CN102967327A - Simplifying soft measurement method for primary variable in production process integrating KPLS (Kernel Partial Least Squares) and FNN (False Nearest Neighbors) - Google Patents

Abstract

The invention discloses a simplifying soft measurement method for a primary variable in a production process integrating KPLS (Kernel Partial Least Squares) and FNN (False Nearest Neighbors). The method is characterized by comprising the following steps: determining n original auxiliary variables possibly related to the primary variable, collecting value data of the n original auxiliary variables and the primary variable, and forming a sample set; respectively calculating weighted values of the n original auxiliary variables by using a method of integrating the KPLS and the FNN; forming an original auxiliary variable sequence; modeling and determining the best auxiliary variable according to a minimum mean square error (MSE); and acquiring a simplifying soft measurement model. According to the method, an auxiliary variable set containing the auxiliary variables with the least number can be found for modeling the primary variable on the basis of the best modeling effect, so that the simplifying soft measurement on the primary variable can be realized.

Description

Merge simplifying of the production run leading variable flexible measurement method of KPLS and FNN

Technical field

The invention belongs to the soft-measuring technique field, be specifically related to a kind of fusion nucleus offset minimum binary (Kernel Partial Least Squares, KPLS) with simplifying of the production run leading variable flexible measurement method of false nearest neighbor point (False Nearest Neighbors, FNN).

Background technology

Up to the present, in actual production process, exist the variable that many because technology or economic cause can't directly be measured, in this case, soft-measuring technique arises at the historic moment.Soft measurement is exactly according to the process variable (being called auxiliary variable) that can survey, easily survey and the mathematical relation that is difficult to the variable to be measured (being called leading variable) of direct-detection, according to certain optiaml ciriterion, adopt various computing method, with measurement or the estimation of software realization to variable to be measured.Soft-measuring technique is a focus of studying at present, for example Chinese patent (patent No.: 200410017533.7) just proposed a kind of soft-measuring modeling method based on support vector machine.

In soft measuring process, the selection of auxiliary variable is the first step.In most of actual production process, people often can not determine which auxiliary variable is relevant with leading variable, or the relevant of much degree arranged, thereby cause the auxiliary variable One's name is legion that participates in calculating.Numerous auxiliary variables by calculating, are realized the soft measurement to leading variable, can bring huge calculated amount, not only take time and effort, and the soft measurement result that obtains also might not be best that this is not wish the thing seen in generative process.How to utilize minimum auxiliary variable set pair leading variable realize effect best soft measurement, become the target that people pursue.

Summary of the invention

The object of the present invention is to provide simplifying of the production run leading variable flexible measurement method of a kind of KPLS of fusion and FNN, can find out in the criterion of modeling best results and contain the minimum auxiliary variable set pair leading variable of auxiliary variable number and carry out modeling, realize the soft measurement to simplifying of leading variable.

Technical scheme of the present invention is as follows: a kind of simplifying of production run leading variable flexible measurement method that merges KPLS and FNN, and its key is to carry out as follows:

Step 1: determine may be relevant with leading variable n original auxiliary variable, gather the value of n original auxiliary variable and leading variable, the composition sample set, the sample set size is m;

Write n original auxiliary variable data as matrix X=[x ₁..., x _m] ^TForm, the leading variable data are write as matrix Y=[y ₁..., y _m] ^T, wherein, x _i∈ R ^{N * 1}, y _i∈ R, i=1,2 ..., m, and with they standardizations;

Described standardization is exactly: if n original auxiliary variable data write as matrix

Form, the leading variable data are write as matrix Y=[y ₁..., y _m] ^TForm, wherein, x _i∈ R ^{N * 1}, y _i∈ R, i=1,2 ..., m, the data matrix that obtains after the standardization is as follows:

$Y={[\frac{y_1-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{y}_j}{\sqrt{\frac{1}{m}\×\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(y_i-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{y}_j)}^2}},...,\frac{y_m-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{y}_j}{\sqrt{\frac{1}{m}\×\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(y_i-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{y}_j)}^2}}]}^T;$

Step 2: merge the weighted value that KPLS and FNN method are calculated respectively n original auxiliary variable;

Step 3: n original auxiliary set of variables becomes original auxiliary Variables Sequence;

Step 4: determine best auxiliary variable collection, may further comprise the steps:

The first step is set cycle index N=n;

Second step selects p sample as training sample at random from sample set, and a remaining m-p sample is as test samples, and described training sample number p generally chooses total sample number m's

About be advisable;

In the 3rd step, according to described training sample, utilize the nonlinear model that comprises variable in the original auxiliary Variables Sequence of BP neural network;

The 4th step inputed to described nonlinear model with the original auxiliary variate-value of described test samples, obtained m-p the leading variable predicted value that test samples is corresponding;

The 5th step, the square error MSE of m-p test samples predicted value of calculating, wherein, square error MSE is calculated as follows: $\mathrm{MSE}=\sqrt{\frac{\underset{t=1}{\overset{m-p}{\mathrm{\Σ}}}{(P_t-{\mathrm{PC}}_t)}^2}{m-p}};$

In the following formula, P _tThe leading variable value that represents t sample in the described m-p test samples, PC _tThe leading variable predicted value that represents t sample in the described m-p test samples;

The 6th goes on foot, and deletes the original auxiliary variable of weighted value minimum in the current original auxiliary Variables Sequence, forms new original auxiliary Variables Sequence, and sets N=N-1, judges this moment, whether N was 0:

If the 3rd step was then got back to in N ≠ 0;

If N=0, then the corresponding original auxiliary Variables Sequence of minimum MSE is best auxiliary variable collection;

Step 5: best auxiliary variable collection corresponding nonlinear model in step 4 is simplifying soft-sensing model.

The weighted value that described fusion KPLS and FNN method are calculated certain original auxiliary variables A carries out as follows:

(1): the pivot score matrix T=[t that k the KPLS pivot score vector that utilizes the KPLS algorithm to calculate sample set forms ₁..., t _k], carry out as follows:

(1): calculate nuclear matrix K, wherein, the ij bit of K element is K _Ij=κ (x _i, x _j), i, j=1,2 ..., m;

In the calculating of nuclear matrix, generally adopt gaussian kernel, namely

K _ij=κ(x _i，x _j)=exp(-||x _i-x _j|| ²/c)，i，j=1，2，…，m，

Wherein, c is the gaussian kernel width parameter, generally gets in the 0.1-1 scope;

(2): the centralization nuclear matrix $K\←(I_m-\frac{1}{m}\×1_m\×{1_m}^T)\×K\×(I_m-\frac{1}{m}\×1_m\×{1_m}^T),$ Wherein, I _mBe m rank unit matrix,

(3): the direction vector u of initialization dual projection _i=Y, and make K ₁=K;

(4): from i=1,2 ... the circulation execution in step:

① $t_i=K_i{u}_i/\sqrt{{u_i}^T{K}_i{u}_i};$

② $q_i=Y_i{t}_i/\left|\right|t_i^T{t}_i\left|\right|;$

③ $u_{i+1}=\frac{Y_i{q}_i}{q_i^T{q}_i};$

Judge u _I+1Whether restrain, namely judge || u _i-u _I+1|| whether≤0.001 set up, if set up, then thinks u _I+1Restrain, then enter step (5), and obtain KPLS pivot score vector number k=i, otherwise think u _I+14. not yet convergence is then carried out;

4. carry out and contract $K_{i+1}=(I-t_i{t}_i^T/t_i^T{t}_i)K_i(I-t_i{t}_i^T/t_i^T{t}_i);$

5. carry out and contract $Y_{i+1}=(I-t_i{t}_i^T/t_i^T{t}_i)Y_i;$

6. be back to 1.;

(5): obtain matrix U=[u ₁..., u _k] and k the pivot score matrix T=[t that KPLS pivot score vector forms ₁..., t _k];

(2): calculate the weighted value of certain original auxiliary variables A by the FNN method, carry out as follows:

(1): the value of the original auxiliary variables A that original sample is concentrated all is set to zero, and other original auxiliary variable-values are constant, obtain new sample set matrix

Wherein,

i=1，2，…，m；

(2): calculate nuclear matrix

Wherein,

Ij bit element be

$\stackrel{\‾}{K_{\mathrm{ij}}}=\mathrm{\κ}(\stackrel{\‾}{x_i},x_j)=\exp (-{\left|\right|\stackrel{\‾}{x_i}-x_j\left|\right|}^2/c),$ i，j=1，2，…，m；

(3): the centralization nuclear matrix $\stackrel{\‾}{K}\←(I_m-\frac{1}{m}\×1_m\×{1_m}^T)\×\stackrel{\‾}{K}\×(I_m-\frac{1}{m}\×1_m\×{1_m}^T),$ Wherein, I _mBe m rank unit matrix,

(4): calculate the KPLS pivot score matrix under the original auxiliary variables A zero setting

Wherein, U, T, K are the corresponding matrix that calculates in the step ();

(5): carry out following calculating

$D=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\left|\right|T(i,:)-W_A(i,:)\left|\right|$

Wherein, and T (i :), W _A(i :) all the i of representing matrix is capable, that is original sample collection and with i the projection coordinate of sample in the KPLS principal component space of gained sample set after the original auxiliary variables A zero setting;

(6)： $d=\frac{1}{m}\×D$

The d value namely is the weighted value of original auxiliary variables A.

This d value has been portrayed original auxiliary variables A zero setting front and back to the situation of change of the projection coordinate of sample set in the KPLS principal component space, the d value is larger, the change that original auxiliary variables A zero setting front and back projection coordinate is described is larger, thereby illustrate that original auxiliary variables A is stronger to the interpretability of leading variable, namely can measure with the d value weighted value of original auxiliary variables A.

The weighted value of all n original auxiliary variables calculates by the weighted value computing method of original auxiliary variables A.

In utilizing the original auxiliary Variables Sequence of BP neural network, comprise in the process of nonlinear model of variable, the node number of input layer equals the variable number that comprises in the current original auxiliary Variables Sequence, the node number of hidden layer is determined by cross verification, the node number of output layer is 1, wherein, the transport function of hidden layer is: The transport function of output layer is: purelin (x)=x;

After obtaining simplifying soft-sensing model, in the production run afterwards, only need to measure the value that best auxiliary variable is concentrated auxiliary variable, simplifying of substitution soft-sensing model just can obtain the value of leading variable.

Remarkable result of the present invention: in numerous original auxiliary variables, find out the crucial auxiliary variable that has key effect with leading variable, realized that utilization contains the minimum auxiliary variable set pair leading variable of auxiliary variable number and realizes the best soft measurement of effect, save manpower, material resources and financial resources, and greatly improved the efficient of measuring.

Description of drawings

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is the process flow diagram of determining best auxiliary variable collection among the present invention;

Fig. 3 is the battery chemical synthesis technology process flow diagram among the embodiment 1.

Embodiment

The invention will be further described below in conjunction with drawings and Examples:

Embodiment 1:

Such as Fig. 1, merge simplifying of the production run leading variable flexible measurement method of KPLS and FNN, carry out as follows:

Step 1: determine may be relevant with leading variable n original auxiliary variable, gather the value of n original auxiliary variable and leading variable, form sample set, the sample set size is m, and is write the individual original auxiliary variable data of n as matrix Form, the leading variable data are write as matrix Y=[y ₁..., y _m] ^TForm, wherein, x _i∈ R ^{N * 1}, y _i∈ R, i=1,2 ..., m, and further they are done following standardization, the data matrix after obtaining processing:

$Y={[\frac{y_1-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{y}_j}{\sqrt{\frac{1}{m}\×\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(y_i-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{y}_j)}^2}},...,\frac{y_m-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{y}_j}{\sqrt{\frac{1}{m}\×\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{(y_i-\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{y}_j)}^2}}]}^T;$

Step 2: merge the weighted value that KPLS and FNN method are calculated respectively n original auxiliary variable;

The weighted value that described fusion KPLS and FNN method are calculated certain original auxiliary variables A carries out as follows:

(1): the pivot score matrix T=[t that k the KPLS pivot score vector that utilizes the KPLS algorithm to calculate sample set forms ₁..., t _k], carry out as follows:

(1): calculate nuclear matrix K, wherein, the ij bit of K element is K _Ij=κ (x _i, x _j), i, j=1,2 ..., m;

(2): the centralization nuclear matrix $K\←(I_m-\frac{1}{m}\×1_m\×{1_m}^T)\×K\×(I_m-\frac{1}{m}\×1_m\×{1_m}^T),$ Wherein, I _mBe m rank unit matrix,

(3): the direction vector u of initialization dual projection _i, might as well get u _i=Y, and make K ₁=K;

(4): from i=1,2 ... the circulation execution in step:

① $t_i=K_i{u}_i/\sqrt{{u_i}^T{K}_i{u}_i};$

② $q_i=Y_i{t}_i/\left|\right|t_i^T{t}_i\left|\right|;$

③ $u_{i+1}=\frac{Y_i{q}_i}{q_i^T{q}_i};$

Judge u _I+1Whether restrain, namely judge || u _i-u _I+1|| whether≤0.001 set up, if set up, then thinks u _I+1Restrain, then enter step (5), and obtain KPLS pivot score vector number k=i, otherwise think u _I+14. not yet convergence is then carried out;

4. carry out and contract $K_{i+1}=(I-t_i{t}_i^T/t_i^T{t}_i)K_i(I-t_i{t}_i^T/t_i^T{t}_i);$

5. carry out and contract $Y_{i+1}=(I-t_i{t}_i^T/t_i^T{t}_i)Y_i;$

6. be back to 1.;

(5): obtain matrix U=[u ₁..., u _k] and k the pivot score matrix T=[t that KPLS pivot score vector forms ₁..., t _k];

The calculating of nuclear matrix is generally adopted gaussian kernel, namely in step (1)

K _Ij=κ (x _i, x _j)=exp (|| x _i-x _j|| ²/ c), and i, j=1,2 ..., m, wherein, c is the gaussian kernel width parameter, generally gets in the 0.1-1 scope;

(2): calculate the weighted value of certain original auxiliary variables A by the FNN method, carry out as follows:

(1): the value of the original auxiliary variables A that original sample is concentrated all is set to zero, and other original auxiliary variable-values are constant, obtain new sample set matrix

Wherein,

i=1，2，…，m；

(2): calculate nuclear matrix

Wherein,

Ij bit element be

$\stackrel{\‾}{K_{\mathrm{ij}}}=\mathrm{\κ}(\stackrel{\‾}{x_i},x_j)=\exp (-{\left|\right|\stackrel{\‾}{x_i}-x_j\left|\right|}^2/c),$ i，j=1，2，…，m；

(3): the centralization nuclear matrix $\stackrel{\‾}{K}\←(I_m-\frac{1}{m}\×1_m\×{1_m}^T)\×\stackrel{\‾}{K}\×(I_m-\frac{1}{m}\×1_m\×{1_m}^T),$ Wherein, I _mBe m rank unit matrix,

(4): calculate the KPLS pivot score matrix under the original auxiliary variables A zero setting

Wherein, U, T, K are the corresponding matrix that calculates in the step ();

(5): carry out following calculating

$D=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\left|\right|T(i,:)-W_A(i,:)\left|\right|$

Wherein, and T (i :), W _A(i :) all the i of representing matrix is capable, that is original sample collection and with i the projection coordinate of sample in the KPLS principal component space of gained sample set after the original auxiliary variables A zero setting;

(6)： $d=\frac{1}{m}\×D$

This d value has been portrayed original auxiliary variables A zero setting front and back to the situation of change of the projection coordinate of sample set in the KPLS principal component space, the d value is larger, the change that original auxiliary variables A zero setting front and back projection coordinate is described is larger, thereby illustrate that original auxiliary variables A is stronger to the interpretability of leading variable, namely can measure with the d value weighted value of original auxiliary variables A.

The weighted value of all n original auxiliary variables calculates by the weighted value computing method of original auxiliary variables A.

Step 3: n original auxiliary set of variables becomes original auxiliary Variables Sequence;

Step 4: determine best auxiliary variable collection, as shown in Figure 2, may further comprise the steps:

The first step is set cycle index N=n;

Second step selects p sample as training sample at random from sample set, and a remaining m-p sample is as test samples, and described training sample number p generally chooses total sample number m's

About be advisable;

In the 3rd step, according to described training sample, utilize the nonlinear model that comprises variable in the original auxiliary Variables Sequence of BP neural network;

In the modeling process, the node number of BP neural network input layer equals the variable number that comprises in the current original auxiliary Variables Sequence, and the node number of hidden layer determines that by cross verification the node number of output layer is 1, wherein, the transport function of hidden layer is: The transport function of output layer is: purelin (x)=x;

The 4th step inputed to described nonlinear model with the original auxiliary variate-value of described test samples, obtained m-p the leading variable predicted value that test samples is corresponding;

The 5th step, the square error MSE of m-p test samples predicted value of calculating, wherein, square error MSE is calculated as follows: $\mathrm{MSE}=\sqrt{\frac{\underset{t=1}{\overset{m-p}{\mathrm{\Σ}}}{(P_t-{\mathrm{PC}}_t)}^2}{m-p}};$

In the following formula, P _tThe leading variable value that represents t sample in the described m-p test samples, PC _tThe leading variable predicted value that represents t sample in the described m-p test samples;

The 6th goes on foot, and deletes the original auxiliary variable of weighted value minimum in the current original auxiliary Variables Sequence, forms new original auxiliary Variables Sequence, and sets N=N-1, judges this moment, whether N was 0:

If the 3rd step was then got back to in N ≠ 0;

If N=0, then the corresponding original auxiliary Variables Sequence of minimum MSE is best auxiliary variable collection;

Step 5: best auxiliary variable collection corresponding nonlinear model in step 4 is simplifying soft-sensing model.

After obtaining simplifying soft-sensing model, in the production run afterwards, only need to measure the value that best auxiliary variable is concentrated auxiliary variable, simplifying of substitution soft-sensing model just can obtain the value of leading variable.

Capacity final discharging voltage in the derivation lead-acid accumulator production process is as example, in the battery production process, the artwork that battery changes into as shown in Figure 2, battery changes into and will carry out the capacity spark gap inspection through after the discharging and recharging of six stages again, and measures 10 hour rate final discharging voltages and relate in the capacity discharge examination.

We determine that leading variable is that 10h leads final discharging voltage, select battery conductance, charging 8h cell voltage, charging 31h cell voltage, charging 26h cell voltage, change into discharge 0h cell voltage, change into discharge 6h final voltage, charging 6h cell voltage, charging 32h cell voltage be as original auxiliary variable.

By step 1, collect the sample set of leading variable and 8 original auxiliary variables, sample size is 9, and the sample set size is 172, and it is 9 sample that 172 sizes are namely arranged, and sees Table 1:

Table 1. sample set

Continued 1

The weighted value that fusion KPLS and FNN method obtain 8 original auxiliary variables is followed successively by:

Choose at random 130 samples as training sample from sample set, remaining 42 is test samples.Delete successively the original auxiliary variable of weighted value minimum in the original auxiliary Variables Sequence, after utilizing BP neural network nonlinear model, the square error MSE of the test samples that calculates, next coming in order have listed variable number in the original auxiliary Variables Sequence and have been respectively 8,7,6,5,4,3,2 and the square error MSE of 1 o'clock test samples:

Original auxiliary variable in the original auxiliary Variables Sequence of square error 0.0013 correspondence is best auxiliary variable, and corresponding nonlinear model is simplifying soft-sensing model.

Best auxiliary variable collection in the present embodiment comprises: battery conductance, charging 6h cell voltage, charging 26h cell voltage, charging 31h cell voltage, charging 8h cell voltage.In simplifying of foundation soft-sensing model, the input layer of BP neural network is above-mentioned five best auxiliary variable values, determines that through cross verification the hidden layer node number of BP neural network is 11.

Thereby obtain the simplifying soft-sensing model of this example:

I neuron output of BP neural network hidden layer $y_i=\tan \mathrm{sig}(\underset{j=1}{\overset{5}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00002606938900021.png"\; state="\{\{state\}\}">w</figure-callout>}1}_{\mathrm{ij}}{x}_j+{b1}_i),$ i=1，2，…，11，

The output of output layer neuron $z_k=\mathrm{purelin}(\underset{i=1}{\overset{11}{\mathrm{\&Sigma;}}}{w2}_{\mathrm{ki}}{y}_i+{b2}_k),$ K=1, wherein,

$\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="HDA00002606938900021.png"\; state="\{\{state\}\}">w</figure-callout>}1=\left[\begin{array}{ccccc}-3.5242& 0.5320& -2.2243& 3.9044& 1.8244\\ -0.8080& 0.9534& -0.8951& 1.8511& -1.7085\\ -0.4107& 3.8336& 3.6041& 3.1672& 0.7346\\ -2.2331& 0.8456& -3.6018& 3.3664& 2.7009\\ -4.2798& 2.0504& 1.7775& -6.9620& 1.8997\\ 0.9061& -4.9600& -8.7325& 1.7456& -2.3443\\ -2.9174& 0.9658& -0.0163& -2.8345& 1.8397\\ -4.1528& 0.5667& 1.4217& -1.0691& 0.7873\\ 1.2421& 0.5627& 0.3713& 1.1766& 0.2913\\ -5.3515& -1.7840& -0.7273& -2.3854& 5.6311\\ -1.1644& -2.1423& -3.5158& -3.2748& 5.8375\end{array}\right],$ $\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="HDA00002606938900021.png"\; state="\{\{state\}\}">b</figure-callout>}1=\left[\begin{array}{c}1.6746\\ -3.8373\\ -5.1000\\ -0.3121\\ -0.3606\\ 0.3025\\ -0.2491\\ 1.4171\\ -0.7017\\ -1.8062\\ -1.5856\end{array}\right]$

$w2=\left[\begin{array}{c}0.0615\\ -0.5219\\ -0.2223\\ 0.0244\\ 0.0329\\ -0.2041\\ -0.3414\\ 0.8187\\ 0.4735\\ 0.0085\\ -0.1347\end{array}\right],$ B2=-0.9691, w1, w2 are respectively the connection weight value matrix of input layer to hidden layer, hidden layer to output layer, and b1, b2 are respectively the threshold matrix of hidden layer, output layer, x _jJ dimension auxiliary variable value for input sample x.

Claims (3)

1. simplifying of production run leading variable flexible measurement method that merges KPLS and FNN is characterized in that carrying out as follows:

Step 1: determine may be relevant with leading variable n original auxiliary variable, gather the value of n original auxiliary variable and leading variable, the composition sample set, the sample set size is m;

Write n original auxiliary variable data as matrix X=[x ₁..., x _m] ^TForm, the leading variable data are write as matrix Y=[y ₁..., y _m] ^T, wherein, x _i∈ R ^{N * 1}, y _i∈ R, i=1,2 ..., m, and they are carried out standardization;

Step 2: merge the weighted value that KPLS and FNN method are calculated respectively n original auxiliary variable;

Step 3: n original auxiliary set of variables becomes original auxiliary Variables Sequence;

Step 4: determine best auxiliary variable collection, may further comprise the steps:

The first step is set cycle index N=n;

Second step selects p sample as training sample at random from sample set, and a remaining m-p sample is as test samples;

In the 3rd step, according to described training sample, utilize the nonlinear model that comprises variable in the original auxiliary Variables Sequence of BP neural network;

The 4th step inputed to described nonlinear model with the original auxiliary variate-value of described test samples, obtained m-p the leading variable predicted value that test samples is corresponding;

The 5th step, the square error MSE of m-p test samples predicted value of calculating;

The 6th goes on foot, and deletes the original auxiliary variable of weighted value minimum in the current original auxiliary Variables Sequence, forms new original auxiliary Variables Sequence, and sets N=N-1, judges this moment, whether N was 0:

If the 3rd step was then got back to in N ≠ 0;

If N=0, then the corresponding original auxiliary Variables Sequence of minimum MSE is best auxiliary variable collection;

Step 5: best auxiliary variable collection corresponding nonlinear model in step 4 is simplifying soft-sensing model.

2. simplifying of the production run leading variable flexible measurement method of fusion according to claim 1 KPLS and FNN, it is characterized in that: the weighted value that the described KPLS of fusion and FNN method are calculated certain original auxiliary variables A carries out as follows:

(1): the pivot score matrix T=[t that k the KPLS pivot score vector that utilizes the KPLS algorithm to calculate sample set forms ₁..., t _k], carry out as follows:

(1): calculate nuclear matrix K, wherein, the ij bit of K element is K _Ij=κ (x _i, x _j), i, j=1,2 ..., m;

(2): the centralization nuclear matrix $K\&LeftArrow;(I_m-\frac{1}{m}\&times;1_m\&times;{1_m}^T)\&times;K\&times;(I_m-\frac{1}{m}\&times;1_m\&times;{1_m}^T),$ Wherein, I _mBe m rank unit matrix,

(3): the direction vector u of initialization dual projection _i=Y, and make K ₁=K;

(4): from i=1,2 ... the circulation execution in step:

① $t_i=K_i{u}_i/\sqrt{{u_i}^T{K}_i{u}_i};$

② $q_i=Y_i{t}_i/\left|\right|t_i^T{t}_i\left|\right|;$

③ $u_{i+1}=\frac{Y_i{q}_i}{q_i^T{q}_i};$

Judge u _I+1Whether restrain, namely judge || u _i-u _I+1|| whether≤0.001 set up, if set up, then thinks u _I+1Restrain, then enter step (5), and obtain KPLS pivot score vector number k=i, otherwise think u _I+14. not yet convergence is then carried out;

4. carry out and contract $K_{i+1}=(I-t_i{t}_i^T/t_i^T{t}_i)K_i(I-t_i{t}_i^T/t_i^T{t}_i);$

5. carry out and contract $Y_{i+1}=(I-t_i{t}_i^T/t_i^T{t}_i)Y_i;$

6. be back to 1.;

(5): obtain matrix U=[u ₁..., u _k] and k the pivot score matrix T=[t that KPLS pivot score vector forms ₁..., t _k];

(2): calculate the weighted value of certain original auxiliary variables A by the FNN method, carry out as follows:

(1): the value of the original auxiliary variables A that original sample is concentrated all is set to zero, and other original auxiliary variable-values are constant, obtain new sample set matrix

Wherein,

i=1，2，…，m；

(2): calculate nuclear matrix

Wherein, Ij bit element be

$\stackrel{\&OverBar;}{K_{\mathrm{ij}}}=\mathrm{\&kappa;}(\stackrel{\&OverBar;}{x_i},x_j)=\exp (-{\left|\right|\stackrel{\&OverBar;}{x_i}-x_j\left|\right|}^2/c),$ i，j=1，2，…，m；

(3): the centralization nuclear matrix $\stackrel{\&OverBar;}{K}\&LeftArrow;(I_m-\frac{1}{m}\&times;1_m\&times;{1_m}^T)\&times;\stackrel{\&OverBar;}{K}\&times;(I_m-\frac{1}{m}\&times;1_m\&times;{1_m}^T),$ Wherein, I _mBe m rank unit matrix,

(4): calculate the KPLS pivot score matrix under the original auxiliary variables A zero setting

Wherein, U, T, K are the corresponding matrix that calculates in the step ();

(5): carry out following calculating

$D=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\left|\right|T(i,:)-W_A(i,:)\left|\right|$

Wherein, and T (i :), W _A(i :) all the i of representing matrix is capable, that is original sample collection and with i the projection coordinate of sample in the KPLS principal component space of gained sample set after the original auxiliary variables A zero setting;

(6)： $d=\frac{1}{m}\&times;D$

The d value namely is the weighted value of original auxiliary variables A.

3. simplifying of the production run leading variable flexible measurement method of fusion according to claim 1 KPLS and FNN, it is characterized in that: in utilizing the original auxiliary Variables Sequence of BP neural network, comprise in the process of nonlinear model of variable, the node number of input layer equals the variable number that comprises in the current original auxiliary Variables Sequence, the node number of hidden layer is determined by cross verification, the node number of output layer is 1, wherein, the transport function of hidden layer is:

The transport function of output layer is: purelin (x)=x.

Images