
Large Scale ◽  
Forward Modeling ◽  
Induced Polarization ◽  
Inversion Method ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Data Set ◽  
Complex Resistivity ◽  
Data Inversion

The conductive and capacitive material properties of the subsurface can be quantified through the frequency-dependent complex resistivity. However, the routine three-dimensional (3D) interpretation of voluminous induced polarization (IP) data sets still poses a challenge due to large computational demands and solution nonuniqueness. We have developed a flexible methodology for 3D (spectral) IP data inversion. Our inversion algorithm is adapted from a frequency-domain electromagnetic (EM) inversion method primarily developed for large-scale hydrocarbon and geothermal energy exploration purposes. The method has proven to be efficient by implementing the nonlinear conjugate gradient method with hierarchical parallelism and by using an optimal finite-difference forward modeling mesh design scheme. The method allows for a large range of survey scales, providing a tool for both exploration and environmental applications. We experimented with an image focusing technique to improve the poor depth resolution of surface data sets with small survey spreads. The algorithm’s underlying forward modeling operator properly accounts for EM coupling effects; thus, traditionally used EM coupling correction procedures are not needed. The methodology was applied to both synthetic and field data. We tested the benefit of directly inverting EM coupling contaminated data using a synthetic large-scale exploration data set. Afterward, we further tested the monitoring capability of our method by inverting time-lapse data from an environmental remediation experiment near Rifle, Colorado. Similar trends observed in both our solution and another 2D inversion were in accordance with previous findings about the IP effects due to subsurface microbial activity.

scholarly journals Angle of Arrival Passive Location Algorithm Based on Proximal Policy Optimization

Electronics ◽  
2019 ◽  
Vol 8 (12) ◽  
pp. 1558 ◽  
Author(s):  
Yao Zhang ◽  
Zhongliang Deng ◽  
Yuhui Gao
Keyword(s):  
Measurement Data ◽  
Gradient Methods ◽  
Least Square ◽  
Passive Location ◽  
Residential Areas ◽  
Angle Of Arrival ◽  
Data Set ◽  
Research Attention ◽  
Location Algorithm ◽  
Policy Optimization

Location technology is playing an increasingly important role in urban life. Various active and passive wireless positioning technologies for mobile terminals have attracted research attention. However, positioning signals experience serious interference in high-density residential areas or in the interior of large buildings. The main type of interference is that caused by non-line-of-sight (NLOS) propagation. In this paper, we present a new method for optimizing the angle of arrival (AOA) measurement to obtain high accuracy location results based on proximal policy optimization (PPO). PPO is a new family of policy gradient methods for reinforcement learning, which can be used to adjust the sampling data under different environments using stochastic gradient ascent. Therefore, PPO can correct the NLOS propagation errors to produce a clear AOA measurement data set without building an offline fingerprinting database. Then, we used the least square method to calculate the location. The simulation result shows that the AOA passive location algorithm based on PPO produced more accurate location information.

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