CN111256745A - Data calibration method for portable air quality monitor - Google Patents
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Abstract
The invention discloses a data calibration method of a portable air quality monitor, which constructs an independent variable monitoring data matrix by setting independent variables and dependent variables, creatively calibrates air quality monitoring data by using a partial least square regression model, integrates the advantages of principal component analysis, typical correlation analysis and linear regression analysis in multiple regression analysis in view of the diversity and cross influence of error factors generated by the monitoring data, compared with real data, the calibrated data are obviously reduced in absolute error and total relative error, the simulation has repeatability, the precision of the monitoring data is improved, and the calibrated data information can be obtained only by introducing the monitoring data into a program of a computer through a USB interface, so that the data calibration method is simple and easy to operate.
Description
Technical Field
The invention relates to the technical field of air quality detection, in particular to a data calibration method for a portable air quality monitor.
Background
Currently, the quality of air is usually monitored by "four-dust" (PM2.5, PM10, CO, NO)2、SO2、O3) Monitoring of the concentration. Generally, a plurality of monitoring points are selected as national monitoring and control sites in a city, relevant monitoring data are issued at regular intervals, and the data can accurately reflect the air quality conditions around the monitoring points, but the national monitoring points are usedThe air quality monitoring and forecasting cannot be given in real time due to the reasons of less distribution and control, lag in data release time, higher cost and the like.
The portable miniature air quality monitor can monitor the air quality of a certain area in a real-time gridding manner, and can monitor meteorological parameters such as temperature, humidity, wind speed, air pressure, precipitation and the like at the same time. However, since the monitor generates a certain zero drift and range drift due to its own technical reasons, the sensor is affected by unconventional gaseous pollutants and weather factors, which causes a certain difference between the data monitored by the micro air quality monitor and the data of the national control point at the same time.
Disclosure of Invention
In view of the above, an object of the present invention is to provide a data calibration method for a portable air quality monitor, which calibrates monitoring data measured by the portable air quality monitor.
Based on the above purpose, the present invention provides a data calibration method for a portable air quality monitor, which comprises:
PM2.5, PM10, CO and NO of the state control point2、SO2、O3The monitoring data of (2) and the monitoring data of temperature, humidity, wind speed, air pressure and precipitation of the self-building point are used as independent variables, and the PM2.5, PM10, CO and NO of the self-building point are used as independent variables2、SO2、O3The calibration value of the monitoring data is used as a dependent variable;
constructing an independent variable monitoring data matrix according to the time point of the independent variable monitoring data release;
converting the index value of each original independent variable in the independent variable monitoring data matrix into a standardized index value;
calculating a correlation coefficient matrix of 6 dependent variables and 11 independent variables;
respectively extracting the components of the independent variable group and the dependent variable group;
solving a regression equation between the independent variable group and the dependent variable group and the components of the 6 independent variable groups of the proposed national control points by taking p pairs of principal components, wherein the ratio of p principal components to explain the independent variables is more than 90%;
substituting the proposed independent variable group components into regression equations between the independent variable group and the dependent variable group and the proposed components of the 6 independent variable groups of the national control points to obtain the regression equations between the standardized index variables;
respectively reducing the standardized index variables into original variables to obtain a calibration regression equation;
and inputting the independent variable monitoring data into a calibration regression equation to obtain calibrated independent variable monitoring data.
Preferably, PM2.5, PM10, CO and NO of the national control point2、SO2、O3The monitoring data of (2) and the monitoring data of temperature, humidity, wind speed, air pressure and precipitation of the self-building point are used as independent variables, and the PM2.5, PM10, CO and NO of the self-building point are used as independent variables2、SO2、O3As a dependent variable, the calibration value of the monitoring data comprises:
by x1，x2，...，x6PM2.5, PM10, CO, NO respectively representing State control points2、SO2、O3The monitoring data of (1);
by x7，x8，...，x11Respectively representing monitoring data of temperature, humidity, wind speed, air pressure and rainfall meteorological indexes of the self-building point;
by zjJ ═ 1,2,, 6 denote self-construction points PM2.5, PM10, CO, NO, respectively2、SO2、O3A calibration value of the monitoring data of (1);
wherein x1，x2，...，x11Are all independent variables, zjJ 1,2, 6 are all dependent variables.
Preferably, the constructing of the independent variable monitoring data matrix according to the time point of the release of the independent variable monitoring data comprises:
by i1，i2，...，imRespectively representing the 1 st, 2 nd, … th, m th time points of the independent variable monitoring data distribution, the ith time point x1，x2，…，x11The index values of the independent variable monitoring data are respectively recorded as [ a ]i1,ai2,…,ai,11]Constructing a monitoring data matrix A ═ (a)ij)m×11。
Preferably, converting the index value of each original independent variable in the independent variable monitoring data matrix into a standardized index value comprises:
index value a of the independent variableijConversion into a normalized index value
Wherein the content of the first and second substances,
balance
Is a normalized index variable;
similarly, the index value b of the dependent variableijConversion into a normalized index value
Wherein the content of the first and second substances,
correspondingly, call
Are the corresponding normalized variables.
Preferably, the correlation coefficient matrix of 6 dependent variables and 11 independent variables is calculated as:
calculating a correlation coefficient matrix R of 6 dependent variables plus 11 independent variables by using MATLAB software17×17。
Preferably, the components of the independent variable group and the dependent variable group are respectively proposed, and comprise:
using Matlab software, each pair of components was found to be:
wherein s and t are both coefficients in the correlation coefficient matrix.
Preferably, the regression equation between the set of independent variables and the set of dependent variables and the components of the set of 6 independent variables of the proposed national control point is taken for p principal components, wherein the ratio of p principal components to explain the independent variables is more than 90%, including
Taking p pairs of principal components to obtain an independent variable group, a dependent variable group and u1,u2,…,u6Regression equation between
Wherein the ratio of p principal components to explain the independent variable reaches more than 90%, and m and u are both coefficients in the correlation coefficient matrix. .
Preferably, substituting the proposed independent variable set components into a regression equation between the independent variable set and the dependent variable set and the components of the 6 independent variable sets of the proposed national control point to obtain a regression equation between the standardized index variables includes:
substituting the proposed independent variable group component into uiRegression equation z E between independent variable group and dependent variable group and components of 6 independent variable groups of proposed national control pointsiObtaining a regression equation between the normalized index variables
z1＝k1+q11x1+q12x2+…+q1,11x11
z2＝k2+q21x1+q22x2+…+q2,11x11
z6＝k6+q61x1+q62x2+…+q6,11x11
Wherein k isi(i ═ 1,2, … 6) is a constant term of the regression equation, qij(i-1, 2, … 6; j-1, 2, … 11) is a regression coefficient.
As can be seen from the above, the data calibration method for the portable air quality monitor provided by the present invention constructs an independent variable monitoring data matrix by setting independent variables and dependent variables, converts the index values of each original independent variable in the independent variable monitoring data matrix into standardized index values, calculates the correlation coefficient matrices of 6 dependent variables and 11 independent variables, provides the components of the independent variable set and the dependent variable set, respectively, obtains the regression equations between the independent variable set and the dependent variable set and the components of the 6 independent variable sets of the proposed national control points, brings the provided components of the independent variable set into the regression equations between the independent variable set and the dependent variable set and the components of the 6 independent variable sets of the proposed national control points, obtains the regression equations between the standardized index variables and reduces the standardized index variables into the original variables, respectively, obtains the calibrated regression equations, inputs the independent variable monitoring data into the calibrated regression equations, the method can obtain the calibrated independent variable monitoring data, can effectively calibrate the monitoring data of the portable air quality monitor, improves the precision of the monitoring data, can obtain the calibrated data information only by leading the monitoring data into a program of a computer through a USB interface, is simple and easy to operate, and has the advantages of centralized principal component analysis, typical correlation analysis and linear regression analysis in processing multiple regression analysis and stronger pertinence and technical advantages in solving the problem of calibrating the air quality monitoring data.
Drawings
FIG. 1 is a schematic flow chart of a data calibration method for a portable air quality monitor according to an embodiment of the present invention;
FIG. 2 is a graph of calibrated data prediction according to an embodiment of the present invention;
FIG. 3 is a graph showing a comparison of the total relative error before and after calibration of data according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
It should be noted that all expressions using "first" and "second" in the embodiments of the present invention are used for distinguishing two entities with the same name but different names or different parameters, and it should be noted that "first" and "second" are merely for convenience of description and should not be construed as limitations of the embodiments of the present invention, and they are not described in any more detail in the following embodiments.
A data calibration method for a portable air quality monitor comprises the following steps:
s101, the PM2.5 of the state control point, namely the state monitoring and control site,PM10、CO、NO2、SO2、O3(the two-dust four-gas is collectively called as an air quality index) monitoring data and the temperature, humidity, wind speed, air pressure and precipitation (collectively called as meteorological indexes) monitoring data of the self-building point are used as independent variables, and the PM2.5, PM10, CO and NO of the self-building point are used as independent variables2、SO2、O3The calibration value of the monitoring data is used as a dependent variable;
s102, constructing an independent variable monitoring data matrix according to the time point of independent variable monitoring data release;
for example, the release time points may be 1 hour apart each time.
S103, converting the index value of each original independent variable in the independent variable monitoring data matrix into a standardized index value;
s104, calculating a correlation coefficient matrix of 6 dependent variables and 11 independent variables;
s105, respectively extracting the components of the independent variable group and the dependent variable group;
s106, solving a regression equation between the independent variable group and the dependent variable group of the main components and the components of the 6 independent variable groups of the proposed national control points, wherein the ratio of p main components to explain the independent variables is more than 90%;
s107, substituting the provided independent variable group components into regression equations between the independent variable group and the dependent variable group and the provided components of the 6 independent variable groups of the national control points to obtain regression equations between the standardized index variables;
s108, respectively reducing the standardized index variables into original variables to obtain a calibrated regression equation;
s109, inputting the independent variable monitoring data into the calibration regression equation to obtain calibrated independent variable monitoring data.
The partial least squares regression model provides a multivariate linear regression modeling method, and particularly when the number of variables is large and multiple correlations exist due to cross influence, the regression model integrates the advantages of principal component analysis, typical correlation analysis and linear regression analysis in processing multiple regression analysis.
Currently, such regression models are mainly used for multiple linear regression analysis problems, such as: yan constant-dryness, Hongmei, Zhanglian, etc. weather index feature judgment was studied in the text "feature diagnosis of northern Pacific storm axis index in winter based on partial least squares regression" (weather science, 2018, phase 5); lanjian studied the factor of urban real estate price influence in "analysis of influence factor of real estate price in large and medium cities of the whole nation based on partial least squares regression" (yunan university, master paper, 2018.5); the relation between water vapor and ground air temperature is researched in the article of application research of partial least squares regression in multi-mode integrated forecast of water vapor and ground air temperature of Li Jiangfeng (Nanjing university of information engineering, Master paper, 2018.5).
At present, on the one hand, the application research of partial least squares regression analysis mostly shows that a linear regression equation between two variables is explored, and the regression analysis between multiple variables is not related much; on the other hand, the existing research has not been concerned with the problem of calibrating data, especially the field of calibrating air quality monitoring data. Therefore, portable air quality monitors on the market currently have no corresponding calibration system, resulting in low accuracy of monitoring data.
The method comprises the steps of setting independent variables and dependent variables, constructing an independent variable monitoring data matrix, converting index values of all original independent variables in the independent variable monitoring data matrix into standardized index values, calculating correlation coefficient matrixes of 6 dependent variables and 11 independent variables, respectively providing components of an independent variable group and a dependent variable group, solving regression equations between the independent variable group and the dependent variable group and the components of the 6 independent variable groups of the provided national control points, substituting the provided components of the independent variable group into the regression equations between the independent variable group and the dependent variable group and the components of the 6 independent variable groups of the provided national control points, obtaining regression equations between the standardized index variables and respectively reducing the standardized index variables into the original variables to obtain calibrated regression equations, inputting the independent variable monitoring data into the calibrated regression equations to obtain calibrated independent variable monitoring data, the method has the advantages that the monitoring data of the portable air quality monitoring instrument can be effectively calibrated, the precision of the monitoring data is improved, the calibrated data information can be obtained only by leading the monitoring data into a program of a computer through a USB interface, the method is simple and easy to operate, the partial least square regression analysis used in the method integrates the advantages of principal component analysis, typical correlation analysis and linear regression analysis in processing multiple regression analysis, and the method has strong pertinence and technical advantages in solving the problem of air quality monitoring data calibration.
In one embodiment, the control points are PM2.5, PM10, CO and NO2、SO2、O3The monitoring data of (2) and the monitoring data of temperature, humidity, wind speed, air pressure and precipitation of the self-building point are used as independent variables, and the PM2.5, PM10, CO and NO of the self-building point are used as independent variables2、SO2、O3As a dependent variable, the calibration value of the monitoring data comprises:
by x1，x2，…，x6PM2.5, PM10, CO, NO respectively representing State control points2、SO2、O3The monitoring data of (1);
by x7，x8，…，x11Respectively representing monitoring data of temperature, humidity, wind speed, air pressure and rainfall meteorological indexes of the self-building point;
by zjJ-1, 2, …, 6 respectively represent self-establishing points PM2.5, PM10, CO, NO2、SO2、O3A calibration value of the monitoring data of (1);
wherein x1，x2，…，x11Are all independent variables, zjJ 1,2, 6 are all dependent variables.
As an embodiment, constructing an independent variable monitoring data matrix according to a time point of the independent variable monitoring data release includes:
by i1，i2，…，imRespectively representing the 1 st, 2 nd, … th, m th time points of the independent variable monitoring data distribution, the ith time point x1，x2，…，x11The index values of the independent variable monitoring data are respectively recorded as [ a ]i1,ai2,…,ai,11]Constructing a monitoring data matrix A ═ (a)ij)m×11。
As an embodiment, converting the index value of each original independent variable in the independent variable monitoring data matrix into a normalized index value includes:
index value a of the independent variableijConversion into a normalized index value
Wherein the content of the first and second substances,
balance
Is a normalized index variable;
similarly, the index value b of the dependent variableijConversion into a normalized index value
Wherein the content of the first and second substances,
correspondingly, call
Are the corresponding normalized variables.
As an embodiment, the matrix of correlation coefficients of 6 dependent variables and 11 independent variables is calculated as:
calculating a correlation coefficient matrix R of 6 dependent variables plus 11 independent variables by using MATLAB software17×17。
As an embodiment, the components of the independent variable group and the dependent variable group are respectively provided, and the components comprise:
using Matlab software, each pair of components was found to be:
as an embodiment, a regression equation between the components of the independent variable group and the dependent variable group and the 6 independent variable groups of the proposed country control point is obtained for p pairs of components, wherein the ratio of p principal components to explain the independent variables is more than 90%, including
Taking p pairs of components to obtain an independent variable group, a dependent variable group and u1,u2,…,u6Regression equation between
The ratio of p principal components in the p principal component interpretation independent variables is more than 90%.
As an embodiment, substituting the proposed independent variable set components into a regression equation between the independent variable set and the dependent variable set and the components of the 6 independent variable sets of the proposed national control point to obtain a regression equation between the normalized index variables includes:
substituting the proposed independent variable group component into uiRegression equations between the independent and dependent variable sets and the components of the 6 independent variable sets of the proposed national control points
Obtaining a regression equation between the variables of the standardized index
z1＝k1+q11x1+q12x2+…+q1,11x11
z2＝k2+q21x1+q22x2+…+q2,11x11
z6＝k6+q61x1+q62x2+…+q6,11x11.
In one embodiment, the model created by this patent was verified using a set of real data (data provided by the 2019 national university student math modeling contest D).
According to the steps, the regression equation among the 6 air quality index variables of the self-construction point and the six air quality index variables and the five meteorological index variables of the national control point is obtained as follows:
z1＝11.0643+0.5024x1+0.1798x2-0.3086x3+0.1574x4+0.0830x5-0.1276x6
-0.3588x7+0.0020x8-0.0604x9+0.5365x10-0.2250x11
z2＝25.0139+0.6168x1+0.2175x2-0.6121x3+0.4136x4+0.5658x5-0.1466x6
-0.7187x7+0.0166x8-0.0842x9+0.7637x10-0.7495x11
z3＝0.5533+0.0055x1+0.0017x2-0.0011x3+0.0039x4-0.0027x5-0.0014x6
-0.0013x7-0.0002x8+0.0000x9+0.0089x10-0.0007x11
z4＝58.2450+0.1575x1-0.0081x2-0.4490x3+0.4167x4+0.3767x5-0.5143x6
-0.3375x7+0.0047x8-0.0134x9+0.1991x10-0.5401x11
z5＝-27.1380+0.0129x1+0.0544x2+0.1496x3+0.0317x4+0.0834x5+0.3595x6
+0.0154x7+0.0054x8+0.0190x9-0.1371x10+0.1158x11
z6＝109.2272-0.0342x1-0.0876x2-0.5821x3-0.2559x4-0.7096x5-0.0110x6
-0.4376x7+0.0009x8-0.0235x9+1.5778x10-0.4377x11
to test the accuracy of the 6 regression equations of the model to
For the coordinate values, a prediction map is plotted for all sample points.
Is the jth dependent variable index at the ith sample point (y)ij) On the prediction map, if soThe points can be uniformly distributed near the diagonal line of the graph, so that the difference between the fitting value of the equation and the original value is small, and the fitting effect of the equation is satisfactory. Using MATLAB software, a prediction map was generated as shown in FIG. 2.
It can be seen that from the fitting prediction chart of the calibration data, the fitting effect of PM2.5 and PM10 is more ideal, and CO and NO are2、O3The fitting effect of (1) is good, only SO2The fitting effect of one index is not ideal.
Substituting 11 index data (including 6 air quality indexes and 5 meteorological indexes) of the self-establishing points into the regression equation to obtain calibrated data, analyzing the total relative error between the calibrated data and the data of the national control points in order to visually quantify the accuracy of the evaluation model, and drawing the total relative error before and after calibration into a histogram, as shown in FIG. 3, it can be seen that SO is obtained from the 6 indexes2The overall relative error of the data calibrated by other indexes is obviously reduced, so that the established regression equation can effectively calibrate the data of the self-established point.
Those of ordinary skill in the art will understand that: the discussion of any embodiment above is meant to be exemplary only, and is not intended to intimate that the scope of the disclosure, including the claims, is limited to these examples; within the idea of the invention, also features in the above embodiments or in different embodiments may be combined, steps may be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.
The embodiments of the invention are intended to embrace all such alternatives, modifications and variances that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, substitutions, improvements and the like that may be made without departing from the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (8)
1. A data calibration method for a portable air quality monitor is characterized by comprising the following steps:
PM2.5, PM10, CO and NO of the state control point2、SO2、O3The monitoring data of (2) and the monitoring data of temperature, humidity, wind speed, air pressure and precipitation of the self-building point are used as independent variables, and the PM2.5, PM10, CO and NO of the self-building point are used as independent variables2、SO2、O3The calibration value of the monitoring data is used as a dependent variable;
constructing an independent variable monitoring data matrix according to the time point of the independent variable monitoring data release;
converting the index value of each original independent variable in the independent variable monitoring data matrix into a standardized index value;
calculating a correlation coefficient matrix of 6 dependent variables and 11 independent variables;
respectively extracting the components of the independent variable group and the dependent variable group;
solving a regression equation between the independent variable group and the dependent variable group of the p pairs of components and the components of the 6 independent variable groups of the proposed national control points, wherein the ratio of p main components to explain the independent variables is more than 90%;
substituting the proposed independent variable group components into regression equations between the independent variable group and the dependent variable group and the proposed components of the 6 independent variable groups of the national control points to obtain the regression equations between the standardized index variables;
respectively reducing the standardized index variables into original variables to obtain a calibration regression equation;
and inputting the independent variable monitoring data into the calibration regression equation to obtain calibrated independent variable monitoring data.
2. The data calibration method for the portable air quality monitor according to claim 1, wherein the PM2.5, PM10, CO and NO of the national control point2、SO2、O3The monitoring data of (2) and the monitoring data of temperature, humidity, wind speed, air pressure and precipitation of the self-building point are used as independent variables, and the PM2.5, PM10, CO and NO of the self-building point are used as independent variables2、SO2、O3As a dependent variable, the calibration value of the monitoring data comprises:
by x1，x2，…，x6PM2.5, PM10, CO, NO respectively representing State control points2、SO2、O3The monitoring data of (1);
by x7，x8，…，x11Respectively representing monitoring data of temperature, humidity, wind speed, air pressure and rainfall meteorological indexes of the self-building point;
by zjJ-1, 2, …, 6 respectively represent self-establishing points PM2.5, PM10, CO, NO2、SO2、O3A calibration value of the monitoring data of (1);
wherein x1，x2，…，x11Are all independent variables, zjJ-1, 2, …, 6 are all dependent variables.
3. The method for calibrating data of a portable air quality monitor according to claim 2, wherein constructing the independent variable monitoring data matrix according to the time point of the release of the independent variable monitoring data comprises:
by i1，i2，…，imRespectively representing the 1 st, 2 nd, … th, m th time points of the independent variable monitoring data distribution, the ith time point x1，x2，…，x11The index values of the independent variable monitoring data are respectively recorded as [ a ]i1,ai2,…,ai,11]Constructing a monitoring data matrix A ═ (a)ij)m×11。
4. The method of claim 3, wherein converting the indicator value for each of the raw independent variables in the independent variable monitoring data matrix to a normalized indicator value comprises:
index value a of the independent variableijConversion into a normalized index value
Wherein the content of the first and second substances,
balance
Is a normalized index variable;
similarly, the index value b of the dependent variableijConversion into a normalized index value
Wherein the content of the first and second substances,
correspondingly, call
Are the corresponding normalized variables.
5. The method of claim 4, wherein the matrix of correlation coefficients for the 6 dependent variables and the 11 independent variables is calculated as:
calculating a correlation coefficient matrix R of 6 dependent variables plus 11 independent variables by using MATLAB software17×17。
6. The method of calibrating portable air quality monitor data according to claim 5, wherein said separately extracting the composition of the independent variable group and the dependent variable group comprises:
using Matlab software, each pair of components was found to be:
where s and t are both coefficients in the correlation coefficient matrix, u represents the proposed component of the independent variable group, and v represents the proposed component of the dependent variable group.
7. The method of claim 6 wherein the taking p pairs of components to solve regression equations between the components of the independent and dependent variable sets and the 6 independent variable sets of the proposed national control points, wherein the ratio of p principal component to the explained independent variables is above 90%, includes
Taking p pairs of components to obtain an independent variable group, a dependent variable group and u1,u2,…,u6Regression equation between
Wherein the ratio of p principal components to explain the independent variable reaches more than 90%, and m and n are both coefficients in the correlation coefficient matrix.
8. The method of calibrating data for a portable air quality monitor according to claim 7, wherein the step of introducing the proposed independent variable set components into a regression equation between the independent variable set and the dependent variable set and the components of the 6 independent variable sets of the proposed national control points to obtain a regression equation between the standardized index variables comprises:
substituting the proposed independent variable group component into uiRegression equations between the independent and dependent variable sets and the components of the 6 independent variable sets of the proposed national control points
Obtaining a regression equation between the variables of the standardized index
z1＝k1+q11x1+q12x2+…+q1,11x11
z2＝k2+q21x1+q22x2+…+q2,11x11
z6＝k6+q61x1+q62x2+…+q6,11x11
Wherein k isi(i ═ 1,2, … 6) is a constant term of the regression equation, qij(i-1, 2, … 6; j-1, 2, … 11) is a regression coefficient, k isiAnd q isijAre all calculated by MATLAB softwareThus obtaining the product.
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