KR101469168B1 - Method for verifying representativeness of sample using spatial correlation analysis - Google Patents

Abstract

The present invention relates to a method for evaluating a representative sample by using spatial correlation analysis capable of increasing reliability of the representative sample used for the final situation investigation of a dismantlement site and decreasing the number of selected samples. Provided is the method for evaluating the representative sample by using the spatial correlation analysis comprising a variogram analyzing step for analyzing a spatial correlation of an evaluated model derived by writing the variogram of a sample (S101); a pollution level evaluating step for evaluating the total pollution level of a pollution area by using a linear collection of the evaluated model (S102); a pollution distribution stabilization step for calculating the standard deviation and the average of pollution distribution by performing conditional simulation for the stabilization of the pollution distribution (S103); and an MARSSIM evaluating step for evaluating the representation of the sample by applying an MARSSIM method theory to the standard deviation and the average for the pollution distribution (S104).

Description

METHOD FOR REPRESENTATIVENESS OF SAMPLE USING SPATIAL CORRELATION ANALYSIS < RTI ID = 0.0 >

TECHNICAL FIELD The present invention relates to a method of evaluating the representativeness of a sample using spatial correlation analysis so as to increase the reliability of representative samples used in the final status survey of dismantling sites and to reduce the number of samples to be selected.

In general, the site of the waste to be dismantled is ultimately opened through a series of processes of residual radioactivity evaluation and removal of contaminants.

There are two known methods for evaluating contaminants such as radioactivity contained in wastes to be deregulated.

First, as a homogenization method, there is a method of using the result of radioactivity analysis of a sample obtained by uniformly mixing the same kinds of whole wastes.

The second is a method of averaging, in which a large number of samples are sampled randomly among the same kinds of wastes and the average value of the analyzed radioactivity concentration is applied.

According to the current regulatory standards in the world, it is recommended to evaluate the target waste by taking both homogenization and averaging measures together.

It is very important to select a sample that is used for the evaluation of the target wastes as much as possible to reflect the population as much as possible.

As an example, an arbitrary soil waste drum is selected to measure the surface dose rate, the contents are poured into TRAY, spread out evenly, and the foreign substances other than the soil are collected separately, And the surface dose rate is measured.

Then, the GRID prepared in the TRAY of the soil after the above process is placed, and the soil is divided into several tens to hundreds of areas as a whole, and serial numbers are assigned to the respective areas. Then, in the final stage, the uniform distribution (UNIFORM) (Random Number Sampling) is used to generate samples of about 30 random numbers (RANDOM NUMBER).

A representative sample was obtained by performing nonparametric verification (NON PARAMETRIC) using the results of analysis of some samples, assuming that the contamination level of the site is homogeneous.

Therefore, the site where the actual demolition and contamination are removed is wide, and if the existing evaluation method is simply applied due to various pollution distribution, the pollution characteristic of the demolition site is not reflected. Therefore, Which results in an increase in the cost of the investigation and an incorrect evaluation result.

As an example of a conventional technique for evaluating such representative samples, Korean Patent Laid-Open No. 10-2002-0068206 entitled " Method of Representative Verification of Samples Collected from Contaminated Soils " The content of trace elements in the minerals residue is analyzed to determine the sampling intervals and the number of representative samples so that a representative sample can be collected to evaluate the representativeity.

To this end, Korean Patent Laid-Open No. 10-2002-0068206 discloses a method for collecting samples of soil in a horizontal interval and a vertical interval based on a surface of contaminated soil, Analyzing the collected samples by the sampling interval to measure the total content of trace elements; And determining the horizontal and vertical sampling interval and number of the sample on the basis of a statistical analysis result on the total content of the trace elements.

However, as disclosed in Korean Patent Laid-Open No. 10-2002-0068206, in order to increase the accuracy of the measurement of the content of trace elements contained in the soil, it is necessary to collect a large number of samples from the soil, In addition, there is a problem that the evaluation of the representative sample becomes inaccurate by simply measuring the trace element content of the randomly sampled sample and giving the statistics.

In addition, Korean Patent No. 10-1122175 describes the possibility of contamination possibility by preparing a probability map of the contamination possibility by using a variogram analysis and an indicator kriging to the data obtained from the groundwater quality data investigation point or the soil for pollution evaluation A description of the method of evaluation is described.

Korean Patent Registration No. 10-1122175 includes a method for probabilistically evaluating the possibility of contamination of groundwater and soil by harmful organic matter.

In addition, the probability of contamination can be assessed stochastically compared with the existing indexing method, and the principle and method of regular kriging are utilized, so that it is easy to use and has a short calculation time.

However, the probabilistic measurement by the indicator kriging tends to reduce the variance of the predicted values in large variance data, so that it is not possible to analyze the sensitivity by estimating various probabilistic equivalent values. There is a problem that must be applied.

Domestic public patent No. 2012-0068206 Korean Patent No. 10-1122175

The present invention, which has been made in view of the above-mentioned problems, can be applied to an indicator that reflects the pollution characteristics of a contaminated site by spatial analysis and conditional simulation by applying MARSSIM (MULTI-AGENCY RADIATION SURVEY AND SITE INVESTIGATION MANUAL) REPRESENTATIVENESS OF SAMPLE) to improve the accuracy of the representative sample evaluation for dismantling site investigation and to reduce the number of samples to be selected, thereby reducing the time and cost required for the representative evaluation of the sample And the like.

According to the present invention, a VARIOGRAM of a sample taken from a contaminated site is created, and a spatial correlation of an optimized theoretical model is analyzed based on an experimental model of a variogram A pollution degree evaluation step of measuring the pollution degree of the whole of the contaminated site by linear combination of the measurement position and the result based on the variogram analysis step and the derived theoretical model and performing a conditional simulation for normalizing the pollution degree distribution, And a standard deviation and an average of the pollution degree distribution calculated through the pollution distribution normalization are applied to the sample to calculate a standard deviation and an average of the distribution And the use of spatial correlation analysis, which consists of the evaluation stage of MARSSIM Representative evaluation method is provided.

According to the sample representative evaluation method according to the present invention, the reliability of the representative evaluation result of the sample for surveying the residual pollution degree of the disposal site can be enhanced.

Further, according to the present invention, it is possible to reduce the number of samples to be selected for surveying the residual contamination degree of the dismantling site, and it is possible to reduce the time and cost required for the evaluation of the representativeness of the sample.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a flow chart illustrating a method of sample representative evaluation according to an embodiment of the present invention. FIG.
FIG. 2 is a conceptual diagram illustrating a spatial correlation analysis process using a variogram in the present embodiment. FIG.
3 is a graph showing the geometrical meanings of the variogram shown by this embodiment.
4 is a barberogram wherein the separation distance is increased in the variogram shown by this embodiment.
5 is a conceptual diagram illustrating a cross validation process according to the present embodiment.
6 is a conceptual diagram showing the result of the contaminated site analysis analyzed by the present embodiment.
7 is a conceptual diagram illustrating a process of evaluating the kriging result analyzed by the present embodiment through conditional simulation.

BACKGROUND OF THE INVENTION 1. Field of the Invention [0001] The present invention relates to a method of evaluating the representativeness of a sample using spatial correlation analysis, in which the reliability of REPRESENTATIVE SAMPLE used for surveying the final status of dismantling sites is increased and the number of samples to be selected can be reduced .

It is used in the evaluation of representative samples used for residual contamination evaluation in the final status survey for SITE RELEASE after restoration activities to remove residual pollution on site and buildings after decommissioning of nuclear facilities.

Therefore, investigation and evaluation should be conducted so that the residual contamination level can be a clear reference to determine whether or not the open standards for reuse of the site can be met.

According to the present invention, the method of representing the sample according to the present invention creates an experimental variogram (VARIOGRAM) using the measurement result and the position information of the sample taken from the contaminated site, and based on this, the theoretical model is selected and the spatial analysis method of the geological statistics is applied It is possible to extract meaningful and precise results for the purpose of analyzing spatial data.

In order to predict the characteristic value of the region of interest by using the variogram, spatial correlation can be analyzed by linear combination of the measured values and the value can be predicted. This method is KRIGING.

According to Kriging, unexpected values can be derived by minimizing the error variance by using a weighted linear combination of known data. However, if the variance of the data is large, It is not possible to analyze sensitivity by producing equivalent value.

The SPATIAL ANALYST method of geological statistics makes it possible to extract meaningful results by processing data in different forms for spatial data analysis.

This is to analyze the form and area of heterogeneity and find out the background of spatial correlation (ASSOCIATION), cluster (CLUSTER), outliers (OUTLIER) and local pollution (HOT SPOT) And to understand the distribution of geographical data.

By using the mean and standard deviation of potential site contamination derived from the characterization using the differential approach for survey design in order to secure the representative sample using the MARSSIM methodology, a simple statistical evaluation method by SURVEY UNIT To evaluate sample representativeness.

Accordingly, the present invention estimates the contamination distribution over the entire contaminated site by performing spatial correlation analysis and conditional simulation to evaluate representative samples reflecting the pollution characteristics of the site, and evaluating the result and the geological statistical method Thus, it is possible to increase the accuracy of the representative sample selection and reduce the number of samples required for the dismantling site investigation.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings, which illustrate exemplary embodiments of the present invention. The present invention is not limited to these embodiments.

FIG. 1 is a flowchart showing steps of a sample representative evaluation method according to the present invention.

As shown in FIG. 1, according to the sample representative evaluation method of the present invention, first, a variogram analysis step of analyzing the spatial correlation by creating a variogram using the analysis result of the position and the pollution degree of the sample collected from the contaminated site S101) is executed.

The variogram analysis step S101 includes, for example, a process of deriving an optimized theoretical model by selecting a spherical model of the variogram and analyzing it by a geological statistical spatial analysis method.

Then, a contamination degree evaluation step (S102) for predicting the contamination degree of the contaminated site in the region of interest is executed through the result of the variogram.

In the pollution measurement evaluation (S102), a linear combination of the experimental model and the theoretical model of the variogram predicts the contamination level of the entire contaminated site through the KRIGING process.

In this case, we can exclude the anomalies biased in the relative error range by comparing and analyzing the experimental model and the theoretical model, and the cross validation can be performed. In particular, the spatial correlation, It analyzes the spatial changes in patterns of local pollution and anomalous points and improves the reliability of pollution evaluation results.

Then, the step 103 of normalizing the pollution degree distribution by the conditional simulation is executed.

In the site contamination distribution normalization step (103), a conditional simulation for normalizing the pollution distribution map is executed to calculate an average (AVERAGE) and a standard deviation (STANDARD DEVIATION) for the pollution degree distribution. At this time, the average and standard deviation derived from the conversion of the pollution degree distribution to the normal distribution can be used to obtain representative of the residual pollution degree of the site and to calculate the improved standard deviation.

Finally, a MARSSIM evaluation step (S104) is performed in which the statistical methodology of MARSSIM is applied to the normalized contamination distribution to evaluate the number of sample samples required for the final status investigation.

The MARSSIM evaluation step (S104) evaluates the representativeity of the sample by applying the WRS (WILCOXON RANK SUM) test, which is a statistical method, using the mean and standard deviation derived from the normalization of the contamination distribution.

Hereinafter, an embodiment of the present invention will be described in detail.

1. Sampling of contaminated site

In order to investigate the residual contamination of the site, samples are taken from the contaminated soil at regular intervals.

2. Variogram  analysis

2 shows the process of the variogram analysis step S101.

Referring to FIG. 2, in the variogram analysis step (S101), the position (distance) and the degree of contamination of the sample collected from the contaminated site are first analyzed, and a variogram is created. The optimized theoretical model based on the experimental model of the created variogram Select the model.

The variogram analysis generally shows that the closer the distance is, the bigger the autocovariance, and the larger the distance, the smaller the autocovariance.

In addition, there is no correlation at a certain distance, and the data at a certain distance (RANGE) show similarity with each other.

Therefore, as shown in Equation (1), variogram is an expectation of squaring the difference between two data separated by a certain distance h. As the distance is close, the values are generally small, and as the distance becomes longer, Value tend to appear.

Equation (1)

3 shows the geometric meanings expressed by the variogram. Particularly, FIG. 3 shows the relationship between z (x) and z (x + h) at the distance h given in the variogram on the two- Represents the distance to a straight line of the linear equation y = x with a slope of 1.

At this time, it can be seen that the square mean value of the distance from the straight line of y = x becomes a semi-variogram as shown in the following equation (2), and the semi-variogram is half the value of the variogram It shows how the distance of a certain distance is different on average.

That is, as the separation distance h increases, the correlation decreases and moves away from the straight line of y = x, and the separation distance, which is a quantitative measure for the distance, can be analyzed through the variogram.

수학식 (2)

Equation (2)

Figure 4 shows a general non-variogram with no threshold.

As shown in FIG. 4, when the separation distance increases, a certain distance (S (SIL)) in which the correlation of data disappears and a certain value converges appears.

In addition, the correlation distance R (RANGE) indicating the maximum separation distance in which these evaluation models are correlated, and the nugget (N: NUGGET) in which the variogram has a constant value even when the separation distance is "0" have.

Here, the threshold (S) represents the variance of the data, and the nugget (N) represents the uncertainty of the data.

In particular, variograms according to this embodiment simultaneously provide a measure of non-similarity over a distance, while other measures, such as dispersion function, correlationgram, etc., only show similarity over a certain distance.

3. Measurement of contamination level of contaminated site

Next, step 102 is performed to assess the degree of contamination of the entire contaminated site through the results analyzed through the variogram.

In this case, the pollution degree of contaminated site can be estimated by linear combination of measured results by analyzing spatial correlation by applying geological statistical technique to the result of spatial distribution measured with variogram, (KRIGING).

Kriging is a representative method of geological statistics. It is a process of estimating a best estimate (BEST LINEAR UNBIASED ESTIMATOR) for λi in the following equation (3) to obtain a value of a point not yet observed. It is a weighted average that minimizes the variance of the prediction error.

In other words, this method estimates the unknown value by weighted linear combination of data already measured by kriging.

수학식 (3)

Equation (3)

In the measurement of contamination by kriging, patterns of spatial correlation (ASSOCIATION), clustering (CLUSTER), outliers (OUTLIER) and local pollution (HOT SPOT) of the experimental model and theoretical model through variogram are found out and heterogeneity The degree of contamination is evaluated by analyzing changes in spatial patterns of shapes and regions.

In particular, in order to evaluate the pollution degree of the polluted site, the spatial correlation through the variogram of the measurement result is analyzed to perform the cross validation with the difference according to the spatial correlation.

In particular, cross-validation is performed so that the evaluation model of an outlier (O (OUTLIER) with low spatial correlation is excluded from evaluation.

FIG. 5 shows a process of setting an anomaly point (O) of an evaluation model derived based on an experimental variogram, and executing a cross validation that excludes the anomalous point O from the evaluation.

In case of restoration of contaminated site, residual pollution level after restoration is considered to be similar level. Therefore, it is necessary to compare the experimental variogram with the prediction result of evaluation model, It is possible to improve the reliability by excluding the result.

The results of analyzing the contaminated site are shown in FIG.

As shown in Fig. 6, the pollution degree of the entire site was predicted by the geological statistical method using kriging by applying a 10m correlation distance and a spherical model of the variogram, and the sampling position (+ ) Can be expressed in map form.

4. Evaluate the mean and standard deviation of pollution degree (conditional simulation execution)

Next, in order to calculate the number of samples required for evaluation of the residual pollution degree in the final status survey, a contamination distribution normalization step S103 (S103) for converting the pollution degree distribution into a normal distribution and calculating an average (AVERAGE) and a standard deviation (STANDARD DEVIATION) ) Is executed.

FIG. 7 shows a process of evaluating KRIGING results through conditional simulation.

Kriging has a very good prediction ability for the material parameters that are appropriate to apply the arithmetic mean with slowly varying characteristic values of the data.

However, even with the same mean, the variance of the kriging predictors tends to decrease sharply in large variance data.

Therefore, in kriging, if the variance of the data is large, it is not possible to reduce the variance of the predicted value and to produce various probabilistic equivalent values and to analyze the sensitivity.

Accordingly, in the present invention, the pollution degree distribution over the entire polluted site is normalized through the conditional simulation process, and the average and standard deviation are calculated.

Conditional simulation is a variable generation technique that preserves a given data value while maintaining the mean and variance of the random variable.

Conditional simulations may include, for example, radnom residual addition (RRA), which adds residuals to predicted values at unknown points of a data value, sequential gauss simulations for conditional simulation of data following a normal distribution ), Sequential indicator simulation (Fractal Simulation) that allows the use of given data in various conditions and distribution of singular values of data without needing to follow the normal distribution.

5. Representative Evaluation of Samples

Next, a MARSSIM evaluation step (S104) for evaluating the representativeity of the sample by applying the statistical evaluation method provided by the MARSSIM methodology to the average or standard deviation of the pollution degree calculated through the conditional simulation is executed.

At this time, the MARSSIM methodology uses the WRS (WILCOXON RANK SUM) test, which is a statistical method, to evaluate the number of representative samples for investigating the residual contamination site.

In the MARSSIM methodology, the survey area and the survey unit are separated and the results are evaluated by the survey design for each survey unit.

To this end, a differential approach for survey design is applied, which establishes a survey procedure based on standardization to enable efficient site investigation.

Therefore, by assigning the grade of the site according to the pollution level of the contaminated site and improving the simple statistical evaluation method by the investigation unit, it is possible to combine the pollution degree measurement result and the active investigation strategy to judge the representativeness of the sample to judge the pollution characteristics of the site, Can be effectively determined.

On the other hand, in the case of simple application of the MARSSIM methodology as in the past, it is judged based on the assumption that the contamination degree distribution follows the binomial distribution and the normal distribution in order to utilize the average standard deviation, Down.

Therefore, in reality, the degree of contamination does not follow the binomial distribution and the normal distribution, so that the accuracy of the contamination degree determination is limited, thereby increasing the number of samples to be selected.

However, the present invention applies a geological statistical method by conditional simulation to evaluate a representative sample reflecting the characteristics of the dismantling site contamination, estimates the contamination distribution over the entire dismantling site, and evaluates the result through a normalization process The number of samples to be selected can be reduced and the time and cost required for sample representative evaluation can be greatly reduced.

Table 1 below compares the results of the sample representability evaluation method according to the present embodiment and the results of the conventional method of simply applying the WRS TEST.

Existing MARSSI evaluation method In this embodiment Remarks Statistical evaluation method WRS test Geostatistice + WRS test LBGR 1.65 1.65 Sigma (s) 1.78 0.90 Type I & II error 0.05 / 0.05 0.05 / 0.05 95% confidence interval Required Sample (N) 14 9 35% reduction

Thus, the present invention is able to reduce the number of samples to be selected by 35% as compared with the case where the WRS test is simply applied as a result of the normalization of the result of analyzing the spatial correlation by the variogram through the conditional simulation and the WRS test At the same time, the reliability of the selected representative sample remains unchanged.

As described above, in order to evaluate a representative sample reflecting the disposal site contamination characteristic, a geological statistical method by conditional simulation is applied to predict the distribution of the contamination degree over the entire disposal site, and the result is evaluated through a normalization process, The number of samples to be selected can be reduced, and the time and cost required for sample representative evaluation can be greatly reduced.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. It is to be understood that various changes and modifications may be made without departing from the scope of the appended claims.

Claims (6)

A computer processor generates an experimental VARIOGRAM model using the measured values of a sample taken from the site and derives a theoretical variogram model based on the generated experimental variogram model to calculate the measured value A variogram analysis step for analyzing the spatial correlation of the images;
A computer processor for evaluating the degree of contamination of the site based on the derived theoretical variogram model;
A computer processor executing a conditional simulation to normalize the contamination distribution to calculate a standard deviation (STANDARD DEVIATION) and an average (AVERAGE) for the contamination distribution; And
A MARSSIM evaluation step of evaluating the representativeity of the sample by applying a standard deviation of the contamination distribution calculated through the normalization and a method of MULTI-AGENCY RADIATION SURVEY AND SITE INVESTIGATION MANUAL (MARSSIM) to the average;
A method for evaluating the representativeness of a sample using spatial correlation analysis.
The method according to claim 1,
The pollution degree evaluation step compares the pollution degree evaluation result of the site using the measured value and the theoretical variogram model and performs cross validation to exclude an anomaly point (OUTLIER) A method of sample representation evaluation using spatial correlation analysis.
The method according to claim 1,
The contamination degree evaluation step may include analyzing spatial changes in at least one of spatial correlation, clusterability, local contamination, and OUTLIER pattern of the linear combination of the experimental variogram model and the theoretical variogram model, To do;
A method for evaluating the representativeness of a sample using spatial correlation analysis.
The method according to claim 1,
Wherein the contamination distribution normalization step is performed by performing a conditional simulation process to predict the degree of contamination on the site and to improve the standard deviation through normalization of the contamination distribution.
The method according to claim 1,
Wherein the variogram analysis step is a geological statistical spatial analysis method;
A method for evaluating the representativeness of a sample using spatial correlation analysis.
The method according to claim 1,
In the MARSSIM evaluation step, a WRS (WILCOXON RANK SUM) test is applied as a statistical method;
A method for evaluating the representativeness of a sample using spatial correlation analysis.

Images