scholarly journals A least squares method for identification of unknown groundwater pollution source

2021 ◽  
Author(s):  
Zhukun He ◽  
Rui Zuo ◽  
Dan Zhang ◽  
Pengcheng Ni ◽  
Kexue Han ◽  
...  
Keyword(s):  
Least Squares ◽  
Groundwater Pollution ◽  
Least Squares Method ◽  
Transport Model ◽  
Pollution Prevention ◽  
Pollution Source ◽  
Pollution Sources ◽  
Observation Data ◽  
Tank Experiment ◽  
Gas Station

Abstract The identification of unknown groundwater pollution sources is one of the most important premises in groundwater pollution prevention and remediation. In this paper, an exploratory application of a least squares method to identify the unknown groundwater pollution source is conducted. Supported by a small amount of observation data and the analytical solutions of the pollutant transport model, the initial concentration, the leakage location and the pollutant mass are identified by using the least squares method under a sand tank experiment and a gas station area. In the sand tank experiment, it is found that the fitting errors of three cross-sections are within 6%. In the gas station area, it is found that the results are nearly consistent with the site investigation information. The results indicate that the least squares method has considerable application values in the identification of groundwater pollution sources.

Wavelet denoising and cubic spline interpolation for observation data in groundwater pollution source identification problems

2019 ◽  
Vol 19 (5) ◽  
pp. 1454-1462 ◽  
Author(s):  
Ying Zhao ◽  
Qiang Fu ◽  
Wenxi Lu ◽  
Ji Yi ◽  
Haibo Chu
Keyword(s):  
Missing Data ◽  
Groundwater Pollution ◽  
Source Identification ◽  
Noise Level ◽  
Spline Interpolation ◽  
Wavelet Denoising ◽  
Pollution Source ◽  
Observation Data ◽  
Concentration Data ◽  
Cubic Spline Interpolation

Abstract As the identified results of groundwater pollution source identification (GPSI) can influence the cost for the polluter in paying for remediating groundwater resources, it is important that the accuracy of the estimated result should be as high as possible. However, many factors can influence the result, such as noisy concentration data and incomplete concentration data. Thus, this paper is aimed at studying the difference between using the observation data before and after denoising and interpolating for solving GPSI problems. Four kinds of noise level and 20 groups of missing data were designed to test the performance of wavelet denoising and cubic spline interpolation, respectively. The results show that the denoising process can improve the estimated result for the GPSI problem, and the higher the noise level, the stronger this effect. In terms of interpolation, more accurate results can be made after interpolating if the missing data belong to the period after the source releases the pollutant. If the missing data are from when the pollution source is active, interpolation cannot help increase the estimated performance.

The Application of Total Least Squares Method in Data Fitting of Speed Radar

2012 ◽  
Vol 203 ◽  
pp. 69-75 ◽  
Author(s):  
Cheng Chen ◽  
Chang Jin Liu
Keyword(s):  
Least Squares ◽  
Initial Velocity ◽  
High Speed ◽  
Least Squares Method ◽  
Data Fitting ◽  
Total Least Squares ◽  
Measure Data ◽  
Observation Data ◽  
Unknown Parameters ◽  
Observation Matrix

For acquiring the initial velocity of high-speed object, it needs data fitting to get the unknown parameters. Least squares method(LS) is usually uses to complete this work, but LS method takes no account of the errors in the observation matrix, not only may makes error in unknown parameters' fitting, but also do harm to the further analysis. Therefore, this paper lead total least squares method(TLS) into data fitting, it can at the same time in consideration of observation data and its error margin, and at last in actually measure data analysis to prove TLS compare to LS enjoy higher accuracy.

scholarly journals An Effective Kalman Filter-Based Method for Groundwater Pollution Source Identification and Plume Morphology Characterization

Water ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 1063 ◽  
Author(s):  
Simin Jiang ◽  
Jinhong Fan ◽  
Xuemin Xia ◽  
Xianwen Li ◽  
Ruicheng Zhang
Keyword(s):  
Kalman Filter ◽  
Groundwater Pollution ◽  
Source Identification ◽  
Programming Model ◽  
Concentration Field ◽  
Identification Problem ◽  
Pollution Source ◽  
Pollution Sources ◽  
Optimization Approach ◽  
Pollution Source Identification

The identification of unknown groundwater pollution sources and the characterization of pollution plume remains a challenging problem. In this study, we addressed this problem by a linked simulation-optimization approach. This approach couples a contaminant transport simulation model with a Kalman filter-based method to identify groundwater pollution source and characterize plume morphology. In the proposed methodology, the concentration field library, the covariance reduction with a Kalman filter, an alpha-cut technique of fuzzy set, and a linear programming model are integrated for solving this inverse problem. The performance of this methodology is evaluated on an illustrative groundwater pollution source identification problem. The evaluation considered the random hydraulic conductivity filed, erroneous monitoring data, a prior information shortage of potential pollution sources, and an unexpected and unknown pumping well. The identified results indicate that, under these conditions, the proposed Kalman filter-based optimization model can give satisfactory estimations to pollution sources and plume morphology for domains with small and moderate heterogeneity but cannot validate the transport in the relatively high heterogeneous field.

Research on GIS-Based Risk Assessment Method of Groundwater Pollution and its Application

2011 ◽  
Vol 356-360 ◽  
pp. 819-824 ◽  
Author(s):  
Li Ping Bai ◽  
Ye Yao Wang ◽  
Fa Sheng Li
Keyword(s):  
Risk Assessment ◽  
Groundwater Pollution ◽  
Pollution Prevention ◽  
Groundwater Vulnerability ◽  
Assessment Method ◽  
Pollution Sources ◽  
Assessment Model ◽  
Multi Index ◽  
Pollution Risk ◽  
Risk Assessment Method

The risk assessment model and parameter system of groundwater pollution were established in this paper. The multi-index evaluation method of groundwater pollution sources was proposed, and the GIS-based risk assessment method of groundwater pollution was produced in comprehensive consideration of groundwater vulnerability and groundwater pollution sources. The multi-index method suggested in this paper was used in the risk assessment of groundwater pollution at a plain area of a big city in North China, and the different grades of groundwater pollution risk were computed. The evaluation results show that the groundwater pollution risk is determined by the combined action of ground pollution sources and groundwater vulnerability. The established risk assessment method of groundwater pollution could give a scientific support for the regional groundwater pollution prevention and control planning.

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

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