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A Sub-stage Moving Window GRNN Quality Prediction Method for Injection Molding Processes Xiao-Ping Guo1,2, Fu-Li Wang1, and Ming-Xing Jia1 1

Information Science and Engineering School, Northeastern University, Shenyang, China [email protected], [email protected] 2 Information Engineering School, Shenyang Institute of Chemical Technology, Shenyang, China [email protected]

Abstract. For injection molding process, a typical multistage batch process, the final product qualities are usually available at the end of the batch, which make it difficult for on-line quality control. A sub-stage moving window generalized regression neural network (GRNN) is proposed for dedicating to reveal the nonlinearly and dynamic relationship between process variables and final qualities at different stages. Firstly, using an clustering arithmetic, PCA Ploading matrices of time-slice matrices is clustered and the batch process is divided into several operation stages, the most relevant stage to the quality variable is defined, and then applying moving windows to un-fold stage data according to time, and sub-stage GRNN models are developed for every windows for on-line quality prediction. For comparison purposes a sub-MPLS quality model of every moving window was establish. The results prove the effectiveness of the proposed quality prediction method is supervior to subMPLS quality prediction method.

1 Introduction Injection molding processes, a typical multistage batch process, is an important polymer processing technique and transforms polymer materials into various shapes and types of products. However, due to the process high dimensionality, complexity, batch-to-batch variation, and also limited product-to-market time, the final product quality are usually available at the end of the batch, which is analyzed (mostly offline) after the batch completion although if feasible and economical, the product quality measurements are also done at finite time intervals as the batch run progresses make, it is difficult for on-line quality control. Several statistical modeling methods such as multi-way partial least square (MPLS) models, have been reported recently for batch processes[1], Nevertheless, MPLS method is inefficient in revealing time-specific relationships for some multi stage processes and is linear methods. consequently, these methods perform poorly in predicting response variables of nonlinearly behaving batch processes, which are abundant in the chemical/biochemical industry. However, an artificial neural network (ANN) had the capability to handle the modeling problems associated with nonlinear static or dynamic behaviors. The J. Wang et al. (Eds.): ISNN 2006, LNCS 3973, pp. 1138 – 1143, 2006. © Springer-Verlag Berlin Heidelberg 2006

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NNPLS method [2]differs from the direct ANN approach in that, the input–output data are not directly used to train the FFNN, but are preprocessed by the PLS outer transform. Jiabo Zhu et al (1998) [3] proposed a time-delay neural network (TDNN) modeling method for predicting the treatment result. GRNNs are based feedforward networks which were introduced [4] as a generalization of both the radial basis function networks (RBFNs) and probabilistic neural networks (PNNs). With increasing number of training samples, the GRNN asymptotically converges to the optimal regression surface. In addition to having a sound statistical basis, the GRNNs possess a special property in that the networks do not require iterative training. For multi-stage batch processes,each stage has its own underlying characteristics, and a batch process can exhibit significantly different behaviors over different stages. It is therefore natural to develop stage-based statistical modeling methods to reflect the inherent stage nature to improve the performances of quality control. A stagebased sub-PCA modeling method[5] has been developed, and it has been shown that the stage PCA modeling can overcome many difficulties of MPCA-based monitoring for batch processes. Thus, in the present paper, for injection molding process, a sub-stage generalized regression neural network (GRNN) is proposed for dedicating to reveal the nonlinearly and dynamic relationship between process variables and final qualities at different stages, and to build a stage-based moving windows on-line quality prediction model. Firstly, using an clustering arithmetic,PCA P-loading matrices of time-slice matrices is clustered and the batch process is divided into several operation stages according to the change of process correlation, the most relevant stage to the quality variable is defined, and then applying moving windows to un-fold stage data according to time, and substage GRNN models are developed for every windows for on-line quality prediction. For comparison purposes a sub-MPLS quality model of every moving window was established. The results prove the effectiveness of the proposed quality prediction method is supervior to sub- MPLS quality prediction method.

2 Process Description Injection molding [6], an important polymer processing technique, transforms polymer materials into various shapes and types of products. As a typical multistage process, injection molding operates in stages, among which, filling, packing-holding, and cooling are the most important phases. During filling, the screw moves forward and pushes melt into the mold cavity. Once the mold is completely filled, the process then switches to the packing-holding stage, during which additional polymer is “packed” at a high pressure to compensate for the material shrinkage associated with the material cooling and solidification. The packing-holding continues until the gate freezes off, which isolates the material in the mold from that in the injection unit. The process enters the cooling stage; the part in the mold continues to solidify until it is rigid enough to be ejected from the mold without damage. Concurrently with the early cooling phase, plastication takes place in the barrel where polymer is melted and conveyed to the front of barrel by screw rotation, preparing for next cycle. For injection molding, high degree of automation is possible. After the process conditions are properly set, the process repeats itself to produce molded part at a high rate. The process is, however, susceptible to the production of off-spec products due

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to various process malfunctions, drifting of process conditions, changes in materials, and unknown disturbances. Abrupt, gross faults in the key process variables can be easily and reliably detected by the conventional SPC chart. Slow drift or faults involving multiple process variables, however, can not be detected. These process faults, even if they are small and not common, can lead to production of large quantity of bad parts, if they are not detected earlier. The material used in this work is high-density polyethylene (HDPE). Ten process variables are selected for modeling, that is, Nozzle Pressure, Stroke, Injection Velocity, Hydraulic Pressure, Plastication Pressure, Cavity Pressure, Screw Rotation Speed, SV1 valve opening, SV2 valve opening, and Mold Temperature, respectively. The sampling rates of these process variables are 20 ms. The operating conditions are set as follows: injection velocity is 25mm/sec; mold temperature equals 25ºC; sevenband barrel temperatures are set to be (200, 200, 200, 200, 200, 180, 160, 120) ºC; packing-holding time is fixed to be 3 second. Quality variables are part weight. Totally, 60 batch runs are conducted under 19 different operation conditions, which can cover all the normal operation range. Based on these data, an stage-based subMPLS model and GRNN model is developed for process analysis and quality prediction.

3 A Stage-Based Moving Window GRNN Modeling 3.1 Generalized Regression Neural Networks (GRNNs) [4] Consider a J-dimensional vector, x = ⎡⎣⎢ x1 , x2 ,..., x j ⎤⎦⎥ ,describing process input variables T

and the corresponding scalar output, y, representing the quality (output) variable.GRNN performs the regression by computing the conditional expectation of y given x. Specifically, the GRNN estimates the joint probability density function (PDF) of x and y, i.e. f(x, y), to create a probabilistic model for predicting y. The PDF estimator model is constructed from the training input–output data set { xi , yi } ; i = 1, 2,..., I , via nonparametric density estimation (NDE). Given x and assuming that the function being approximated is continuous and smooth, the expected value of y, E ⎡⎣ y x⎤⎦ can be E ⎡⎣ y x⎤⎦ = ∫

∞ −∞

yf ( x, y )dy

∫

∞ −∞

f ( x, y )dy

(1)

estimated as Using the training set and assuming Gaussian PDF, the function f ( x, y ) can be defined as

f ( x, y) = ×

1 (2π)( J +1) / 2 σ J +1

⎛−( y − yi )2 ⎞⎟ 1 I ⎡⎢ ⎛⎜−( x − xi )T ( x − xi ) ⎞⎟⎤⎥ ⎟⎟ ×exp⎜⎜ ⎟⎟ exp⎜⎜ ∑ 2 2 ⎢ ⎥ I i=1 ⎣⎢ ⎜⎝ 2σ ⎠⎟⎦⎥ ⎝⎜⎜ 2σ ⎠⎟

(2)

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Where x and y respectively denote the ith training input vector and the i corresponding output, and σ denotes the width (smoothing parameter or spreading factor) of the Gaussian PDF. Given x , the corresponding regression estimate, yˆ( x) , can be determined as a conditional mean by substituting Eq. (2) in Eq. (1).

∑ yˆ( x) = E ⎡⎣ y x⎤⎦ = ∑ I

⎡ d2 ⎤ ; hi = exp ⎢− i 2 ⎥ ⎢ 2σ ⎥ h ⎣ ⎦ i =1 i

i =1 I

yi hi

(3)

where hi denotes the Gaussian radial basis function and σ 2 represents the squared Euclidean distance between vectors x and xi defined as di2 = ( x − xi )T ( x − xi ) .

(4)

3.2 Sub-GRNN Modeling

The data gathered from injection molding process forms a three-dimensional data matrix, X( I × J × K ) , where for batch process applications, I denotes cycle number,

J denotes variable number, and K denotes the number of samples within a cycle. Wold et al. [7] proposed to solve this problem by rearranging the data matrix into two-dimensional form. The X ( I × J × K ) is unfolded, with each of the K time slabs concatenated to produce a two-way array, Xnew ( I × JK ) . The multi-way unfolding procedure is graphically shown in Fig. 1. k

i

K

1

1

2

k

K

~ X1

~ X2

~ Xk

~ XK

~ P1

~ P2

Clustering algorithm

stage1 Sub-model 1

stage c

Moving step k

~ PK

~ Pk

( k = 1, L , m - n )

2

k+1

......

PCA

k

2

...

Bat ch

j

1

~ Xk

~ X k1

I : batch numbers; m : the number of process variables after un-fold data of an stage; n : variable number of an window; k : windows number.

Y Window length

i

1,  , n

Sub-model c

I 1

Fig. 1. Sub-stage modeling method

m

2

Fig. 2. Illustration moving windows of an stage

，

Based on the work of sub-PCA stage partition strategy[5] an batch run is divided into several stages. A moving window of all un-fold data of every stage is proposed to extract the local covariance information of process variable and quality variable. All un-fold data of one stage represented as X ( I × m ) , where I is batch numbers, and m is the number of process variables after un-fold data of the stage. Moving step can be

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set n which can be set as small as 1. With this arrangement, ( m − n ) number of windows can be resulted for each stage, designated as, X k ( k = 1, " , m − n) shown in Fig. 2. Using every moving windows data and quality data establish a sub-GRNN quality model. For comparison purposes a sub-MPLS quality model of every moving window was established.

4 Experimental Results Without using any prior process knowledge, using sub-PCA based stage-division algorithm, the trajectories of an injection molding batch run is divided into four stages according to the change of local covariance structure, correspond to the four physical operation stages, i.e., injection, packing-holding, plastication and cooling stages shown in Fig. 3. Stages defined by the proposed method 0 1 72

2

219 250

0 72 248 Injection Packing-Holding

3

565 578

557 Plastication Physical Operating Stages

4

Cooling

1000

1000

Fig. 3. Stage division results for injection molding process

The final quality variables have weak relation with the plastication and cooling stage. The on-line quality prediction model is a distributed model, the weight variables are estimated by the sub-MPLS models and sub-GRNN models in packing stage. For illustration, the results of the GRNN and PLS-based output prediction for 30 batches using the 100 sample time of packing stage are shown in Fig. 4. In Fig. 4 the solid line with circle symbols indicates the weight measurements, and the solid line with square symbols plots the corresponding weight prediction using subMPLS model and the solid line with triangle symbols plots the corresponding weight prediction using sub-GRNN model. It is clear that the product weight predicted can be more roughly predicted. But there exists an obvious offset between the measured and predicted values for these methods, and the value of the offset varies with different operating conditions, for instance, the offset for batch 5 is much smaller than that of batch 20 for sub-MPLS. An analysis suggests that the problem was caused by forepart data of packing stages. Based on sub-MPLS and sub-GRNN weight prediction model of the packing stage, using the200 sample time of packing stage 30 batch weight prediction result are shown in Fig. 5. Compared to Fig. 4, the predictions of two methods are much closer to the actual weight measurements, indicating significant improvement by using tail data of the packing stage prediction model. But the product weight predicted by sub-GRNN model can be more exactly predicted.

，

A Sub-stage Moving Window GRNN Quality Prediction Method 28.5

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28.5

design GRNN MPLS

28.0

Desired GRNN MPLS

28.0

27.5

Weight

Weight

27.5

27.0

27.0

26.5

26.5

26.0

26.0 5

10

15

20

25

30

Batch Number

Fig. 4. Predicted results for weight variables using the 100th sample time data

5

10

15

20

25

30

Batch Number

Fig. 5. Predicted results for weight variables using the 200th sample time data

5 Conclusion For injection molding process, an typical multi-stage batch process, a new quality prediction method has been applied. Firstly, Process stages are determined by analyzing the change of process covariance structure and partitioning time-slice PCA loading matrices using a new clustering algorithm. Then applying moving windows to un-fold stage data, for each windows an sub-GRNN model is developed In addition, the predicted result of sub-GRNN model is compared with the one of the sub-MPLS model, the predicted precision of sub-GRNN model is superior to the one of the subMPLS model.

Acknowledgement This work was supported by the National Science Foundation of China under Grant 60374003 and project 973 under Grant 2002CB312200.

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