Inner-phase and inter-phase analysis based operating performance assessment and nonoptimal cause identification for multiphase batch processes

Chemical Engineering Research and Design 1 3 4 ( 2 0 1 8 ) 292–308

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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd

Inner-phase and inter-phase analysis based operating performance assessment and nonoptimal cause identification for multiphase batch processes Yan Liu a,b,c,∗, Ruicheng Ma d, Fuli Wang a,b, Yuqing Chang a,b, Furong Gao c a

College of Information Science & Engineering, Northeastern University, Shenyang, Liaoning 110819, China State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, Liaoning 110819, China c Department of Chemical and Biological Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong d School of Mathematics, Liaoning University, Shenyang 110036, China b

a r t i c l e

i n f o

a b s t r a c t

Article history:

Batch processes play a significant role in modern industrial processes. Nevertheless, the

Received 6 November 2017

process operating performance may degrade from optimal level, which cancels the eco-

Received in revised form 22 March

nomic profits of the plant, and effective techniques for operating performance assessment

2018

are essential. Although multimodel approaches are proposed to fit its multiphase character-

Accepted 10 April 2018

istic, the effect of combined action of multiple phases on the operating performance of the

Available online 19 April 2018

overall batch, which is very important for operating performance assessment, is neglected. In this study, a novel inner-phase and inter-phase analysis based operating performance

Keywords:

assessment and nonoptimal cause identification strategy is proposed to overcome it. The

Batch processes

key characteristic of the proposed method is that the inter-phase assessment models are

Operating performance assessment

developed based on the inner-phase assessment models of each phase, which takes the

Inner-phase

correlations and interactions between phases into consideration and reveals the combined

Inter-phase

effect of multiple phases on the operating performance of the overall batch. Furthermore,

Nonoptimal cause identification

online local and global assessments are performed to master the operating performance from different perspectives and improve the algorithm performance. Possible cause variables can be determined by variable contributions under nonoptimal level. The effectiveness of the proposed methodology is demonstrated through a fed-batch penicillin fermentation process and a injection molding process. © 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

1.

Introduction

In the aspect of producing low-volume and high-value added products, batch and semi-batch processes play an increasingly important role in modern industrial production. However, because of the disturbance, noise, and other uncertain causes, the process operating performance

may deteriorate away from optimal level, which discounts the benefits of preliminary designs from process optimization and results in degraded operating behaviors. Hence, it is very necessary to put forward an effective operating performance assessment strategy for batch processes. In the past several decades, many methods about process monitoring of batch processes have been developed (Louwerse and Smilde,

∗ Corresponding author at: College of Information Science & Engineering, Northeastern University, 3 Lane 11, Wenhua Road, Heping District, Shenyang, Liaoning 110819, China. E-mail address: [email protected] (Y. Liu). https://doi.org/10.1016/j.cherd.2018.04.013 0263-8762/© 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Chemical Engineering Research and Design 1 3 4 ( 2 0 1 8 ) 292–308

2000; Nomikos and MacGregor, 1995; Meng et al., 2010; Jia et al., 2010), among which multiway principal component analysis (MPCA) is most widely used (Nomikos and MacGregor, 1994). Subsequently, several extensions to deal with various factors such as process dynamicity (Chen and Liu, 2002), nonlinearit (Lee et al., 2004), non-Gaussianity (Yoo et al., 2004) of batch processes are available. However, since conventional MPCA method takes the entire batch data as a single object, it is difficult to reveal the changes of process correlations between

293

More recently, a multiple hypotheses testing (MHT) based assessment approach was developed for multiphase batch processes (Liu et al., 2016b), though it neglected the effect of the combined action of multiple phases on the operating performance of the overall batch run. The advantage of quantitative information based assessment methods

phases and often ill-suited for multiphase batch processes. So far, dif-

is that more accurate, detailed and objective assessment results can be obtained when the quantitative information is used in evaluation. However, subjecting to the objective reasons, some actual production processes do not have sufficient instrumentations for data collection,

ferent phase division methods have been proposed (Zhang et al., 2018; Zhao and Sun, 2013; Yu and Qin, 2009) and different modeling methods have been developed that take the phase effects into consideration,

while a wealth of qualitative information is available. In this case, the quantitative and qualitative information complement each other and should be used together to evaluate the operating performance

including Undey and Cinar, Srinivasan et al., Lu et al., Zhao et al., Sang et al., etc. (Undey and Cinar, 2002; Lu et al., 2004a; Muthuswamy and Srinivasan, 2003; Doan and Srinivasan, 2008; Zhao et al., 2007a; Sang et al., 2008). These methods can be roughly summarized into two categories: multiblock methods and phase-divided methods (Yao

of the processes. In view of this, Zou et al. (2017, 2018) proposed the assessment techniques based on dynamic causal diagram (DCD). The modified DCD was developed to deal with the qualitative information

and Gao, 2009). The multiblock methods characterize the multiphase batch process through a single model structure by grouping the batch

processes, however, the assessment results usually appear rough and may be seriously affected by subjective factors and the adopted infor-

process into several blocks, while the phase-divided methods build separated models for each phase. However, these studies ignore the inter-phase relationships and are incapable of modeling the correla-

mation fusion strategy. Thus, we focus on the research of quantitative

tions and interactions between phases, though they have significant impacts on process monitoring. More recently, Ng and Srinivasan (2009)

timode processes due to its multiphase characteristic, it still has some special intrinsic characteristics that causes the existing assessment

recognized this issue and proposed the adjoined principal component analysis (AdPCA) by using the overlapping PCA model to characterize

methods of multimode continuous processes to be unsuitable for multiphase batch processes. They are summarized as follows:

and Dempster–Shafer theory of evidence (DST) was used to handle the information fusion. Such approaches can be applied to many industrial

information based assessment strategy in this study. Although the batch process is usually considered as a kind of mul-

the transient operations between phases. Taking a different approach, Zhao et al. (2007a) developed the stage-based soft-transition multiple PCA method, and the transiting characteristics are monitored by weighting several sub-PCA models with the degree of membership as weight coefficients. The pioneer work has provided abundant theoretical bases for our following work. In actual processes, the main task of process monitoring is to ensure the production safety under normal operating conditions, but it cannot satisfy the quest by enterprises for profits any longer. For most of plants, the production goal is to profit, and an effective way is to maintain the process on optimal operating level throughout the batch production. By this point, the operating performance assessment of industrial processes came into being (Ye et al., 2009). The purpose of process operating performance assessment is to get a measure on how far the current operating condition is from the optimum (or how optimal the current operating state is) on the premise of normal operating conditions. According to process characteristics and plant personnel’s attitudes of the operating performance, the performance levels in the normal operating range can be further divided into several grades, such as optimal, suboptimal, general, and poor. Through operating performance assessment, operators and managers can make a deeper understanding and mastering with the process operating performance, and propose reference suggestions on the operating adjustment and performance improvement.

1) Correlations between modes. For continuous multimode processes, the multimode characteristic is usually due to changes in external environment, production conditions, and product specification, etc (Tan et al., 2011). Therefore, each mode exhibits an independent working state, and there is no necessary connections between different modes. By comparison, different phases of a batch serve the products with the same type, specification, and composition of a batch process. It is not independent among phases. They influence each other, restrict each other, and achieve the predetermined production goal through the organic synergy. 2) Sequential nature between modes. In continuous multimode processes, the active transformation from one mode to another usually depends on the change of the production scheme and has no particular order to be followed. On the contrary, in batch processes, switching from one phase to the next must adhere to a particular order strictly to achieve the predetermined production target. Thus, the sequential nature contains in batch processes.

In this study, a novel inner-phase and inter-phase analysis based operating performance assessment approach is proposed for multiphase batch processes with the consideration of the combined action of multiple phases on the operating performance of the overall batch.

Some methods about operating performance assessment of indus-

First, the Gaussian mixture model based phase successive division

trial processes have been proposed in recent years. Depending on the natures of the information used, they are divided into two categories: quantitative information based methods and coexistence of

algorithm (GMM-PSD) (Liu et al., 2016b) is used for phase division on account of its advantages that can not only ensure each phase containing a series of consecutive sampling instants but also retain

quantitative and qualitative information based methods. The quantitative information refers to the numerical measurement data, while the qualitative information indicates the state descriptions or semantics,

the uneven-length characteristics in each individual phase to achieve accurate process information. Then the influences of the process

such as big, medium, small, and other fuzzy information. Therefore, the quantitative information based assessment methods are usually oriented to the processes with sufficient data collecting instru-

actions between phases on the operating performance are analyzed by establishing two types of assessment models: inner-phase and inter-

ments and the process operating performance can be fully reflect by

established for each phase based on its unique process characteristics

the measurements. Several assessment methods based on the quantitative information have been reported. The assessment methods

extracted by total projection to latent structures (T-PLS) (Zhou et al., 2010). They reveal the impact of the behavior on the local operation

based on performance-related information were developed (Liu et al.,

performance and play a part in online phase identification and nonop-

2014, 2016a) for continuous processes, where the performance-related information of each performance grade was extracted by multivariate statistical technologies. With regard to multimode continuous

timal cause identification. By comparison, the inter-phase assessment models are built for a number of successive phases on the foundation of inner-phase assessment models. They characterize the combined

processes, Gaussian mixture model (GMM) (Ye et al., 2009) and comprehensive economic index prediction based (Liu et al., 2015) methods were proposed sequentially on operating performance assessment.

behaviors of multiple phases under the consideration of the correlations and interactions among them and show their effect on the operating performance of the whole batch. In batch processes, since

characteristics of each individual phase and the correlations and inter-

phase assessment models. The inner-phase assessment models are

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the operating performance of the previous phase may have an impact on that of the next phase and even those of the subsequent phases, the establishment of the inter-phase assessment models is conducive to grasp the operation performance from a global point of view and provide the reference standards for online evaluation. In online assessment, both local and global assessment strategies are proposed. The local assessment lays the foundation for global assessment and assists in locating the phase responsible for nonoptimality, while the global assessment is to evaluate the operating performance based on the behaviors of all phases that have been activated. Furthermore, when the process operating performance is nonoptimal, the phase where the nonoptimal operating performance happens is first determined according to the local assessment result, and the cause identification strategy based on variable contributions is designed to find the nonoptimal reasons. Then the managers and operators can take appropriate operating adjustment strategies by combining their experience and the identified nonoptimal causes for the improvement of operating performance. Main contributions of this paper are summarized as follows: (i) besides the inner-phase assessment models of each phase, the interphase assessment models across multiple phases are developed under the consideration of correlations and interactions among phases, as well as their combined effect on the operating performance of the overall batch run, which provides more reasonable reference standards for online evaluation; (ii) while T-PLS is successful in process monitoring, it is used in the operating performance assessment of batch processes for the first time; (iii) the proposed online assessment strategies help to learn the process operating level from local and global perspectives and improve the performance of the algorithm; (iv) the responsible phase identified by local assessment narrows the focus of nonoptimal cause identification, and then the possible cause variables are determined based on variable contributions. The remainder of this paper is organized as follows. First, some preparatory theoretical supports are framed by revisiting to the existing offline phase division and online phase identification algorithms in Section 2. In Section 3, the proposed inner-phase and inter-phase analysis based approach is introduced for the operating performance assessment of batch processes, including the establishment of assessment models, online operating performance assessment, and nonoptimal cause identification. In case studies, two typical batch processes, fed-batch penicillin fermentation process and injection molding process, are studied to demonstrate the feasibility and efficiency of the proposed method. Finally, the paper ends with some conclusions and acknowledgements.

2.

State of the art

In this study, only the existing methods of offline phase division and online phase identification are used and the main efforts are focused on offline modeling, online operating performance assessment and nonoptimal cause identification for batch processes. The offline phase division and online phase identification approaches used in the remainder of this study are introduced in this section.

2.1.

Offline phase division

Multiphase characteristic is very common in batch processes, and each individual phase shows unique feature. Offline phase division is to divide the training batches into different data sets with respect to different phases, and it is also the basis of assessment modeling and operating performance analysis. Being different from the stages which focus on describing the physical operation units of batch processes, the phases lay particular emphasis on the expression of process characteristics, i.e., variable relationships, data distributions, dynamic trajectories, amplitudes of measurements, etc. Thus, the phases and stages corresponding to the same batch process

may be inconsistent, no matter number or span. For example, in the fed-batch penicillin fermentation process, there are two physical operation stages: preculture and fed-batch, but it is more than two phases divided based on the variable relationships known from Zhao et al. (2007a, 2007b). Another example is the injection molding process, which is usually composed of four stages: injection, packing-holding, plastication, and cooling. However, there are up to 10 phases according to Zhao et al. (2007b). In order to learn more about the intrinsic process characteristics and reinforce understanding, it is committed to divide the batch process into several phases in this study. Due to different operation settings and goals in a cycle of the batch production, the process data usually present different data distributions in different parts. Thus, the GMMPSD method was proposed for multiphase and uneven-length batch processes (Liu et al., 2016b). The basic idea of this method is to divided training batches into several data sets according to the data distributions, and each set that has identically distribution actually corresponds to a phase. First of all, I uneven-length training batches Xi = [xi,1 , xi,2 , . . ., xi,Ki ]T ∈ RKi ×J , i = 1, 2, . . ., I, are unfolded into a two-dimensional matrix T X = [XT(1) , XT(2) , . . ., XT(K ) ] ∈ RK×J as shown in Fig. 1. Ki is the max

number of samples of Xi , and K˜ =

I 

Ki ; J is the number of

i=1

process variables; X(k) is the matrix made up of the samples of different batches at the k th moment; xi,k indicates the k th sample of the ith batch, and Kmax = max (Ki ). i=1,2,...,I

The GMM with M Gaussian components is established based on X. In order to determine the Gaussian component that the first phase corresponds to, the first h samples of different batches are picked out, and the posterior probabilities of those samples with respect to each Gaussian component are calculated as follows: P(Cm |xi,h ) =

ωm g(xi,h |m , ˙ m ) M 

,

ωm g(xi,h |m , ˙ m )

(1)

m=1

i = 1, 2, ..., I, m = 1, 2, ..., M, h = 1, 2, ..., h, where g(xi,h |m , ˙ m ) is the multivariate Gaussian density function of the m th Gaussian component Cm ; m , m and ωm are the corresponding mean vector, covariance matrix and prior probability, respectively. Furthermore, for each Gaussian component, the mean of the corresponding posterior probabilities is calculated by 1  P(Cm |xi,h ), m = 1, 2, ..., M. Ih I

P¯ m =

h

(2)

i=1 h =1

Then the Gaussian component corresponding to the maximum mean is determined as the target Gaussian component of phase 1. Thereafter, from the h + 1 th sample of each batch, only the posterior probabilities with respect to the target Gaussian component of phase 1 are calculated and then compared with a given threshold to judge whether they are still subject to this distribution. If the posterior probability is greater than the threshold, it means that the sample still belongs to phase 1 and continue to calculate the posterior probability for the next sample; otherwise, it can be inferred that phase 1 of the current batch is over. When all process data belonging to phase 1 are identified, the phase division for phase 1 finishes. Exclude the process data of phase 1 from each batch and use

Chemical Engineering Research and Design 1 3 4 ( 2 0 1 8 ) 292–308

295

Fig. 1 – Construction of the training batches for phase division.

Fig. 2 – Removal of phase 1 from the training batches. the same procedures mentioned above to identify the second phase. Taking a batch process with three phases as an example, the removal of phase 1 from the training batches is shown in Fig. 2. The phase division is conducted iteratively until all the process data of all batches find their ownership. The GMM-PSD method not only has the ability to handle the batch process with uneven-length phase and batch, but also no need for extra post-processing that exists in most of the existing methods. Thus, it will be used in this study.

2.2.

Online phase identification

Before online operating performance assessment, the current active phase has to be determined. In a variety of online phase identification methods, time instant is always the most intuitive ways to identify the phase. In Liu et al. (2016b), an online phase identification strategy is proposed to deal with the phase identification of multiphase and uneven-length batch processes. Without loss of generality, assuming that there are a total of C phases. On the basis of the offline phase division result, the earliest start and the latest end moment of phase c, c = 1, 2, ..., C are obtained and c c and tout , respectively. Then the interval of phase denoted as tin c c c, i.e., [tin , tout ], is known accordingly. Owing to the fact that the uneven-length characteristic is reflected in both phases and c−1 c batchs, the situation of tin < tout may occur, which leads to the intervals of two adjacent phases overlap. For a new batch, c−1 c+1 if the new sampling belongs to the interval of (tout , tin ), c = 2, 3, ..., C − 1, one can be sure that the new batch is running in phase c, and this kind of interval is named as certain interval in online phase identification. Particularly, the certain inter2) vals of phase 1 and phase C are separately denoted as [1, tin C−1 C and (tout , tout ]. If the new sampling falls into the interval of c−1 c , tout ], the new batch may operates in either phase c − 1 or [tin

c, and this kind of interval is defined as fuzzy interval between two adjacent phases. In this online phase identification method, two remarks are given for the extreme cases: (i) Because the training batches are assumed to cover all normal process disturbances, any case in which the earliest start or the latest end moment of a new batch outside the interval of phase c will be considered as nonoptimal operating performance by the assessment procedure. (ii) It is worth noting that the intervals of a phase across different batches may be large difference in length, thus a fuzzy interval could cover more than two phases. For this case, it is not required special treatment, because it just increases the number of the optional phases in the fuzzy interval and does not affect the phase identification procedure. For simplicity, it is only assumed that there are at most two phases in the fuzzy interval in this text, and the case of more than two phases can be treated in the similar way.

3.

Method development

3.1.

Establishment of assessment model

In this section, the inner-phase and inter-phase assessment models are established, respectively. The inner-phase assessment models play a part in online phase identification and nonoptimal cause identification, and they also lay the foundation of inter-phase assessment models. While the inter-phase assessment models are used to provide the references for online operating performance assessment of the batch processes. In addition, only the training batches under optimal operating performance are collected for modeling, and they

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are selected according to the expert experience or process knowledge. Then the operating performance of the new batch can be clearly identified based on its degree of matching with the assessment models. The high degree of matching implies the optimal operating performance; otherwise, nonoptimal operating performance may occur.

3.1.1.

Inner-phase assessment model

Generally, the process operating performance has a close relationship with the comprehensive economic index of the actual production process. The comprehensive economic index may be costs, profits, total revenue, product quality or the weighted integration of several important production indices. The satisfactory comprehensive economic index usually corresponds to the optimal operating performance. However, it is usually not available until the end of the batch, which affects the timeliness of the online operating performance assessment. By contrast, the process data can be collected at high frequency in real time, and the important information related to the comprehensive economic index and process operating performance contains in these process data. The information related to the process operating performance is named as performance-related information. To accurately describe the process characteristics of operating performance, the performance-related information should be extracted from the process data of each phase respectively, and this process is essentially the establishment of the inner-phase assessment models for different phases. In view of this, the choice of a suitable information extraction tool is particularly critical. On account of the good ability in extracting the output-related information from the process data, T-PLS are used here to establish the assessment models. Assuming that I optimal training batches are collected from the historical production data. For the ith batch, the process data and the comprehensive economic indices at the end of the batch are denoted as Xi = [xi,1 , xi,2 , . . ., xi,Ki ]T ∈ RKi ×Jx and yi = [yi,1 , yi,2 , . . ., yi,Jy ]T ∈ RJy ×1 , i = 1, 2, . . ., I, where Jx and Jy are the numbers of process variables and comprehensive economic indices, respectively. Furthermore, the process data of phase c, c = 1, 2, . . ., C and the comprehensive economic indices ¯ c = [x¯ c1 , x¯ c2 , ..., x¯ cI ]T ∈ RI×Jx , and Y = [y1 , y2 , are expressed as X . . ., yI ]T ∈ RI×Jy respectively, where x¯ ci , i = 1, 2, ..., I is the mean of the samples from phase c of the i th batch. The training data are normalized to zero mean and unit variance before modeling, and the normalized forms are still denoted as ¯ 1, X ¯ 2 , . . ., X ¯ C and Y for simplicity. X

I×Ac

¯ c = T c PcT + Ec X Y = T c Q cT + F c

(5)

˜ xnew ∈ R x˜ r,new = (I-Pr Pr )(I-P R )xnew = G −1

c

Here, Rc = W c (PcT W c ) ∈ RJx ×A is the original weight matrix c (de Jong, 1993), and W is the weight matrix obtained from PLS. Based on the property of PLS, Rc can be used to calculate the ¯ c , i.e., T c = X ¯ c Rc . score matrix Tc directly from X Since the score matrix T cy directly correlated to Y is precisely the performance-related information, only T cy and tcy,new are useful from the perspective of operating performance assessment, and Gcy is essentially the parameter of the inner-phase assessment model of phase c.

3.1.2.

Inter-phase assessment model

On the basis of the inner-phase assessment models established for different phases, the inter-phase assessment models are developed to describe the combined effect of multiple phases under the consideration of correlations and interactions between phases on the operating performance of the whole batch. In this procedure, the performance-related information T 1y , T 2y , ..., T Cy are used instead of the original pro¯ 1, X ¯ 2 , ..., X ¯ C , and then the inter-phase assessment cess data X models are established sequentially in the order of phases. To establish the inter-phase assessment model of phase 1 and 2, the process information is constructed by the performance-related information T 1y and T 2y , i.e., T 12 =





12

T 1y T 2y ∈ RI×J , J12 = A1y + A2y . Firstly, the PLS model is established as below:



T 12 = T 12 P12T + E12 Y = T 12 Q 12T + F 12

,

(6)

Then the inter-phase assessment model of phase 1 and 2 is developed by T-PLS as (3)

,

c

where Tc ∈ RI×Ac is the score matrix; Pc ∈ RJx ×A and Q c ∈ c ¯ c and Y, respectively; Ec ∈ RJy ×A are the loading matrices of X I×J c I×J R x and F ∈ R y are the residual matrices corresponding to ¯ c and Y; Ac is the number of reserved components. X Then the inner-phase assessment model of phase c is established based on T-PLS as follows:



c

⎧ Acy ×1 c cT c ⎪ tcy,new = Q cT y Q R xnew = Gy xnew ∈ Ry ⎪ ⎪ ⎪ ⎪ ⎨ tc (Ac −Acy )×1 c cT c c cT c cT o,new = Po (P -Py Q y Q )R xnew = Go xnew ∈ R ⎪ c c cT Acr ×1 ⎪ tcr,new = PcT ⎪ r (I-P R )xnew = Gr xnew ∈ R ⎪ ⎪ ⎩ c c c cT c cT Jx ×1

In order to establish the inner-phase assessment model of phase c, the PLS model must be developed firstly, i.e.,



I×(Ac −Ac )

y , and T c ∈ RI×Ar are the score where T cy ∈ R y , T co ∈ R r matrices directly correlated to Y, orthogonal to Y, and the J ×Ac J ×(Ac −Acy ) , and main part of Ec , respectively; Py ∈ R x y , Po ∈ R x c Pr ∈ RJx ×Ar are the loading matrices separately corresponding ¯ c and repto T cy , T co , and T cr ; Ecr ∈ RI×Jx is the residual part of X c c resents the noise; Ay and Ar are the numbers of Y-related and Y-unrelated components. The detailed procedures of T-PLS can be seen in Zhou et al. (2010). For a new sample xnew ∈ RJx ×1 , the scores and residual can be calculated as follows:

c cT c cT c ¯ c = T cy PcT X y + T o P o + T r P r + Er c Y = T cy Q cT y +F

,

(4)



12T 12T 12 12T 12 T 12 = T 12 + T 12 y Py o Po +T r Pr +Er

(7)

12T Y = T 12 + F 12 y Qy

with

the

parameter 12 −1

12T 12 12T G12 , y = Qy Q R

where

R12 =

W 12 (P12T W ) , and W12 is the weight matrix obtained 12 is from PLS.Here, the score matrix T 12 y extracted from T directly correlated to Y, so it is also the performance-related information. Compared with T 1y and T 2y , T 12 y not only contains the process variation information of phase 1 and 2 but also characterizes the correlations and interactions between them.

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Fig. 3 – Diagram of the establishment of assessment models.

Similarly, the inter-phase assessment model from phase 1 to c can be established as follows:



T 1c = T 1c P1cT + E1c Y = T 1c Q 1cT + F 1c



,

(8)

1cT 1c 1cT 1c 1cT 1c T 1c = T 1c y Py + T o Po +T r Pr +Er 1cT 1c Y = T 1c y Qy + F



where T 1c = T 1y T 2y . . . T cy J1c =

c 



,

(9)

1c

∈ RI×J is the process information,

p

Ay , and the assessment model parameter is G1c y =

p=1 p

1c 1cT Q 1cT . In comparison with T y , p = 1, 2, ..., c, T 1c y not only y Q R contains the process variation information of each phase but also characterizes the correlations and interactions among them. The diagram of the establishment of assessment models is shown in Fig. 3.

3.2.

Online operating performance assessment

As known from the online phase identification method introduced in Section 2.2, the phase identification result may be a certain interval or the fuzzy interval between two adjacent phases. Without loss of generality, it is supposed that the current active phase of the new batch is phase c, and taking it as an example to demonstrate the proposed online assessment strategy. For the case of the fuzzy interval, the assessment result can be treated as the mean of the results obtained from two adjacent phases. Additionally, based on the fact that the same operating performance contains similar performance-related information, the process operating performance of the new batch can be evaluated based on the similarity matching degree between the performance-related information of the online data and those within the assessment models. In order to make full use of the online data, a cumulative data window is used in online assessment. Assuming that K is the moment of the most recent sampling of the new batch, the cumulative data window is denoted as Xnew = [xnew,1 , xnew,2 , . . ., xnew,K ]T , and xnew,k , k = 1, 2, . . ., K represents the sample at moment k. Then it is divided into c sets, i.e., Xnew = [x1new,1 , x1new,2 , ..., x1new,l |x2new,1 , x2new,2 , ..., x2new,l |...|xcnew,1 , p

1

p

c

Based on the inner-phase and inter-phase assessment models, the local and global online assessment strategies are developed. The online assessment based on the inner-phase assessment models is designated as local assessment and that based on the inter-phase assessment models is named as global assessment. Owing to the fact that the operating performance of the batch processes depends on the behaviors of all phases that have been activated, the global assessment result can truly reflect the operating performance of the new batch. In addition, because only the characteristic of single phase is described by the inner-phase assessment model, the local assessment result is more suitable for correcting the preliminary result of online phase identification within the fuzzy intervals. Furthermore, according to the local assessment result, the phase where the nonoptimal operating performance occurs can be directly located, and it helps to narrow the search and improve the accuracy of the cause identification result. Therefore, the global assessment result is used to judge whether the online operating performance is optimal or not, and the local assessment result is used for online phase identification and nonoptimal cause identification.

2

p

xcnew,2 , ..., xcnew,l ]T , where xnew,1 , xnew,2 , ..., xnew,l and lp are the p

samples and number of samples belonging to phase p, p = 1, 2, . . ., c,

c 

lp = K.

p=1

As preparation, all the samples of Xnew must be normalized with the means and standard deviations of the corresponding phases before modeling. In addition, assuming that the score vectors of phase 1, 2,. . ., c − 1 have been calculated when the process runs in phase c, only the score vector of phase c is calculated as follows: tcy,new = Gcy x¯ cnew ,

where

x¯ cnew =

(10) lc 

xcnew,l /lc c

is

the

mean

vector

of

l=1 xcnew,1 , xcnew,2 , ..., xcnew,l . c

Then the distance of the performance-related information between the new batch and the inner-phase assessment model is measured as follows: 2

c dc = tcy,new − t¯ y  ,

(11)

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c

where t¯ y =

I 

Gcy x¯ ci /I is the mean of the score vectors of mod-

i=1

eling data of phase c. c According to the property of T-PLS, t¯ y = 0. Thus, the disc tance d can be rewritten as follows: 2

dc = tcy,new  .

(12)

In order to facilitate the online assessment, the local assessment index is defined based on dc as follows: c local = exp(−˛ · dc ),

(13)

where ˛ is a user-defined adjustable parameter. Mathematc ically, the local assessment index local is the exponential c c is function of the distance d with the range of (0,1]. When local c close to 1, it means that d is close to 0 and the distance of the performance-related information between the new batch and the inner-phase assessment model is very closely. So one can consider the process operating performance is satisfactory in c is close to 0, it indicates that phase c. On the contrary, if local the process operating performance in phase c is barely satisfactory. The parameter ˛ is used to determine the shape and gradient of the function. The larger ˛ is, the steeper the funcc decreases. An appropriate value of ˛ tion is and the faster local c close to 1 when the process opershould be able to make local ating performance is optimal and close to 0 under the worst operating performance. Meanwhile, it should ensure that the c values of local are separated as far as possible under different kinds of operating performances. To do this, the batch data under different operating performances should be selected from the historical data according to the level of the comprehensive economic index, and then the local assessment indices are calculated respectively. Thereafter, the value of ˛ can be determined based on expert experience. To calculate the global assessment index, the score vectors obtained from the local assessment are grouped into the



T

1T 2T cT , and the score vector form of t1c y,new = t y,new t y,new . . .t y,new with respect to the inter-phase assessment model is 1c 1c t1c y,new = Gy t new , c = 2, 3, ...C.

(14)

The distance between the performance-related information of the new batch and the inter-phase assessment model is measured as follows: 1c 2

¯ d1c = t1c y,new − t y  , c = 2, 3, ..., C

(15)

the nonoptimal operating performance, the local assessment 1 ,  2 , ...,  c are compared with the threshold indices local local local the phase p∗ that satisfies the condi respectively, and

p  ∗ tion p = min arg p|local < , p = 1, 2, ..., c is considered as p

the nonoptimal phase. In practical application, the threshold  is usually determined using the historical batch data by trial and error through cross-validation so that the numbers of online false and missing alarms are minimized, and it affects the assessment results to some extent. If it is too high, the optimal process operating performance may be evaluated as nonoptimal for the effect of interferences. That is to say, the robustness of the assessment method is reduced. However, if it is too low, the nonoptimal operating performance may be evaluated as optimal, which increases the rate of error evaluation and reduces the accuracy of the assessment result. In the fuzzy interval between two adjacent phases, e.g., c−1 phase c − 1 and c, both of the local assessment indices local c and local are calculated, respectively. If one of them is greater c−1 c than or equal to , e.g., local ≥  but local < , it indicates that the local process operating performance is satisfactory and it belongs to phase c − 1. Then the global assessment index is c−1 c and local are less than calculated by Eqs. (14)–(16). If both local , the phase number is still unknown. In this case, the local and c−1 c global assessment indices are defined as local = (local + local )/2 c−1 c and global = (global + global )/2, respectively. The step-by-step procedure of the online local and global operating performance assessment strategies is given below and the flow diagram is shown in Fig. 4. (1) Construct the cumulative data window and divide it into several sets corresponding to different phases. (2) Normalize the online data with same means and standard deviations of the modeling data. (3) Calculate the score vectors of the new batch with respect to the inner-phase assessment model. (4) Calculate the distance of the performance-related information between the new batch and the inner-phase assessment model. (5) Construct the local assessment index. (6) Integrate the score vectors and calculate the score vector with respect to the corresponding inter-phase assessment model. (7) Measure the distance of the performance-related information between the new batch and the inter-phase assessment model. (8) Calculate the global assessment index and compare it to the threshold  to evaluate the process operating performance of the new batch from an global perspective.

1c 1c can be denoted as with t¯ y as the mean of T 1c y . Similarly, d 2

1c

¯ t1c y,new  for t y = 0 according to the property of T-PLS. Using d1c , the global assessment index is constructed as below: c global = exp(−ˇ · d1c ), c = 2, 3, ..., C,

(16)

where ˇ is a adjustable parameter and its value can be determined like that for ˛. In order to make a strict distinction between optimal and nonoptimal operating performance, a assessment index c threshold (0.5 <  < 1) is introduced. If global ≥ , it means that the process operating performance of the new batch is optimal up to now; otherwise, the nonoptimal operating performance may occur. In order to identify the location of

3.3.

Nonoptimal cause identification

Nonoptimal operating performance is not expected in actual production process. Thus, to find the responsible cause is very important for assisting the managers and operators to make the production adjustment and the performance improvement. In the absence of rich process information and expert knowledge, the variable contributions based nonoptimal cause identification method can identify the possible cause variables responsible for the nonoptimal operating performance. The basic idea is to decompose the assessment index into the weighted sum of different process variables approximately, and then define each item as the variable contribution to the assessment index. Owing to the fact that the

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299

c Hence, the contribution of the j th variable to local is defined as follows: 2

c contrjc,raw = gcy,j x¯ new,j  , j = 1, 2, ..., Jx .

(18)

Under the optimal operating performance, the contributions of different process variables are not necessarily equal, it is meaningful to normalize the raw contribution contrjc,raw to ensure all variables giving the same contribution statistically in this sense. The normalization of contrjc,raw is as below:

contrjc =

contrjc,raw c

contrj

c

where contrj =

, j = 1, 2, ..., Jx ,

I 

(19)

c 2 gcy,j x¯ i,j  /I is the mean contribution of the

i=1

c j th variable calculated with the modeling data of phase c, x¯ i,j

is the j th variable of x¯ ci , i = 1, 2, ..., I. According to Eqs. (17)–(19), it can be seen that the greater c x¯ new,j is, the larger contrjc and dc are, and then the value of c is lower. Therefore, the process local assessment index local variables with relatively great contributions are considered as the responsible variables for the nonoptimal operating performance. When the process is running in a fuzzy interval, the variable contributions should be calculated as the mean of those of the two adjacent phases.

4.

In this section, two case studies are provided, which are simulation case study of the fed-batch penicillin fermentation process and industrial application study of the injection molding process.

Fig. 4 – Flow diagram of the online local and global operating performance assessment strategy.

reduction of the assessment index is usually attributed to the variables with large contributions, they are naturally considered as the possible cause variables for the nonoptimality. For different assessment indices, the variable contributions are differ in terms of expression, but the essence is consistent. In this section, the idea of variable contributions based method is utilized for nonoptimal cause identification. Since the nonoptimal operating performance results from the degenerate behavior of a certain phase, and the corresponding phase is known from the local assessment result, only the variable contributions with respect to the local assessment index are calculated and used to identify the nonoptimal cause. It can not only locate the nonoptimal operating performance accurately but also find the responsible cause variables, which is conducive to guiding operation optimization. Learning from Eq. (13), the variable contributions to the c is equivalent to those to the dislocal assessment index local c tance d , and it can be decomposed into the following form:

c

d =

2 tcy,new 

=

2 Gcy x¯ cnew 

J 

=

2 c gcy,j x¯ new,j 

,

(17)

j=1

c is the j th variable where gcy,j is the j th column of Gcy , and x¯ new,j

of x¯ cnew .

Case studies

4.1. Fed-batch penicillin fermentation process simulation study The fed-batch penicillin fermentation process (Birol et al., 2002a, 2002b) is a typical multiphase batch process. From the operational point of view, there are two physical stages in this process: preculture and fed-batch. The preculture stage starts with small amount of biomass and substrate which are added to the fermentor from the beginning of the batch operation. Most of the initially added substrate is consumed by the microorganisms after about 45 h, and then the process converts from preculture stage to fed-batch stage. The fed-batch stage continues about 355 h. In this stage, the penicillin increases exponentially until the stationary procedure. Because the biomass growth rate must be kept constant for the aim of optimizing penicillin production, the substrate (glucose) is supplied continuously into the fermentor instead of being added all at once in the beginning. Meanwhile, in order to maintain the constant temperature and pH values, two proportional-integral-derivative (PID) control loops are implemented in the fermentor for manipulating the acid/base and hot/cold water flow ratios, respectively. In 2002, a modular simulator (PenSim v2.0) for fed-batch fermentation was developed by Ali C¸inar et al. from the Monitoring and Control Group of the Illinois Institute of Technology. It can simulate the concentrations of biomass, CO2 , hydrogen ion, penicillin, carbon source, oxygen, and heat generation under various operating

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Table 2 – Initial operating conditions of penicillin fermentation process. Process variables

Initial operating conditions

Substrate concentration (g/L) Dissolved oxygen concentration (%) Biomass concentration (g/L) Penicillin concentration (g/L) Culture volume (L) Carbon dioxide concentration (mole/L) pH Fermentor temperature (K) Generated heat (kcal/h)

15 1.16 0.1 0 100 0.5 5 298 0

Table 3 – Offline phase division of penicillin fermentation process. Fig. 5 – Flow diagram of penicillin fermentation process (Zhao et al., 2008). Table 1 – Process variables and parameter operating settings of penicillin fermentation process. No.

Process variables

Parameter operating settings Normal

1 2 3 4 5 6 7 8 9 10 11

Aeration rate (L/h) Agitator power (W) Substrate feed rate (L/h) Substrate feed temperature (K) Substrate concentration (g/L) Dissolved oxygen concentration (%) Biomass concentration (g/L) Culture volume (L) Carbon dioxide concentration (mole/L) pH Generated heat (kcal/h)

Optimal

3–10 20–50 0.035–0.045 296–298

8.5–10 29–31 0.042–0.045 296–298

5–50

5–50

1.16

1.16

0–0.2

0–0.2

100–200 0.5–1

100–200 0.5–1

4–6 0

4.9–5.1 0

conditions. The diagram of the penicillin fermentation process is shown in Fig. 5. As known from the mechanism of penicillin fermentation process, the process operating performance depends on the final penicillin concentration. Under the normal operating conditions, the higher penicillin concentration corresponds to the better operating performance, while the lower penicillin concentration attributes to the poorer operating performance. Thus, the comprehensive economic index is the final penicillin concentration, and the process variables related to it are listed in Table 1, as well as their operating settings under normal and optimal operating conditions. Table 2 shows the initial operating conditions of the production. To establish the assessment models, a total of 350 training batches are produced by running the simulator repeatedly. Among them, 200 batches have high penicillin concentrations and correspond to the optimal operating performance. They are produced by adjusting the aeration rate, agitator power, substrate feed rate, and pH within the optimal operating settings given in Table 1. The other 150 batches are with respect to different nonoptimal operating performances. The durations of all training batches are uneven-length and fluctuate between 390 h and 420 h with a sampling interval of 1 h. 150 optimal batches are randomly selected for modeling. The addi-

Phase no.

Earliest start Latest end moments moments

Preliminary phase identification results

1 2 3 4 5

1 29 44 105 197

Phase 1: k ∈ [1, 29) Phase 1 or 2: k ∈ [29, 31] Phase 2: k ∈ (31, 44) Phase 2 or 3: k ∈ [44, 46] Phase 3: k ∈ (46, 105) Phase 3 or 4: k ∈ [105, 119] Phase 4: k ∈ (119, 197) Phase 4 or 5: k ∈ [197, 218] Phase 5: k ∈ (218, 420]

31 46 119 218 420

tional 50 optimal and 150 nonoptimal batches are together used to determine the values of parameters ˛, ˇ and . The local and global assessment indices of each phase are calculated using these training batches. Then the values of ˛, ˇ and  can be determined by trial and error through cross-validation and expert experience, respectively. Using the offline phase division method introduced in Section 2.1, the training batches are divided into five phases. Then the process data of different phases and the com¯ 1 ∈ R150×11 , prehensive economic index are expressed as X 2 3 4 5 150×11 150×11 150×11 150×11 ¯ ∈ R ¯ ∈ R ¯ ∈ R ¯ ∈ R ,X ,X ,X and Y ∈ X R150×1 , respectively. Furthermore, the inner-phase and interphase assessment models are established by T-PLS. The parameters are determined as  = 0.8, ˛ = ˇ = 50 by trial and error and combining the experts experience, and they can ensure that the numbers of online false and missing alarms are minimized. Table 3 summarizes the earliest start and latest end moments of each phase counted from the result of offline phase division. It is worth noting that the phases identified by the methodology are different from the physical stages. The preculture and fed-batch stages are further divided into two and three phases, respectively. It attributes to the fact that a stage could contain a variety of data distributions caused by the intrinsic biochemical reactions or the changes in external operating conditions. For comparison, MHT method (Liu et al., 2016b) and AdPCA method (Ng and Srinivasan, 2009) are also applied here. Five phases are identified by MHT method, where phase 1 and 2 correspond to the preculture stage and phase 3–5 make up the fed-batch stage. By AdPCA method, eight models are obtained, and model 1 corresponds to the preculture stage while the remaining correspond to fed-batch stage. In addition, the Hotelling’s T2 statistic is used as the assessment index in AdPCA. During online assessment, two test batches under optimal and nonoptimal operating performances are produced,

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Table 4 – Online phase identification of optimal test batch of penicillin fermentation process. Phase no.

1 2 3 4 5

Time (h) The proposed method

The MHT method

1–28 29–45 46–112 113–213 214–404

1–28 29–46 47–119 120–215 216–404

Fig. 7 – Online assessment of optimal test batch of penicillin fermentation process using MHT method.

Fig. 6 – Online assessment of optimal test batch of penicillin fermentation process using the proposed method. respectively. The optimal test batch is simulated by maintaining the operating settings within the optimal ranges, whereas the substrate feed rate is set as 0.035 L/h in the nonoptimal test batch, which is within the normal range but outside its optimal range. Thus, the final penicillin concentration is much lower than those of optimal ones. The reason can be attributed that the decrease in substrate feed rate leads to low substrate concentration, eventually results in the decline of penicillin production since glucose is the main carbon source fed during penicillin fermentation (Birol et al., 2002a). First of all, the optimal test batch with a duration of 404 h is tested. The results of online phase identification with respect to the proposed method and MHT method are shown in Table 4. As can be seen from Table 4, although the identification results are slightly different due to the different construction of the assessment indices, there is no fuzzy interval between any two adjacent phases with both methods. It is because that each sample of the test batch can exactly match the current active phase, and the preliminary phase identification results in the fuzzy intervals are corrected by the online local assessment results. Fig. 6 shows that both local and global assessment indices are greater than 0.8 based on the proposed method. It indicates that the operating performance of this test batch is optimal throughout the batch run, and the assessment result is consistent with the actual situation. The assessment results using MHT method and AdPCA method are shown in Figs. 7 and 8, respectively. As can be seen from Fig. 7, although the local assessment result is in line with the reality, the global assessment result only can be achieved at the end of the batch, so it cannot reflect the operation performance of the overall batch in real time from a global point of view. Fig. 8 displays the assessment result by AdPCA method, as well as the PCA model used at each instant. The local assessment performance of

Fig. 8 – Online assessment of optimal test batch of penicillin fermentation process using AdPCA method. Table 5 – Online phase identification of nonoptimal test batch of penicillin fermentation process. Phase no.

Time (h)

1 2 3 3.5 4 4.5 5

1–28 29–46 47–104 105–119 120–196 197–218 219–419

AdPCA is comparable to the other two methods, but it also neglects the global assessment as that in MHT method. For the nonoptimal test batch, the results of online phase identification with respect to the proposed method and MHT method are the same and tabulated in Table 5. The duration of this test batch is 419 h and the nonoptimal operating performance occurs in 47 h. As seen from Table 5, the fuzzy intervals from 29 h to 31 h and 44 h to 46 h are corrected to phase 2 and 3 based on the local assessment results, respectively. According to the mechanism of the penicillin fermentation process, although the substrate feed rate is set to 0.035 L/h, it usually begins to work after about 45 h. Thus, the operating performance of the nonoptimal test batch is essentially optimal in the first two fuzzy intervals. Nevertheless, under the nonoptimal operating performance, the fuzzy interval between phase

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Fig. 9 – Online assessment of nonoptimal test batch of penicillin fermentation process using proposed method.

Fig. 11 – Online assessment of nonoptimal test batch of penicillin fermentation process using AdPCA method.

Fig. 10 – Online assessment of nonoptimal test batch of penicillin fermentation process using MHT method.

Fig. 12 – Variable contributions of penicillin fermentation process using proposed method.

3 and 4 still exists, as well as that between phase 4 and 5. In this case, both local and global assessment indices during these fuzzy intervals are calculated by averaging those of two adjacent phases. Fig. 9 presents the results of online local and global operating performance assessment for the nonoptimal test batch based on the proposed assessment method. As shown in Fig. 9, the values of local and global assessment indices are greater than 0.8 during the first 46 h, while they are less than the threshold from 47 h to the end. That is to say, the process operating performance changes from optimality to nonoptimality from 47 h, and the nonoptimal operating performance lasts to the end, which is accord with the actual circumstance. The online assessment results by MHT method and AdPCA method are shown in Figs. 10 and 11 , respectively. The values of the local assessment index from MHT method are also less than 0.8 from 47 h, but the global assessment only can be get at the end of the batch. As previously analyzed, since the local assessment result cannot reflect the influence of correlations and interactions between phases on the operating performance of the whole batch process, it just only provides with reference value in online assessment. In addition, it cannot track the development of the operating performance according to the global assessment result in MHT method. As seen in Fig. 11, the turning point from optimality to nonoptimality is in 50 h identified by AdPCA, which is a lit-

tle later than that by the proposed method. It is because that T-PLS and PCA are driven by different targets in information extraction. PCA seeks to extract the main variation information from the original data by maximizing the covariance information, while some performance- unrelated information may mix in it; whereas T-PLS is committed to extracting the performance-related information from original measurements under the supervision of the comprehensive economic index. The performance-related information has a closer relationship with the process operating performance than the main variation information extracted by PCA. Thus, the proposed method has higher sensitivity than AdPCA method for the changes related to the process operating performance and captures it earlier. To identify the nonoptimal cause, the formula of variable contributions used in Qin et al. (2001) is adopted here for AdPCA method. Then the variable contributions based on the proposed method, MHT method and AdPCA method are calculated and displayed in Figs. 12–14 respectively. Seeing from them, the contributions of substrate feed rate and substrate concentration are significantly greater than those of other variables. Knowing from the process mechanism, biomass growth has a high degree of dependence on both the carbon source (glucose) and oxygen as substrates. When the substrate feed rate reduces, the substrate concentration reduces accordingly, which further affects the utilization of substrate and the

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Table 6 – Process variables of injection molding process. No. 1 2 3 4 5 6 7

Fig. 13 – Variable contributions of penicillin fermentation process using MHT method.

Fig. 14 – Variable contributions of penicillin fermentation process using AdPCA method. production of penicillin. Therefore, the substrate feed rate and substrate concentration are considered as the possible cause variables responsible for nonoptimal behavior. In addition, because the substrate feed rate is directly adjusted to 0.035 L/h, it is the real cause variable for the nonoptimal operating performance. The contribution of substrate feed rate is larger than that of substrate concentration according to the proposed method as shown in Fig. 12, whereas it is just opposite based on MHT seen from Fig. 13. Note that the performance of AdPCA is comparable to the proposed method in terms of nonoptimal cause identification, as show in Fig. 14. In summary, the proposed method gives better assessment performance on its timeliness and global perspective and identifies the nonoptimal cause more consistent with the actual situation.

4.2.

Injection molding process application study

Another example is the injection molding process (Rubinbejerano, 1972; Frizelle, 2017), which is a wellestablished technique widely applied in the polymer processing industry. It is also a typical multiphase batch process and has been widely used in process monitoring and quality analysis (Lu et al., 2004b; Yang and Gao, 1999; Zhao et al., 2014). A simplified diagram of a typical reciprocatingscrew injection molding machine is shown in Fig. 15. In general, a injection molding process consists of four major physical stages, i.e., filling, packing–holding, plastication and

Process variable

Unit

Injection velocity Stroke Nozzle pressure Plastication pressure Cavity pressure Hydraulic pressure Cavity temperature

mm/s mm Bar Bar Bar Bar ◦ C

cooling. In the filling stage, the screw moves forward and pushes the polymer melt into the mould cavity. After the mould cavity is fully filled, the packing–holding stage starts. During this stage, additional material is packed into the cavity to supplement the material shrinkage caused by the material cooling and solidification, and it continues until the gate freezes off. Thereafter, the process shifts to the cooling stage, where the material is cooled down in the mould cavity. Cooling stage lasts until the part in the mould is sufficiently solidified and rigid enough to be ejected from the mould without damage. In addition, plastication happens in the early part of this stage. Finally, the screw rotates to shear and melt the material in the barrel, and conveys the polymer melt to the front of the screw, preparing for next cycle. In the production, the feed material is high-density polyethylene (HDPE), and all key process variables such as temperatures, pressures, displacement, and velocity can be measured online by the sensors, which provides abundant process data for academic research. Additionally, knowing from the production experience, the product weight measured at the end of each batch is directly related to the amount of the polymer injected into the mould cavity. Under the condition of without affecting the production safety and product quality, the more amount of polymer injected is, the heavier the product weight is, and it greatly increases the production cost. Therefore, the satisfactory operating performance should control the product weight within a certain range by proper parameter setting and operation, and too high weight is not expected in production. That is to say, the product weight is a good representative of the process operating performance and of great commercial interest, thus it is used as the comprehensive economic index in this case study. It can be directly measured by instruments. The process variables closely related to the final product weight are used in operating performance assessment and listed in Table 6. Learning from the process mechanism, injection velocity is a key process variable that affects the product weight. The higher the injection velocity is, the more amount of polymer is injected into the mould cavity, which results in heavier product. Injection velocity has close relationships with stroke, plastication pressure, nozzle pressure and cavity pressure. Moreover, cavity pressure is a dominant process variable reflecting variations in the product weight. It is because that cavity pressure is mainly determined by the volume of polymer injected in the cavity and closely related to nozzle pressure before the mold gate is frozen in the earlier stage of plastication. The greater the cavity is, nozzle and hydraulic pressures are, the more polymer is squeezed into the cavity, and then the product weight increases. Also, cavity temperature affects the product weight. Since the density of polymer fluid increases with the decrease of temperature, polymer of the same volume injected into the cavity would cause an

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Fig. 15 – Diagram of the reciprocating-screw injection molding machine.

Table 7 – Parameter operating settings of injection molding process.

Table 8 – Offline phase division of injection molding process.

Process variables

Phase no.

Earliest start moments

Latest end moments

Preliminary phase identification results

1 2 3 4 5

1 15 82 379 732

30 102 411 780 1194

Phase 1: k ∈ [1, 15) Phase 1 or 2: k ∈ [15, 30] Phase 2: k ∈ (30, 82) Phase 2 or 3: k ∈ [82, 102] Phase 3: k ∈ (102, 379) Phase 3 or 4: k ∈ [379, 411] Phase 4: k ∈ (411, 732) Phase 4 or 5: k ∈ [732, 780] Phase 5: k ∈ (780, 1194]

Parameter operating settings Normal

Injection velocity (mm/s) Packing pressure (bar) Barrel temperature (◦ C) Mold temperature (◦ C) Stroke (mm) Packing-holding time (s) Plastication back pressure (bar) Screw rotation speed (rpm) Cooling time (s)

20–40 180–450 160–220 15–55 39 5 5.5 75 15

Optimal 20–24 180–200 20–220 50–55 39 5 5.5 75 15

increase in the product weight. In conclusion, greater pressures and lower temperatures result in heavier products. In the injection molding process, the uneven-length batches are attributed to the change of the injection velocity. A slower injection velocity requires a longer filling time and further results in a longer batch with more process data than a batch operation with a faster injection velocity. To establish the assessment model, a total of 336 uneven-length training batches are selected from the historical production data, where the durations are between 1185 and 1194 samples with a sampling interval of 0.02 s. Based on the production principle and expert experience, the parameter operating settings under normal and optimal operating conditions are shown in Table 7, respectively. It can be seen that the injection velocity, packing pressure, barrel temperature and mold temperature float within a certain area, respectively. There are 166 training batches that meet the condition of optimal operating settings, where 150 batches are randomly picked out and used for modeling. The additional 16 optimal and 170 nonoptimal training batches are combined to determine the values of parameters ˛, ˇ and . In offline analysis, the training batches are divided into five phases, and the earliest start and latest end moments of each phase are shown in Table 8. In this case, the result of phase division basically matches with the actual situation, and phase 3, 4 and 5 separately correspond to the stages of

packing–holding, plastication and cooling. A slightly different is that the filling stage is further divided into two phases, i.e., phase 1 and 2. It is because that the injection velocity speeds up from zero to the setting point in the early part of the filling stage, which causes the data to subject to an unique distribution from those in the later part of this stage. The inner-phase and inter-phase assessment models are separately established based on the modeling data of each phase. To minimize the online false and missing alarms, the parameters ˛, ˇ and  are set as 0.6, 0.6 and 0.8 respectively by trial and error based on the training data and experts experience. In both MHT method and AdPCA method, it is also divided into five phases, and the correspondences between the identified phases and physical operation stages are similar with that of the proposed method. Then MHT method and AdPCA method are trained using the same training data. During online assessment, two test batches corresponding to optimal and nonoptimal operating performance are collected from the historical production data. The durations of them are 1193 and 1164 samples, respectively. In the nonoptimal test batch, the injection velocity is set as 40 mm/s, which deviates significantly from the optimal operating range and leads to an increase in product weight. Fig. 16 shows the process variable trajectories of optimal and nonoptimal test batches.

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305

Fig. 16 – Process variable trajectories of optimal (blue line) and nonoptimal (red line) test batches. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 9 – Online phase identification of optimal test batch of injection molding process. Phase no.

1 2 3 4 5

Time (sample) The proposed method

The MHT method

1–19 20–91 92–385 386–760 761–1193

1–21 22–95 96–390 391–760 761–1193

For the optimal test batch, the results of online phase identification with respect to the proposed method and MHT method are listed in Table 9. The identification results obtained from two different assessment models are not complete coincident with different assessment indices constructed. However, what they have in common is that the fuzzy interval does not appear. It indicates that the samples well match the current active phases, which effectively corrects the preliminary phase identification results in fuzzy intervals. The online assessment results of the proposed method, MHT method and AdPCA method are shown in Figs. 17–19, respectively. As seen from Fig. 17, the values of local and global assessment indices are greater than 0.8, and the process operating performance is optimal throughout the optimal test batch, which is consistent with the actual situation. Although the local assessment result based on MHT method is generally in line with the reality as shown in Fig. 18, some false alarms occur. In addition, only the global assessment result at the end of the batch is achieved and cannot reflect the operating performance in real time from the global point of view. As shown in Fig. 19, AdPCA method improves the accuracy by reducing false alarms compared to MHT method, but some false positives still discounts its performance. Also, the lack of global assessment makes it only provide local operating performance and impossible reveal the operating performance of overall batch run. The proposed method hence shows better performance under the global perspective and high reliability with no occurrence of false positives.

Fig. 17 – Online assessment of optimal test batch of injection molding process using proposed method.

Fig. 18 – Online assessment of optimal test batch of injection molding process using MHT method.

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Fig. 19 – Online assessment of optimal test batch of injection molding process using AdPCA method. Table 10 – Online phase identification of nonoptimal test batch of injection molding process. Phase no.

1 1.5 2 2.5 3 3.5 4 4.5 5

Time (sample) The proposed method

The MHT method

1–15 16–30 31–81 82–102 103–378 379–411 412–731 732–776 777–1164

1–15 16–30 31–81 82–102 103–378 379–411 412–731 732–780 781–1164

Fig. 20 – Online assessment of nonoptimal test batch of injection molding process using the proposed method. For the nonoptimal test batch, the results of online phase identification based on the proposed method and MHT method are tabulated in Table 10. The identification results are slightly different but basically the same. Learning from Fig. 16, the differences between the variable trajectories of optimal and nonoptimal test batches are mainly in the intervals of [8, 100] and [349, 760], so the local operating performances in these intervals are essentially nonoptimal. Fig. 20 shows the online assessment results based on the proposed method. The values of local and global assessment indices are greater than 0.8 before the 14th sample, and then the nonoptimality

Fig. 21 – Online assessment of nonoptimal test batch of injection molding process using MHT method.

occurs and continues to the 103rd sample by local assessment and 138th sample by global assessment, respectively. It means that the process operating performance changes from optimality to nonoptimality from the 14th sample and lasts for a period of time. Another deterioration of the operating performance occurs at the 350th and 352nd samples based on local and global assessments. Although the values of the local assessment index fluctuate near 0.8 after the 761st sample, the values of the global assessment index are always lower than the threshold to the end. That is to say, the operating performance of the overall batch run is still not excellent by taking into account the combined effect of all the phases that have been activated. Thus, the assessment result based on the proposed method not only conforms with the actual situation, but also provides more local and global information to show the development and changes of the process operating performance. Fig. 21 shows the online assessment result by MHT method. Obviously, the local assessment results cannot correctly reflect the local operating performance and with a lot of false alarms, which further results in the unbelievable global assessment result. It may be due to the fact that there are more noise and unknown disturbances in the real life data, and the probability assessment model based on MHT method is more easily affected by interferences, so its accuracy and reliability are discounted; while the assessment model based on statistical analysis can effectively overcome the noise and unknown disturbances, and ensures the accuracy of the assessment result. AdPCA method greatly improves the accuracy of the assessment result compared to MHT method as shown in Fig. 22, but two turning points from optimality to nonoptimality identified by AdPCA method are 20th and 361st samples, respectively, which is a little later than those obtained using the proposed method. It is because that the performance-unrelated information mixes in the main variation information and affects the sensitivity of AdPCA method to the change of process operating performance. While the performance-related information extracted by the proposed method has a closer relationship with the process operating performance and can reflect its change earlier. Additionally, the values of T2 statistic are less than the confidence limit from the 761 st sample to the end, which means that the process operating performance is back to optimality, however, it’s actually not the case. Thus, the proposed method gives the best performance in this case.

Chemical Engineering Research and Design 1 3 4 ( 2 0 1 8 ) 292–308

Fig. 22 – Online assessment of nonoptimal test batch of injection molding process using AdPCA method.

307

Fig. 25 – Variable contributions of injection molding process using AdPCA method.

ment result based on MHT is wrong, this identification result is unbelievable. In AdPCA method, the contributions of injection velocity, stroke, nozzle pressure, plastication pressure and cavity pressure are all large at the 20th sample, which is due to the spread of nonoptimality and may cause some confusions in the determination of nonoptimal causes. Therefore, It can be concluded that the cause identification result obtained from the proposed method is more accurate and in accord with the actual situation than those from other two assessment technologies.

5.

Fig. 23 – Variable contributions of injection molding process using the proposed method.

Fig. 24 – Variable contributions of injection molding process using MHT method. Variable contributions calculated from the three methods are displayed in Figs. 23–25, respectively. In Fig. 23, the contribution of injection velocity is obviously larger than those of other variables based on the proposed method, and it is naturally identified as the responsible cause variable for the nonoptimal operating performance, which is correct and conforming to the reality. Fig. 24 presents the result obtained from MHT method at the 1st sample. Since the local assess-

Conclusions

This paper proposes a novel operating performance assessment and nonoptimal cause identification method for multiphase batch processes. The T-PLS based inner-phase assessment models are established for each phase to describe the local characteristics of the batch process, and they play a role in online phase identification and nonoptimal cause identification. In addition, the inter-phase assessment models focus on describing the combined behaviors of multiple phases under the consideration of their correlations and interactions. It reveals the effect of them on the operating performance of the whole batch and provides the reference standard for online global assessment. During online assessment, the proposed method performs local and global assessments concurrently, and this provides the possibility of understanding the operating performance of batch processes from multiple perspectives. Furthermore, variable contributions to the local assessment index are calculated to identify the cause variables for the nonoptimality. The feasibility and effectiveness of the proposed approach are verified through two case studies. In the simulations, no matter for the optimal test batch or the nonoptimal one, the proposed method can evaluate the process operating performance accurately in real time, and also can find the responsible cause variables properly. Comparing to MHT method and AdPCA method, the inner-phase and inter-phase analysis based operating performance assessment method proposed in this study is more consistent with the characteristics of batch processes and shows better performance. Also, it can obtain the global assessment result in real time to track the development of the operating performance, which provides much more important information for operation engineer.

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Declaration of interest None.

Acknowledgments This work was supported by the National Natural Science Foundation of China [grant numbers 61703078, 61673198 and 61533007]; the China Postdoctoral Science Foundation [grant number 2017M611247]; the Fundamental Research Funds for the Central Universities [grant number N160403002]; the Postdoctoral Science Foundation of Northeastern University [grant number 20170309]; Hong Kong Research Grant Council on Synchronized Process Control of Hot-Runner Temperatures (No. 670525433); the Funds for Creative Research Groups of China [grant number 61621004]; Stat Key Laboratory of Synthetical Automation for Process Industries Fundamental Research Funds [grant number 2013ZCX02-04].

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