Physicochemical parameter based estimation of discarding points for frying oil using data interpolation and principal component transformation

Abstract Data interpolation and principal component transformation (PCT) were used to compute the discarding points of a frying oil by measuring the physicochemical parameters—acid value, carbonyl value, and total polar compounds. Herein, the discarding point refers to the time point (associated with the value of each physicochemical parameter) at which the frying oil should be discarded. First, a primary visual analysis was performed for the obtained data by using line charts. Second, a curve interpolation method was used to compute the discarding points for each parameter and thus determine the discarding points for the frying oil. At 190, 205, and 220°C, the frying oil reached the discarding points at 22.1, 17.7, and 13 hr, respectively. The discarding area was also visualized on the corresponding surfaces for the originally obtained data and the interpolated data to investigate the discarding points. Third, the PCT was conducted for the three parameters at each temperature; the discarding point estimation for the three parameters could be reduced to the estimation from the first principal component (FPC), thereby simplifying this process. At 190, 205, and 220°C, the frying oil reached the discarding points when the FPCs were 10.4524, 6.2881, and −1.7629 at the time points 22.1, 17.7, and 13 hr, respectively. Finally, a verification experiment revealed that the correlation between the results obtained by our interpolation method or PCT and the verified data was higher than 0.98, which demonstrates the effectiveness of our method.

According to Chinese Hygienic Standard (Ministry of Health of the People's Republic of China, 2004), if the AV, CV, or TPC is ≥5 mg KOH/g, 50 meq/kg, or 27%, respectively, the frying oil should be discarded. Here, the values 5, 50, and 27 can be referred to as the discarding values corresponding to AV, CV, and TPC, respectively. During the actual frying process, if the time point when a parameter exactly reaches the discarding value can be obtained, the discarding time point of the whole frying oil can be determined on the basis of the considered parameters. The discarding time point can be utilized for practical application because the frying oil users can easily estimate the oil change time; additionally, the direct monitoring of the frying oil quality is beneficial for consumers, as well as food safety departments. However, it is difficult to determine the exact time point at which a parameter reaches the corresponding discarding value. Therefore, we can consider the time point at which a parameter value is just greater than or equal to the corresponding discarding value. Here, we call this time point with the corresponding parameter value as the discarding point of that parameter. The whole frying oil should be discarded when one of the studied parameters reaches its discarding point. Therefore, the discarding point of the whole frying oil is the earliest discarding time point obtained for the considered parameters (associated with all the corresponding studied physicochemical parameter values at the time point). Determining the discarding point of a frying oil is not an easy task for scientists or food industry operators (Song et al., 2017); nevertheless, we have attempted to resolve this challenging problem.
The oil's discarding point for a physicochemical parameter can be obtained by continuously measuring or predicting the parameter value on the basis of the obtained data.
However, it is rather tedious and time consuming to measure the physicochemical parameters through chemical analysis (a standard measuring method), which involves chemical reagents and sample preparation steps, and this measurement process is nearly impossible to conduct in real time (Hammouda et al., 2019;Kim, Yu, Kim, Lim, & Hwang, 2018;Shahidi Noghabi et al., 2015).
A few rapid measurements, such as piezoelectric (using sensors) and optical property measurements (Ali, Angyal, Weaver, Rader, & Mossoba, 1996;Xu, Zhu, Yu, Huyan, & Wang, 2018), are not suitable to be conducted at high temperatures; moreover, certain parameters cannot be measured because of the limited detection area of the employed equipment. Other rapid measurement methods such as gas chromatography (GC) separation and liquid chromatography (LC) separation (Ali et al., 1996;Feitosa, Boffo, Batista, Velasco, & Silva, 2019;Fritsche et al., 1998;Zribi et al., 2016) also have limitations in measuring the types of parameters because of the different physical and chemical properties.
Moreover, these rapid methods cannot directly measure the parameter values; instead, they compute them through conversion between the characteristic values of the piezoelectric frequency, spectra or chromatograms, and the parameter values. Hence, we can surmise that the standard measuring method is more accurate than the other methods because it directly measures the parameters from the fried oil sample (Chen, Chiu, Cheng, Hsu, & Kuo, 2013;Nayak et al., 2016;Wang, Su, Wang, & Nie, 2019;Yang, Zhao, & He, 2016); in addition, the standard measuring method is the most commonly used method, and it can measure many common physicochemical parameters.
On the other hand, because the real-time measurement of parameters is exceedingly difficult, research is underway to identify alternative time-saving, labor-saving, and relatively safer methods for the quick estimation of the changing trends in physicochemical parameters on the basis of the obtained data to monitor the frying oil quality in a better way. Many researchers have predicted the physicochemical parameters through regression or fitting between the physicochemical parameters and frying time, temperature, and other conditions according to the obtained data. The partial least squares regression model has been established between NIR spectra and the AV and TPC (Ma et al., 2014); thus, the AV and TPC can be predicted by observing the NIR spectra, which are measured directly from the hot frying oil. In one study (Li, Wu, Liu, Jin, & Wang, 2015), a regression model between the oil viscosity and temperature was evaluated. In another study (Wang, Su, Wang, & Nie, 2019), a regression model was established between water/oil contents and LF-NMR parameters. In yet another study (Franklin, Pushpadass, Neethu, Sivaram, & Nath, 2017), a regression analysis was performed between the frying time and the parameters-moisture content, fat content, expansion ratio, apparent density, browning index, and hardness-at 125, 135, and 145°C.
Additionally, in various studies (Franklin et al., 2017;Shahidi Noghabi et al., 2015), artificial neural networks (ANN) have been used to predict physicochemical parameters. Considering temperature and time as independent variables, and moisture content, fat content, expansion ratio, apparent density, porosity, browning index, and hardness as dependent variables, the ANN has been used to fit the relationship (Franklin et al., 2017). Considering time, temperature, and concentration of antioxidant tert-butylhydroquinone as independent variables, and peroxide value (PV), CV, and TPC as dependent variables, the ANN has been used to fit the relationship (Shahidi Noghabi et al., 2015). All of the abovementioned studies only predict the parameter value and do not give a time estimate for a particular parameter to reach the discarding point in their frying environment, except for the following studies reported by Ravelli, Matsuoka, Modesta, and Vieira (2010) and Song Kim Kim and Lee (2017), wherein Ravelli et al. (2010) mainly discussed whether trained panelists could identify the deteriorated frying oil with the same effect as the sensory evaluation does. In their experiments, potato chip portions (400-550 g) were fried in 3.5 L of soybean oil; the frying time of each portion ranged from 8 to 15 min; and fresh oil was added as makeup oil after each frying instance to maintain the original amount of oil in the fryer. The selected and trained panelists gave the conclusion that the disposal time of the soybean oil used for the deep frying of potato chips at a maximum temperature of 180°C is 4 hr by identifying the frying oil on the basis of color, aroma, viscosity, and flavor. Their conclusion was consistent with the partial physicochemical parameters evaluated via applied sensory analysis. Song et al. (2017) believe that determining the discarding points of the used frying oils is not an easy task for scientists or food industry operators. In their experiment, the frying pot was filled with 3.5 kg of fresh soybean oil and heated to 180°C for 170 hr; then, chicken frying was performed 130 cycles. They studied the changes in certain physicochemical parameters during the oil-heating and frying cycles. They concluded that the TPC values ≥24% were obtained after 109 hr of heating the oil and after 100 cycles for the oil used to fry chicken, and 24% of the TPC was the discarding criterion in a few countries.
From the above discussion, first, the discarding point estimation for a frying oil is quite difficult, whether by continuous measurement or by prediction on the basis of the obtained data. Most of the literature studies only predict the investigated physicochemical parameters for the frying oil and do not explicitly determine the discarding time points for the parameters or for the whole frying oil. Second, from the two studies (Ravelli et al., 2010;Song, Kim, Kim, & Lee, 2017) that reported the discarding time points, different discarding time points can be obtained by varying the operating environments (e.g., oil amount, temperature, types of frying food, or physicochemical parameters). If certain standard and specific frying environments and operating processes could be developed, the quality monitoring of the frying oil would become quite convenient, and the estimation of the discarding point would become quick.
Before formulating a specification, we continue to estimate the discarding points in various environments, and this is of great significance. Therefore, we measured relevant data in large intervals of time points via the standard measuring method, which is relatively accurate, and then predicted the physicochemical parameter values in certain intervals of time points to provide relatively accurate discarding points and monitor the frying oil quality. Moreover, a comprehensive study of several physicochemical parameters revealed that the discarding time points for multiple parameters at the same temperature were not consistent with each other. Therefore, finding a comprehensive indicator based on multiple parameters to predict the discarding points for the whole frying oil is also extremely important. Herein, PCT was used for finding the comprehensive indicator.

| Experimental procedure
The temperatures were set to 160 ± 2, 175 ± 2, 190 ± 2, 205 ± 2, and 220 ± 2°C. The experiments involved setting the oil bath at each of the aforementioned temperatures; 15 L of the soybean oil was poured into the constant temperature oil bath, continuously frying every day for 31 hr. In the entire frying process, the oil temperature was maintained constant, and six batches of potato chips (each batch was 100-200 g) were fried in 1 hr. Each batch of potato chips was fried for 3 min, and then, the fried oil was kept at the same temperature for 7 min to maintain the frying conditions stable. After the oil was heated to the specified temperature, the first 150 ml of the oil sample was taken out, and the corresponding time point was denoted as the 0th hour. Next, the first six batches of potato chips were fried; then, another 150 ml of the oil sample was taken out, and the time was denoted as the 1st hour. These were repeated until the 30th hour was denoted. Totally, 31 oil samples were obtained.
Additionally, no new oil was added throughout the frying process as the initial amount of oil that was poured into was sufficient. Each oil sample was cooled to ambient temperature, filtered to remove the solid residues, and then stored in a sample bottle at −20°C for measuring the corresponding physicochemical parameters by using a chemical method. From the 0th to 30th hour, at each temperature, 31 oil samples were taken out for the measurement of each parameter, and 155 oil samples were taken out altogether at five temperatures for measuring the three parameters.

| Line chart visualization of obtained data
The obtained data were analyzed in both cases through line charts.
One type of line charts shows the changes in one parameter at five temperatures. Another type of line charts shows the changes in the three parameters at each temperature.

| Surface visualization of the parameters and the corresponding discarding area
On the basis of the originally obtained data, the interpolated data were computed at smaller time points from 0th to 30th hour (with 0.1 hr incremental step) and at low-temperature points from 160 to 220°C (with 1°C as the incremental step) by using MATLAB.
Then, two surfaces of the originally obtained data and the interpolated data were drawn. Moreover, we presented the discarding area on the surface with red color and also labeled several discarding points on the surface to see the distribution of the discarding points.

| PCT for discarding point estimation
At each temperature, the PCT was carried out on the obtained data for the three parameters by using MATLAB. The contribution rates of the FPC were exceedingly high, and this indicates that the FPC could almost represent all three parameters. Therefore, the discarding points could be estimated in terms of the FPC. We also obtained the transformation expression between the FPC and the three parameters to determine the discarding values from the new parameter values.

| Line charts for each parameter at different temperatures
The line charts for the three parameters-AV, CV, and TPC-recorded at 160, 175, 190, 205, and 220°C, are shown in Figures 2-4, and the figures show that the AV, CV, and TPC increase with the increase in time and temperature. The CV grows in an oscillating manner, whereas the AV and TPC grow gradually.

F I G U R E 6 Three parameters at 175°C
F I G U R E 7 Three parameters at 190°C

| Line charts of different parameters at the same temperature
The line charts for AV, CV, and TPC, recorded at 160, 175, 190, 205, and 220°C, are shown in Figures 5-9.
When the temperature was low, the lines were relatively flat for the AV and TPC; thus, the parameters changed slowly. With an increase in temperature, the lines became steeper, and the parameter values sharply increased. However, the CV behaved differently: no matter the temperature is high or low, the change is quite intense.
The AV gradually increased with an increase in temperature in the low-temperature range; however, with further increase in the temperature, the rate of change was slightly higher. The change in TPC was very sharp when the temperature was increased from 190 to 220°C.

| Discarding point estimation at different temperatures via data interpolation
All the discarding points found through data interpolation for the three parameters are shown in Tables  For 160 and 175°C, we could not find any discarding points within 30 hr (Tables 1 and 2). With an increase in temperature, the discarding time points shift to lower values (Tables 3-5); then, the discarding time points for the CV were greater than those for the other two parameters at 205 and 220°C, and this shows that the CV increased relatively slowly when the temperature was increased. However, the TPC reached the discarding point first. This implies that at high temperatures, the TPC increased faster than the other two, and therefore, it decides the discarding point for the frying oil; this may be the reason that many rapid measuring devices are only designed to measure the TPC.

| Surface visualization of the three parameters and their discarding area
To estimate the AV, the surface for the originally obtained data and the interpolated surface are presented in Figures 10 and 11.
The surface graph in Figure 10 is not quite smooth; nevertheless, the whole surface is relatively uniform. This implies that the AV evenly increased. For the marked discarding points in Figures 10 and 11, X represents time, Y represents temperature, and Z is the interpolated AV. The discarding time decreased with the increase in temperature. Additionally, these marked discarding points were above the horizontal level of Z ≥ 5 because the standard discarding value was 5. Moreover, we constructed a red area on the surfaces to indicate the discarding region in which all AVs were ≥5.
Furthermore, the curves at a particular temperature and at a particular time point were sliced out from the interpolation surface, as shown in Figures 12 and 13.
In fact, from the interpolation surface, we could obtain the sliced curve at any temperature from 160 to 220°C with an interval of 1°C, or we could obtain the sliced curve at any time from the 0th to 30th hour with an interval of 0.1 hr. Therefore, we could observe the change in the parameters at shorter time intervals or lower temperature values. In Figure 12, the last small segment of the line slightly bends down, indicating a decrease in the parameter values; this decrease may be because the last two values at 175°C in the original data showed a downward trend, thereby affecting the interpolation.
In Figure 13, the last part of the line implies that the AVs were ≥5, and the oil should be discarded.
For estimation of the CV, the surface of the originally obtained data and the interpolated surface are presented in Figures 14 and 15.

F I G U R E 1 2 Sliced curve of the acid value at 184°C
F I G U R E 1 3 Sliced curve of the acid value at the 28.2 hr F I G U R E 1 4 Surface of time-temperature-carbonyl value on the original measured data Figure 14 shows that the surface growth is not uniform; the surface in Figure 15 is also not too uniform and has some irregular pits.
This phenomenon also indicates that the CVs at various temperatures and time points were somewhat different from the AVs and the TPC. The standard discarding value is 50, and the Z coordinates of the marked points were ≥50. Moreover, with an increase in temperature, the discarding point decreased in value. Similarly, we have labeled the red discarding area on surfaces to indicate the discarding region in which all CVs were ≥50.
The similarly sliced curves for the CV are shown in Figures 16 and 17.
As shown in Figure 16, at 184°C, the CV increased, accompanied by oscillations. In Figure 17, at the 28.2th hour, the CV rapidly increased at temperatures below 180°C and above 200°C and gradually increased in the temperature range 180-200°C. In Figure 17, the last part of the line indicates that the CVs were ≥50, and the oil should be discarded.
For the TPC, the surface of the originally obtained data and the interpolated surface are presented in Figures 18 and 19.
The surfaces for the TPC were more similar to those for the AVs; only their standard discarding values were different.
The similarly sliced curves for TPC are shown in Figures 20 and 21.
The first few values at 175°C were smaller than those at 160°C in the originally obtained data; therefore, after interpolation, the sliced curve in Figure

| Discarding point estimation based on PCT
The cumulative contribution rate for the FPC is shown in Table 6.
The contribution rate of the FPC was exceedingly high, indicating that the FPC could almost represent all of the three parameters.
We selected the FPC to analyze the discarding points and denoted it as y. Additionally, we obtained the expression between y and the three parameters (AV as x 1 , CV as x 2 , and TPC as x 3 ), as presented in Table 7.
The coefficients of the CV were relatively larger than those of the other two, and their contribution to the first component was the greatest. The coefficients of the AV were relatively smaller, and their contribution to the first component was the lowest. The coefficients of the TPC were in between the other two, except in the expression at 220°C. These coefficients suggest that the CV was sensitive and that it played a great role in the PCT. When the temperature reached 220°C, the change in the TPC was severe.
Afterward, at a certain temperature, we could choose the three parameter values from the last columns in Tables 3-5 as x 1 , x 2 , and x 3 ; we subtracted the mean values of the corresponding original data in terms of the rule of the PCT and plugged them into the expression given in Table 7; y could be computed as the discarding point for the FPC. The computed results are presented in Table 8.

| CON CLUS ION
This study evaluated the AV, CV, and TPC during the frying process from 0 to 30 hr at 160, 175, 190, 205, and

ACK N OWLED G M ENTS
This work was supported by Beijing Municipal Science and Technology Project (Z171100001317004), Natural Science Foundation of China (11101012, A011402), and Natural Science Funds of the Beijing Municipality (9192008).

CO N FLI C T O F I NTE R E S T
The authors declare that they do not have any conflict of interest.

E TH I C A L A PPROVA L
This study does not involve any human or animal testing.

I N FO R M E D CO N S E NT
Written informed consent was obtained from all participants.