CN103116306B - Automatic stepping type ordered time interval dividing method - Google Patents

Abstract

The invention discloses an automatic stepping type ordered time interval dividing method which can be used for dividing an interval of a multi-operation procedure into different sub time intervals according to change of process characteristics. Each time interval has similar process characteristic and can be represented by the same model, while different time intervals have different characteristics so that different models are needed to be built, and accordingly, the number of the models and complexity are reduced greatly. Online monitoring indexes are used as the judgment basis for time interval dividing, and thus, precision of the models for the time interval dividing is improved, and subsequent process online monitoring performance is improved greatly. In addition, the automatic stepping type ordered time interval dividing method is easy to implement and is applied successfully in the mold injection process, assists people to learn the specific process characteristics, enhances reliability and confidence of the actual online process monitoring, assists engineers to make correct judgment for the process running states and find out fault in time, and accordingly guarantees safe and reliable running of actual production and high quality of products.

Description

A kind of orderly Time segments division method of step-by-step movement automatically

Technical field

The invention belongs to batch process statistical monitoring field, particularly relate to a kind of method can carrying out automatic Time segments division for multioperation period batch production process.

Background technology

As the important mode of production a kind of in commercial production, the life of batch process and people is closely bound up, has been widely used in the fields such as fine chemistry industry, bio-pharmaceuticals, food, polymer reaction, intermetallic composite coating.In recent years, along with the market demand that modern society is more urgent to multi items, many specifications and high quality of products, commercial production relies on the batch process in production short run, high value added product more for counsel.The safe and reliable operation of batch production and the high-quality of product pursue the focus having become people and paid close attention to.Multivariate statistical analysis technology based on data needs the process data under nominal situation to carry out Modling model because of it, and they have unique advantage when processing higher-dimension, height coupling data simultaneously, are more and more subject to the favor of researchist and field engineer.The statistical modeling of batch process, on-line monitoring, fault diagnosis and prediction of quality have become research topic widely.But multidirectional pivot analysis (MPCA) and multidirectional minimum inclined two takes advantage of the statistical analysis technique of recurrence (MPLS) all data of an intermittently operated to be treated as an entirety, can not reflect the change of the correlativity of variable on time orientation.In addition, during application on site, unknown measurement data must be estimated, therefore be difficult to realize on-line implement, hinder its widespread use in actual production.

It is found that batch process procedures has period characteristic through research.Process variable correlationship in intermittently operated is moment change in time not, but follows the change of the change Development pattern of process operation process or process mechanism characteristic, presents segmenting.In Different periods, each period has different process variable track, operational mode and correlative character, and there were significant differences for correlation of variables.In the same period, the correlationship of different sampling instant process variable is approximate consistent.Consider the multi-period characteristic of batch process, people expect whole batch process to be divided into Different periods, thus can set up the multiple models based on the period, and for online process monitoring, thus can detection failure occur timely and effectively, guarantee commercial production safety.For a typical multi-period batch production process-injection mo(u)lding-.Injection moulding process is a typical interval industrial process, is also the embody rule context process of the Time segments division method proposed in this patent.Here the structure of injection machine and the basic functional principle of injection moulding process is simply introduced.Injection moulding is one of main forming method of thermoplasticity or thermosetting plastics product.Plastic products nearly 1/3 in our life are all produced by injection moulding process.A general injection machine forms primarily of injection device, mold closing mechanism, hydraulic system and electric control system.As a typical multioperation stage batch process, a complete injection moulding process is ejected supervisor formed by mold closing, injection seat advance, injection, pressurize, plasticizing, cooling, die sinking, product, and injection portion, pressurize section and cooling section are most important three operational phases determining product quality.In injection portion, plastics rheid is injected die cavity, until die cavity is full of by fluid by hydraulic system lead-screw.When process is in pressurize section, a small amount of rheid is still had to be got in die cavity by high pressure, to compensate the volumetric contraction that plastics rheid causes when cooling and plastify.Packing stage is continued until the gate freeze of die cavity, and process enters cooling stage.While the solidification of cooling stage die cavity inner fluid, under the heating arrangement of the plastic grain in machine bucket outside machine bucket and screw rod rotate the effect of the shear heat produced, realize the change of its physical state, become plastics viscous state and be transported to the head of screw rod.When screw head melt increases gradually, when its pressure is greater than the back pressure of injection cylinder, screw retreats starts volume calculations simultaneously.After head melt reaches certain injection volume, screw rod stops retreating and rotating, and process status is during this period of time also referred to as plastic phase.Along with the continuation of melt in die cavity cools, plastics return to glassy state from viscous state and shape.When plastic solidifies completely, mould is opened, and plastic is ejected, thus completes a working cycle.

How a batch process being reasonably divided into different sub-periods is follow-up basis and key of carrying out statistical modeling and real-time fault detection based on the period, and direct relation the accuracy and confidence of process monitoring.Forefathers have made corresponding research and discussion to this, propose identification of corresponding period way based on different angles.Be summed up following three kinds: method (b) characteristic signal variable analysis method (c) automatic identifying method of (a) foundation process mechanism knowledge and expertise.The each have their own applicable situation of above-mentioned several period recognition methodss and relative merits.Clustering method is the period Automated Partition Method relatively commonly used, and lays particular emphasis on the change analyzing tracing process correlation properties.But, based on the Time segments division method of cluster, do not consider the timing of period.If only consider the similar characteristic of process, sampling instant in different time region can be put under in same sub-period by mistake, and at the same time in region in time point also can be divided in Different periods, this will cause division result intricate, be difficult to understand.In addition, Interim intersegmental when these Time segments division methods are not considered, and timeslice was strictly divided in certain period.In the transitional region that procedural correlation changes, if the procedure schema belonged to has during this period of time been divided in two subclasses by rigid, likely cause " misclassification ".Transition mode is included in the accuracy that can affect sub-period model in sub-period on the one hand; On the other hand, transition mode is buried in sub-period, can increase the probability of the first kind metrical error during on-line monitoring period transitional region.Can say, period automatic partition method before all do not consider the timing of process operation and the period transitional, thus directly or intermittent effects follow-up process model building precision and Monitoring Performance.

Content of the present invention deeply considers the impact for Monitoring Performance afterwards of timing that the time variation of the potential characteristic of batch process and real process run and Time segments division result, proposes a kind of new sub-period Automated Partition Method.Up to the present, there is not yet research report related to the present invention.

Summary of the invention

The object of the invention is to the deficiency for the existing Time segments division technology for batch production process, a kind of orderly Time segments division method of step-by-step movement is automatically provided.The method automatically can run according to batch production process the development and change that order catches latent process characteristic, determine the local time's block on time orientation, i.e. sub-period and transition mode, based on this Time segments division result modeling, can improved model precision and improve online process monitoring performance, and finally can be applicable to actual industrial production scene, guarantee that the safe and reliable operation of batch production and the high-quality of product are pursued.

The object of the invention is to be achieved through the following technical solutions: a kind of orderly Time segments division method of step-by-step movement automatically, the method comprises the following steps:

Step 1: acquisition process analyzes data: establish an intermittently operated to have J measurand and K sampled point, then each measures batch matrix that can obtain a K × J, and after repeating the measuring process of I batch, the data obtained can be expressed as a three-dimensional matrice wherein measurand is state parameter that can be measured in batch operational processs such as temperature, speed, pressure, displacement;

Step 2: data prediction: by three-dimensional matrice launch according to collection batch direction, to arrange according to time sequencing by the variable on each sampled point in an operation batch and obtain two-dimensional matrix X (I × KJ), by K timeslice matrix X _k(I × J) forms, and wherein, subscript k is time index;

If two-dimensional matrix X _kthe variable of interior any point is x _{k, i, j}average, standardization divided by standard deviation are subtracted to this variable, wherein, subscript i representative batch, j represents variable, and the computing formula of standardization is as follows:

$x_{k,i,j}=\frac{x_{k,i,j}-{\stackrel{\‾}{x}}_{k,j}}{s_{k,j}};---\left(1\right)$

Wherein: k is timeslice index. x _kthe average of the arbitrary row of matrix, s _{k, j}x _kthe standard deviation of square respective column,

${\stackrel{\‾}{x}}_{k,j}=\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{x}_{k,i,j},$

$s_{k,j}=\sqrt{\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{(x_{k,i,j}-{\stackrel{\‾}{x}}_{k,j})}^2/(I-1)};---\left(2\right)$

Step 3: timeslice PCA modeling, this step is realized by following sub-step:

(3.1) to each the timeslice matrix X after step 2 standardization _k(I × J) perform PCA decompose, Time Created sheet pca model, wherein PCA decomposition formula is as follows:

$X_k=T_k{P_k}^T=\underset{r=1}{\overset{J}{\mathrm{\Σ}}}{t}_{k,r}{p}_{k,r};---\left(3\right)$

Wherein: t _{k, n}for orthogonal principal component vector, p _{k, n}for the load vector of orthonomalization, r represents that different PCA decomposes direction, the transposition of subscript T representing matrix; T _k(I × J) representative retains the score matrix of whole pivot, P _k(J × J) represents corresponding load matrix.

(3.2) choose pivot number, formula (3) re become following form:

$X_k=T_k{P_k}^T+E_k=\underset{r=1}{\overset{R}{\mathrm{\Σ}}}{t}_{k,r}{p}_{k,r}+E_k---\left(4\right)$

Wherein: r represents that different PCA decomposes direction; T _k(I × R _k) and P _k(J × R _k) represent load matrix be respectively retain R _kscore matrix after individual pivot and load matrix, E _kfor residual matrix.By above-mentioned conversion, original data space is decomposed into principal component space and residual error space by multidirectional principle component analysis model, represents main systematic procedure fluctuation information in principal component space; Here retained pivot number R _kthe process variation information of in former process 90% can be reflected.Consider overall process, choose the R that occurrence number is maximum _kprimary system one is final modeling pivot number R, and namely all timeslice models retain identical pivot number.

(3.3) the SPE index of each batch corresponding in each timeslice k in residual error space is calculated:

SPE _k，i=e _k，i ^Te _k，i（5）

Wherein, subscript i represent in timeslice batch, e _{k, i}it is the residual error column vector in corresponding k moment i-th batch.The χ of Weight coefficient is obeyed according to the SPE value going up different batches mutually in the same time ²distribution, thus determine the control limit Ctr on each time point _k, it has reacted the re-configurability of timeslice pca model.

Step 4: determine that the SPE norm controlling based on variable expansion model is limit: from batch process initial point, combines next timeslice and timeslice before and launches to obtain time block X by variable mode successively _{v, k}(Ik × J), wherein subscript v represents variable expansion mode.PCA analysis is carried out to new time block matrix, extracts load matrix P _{v, k}(J × R).Calculate its SPE value and according to the χ of SPE value obedience Weight coefficient go up mutually different batches in the same time ²distribution, thus determine the control limit Ctr on each time point _k.

Step 5: determine the first Time segments division point k ^*: compare Ctr on each time point in same time region _kand Ctr _{v, k}size, if find that continuous three samples present Ctr _{v, k}> α Ctr _k, the timeslice so newly added has great impact to the PCA monitoring model of this time block and corresponding Monitoring Performance.Moment before note adds new timeslice is k ^*.Wherein, α depends on Ctr _kconstant, be called the mitigation factor, its reflection be compared with timeslice model, time block model allow monitoring accuracy loss degree.Then k ^*timeslice before moment can think a sub-period.

Step 6: process analysis procedure analysis Data Update, determines all division periods: according to the moment k obtained in step 5 ^*instruction, remove first sub-period, the batch process data of remainder to be brought in the 5th step as new input data and to repeat above-mentioned steps 5-6, dividing different time sections, until do not have data remaining.

Step 7: the statistical modeling based on Time segments division result: according to step 6 Time segments division result, the timeslice in each period is combined into the representative modeling data group of sub-period according to variable expansion mode, X _c(IK _c× J), wherein, subscript c is period index.The potential characteristic of process similar in each period can be passed through X _c(IK _c× J) implement PCA decompose extract:

T _c=X _cP _c

${\hat{X}}_c=T_c{P_c}^T=X_c{P}_c{P_c}^T---\left(6\right)$

$E_c=X_c-{\hat{X}}_c$

Wherein, P _c(J × R _c) be the PCA load matrix of this sub-period, disclose the main fluctuation direction in this sub-period, R _crepresent the PCA pivot number that this sub-period model retains.T _c(IK _c× R _c) represent the pivot score matrix of this sub-period.Therefore, T is passed through in the main fluctuation of this period _cp _c ^tcharacterize, represent the main fluctuation information in this sub-period; Remaining as sub-period residual matrix, E _c(IK _c× J) represent noise information in this sub-period.Each timeslice pivot score, T _k(I × R _c), can be easy to from sub-period score matrix T _c(IK _c× R _c) in extract according to the process time of correspondence and obtain, thus the covariance relationship S in each sampling instant can be calculated accordingly _k.Each timeslice residual matrix E _k(I × J) can also from sub-period residual matrix E _c(IK _c× J) middle corresponding acquisition.

Step 8: calculate Real-Time Monitoring statistical indicator: the pivot according to obtaining in the result calculated from formula (6) obtains time-slotting T _k(I × R _c) and residual matrix timeslice E _k(I × J) can calculate two monitoring and statistics index: Hotelling-T in each moment ²statistical indicator and SPE statistic.

Hotelling-T ²statistical indicator is used for measuring the distance that each sampling instant process variable departs from mean trajectory under nominal situation, and its control limit under level of significance α is calculated as:

$T_{i,k}^2-{(t_{i,k}-{\stackrel{\‾}{t}}_k)}^T{S}_k^{-1}(t_{i,k}-{\stackrel{\‾}{t}}_k)~\frac{R_c(I-1)}{I-R_c}{F}_{R_c,{I-R}_c,\mathrm{\α}}---\left(7\right)$

Wherein, R _cit is the pivot number retained in this period pca model; t _{i, k}(R _c× 1) be the pivot score in kth moment the i-th batch, i.e. corresponding timeslice score matrix T _k(I × R _c) the i-th row; And t _k(I × R _c) for the mean vector of different batches, due to each timeslice measurement data when data prediction center turn to zero-mean, here be exactly null vector in fact.

For residual error subspace, the SPE normalized set of each moment different batches is:

${\mathrm{SPE}}_{i,k}{(x_{i,k}-{\hat{x}}_{i,k})}^T(x_{i,k}-{\hat{x}}_{i,k})---\left(8\right)$

Wherein, x _{i, k}represent the process measurement vector in k moment the i-th batch, it is then the corresponding result reconstructed by pca model.Result of calculation in formula (8) can form an I × 1 vector [SPE in each moment _{1, k}, SPE _{2, k}..., SPE _{i, k}] ^t, and this vector approximation obeys weighting χ ²distribution, thus the Monitoring and Controlling limit obtaining each moment SPE.

Step 9: based on time segment model online process monitoring: two monitoring and statistics amounts of the period divided based on step 6, period model assay system that step 7 is set up and step 8 gained can the new state running batch process such as on-line monitoring injection mo(u)lding.This step is realized by following sub-step:

(9.1) new measurement data and new measurement data pre-service is gathered: during on-line monitoring, collect new process measurement data x _newafter (J × 1), wherein, subscript n ew represents new samples, and J is measurand, identical with the measurand in step 1; First need to carry out data prediction.According to the average obtained in step 2 and standard deviation, call the average in moment and standard deviation carrying out standardization pre-service to the process measurement data collected as shown in formula (1) according to the instruction of process time.

(9.2) calculate new monitoring and statistics amount: after data prediction, according to the PCA sub-period model that formula (6) calculates, call should the model P of newly sampling instant place period _c(J × R _c), calculate pivot score in the following manner, estimate the Hotelling-T of residual error and correspondence thereof ²with SPE two monitoring and statistics indexs:

t _new ^T=x _new ^TP _c

${\hat{x}}_{\mathrm{new}}=P_c{t}_{\mathrm{new}}$ $\left(9\right)$

$T_{\mathrm{new}}^2={(t_{\mathrm{new}}-{\stackrel{\‾}{t}}_k)}^T{S_k}^{-1}(t_{\mathrm{new}}-{\stackrel{\‾}{t}}_k)$

${\mathrm{SPE}}_{\mathrm{new}}={(x_{\mathrm{new}}-{\hat{x}}_{\mathrm{new}})}^T(x_{\mathrm{new}}-{\hat{x}}_{\mathrm{new}})$

Wherein, new process measurement data, according to the T that training data obtains before being _kmean vector, S _kx _kcovariance matrix.

(9.3) online deterministic process running status: compare the Statisti-cal control limit that two monitoring indexes are respective with it in real time, if two monitoring indexes are all positioned within Statisti-cal control limit, shows that process operation is normal; Normally control limit if there is more than one monitoring index to exceed, show that process has unusual condition to occur.

Further, in described step 1, described measurand is following 9: pressure valve aperture, flow valve aperture, screw stroke, screw speed, injection pressure, nozzle temperature, machine bucket head temperature, machine bucket medium temperature and machine bucket tail temperature.

Compared with prior art, the invention has the beneficial effects as follows: the present invention provides new Research Thinking without the multistage process Time segments division under process priori condition, modeling and monitoring.The sub-period Automated Partition Method proposed can be applied to the batch production process of a class many operation periods, be divided into different sub-period according to the change of process characteristic, and the precision of the sub-period model of foundation and the performance of subsequent process on-line monitoring can be improved.The method proposed has done detailed experimental study in injection industry process, obtain successful Application, the method is by the automatic division to batch process many operation periods, enhance the understanding to detailed process operation characteristic, improve the monitoring efficiency of process monitoring process and the accuracy of failure detection result, finally can be applicable to actual industrial production scene, guarantee that the safe and reliable operation of batch production and the high-quality of product are pursued.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the orderly Time segments division method of automatic step-by-step movement of the present invention;

Fig. 2 is the three-dimensional data expansion model schematic diagram of the orderly Time segments division method of automatic step-by-step movement of the present invention;

Fig. 3 is the inventive method Time segments division result in the specific embodiment of the invention and classic method division result comparison diagram.

Embodiment

Below in conjunction with accompanying drawing and instantiation, the present invention will be further described.

Injection molding process is typical multi-period batch production process, is generally made up of injection, pressurize, cooling three phases.In addition, plasticizing process completed in the cooling starting stage.Specifically, at injection stage, plastics rheid is injected die cavity, until die cavity is full of by fluid by hydraulic system lead-screw.When process is in packing stage, a small amount of rheid is still had to be got in die cavity by high pressure, to compensate the volumetric contraction that plastics rheid causes when cooling and plastify.Packing stage is continued until the gate freeze of die cavity, and process enters cooling section.When screw head melt increases gradually, after reaching certain injection volume, screw rod stops retreating and rotating, and process status during this period of time also claims fluxing zone.Along with melt in die cavity continues cooling, plastic solidifies completely, and mould is opened, and plastic is ejected, thus completes a working cycle.

The orderly Time segments division method of the automatic step-by-step movement of the present invention, comprises the following steps:

1, acquisition process analyzes data

If an intermittently operated has J measurand and K sampled point, then each measures batch matrix that can obtain a K × J, and after repeating the measuring process of I batch, the data obtained can be expressed as a three-dimensional matrice wherein measurand is state parameter that can be measured in batch operational processs such as temperature, speed, pressure, displacement; In this example, acquire 526 samples, measurand is 9: pressure valve aperture, flow valve aperture, screw stroke, screw speed, injection pressure, nozzle temperature, machine bucket head temperature, machine bucket medium temperature, machine bucket tail temperature.In this example, 30 normal batch for testing the Time segments division method of the present invention's proposition and setting up corresponding on-line monitoring system.Namely three-dimensional modeling data matrix is in addition, experiment acquisition three kinds of faults are batch for verifying the online fault detect performance of set up monitoring system, and wherein often kind of fault comprises 49 batches.These three kinds of faults are: the fault of thermopair 90% efficiency, the fault of heating collar 80% efficiency under open loop, and the fault of batch mixing (namely original high density polyethylene raw material adds blue polypropylene).

Step 2: data prediction: by three-dimensional matrice launch according to collection batch direction, to arrange according to time sequencing by the variable on each sampled point in an operation batch and obtain two-dimensional matrix X (I × KJ), by K timeslice matrix X _k(I × J) forms, and wherein, subscript k is time index;

If two-dimensional matrix X _kthe variable of interior any point is x _{k, i, j}average, standardization divided by standard deviation are subtracted to this variable, wherein, subscript i representative batch, j represents variable, and the computing formula of standardization is as follows:

$x_{k,i,j}=\frac{x_{k,i,j}-{\stackrel{\‾}{x}}_{k,j}}{s_{k,j}};---\left(1\right)$

Wherein: k is timeslice index. x _kthe average of the arbitrary row of matrix, s _{k, j}x _kthe standard deviation of square respective column,

${\stackrel{\‾}{x}}_{k,j}=\frac{1}{I}\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{x}_{k,i,j},$

$s_{k,j}=\sqrt{\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{(x_{k,i,j}-{\stackrel{\‾}{x}}_{k,j})}^2/(I-1)};---\left(2\right)$

Step 3: timeslice PCA modeling, this step is realized by following sub-step:

(3.1) to each the timeslice matrix X after step 2 standardization _k(I × J) perform PCA decompose, Time Created sheet pca model, wherein PCA decomposition formula is as follows:

$X_k=T_k{P_k}^T=\underset{r=1}{\overset{J}{\mathrm{\Σ}}}{t}_{k,r}{p}_{k,r};---\left(3\right)$

Wherein: t _{k, n}for orthogonal principal component vector, p _{k, n}for the load vector of orthonomalization, r represents that different PCA decomposes direction, the transposition of subscript T representing matrix; T _k(I × J) representative retains the score matrix of whole pivot, P _k(J × J) represents corresponding load matrix.

(3.2) choose pivot number, formula (3) re become following form:

$X_k=T_k{P_k}^T+E_k=\underset{r=1}{\overset{R}{\mathrm{\Σ}}}{t}_{k,r}{p}_{k,r}+E_k---\left(4\right)$

Wherein: r represents that different PCA decomposes direction; T _k(I × R _k) and P _k(J × R _k) represent load matrix be respectively retain R _kscore matrix after individual pivot and load matrix, E _kfor residual matrix.By above-mentioned conversion, original data space is decomposed into principal component space and residual error space by multidirectional principle component analysis model, represents main systematic procedure fluctuation information in principal component space; Here retained pivot number R _kthe process variation information of in former process 90% can be reflected.Consider overall process, choose the R that occurrence number is maximum _kprimary system one is final modeling pivot number R, and namely all timeslice models retain identical pivot number.

(3.3) the SPE index of each batch corresponding in each timeslice k in residual error space is calculated:

SPE _k，i=e _k，i ^Te _k，i（5）

Wherein, subscript i represent in timeslice batch, e _{k, i}it is the residual error column vector in corresponding k moment i-th batch.The χ of Weight coefficient is obeyed according to the SPE value going up different batches mutually in the same time ²distribution, thus determine the control limit Ctr on each time point _k, it has reacted the re-configurability of timeslice pca model.

Step 4: determine that the SPE norm controlling based on variable expansion model is limit: from batch process initial point, combines next timeslice and timeslice before and launches to obtain time block X by variable mode successively _{v, k}(Ik × J), wherein subscript v represents variable expansion mode.PCA analysis is carried out to new time block matrix, extracts load matrix P _{v, k}(J × R).Calculate its SPE value and according to the χ of SPE value obedience Weight coefficient go up mutually different batches in the same time ²distribution, thus determine the control limit Ctr on each time point _k.

Step 5: determine the first Time segments division point k ^*: compare Ctr on each time point in same time region _kand Ctr _{v, k}size, if find that continuous three samples present Ctr _{v, k}> α Ctr _k, the timeslice so newly added has great impact to the PCA monitoring model of this time block and corresponding Monitoring Performance.Moment before note adds new timeslice is k ^*.Wherein, α depends on Ctr _kconstant, be called the mitigation factor, its reflection be compared with timeslice model, time block model allow monitoring accuracy loss degree.Then k ^*timeslice before moment can think a sub-period.

Step 6: process analysis procedure analysis Data Update, determines all division periods: according to the moment k obtained in step 5 ^*instruction, remove first sub-period, the batch process data of remainder to be brought in the 5th step as new input data and to repeat above-mentioned steps 5-6, dividing different time sections, until do not have data remaining.

Step 7: the statistical modeling based on Time segments division result: according to step 6 Time segments division result, the timeslice in each period is combined into the representative modeling data group of sub-period according to variable expansion mode, X _c(IK _c× J), wherein, subscript c is period index.The potential characteristic of process similar in each period can be passed through X _c(IK _c× J) implement PCA decompose extract:

T _c=X _cP _c

${\hat{X}}_c=T_c{P_c}^T=X_c{P}_c{P_c}^T---\left(6\right)$

$E_c=X_c-{\hat{X}}_c$

Wherein, P _c(J × R _c) be the PCA load matrix of this sub-period, disclose the main fluctuation direction in this sub-period, R _crepresent the PCA pivot number that this sub-period model retains.T _c(IK _c× R _c) represent the pivot score matrix of this sub-period.Therefore, T is passed through in the main fluctuation of this period _cp _c ^tcharacterize, represent the main fluctuation information in this sub-period; Remaining as sub-period residual matrix, E _c(IK _c× J) represent noise information in this sub-period.Each timeslice pivot score, T _k(I × R _c), can be easy to from sub-period score matrix T _c(IK _c× R _c) in extract according to the process time of correspondence and obtain, thus the covariance relationship S in each sampling instant can be calculated accordingly _k.Each timeslice residual matrix E _k(I × J) can also from sub-period residual matrix E _c(IK _c× J) middle corresponding acquisition.

Step 8: calculate Real-Time Monitoring statistical indicator

Pivot according to obtaining in the result calculated from formula (6) obtains time-slotting T _k(I × R _c) and residual matrix timeslice E _k(I × J) can calculate two monitoring and statistics index: Hotelling-T in each moment ²statistical indicator and SPE statistic.

Hotelling-T ²statistical indicator is used for measuring the distance that each sampling instant process variable departs from mean trajectory under nominal situation, and its control limit under level of significance α is calculated as:

$T_{i,k}^2-{(t_{i,k}-{\stackrel{\‾}{t}}_k)}^T{S}_k^{-1}(t_{i,k}-{\stackrel{\‾}{t}}_k)~\frac{R_c(I-1)}{I-R_c}{F}_{R_c,{I-R}_c,\mathrm{\α}}---\left(7\right)$

Wherein, R _cit is the pivot number retained in this period pca model; t _{i, k}(R _c× 1) be the pivot score in kth moment the i-th batch, i.e. corresponding timeslice score matrix T _k(I × R _c) the i-th row; And t _k(I × R _c) for the mean vector of different batches, due to each timeslice measurement data when data prediction center turn to zero-mean, here be exactly null vector in fact.

For residual error subspace, the SPE normalized set of each moment different batches is:

${\mathrm{SPE}}_{i,k}{(x_{i,k}-{\hat{x}}_{i,k})}^T(x_{i,k}-{\hat{x}}_{i,k})---\left(8\right)$

Wherein, x _{i, k}represent the process measurement vector in k moment the i-th batch, it is then the corresponding result reconstructed by pca model.Result of calculation in formula (8) can form an I × 1 vector [SPE in each moment _{1, k}, SPE _{2, k}..., SPE _{i, k}] ^t, and this vector approximation obeys weighting χ ²distribution, thus obtain the Monitoring and Controlling line of each moment SPE.

Step 9: based on time segment model online process monitoring

Two monitoring and statistics amounts of the period divided based on step 6, period model assay system that step 7 is set up and step 8 gained can the new state running batch process such as on-line monitoring injection mo(u)lding.This step is realized by following sub-step:

(9.1) new measurement data and the new measurement data of pre-service is gathered

During on-line monitoring, collect new process measurement data x _newafter (J × 1) (wherein subscript n ew represents new samples), first need to carry out data prediction.According to the average obtained in step 2 and standard deviation, call the average in moment and standard deviation carrying out standardization pre-service to available data as shown in formula (1) according to the instruction of process time.

(9.2) new monitoring and statistics amount is calculated

After data prediction, according to the PCA sub-period model that formula (6) calculates, call should the model P of newly sampling instant place period _c(J × R _c), calculate pivot score in the following manner, estimate the Hotelling-T of residual error and correspondence thereof ²with SPE two monitoring and statistics indexs:

t _new ^T=x _new ^TP _c

${\hat{x}}_{\mathrm{new}}=P_c{t}_{\mathrm{new}}$ $\left(9\right)$

$T_{\mathrm{new}}^2={(t_{\mathrm{new}}-{\stackrel{\‾}{t}}_k)}^T{S_k}^{-1}(t_{\mathrm{new}}-{\stackrel{\‾}{t}}_k)$

${\mathrm{SPE}}_{\mathrm{new}}={(x_{\mathrm{new}}-{\hat{x}}_{\mathrm{new}})}^T(x_{\mathrm{new}}-{\hat{x}}_{\mathrm{new}})$

Wherein new process measurement data, according to the T that training data obtains before being _kmean vector, S _kx _kcovariance matrix.

(9.3) online deterministic process running status

Compare the Statisti-cal control limit that two monitoring indexes are respective with it in real time, if two monitoring indexes are all positioned within Statisti-cal control limit, show that process operation is normal; Normally control limit if there is more than one monitoring index to exceed, show that process has unusual condition to occur.At this moment just can adopt suitable method for diagnosing faults, such as contribution plot methods analyst isolates possible fault variable.

According to the monitoring model that sub-period division result is set up, slip-stick artist can obtain the on-line monitoring result of new process sampled data in real time, and contrast corresponding monitoring and statistics amount control line, thus automatically can carry out enforcement judgement to the state of new operational process, detect and whether have fault to occur.In time having continuous 5 monitoring and statistics amounts to exceed normal control line, show have certain fault to occur in process operation, this moment represents report to the police the moment first (FAT), and this index may be used for the sensitivity assessing fault detect.In this example application of injection mo(u)lding, for often kind of fault type, there are 49 lot data, monitoring model that the average (Mean) of FAT and mean absolute deviation (MAD) set up for comprehensive assessment can be calculated for the fault detect performance of 49 batches.As shown in table 1, contrast based on the method in the present invention and the fault detect performance based on traditional clustering.First, for the monitoring model based on cluster Time segments division, from different θ values (as shown in Figure 3), choose best Monitoring Performance show.And utilizing the monitoring model that division methods of the present invention is set up, then the α span being better than clustering method in the monitoring result it obtained all is shown.In addition, from these results, choose optimum and the poorest monitoring result and contrast based on the monitoring result of clustering method.On the whole, monitoring model based on the Time segments division strategy foundation of the present invention's proposition obtains and is far superior to the Monitoring Performance of tradition based on the Time segments division method of cluster, substantially increase reliability and the confidence level of actual online process monitoring, contribute to Industrial Engineer and accurate judgement is made to process operation state, ensure the safe and reliable operation of actual production process.

Table 1: monitor comparing result based on Time segments division method of the present invention and the online SPE based on traditional division methods.

In table, ^*: the on-line monitoring performance based on Time segments division method acquisition of the present invention is better than the span of the α of clustering method;

: from the different values of secondary series α, choose best SPE on-line monitoring result show;

ο: choose the poorest SPE on-line monitoring result and show from the different values of secondary series α.

The orderly period Automated Partition Method of step-by-step movement of the present invention, by analyzing the change impact of model reconstruction precision and Monitoring Performance being carried out to capture-process characteristic, successfully prove that the batch production process represented with injection mo(u)lding etc. can be divided into Different periods by automatically by being applied to the multi-period batch production processes such as injection mo(u)lding, avoid the subsequent processing steps that classic method is complicated, and substantially increase the precision of the period monitoring model of foundation and the accuracy of follow-up online process monitoring.First the method constructs timeslice model, constantly timeslice fusion is carried out again from process initial time, the sub-period model that the built-in variable that is based on launches in a period of time region and timeslice model contrast, and whether the timeslice process characteristic analyzed in this section of time zone is similar; After determining to comprise the sub-period of similar times sheet, or else disconnected iteration repeats to obtain follow-up sub-period.The process monitoring system set up based on Time segments division result can provide high-precision online process monitoring result for the technical management department at actual industrial production scene, for real-time judge production run state, identified whether fault and reliable basis is provided, and the high-quality pursuit of the final safe and reliable operation for production and product is laid a good foundation.

Should be appreciated that, the present invention is not limited to the injection moulding process of above-mentioned specific embodiment, every those of ordinary skill in the art also can make equivalent variations or replacement under the prerequisite without prejudice to spirit of the present invention, and these equivalent modification or replacement are all included in the application's claim limited range.

Claims (2)

1. the orderly Time segments division method of automatic step-by-step movement, it is characterized in that, the method comprises the following steps: step 1: acquisition process analyzes data: establish an intermittently operated to have J measurand and K sampled point, then each measures batch matrix that can obtain a K × J, after repeating the measuring process of I batch, the data obtained can be expressed as a three-dimensional matrice x(I × J × K), wherein measurand is state parameter that can be measured in batch operational process, comprises temperature, speed, pressure and displacement;

Step 2: data prediction: by three-dimensional matrice xlaunch according to collection batch direction, to arrange according to time sequencing by the variable on each sampled point in an operation batch and obtain two-dimensional matrix X (I × KJ), by K timeslice matrix X _k(I × J) forms, and wherein, subscript k is time index;

If two-dimensional matrix X _kthe variable of interior any point is x _{k, i, j}average, standardization divided by standard deviation are subtracted to this variable, wherein, subscript i representative batch, j represents variable, and the computing formula of standardization is as follows:

Wherein: k is timeslice index, x _kthe average of the arbitrary row of matrix, s _k,jx _kthe standard deviation of square respective column,

Step 3: timeslice PCA modeling, this step is realized by following sub-step:

(3.1) to each the timeslice matrix X after step 2 standardization _k(I × J) perform PCA decompose, Time Created sheet pca model, wherein PCA decomposition formula is as follows:

Wherein: t _k,nfor orthogonal principal component vector, p _k,nfor the load vector of orthonomalization, r represents that different PCA decomposes direction, the transposition of subscript T representing matrix; T _k(I × J) representative retains the score matrix of whole pivot, P _k(J × J) represents corresponding load matrix;

(3.2) choose pivot number, formula (3) re become following form:

Wherein: r represents that different PCA decomposes direction; T _k(I × R _k) and P _k(J × R _k) represent load matrix be respectively retain R _kscore matrix after individual pivot and load matrix, E _kfor residual matrix; By formula (4), original data space is decomposed into principal component space and residual error space by multidirectional principle component analysis model, represents main systematic procedure fluctuation information in principal component space; Here retained pivot number R _kthe process variation information of in former process 90% can be reflected; Consider overall process, choose the R that occurrence number is maximum _kprimary system one is final modeling pivot number R, and namely all timeslice models retain identical pivot number;

(3.3) the SPE index of each batch corresponding in each timeslice k in residual error space is calculated:

SPE _k,i＝e _k,i ^Te _k,i(5)

Wherein, subscript i represent in timeslice batch, e _k,iit is the residual error column vector in corresponding k moment i-th batch; The χ of Weight coefficient is obeyed according to the SPE value going up different batches mutually in the same time ²distribution, thus determine the control limit Ctr on each time point _k, it has reacted the re-configurability of timeslice pca model;

Step 4: determine that the SPE norm controlling based on variable expansion model is limit: from batch process initial point, combines next timeslice and timeslice before and launches to obtain time block X by variable mode successively _v,k(Ik × J), wherein subscript v represents variable expansion mode; PCA analysis is carried out to new time block matrix, extracts load matrix P _v,k(J × R); Calculate its SPE value and according to the χ of SPE value obedience Weight coefficient go up mutually different batches in the same time ²distribution, thus determine the control limit Ctr on each time point _k;

Step 5: determine the first Time segments division point k ^*: compare Ctr on each time point in same time region _kand Ctr _v,ksize, if find that continuous three samples present Ctr _v,k> α Ctr _k, the timeslice so newly added has great impact to the PCA monitoring model of this time block and corresponding Monitoring Performance; Moment before note adds new timeslice is k ^*, wherein, α depends on Ctr _kconstant, be called the mitigation factor, its reflection be compared with timeslice model, time block model allow monitoring accuracy loss degree; Then k ^*timeslice before moment can think a sub-period;

Step 6: process analysis procedure analysis Data Update, determines all division periods: according to the moment k obtained in step 5 ^*instruction, remove first sub-period, the batch process data of remainder to be brought in the 5th step as new input data and to repeat above-mentioned steps 5-6, dividing different time sections, until do not have data remaining;

Step 7: the statistical modeling based on Time segments division result: according to step 6 Time segments division result, the timeslice in each period is combined into the representative modeling data group of sub-period according to variable expansion mode, X _c(IK _c× J), wherein, subscript c is period index; The potential characteristic of process similar in each period can be passed through X _c(IK _c× J) implement PCA decompose extract:

T _c＝X _cP _c

Wherein, P _c(J × R _c) be the PCA load matrix of this sub-period, disclose the main fluctuation direction in this sub-period, R _crepresent the PCA pivot number that this sub-period model retains; T _c(IK _c× R _c) represent the pivot score matrix of this sub-period; Therefore, T is passed through in the main fluctuation of this period _cp _c ^tcharacterize, represent the main fluctuation information in this sub-period; Remaining as sub-period residual matrix, E _c(IK _c× J) represent noise information in this sub-period; Each timeslice pivot score, T _k(I × R _c), can be easy to from sub-period score matrix T _c(IK _c× R _c) in extract according to the process time of correspondence and obtain, thus the covariance relationship S in each sampling instant can be calculated accordingly _k; Each timeslice residual matrix E _k(I × J) can also from sub-period residual matrix E _c(IK _c× J) middle corresponding acquisition;

Step 8: calculate Real-Time Monitoring statistical indicator: the pivot according to obtaining in the result calculated from formula (6) obtains time-slotting T _k(I × R _c) and residual matrix timeslice E _k(I × J) can calculate two monitoring and statistics index: Hotelling-T in each moment ²statistical indicator and SPE statistic;

Hotelling-T ²statistical indicator is used for measuring the distance that each sampling instant process variable departs from mean trajectory under nominal situation, and its control limit under level of significance α is calculated as:

Wherein, R _cit is the pivot number retained in this period pca model; t _i,k(R _c× 1) be the pivot score in kth moment the i-th batch, i.e. corresponding timeslice score matrix T _k(I × R _c) the i-th row; And t _k(I × R _c) for the mean vector of different batches, due to each timeslice measurement data when data prediction center turn to zero-mean, here be exactly null vector in fact;

For residual error subspace, the SPE normalized set of each moment different batches is:

Wherein, x _i,krepresent the process measurement vector in k moment the i-th batch, it is then the corresponding result reconstructed by pca model; Result of calculation in formula (8) can form an I × 1 vector [SPE in each moment _{1, k}, SPE _{2, k}..., SPE _i,k] ^t, and this vector approximation obeys weighting χ ²distribution, thus the Monitoring and Controlling limit obtaining each moment SPE;

Step 9: based on time segment model online process monitoring: the period model assay system that the period divided based on step 6, step 7 are set up and two monitoring and statistics amount on-line monitorings of step 8 gained newly run the state of batch process; This step is realized by following sub-step:

(9.1) new measurement data and new measurement data pre-service is gathered: during on-line monitoring, collect new process measurement data x _newafter (J × 1), wherein, subscript n ew represents new samples, and J is measurand, identical with the measurand in step 1; First need to carry out data prediction; According to the average obtained in step 2 and standard deviation, call the average in moment and standard deviation carrying out standardization pre-service to the process measurement data collected as shown in formula (1) according to the instruction of process time;

(9.2) calculate new monitoring and statistics amount: after data prediction, according to the PCA sub-period model that formula (6) calculates, call corresponding new process measurement data x _newthe model P of (J × 1) place period _c(J × R _c), calculate pivot score in the following manner, estimate the Hotelling-T of residual error and correspondence thereof ²with SPE two monitoring and statistics indexs:

t _new ^T＝x _new ^TP _c

(9)

Wherein, new process measurement data, according to the T that training data obtains before being _kmean vector, S _kx _kcovariance matrix;

(9.3) online deterministic process running status: compare the Statisti-cal control limit that two monitoring indexes are respective with it in real time, if two monitoring indexes are all positioned within Statisti-cal control limit, shows that process operation is normal; Normally control limit if there is more than one monitoring index to exceed, show that process has unusual condition to occur.

2. the automatic orderly Time segments division method of step-by-step movement according to claim 1, it is characterized in that, in described step 1, described measurand is following 9: pressure valve aperture, flow valve aperture, screw stroke, screw speed, injection pressure, nozzle temperature, machine bucket head temperature, machine bucket medium temperature and machine bucket tail temperature.