Interpretation of the effect of transient process data on part quality of injection molding based on explainable artificial intelligence

This paper proposes an interpretation methodology for the effect of transient process data on quality of injection molded parts. The transient process data measured in the actual processing space have been regarded as the most relevant information to manufacturing processes and product quality. However, its interpretation to pinpoint which feature in the data would affect part quality has traditionally relied on knowledge and understanding of the manufacturing process. The main objective of this method is to reduce the dependency of the transient process data analysis on process knowledge and understanding by using explainable artificial intelligence (XAI). The contribution of the ‘section-wise' features in the transient process data to the quality prediction of machine learning (ML) models was investigated for the first time. The interpretation results of the effect of cavity pressure and mold surface temperature on four different quality factors represented reasonable explanations of the characteristics of the polymer materials, product geometry, and molding process. Due to the intermediate relationship of the transient process data with the user-specified process parameters and the resulting quality variables, the interpretation results can be further utilized to optimize the process and provide the optimal transient process data profile for best part quality. GRAPHICAL ABSTRACT


Introduction
Transient process data measured by in-mold sensors are the most relevant information to product quality in the actual manufacturing space, where material is actually deformed and shaped into the final form.This is because they represent the details of the actual process conditions and connect the user-specified process parameters with the resulting product quality.As illustrated in Figure 1, manufacturing processes at the 'physical level' can be understood as the impact flow from the process setting of the manufacturing equipment to This is because inconsistent performance of manufacturing equipment, variation of material characteristics, and fluctuation of ambient conditions make the relationship between process parameters and quality unreliable (Menges, Michaeli, and Mohren 2001).
Application of the transient process data requires knowledge and understanding of the manufacturing process because it requires the physical meaning of the data.This is especially true for injection molding that this work focuses upon.Analysis of the transient process data is a highly human-dependent task because the transient process data strongly depend on the product geometry, material characteristics, process settings, and molding machine.Therefore, reducing the dependency on prior knowledge and understanding for the analysis of transient process data is critical for automated process optimization and intelligent manufacturing in Industry 4.0.
Injection molding is one of the most important massproduction processes, which accounts for most discrete plastic products worldwide (Bonten 2019) while processing more than one third of all thermoplastic materials (Zhao et al. 2020).Due to the excellent dimensional tolerance, surface quality, production efficiency, and repeatability, injection molding has been employed to mass production of not only typical thermoplastics and thermosets but also fiber reinforced plastics, ceramics (Rogers and Jain 2014), metals (Oh et al. 2018), and glass (Mader et al. 2021).In injection molding, the polymer materials supplied into the injection unit (Figure 2a) is melted by the heat from the band heaters and the shear heating from the screw rotation and molecular friction.After plasticization, the forwarding movement of the reciprocating screw injects the molten polymer material (polymer melt) into the part-shaped cavity in the mold through the melt delivery system.The polymer melt undergoes three main process stages of filling, packing, and cooling in the cavity.In the filling stage (Figure 2b), polymer melt forms advancing flow front and fills the cavity.After contact with the cold mold surface, the polymer melt loses heat to the cooling channels through the mold, and an outer solidified layer (frozen layer) is formed at the melt-mold interface.Due to the shrinkage of the polymer melt during cooling, a small amount of polymer melt is injected into the cavity under the packing pressure for compensation of the shrinkage in the packing stage (Figure 2c).After the end of packing stage, the polymer continues to cool down and gains sufficient stiffness to resist any deformation from the mold opening and ejection actions (Figure 2d).
The transient process condition in the cavity is represented by the transient (time series) process data directly measured by the sensors in the mold (in-mold sensor).
Even though the measurement of transient process conditions requires the placement of sensors involving higher tooling costs, the transient process data have been used for process monitoring and control (Giannekas, Zhang, and Tosello 2018;Rønsch, Kulahci, and Dybdahl 2021).Various types of in-mold sensors have been employed (Ageyeva, Horváth, and Kovács 2019) such as strain sensors for measuring the mold deformation (Wu and Huang 2007), capacitance sensors for measuring the advancing flow front or shear stress (Chen, Chen, and Gao 2004;Peng, Li, and Turng 2010), and cavity air temperature sensors for measuring gas emission and venting condition (Kim et al. 2021).Cavity pressure and mold surface temperature sensors are the most widely used inmold sensors in the injection molding industry because characteristics of polymer materials are highly sensitive to pressure and temperature (Zhao et al. 2020).For example, process control methodologies using cavity pressure and mold temperature based on the pvT (pressure, specific volume, and temperature) relationship have been proposed to maintain stable part weight under varying molding conditions (Michaeli and Schreiber 2009;Wang and Mao 2013).Similarly, a holding pressure adjustment technique based on the cavity pressure has been developed to enhance the consistency of injection molding quality (Huang, Ke, and Liu 2021).In addition to the pvT relationship, the rheological properties of polymer melt can be characterized using pressure and temperature sensors installed in the injection mold (Sykutera et al. 2018).The measured pressure represents cavity pressure including a rising filling pressure, a nearly constant packing pressure, and a diminishing pressure in the cooling stage as shown in Figure 3a.The measured mold surface temperature represents the fluctuating mold surface temperature after the polymer melt reaches the sensor location typically at the end of the fill, as shown in Figure 3b.
Many researchers have proposed the application of transient process data for process monitoring and quality prediction because they contain various types of useful information on the process as shown in Figure 3.For monitoring purposes, Chen, Tseng, and Huang proposed various quality indices that exhibit a high correlation to part weight and wall thickness (Chen, Tseng, and Huang 2019).For the quality prediction using machine learning, Chang et al. suggested peak and integration values of cavity pressure profile as quality indices (Chang et al. 2022).Chen, Guo, and Wang used the average mold surface and coolant temperatures, average packing pressure, and integration of cavity pressure for input features of part size prediction (Chen, Guo, and Wang 2020).Most of the application of transient process data is based on the predetermined features that are expected to have a high correlation on part quality.Determining the influential features such as characteristic points as well as peak, integral, and derivative of the profiles in the transient process data has traditionally relied on knowledge and understanding of injection molding.The first reason is the dependency of the transient process data on the product geometry, material characteristics, molding equipment, and type of quality factors.The second reason is the coupled response of each feature, which makes it difficult to apply the typical design of experiment (DoE) analysis method to each feature.Therefore, the determination of the influential features has been carried out by investigating the correlation, such as linear correlation coefficient, between the predetermined features and the quality.However, evaluating the linear correlation coefficient is insufficient to determine influential features having a major effect on quality.This is because the linear correlation coefficient does not provide sensitivity of quality to the feature, and the coupled response of the features could result in multiple features having high correlations with the quality.For example, at a given injection speed, the duration from when the melt reaches the sensor location till the end of fill will be a constant that depends on cavity geometry.That means the difference between the time instant of the second characteristic point in Figure 3a, which represents the transition from filling to packing (or end of fill), and the time instant of the first characteristic point, which signals melt arrival at the sensor location, will be the same.If the time instant of the first characteristic point has a high linear correlation coefficient with quality, then the linear correlation coefficient between the time instant of the second characteristic point and quality will be high as well.Therefore, analyzing the correlation between the features in the transient process data and quality is not enough for determination of influential features, and it is necessary to investigate the effect of the features in the transient process data on part quality with less dependency on prior knowledge and understanding.
Fast-developing artificial intelligence (AI) and machine learning (ML) have been applied to facilitate the understanding of physical phenomena beyond the sole prediction purpose.Especially, explainable artificial intelligence (XAI) and interpretable machine learning (IML) make it possible to quantify the contribution or sensitivity of input features on the prediction results.The interpretation result of the ML models enables the extraction of additional insights into the physical phenomena as well as manufacturing processes (Chen et al. 2023).Román et al. sorted the feature influences of material characteristics on surface defects and refined the ML model to achieve a higher prediction performance with selected input features (Román et al. 2021).Lockner, Hopmann, and Zhao filtered effective input features among 220 material features in the material database of molding simulation software to apply transfer learning to different polymer materials and molding machines (Lockner, Hopmann, and Zhao 2022).
Recently, the input feature importance of ML models with features from the transient process data has been compared.Farahani et al. compared the maximum weight of input features of ML models trained by various sensor data such as cavity pressure and mold temperature (Farahani et al. 2021).By analyzing the weight of the data points composing the transient process data from various sensors, influential time sections in different sensor data were estimated.The proposed method did not consider the similarity between the transient process data profiles, even though the transient process data profiles of different molding cycles can be warped with each other.Jung et al. evaluated input feature importance of quality prediction ML model to search for influential features (Jung et al. 2021).However, those input features were single-value data instead of the transient process data from each molding cycle.Similarly, Wang et al. had determined the influential features in cavity pressure and temperature data using important factor analysis and the random forest model (Wang et al. 2023).Still the input features were preselected representative features such as time instance of a specific event, pressure integration, and maximum pressure.The usage of simple representative features from the transient process data offers such advantages as small ML models and easier interpretation.However, the determination of representative features for the transient process data requires prior knowledge and manual intervention and could omit other relevant information to the manufacturing processes.
In this work, a novel approach was proposed to interpret the transient process data and understand which sections in the transient process data have an effect on part quality and their degree of influence.The effect of cavity pressure and mold surface temperature on various quality factors will be interpreted and its validity will be investigated.The proposed methodology takes into account the similarity of the transient process data of different molding cycles by extracting characteristic points that showing the warping paths between different profiles, rather than a simple average, min, and/or max value or direct usage of numerous data points composing the time series data.The contribution of the 'section-wise' features in the transient process data to the quality prediction of machine learning (ML) models was investigated using XAI.As a result, the proposed methodology is expected to provide better interpretation results than the pointwise interpretation (Gim and Rhee 2021).This approach can also reduce the dependency on human knowledge and intervention in contrast to previous approaches that rely on preselected data features based on prior knowledge and understanding of the materials and processes.The extended scope of this approach will be proposed at the end of this paper.

Methodology
The methodology to interpret the effects of each feature in the transient process data consists of three steps, namely, measurement of the transient process data and quality, segmentation of the transient process data and ML model training, and interpretation of the transient process data (cf.Graphical Abstract).Due to the pvT characteristics of polymer materials, transient cavity pressure and mold surface temperature are the most selected transient process data for injection molding.The measured transient process data by in-mold sensors are first segmented using geometrical features on the transient process data profile.The information associated with each geometrical feature such as time duration, pressure, and temperature values are related to each process stage.Thereafter, each quality factor is predicted by the ML model with the feature information as input features.Finally, XAI technique is applied to interpret the effects of each feature in the transient process data on product quality.
The following sections cover introductory information on the experimental design for preparing the dataset, quality characterization, pre-processing of the transient process data, as well as ML and XAI technique used for this study.

Transient process data acquisition and pre-processing
An injection mold with box-shaped cavity geometry (Figure 4a) was used for this study.Polymer melt from the injection unit is delivered through the sprue of 60 mm in length and a melt entrance (sprue gate) of 8 mm in diameter to the cavity.A hydraulic-type injection molding machine (Arburg Allrounder 320S 500-150, Arburg GmbH + Co KG, Germany) was used to conduct the molding trials.The polymer material used was polyamide (PA) 66 (Torzen T2021HSL BK01, Radici Plastics USA Inc., USA).To prevent the effects of moisture content, the material was dried at least 4 h prior to molding trials using an industrial material drier (NWB-75, NovaTech LLC, USA).

Cavity pressure and mold surface temperature
A strain-gauge-type pressure sensor (PT465XL-7.5M,Dynisco LLC, USA) was located near the gate and a Ktype thermocouple (type 6192B, Kistler Holdings AG, Switzerland) was located near the end of fill (EOF) position as shown in Figure 4a.The location of the pressure sensor near the gate enables measurement of cavity pressure from the start of the cavity filling.Also, the difference between the pressure and temperature sensors' locations allows the transient process data to cover the filling rate of the entire cavity.The pressure and temperature sensors were connected to a bridge input module (SCC-SG24, National Instruments Corp., USA) and thermocouple input module (SCC-TC02, National Instruments Corp., USA), respectively, both of which were installed in its own data acquisition (DAQ) device (SC-2346 and PCI-6024E, National Instruments Corp., USA).The onset of the injection signal from the molding machine measured by the digital input module (SCC-DI01, National Instruments Corp., USA) was used for the triggering of data measurement and the time reference of the transient process data.The cavity pressure (Figure 4b) and mold surface temperature (Figure 4c) were measured at a sampling rate of 100 Hz to ensure a high resolution for the drastic changes in pressure and temperature during the short filling stage.

Design of experiment (DoE)
Four process parameters having dominant effects on the filling, packing, and cooling stages were selected as the main process parameters for DoE.In particular, injection speed (InjSpd) is the main process parameter for the filling stage while packing pressure (PackPres) and packing time (PackTime) are critical to the packing stage (Ardestani et al. 2023).Finally, coolant temperature (CoolTemp) is the dominant process parameter dictating the mold temperature and affecting the overall process cycle, especially during the cooling stage.The range of each process parameter (see Table S1) without abnormal molding conditions (e.g.overpacking) or flash defects was determined by preliminary molding trials.Specific information about the process setting is tabulated in Table S1.
Experimental points of the main process variables were sampled by the Hammersley sequence sampling (HSS) method, one of the low-discrepancy sampling methods based on the Hammersley sequence, to minimize overlapping experimental conditions and getting a low correlation between multi-dimensional variables.Especially for supervised learning of neural networks, HSS is better than other DoE sampling strategies such as classical factorial design and Latin Hypercube sampling because it covers the design space better (Das and Tesfamariam 2022).Over the predetermined range (cf.Table S1), 170 experimental points were sampled as plotted in Figure 5.After the process reached a steady state, three molded samples were collected under each experimental condition to examine the process stability.While performing the molding trials with this minimized overlapping settings takes a lot of process setting changes, it can be easily automated by manufacturing execution systems (MES) with communication protocols such as OPC-UA (Open Platform Communications United Architecture) or Modbus.

Feature extraction
In this work, Process State Points (PSPs) (Gim and Rhee 2021) that characteristically define the geometrical feature of the transient process data profiles were selected as input features instead of the traditional standard features (SFs) such as peak, integral, and derivative of the profiles.Various cavity pressure and mold surface temperature profiles can be defined by tracing these characteristic points according to the molding conditions.For example, the increment of the injection speed is represented by the shifted characteristic points to earlier time instants.PSPs as the characteristic points on the transient process data profile provide more detailed information than SFs as shown in Figure 3. Similar approaches using geometrical feature points for analysis has been tried for other transient process data such as injection pressure and screw position (Baruffi, Calaon, and Tosello 2018).Using PSPs, the transient process data can be succinctly represented with less loss of overall profile shape.
The features of the cavity pressure profiles from the box-shaped cavity were represented by six PSPs as shown in Figure 6a.Three more PSPs represented the features of the mold surface temperature as shown in Figure 6b.In contrast to the terminal PSP in pressure profiles, it is difficult to find the last PSP of the temperature profile due to gradual decrease of the temperature in the cooling stage.The last PSP in the temperature profile was determined by a 63.2% (1 − e −1 ) temperature drop from the peak temperature.Therefore, the time difference between the second PSP (peak temperature) and the last PSP represents the time constant of part cooling in the cooling stage.As shown in Figure 6, the extraction of PSPs using perceptually important points (PIP) (Fu, Hung, and Chung 2017), one of the time-series segmentation algorithms, yielded fairly reliable results.The detailed procedure extracting PSPs from a cavity pressure and mold surface temperature profile is described in Algorithm S1.
In the previous work (Gim and Rhee 2021), point-wise information from the absolute time and pressure values of PSPs (aPSP) were used as input features of the ML model for weight prediction.Alternatively, differences of adjacent PSPs (dPSP), i.e. time ( t), pressure ( P), and temperature ( T), can be treated as section-wise input features.In this work, the prediction performance and interpretability of ML models based on both of the point-wise (aPSP) and section-wise (dPSP) input features approaches are compared.
The pressure values of the first and the last PSPs in the cavity pressure data are always zero under the normal injection molding condition.Therefore, they were excluded from the features of aPSP and dPSP.Similarly, the pressure drop from the second-to-last PSP to the last PSP in the cavity pressure data is always the same as the sum of the pressure changes of PSPs before the secondto-last PSP.Therefore, it was not included in the feature of dPSP.The temperature of the last PSP in the mold surface temperature profiles was calculated from the previous two PSPs, so the temperature or temperature difference to the last PSP had no meaning on the process and were also excluded from aPSP and dPSP.The absolute value of the first PSP point was used as the temperature value of the first PSP section of the mold surface temperature.

Quality measurement
The responses of different quality factors were expected to have different relationships with each point or section in the transient process data.Therefore, various quality factors were chosen and compared.Weight as a widely used quality factor (Chen and Turng 2007) represents the amount of material consumption for the part and directly relates to material cost and cycle-to-cycle consistency.Shrinkage and warpage were selected as quality factors to represent the dimensional and geometrical accuracy of final molded parts, respectively.Due to the different thicknesses of the thick (narrow) and thin (wide) side walls of the box part geometry shown in Figure 4a, the warpage at the thick walls (Warp-ThickWall) and thin walls (Warp-ThinWall) had unique responses and were treated as different quality factors.
Part weight was measured by a precision balance (NewClassic MF MS303S, Mettler Toledo GmbH, Switzerland) with 1 mg resolution.To measure shrinkage and warpage, image processing was employed because it is nondestructive and fast (Gim and Turng 2022).A photographic studio including sample fixture and alignment chart was designed (cf. Figure S1a).Raw sample images were corrected and calibrated by the alignment markers (cf. Figure S1b).The shrinkage and warpage were measured by the detected corner points and area of warped shape (cf. Figure S1c).Detailed processing is presented in Figure S2

Regression model
Various types of ML models have been employed to build regression models for the prediction of quality using the transient process data.Especially, Long Short Term Memory (LSTM) (Nagorny et al. 2017), Recurrent Neural Networks (RNN) (Lu et al. 2007), and Convolutional Neural Networks (CNN) (Punnoose et al. 2021) showed good results for the raw transient process data.These approaches treated each point in the raw profile as independent input features.Interpretation of the transient process data using these ML approaches would represent the effect of every single points in the transient process data.However, it is better to understand the transient process data profile by warping of profiles based on the characteristic points (PSPs) as shown Figure 6.Artificial neural networks (ANN) have been widely used for quality prediction due to their modeling capability for highly nonlinear and complicated relationships, even though the interpretability of ANN is lower than other ML models (Angelov et al. 2021;Minh et al. 2022).Recently, transfer learning of ANN models to other manufacturing equipment and materials has expanded the usage of ANN for manufacturing (Gim, Yang, and Turng 2023;Lockner, Hopmann, and Zhao 2022;Lockner and Hopmann 2021;Tercan et al. 2018).AutoML techniques have relieved the time-consuming and iterative task to optimize hyperparameters of ANN (Bahri et al. 2022).Therefore, it was expected that ANN is sufficient and effective for the quality prediction regression model using PSPs.
Getting sufficiently large datasets for model training is difficult in actual manufacturing processes because of labor cost, material cost, machine downtime, and other factors that make the real process data from the shop floor expensive.Therefore, hyperparameters of ML models are normally set by insufficient and partial datasets, and various combinations of hyperparameters could be optimal depending on the dataset even though the data is from the same mold and molding machine.To reflect this issue, hyperparameters were optimized by every randomly split partial dataset from the whole dataset.After optimization of hyperparameters, the ANN model was trained using the same dataset.Statistical result on the prediction performance was calculated from 20 randomly initialized trials (Colas, Sigaud, and Oudeyer 2018) due to the stochastic nature of ML.The range of each hyperparameters of ANN is tabulated in Table S2.The ANN and hyperparameter optimization were implemented using Python version 3.7, TensorFlow version 2.9.2 (Abadi et al. 2016), and Optuna 3.0.2(Akiba et al. 2019).The detailed procedure on the model training and hyperparameter optimization is presented in Figure S5.

Model interpretation
ML models have been treated as 'black box' (Ribeiro, Singh, and Guestrin 2016) that its prediction results cannot be explained or interpretable directly due to the numerous numbers of weight and bias values incorporated in the ML models.Especially, interpretation of the inter-relationship between input and output of the neural networks for injection molding has been regarded as impossible (Kashyap and Datta 2015).As attempts to extract influential features from the transient process data from the molding machine (Zhou et al. 2018), XAI and IML have been employed to understand the relationship between process parameters and quality (Gim and Rhee 2021) or defects (Román et al. 2021).
SHapley Additive exPlanation (SHAP) is an XAI technique for investigating the importance of input feature based on the game theoretical Shapley values for ML models (Lundberg and Lee 2017;Lundberg et al. 2020).SHAP regards each input feature as a participant in a cooperative game and allocates the difference between the base value (mean) and a specific prediction according to contribution of each input feature in additive manners as expressed in Equation (1) below, ( 1 ) where P k is the prediction result of k-th sample, P is the base value of the mean of all prediction results, C ik is the contribution of i-th input feature for the k-th sample prediction, and N is the number of the input features.Therefore, the sum of every contribution of input features is the difference between the base value and a specific prediction.Overall effect of i-th input feature, Ci is the mean of absolute contributions from M samples, as presented in Equation ( 2).If the input feature and its contribution have a strong linear relationship in SHAP results, the overall effect of the input feature is 1/4 of the maximum deviation of contributions or the maximum deviation of prediction results based on the input feature, P i,max , as shown in Equation (3) and Equation (4).

Results
The main objective of this work is to interpret the effect of the transient process data on various quality factors based on XAI.The prediction performance of ML models for each quality factor using point-wise and section-wise features from the transient process data will be compared followed by proposal of the approach with better interpretability.

Quality prediction by the transient process data
The validity of the interpretation results of the transient process data using XAI is based on the high prediction performance of the ML model used.Because ML models with high prediction performance sufficiently represent the actual relationship between the transient process data and quality, the interpretation of ML models can be regarded as the interpretation of the actual physical relationship in manufacturing processes.Figure 8 presents the prediction performances of each ML model trained by the input feature from the point-wise (aPSP) and section-wise (dPSP) approaches.
The index representing the prediction performance of the regression ML models is the R 2 score as defined in Equation ( 5).R 2 has been widely used as a prediction performance index for quality prediction in the manufacturing field (Aminabadi et al. 2022;Gim, Yang, and Turng 2023;Ruiz et al. 2020).It has also been recommended as a standard metric to evaluate regression analysis (Chicco, Warrens, and Jurman 2021).
where y i , ŷi , ȳ are a true value, predicted value, and average of true values, respectively.SS res and SS tot are the residual sum of squares and the total sum of squares, respectively.R 2 score is different from the typical square of the linear correlation coefficient (Pearson correlation coefficient) and can be negative if the prediction performance is worse than the average value as the prediction.R 2 has an advantage in the comparison of prediction performance for various quality factors with different scales.
While the root mean square error (RMSE) and mean square error (MSE) are dependent on the scale or unit of the output data, R 2 is independent of the scale of the output and hence appropriate to compare the prediction performance of different quality factors (Lockner and Hopmann 2021).
As can be seen in Figure 8, both point-wise and section-wise approaches yielded high prediction performance with a R 2 score above 0.95 for weight and shrinkage prediction.For the prediction of warpage at the thick walls and thin walls, the prediction performances of both approaches were around 0.9 in terms of R 2 score, which was lower than the weight and shrinkage prediction.This is because of the nonlinear response of the warpage.The less complicated responses of weight and shrinkage than those of warpage were exhibited in the measurement results shown in Figure S6.According to the pvT characteristics of polymer materials, pressure and temperature have a straightforward influence on the specific volume and density of polymer materials.Therefore, ML models can easily predict weight and shrinkage using the transient process data of pressure and temperature.However, the warpage is a more complicated factor involving differential shrinkage and temperature difference across the part walls.
Both point-wise and section-wise approaches exhibited similar prediction performance for each quality factor.The point-wise and section-wise features were extracted from the same transient process data and can be converted easily to each other.Therefore, the similar prediction performance is due to the same fundamental information in the point-wise and section-wise features on the process.This suggests both approaches that extract the information from the transient process data are suitable for quality prediction purposes.

Comparison of point-wise and section-wise interpretation
Point-wise and section-wise interpretations are different interpretation approaches using the transient process data.Point-wise interpretation concentrates on the direct effect of the PSPs on part quality.Section-wise interpretation explains the effect of differences in time instant and physical value (of pressure and temperature) in each section separated by adjacent PSPs on part quality.
To determine which interpretation approach gives better interpretability of the transient process data, the interpretation results concerning the effect of aPSP and dPSP need be compared.Part weight was selected as the target quality factor for validation of interpretation results.This is because the interpretation of the ML models for weight prediction is most dependable due to the highest prediction performance.Also, the response of the weight to the process parameters is linear over a wide range of process parameters as shown in Figure S6.Therefore, the interpretation results of the transient process data and the effect of process parameters can be easily compared.
Figure 9 shows the interpretation results concerning the effect of each PSP point (aPSP) or section (dPSP) on weight.The effect of PSP on quality (y-axis) in the interpretation results (Figure 9c-f) corresponds to the mean of the absolute contribution of each PSP, which is based on the difference between the predicted quality value and the average (base) quality value, as defined in Equation (2).Thus, the effect of PSP on quality can be understood as the overall average influence of each PSP on quality.Both approaches showed that the temperature of T1 (T T1 ) point or -T1 section (T −T1 ), which represented the initial mold temperature, and the time instant of P5 (t P5 ) or the time difference of P4-P5 section ( t P4−P5 ) are the most influential features on the weight.The point-wise interpretation showed the effect of T T1 was twice of that of t P5 whereas similar effect of T −T1 and t P4−P5 was observed based on the section-wise interpretation.The second most influential feature predicted by both interpretation results were different, especially the effect of the P3 pressure and that of the P2-P3 section pressure difference, as shown in Figure 9c and e.
In the injection molding cavity pressure profiles, the early rapid pressure increase section is typically associated with the filling stage whereas and the following section with a constant pressure signifies the packing stage.Therefore, the time instant of P2 (t P2 ) or time difference of P1-P2 section ( t P1−P2 ) in the early pressure increase section is directly correlated to the injection speed, which is the process parameter for the filling stage.The pressure of P3, P4, and P5 (P P3 , P P4 , and P P5 ) and the pressure difference of P2-P3 section ( P P2−P3 ) are strongly related to the packing pressure.Similarly, the time instant of P5 (t P5 ) and the time difference of P4-P5 section ( t P4−P5 ) correspond to the packing time.The temperature of T1 point (T T1 ) and -T1 section (T −T1 ) is dictated by the coolant temperature.Therefore, the interpretation result of the PSP points or sections can be directly compared to the effect of each process parameter on part weight to validate the interpretation results.Figure 10 shows the effect of each PSP point or section that are directly correlated with each process parameter, the overall effect of each process parameter on part weight, and the linear correlation coefficient between the PSPs and process parameters.The deviation of weight due to the minimum and maximum process parameters was regarded as the overall effect of each process parameter.
The relative differences of the effect of PSP should show similar differences to the overall effect of the process parameter because the linear correlation coefficient, ρ, between each process parameter and PSP point or section was almost 1 or -1.The effect of pressure of P3 (P P3 ) was interpreted as being smaller than T T1 and t P5 , even though the corresponding process parameter of packing pressure exhibited a much stronger effect, similar to coolant temperature and packing time (cf. Figure 10a).In comparison, the effect of each PSP section showed similar trends to the overall effect of process parameters (cf. Figure 10b).The effect of PSP sections was about 1/4 of the overall effect of process parameters, which corresponded to Equation (4).Recall that Equation ( 4) is the relationship between the deviation of predicted quality and interpreted effect according to SHAP.The dominant effect of PSP sections related to coolant temperature, packing pressure, and packing time has been found to correspond to the general response of the weight of injection-molded products (Hopmann et al. 2019).This suggests that the section-wise approach is capable of interpreting the effect of the transient process data on quality.In the following sections, the section-wise PSP approach will be used to investigate the effect of the transient process data on shrinkage and warpage.

Shrinkage
Figure 11a and b present the effect of the transient process data on the shrinkage.The temperature of -T1 section (T −T1 ) corresponding to the initial mold temperature had the largest effect on the shrinkage.The next most influential feature was the pressure difference of P2-P3 section ( P P2−P3 ).Overall, the T −T1 showed a dominant influence over the other features.
The shrinkage can be mainly understood by the change of specific volume under the isothermal, isobaric, and isochoric conditions according to the pressure and temperature changes during the various process stages in injection molding (Hopmann and Heinisch 2018).Figure 12 is the pvT diagram of the PA66 polymer material used for the molding trials.The filling stage can be regarded as isothermal compression (A-B) at the melt temperature (T melt ) because of the increasing cavity pressure and a nearly constant melt temperature.The packing stage can be approximated by the isobaric cooling (B-C) due to the constant packing pressure and heat removal by the mold.The isobaric curves of 350 and 550 bar correspond to the actual packing pressure range in the cavity as shown in Figure 4b.The cooling stage can be treated as isochoric cooling (C-D) due to the gradual decrease of pressure and an approximately fixed amount of the polymer material in the cavity.After the pressure reaches the atmospheric pressure (p = 1 bar), additional cooling would only decrease the specific volume following the isobaric cooling (D-E) curve to the ambient temperature (T amb ).In case of the constraint-free shrinkage such as that in the thickness direction, the theoretical shrinkage would be the differences in the specific volume marked by (D-F).In case of shrinkage being restricted by the mold geometry, the shrinkage results from and the reduction of specific volume after the ejection (E-F).In this study, the measured shrinkage was taken as the diagonal distance reduction of the sidewall corners.The diagonal distance was restricted by the mold core until the ejection.Therefore, the shrinkage was highly correlated to the change of specific volume after the ejection (v E − v F in Figure 12).Based on the cooling time (45 s) and the molding simulation results (cf. Figure S7), the wall center temperature at the ejection point (E and E') was 66 and 110 ˚C for the lowest and highest mold temperature condition, respectively.While packing pressure would lead to different traces on the pvT diagram (i.e.A-B-C-D-E and A-B''-C''-D''-E), its effect on the change of specific volume after the ejection point E was relatively small.In fact, the change of the specific volume after the ejection is mainly affected by the temperature at the ejection regardless of the packing pressure.Therefore, the interpretation results pointing to the dominant effect of the initial mold temperature (cf. Figure 11a  and b) on the shrinkage reasonably reflect the material characteristics.

Warpage
Figure 11c-f show the effect of the transient process data on the warpage at the thick walls (Warp-ThickWall) and the thin walls (Warp-ThinWall), respectively.Both warpage at the thick walls and thin walls were highly influenced by the initial mold temperature (T −T1 ).It is well-known that the main driving factor of warpage is the bending moment resulting from residual stresses induced by differential shrinkage across the thickness direction (Bociga et al. 2010).Generally speaking, polymer material under a higher mold temperature condition tends to shrink more and warps toward the hotter mold surface resulting in a concave shape (Beaumont 2019).With a sufficient cooling time used in this study, the coolant temperature would dictate the initial mold temperature (Pearson correlation coefficient 0.999, cf. Figure S8a).With a higher coolant temperature (and thus a higher initial mold temperature), the temperature difference across the thick walls and thin walls increased as shown in Figure S8b.Therefore, the initial mold temperature was strongly related to the main driving factor of the warpage.
The effect of the time difference of P4-P5 section ( t P4−P5 ) showed a similar effect to the pressure difference of P2-P3 section ( P P2−P3 ) for Warp-ThinWall, but it was smaller than P P2−P3 for Warp-ThickWall.To verify this interpretation results, the filling patterns of the thick and thin walls were be investigated, and the effect of the packing stage was be compared.Figure 13 presents the filling patterns of the cavity.Due to the rectangular shape of the upper side of the part and the radial filling pattern from the gate, the melt started to fill the thin walls (the longer sides) before it reached the thick walls (cf.Position A in Figure 13a).However, since the melt Temperature of D and E points were based on simulation results (c.f. Figure S7).The pvT model coefficients were based on the material database of the injection molding simulation software, Moldex3D (CoreTech system Co., Ltd., Taiwan).
always preferred the path of the least resistance, the thick walls were completely filled (cf.Position B in Figure 13a).After filling the thick walls, the melt filled the rest of the thin walls (cf.Position C in Figure 13a).The filling of the rest of the thin walls was represented in the transient process data shown in Figure 13b.The high flow resistance of the thin walls was evidenced by the sharp pressure increase at P2 point.The reading change of the mold surface temperature at T1 point indicated the complete filling of the thin walls as the melt reached the temperature sensor at the last filled point.
The packing stage reduced shrinkage at both the thin and thick walls and therefore suppressed the warpage.The actual packing pressure and duration were dominated by P P2−P3 and t P4−P5 , respectively.Solidification of the polymer melt in the walls increased the pressure drop and hampered the effect of packing.The polymer material in the thin walls would experience the packing pressure at the early packing stage (P3) because the thin walls were filled right before the packing started and were still at a higher temperature due to fresh melt and shear heating.Therefore, both packing pressure and packing time were effective for the warpage of the thin walls.However, the polymer material in the thick walls had started to solidify prior to the packing stage because the thick walls were already filled at P2 before the thin walls were completely filled.Therefore, the pressure increase over the P2-P3 section ( P P2−P3 ) shortly after the filling of the thick walls had a higher effect on the warpage than the time difference of P4-P5 section ( t P4−P5 ), which happened long after the filling of the thick walls.As a result, the interpreted effect of the transient process data on the warpage truthfully reflected the actual filling patterns and the thermomechanical histories of the material elements.

Effect of melt temperature on weight
For the manufacturing industry, the practical limitations and high costs associated with building an experimental dataset from the shop floor make it difficult to consider all process parameters as process variables for DoE.Therefore, it is difficult to obtain additional insights into those unselected process parameters through other selected process parameters as features for modeling or prediction.For example, in this work the process parameters for building of experimental dataset did not include the barrel temperature, which directly affects the temperature of polymer melt (melt temperature).Therefore, one would expect that it would be difficult to investigate the effect of the melt temperature on quality.Nonetheless, the transient process data do include the effect of not only main process variables selected for DoE, but also unselected process parameters.Therefore, interpretation of the transient process data can provide additional insights into unselected process parameters, which could improve process modeling, prediction, optimization, and further experiment design.
The peak temperature of the mold surface represents the melt-mold contact temperature (T c ) as shown in Figure 3b and it follows the relationship below.
where, b mold and b melt are the thermal effusivities or heat penetration coefficient of the mold and polymer melt, respectively.T mold and T melt are the initial mold temperature and melt temperature, respectively (Hopmann, Lammert, and Zhang 2017).The temperature difference of the T1-T2 section ( T T1−T2 ) is the temperature difference between the melt-mold temperature and the initial mold temperature (T c − T mold ), and it is dominated by the melt temperature due to the much higher melt temperature than the mold temperature.Therefore, the effect of T T1−T2 can be regarded as the effect of melt temperature on quality.
The effect of T T1−T2 was relatively higher on weight (cf. Figure 9f) than the effect of other features except for the 1st to 3rd features (cf. Figure 11b, d, and f).This implies that the melt temperature is an influential factor on weight just like the initial mold temperature (T-T1 ), packing time ( t P4−P5 ), and packing pressure ( P P2−P3 ) in the cavity.Therefore, to control the weight, the barrel temperature can be another process parameter for the control factors together with the coolant temperature, packing time, and packing pressure of the machine side.

Solidification of melt in the delivery system
Coupled responses of the features in the transient process data make it difficult to investigate the effects of each feature on the quality independently, even though the features carry meaningful information on the process.This is because independent control of each feature is not possible.For example, the pressure loss during the packing stage is related to the solidification of the melt in the delivery system, such as sprue, runner, and gate, that connects the machine nozzle and cavity.Solidification increases the viscosity of the polymer melt and pressure loss in the melt delivery system.Coolant or mold temperature can be changed to investigate the effect of solidification of the melt in the delivery system because the cooling condition dominates the solidification.However, other features are also changing due to the changing cooling condition, thereby, making it difficult to determine the independent and individual effect of melt solidification in the delivery system on quality.
Figure 14 exhibits the solidification effect of the melt in the delivery system on the warpage of the thick walls and thin walls.Each point represents the sampling point that was used for model interpretation.Positive effect in Figure 14a means suppression of the concave-shaped warpage at thick walls.Negative effect in Figure 14b means suppression of the convex-shaped warpage at thin walls.Both results supported that an effective packing stage with less pressure loss suppressed the warpage, as explained in section 3.3.2.
The slope in Figure 14 means the sensitivity of the warpage to the solidification effect of the melt in the delivery system.In contrast to the warpage at thin walls, the warpage at thick walls (Figure 14a) showed a different degree of sensitivity due to the initial mold temperature.As presented in the short-shot test results (Figure 13), the thick walls were filled earlier than the thin walls prior to the packing stage.Therefore, the thick walls would already start solidifying prior to the packing stage.A higher mold temperature would delay the solidification, thereby enhancing the effect of the packing stage on warpage at thick walls.Hence, the solidification effect of the melt in the delivery system to the warpage at thick walls is more sensitive to higher mold temperatures.In the case of the thin walls that were filled right before the packing stage, the packing stage is effective for a wider mold temperature range due to much less solidification.Therefore, the interaction with the mold temperature is much smaller than the warpage at the thick walls.

Discussion
The proposed interpretation method concerning the effect of the transient process data on quality enabled (1) reduction of the dependency on prior knowledge and understanding for the interpretation of the transient process data, including various information about the manufacturing process, and (2) investigation of the effect of the features in the transient process data on quality, which are difficult to discern independently.The transient process data such as cavity pressure and mold surface temperature were measured by in-mold sensors in the cavity where the actual molding process was carried out.The geometrical features of the transient process data profile were extracted to be used as input features of the ML models that characterize the relationship between the transient process data and quality.The contribution of each feature of the transient process data to quality was determined by the XAI technique, and its validity was confirmed via an in-depth analysis of the data and polymer material characteristics.
The comparison of the point-wise interpretation and section-wise interpretation based on the selections of the absolute and difference values of the feature points and the transient process data showed that the section-wise interpretation was more reasonable than the point-wise interpretation.It implies that the section-wise approach to interpreting or understanding the transient process data is more appropriate for the actual manufacturing process.This finding confirms the validity of previously proposed approaches that investigated the relationship between the pressure integration and quality of injectionmolded products (Chang et al. 2022;Chen, Tseng, and Huang 2019;Ke and Huang 2020;Párizs et al. 2022).
As shown in section 3.3, the proposed interpretation method could determine the effect of each feature in the transient process data on various quality factors, and the interpretation reasonably corresponded to the experimental results and polymer materials characteristics.This is because (1) ML can model the relationship between the transient process data and quality through the experimental data without prior knowledge and understanding, and (2) XAI techniques enable calculating the contribution of each input feature to the prediction results.The only procedures requiring human knowledge and understanding were the determination of the experimental space of the process parameters for the design of experiments (section 2.1.2.) and excluding of insignificant features among the extracted features from the transient process data (section 2.1.3.).The molding trials and quality characterization for building highquality experimental datasets, extraction of the features in the transient process data, optimization and training of ML models, and interpretation can be automated using up-to-date technologies of Industry 4.0 and AI.This means that the analysis task of manufacturing processes that traditionally requires human knowledge can now be automated with less dependency on prior knowledge and understanding of the manufacturing process.
A deeper insight into the manufacturing process can be further revealed by the interpretation results.Especially, with prior knowledge and understanding of the manufacturing process, the effect of unselected features or process parameters on quality (section 3.4.1.)and the interaction of the features in the transient process data (section 3.4.2.) can be evaluated.This is beneficial for process optimization or further experiments of manufacturing processes that have inherent limitations in the number of process parameters for building experimental datasets due to the cost.

Applications
Building connections between sensors and auxiliary devices to main manufacturing equipment enables more transient process data to be measured and various applications to be implemented.However, it is difficult to handle the ever-increasing process data, especially those transient or time-series process data, using the relatively limited computational power of the manufacturing equipment.Therefore, extraction of the influential features from the transient process data is required to reduce the computational load.As proposed previously (Román et al. 2021), filtering the influential features using XAI could help build smaller and simpler ML models and deliver higher prediction performance (Minh et al. 2022).Therefore, the proposed methodology can contribute to building a smaller ML model and improve the reliability of the application of ML for manufacturing processes.
The proposed methodology in this study will be expanded to process optimization and control.As mentioned above, the process parameters on the machine side are insufficient to process optimization because it cannot consider possible process disturbances such as the variation of material characteristics and fluctuation of machine performance.Therefore, process optimization and control based on the transient process data from the actual processing space, such as the cavity in the mold, has been recommended.The transient process data profiles can be optimized by the ML model that characterizes the relationship between the transient process data and quality.The optimal set of the process parameters at the machine side can be optimized to deliver the optimal transient process data profile.Because the gap between the process parameter and the transient process data is smaller than the gap between the process parameter and quality, the relationship can be modeled more easily using ML. Figure 15 is an example of the prediction results of the transient process data using the process parameter and verification.The PSPs in Figure 15 were predicted by ANN which was optimized by the hyperparameter optimization procedure used for the quality prediction model (c.f.section 2.3.1, Figure S5, and Table S2).A feature in the transient process data having a high effect on quality can be weighted in a multi-objective optimization problem to achieve the optimal transient process data profile.
It is expected that the proposed approach can be generalized and applied to many other batch manufacturing processes such as thermoforming, blow molding, compression molding, die casting, just to name a few.This is because (1) the processing condition of each repeated production cycle is similar to each other, and the quality variation induced by processing condition differences are captured by the transient process data, (2) automated extraction of the features from the transient process data profiles are applicable to those batch manufacturing processes, and (3) the XAI interpretation augments the use of the transient process data and ML-based quality prediction.
In addition to the ANN used in this study, the present approach could be expanded to other ML models such as tree-based models, ensemble models, and support vector machines.This is because the XAI technique used herein, SHAP, can work with any black-box ML models with an unknown structure (Minh et al. 2022).Other model-agnostic XAI libraries such as LIME (local interpretable model-agnostic explanations) (Ribeiro, Singh, and Guestrin 2016) could be utilized instead of SHAP.The comparison of interpretation results of the transient process data using different ML models and XAI techniques warrants further study.
Getting insight into the manufacturing processes with less manual intervention by the proposed approach means it can contribute to faster decision-making for process optimization and better process monitoring.With this approach, the information of the transient process data can be condensed into a few influential features.It can be critical for process optimization strategy and process monitoring because the interpretation is done by machine intelligence so that the subjectivity of the process analysis can be reduced, and objective decisions can be made.Furthermore, the ML models predicting the quality using the transient process data can be utilized for mold management and site production.The relationship between the transient process data and quality is intrinsic to a specific product geometry and polymer material.Therefore, the trained ML model can be associated with the mold using a mold management system such as a QR code or an RFID (radio-frequency identification) tag.When the mold is transferred to another production site or remounted to another molding machine, the trained ML model can be readily loaded from the MES server and used for quality prediction and control.

Limitations
Similar transient process data profiles, reliable measurement of the process data with high signal-to-noise ratios, properly selected process parameter range, and consistent time references, are keys to the general applicability of the proposed methodology to other materials and product geometries.

Conclusion
This work proposes an interpretation methodology concerning the effect of the transient process data on quality for an injection molding application.The transient process data from the actual processing space, such as the cavity in the mold, has been regarded as the most reliable process data for monitoring, quality prediction, and process optimization.However, its interpretation has traditionally relied on prior knowledge and understanding of the manufacturing process.The interpretation of the transient process data was derived from the machine learning model with the section-wise features of the data profile and explainable artificial intelligence.The interpretation results provided reasonable explanations for how the influential features of the transient process data affect various quality factors such as weight, shrinkage, and warpage.As a result, this approach can reduce the dependency on prior knowledge and understanding for the interpretation of the transient process data in realworld manufacturing processes.
Furthermore, this approach could be extended to build a smaller machine learning model that requires a less computational load and provides better prediction performance by using only the most influential features as inputs.Process optimization based on the optimal profile of the transient process data could use the interpretation result and select the main feature to be optimized.In the end, the proposed methodology can contribute to intelligent manufacturing processes and Industry 4.0.

Figure 1 .
Figure 1.Overview of impact flow from process parameters to quality in injection molding.

Figure 2 .
Figure 2. (a) Schematic of the injection molding process and three main process stages of (b) filling, (c) packing, and (d) cooling.

Figure 3 .
Figure 3. Example of characteristic points in typical transient process data of injection molding; (a) cavity pressure, and (b) mold surface temperature.EOF means end of fill.

Figure 4 .
Figure 4. Transient process data acquisition from the injection molding trials.(a) Box-shaped part geometry and positions of in-mold pressure and temperature sensors.Variation of transient molding conditions represented by (b) cavity pressure profiles and (c) mold surface temperature profiles.

Figure 5 .
Figure 5. Experimental points of DoE by the Hammersley sequence sampling (HSS) method. 1 bar is 0.1 MPa.

Figure 6 .
Figure 6.Example of the extracted process state points (PSP) from the transient process data of (a) cavity pressure, and (b) mold surface temperature.ClntTemp: coolant temperature, InjSpd: injection speed, PackPres: packing pressure, and PackTime: packing time.
based on image processing functions of OpenCV and scikit-image (Van der Walt et al. 2014).Calculation of shrinkage and warpage are detailed in Figures S3 and 4. Figure 7 presents the distribution of each quality factors.

Figure 7 .
Figure 7. Distribution of quality factors, (a) weight, (b) shrinkage, (c) warpage at thick walls, and (d) warpage at thin walls.Positive and negative warpage values in (c) and (d) mean convex and concave warpage shapes toward the inner direction of the part, respectively.

Figure 8 .
Figure 8.Comparison of quality prediction performance.

Figure 9 .
Figure 9.Effect of transient process data on weight, (a) cavity pressure profile and PSPs, (b) mold surface temperature profile and PSPs, point-wise interpretation for (c) cavity pressure and (d) mold surface temperature, section-wise interpretation for (e) cavity pressure and (f) mold surface temperature.

Figure 10 .
Figure 10.Comparison of the overall effect of process parameters on weight with (a) point-wise interpretation, (b) section-wise interpretation, and (c) relationship between process parameter, interpretation result, and part weight quality presented in (a) and (b).Pearson correlation coefficient, ρ between process parameters (shown in the lower labels) and PSP or PSP sections (shown in the upper labels) are presented by the color bars and the circle or square symbols, respectively.

Figure 11 .
Figure 11.Effect of the transient process data on quality factors, (a) effect of cavity pressure and (b) effect of mold surface temperature on shrinkage, (c) effect of cavity pressure and (d) effect of mold surface temperature on warpage at thick walls, and (e) effect of cavity pressure and (f) effect of mold surface temperature on warpage at thin walls.

Figure 12 .
Figure 12. pvT diagram of the PA66 polymer material used and traces of material's thermomechanical histories during injection molding.Temperature of D and E points were based on simulation results (c.f.FigureS7).The pvT model coefficients were based on the material database of the injection molding simulation software, Moldex3D (CoreTech system Co., Ltd., Taiwan).

Figure 13 .
Figure 13.(a) Short shot test results showing the filling patterns, and (b) cavity pressure profile measured near the gate and mold surface temperature profile measured at the end of fill (EOF) location.Position A -melt first reached the thin walls, Position B -melt filled the thick walls and started filling the thin walls, and Position C -melt touched the temperature sensor at a thin wall near the end of cavity filling.

Figure 14 .
Figure 14.Effect of the melt solidification in the delivery system during the packing stage on (a) warpage at thick walls, and (b) warpage at thin walls with interaction of the initial mold temperature.

Figure 15 .
Figure 15.Comparison of predicted PSP and the measured transient process data, (a) cavity pressure, and (b) mold surface temperature.