KR101208595B1 - Gross error detecting method and system using lagrangian multiplier, and data reconciliation method using gross error detecting system - Google Patents

Abstract

The present invention has been made in order to retrieve data including gross errors and to use accurate measurement data. The present invention provides a method for detecting gross errors and a method for correcting data to ensure accuracy in process operation. It is intended to provide a way to do this.
It is also an object of the present invention to provide a method and system capable of detecting gross errors under constraints of mass conservation equations using Lagrange multiplier.
The gross error detection method using the Lagrange multiplier method according to the present invention comprises the steps of measuring the process variable to generate measurement data; Generating estimated data of the process variable by applying a Lagrange multiplier method to the measured data; And detecting a gross error of the measured data based on the measured data, the estimated data, and a standard deviation of the measured data.

Description

GROSS ERROR DETECTING METHOD AND SYSTEM USING LAGRANGIAN MULTIPLIER, AND DATA RECONCILIATION METHOD USING GROSS ERROR DETECTING SYSTEM}

The present invention relates to a gross error detection method and system using the Lagrange multiplier, and a data correction method using the gross error detection system. A method and system for calibrating data to include.

In the wastewater treatment process, the A2O process refers to a process widely used to remove whole human and total nitrogen from wastewater by using microorganisms of different environmental conditions.

1 is a block diagram of the A2O method, referring to FIG. 1, the A2O method is an anaerobic reactor (Anaerobic Reactor, 10), anoxic reactor (Anoxic Reactor, 20), aerobic reactor (Aerobic Reactor, 30) and sedimentation tank (Clarifier, 40). In the A2O process, the wastewater enters the anaerobic reactor 10, and the A2O process includes two regeneration streams, one of which includes nitrates from the aerobic reactor 30 to increase the efficiency of the denitrification reaction. 20), and the other is a regeneration stream which carries sludge from the settling tank 40 to the anaerobic reactor 10 in order to maintain the mixed liquid suspended solids.

Wastewater from the A2O process flows into the river and the sludge is further subjected to sludge treatment.

In the A2O process, the anaerobic reactor 10 is used to remove whole humans. The anoxic reactor 20 and the aerobic reactor 30 are used to remove all nitrogen, and denitrification and nitrification occur in each reactor.

The denitrification reaction is for converting nitrite and nitrate into nitrogen gas, and the nitrification action is for oxidizing ammonia to nitrite and nitrate.

In the aerobic reactor 30, oxidation of the carbon material and accumulation of phosphorus also occur. Oxidation of carbon matter affects the formation of CO ₂ . As such, the amount of oxygen required for the oxidation reaction is referred to as chemical oxygen demand (COD).

While generating the N ₂ gas in the oxygen-free reactor 20, the aerobic reactor 30 generates CO ₂ and discharges it to the outside of the wastewater treatment process.

In this A2O process, looking at the inflow and outflow of the process, COD, total phosphorus, total nitrogen and total suspended solids, and the final discharge is COD, total nitrogen (TN), total phosphorus (Total Phosphorous (TP)) and Total Suspended Solids (TSS). The intermediate emissions include N ₂ gas and CO ₂ gas along with COD, transfer, total nitrogen, and suspended solids.

Even in this A2O process, the law of mass conservation must be satisfied, so the amount of incoming material must satisfy the mass conservation equation that the mass of the final or intermediate discharged material must be equal.

There are large and small errors in the raw data throughout the A2O process, depending on the accuracy of the individual measuring devices, and often cause relatively large gross errors due to instrument breakdowns, miscalibration, and pipe leaks. It can also be included. Measurements with these errors show inconsistencies that do not satisfy the steady-state balance of the plant as a whole, and tend to conflict with each other. In addition, it is necessary to estimate parameters not directly measured due to technical difficulties and economic reasons, and parameters indicating the performance of each unit.

However, in this A2O method, in order to correct the measurement data, it is considered that there is a case where there is a constraint of the mass conservation formula. This is because N ₂ and CO ₂ discharged to the outside in the A ₂ O method are discharged to the air, so that the measurement is not actually made and the mass preservation equation does not appear to be satisfied. Therefore, gross error detection and data correction should be performed under such constraints.

It is an object of the present invention to retrieve data including gross errors so that accurate measurement data can be used.

It is another object of the present invention to provide a method and system capable of detecting gross errors under constraints of mass conservation equations using Lagrange multiplier.

It is another object of the present invention to provide a method for correcting data, together with a method for detecting gross errors, to ensure the accuracy of process operation.

In order to achieve the above object, the present invention, the gross error detection method using the Lagrange multiplier method, comprising the steps of measuring the process variable to generate the measurement data; Generating estimated data of the process variable by applying a Lagrange multiplier method to the measured data; And detecting a gross error of the measured data based on the measured data, the estimated data, and a standard deviation of the measured data.

Gross error detection system using the Lagrange multiplier method of the present invention, the data measuring unit for generating the measurement data for the process variable in each step of the wastewater treatment process; A data calculator for calculating an average value and a standard deviation value of the measured data and calculating estimated data of a process variable based on a weight matrix, a process matrix, and the measured data based on the standard deviation value; A preset storage unit for storing the process matrix; A data storage unit for storing the standard deviation value, the measurement data, and the estimated data; And a gross error detection unit determining whether gross error is included in the measurement data based on the measurement data, the estimated data, and the standard deviation value.

According to a third aspect of the present invention, a data correction method using a gross error detection system includes: generating measurement data on a process variable from a wastewater treatment process; Calculating an average value and a standard deviation value of the measured data; Calculating estimated data of a process variable based on the weight matrix, the process matrix, and the measured data based on the standard deviation value; Determining whether a gross error is included based on the measured data, the estimated data, and the standard deviation; And correcting the measurement data by removing the measurement data including a gross error and replacing it with the estimated data.

The present invention has the effect of extracting data including gross errors, so that accurate measurement data can be used, and also providing a method for correcting data in addition to a method for detecting gross errors, thereby improving process operation accuracy. There is an effect that can provide a way to secure.

Moreover, by using the Lagrange multiplier method, there is an effect that the gross error can be detected under the constraint of the mass conservation equation.

1 is a block diagram of the A2O method according to the prior art,
2 is an exemplary view for explaining a gross error detection method using the Lagrange multiplier method,
3 is a block diagram of a gross error detection system using the Lagrange multiplier method, according to an embodiment of the present invention; and
4 is a flowchart of a data correction method using a gross error detection system according to an exemplary embodiment of the present invention.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. Prior to this, terms and words used in the present specification and claims should not be construed as limited to ordinary or dictionary terms, and the inventor should appropriately interpret the concepts of the terms appropriately It should be interpreted in accordance with the meaning and concept consistent with the technical idea of the present invention based on the principle that it can be defined. Therefore, the embodiments described in this specification and the configurations shown in the drawings are merely the most preferred embodiments of the present invention and do not represent all the technical ideas of the present invention. Therefore, It is to be understood that equivalents and modifications are possible.

Data correction is a more accurate adjustment or correction of the data measured in the process to match mass conservation and energy conservation. Data correction is the conversion of real-time process data, including random and gross errors, into reliable data consistent with the conservation law.

Such data are essential for effective process operation and management and are commonly used for process monitoring, analysis, monitoring and optimization.

First, when data is measured, it is determined whether the data contains a gross error, the data containing the gross error is discarded, and the data without the gross error is used as the measurement data. The data including the random error is generally subjected to data correction, and can be represented by Equation 1 below.

Where y _meas is a vector of measurements, y _model is a vector of actual values, and ε is a random vector of measurement errors.

Data correction is the process of minimizing the sum of squares of actual and measured values while following the constraints of mass conservation. Mathematically, the data correction problem may be expressed as in Equation 2 below.

Where Ψ is a weight matrix expressed by Equation 3 below, and A ₁ is a process matrix including coefficients of a mass conservation equation.

Substituting Equation 3 into Equation 2 may result in Equation 4 below.

As a result, Equation 4 represents the problem of optimization to minimize the measurement error of the wastewater treatment process measurement data.

However, in the wastewater treatment process, in order to minimize the measurement error of measurement data, it should be considered that there is a constraint of mass conservation formula.

In order to solve such a problem, the Lagrange multiplier method is used in the present invention.

Lagrange multiplier transforms the problem of optimization under constraint into the problem of unconstrained optimization so that the first-order requirements can be applied without constraint.

If the Lagrange multiplier method is applied to Equation 2 and developed so that there is no constraint, it can be developed as shown in Equation 5 below.

Here, lambda is a Lagrange multiplier and may be expressed as in Equation 6 below.

Substituting Equation 1 into Equation 5 may be expressed as Equation 7 below.

If Equation 7 is differentiated with respect to ε and λ, respectively, and the derivative value is set to 0, it can be expressed as Equation 8 and Equation 9 below.

By simplifying Equation 8, a relational expression as in Equation 10 can be derived.

When both sides of Equation 10 are multiplied by A ₁ and rearranged, Equation 11 may be developed. Subsequent substitution of Equation 9 may result in a relation of Equation 12 below.

Substituting Equation 12 into Equation 10 may yield a relational expression as in Equation 13.

By introducing Equation 13 into Equation 1, an estimate y _esti of a process variable having a relational expression of Equation 14 can be derived as a result.

It is Gross Error Detection (GED) to identify false measurements from the measurement data of the process.

If the measurement has a large deviation from the estimate, it means that there is a gross error.

In the present invention, a relative error (RE) is used as a method for identifying a measurement having a gross error.

The relative error is defined as in Equation 15 below.

Where y _meas is a process measurement value, y _esti is an estimated value of a process variable obtained after performing data correction of Equation 14, and sigma represents a standard deviation of the measured value.

Here, the gross error can be determined by applying the reliability to the calculated value of the relative error. That is, assuming that the estimated value on the process follows a normal distribution, the gross error can be detected using the average value of the measured value and the standard deviation thereof.

For example, when applying a 95% confidence interval, if the relative error calculation value is greater than 1.96, which represents a 95% confidence level in the normal distribution, this measurement data can be judged as data containing a gross error. If the relative error calculation is less than 1.96, this measurement data can be regarded as data without gross errors.

That is, only when the condition of the following expression (16) is satisfied, it can be determined that there is no gross error in the measurement data.

Subsequently, depending on whether the gross error is detected, data reconciliation may be performed by replacing the estimated value with measurement data except for the data including the gross error. As a result, the estimate is used as measurement data with data that does not include gross errors.

Here, selecting the reliability as 95% is an example for easily describing the invention, and is not intended to limit the invention, and may be changed as many as the conditions of the process and the operator's choice.

2 is an exemplary diagram for describing a gross error detection method using the Lagrange multiplier method. As shown in FIG. 2, the A 2 O process can be largely described as eight flow rates. In this case, f8 represents the flow of the treated wastewater into the river, etc., f5 represents the flow of the treated wastewater to treat the waste sludge, and f6 and f7 represent two regeneration streams present in the A2O process. Where f7 represents the regeneration of nitrate and f6 represents the regeneration flow of sludge.

Under these conditions, assuming that the average value, standard deviation, and variance of the flow rate measured between f1 and f8 are as shown in Table 1 below, the weight matrix Ψ can be derived using Table 1 below.

division f1 f2 f3 f4 f5 f6 f7 f8 유율
(Measures) 2041 4133.9 5981.7 4215.1 1963.5 2062.1 1954.8 42.3 σ 686 1358 2044 1358 652 686 686 13.75 σ ² 470878 1845931 4181496 1845937 425525 470879 470879 198

That is, it is expressed by the following equation 17 by using the square of the variance σ ² in Ψ expressed by the above equation (3).

In addition, when the mass conservation formula is applied to the A 2 O process of FIG. 2 in order, it may be expressed as in Equation 18 below.

Q represents a flow rate corresponding to f1 to f8, and when the process matrix A ₁ is calculated using the mass storage formula, the process order is arranged in rows, and the coefficients corresponding to f1 to f8 are arranged in columns. It can be expressed as 19.

As a result, since all variables required to obtain y _esti described in Equation 14 are derived, the estimated value of the flow rate can be derived using Equation 14, and the derivation values are shown in Table 2 below.

division f1 f2 f3 f4 f5 f6 f7 f8 유율
(Estimated value) 2032.6 4115.1 6061.0 4115.1 1990.3 2082.6 1945.9 42.3

Since the y _esti value is derived, it is possible to determine whether the individual measurement data y _meas includes a gross error using Equation 15 and Equation 16.

For example, when using Equation 16, since the standard deviation σ is 686 and the measured value y _esti is 2032.6 with respect to f1, it is determined that there is no gross error in the measured data only when the condition of Equation 20 is satisfied. Can be.

3 is a block diagram of a gross error detection system using the Lagrange multiplier method according to an embodiment of the present invention. Referring to FIG. 3, the gross error detection system using the Lagrange multiplier method includes a data measuring unit 110, a data calculating unit 120, a preset setting unit 130, a gross error detecting unit 140, and a data storing unit 150. ). The gross error detection system may further include a data corrector 160 for performing correction of measurement data including gross errors.

First, the data measuring unit 110 generates measurement data by measuring process variables at each step of the wastewater treatment process. Process variables measured by the data measuring unit 110 are flow rates of whole phosphorus (TP), total nitrogen (TN), chemical oxygen demand (COD), total oil substance (TSS), and the like. The data measuring unit 110 receives the measured value sensed by the sensors installed in the wastewater treatment process, or generates the measurement data based on an external input of the user, and stores the data to the data storage unit 150.

The measurement data may be periodically updated at predetermined time intervals, and the accumulated measurement data may be used by the data operation unit 120 to calculate an average value and a normal distribution value.

The data operation unit 120 calculates an average value and a normal distribution value of the measured data stored in the data storage unit 150, and calculates a process variable estimation value using the normal distribution value, the process matrix read from the preset setting unit, and the measurement data. To generate the estimated data.

In this case, the data calculating unit 120 may calculate the data estimated value based on Equation 14 arranged by the Lagrange multiplier method. Here, the process matrix A ₁ may use a value stored by the preset setting unit, and the weight matrix Ψ may use a standard deviation stored in the data storage unit.

That is, the data operation unit 120 reads the measurement data, the weight matrix calculated from the standard deviation, and the process matrix from the preset setting unit 130 to generate the estimated data.

The preset setting unit 130 stores a process matrix that the data calculating unit 120 can use to calculate the estimated value. In this case, the process matrix may be derived using coefficient values of the mass storage equation in each step of the wastewater treatment process.

The gross error detection unit 140 is a function unit that detects a gross error by comparing the estimated data calculated by the data operation unit 120 with the measurement data stored in the data storage unit 150. In this case, in detecting the gross error, the reliability and the standard deviation stored in the data storage unit 150 may be used. Reliability is an item that can be adjusted by the administrator and can be changed according to external input.

For example, the gross error detector may determine the gross error by determining whether the condition of Equation 16 is satisfied. According to another embodiment, when the reliability is 99%, a gross error may be detected using Equation 21 below.

That is, the gross error detector 140 may determine whether the gross error is included in the measurement data based on the generalized equation of Equation 22 below.

In Equation 22, y _meas is measured data, y _esti is estimated data, σ is a standard deviation of measured data, and P _i is a value representing a confidence level of i% in a normal distribution.

The data storage unit 150 is a function unit for storing measured data, average values and standard deviation information of the measured data, and estimated data calculated by the data calculating unit 120. The data storage unit 150 may use a magnetic recording medium such as RAM and ROM. In addition, in consideration of the capacity limit of the data storage unit 150, if a predetermined number of times of measurement data is stored, starting from the next measurement data, the first recorded measurement data may be deleted and the newly stored measurement data may be stored.

The data corrector 160 removes the measurement data determined as data including the gross error from the gross error detector 140, and replaces the measured data with the estimated data. That is, data correction is performed by replacing measured data with estimated data.

4 is a flowchart of a data correction method using a gross error detection system according to an exemplary embodiment of the present invention.

Referring to FIG. 4, first, the data measuring unit generates measurement data on process variables from a wastewater treatment process (S410). In this case, the measurement data may be continuously updated at predetermined time intervals. Thereafter, the data operation unit calculates an average value and a standard deviation value of the measured data (S420), and calculates estimated data of the process variable based on the weight matrix, the process matrix, and the measured data based on the standard deviation value (S430). The gross error detector determines whether to include a gross error based on the measured data, the estimated data and the standard deviation (S440), and the data compensator corrects the measured data by replacing the measured data including the gross error with the estimated data. It is made (S450).

As described above, although the present invention has been described by way of limited embodiments and drawings, the present invention is not limited thereto and is intended by those skilled in the art to which the present invention pertains. Various modifications and variations are possible within the scope of equivalents of the claims to be described.

10: anaerobic reactor
20: Anaerobic Reactor
30: aerobic reactor
40: settling tank
110: data measuring unit
120: data operation unit
130: preset unit
140: process error detection unit
150: data storage
160: data correction unit

Claims (17)

Generating measurement data by measuring process variables in the wastewater treatment process;
Generating estimated data of the process variable according to the following equation by applying the Lagrange multiplier method to the measured data;
Detecting whether a measurement error includes a gross error based on the measurement data, the estimated data, and a standard deviation of the measurement data.
A gross error detection method using a Lagrange multiplier comprising a.
[Mathematical Expression]

(Where y _esti is estimated data, y _meas is measured data, Ψ is the weight matrix, and A ₁ is the process matrix containing the coefficients of the mass conservation equation.)
delete The method of claim 1, wherein the detecting of the gross error comprises:
A gross error using a Lagrange multiplier method, characterized in that a relative error is calculated based on the measured data, the estimated data and the standard deviation, and the gross error is detected based on the relative error and a reliability value. Detection method.
The method of claim 3, wherein
The relative error is a gross error detection method using the Lagrange multiplier, characterized in that calculated based on the following equation.

[Mathematical Expression]

(Where RE is relative error, y _meas is measured data, y _esti is estimated data, and σ is the standard deviation of the measured data.)

The method of claim 1, wherein the detecting of the gross error comprises:
Based on the following equation, the gross error detection method using the Lagrange multiplier characterized in that it is determined whether or not the gross error included in the measurement data.

[Mathematical Expression]

(Where y _meas is measured data, y _esti is estimated data, σ is the standard deviation of the measured data, and P _i is the value representing the confidence level of i% in the normal distribution.)
The method of claim 1, wherein after the detecting of the gross error,
And a data correction step of replacing the measured data including a gross error with the estimated data.
A data measuring unit generating measurement data on process variables in each step of the wastewater treatment process;
A data calculator for calculating an average value and a standard deviation value of the measured data and calculating estimated data of a process variable based on a weight matrix, a process matrix, and the measured data based on the standard deviation value;
A preset storage unit for storing the process matrix;
A data storage unit for storing the standard deviation value, the measurement data, and the estimated data; And
And a gross error detection unit determining whether gross error is included in the measurement data based on the measurement data, the estimated data, and the standard deviation value.
And a data error calculating unit using a Lagrange multiplier method for calculating the estimated data based on the following equation.
[Mathematical Expression]

Where y _esti is estimated data, y _meas is measured data, Ψ is a weight matrix, and A ₁ is a process matrix containing the coefficients of the mass conservation equation.
The method of claim 7, wherein
The gross error detection system using the Lagrange multiplier, characterized in that the data measuring unit generates the measurement data at a predetermined time interval.
The method of claim 7, wherein
The weight error detection system using a Lagrange multiplier, characterized in that the weight matrix is derived based on the following equation.

[Mathematical Expression]

Where Ψ is the weight matrix and σ is the standard deviation.
delete The method of claim 7, wherein
The process matrix is a gross error detection system using the Lagrange multiplier, characterized in that generated based on the coefficient value of the energy conservation equation of each step of the wastewater treatment process.
The method of claim 7, wherein the gross error detection unit,
A gross error using a Lagrange multiplier method, characterized in that a relative error is calculated based on the measured data, the estimated data and the standard deviation, and the gross error is detected based on the relative error and a reliability value. Detection system.
13. The method of claim 12,
The relative error is a gross error detection system using the Lagrange multiplier, characterized in that calculated based on the following equation.

[Mathematical Expression]

(Where RE is relative error, y _meas is measured data, y _esti is estimated data, and σ is the standard deviation of the measured data.)
The method of claim 7, wherein the gross error detection unit,
A gross error detection system using the Lagrange multiplier, characterized in that it is determined whether the measurement data includes a gross error based on the following equation.

[Mathematical Expression]

(Where y _meas is measured data, y _esti is estimated data, σ is the standard deviation of the measured data, and P _i is the value representing the confidence level of i% in the normal distribution.)
15. The method of claim 14,
Wherein Pi is 1.96 gross error detection system using the Lagrange multiplier method.
The method of claim 7, wherein
A gross error detection system using the Lagrange multiplier method further comprises a data correction unit for replacing the measured data including a gross error with the estimated data.
Generating measurement data for process variables from the wastewater treatment process;
Calculating an average value and a standard deviation value of the measurement data;
Calculating estimated data of a process variable based on the weight matrix, the process matrix, and the measurement data based on the standard deviation value according to the following equation;
Determining whether a gross error is included based on the measured data, the estimated data, and the standard deviation; And
Correcting the measurement data by removing the measurement data including a gross error and replacing it with the estimated data
Data correction method using a gross error detection system comprising a.
[Mathematical Expression]

Where y _esti is estimated data, y _meas is measured data, Ψ is a weight matrix, and A ₁ is a process matrix containing the coefficients of the mass conservation equation.

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