Mass-balance based soft sensor for monitoring ash content at two-ply paperboard manufacturing

Quality measurements in paperboard manufacturing

Sensors measuring the paperboard quality online are attached to measurement platforms that move across the paperboard web and continuously scan and measure the product characteristics from edge to edge. The primary measurements are the basis weight, moisture content and ash percentage, which are validated via internal protocols of production plants (comparison between online and off-line measuring system). This research work utilizes the basis weight, moisture content and ash content online measurements at the reeling stage of paperboard machine. In addition, the online fiber amount measurement at the same position is considered.

The ash content of the paperboard consists of for instance filling, coating, pigmenting and other added materials. The online ash measurement is based on the energy selective absorption of x-rays. The sensor measures the absorption of the x-rays in the web, and the sensor data is automatically transformed into ash measurement and standardized. (Holik 2006) Typically the online ash measurement accuracy is in the range of 0.5 to 1 % (Hu et al. 2020).

Basis weight is the most important quality variable measured at the paper or paperboard manufacturing. The basis weight is the mass of one square meter of paperboard in grams (g^m-2). The basis weight consists of dry weight and the water weight of the paperboard. Dry weight is the mass of one square meter of paperboard in grams (g^m-2) after drying. The water weight is defined as the difference of masses of paperboard measured before and after drying or calculated based on the moisture content measurement. The online non-contact basis weight measurement is commonly based on the absorption of beta radiation or infrared (IR) absorption measurement. (Holik 2006)

Moisture content, another important quality variable, can be calculated indirectly by dividing the water weight with the basis weight value obtained. That is, the moisture of paperboard is given as a percentage of original mass. The most common online moisture measurement principle at paperboard manufacturing is based on IR technique. The principle of the IR measurement is based on the specific absorption of water molecules at the near infrared (NIR) range. The IR method can be used for paperboards at basis weight range of 10–500  g^m-2. Frequent automatic internal calibration is required in order to remove the sensor-related errors (dirt etc.). (Holik 2006)

Spectroscopic measurement can also be used for determining the amount of fiber in the paper web (Mäntylä 2017). The method utilizes a fiber-specific absorption band and several baseline wavelengths which are chosen for their response to water and fiber (organic dry matter). The measurement technique utilized in this research was based on the NIR spectroscopic method. Here, the sensor that measured the water weight (moisture content), also measured the amount of fibers of the paperboard. However, this feature of the NIR measurements was not under internal use and was therefore without continuous validation and calibration at the mill. Therefore, the fiber measurement was deemed to carry the highest uncertainty within the studied measurements.

Dataset

The data used in this research was collected using measurements at a two-ply kraft paperboard machine with product basis weight ranging from circa 125 to 240 g^m-2 during two separate collection campaigns between January and August 2020. The data was acquired at five seconds interval and saved to the automation system of the mill. For training data of the soft sensor, the shortest possible subset of data where all paperboard grades were present was selected. Hence, for the testing, a vast amount data was left available for exploring the robustness of the developed soft sensor. The both, training and testing, subsets of data included the produced paperboards in range of measured dry weight between circa 115 and 220 g^m-2 and ash content between 0 % and 7 %. The training data set omitted production breaks and it was almost free from severe measurement errors. Therefore, the data was deemed to be suitable for identifying the soft sensor. The length of the training set was circa 5 days (80 001 data points) and the length of the dataset for testing the soft sensor was circa 25 days.

Figure 1

The framework of the real-time soft sensor for monitoring the ash content.

Theoretical framework of the soft sensor

The development of the soft sensor for online monitoring of ash content was carried out following the steps and equations presented below and utilizing the selected training data described in the previous section. The proposed concept for the soft sensor is illustrated in Figure 1 with the model identification stage presented as dashed lines and the soft sensor testing presented as solid lines. Figure 1 also shows the data flow in case of training and testing stages. In Figure 1, the white background illustrates the measurements, the light grey background illustrates the training stage, and the dark grey background illustrates the testing stage of the identified model. The subscript m denotes the weight (g^m-2), whereas the subscript c refers to content (w-%). The measurements utilized in the soft sensor development were from the same measurement platform at the reeling stage of the paperboard machine, and thus there is similar lag between the measurements.

The development of the ash soft sensor includes two steps, namely the fiber measurement calibration and the ash content estimation, and it bases on the mass balance of instantaneous values of the four properties with their dependencies written as in Equation (1).

The ash content and moisture are typically expressed as percentages (%) so they need to be converted into masses (g^m-2) by multiplication of basis weight and moisture content, and basis weight and ash content, respectively. The W a t e r w e i g h t m is the weight of water in paperboard based on the measured moisture content at the reeling stage as determined in Equation (2):

where M o i s t u r e c is the measured moisture content (%) and the B a s i s w e i g h t m is the total weight of the paperboard (g^m-2) measured at the reeling stage. The dry weight (g^m-2) of the paperboard is determined by subtracting the measured water weight from the basis weight (g^m-2) as in Equation (3).

where B a s i s w e i g h t m is the total weight of the paperboard (g^m-2) measured at the reeling stage and the W a t e r w e i g h t m is the weight of water determined with Equation (2).

The absolute amount of Ash (g^m-2) is calculated as in Equation (4).

where D r y w e i g h t m is the dry weight (g^m-2) of the paperboard calculated in Equation (3) and the A s h c is the ash content (%) measured at the reeling stage.

In the first phase, the uncertainties in fiber measurement are solved. The errors can be seen by comparing the calculated fiber from the mass balance and the measured fiber from the reel. Hence, the fiber measurement requires calibration. Here, the online data from the training dataset is utilized. However, calibration can also be based on laboratory data from the basis weight, water weight (moisture) and ash aligned with the online fiber measurement data. The calibration of fiber measurement is performed with the following equations.

The amount of fiber (g^m-2) is calculated as in Equation (5) and compared with the amount of fiber (g^m-2) measured at the reeling stage. The difference (g^m-2) between the calculated and measured fiber amount is calculated as in Equation (6).

where D r y w e i g h t m is the dry weight (g^m-2) of the paperboard at the reeling stage and A s h m is the absolute amount of ash (g^m-2) calculated in Equation (4).

A linear fitting with the measured and calculated amount of fibers is carried out to determine the coefficients A and B for calculating the corrected fiber (g^m-2) values as in Equation (7). As there are one dependent variable (corrected amount of fiber) and only one independent variable (measured amount of fiber), the procedure is a simple linear regression.

where A is the slope of the fitting line, F i b e r m (measured) is the amount of measured fiber (g^m-2), and B is the y-intercept of the fitting line. Hence, the corrected fiber values were determined and compared with the calculated fiber values as in Equation (8).

The second step uses the mass balance (Equation (1)), but with the corrected fiber measurement (i. e. the linear model coefficients and measured fiber) and the online measurements from the basis weight and water weight (moisture). The calculated and estimated ash content (%) is determined using the corrected amount of fiber (g^m-2) from Equation (7) and dry weight (g^m-2) from Equation (3) as shown in Equation (9).

where D r y w e i g h t m is the dry weight (g^m-2) of the paperboard determined in Equation (3) and F i b e r m is the corrected amount of fiber calculated in Equation (7). The calculated and estimated ash content (%) are compared with the ash content (%) measured at the reel as in Equation (10).

Figure 2

The measured ash content (%) at the reel and the amount of calculated ash (g^m-2) (right axis) with the range of paperboard dry weight (g^m-2) (left axis) during the circa 5 day training period.

Figure 3

The measured ash content (%) at the reel and the amount of calculated ash (g^m-2) (right axis) with the range of paperboard dry weight (g^m-2) (left axis) during the circa 25 day testing period.

Data

The range of paperboard dry weight (g^m-2) during the training stage is presented in Figure 2 with the calculated amount of ash (g^m-2) and the ash content (%) measured at the reel. It can be observed that the selected training data included paperboard grades with a dry weight range from circa 115 g^m-2 to 218 g^m-2. No cleaning or smoothing of the data was performed and hence at day 2 there is a spike in the measured dry weight and at day 3 a notable spike is shown in the measured ash content. These and other spikes shown last generally only a few minutes and may be resulted from an error of hardware measurements or measurement internal standardization. The spikes are also shown in corrected fiber and calculated ash content figures presented in Soft sensor training section. The ash content measured at the reel and the amount of calculated ash (g^m-2) during the testing period are presented in Figure 3 with the range of paperboard dry weight (g^m-2).

Figure 4

The measured amount of fiber (g^m-2), the calculated amount of fiber (g^m-2), and their difference (g^m-2).

Soft sensor training

The soft sensor development for the redundant online ash measurement was carried out following the steps described above. The calculated fiber, the measured fiber and their difference are presented in Figure 4. As seen, there is a notable difference between the measured and calculated fiber, indicating poor calibration of the IR-based fiber measurement. As mentioned in Quality measurements in paperboard manufacturing section, this additional feature of IR measurement was utilized at the mill for the first time, and thus lacking routine calibration. Therefore, a linear fitting with the measured and calculated fiber was carried out to determine the coefficients for calculating the corrected fiber values (Figure 5). The coefficients A = 0.965 and B = −2.56 g^m-2 were achieved based on the linear fitting and new corrected fiber values were determined as described earlier. The comparison of the corrected fiber and calculated fiber is presented in Figure 6. The difference after the calibration is small, in average 0.015 g^m-2 during the training period (Table 1).

Figure 5

The linear fitting of the calculated and the measured fiber.

Figure 6

The calculated amount of fiber (g^m-2) and the corrected amount of fiber (g^m-2), and their difference (g^m-2).

The calculated ash content was determined as in Equation (9) and compared with the measured ash content (see Figure 7). As seen, the difference is small, on average only 0.01 percentage points (standard deviation 0.2) with training data (Table 1). The calculated Mean Absolute Percentage Error (MAPE) during the training period was 0.078. Therefore, the accuracy of the developed soft sensor is within the appointed target value +-0.5 percentage points in the training data, namely exhibiting the same scale of accuracy as a hardware sensor (see Hu et al. 2020). However, there are short periods when the difference is larger, due to some unknown process conditions or stock properties that cause abrupt spikes or changes to the measured values. It should be also noted that the calculations related to the training procedure utilize the measured online ash content information. The ash content information would also be available through regular laboratory ash analyses as an alternative reference measurement.

Figure 7

The calculated and the measured ash content (%) and their difference during the training period.

Figure 8

The Normal Probability Plot of the training error.

In Figure 8, the Normal Probability Plot (NPP) of the developed soft sensor error values (shown in Figure 7) during the training period is presented. The NPP is a graphical technique for assessing the normality assumption of a data set (NIST 2021). There, data with a normally distribution appears approximately along the reference line and departures from abnormal distribution introduces curvature in the plot. Quantiles of the data are matched here to the quantiles of the normal distribution. The data is sorted and plotted on the x-axis and the y-axis represents the quantiles of the normal distribution converted into probability values. As seen in the Figure 8, the modelling error NPP of the developed soft sensor with training data indicates that residuals are reasonably normally distributed, excluding the few data point considered as outliers resulting left-skewed tails to the plot. Furthermore, the estimates are almost unbiased (Table 1).

Figure 9

The measured fiber (g^m-2), the calculated fiber (g^m-2), and their difference (g^m-2) during the testing period.

Soft sensor testing

The performance of the developed soft sensor was evaluated by determining the estimated ash content and comparing it with the measured ash content using the test data described in Dataset section. Again, the calculated fiber was determined as described earlier and is presented with the measured fiber in Figure 9. As seen in the difference trend, there is a notable and varying difference between the measured and the calculated fiber. No refitting was performed, instead the corrected fiber values (Figure 10) for the testing data were calculated using the predetermined coefficients A and B, and thereafter the average difference between the calculated fiber is only 0.145 g^m-2 (Table 1). Although this error is ten times higher than in the absolute error with training data (0.015), the relative error between the corrected and measured fiber is small considering the length of the testing data (circa 25 days) and the variations in the process conditions (basis weight ranging between 125 and 240 g^m-2).

Figure 10

The corrected fiber (g^m-2), the calculated fiber (g^m-2), and their difference (g^m-2) during the testing period.

Figure 11

The estimated and the measured ash content (%) and their difference during the testing period.

The difference between estimated and measured ash content is presented in Figure 11. During the testing with measured data, the determined mean difference was only 0.12 percentage points (Table 1) with standard deviation 0.65. The calculated MAPE was 11.80. It should be noted that the large spikes and some unexplainable disturbances have increased the calculated error values. The drift seen in Figure 11 in estimated values is probably due to a fouling of the IR fiber sensor which data was utilized in the calculations. One interesting event takes place just before day 12; the dry weight is constant, but there is a significant change (increment) in the measured ash content. This is propagated into calculated fiber as a decreased value as well as to the predicted ash content. Another remarkable occurrence of the error is after day 18 where the calculated ash content starts to drift (overestimation of the ash content). However, the further root cause analyses for the observed errors was excluded from this research. The observed examples above give indication to the possible utilization of the developed ash measurement validation framework together with fault detection and diagnostics methods such as (Weidl and Dahlquist 2002) and (Karlsson 2020).

In Figure 12, the Normal Probability Plot of the ash content error values (shown in Figure 11) with test data is presented. Here, the NPP reveals reasonably normally distributed modeling error within the center line but includes also a right-skewed tail. Skewed tails to the plot are here due to the few outliers seen in Figure 11, which are caused by the errors in measurement used in the calculations described above. However, based on the NPP, the proposed model structure seems to be feasible choice for the task.

Figure 12

The Normal Probability Plot of the testing error.

Practical implications

The earlier studies with statistical models have shown that the paper properties can be predicted with good reliability. However, with prolonged periods of operation, their performance was significantly reduced (Avelin et al. 2009). In the approach presented in this paper, the known physical dependencies between the measured variables are utilized to build the mass-balance based robust soft sensor capable of describing the intragrade variations in paperboard ash content. The approach also includes a new way to utilize the existing measurement hardware at the paperboard machine allowing online determination of amount of fiber. In general, the achieved result of the single soft sensor for multiple grades can be considered very good as the independent test data involved a long time period with a large variation of paperboard grades and process conditions. The measured data was utilized without preprocessing that potentially reduces the manual work needed for implementation and maintenance the soft sensor. In addition, no recalibration of the soft sensor was made before or during the simulation with measured test data comprising approximately one month. The routine laboratory analyses and measurement quality protocols in paperboard machines consider shorter intervals, meaning that also updates to the model coefficients could take place within the studied test data. Alternatively, automated update methods or alarms for manual calibration (Lu and Chiang 2018) could also be considered to improve the soft sensor performance and robustness further.

The developed soft sensor seems to be suitable for estimating the ash content of the paperboard robustly. Thus, it potentially can also indicate the abnormal behavior of the hardware sensor, therefore having possible use in data reconciliation and fault detection. According to the results, the accuracy of the soft sensor is occasionally high enough to replace the hardware sensor during normal process situations. In abnormal process situations, such as recovering from sheet breaks, the ash content could be alternatively estimated utilizing headbox and whitewater measurements (Nobakhti and Wang 2010). Utilizing the developed mass-balance based soft sensor together with another soft sensor based on independent measurements, an ensemble model could be then built, allowing these several redundant estimators simultaneously to further reduce estimation uncertainty, thus bringing new tools to improve the process performance. As this soft sensor is intended to operate mainly without manual labor opposite to laboratory analyses, it is therefore usable in large scale autonomous processes. Validated measurement also gives more opportunities to advanced data analytics and real-time quality control.