CN103310095A - Intermittent process quality index soft measuring method - Google Patents

Abstract

The invention belongs to the field of the prediction of the product quality, and particularly discloses an intermittent process quality index measuring method. The method comprises the following steps of measuring J measured variables on K sampling points for I times to obtain a I*J*K process data matrix X, and providing Z quality results corresponding to each sampling; resolving the process data matrix X and a quality index matrix Y to obtain a regression coefficient theta; resolving the regression coefficient to obtain K modes; and averaging the mode coefficient in each cluster to obtain an average value of a cth stage, and finally calculating the quality index prediction value at the moment N. According to the method, the regression matrix is resolved and deformed according to the time slice to identify an intrinsic relation between the process data matrix and the quality index matrix, and not only is the stage characteristic in the batch of the intermittent process utilized, but also the repetition characteristics among different batches are utilized, so that the prediction complexity is reduced, and the prediction precision for the quality index also can be improved.

Description

Batch process quality index flexible measurement method

Technical field

The present invention relates to the product quality forecast field, be specifically related to the method for the soft measurement of a kind of batch process quality index.

Background technology

Batch process refers to starting material are processed into the product that meets demand according to pre-set operation, and the process that constantly repeats, and is applicable to the production short run, high value-added product, for example pharmacy, injection moulding, semiconductor packages etc.Quality index (the crystallinity of batch process product, internal stress, weight, volume) is difficult to on-line measurement, usually to after one-period finishes, use the quality analysis means of specialty just can obtain by the professional, also need to use expensive chemical apparatuses in some situation, therefore, the hysteresis quality of quality index being measured and expensive be one of the puzzlement of batch process field of quality control always.

And on the other hand, batch process is the most process variable of on-line measurement like a cork, such as pressure, temperature, flow etc.But the process variable measurement that these high frequencies gather except the abundant information that contains reflection process operation state, is also containing the quality information of batch process final products.By the variation of research process variable track, analyze the also quality condition of on-line prediction final products, become researchist's the focus of attention.Such as Sub-PLS qualitative forecasting method of the prior art, adopted the timeslice information of historical data to set up the PLS model, then utilize the regression relation of process variable and quality index on the timeslice to come cluster to set up PLS forecast model based on the period, but the method has just been utilized the period characteristic of batch process, do not consider its repeat property, acquired results is more unilateral, and all the other study emphatically less its stage characteristic of considering in the method for repeated feature of batch process, in the prediction of quality field to the batch process product, also there are not at present a kind of repeat property of taking into account batch process and stage in the method for one.

Summary of the invention

For the deficiencies in the prior art, the present invention proposes a kind of batch process quality index flexible measurement method, the method can further reduce the interference of irrelevant information, can also improve precision of prediction in the complexity that reduces prediction.

For this reason, a kind of batch process quality index flexible measurement method of the present invention may further comprise the steps:

A kind of batch process quality index flexible measurement method may further comprise the steps:

The S1 model data collecting

If a batch process has J detection variable, K sampled point and Z quality index, then each measures batch process data matrix and Z the quality results data matrix that can obtain a J*K, after repeating I batch measuring process, be a three-dimensional matrice X (I*J*K) with process data representation, the quality results data are expressed as two-dimensional matrix Y (I*Z);

The S2 three-dimensional data is launched

Three-dimensional matrice X (I*J*K) is launched by gathering batch direction, be about to variable on each sampled point in the operation batch and arrange according to time sequencing and obtain two-dimensional matrix X ', wherein, X ' be the matrix that the capable KJ of I is listed as;

The multidirectional partial least square method modeling of S3

If process data matrix and quality index matrix that upper two steps obtain are respectively X (I*JK), Y(1*Z), it is carried out multidirectional partial least square method modeling, obtain the regression relation between process data matrix X and the quality index matrix Y, wherein, the formula of multidirectional partial least square method modeling is as follows:

$X=T_R{\left(P_R\right)}^T+E=\underset{r=1}{\overset{R}{\mathrm{\Σ}}}{t}_r{p}_r^{\′}+E$

$Y=U_R{\left(Q_R\right)}^T+F=\underset{r=1}{\overset{R}{\mathrm{\Σ}}}{u}_r{q}_r^{\′}+F;---\left(1\right)$

Y=X·θ+F ^*

Wherein: the X decomposition obtains score matrix T _R(I * R) and load matrix P _R(JK * R), t _r, p _rIt is respectively vector in the matrix wherein;

The Y decomposition obtains score matrix U _R(I * R) and load matrix Q _R(Z*R), u _r, q _rIt is respectively vector in the matrix;

E, F, F ^*Be residual information, θ is the regression coefficient of X and Y, and R is the latent variable number;

The S4 regression coefficient is decomposed

A process of among the S41 refer step S2 three-dimensional matrice X (I*J*K) being launched by collection batch direction, the regression relation matrix θ (JK * Z) the similar restructuring of counter movement that will comprise process variable and the quality index of K timeslice, because step S3 execution X (I * JK), (I * Z) decomposition does not change sequential relationship wherein to Y, among the regression coefficient θ every J capable be the regression relation of a sampling instant, this K sheet is reassembled as a three-dimensional data matrix according to sequential relationship;

S42 downcuts the three-dimensional data matrix among the step S41 and removes to consist of two-dimensional matrix according to the direction of time k

The regression coefficient that then exists with matrix form can be stated following version by K associative mode combination as:

$\mathrm{\θ}=\{{\mathrm{\θ}}_1^K,{\mathrm{\θ}}_2^K,...,{\mathrm{\θ}}_K^K\};---\left(2\right)$

Wherein,

(k=1,2 ..., K) be associative mode;

The S5K-means cluster analysis

This step selects the distance that defines below as the index of measuring two associative mode similarity degree, to K associative mode

(J * Z) carry out the K-means cluster analysis, the pattern with same phase characteristic can be divided into a class, and different classifications represents different stage characteristics, and above-mentioned distance is defined by following formula:

$\mathrm{dist}({\mathrm{\θ}}_1^K,{\mathrm{\θ}}_2^K)={\left(\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{({\mathrm{\θ}}_{1,j}^K-{\mathrm{\θ}}_{2,j}^K)}^T({\mathrm{\θ}}_{1,j}^K-{\mathrm{\θ}}_{2,j}^K)\right)}^{1/2}---\left(3\right)$

The input of K-means algorithm is K associative mode set

And the minimum threshold of distance θ at two subclass centers, the output of algorithm is subclass quantity C, the subclass center is made as { W ₁, W ₂..., W _C, and each associative mode belongs to the membership of different subclasses

Variable i is the index of iterations in the algorithm, and k is the index of classification mode, and c then is the index of cluster centre, and algorithm steps is as follows:

A, from K associative mode, select arbitrarily C ₀Individual associative mode is as initial cluster center W _{I, c}(c=1,2 ..., C ₀), for W _{I, c}Choose, common method is evenly to extract C from be classified pattern ₀Individual associative mode, suggestion C ₀In interval (value in the K/3～K/2);

If two subclass centers of b apart from dist (W _{I, c1}, W _{I, c2}) less than predetermined threshold value θ, then reject one of them cluster centre;

C, calculate each associative mode

Distance to all cluster centres

If

With c ^*The center of class

Distance minimum, then will

Membership be defined as m (k)=c ^*

D, I _NumAfter the inferior iteration, if the associative mode (for example not surpassing 5 associative modes) of some is not captured at certain subclass center, then reject this strange class;

E, renewal subclass quantity are C _I+1, and recomputate new cluster centre W according to the membership of associative mode _{I+1, c}(c=1,2 ..., C _I+1);

If algorithm satisfies the condition of convergence then finishes, otherwise return step b, carry out next iteration and calculate, it is a class that above process incorporates the process sampled point that has an internal relation with quality index Y into, finishes the stage of multistage batch process is divided;

S6 obtains the predicted value of quality index

If the cluster analysis of step S5 obtains C representative stage, the then regression relation in C stage

Can be expressed as this stage n _sThe mean value of individual modes relationships, as shown in the formula:

${\mathrm{\θ}}_c^{*}=\underset{k=1}{\overset{n_s}{\mathrm{\Σ}}}{\mathrm{\θ}}_k/n_s;---\left(4\right)$

Further, the projected relationship of quality index and process data can be expressed as following formula

${\hat{y}}_n=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i*{\mathrm{\θ}}_c^{*};---\left(5\right)$

Wherein: c=1,2 ..., K; I=1,2 ..., N;

Quality index namely characterizes the quality according to the resulting product of batch process.

As a kind of specific embodiment, after the described step S2, also comprise the standardized step of two-dimensional matrix, it comprises:

S100 course of standardization process data matrix X

If the variable of the interior any point of two-dimensional matrix X ' is x _Ijk', to this variable subtract average, divided by the standardization of variance, obtain newcomer x _Ijk*, wherein the mathematic(al) representation of standardization is as follows:

$x_{\mathrm{ijk}}^{*}=\frac{x_{\mathrm{ijk}}^{\′}-{\stackrel{\‾}{x}}_{\mathrm{jk}}}{s_{\mathrm{jk}}};---\left(6\right)$

Wherein:

Be the average of arbitrary row among the two-dimensional matrix X ', S _JkBe the variance of arbitrary row among the two-dimensional matrix X ', the computing method of the two are as follows:

${\stackrel{\‾}{x}}_{\mathrm{jk}}=\frac{1}{I}*\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{x}_{\mathrm{ijk}}^{\′};---\left(7\right)$

$S_{\mathrm{jk}}=\sqrt{\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{(x_{\mathrm{ijk}}^{\′}-{\stackrel{\‾}{x}}_{\mathrm{jk}})}^2/(I-1)};---\left(8\right)$

S200 standardization quality index matrix Y

Y carries out standardization to the quality index matrix, namely two-dimensional matrix Y is carried out to subtract average divided by the operation of variance, obtains

The mathematic(al) representation of standardization is as follows:

$y_{\mathrm{iz}}^{*}=\frac{y_{\mathrm{iz}}-{\stackrel{\‾}{y}}_z}{s_z};---\left(9\right)$

Wherein,

Be the average of arbitrary row among the two-dimensional matrix Y, S _zBe the variance of arbitrary row among the two-dimensional matrix Y, the computing method of the two are as follows:

${\stackrel{\‾}{y}}_z=\frac{1}{I}*\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{y}_{\mathrm{iz}}---\left(10\right)$

$S_z=\sqrt{\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{(y_{\mathrm{iz}}-{\stackrel{\‾}{y}}_z)}^2/(I-1)}---\left(11\right)$

As a kind of specific embodiment, among the described step S5, K-means convergence of algorithm condition is associative mode in each subclass

To the square distance at subclass center and reach minimum or subclass between square distance and reach minimum.

As a kind of specific embodiment, among the described step S1, measure the number of times of batch I greater than 50, the quantity of sampled point K is less than 1000.

As a kind of specific embodiment, among the described step S3, described latent variable number is between 1-1000.

As a kind of specific embodiment, among the described step S3, described latent variable number is between 1-10.

The present invention has also obtained following beneficial effect: the present invention comes the internal relation of identification process data matrix and quality index matrix through decomposing distortion according to time slot sequence by regression matrix, not only utilized the stage characteristic in the batch process batch, utilized simultaneously the repeat property between its batch, further reduce the interference of irrelevant information, can also improve the precision of prediction to quality index when reducing the complexity of prediction, for the on-line prediction of batch process quality index provides new possibility.

Description of drawings

Below in conjunction with accompanying drawing the specific embodiment of the present invention is described in further detail, wherein:

Fig. 1 is the process flow diagram of embodiment 1 described batch process quality index flexible measurement method;

Fig. 2 is the schematic diagram that in Fig. 1 Plays step process data matrix X is launched according to time sequencing;

Fig. 3 is the schematic diagram that among Fig. 1 regression coefficient θ was decomposed by the time;

Fig. 4 is that sampled data when using k constantly among the step S6 is as the sampled data schematic diagram after the moment k;

Fig. 5 is that the injection phase in the injection molding process is divided result schematic diagram;

Fig. 6 is the schematic diagram that calculates quality index in the injection molding process.

Fig. 7 is the process flow diagram of embodiment 2 described batch process quality index flexible measurement methods;

Embodiment

Further specify the present invention below by object lesson, expectation makes those skilled in the art can further understand the intent of the present invention and technical conceive by these object lessons.

Embodiment 1

Injection mo(u)lding is typical multistage process, and it mainly comprises injection, pressurize, plasticizing, cooling four-stage, and there are its specific control target, different leading variables and process characteristic each period of injection moulding process.Specifically, at injection stage, the pushed at high pressure screw rod of hydraulic cylinder is shifted the molten plastic in the barrel onto die cavity forward, is filled fully or nearly full the time when die cavity, and process switches to packing stage; At packing stage, high pressure continues a small amount of material to be filled in the die cavity, to replenish owing to cooling and to solidify the Material shrinkage that brings; When the Jiao Kou cooling, when the material in the die cavity no longer was injected the nozzle impact, the pressurize section finished, and cooling section begins.When material in the mould reached the hardness that can be ejected, cooling stage finished.In addition, in cooling, also carrying out the plasticizing action in the barrel, plastic grain in the barrel outside barrel heating arrangement and the effect of the shear heat that produces of screw rod rotation under realize the variation of its physical state, become the plastics viscous state and be transported to the head of screw rod.When the screw head melt increases gradually, its pressure is during greater than the back pressure of injection cylinder, and screw rod retreats and begins simultaneously volume calculations.After the head melt reached certain injection volume, screw rod stopped to retreat and rotating, and plastic phase finishes.

The present embodiment specifically discloses a kind of batch process quality index flexible measurement method based on the multidirectional offset minimum binary of burstization take above-mentioned injection moulding process as example, said method comprising the steps of:

The S1 model data collecting

If a batch process has J detection variable, K sampled point and Z quality index, then each measures batch process data matrix and Z the quality results data matrix that can obtain a J*K, after repeating I batch measuring process, process data can be expressed as a three-dimensional matrice X (I*J*K), and the quality results data can be expressed as two-dimensional matrix Y (I*Z); Contain enough for a long time working range in order to ensure detecting data, the value of data batch I of modeling be used on the general industry greater than 50, be preferably more than 100 in the present embodiment, measurand be can be measured in batch operational processs such as temperature, speed, pressure, stroke state parameter; Whether speed degree and model based on process time length, change in process bear in rational scope, and sampled point K number is generally less than 1000.

The present embodiment is data from injection moulding process, with high density polyethylene (High Density Polyethylene, be called for short HDPE) as raw material, three sections temperature of barrel are set as respectively (210,210,160), injection speed is 35mm/s, the pressure setting of packing stage is 30 Pascals, the time of packing stage is 5s, the time of cooling stage is 15s, sample frequency is 50ms/ time, and collectable variable is 8 (referring to table 1) in the injection machine course of work, is respectively: the pressure valve aperture, the flow valve aperture, injection stroke, injection speed, injection pressure, barrel temperature (3 sections), 270 normal operations batch have been selected in historical data X modeling, and each batch kept 488 sampled points.Quality index Y has selected the weight of product, and 270 operation batch common properties are given birth to 270 groups of weight datas.

Table 1

The S2 three-dimensional data is launched

Referring to Fig. 2, three-dimensional matrice X (I*J*K) is launched by gathering batch direction, be about on each sampled point in the operation batch the volume variable and arrange according to time sequencing and obtain two-dimensional matrix X ', obviously, X ' be the matrix that the capable KJ of I is listed as;

The multidirectional partial least square method modeling of S3

If the process data matrix in the previous step after standardization and quality index matrix are respectively X (I*JK), Y(1*Z), it is carried out MPLS(multi-way partial least square, multidirectional partial least square method, hereinafter to be referred as MPLS) modeling, obtain the regression relation between process data matrix X and the quality index matrix Y.In the present embodiment, so-called MPLS modeling is exactly first the three dimensional process data matrix to be launched into a large two-dimensional matrix, carry out again following NIPALS (Nonlinear Iterative Partial Least Squares algorithm, the nonlinear iterative partial least square method, hereinafter to be referred as NIPALS) decompose, decompose to finish and obtain X, the regression relation of Y

$X=T_R{\left(P_R\right)}^T+E=\underset{r=1}{\overset{R}{\mathrm{\Σ}}}{t}_r{p}_r^{\′}+E$

$Y=U_R{\left(Q_R\right)}^T+F=\underset{r=1}{\overset{R}{\mathrm{\Σ}}}{u}_r{q}_r^{\′}+F;---\left(1\right)$

Y=X·θ+F ^*

Wherein: the X decomposition obtains score matrix T _R(I * R) and load matrix P _R(JK * R), t _r, p _rIt is respectively vector in the matrix wherein;

The Y decomposition obtains score matrix U _R(I * R) and load matrix Q _R(Z*R), u _r, q _rIt is respectively vector in the matrix;

E, F, F ^*Be residual information, θ is the regression coefficient of X and Y, and R is the latent variable number.

The value of latent variable number R is selected in natural number, and the degree of decomposition of X and Y is relevant with choosing of latent variable number R.In general, when the information among the X to quality index Y do not have explanation strengths the time, just stop to decompose.In the present embodiment, latent variable number R selects 4, X that the explanation degree of Y is accounted for 98.2% of total proportion, that is to say, when when selecting 4 latent variable X and Y being decomposed, 98.2% information can be captured by X among the Y.

The S4 regression coefficient is decomposed

A process (Fig. 2) of among the S41 refer step S2 three-dimensional matrice X (I*J*K) being launched by collection batch direction, this step will comprise the regression relation matrix θ (JK * Z) the similar restructuring of counter movement of process variable and the quality index of K timeslice.Because (I * JK), (I * Z) decomposition does not change sequential relationship wherein to Y to NIPILS execution X among the step S3.Among the regression coefficient θ every J capable be the regression relation of a sampling instant, this K sheet can be reassembled as a three-dimensional data matrix according to sequential relationship;

S42 removes the three-dimensional data matrix among the step S41 to consist of two-dimensional matrix according to the direction cutting-out of time k referring to Fig. 3

For convenience of explanation, will

Be called associative mode, the regression coefficient that then exists with matrix form can be stated following version by K associative mode combination as:

$\mathrm{\θ}=\{{\mathrm{\θ}}_1^K,{\mathrm{\θ}}_2^K,...,{\mathrm{\θ}}_K^K\};---\left(2\right)$

Wherein,

(k=1,2 ..., K).

The S5K-means cluster analysis

The regression relation of X and Y can change along with the variation of stage characteristic, and within a certain period, the stage characteristic remains unchanged substantially, and then the regression relation characteristic also remains unchanged substantially.

The K-means method is that n data object is divided into m cluster so that so that the cluster that obtains is satisfied: the object similarity in the same cluster is higher; And the less a kind of algorithm of the object similarity in the different clusters.The cluster similarity is to utilize in each cluster the distance of object and " center object " to calculate.

This step selects the distance that defines below as the index of measuring two associative mode similarity degree, to K associative mode

Carry out the K-means cluster analysis, the pattern with same phase characteristic can be divided into a class, and different classifications represents different stage characteristics, and above-mentioned distance is defined by following formula:

$\mathrm{dist}({\mathrm{\θ}}_1^K,{\mathrm{\θ}}_2^K)={\left(\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{({\mathrm{\θ}}_{1,j}^K,-{\mathrm{\θ}}_{2,j}^K)}^T({\mathrm{\θ}}_{1,j}^K-{\mathrm{\θ}}_{2,j}^K)\right)}^{1/2}---\left(3\right)$

The input of K-means algorithm is K associative mode set

And the minimum threshold of distance θ at two subclass centers, the output of algorithm is subclass quantity C, the subclass center is made as { W ₁, W ₂..., W _C, and each associative mode belongs to the membership of different subclasses

Variable i is the index of iterations in the algorithm, and k is the index of classification mode, and c then is the index of cluster centre, and algorithm steps is as follows:

A, from K associative mode, select arbitrarily C ₀Individual associative mode is as initial cluster center W _{I, c}(c=1,2 ..., C ₀), for W _{I, c}Choose, common method is evenly to extract C from be classified pattern ₀Individual associative mode, suggestion C ₀In interval (value in the K/3～K/2);

If two subclass centers of b apart from dist (W _{I, c1}, W _{I, c2}) less than predetermined threshold value θ, then reject one of them cluster centre;

C, calculate each associative mode

Distance to all cluster centres

If

With c ^*The center of class

Distance minimum, then will Membership be defined as m (k)=c ^*

D, I _NumAfter the inferior iteration, if the associative mode (for example not surpassing 5 associative modes) of some is not captured at certain subclass center, then reject this strange class;

E, renewal subclass quantity are C _I+1, and recomputate new cluster centre W according to the membership of associative mode _{I+1, c}(c=1,2 ..., C _I+1);

If algorithm satisfies the condition of convergence then finishes, otherwise return step b, carrying out next iteration calculates, it is a class that above process incorporates the process sampled point that has an internal relation with quality index Y into, finish the stage division (Fig. 5) to batch process of changeable stage, the described condition of convergence is associative mode in each subclass

To the square distance at subclass center with reach the square distance between minimum (as less than interval [0.0001,0.1]) or the subclass and reach minimum.

S6 obtains the quality index predicted value

Referring to Fig. 4-Fig. 6, in this step, at first with current batch sampling, according to the stage C under each sampled point, find the average characteristics in this stage

The calculated mass index

The cluster analysis of specifically, establishing step S6 obtains C representative stage, the then regression relation in C stage

Can be expressed as this stage n _sThe mean value of individual modes relationships, as shown in the formula:

${\mathrm{\θ}}_c^{*}=\underset{k=1}{\overset{n_s}{\mathrm{\Σ}}}{\mathrm{\θ}}_k/n_s;---\left(4\right)$

Further, the projected relationship of quality index and process data can be expressed as following formula:

${\hat{y}}_n=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i*{\mathrm{\θ}}_c^{*};---\left(5\right)$

Wherein: c=1,2 ..., K; I=1,2 ..., N;

Referring to Fig. 4, the sampled data when above process adopts moment k is as the sampled data after the moment k.

The present embodiment carries out standardization, MPLS modeling by above step to the injection moulding process data and the θ that obtains after the modeling is cut into slices according to time orientation, and it is carried out cluster, obtain result shown in Figure 5, in the present embodiment, the process stage relevant with this index of product weight mainly can be divided into 3 sections.

After this, obtain the average recurrence characteristic of three phases according to step S6

Come quality index is predicted according to step S7, S8 at last, finally finished based on the prediction of process data to quality index.In theory, the quality of product can be by some or several key index (crystallinity of client's concern, internal stress, weight, volume) characterize, therefore, in practical operation, can set up by historical data the statistical relationship of process data and quality index, in production subsequently, concern to come the on-line prediction quality index with this, thereby in time understand the quality state of paying close attention to;

Embodiment 2

The present embodiment is from the different of embodiment 1, in the described batch process quality index of the present embodiment flexible measurement method, before the process data matrix X ' that the quality index matrix Y (I*Z) that step S1 is obtained and step S2 obtain carries out multidirectional partial least square method modeling, first these two two bit matrix are carried out standardization, described normalization step following (Fig. 7):

S100 course of standardization process data matrix X

If the variable of the interior any point of two-dimensional matrix X ' is x ' _Ijk, to this variable subtract average, divided by the standardization of variance, obtain newcomer x _Ijk*, wherein the calculating worker formula of standardization is as follows:

$x_{\mathrm{ijk}}^{*}=\frac{x_{\mathrm{ijk}}^{\′}-{\stackrel{\‾}{x}}_{\mathrm{jk}}}{s_{\mathrm{jk}}};---\left(6\right)$

Wherein: Be the average of arbitrary row among the two-dimensional matrix X ', S _JkBe the variance of arbitrary row among the two-dimensional matrix X ', the computing method of the two are as follows:

${\stackrel{\‾}{x}}_{\mathrm{jk}}=\frac{1}{I}*\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{x}_{\mathrm{ijk}}^{\′};---\left(7\right)$

$S_{\mathrm{jk}}=\sqrt{\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{(x_{\mathrm{ijk}}^{\′}-{\stackrel{\‾}{x}}_{\mathrm{jk}})}^2/(I-1)};---\left(8\right)$

S200 standardization quality index matrix Y

Equally, Y carries out standardization to the quality index matrix, namely two-dimensional matrix Y is carried out to subtract average divided by the operation of variance, obtains

The mathematic(al) representation of standardization is as follows:

$y_{\mathrm{iz}}^{*}=\frac{y_{\mathrm{iz}}-{\stackrel{\‾}{y}}_z}{s_z};---\left(9\right)$

Wherein,

Be the average of arbitrary row among the two-dimensional matrix Y, S _zBe the variance of arbitrary row among the two-dimensional matrix Y, the computing method of the two are as follows:

${\stackrel{\‾}{y}}_z=\frac{1}{I}*\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{y}_{\mathrm{iz}}---\left(10\right)$

$S_z=\sqrt{\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{(y_{\mathrm{iz}}-{\stackrel{\‾}{y}}_z)}^2/(I-1)}---\left(11\right)$

The operation of this step has been equivalent to extract the average running orbit of batch process single job, given prominence to a kind of normal random fluctuation between the batch process different operating batch, above standardisation process does not change the ranks characteristic of former processing process data matrix X ' and quality index matrix Y, and the result after the standardization can be directly used in the step 3 among the embodiment 1.

Should be appreciated that; top specific embodiment has been done detailed description to embodiments of the present invention by reference to the accompanying drawings; but the scope of protection of the invention is not limited to above-mentioned embodiment; in the ken that one skilled in the relevant art possesses; can also under the prerequisite that does not break away from aim of the present invention, make various variations to above-described embodiment, and these variations should be included in all in claims of the present invention scope required for protection.

Claims (6)

1. a batch process quality index flexible measurement method is characterized in that, may further comprise the steps:

The S1 model data collecting

If a batch process has J detection variable, K sampled point and Z quality index, then each measures batch process data matrix and Z the quality results data matrix that can obtain a J*K, after repeating I batch measuring process, be a three-dimensional matrice X (I*J*K) with process data representation, the quality results data are expressed as two-dimensional matrix Y (I*Z);

The S2 three-dimensional data is launched

Three-dimensional matrice X (I*J*K) is launched by gathering batch direction, be about to variable on each sampled point in the operation batch and arrange according to time sequencing and obtain two-dimensional matrix X ', wherein, X ' be the matrix that the capable KJ of I is listed as;

The multidirectional partial least square method modeling of S3

If process data matrix and quality index matrix that upper two steps obtain are respectively X (I*JK), Y(1*Z), it is carried out multidirectional partial least square method modeling, obtain the regression relation between process data matrix X and the quality index matrix Y, wherein, the formula of multidirectional partial least square method modeling is as follows:

$X=T_R{\left(P_R\right)}^T+E=\underset{r=1}{\overset{R}{\mathrm{\Σ}}}{t}_r{p}_r^{\′}+E$

$Y=U_R{\left(Q_R\right)}^T+F=\underset{r=1}{\overset{R}{\mathrm{\Σ}}}{u}_r{q}_r^{\′}+F;---\left(1\right)$

Y=X·θ+F ^*

Wherein: the X decomposition obtains score matrix T _R(I * R) and load matrix P _R(JK * R), t _r, p _rIt is respectively vector in the matrix wherein;

The Y decomposition obtains score matrix U _R(I * R) and load matrix Q _R(Z*R), u _r, q _rIt is respectively vector in the matrix;

E, F, F ^*Be residual information, θ is the regression coefficient of X and Y, and R is the latent variable number;

The S4 regression coefficient is decomposed

A process of among the S41 refer step S2 three-dimensional matrice X (I*J*K) being launched by collection batch direction, the regression relation matrix θ (JK * Z) the similar restructuring of counter movement that will comprise process variable and the quality index of K timeslice, because step S3 execution X (I * JK), (I * Z) decomposition does not change sequential relationship wherein to Y, among the regression coefficient θ every J capable be the regression relation of a sampling instant, this K sheet is reassembled as a three-dimensional data matrix according to sequential relationship;

S42 downcuts the three-dimensional data matrix among the step S41 and removes to consist of two-dimensional matrix according to the direction of time k The regression coefficient that then exists with matrix form can be stated following version by K associative mode combination as:

$\mathrm{\θ}=\{{\mathrm{\θ}}_1^K,{\mathrm{\θ}}_2^K,...,{\mathrm{\θ}}_K^K\};---\left(2\right)$

Wherein,

(k=1,2 ..., K) be associative mode;

S5 K-means cluster analysis

This step selects the distance that defines below as the index of measuring two associative mode similarity degree, to K associative mode

(J * Z) carry out the K-means cluster analysis, the pattern with same phase characteristic can be divided into a class, and different classifications represents different stage characteristics, and above-mentioned distance is defined by following formula:

$\mathrm{dist}({\mathrm{\θ}}_1^K,{\mathrm{\θ}}_2^K)={\left(\underset{j=1}{\overset{J}{\mathrm{\Σ}}}{({\mathrm{\θ}}_{1,j}^K,-{\mathrm{\θ}}_{2,j}^K)}^T({\mathrm{\θ}}_{1,j}^K-{\mathrm{\θ}}_{2,j}^K)\right)}^{1/2}---\left(3\right)$

The input of K-means algorithm is K associative mode set

And the minimum threshold of distance θ at two subclass centers, the output of algorithm is subclass quantity C, the subclass center is made as { W ₁, W ₂..., W _C, and each associative mode belongs to the membership of different subclasses Variable i is the index of iterations in the algorithm, and k is the index of classification mode, and c then is the index of cluster centre, and algorithm steps is as follows:

A, from K associative mode, select arbitrarily C ₀Individual associative mode is as initial cluster center W _{I, c}(c=1,2 ..., C ₀), for W _{I, c}Choose, common method is evenly to extract C from be classified pattern ₀Individual associative mode, suggestion C ₀In interval (value in the K/3～K/2);

If two subclass centers of b apart from dist (W _{I, c1}, W _{I, c2}) less than predetermined threshold value θ, then reject one of them cluster centre;

C, calculate each associative mode

(k=1,2 ..., K) to the distance of all cluster centres

If

With c ^*The center of class

Distance minimum, then will

Membership be defined as m (k)=c ^*

D, I _NumAfter the inferior iteration, if the associative mode (for example not surpassing 5 associative modes) of some is not captured at certain subclass center, then reject this strange class;

E, renewal subclass quantity are C _I+1, and recomputate new cluster centre W according to the membership of associative mode _{I+1, c}(c=1,2 ..., C _I+1);

If algorithm satisfies the condition of convergence then finishes, otherwise return step b, carry out next iteration and calculate, it is a class that above process incorporates the process sampled point that has an internal relation with quality index Y into, finishes the stage of multistage batch process is divided;

S6 obtains the predicted value of quality index

If the cluster analysis of step S5 obtains C representative stage, the then regression relation in C stage

Can be expressed as this stage n _sThe mean value of individual modes relationships, as shown in the formula:

${\mathrm{\θ}}_c^{*}=\underset{k=1}{\overset{n_s}{\mathrm{\Σ}}}{\mathrm{\θ}}_k/n_s;---\left(4\right)$

Further, the projected relationship of quality index predicted value and process data can be expressed as following formula

${\hat{y}}_n=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{x}_i*{\mathrm{\θ}}_c^{*};---\left(5\right)$

Wherein: c=1,2 ..., K; I=1,2 ..., N;

Quality index namely characterizes the quality according to the resulting product of batch process.

2. batch process quality index flexible measurement method as claimed in claim 1 is characterized in that, after the described step S2, also comprises the standardized step of two-dimensional matrix, and it comprises:

S100 course of standardization process data matrix X

If the variable of the interior any point of two-dimensional matrix X ' is x _Ijk', to this variable subtract average, divided by the standardization of variance, obtain newcomer x _Ijk*, wherein the mathematic(al) representation of standardization is as follows:

$x_{\mathrm{ijk}}^{*}=\frac{x_{\mathrm{ijk}}^{\′}-{\stackrel{\‾}{x}}_{\mathrm{jk}}}{S_{\mathrm{jk}}};---\left(6\right)$

Wherein:

Be the average of arbitrary row among the two-dimensional matrix X ', S _JkBe the variance of arbitrary row among the two-dimensional matrix X ', the computing method of the two are as follows:

${\stackrel{\‾}{x}}_{\mathrm{jk}}=\frac{1}{I}*\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{x}_{\mathrm{ijk}}^{\′};---\left(7\right)$

$S_{\mathrm{jk}}=\sqrt{\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{(x_{\mathrm{ijk}}^{\′}-{\stackrel{\‾}{x}}_{\mathrm{jk}})}^2/(I-1);}---\left(8\right)$

S200 standardization quality index matrix Y

Y carries out standardization to the quality index matrix, namely two-dimensional matrix Y is carried out to subtract average divided by the operation of variance, obtains

The mathematic(al) representation of standardization is as follows:

$y_{\mathrm{iz}}^{*}=\frac{y_{\mathrm{iz}}-{\stackrel{\‾}{y}}_z}{S_z};---\left(9\right)$

Wherein,

Be the average of arbitrary row among the two-dimensional matrix Y, S _zBe the variance of arbitrary row among the two-dimensional matrix Y, the computing method of the two are as follows:

${\stackrel{\‾}{y}}_z=\frac{1}{I}*\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{y}_{\mathrm{iz}}---\left(10\right)$

$S_z=\sqrt{\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{(y_{\mathrm{iz}}-{\stackrel{\‾}{y}}_z)}^2/(I-1)}---\left(11\right)$

3. batch process quality index flexible measurement method as claimed in claim 1 is characterized in that, among the described step S5, K-means convergence of algorithm condition is associative mode in each subclass To the square distance at subclass center and reach minimum or subclass between square distance and reach minimum.

4. batch process quality index flexible measurement method as claimed in claim 1 is characterized in that, among the described step S1, measures the number of times of batch I greater than 50, and the quantity of sampled point K is less than 1000.

5. batch process quality index flexible measurement method as claimed in claim 1 is characterized in that, among the described step S3, described latent variable number is between 1-1000.

6. batch process quality index flexible measurement method as claimed in claim 5 is characterized in that, among the described step S3, described latent variable number is between 1-10.

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