Prediction Performance and Economic Efficiency of Soft Sensors for in-Line Water Content Monitoring in Fluidized Bed Granulation: PP-Based Model vs. NIRS-Based Model

Abstract

Soft sensors play a crucial role as process analytical technology (PAT) tools. They are classified into physical models, statistical models, and their hybrid models. In general, statistical models are better estimators than physical models. In this study, two types of standard statistical models using process parameters (PPs) and near-infrared spectroscopy (NIRS) were investigated in terms of prediction accuracy and development cost. Locally weighted partial least squares regression (LW-PLSR), a type of nonlinear regression method, was utilized. Development cost was defined as the cost of goods required to construct an accurate model of commercial-scale equipment. Eleven granulation lots consisting of three laboratory-scale, two pilot-scale, and six commercial-scale lots were prepared. Three commercial-scale granulation lots were selected as a validation dataset, and the remaining eight granulation lots were utilized as calibration datasets. The results demonstrated that the PP-based and NIRS-based LW-PLSR models achieved high prediction accuracy without using the commercial-scale data in the calibration dataset. This practical case study clarified that the construction of accurate LW-PLSR models requires the calibration samples with the following two features: 1) located near the validation samples on the subspace spanned by principal components (PCs), and 2) having a wide range of variations in PC scores. In addition, it was confirmed that the reduction in cost and mass fraction of active pharmaceutical ingredient (API) made the PP-based models more cost-effective than the NIRS-based models. The present work supports to build accurate models efficiently and save the development cost of PAT.

Introduction

Fluidized bed granulation has been extensively used in the manufacture of pharmaceutical tablets to improve drug product quality and manufacturability. The water content profile during granulation impacts the physical properties of the granules, such as particle size distribution and bulk specific volume, which can eventually affect tablet hardness and disintegration time.¹⁾ Conventional water content analysis methods, such as loss on drying (LOD) and Karl Fischer, conduct off-line measurement, but they are not suitable for real-time process monitoring. Thus, in-line water content monitoring utilizing soft sensors is widely adopted for real-time prediction and control.²⁾ Soft sensors play an important role as process analytical technology (PAT) tools.

In general, soft sensors are classified into physical models based on first principles, statistical models, and their hybrid (gray-box) models. Although physical models, such as heat and mass balance models,^3–5) are interpretable, their prediction accuracy is usually insufficient. For example, Wang et al.⁵⁾ constructed a mass balance model to predict granule water content and reported that the predicted values were higher than the reference values. On the other hand, statistical models are generally less interpretable than physical models but have higher prediction accuracy. Statistical models to predict granule properties, such as water content and particle size, have been constructed using linear regression methods, such as multiple linear regression^6,7) and partial least squares regression (PLSR).^8–11) Recently, nonlinear regression methods, such as locally weighted partial least squares regression (LW-PLSR),¹²⁾ have been applied in various industrial processes to increase prediction accuracy.^12–17) However, they have been rarely utilized in fluidized bed granulation processes. Our previous research¹⁸⁾ demonstrated that the LW-PLSR models based on process parameters (PPs) and near-infrared spectroscopy (NIRS) were better estimators of granule water content than the PLSR models.

PP-based and NIRS-based models are standard statistical models used to predict water content. PP-based models do not require a special initial investment because PPs are measured using standard instruments, such as a thermometer, hygrometer, flowmeter, and electric balance. PP-based models are potentially equipment dependent because the relationship between the majority of PPs and water content depends on the intrinsic properties of the equipment, such as the heat transfer coefficient. To obtain a robust PP-based model, sufficient manufacturing data on different scales is required, which increases the development cost. On the other hand, NIRS-based models are generally robust against changes in manufacturing scales, but they have a known drawback of high initial investment cost of the near-infrared (NIR) spectrometer and the probe.

Economic efficiency, as well as prediction accuracy, is a key factor to be considered when choosing between PP-based models and NIRS-based models. Cogdill et al.¹⁹⁾ demonstrated through a hypothetical case study that investment in PAT generated financial benefit through the achievement of real-time release testing (RTRT), which reduces the labor and resources required for the operation of the quality unit. Thus, the economic potential of PAT in a routine production period was revealed. However, an economic case study focusing on the development cost of PAT has not been reported. To maximize the financial benefit of PAT, it is crucial to reduce its development cost.

In the previous paper, the application of the scale-free PP-based LW-PLSR model for water content monitoring was demonstrated.¹⁸⁾ The PP-based LW-PLSR model and the NIRS-based LW-PLSR model, which were constructed using a common calibration dataset, showed equivalent prediction accuracy. However, the influence of the calibration dataset on the prediction accuracy has not been revealed; therefore, further evaluation is needed to understand which properties of the dataset are crucial to building accurate scale-free PP-based LW-PLSR models.

In the present work, two types of statistical models to predict water content, i.e., PP-based and NIRS-based LW-PLSR models, were constructed using different calibration datasets and compared in terms of prediction accuracy and development cost. This study aimed to reveal the following two points: 1) how to prepare the calibration samples required to construct accurate PP-based and NIRS-based LW-PLSR models, and 2) which type of statistical model should be selected depending on the raw material cost, composition of granules, and price of the NIR spectrometer. Clarification of these two points enables to promote the efficiency of building accurate models and save the development cost of PAT, which in turn improves the financial benefit of PAT and enhances more accurate quality control.

Experimental

PP-based and NIRS-based LW-PLSR models were developed, and their prediction accuracy and development cost were compared. The development cost of PAT was defined as the cost of goods required to construct an accurate model of commercial-scale equipment. Various calibration datasets were prepared in accordance with the general process development scenario; that is, the process was scaled-up in order of laboratory, pilot, and commercial-scale. To evaluate the development cost comprehensively, the raw material cost, composition of granules, and price of the NIR spectrometer were taken into account.

Materials

A formulation composed of an active pharmaceutical ingredient (API) (Daiichi Sankyo Co., Ltd., Japan) and several excipients was granulated using three fluidized bed granulators: NFLO-5 (Freund Corp., Japan) for approx. 4-kg scale, GPCG-30 (Powrex Corp., Japan) for approx. 25-kg scale, and WSG-120 (Powrex Corp.) for approx. 100-kg scale. In the present work, the manufacturing scales were defined as follows: approx. 4 kg for the laboratory-scale, approx. 25 kg for the pilot-scale, and approx. 100 kg for the commercial-scale. Eleven granulation lots were manufactured: three lots on a laboratory-scale, two lots on a pilot-scale, and six lots on a commercial-scale. Granules were sampled throughout the granulation runs. The experimental data used in this study is provided in Table 1.

Table 1. Experimental Data for Calibration or Validation Datasets

Dataset	Equipment	Lot No.	Time	PP1	PP2	PP3	PP4	PP5	PP6	PP7	PP8	WC
Calibration	NFLO-5	1	5	2.5	69.3	9.2	66	147	35.5	41.6	34	3.7
Calibration	NFLO-5	1	10	2.5	69.9	9.5	65	147	30.6	36.8	46	4.7
Calibration	NFLO-5	1	15	2.5	70.0	9.8	67	147	29.2	34.1	53	7.9
Calibration	NFLO-5	1	20	2.5	69.6	8.8	69	148	28.5	30.4	70	7.7
Calibration	NFLO-5	1	25	2.6	69.9	9.4	67	149	28.4	29.6	73	9.2
Calibration	NFLO-5	1	29	2.5	70.0	9.6	66	148	28.4	29.1	75	10.2
Calibration	NFLO-5	2	0	2.6	67.4	10.0	70	147	42.0	42.6	16	1.9
Calibration	NFLO-5	2	15	2.0	70.6	10.1	81	148	29.3	31.6	65	9.5
Calibration	NFLO-5	2	20	1.5	70.1	10.2	81	149	28.2	30.3	68	12.5
Calibration	NFLO-5	2	25	1.5	70.1	10.1	71	148	27.7	29.4	69	15.6
Calibration	NFLO-5	3	0	2.6	76.3	10.0	50	149	41.3	39.7	20	2.2
Calibration	NFLO-5	3	5	2.5	82.8	10.0	52	150	39.2	38.3	40	2.9
Calibration	NFLO-5	3	10	2.5	84.7	10.1	55	150	36.7	36.6	48	3.5
Calibration	NFLO-5	3	15	2.0	84.7	10.0	53	150	35.1	35.5	50	4.3
Calibration	NFLO-5	3	20	2.5	84.1	9.3	69	149	35.8	34.3	55	3.5
Calibration	NFLO-5	3	25	2.5	84.8	9.5	53	149	36.2	34.1	56	4.0
Calibration	NFLO-5	3	30	2.5	85.1	9.7	49	148	36.7	34.1	58	3.8
Calibration	GPCG-30	4	10	7.9	87.5	6.5	151	148	44.8	42.9	33	2.8
Calibration	GPCG-30	4	20	8.0	88.7	6.6	150	150	43.0	41.3	38	3.0
Calibration	GPCG-30	4	30	7.9	87.9	6.7	149	148	42.1	40.4	41	3.2
Calibration	GPCG-30	4	40	8.0	88.7	6.3	149	151	41.6	40.0	43	3.3
Calibration	GPCG-30	4	50	7.9	88.0	6.7	149	150	41.0	39.6	44	3.5
Calibration	GPCG-30	4	60	7.9	88.0	6.5	150	148	40.7	39.3	46	3.4
Calibration	GPCG-30	4	72	7.9	87.9	6.7	149	151	40.3	38.8	47	3.5
Calibration	GPCG-30	5	10	8.0	87.0	5.1	180	178	41.2	41.8	34	3.1
Calibration	GPCG-30	5	20	7.9	87.9	5.2	180	175	38.0	38.9	44	3.8
Calibration	GPCG-30	5	30	8.0	88.0	5.3	179	179	36.5	37.3	51	4.1
Calibration	GPCG-30	5	40	7.9	87.9	5.4	180	181	35.5	36.1	57	4.5
Calibration	GPCG-30	5	50	7.9	87.6	5.5	180	182	34.9	35.2	61	4.4
Calibration	GPCG-30	5	59	7.9	87.8	5.5	180	181	34.6	34.6	65	4.8
Calibration	WSG-120	6	10	29.9	90.1	3.6	697	713	42.0	41.1	42	3.5
Calibration	WSG-120	6	20	30.0	90.0	4.0	697	695	39.4	38.9	49	4.0
Calibration	WSG-120	6	30	29.9	90.1	3.7	699	694	38.0	37.7	54	4.4
Calibration	WSG-120	6	40	29.9	90.1	3.8	698	703	37.2	36.9	58	4.7
Calibration	WSG-120	6	50	30.0	90.1	3.8	699	702	36.7	36.3	60	4.7
Calibration	WSG-120	6	62	29.3	90.1	4.0	699	704	36.5	36.0	63	4.8
Calibration	WSG-120	7	10	31.4	95.0	3.7	598	772	47.4	44.9	31	2.8
Calibration	WSG-120	7	20	32.4	95.0	3.7	598	752	47.1	45.0	30	2.7
Calibration	WSG-120	7	30	32.0	95.1	4.0	598	747	47.2	45.3	30	3.0
Calibration	WSG-120	7	40	31.5	95.0	3.8	600	747	47.2	45.5	30	3.0
Calibration	WSG-120	7	50	31.8	95.0	3.7	597	744	47.3	45.5	30	2.9
Calibration	WSG-120	7	60	32.0	95.0	3.7	598	746	47.5	45.7	29	2.9
Calibration	WSG-120	7	72	31.8	95.0	3.9	598	742	47.6	45.9	29	3.0
Calibration	WSG-120	8	10	28.1	85.1	3.9	749	672	38.0	38.7	42	4.1
Calibration	WSG-120	8	20	28.3	85.1	3.7	748	655	34.4	35.5	52	5.3
Calibration	WSG-120	8	30	27.6	85.1	4.0	750	650	32.8	33.7	61	6.2
Calibration	WSG-120	8	40	28.0	85.0	3.8	749	649	31.9	32.7	67	7.1
Calibration	WSG-120	8	50	27.9	85.1	3.9	749	648	31.3	31.9	72	7.6
Calibration	WSG-120	8	59	27.6	85.0	4.1	748	646	31.1	31.5	75	8.2
Validation	WSG-120	9	10	30.0	89.9	2.3	699	715	41.3	40.1	51	3.6
Validation	WSG-120	9	20	30.1	90.0	2.2	699	692	38.7	38.1	54	4.0
Validation	WSG-120	9	30	29.9	90.1	2.4	698	698	37.3	36.9	59	4.3
Validation	WSG-120	9	40	30.0	90.0	2.3	699	698	36.5	36.1	64	4.7
Validation	WSG-120	9	50	30.0	90.1	2.2	698	700	35.9	35.5	67	4.9
Validation	WSG-120	9	62	30.0	90.0	2.3	697	699	35.5	35.1	69	5.0
Validation	WSG-120	10	10	27.4	85.0	4.0	848	650	35.7	37.5	45	4.3
Validation	WSG-120	10	20	28.1	85.0	3.8	849	643	32.2	33.9	59	6.2
Validation	WSG-120	10	30	28.1	85.0	3.8	849	649	30.9	32.2	68	7.6
Validation	WSG-120	10	40	28.1	85.0	3.9	848	646	30.3	31.2	74	9.3
Validation	WSG-120	10	51	28.0	85.0	3.9	848	647	30.1	30.8	78	10.8
Validation	WSG-120	11	10	31.9	94.9	3.8	548	730	49.8	47.0	26	2.6
Validation	WSG-120	11	20	32.1	95.1	3.8	550	712	50.3	48.4	23	2.6
Validation	WSG-120	11	30	31.5	95.1	4.1	548	746	50.8	49.2	22	2.8
Validation	WSG-120	11	40	31.9	95.1	3.8	549	743	51.0	49.5	21	2.6
Validation	WSG-120	11	50	32.0	95.0	3.9	549	742	50.9	49.6	21	2.8
Validation	WSG-120	11	60	31.2	95.0	4.1	549	743	51.0	49.7	21	2.7
Validation	WSG-120	11	70	31.8	95.0	3.9	549	741	51.0	49.7	21	2.6
Validation	WSG-120	11	79	31.6	95.1	3.8	548	741	51.1	49.7	20	2.5

Time: spraying time (min), PP1: inlet air volume (m³/min), PP2: inlet air temperature (°C), PP3: inlet air humidity (g-water/kg-air), PP4: spray rate (g/min), PP5: spray air volume (NL/min), PP6: product temperature (°C), PP7: exhaust air temperature (°C), PP8: exhaust air humidity (%RH), and WC: water content of granules (%).

Reference Measurement

The water content of the granules was measured by the LOD device: HR73 (Mettler-Toledo K.K., Japan) or its equivalent HR83 (Mettler-Toledo K.K.).

Calibration and Validation Datasets

Three commercial-scale granulation lots were selected from the eleven lots as a validation dataset. From the remaining eight granulation lots, ten calibration datasets (calibration dataset A to J) were prepared, as shown in Table 2. The number of granulation lots in the calibration datasets was increased from one (calibration dataset A) to eight (calibration dataset H), considering the general process development scenario; that is, the process is scaled-up in order of laboratory, pilot, and commercial-scale. Additionally, calibration datasets I and J consisted of only pilot and commercial-scale data, respectively. PP-based and NIRS-based models were developed using each calibration dataset.

Table 2. Ten Kinds of Calibration Datasets Consisting of Different Manufacturing Scale Data

Calibration dataset	Lot No.			Number of samples
	Laboratory	Pilot	Commercial	Laboratory	Pilot	Commercial
A	1	—	—	6	0	0
B	1, 2	—	—	10	0	0
C	1, 2, 3	—	—	17	0	0
D	1, 2, 3	4	—	17	7	0
E	1, 2, 3	4, 5	—	17	13	0
F	1, 2, 3	4, 5	6	17	13	6
G	1, 2, 3	4, 5	6, 7	17	13	13
H	1, 2, 3	4, 5	6, 7, 8	17	13	19
I	—	4, 5	—	0	13	0
J	—	—	6, 7, 8	0	0	19

Calibration datasets A, B, and C consisted of one or more laboratory-scale lots, i.e., Lot Nos. 1, 2, and 3. Calibration datasets D and E consisted of three laboratory-scale lots and one or two pilot-scale lots, i.e., Lot Nos. 4 and 5. Calibration datasets F, G, and H consisted of three laboratory-scale lots, two pilot-scale lots, and one or more commercial-scale lots, i.e., Lot Nos. 6, 7, and 8. Calibration dataset I consisted of only two pilot-scale lots, i.e., Lot Nos. 4 and 5. Finally, calibration dataset J consisted of only three commercial-scale lots, i.e., Lot Nos. 6, 7, and 8. The validation dataset consisted of three commercial-scale lots, i.e., Lot Nos. 9, 10, and 11, to judge whether the constructed models could predict water content accurately on a commercial-scale. The water content range of each granulation lot is presented in Table 3.

Table 3. Water Content Range of Each Granulation Lot

Lot No.	Dataset	Equipment	Water content range (%)
			Minimum	Maximum
1	Calibration	NFLO-5	3.7	10.2
2	Calibration	NFLO-5	1.9	15.6
3	Calibration	NFLO-5	2.2	4.3
4	Calibration	GPCG-30	2.8	3.5
5	Calibration	GPCG-30	3.1	4.8
6	Calibration	WSG-120	3.5	4.8
7	Calibration	WSG-120	2.7	3.0
8	Calibration	WSG-120	4.1	8.2
9	Validation	WSG-120	3.6	5.0
10	Validation	WSG-120	4.3	10.8
11	Validation	WSG-120	2.5	2.8

To assess the similarity between calibration and validation samples, principal component analysis (PCA)²⁰⁾ was applied to the calibration dataset H. The validation samples were projected onto the subspace spanned by the first and second principal components (PCs). PCA models were constructed using Python software (Python Software Foundation).

Input Variables

PP-Based Models

Among the eight PPs provided in Table 1, the following four PPs critical to water content at different manufacturing scales were utilized, based on previous research¹⁸⁾: inlet air temperature (°C), product temperature (°C), exhaust air temperature (°C), and exhaust air humidity (%RH). These four PPs were obtained during the granulation process using standard instruments, i.e., thermometers and hygrometers. The normalized PPs were used for modeling, that is, their means were 0 and variances were 1.

NIRS-Based Models

The present work used standard normal variate (SNV)²¹⁾ as the preprocessing method and adopted the wavenumber region from 7212 to 6935 cm⁻¹ based on previous research.¹⁸⁾ This wavenumber region was selected by SFD-NCSC-PLSR, which integrates spectral fluctuation dividing (SFD), nearest correlation spectral clustering (NCSC), and PLSR, to achieve high-performance prediction.²²⁾ The selected wavenumber region includes the first overtone wavenumber region for H₂O.

The NIR spectra of the granules were measured during the granulation process using the Fourier-transform NIR spectrometer MPA (Bruker Optik GmbH, Germany) or Matrix-F (Bruker Optik GmbH) through a fiber-optic probe attached to the fluidized bed granulators. Because MPA and Matrix-F use the equivalent optical device, the NIR spectra obtained with both equipment are comparable.

Regression Method

In both PP-based and NIRS-based models, it was demonstrated that LW-PLSR models were the better estimators of water content than the PLSR models.¹⁸⁾ Hence, in the present work, LW-PLSR, which is a type of just-in-time modeling method and can cope with collinearity and nonlinearity, was used to construct both PP-based and NIRS-based models.

The difference between PLSR and LW-PLSR is the weighting rule for the calibration samples. In PLSR, a prediction model is built utilizing fixed weighting values for all calibration samples. In contrast, in LW-PLSR, the weighting values are determined for each query based on the distances between the query and the calibration samples, and a local PLSR model is built. Hence, LW-PLSR includes PLSR as a special case; LW-PLSR is equivalent to PLSR when the localization parameter is set as 0.

The LW-PLSR models were built using MATLAB^® software (MathWorks, Inc., U.S.A.). The tuning parameters of LW-PLSR, which are the number of latent variables and the localization parameter, were determined to minimize the prediction error sums of squares of the leave-one-out cross validation. The localization parameter was tuned in the range from 0 to 5.

Applicability of Water Content Monitoring on Commercial-Scale

The prediction accuracy of the constructed models was evaluated based on the root mean square error of prediction (RMSEP).

  

(1)

where N is the number of samples, and ŷ_n and y_n are the prediction value and reference value of the water content for the n-th sample, respectively.

Development Cost of PAT

The development cost of PAT ($) was defined as the cost of goods required to construct an accurate model on the commercial-scale. The required criterion of RMSEP was set to 1.0% because Alcalà et al.¹¹⁾ reported that the water content prediction model, whose RMSEP was 0.93%, was useful for monitoring the granulation process.

The development cost of PAT Cost_dev was expressed as:

  

(2)

where Cost_rm is the raw material cost ($) to obtain the experimental data required to build an accurate model, whose RMSEP is smaller than 1.0%, and Cost_inv is the initial investment cost ($), which is the price of the NIR spectrometer. Cost_inv was regarded as a variable; it was set as $2.0 × 10⁴, $1.1 × 10⁵, and $2.0 × 10⁵ considering the actual price of NIR spectrometers.

The raw material cost Cost_rm was calculated by

  

(3)

where Cost_rm,lab, Cost_rm,pilot, and Cost_rm,coml are the raw material cost ($) to obtain the experimental data at the laboratory, pilot, and commercial-scale, respectively. Then, Cost_rm,lab, Cost_rm,pilot, and Cost_rm,coml were written as follows:

  

(4)

  

(5)

  

(6)

where Cost_API is the cost of API ($/kg), G_lab, G_pilot, and G_coml are the mass of the powders charged into the granulator at laboratory, pilot, and commercial-scale (kg), MF_API is the mass fraction of API, Cost_ex is the cost of excipients ($/kg), and N_lab, N_pilot, and N_coml are the minimum required numbers of the experimental lots at the laboratory, pilot, and commercial-scale, which are necessary to construct an accurate model. In the present work, to perform an exhaustive economic evaluation, Cost_API and MF_API were set as variables; Cost_API varied from 0 to 2.0 × 10⁴ $/kg, and MF_API varied from 0 to 1. Cost_ex was fixed at 40 $/kg because it is usually much cheaper than Cost_API. Also, G_lab, G_pilot, and G_coml were set as 4.3, 24.0, and 96.2 kg, respectively.

To compare the economic efficiency of the PP-based model and the NIRS-based model, the difference in development cost was calculated by

  

(7)

where Cost_dev,PP is the development cost of the PP-based model, and Cost_dev,NIRS is that of the NIRS-based model.

Results and Discussion

Prediction Accuracy

PP-Based LW-PLSR Models

Figure 1 shows the RMSEPs of the PP-based LW-PLSR models, constructed utilizing the four PPs: inlet air temperature (°C), product temperature (°C), exhaust air temperature (°C), and exhaust air humidity (%RH). The RMSEPs of LW-PLSR models built using experimental data acquired at only the laboratory-scale, i.e., calibration datasets A, B, and C, were larger than 1.0. In contrast, the LW-PLSR model constructed utilizing the three laboratory-scale lots and one pilot-scale lot (calibration dataset D), met the criterion of RMSEP. Thus, N_lab, N_pilot, and N_coml were determined to be three, one, and zero, respectively.

Fig. 1. Prediction Accuracy of PP-Based LW-PLSR Models

The diagonal bar indicates the calibration dataset with the minimum required number of experimental data to meet the criterion of RMSEP.

PCA was applied to the calibration dataset H. The relationship between the number of PCs and the cumulative proportion is shown in Fig. 2. With the first two PCs, the cumulative proportion surpassed 0.9. The scatter plots of the first and second PCs are provided in Fig. 3. Calibration samples, Lot Nos. 1 and 2, had a considerable distance from the validation samples compared with the other calibration samples. As shown in Table 1, the inlet air temperatures in Lot Nos. 1 and 2 were around 70 °C, which was much lower than 85–95 °C in the validation samples, i.e., Lot Nos. 9, 10, and 11. According to the loading scores, as shown in Fig. 4, the inlet air temperature had an impact on both the first and second PCs. Reflecting the distance between calibration samples and validation samples on the PC1-PC2 subspace, the RMSEPs of 34.1 and 9.7% for the models constructed using datasets A and B considerably exceeded the criterion of 1.0%. On the other hand, the RMSEPs of 4.9 and 0.7% for the models constructed using datasets C and D were remarkably small because the calibration samples, Lot Nos. 3 and 4, were located near the validation samples on the PC1-PC2 subspace. The RMSEP of 0.7% for the model built by dataset D was equivalent to RMSEPs of 0.5, 0.4, 0.5, and 0.5% for the models constructed using datasets E, F, G, and H, respectively. Thus, dataset D contained sufficient data to construct an accurate model, and additional data did not improve prediction performance. Also, the RMSEP of 2.0% for the model constructed by dataset I was smaller than that of 4.9% for the model built by dataset C because the calibration samples consisting of dataset I were closer to the validation samples than those consisting of dataset C on the PC1-PC2 subspace. As shown in Table 2, dataset I consisted of two pilot-scale lots, while dataset C contained three laboratory-scale lots. These results indicated that the prediction accuracy of PP-based LW-PLSR models was dependent on the distance between calibration and validation samples on the PC1-PC2 subspace.

Fig. 2. Relationship between Number of PCs and Cumulative Proportion in PCA Conducted Using Calibration Dataset H

Fig. 3. Scatter Plots with the First and Second PC in PCA Conducted Using Calibration Dataset H, Which Was Utilized to Construct a PP-Based LW-PLSR Model

Orange, green, and blue symbols are calibration samples acquired at laboratory, pilot, and commercial-scale, respectively. Red symbol indicates validation samples projected onto the subspace spanned by the first and second PC.

Fig. 4. Loading Scores of Individual PPs in PCA Conducted Using Calibration Dataset H, Which Was Utilized to Construct a PP-Based LW-PLSR Model

Besides, Fig. 1 shows that the RMSEP of 2.0% for the model constructed by dataset I was larger than that of 0.5% for the model built using dataset E. As shown in Table 2, dataset I consisted of two pilot-scale lots, while dataset E contained three laboratory-scale lots and two pilot-scale lots. Although the calibration samples, Lot Nos. 1 and 2, were far from the validation samples compared to the other calibration samples (Lot Nos. 3, 4, and 5), they contributed to improving the prediction accuracy. Thus, it was concluded that the construction of accurate PP-based LW-PLSR models required the calibration samples with the following two features: 1) located near the validation samples on the subspace spanned by PCs, and 2) having a wide range of variations in PC scores. As provided in Fig. 4, the inlet air temperature and exhaust air humidity affected both the first and second PCs, while the product temperature and exhaust air temperature mainly had an impact on the first PC. The product temperature, exhaust air temperature, and exhaust air humidity correlate with the granule water content regardless of the manufacturing scale, as shown in Fig. 5. These results indicate that the distance between samples on the PC1-PC2 subspace derives from the difference of inlet air temperature and granule water content. The inlet air temperature is an operable PP, and the granule water content is controlled by other two operable PPs, i.e., inlet air volume and spray rate. Hence, regardless of the manufacturing scale, it is possible to obtain the calibration samples located near the validation samples on the PC1-PC2 subspace by setting the inlet air temperature and granule water content to align with the validation samples. Also, we can acquire different samples on the PC1-PC2 subspace by changing inlet air temperature and granule water content independently, which contributes to the preparation of the calibration samples having a wide range of variations in PC scores.

Fig. 5. Relationship between Each PP and Water Content of Granules in Calibration Dataset H, Which Was Utilized to Construct a PP-Based LW-PLSR Model

NIRS-Based LW-PLSR Models

Figure 6 shows the RMSEPs of the NIRS-based LW-PLSR models constructed utilizing the absorbance at the selected wavenumber region of the NIR spectra, i.e., from 7212 to 6935 cm⁻¹. As shown in Fig. 6, the LW-PLSR model constructed using three laboratory-scale lots, i.e., calibration dataset C, fulfilled the criterion of RMSEP. Hence, the values of N_lab, N_pilot, and N_coml were determined to be three, zero, and zero, respectively.

Fig. 6. Prediction Accuracy of NIRS-Based LW-PLSR Models

The diagonal bar indicates the calibration dataset with the minimum required number of experimental data to meet the criterion of RMSEP.

PCA was applied to the calibration dataset H. The relationship between the number of PCs and the cumulative proportion is shown in Fig. 2. With the first PC, the cumulative proportion surpassed 0.9. The scatter plots of the first and second PCs are provided in Fig. 7. Most of the calibration samples existed near the validation samples, which resulted in the RMSEPs of all the models to be around 1.0. It was suggested that the construction of accurate NIRS-based LW-PLSR models requires the calibration samples with the same features as PP-based LW-PLSR models.

Fig. 7. Scatter Plots with the First and Second PC in PCA Conducted Using Calibration Dataset H, Which Was Utilized to Construct a NIRS-Based LW-PLSR Model

Orange, green, and blue symbols are calibration samples acquired at laboratory, pilot, and commercial-scale, respectively. Red symbol indicates validation samples projected onto the subspace spanned by the first and second PC.

Figure 8 indicates that PC1, which was the dominant PC with a high proportion of 0.91, strongly correlated with the water content of granules, regardless of the manufacturing scale. This result means that the NIR spectra of the granules are dependent on the water content, regardless of the manufacturing equipment. Thus, it is possible to obtain calibration samples having desired scores of the dominant PC by setting the calibrated range of granule water content to align with the range of the validation samples.

Fig. 8. Influence of Water Content of Granules on the First (A) and Second (B) PC in PCA Conducted Using Dataset H, Which Was Utilized to Construct a NIRS-Based LW-PLSR Model

Comparison of Development Cost of PAT

Cost_rm of PP-based and NIRS-based LW-PLSR models were calculated according to Eqs. (3)–(6) at the determined values of N_lab, N_pilot, and N_coml (refer to section “PP-Based LW-PLSR Models” and “NIRS-Based LW-PLSR Models”). Cost_dev of both models were computed using Cost_rm and the preset values of Cost_inv according to Eq. (2). Their difference Cost_difference was calculated by Eq. (7). Figure 9 shows the value of Cost_difference depending on Cost_API, MF_API, and Cost_inv. As shown in Fig. 9, the reduction in Cost_API and MF_API made the PP-based LW-PLSR models more cost-effective compared with the NIRS-based LW-PLSR models. This is because the impact of Cost_rm on Cost_dev became smaller than that of Cost_inv on Cost_dev (refer to Eq. (2)). Besides, the area where PP-based LW-PLSR models become more cost-effective was enlarged, along with the increase in Cost_inv.

Fig. 9. Cost_difference Depending on Cost_API, MF_API, and Cost_inv

Cost_inv, the price of the NIR spectrometer, was set as (A) $2.0 × 10⁴, (B) $1.1 × 10⁵, and (C) $2.0 × 10⁵. The area surrounded by red line indicates Cost_dev,PP is smaller than Cost_dev,NIRS.

Conclusion

In the present work, two types of statistical models to predict water content, i.e., PP-based and NIRS-based LW-PLSR models, were evaluated with respect to prediction accuracy and development cost. We demonstrated that both PP-based and NIRS-based LW-PLSR models achieved high prediction accuracy on the commercial-scale, without commercial-scale data in the calibration dataset.

We clarified the key points to construct accurate PP-based and NIRS-based LW-PLSR models. It is crucial to prepare the calibration samples with the following two features: 1) located near the validation samples on the subspace spanned by PCs, and 2) having a wide range of variations in PC scores. In PP-based LW-PLSR models, scores of the dominant PCs depend on inlet air temperature and granule water content regardless of the manufacturing scale. Thus, it is possible to acquire calibration samples with desired PC scores by adjusting inlet air temperature and granule water content independently. In contrast, NIRS-based LW-PLSR models are simple; scores of the dominant PC strongly correlate with granule water content regardless of the manufacturing scale.

Besides, this practical case study revealed which type of LW-PLSR model should be selected depending on the raw material cost, composition of granules, and price of the NIR spectrometer. The reduction in cost and mass fraction of API makes the PP-based LW-PLSR models more cost-effective than the NIRS-based LW-PLSR models. Additionally, the PP-based LW-PLSR models become more cost-effective as the price of the NIR spectrometer increases.

We expect that the present work promotes the efficiency of building accurate models and save the development cost of PAT, which in turn improves the financial benefit of PAT and enhances more accurate quality control.

Conflict of Interest

The authors declare no conflict of interest.

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