CN105445344A - Temperature compensation method of system for detecting heavy metals in water environment - Google Patents

Abstract

The invention discloses a temperature compensation method of a system for detecting heavy metals in a water environment. After acquired polarization current and polarization potential are subjected to smoothing processing through differential filtering, a fitted regression equation inverse model is established, a temperature compensation model is obtained through solution of the deviation, the square deviation and the partial derivative, judgment is performed in combination with the REF (relative error factor), the number of fitting times is increased automatically for fitting again when the standard is not met, a high-order multivariate regression inverse model with the higher precision is constructed, the temperature compensation model is applied to detection of the heavy metals in the water environment, and the detection precision can be improved.

Description

A kind of temperature compensation of water environment heavy metal detection system

Technical field

The present invention relates to detection field, be specifically related to a kind of temperature compensation of water environment heavy metal detection system.

Background technology

Along with the fast development of China's industrialization urbanization, constantly enter rivers and lakes with the industrial waste water of heavy metal, sanitary sewage, heavy metal pollution is day by day serious, has had a strong impact on the life security of people.Heavy metal pollution has become domestic and international problem demanding prompt solution, and the accuracy of heavy metal analysis and validity become particularly important.

The method of existing detection Heavy Metals in Water Environment has electrochemical methods, electrochemical methods carries out chemical reaction according to ion electrode in detected solution during with heavy metal ion, the change of the electric signal of generation carrys out analysis heavy metal concentration, detection method is easily subject to the impact of environment temperature, comparatively big error can be there is in testing result along with the change of environment temperature, the electrode of existing temperature compensation normally correct detection terminal, concentration of heavy metal ion value is gone out according to the electrode signal of the ion-selective electrode rod received and the Electrode Calibration model solution after correcting, algorithm adopts repeatedly the temperature correction mathematical model of one-variable linear regression and dualistic and quadric regression technique study electrode, thus get rid of the disturbing effect of temperature and outside thereof, its shortcoming is that the susceptibility of founding mathematical models to the heavy metal data processing in water environment is poor, cause accuracy of detection low.

Summary of the invention

The invention provides a kind of temperature compensation of water environment heavy metal detection system, solve temperature compensation in the system of existing detection water environment heavy metal and effectively can not improve the problem of water environment heavy metal detection system accuracy of detection.

The present invention solves the problem by the following technical programs:

A temperature compensation for water environment heavy metal detection system, comprises the following steps:

1) gathering heavy metal concentration is C _jpolarization current I (j) of water environment to be measured, polarized potential E (j) and environment temperature U _tj; J is natural number; C _jfor the jth heavy metal concentration gathered, I (j) is the jth polarization current gathered, and E (j) is the jth polarized potential gathered;

2) method of difference filtering is carried out to polarization current I (j) and polarized potential E (j), obtain level and smooth E/I curve, and then obtain electrochemical sensor output peak point current I _cj:

3) model of temperature compensation is set up:

31) gather polarization current and the polarized potential value of n concentration calibration point and m scale of thermometer fixed point, a jth calibration point concentration calculated value is C (I _cj, U _tj), j, m, n are positive integer, and matching regression equation inversion model is:

$C(I_{Cj},U_{Tj})=(d_0+d_1{I}_{Cj}+d_2{U}_{Tj})+(d_3{I}_{Cj}^2+d_4{I}_{Cj}{U}_{Tj}+d_5{U}_{Tj}^2)+...+\mathrm{\ξ},$

In formula, the coefficient d of each rank expression formula _kfor temperature compensation constant coefficient, wherein k is positive integer, and 0≤k≤t-1, the matching item number t of equation is positive integer, and t>=3; ξ is higher order indefinite small; The pass of matching item number t and matching number of times r is:

$t=\frac{(r+3-1)!}{r!(3-1)!}=\frac{(r+2)(r+1)}{2};$

32) heavy metal concentration calibration value C _jrelative C (I _cj, U _tj) deviation be δ _j:

${\mathrm{\δ}}_j^2={\[\underset{k=0}{\overset{t}{\Σ}}{d}_k{p}_{jk}-C_j\]}^2$

In formula, p _jktemperature compensation constant coefficient d in regression equation inversion model _keach term coefficient, calibration point sum of square of deviations L _sfor:

$L_S=\underset{j=1}{\overset{S=m\×n}{\Σ}}{\[\underset{k=0}{\overset{t}{\Σ}}{d}_k{p}_{jk}-C_j\]}^2=L(d_0,...,d_{j-k},...,d_t),$

In formula, S is total number of calibration point, L _stemperature compensation constant coefficient d _kthe t meta-function of coefficient;

33) respectively to L _sask about d _klocal derviation, order k=0,1 ..., t, then model of temperature compensation is:

$\underset{j=1}{\overset{S}{\Σ}}\[\underset{k=0}{\overset{t}{\Σ}}{d}_k{p}_{jk}\]\×p_{jk}=\underset{j=1}{\overset{t}{\Σ}}{C}_j\×p_{jk}$

In formula, j=0,1 ..., S, S=m*n;

34) for weighing the relative error measure coefficient REF of performance be:

$REF=100\×\frac{{\[\underset{j=1}{\overset{n}{\Σ}}{\left(\frac{C_j-C_j^S}{C_j^s}\right)}^2\]}^{\frac{1}{2}}}{\sqrt{s}}$

In formula, C _jfor the concentration of heavy metal ion value that jth time detects, C _j ^sfor the actual value of concentration of heavy metal ion in standard solution when jth time detects, s is for detecting number of times; When REF is greater than the default limits of error, matching number of times r increases by 1 automatically, performs step 31); Otherwise this is set up model of temperature compensation and terminates.

In such scheme, when carrying out the detection of water environment heavy metal concentration, obtain polarization current I by the electrochemical sensor of each monitoring terminal _iwith polarized potential E _i, obtain environment temperature U by the temperature sensor of each monitoring terminal _t, polarization current I _iwith polarized potential E _ipeak point current I is obtained after differential filtering _c, by peak point current I _cwith environment temperature U _tsubstitute into the model of temperature compensation established, obtain the detectable concentration value of water environment to be measured.

Advantage of the present invention and effect are: after the polarization current gathered and polarized potential are passed through the smoothing process of differential filtering, set up matching regression equation inversion model, by asking deviation, deviation square and local derviation, obtain model of temperature compensation, and judge in conjunction with relative error measure coefficient REF, when not meeting standard, the matching again of automatic increase matching number of times, to construct the higher high order multiple regression inversion model of degree of accuracy, this model of temperature compensation is applied to water environment heavy metal analysis, improves its accuracy of detection.

Accompanying drawing explanation

Fig. 1 is the process flow diagram that the present invention sets up model of temperature compensation method.

Fig. 2 is the process flow diagram of the present invention when being applied to water environment heavy metal analysis.

Fig. 3 is the theory diagram of water environment heavy metal detection system in the present invention.

Embodiment

Below in conjunction with embodiment, the invention will be further described, but the present invention is not limited to these embodiments.

A temperature compensation for water environment heavy metal detection system, by set up high order multiple regression inversion model improve detect water environment heavy metal time data processing susceptibility, and then improve the accuracy of detection of water environment heavy metal detection system.

Water environment heavy metal detection system is made up of administrative center and at least one monitoring terminal, and each monitoring terminal is respectively equipped with electrochemical sensor and temperature sensor, for detecting water environment heavy metal and environment temperature; Obtain the polarization current I of water environment _i, polarized potential E _iand environment temperature U _t, and then obtain the concentration of Heavy Metals in Water Environment; Concentration data inputs to administrative center by GPRS network; Be provided with server and management system for monitoring in administrative center, concentration data inputs to server by GPRS network, and server is connected by Internet network with management system for monitoring, as shown in Figure 3.

Ensure the accuracy of the water environment heavy metal concentration obtained, need to carry out temperature compensation.The present invention, by setting up model of temperature compensation under calibration mode, improves the susceptibility of temperature compensation: use model of temperature compensation to carry out heavy metal concentration detection in a detection mode.Below for setting up model of temperature compensation and detecting the step of application of temperature compensation model in heavy metal concentration:

1) under calibration mode, model of temperature compensation is set up:

1.1) gathering heavy metal concentration is C _jpolarization current I (j) of water environment to be measured, polarized potential E (j) and environment temperature U _tj; J is natural number; C _jfor the jth heavy metal concentration gathered, I (j) is the jth polarization current gathered, and E (j) is the jth polarized potential gathered;

1.2) method of difference filtering is carried out to polarization current I (j):

The difference of adjacent two polarization current sampled values is I (j-1)-I (j-2) ≈ I (j)-I (j-1), the estimated value I of I (j) _g(j) be:

I _g(j)＝I(j-1)+[I(j-1)-I(j-2)]≈I(j)+[I(j)-I(j-1)]

According to Ge Labu criterion setting threshold epsilon ₁, when | I _g(j)-I (j) | > ε ₁time, I (j) is rough error, uses estimated value I _gi () replaces sampled value I (j);

Method of difference filtering is carried out to polarized potential E (j):

The difference of adjacent two polarized potential sampled values is E (j-1)-E (j-2) ≈ E (j)-E (j-1), the estimated value E of E (j) _g(j) be:

E _g(j)＝E(j-1)+[E(j-1)-E(j-2)]≈E(j)+[E(j)-E(j-1)]

According to Ge Labu criterion setting threshold epsilon ₂, when | E _g(j)-E (j) | > ε ₂time, E (j) is rough error, uses estimated value E _gj () replaces sampled value E (j);

Use above-mentioned method of difference filtering to obtain I (j) and E (j), after obtaining level and smooth E/I curve, obtain electrochemical sensor accurately and export peak point current I _cj;

1.3) polarization current and the polarized potential value of n concentration calibration point and m scale of thermometer fixed point is gathered, if a jth calibration point concentration calculated value is C (I _cj, U _tj), j is positive integer, n, m be positive integer then matching regression equation inversion model be:

$C\left(I_{Cj},U_{Tj}\right)=\left(d_0+d_1{I}_{Cj}+d_2{U}_{Tj}\right)+\left(d_3{I}_{Cj}^2+d_4{I}_{Cj}{U}_{Tj}+d_5{U}_{Tj}^2\right)+\mathrm{...}+\mathrm{\ξ},$

In formula, the key of model of temperature compensation is to determine temperature compensation constant coefficient d ₀, d ₁, d ₂, d ₃, d ₄, d ₅and follow-up a series of d, the coefficient d of each rank expression formula _kfor temperature compensation constant coefficient k is positive integer, and 0≤k≤(t-1); The matching item number of equation is that to be at least 3, t be positive integer for t, t, i.e. C (I _cj, U _tj) at least comprise 1 rank item (d ₀+ d ₁i _cj+ d ₂u _tj), as C (I _cj, U _tj) when being 2 rank, t is 6; R is variable for matching number of times, and when error is greater than the limits of error preset based on experience value, matching number of times r adds 1 automatically, namely can automatically change matching number of times r, until error is less than the limits of error according to actual conditions; R is variable, can realize high order multiple regression, sets up high order multiple regression inversion model further, and then improves accuracy of detection; ξ is higher order indefinite small;

After matching number of times r increases by 1 automatically,

$C\left(I_{Cj},U_{Tj}\right)=\left(d_0+d_1{I}_{Cj}+d_2{U}_{Tj}\right)+\left(d_3{I}_{Cj}^2+d_4{I}_{Cj}{U}_{Tj}+d_5{U}_{Tj}^2\right)+\mathrm{...}+\mathrm{\ξ}$

Become three rank by second order, three rank expression formulas are:

$(d_6{I}_{Cj}^3+d_7{I^2}_{Cj}{U}_{Tj}+d_8{I}_{Cj}{U^2}_{Tj}+d_9{U^3}_{Tj});$

The pass of matching item number t and matching number of times r is:

$t=\frac{(r+3-1)!}{r!(3-1)!}=\frac{(r+2)(r+1)}{2};$

1.4) heavy metal concentration calibration value C _jrelative C (I _cj, U _tj) deviation be δ _j:

${\mathrm{\δ}}_j^2={\[\underset{k=0}{\overset{t}{\Σ}}{d}_k{p}_{jk}-C_j\]}^2$

In formula, p _jktemperature compensation constant coefficient d in regression equation inversion model _keach term coefficient, i.e. p _j0=1, p _j1=I _cj, p _j2=U _tj, p _j3=I ² _cj, p _j4=I _cju _tj, p _j5=U ² _tj..., all calibration point sum of square of deviations L _sfor:

$L_S=\underset{j=1}{\overset{S=m\×n}{\Σ}}{\[\underset{k=0}{\overset{t}{\Σ}}{d}_k{p}_{jk}-C_j\]}^2=L(d_0,...,d_{j-k},...,d_t),$

In formula, S is the total number of all calibration points, L _stemperature compensation constant coefficient d _kt meta-function;

During t=5, respectively to L _sask d ₀~ d _kask local derviation, order obtain 6 equations:

$\left\{\begin{array}{c}{d}_{0}s+d_1\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}+d_2\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{U}_{Tj}+d_3\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I_{cj}}^2+d_4\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}{U}_{Tj}+d_5\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{U_{Tj}}^2=\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{C}_j\\ d_0\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}+d_1\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I_{cj}}^2+d_2\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}{U}_{Tj}+d_3\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I_{cj}}^3+d_4\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I_{cj}}^2{U}_{Tj}+d_5\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}{U_{Tj}}^2=\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}{C}_j\\ d_0\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{U}_{Tj}+d_1\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}{U}_{Tj}+d_2\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{U_{Tj}}^2+d_3\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I_{cj}}^2{U}_{Tj}+d_4\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}{U_{Tj}}^2+d_5\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{U_{Tj}}^3=\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{U}_{Tj}{C}_j\\ d_0\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I_{cj}}^2+d_1\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I_{cj}}^3+d_2\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I_{cj}}^2{U}_{Tj}+d_3\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I_{cj}}^4+d_4\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I_{cj}}^3{U}_{Tj}+d_5\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}{U_{Tj}}^3=\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I_{cj}}^2{C}_j\\ d_0\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}{U}_{Tj}+d_1\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I_{cj}}^2{U}_{Tj}+d_2\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}{U_{Tj}}^2+d_3\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I_{cj}}^3{U}_{Tj}+d_4\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}{U_{Tj}}^3+d_5\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{U_{Tj}}^4=\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{Cj}{U}_{Tj}{C}_j\\ d_0\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{U_{Tj}}^2+d_1\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}{U_{Tj}}^2+d_2\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{U_{Tj}}^3+d_3\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}{U_{Tj}}^3+d_4\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{U_{Tj}}^4+d_5\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{I}_{cj}=\underset{j=1}{\overset{s}{\mathrm{\Σ}}}{U_{Tj}}^2{C}_j\end{array}\right.$

D is determined by above formula ₀~ d _kvalue, thus determine model of temperature compensation:

$C(I_{Cj},U_{Tj})=d_0+d_1{I}_{Cj}+d_2{U}_{Tj}+d_3{I}_{Cj}^2+d_4{I}_{Cj}{U}_{Tj}+d_5{U}_{Tj}^2+...+\mathrm{\ξ}$

1.5) respectively to L _sask about d _klocal derviation, order then model of temperature compensation is:

$\underset{j=1}{\overset{S}{\Σ}}\[\underset{k=0}{\overset{t}{\Σ}}{d}_k{p}_{jk}\]\×p_{jk}=\underset{j=1}{\overset{t}{\Σ}}{C}_j\×p_{jk}$

In formula, j=0,1 ... S; S=m*n; Above-mentioned steps 1)-step 3) process flow diagram as shown in Figure 1;

1.6) relative error measure coefficient REF is:

$REF=100\×\frac{{\[\underset{j=1}{\overset{n}{\Σ}}{\left(\frac{C_j-C_j^S}{C_j^2}\right)}^2\]}^{\frac{1}{2}}}{\sqrt{s}}$

C in error factor _jfor the concentration of metal ions value that jth time detects, for the actual value of concentration of heavy metal ion in standard solution when jth time detects, s represents detection number of times; The effect of compensation can be found out by REF, weigh the performance of temperature compensation according to REF, investigate compensation effect and whether reach requirement, when REF is greater than the limits of error, matching number of times r increases by 1 automatically, performs step 1.3), rebuild model of temperature compensation; Otherwise, set up model of temperature compensation and terminate.

2) in a detection mode, model of temperature compensation is used to detect Heavy Metals in Water Environment concentration:

Heavy metal analysis is carried out to water environment to be measured, obtains polarization current I by the electrochemical sensor of each monitoring terminal _iwith polarized potential E _i, obtain environment temperature U by the temperature sensor of each monitoring terminal _t, polarization current I _iwith polarized potential E _ipeak point current I is obtained after differential filtering _c, by peak point current I _cwith environment temperature U _tsubstitute into the model of temperature compensation established, i.e. the detectable concentration value of exportable water environment to be measured, application testing process as shown in Figure 2.

Claims (2)

1. a temperature compensation for water environment heavy metal detection system, is characterized in that, comprises the following steps:

1) gathering heavy metal concentration is C _jpolarization current I (j) of water environment to be measured, polarized potential E (j) and environment temperature U _tj; J is natural number; C _jfor the jth heavy metal concentration gathered, I (j) is the jth polarization current gathered, and E (j) is the jth polarized potential gathered;

2) method of difference filtering is carried out to polarization current I (j) and polarized potential E (j), obtain level and smooth E/I curve, and then obtain electrochemical sensor output peak point current I _cj:

3) model of temperature compensation is set up:

31) gather polarization current and the polarized potential value of n concentration calibration point and m scale of thermometer fixed point, a jth calibration point concentration calculated value is C (I _cj, U _tj), j, m, n are positive integer, and matching regression equation inversion model is:

$C\left(I_{Cj},U_{Tj}\right)=\left(d_0+d_1{I}_{Cj}+d_2{U}_{Tj}\right)+\left(d_3{I}_{Cj}^2+d_4{I}_{Cj}{U}_{Tj}+d_5{U}_{Tj}^2\right)+\mathrm{...}+\mathrm{\ξ},$

In formula, the coefficient d of each rank expression formula _kfor temperature compensation constant coefficient, wherein k is positive integer, and 0≤k≤t-1, the matching item number t of equation is positive integer, and t>=3; ξ is higher order indefinite small; The pass of matching item number t and matching number of times r is:

$t=\frac{(r+3-1)!}{r!(3-1)!}=\frac{(r+2)(r+1)}{2};$

32) heavy metal concentration calibration value C _jrelative C (I _cj, U _tj) deviation be δ _j:

${\mathrm{\δ}}_j^2={\[\underset{k=0}{\overset{t}{\Σ}}{d}_k{p}_{jk}-C_j\]}^2$

In formula, p _jktemperature compensation constant coefficient d in regression equation inversion model _keach term coefficient, calibration point sum of square of deviations L _sfor:

$L_S=\underset{j=1}{\overset{S=m\×n}{\Σ}}{\[\underset{k=0}{\overset{t}{\Σ}}{d}_k{p}_{jk}-C_j\]}^2=L(d_0,...,d_{j-k},...,d_t),$

In formula, S is total number of calibration point, L _stemperature compensation constant coefficient d _kthe t meta-function of coefficient;

33) respectively to L _sask about d _klocal derviation, order k=0,1 ..., t, then model of temperature compensation is:

$\underset{j=1}{\overset{S}{\Σ}}\[\underset{k=0}{\overset{t}{\Σ}}{d}_k{p}_{jk}\]\×p_{jk}=\underset{j=1}{\overset{t}{\Σ}}{C}_j\×p_{jk}$

In formula, j=0,1 ..., S, S=m*n;

34) for weighing the relative error measure coefficient REF of performance be:

$REF=100\×\frac{{\[\underset{j=1}{\overset{n}{\Σ}}\left(\frac{C_j-C_j^S}{C_j^S}\right)\]}^{\frac{1}{2}}}{\sqrt{s}}$

In formula, C _jfor the concentration of heavy metal ion value that jth time detects, C _j ^sfor the actual value of concentration of heavy metal ion in standard solution when jth time detects, s is for detecting number of times; When REF is greater than the default limits of error, matching number of times r increases by 1 automatically, performs step 31); Otherwise this is set up model of temperature compensation and terminates.

2. the temperature compensation of a kind of water environment heavy metal detection system according to claim 1, is characterized in that:

When carrying out the detection of water environment heavy metal concentration, obtain polarization current I by the electrochemical sensor of each monitoring terminal _iwith polarized potential E _i, obtain environment temperature U by the temperature sensor of each monitoring terminal _t, polarization current I _iwith polarized potential E _ipeak point current I is obtained after differential filtering _c, by peak point current I _cwith environment temperature U _tsubstitute into the model of temperature compensation established, obtain the detectable concentration value of water environment to be measured.