1.2. Existing Syrup Brix Measurement Methods Research
At present, several measurement methods have been proposed, among which the conductivity method, refractive index method, density method, and microwave method are the most common. The syrup is a mixture containing electrolytes that ionize positive and negative ions in water and thus have electrical conductivity, so the syrup brix can be calculated by measuring the electrical conductivity in the syrup solution. Marzougui et al. [
2] developed a method in which gamma-irradiated solid table sugar was investigated for dosimetry, and the absorbed dose was estimated by measuring the conductivity of aqueous solutions of dissolved irradiated solid sugar. The results showed that the electrical conductivity of the solution increases linearly with the dose absorbed. However, in actual production, the purity of the cane juice that is squeezed from sugarcane of different varieties and different origins varies, and the composition and quantity of the electrolytes contained also vary. Therefore, the conductivity of the syrup mixture fluctuates within a certain range during the production process, that is, there is a large error in the brix value when measured by the conductivity. In contrast, it is more accurate to use the refractive index to measure the syrup brix. Li et al. [
3] developed a refraction laser–CCD molasses malleability sensor with a high stability laser light source and a high-performance CCD charge-coupled device, which can automatically detect the syrup brix and add temperature compensation with a measurement error of 0.3%. Dongare et al. [
4] presented a mathematical model of the optical geometry of a prismatic refractometer for syrup brix measurement, and the simulation and experimental results showed a good correlation. However, due to the poor penetration of the refractometer, a surface layer of 0.1 μm thickness is sufficient to greatly change the intensity of the light transmission. Therefore, when a small amount of dirt is generated on the lens and not cleaned in time, the refractive index will change significantly, which will seriously affect the accurate measurement of the instrument. The density method uses a pre-developed mathematical model of syrup brix and density, including comparison tables, empirical data fitting formulas, etc., in order to obtain the syrup brix measurement by looking up the table or substituting it into the calculation formula after measuring the density of syrup [
5]. Nunak et al. [
6] developed an instrument to measure the concentration of sugar solutions using a relative density. The results showed that the instrument can accurately analyze the concentration. Huang et al. [
7] designed an online automatic detection system for syrup brix based on the density method and PLC technology, and added linear programming correction and temperature compensation, which can obtain a more accurate brix value. Although the density method has a simple measurement principle and low cost, the measurement range is narrow, the structure of the measuring device is complicated, and the measurement accuracy depends on the accuracy of the processing and assembly of the measuring device, which easily leads to large measurement errors and poor stability. Microwave technology can be used as an alternative method for food analysis [
8]. The microwave method has the advantages of a simple mechanical structure, no harm to the sample, and high measurement accuracy. In addition, due to the strong penetration of the microwave, the micro dirt generated in the measurement site has little impact on the measurement, so it has high stability. Hosseini et al. [
9] proposed a new technique that enables a microwave resonator to perform a volume fraction analysis of complex dynamically changing liquids, while maintaining the original characteristics of the microwave resonator sensor. Multiple simulations and experimental results validated the ability of this technique to monitor ethanol, water, and sugar concentrations in real time during fermentation. However, this method cannot yet be used in the sugar production process. Liu et al. [
10] designed a microwave coaxial resonator sensor to characterize the syrup brix by measuring the resonant frequency and quality factor of the syrup, which exhibited an excellent performance when measuring brix, with an accuracy equivalent to that of the brix meter produced by Germany’s proMtec in the actual sugar manufacturing process [
11]. However, this method did not investigate the model used to calculate the syrup brix.
As can be seen, the current measurement of syrup brix is mainly focused on finding more suitable measurement methods, and little research has been conducted in order to improve the accuracy of the brix calculation model. On this basis, this paper adopts the microwave method to measure the syrup brix, using the microwave coaxial resonant cavity in [
10] as the measurement sensor, and conducts further research to improve the accuracy of the sugar brix calculation model.
When the microwave method is used for measurement, the syrup brix is usually calculated by the model based on the mixed dielectric law. The syrup is a mixed solution; hence, the complex permittivity of each component is different. According to the mixed dielectric law, when the proportion of each component is different, their complex permittivity also varies [
12]. According to this feature, a theoretical calculation model can be established to derive the brix from the resonant frequency and quality factor. However, measurement errors are caused by the measurement hardware and the approximate processing of the theoretical calculation model based on the microwave perturbation method and mixed dielectric law. The accumulation of these errors will lead to relatively large measurement errors. A stable measurement system will reduce the fluctuations in the measurement errors of the resonant frequency and quality factor. Therefore, the negative impact of these errors on the measurement accuracy can be reduced or eliminated by directly establishing the numerical values of the resonant frequency, quality factor, and the syrup brix. Regression fitting is a method that is widely used to establish measurement models in measurement technology. Using the regression fitting method to establish the regression equation of the relationship between the resonant frequency, quality factor, and brix, a calculation model can be developed based on multiple regression to reduce the negative impact of the above errors. Multiple regression analysis describes the mathematical relationships between the overall trends in the resonance parameters and syrup brix. However, these cannot be accurately predicted when the data significantly deviate from the fitting curve.
The support vector machine (SVM) is a new machine learning algorithm that was proposed by Vapnik et al. based on the statistical learning theory, which can be used for the classification of small samples [
13]. The SVM performs the nonlinear mapping of the input vector from the low-dimensional to the high-dimensional feature space. It adopts the principle of structural risk minimization to improve the generalization ability of the model and avoid the “dimensional disaster”. For regression fitting, Vapnik et al. [
14] proposed the insensitive loss function
based on the SVM classification to enable the construction of a support vector regression (SVR) algorithm with superior performance. Compared with other algorithms, such as random forest (RF), radial basis function (RBF), and artificial neural network (ANN), SVR is more suitable for complex and nonlinear regression problems when they are based on statistical supervised learning theory and structural risk minimization. It has a sound theoretical foundation, strong fitting ability, strong generalization ability, and strong robustness [
15]. SVR has been applied to solve many problems. Castro-Neto et al. [
16] presented the application of a supervised statistical learning technique called Online-SVR, which was used to predict the short-term traffic flow; the results showed that its performance was better than other models. Liang et al. [
17] proposed a fuzzy multilevel algorithm based on PSO to optimize SVR in order to realize the real-time dynamic evaluation of drilling risk; the results showed that the accuracy of the PSO–SVR model can reach 99.99%, which is obviously better than that of the multilayer perceptron neural network model. Quan et al. [
18] established an SVR model by using the measured water temperature data in a reservoir for many years, and the genetic algorithm was introduced to optimize the parameters; the results showed that this model could predict the vertical water temperature and water temperature structure in the reservoir area well. Benkedjouh et al. [
19] presented a method that was based on nonlinear feature reduction and SVR in order to assess the condition of tools and predict their life; the results showed that the proposed method was suitable for assessing the wear evolution of the cutting tools and predicting their remaining useful life. Paniagua-Tineo et al. [
20] presented a method based on SVR for daily maximum temperature prediction, and different meteorological variables were obtained, including temperature, precipitation, relative humidity, air pressure, the synoptic situation of the day, and the monthly cycle. By using this pool of prediction variables, it was shown that the SVR could accurately predict the maximum temperature 24 h later. Li et al. [
21] developed an improved gray wolf optimization algorithm to optimize the SVR in order to estimate knee joint extension force accurately and timely; the indexes showed that this model provided the best performance and was better than other models. In summary, it can be seen that SVR can be used for syrup brix prediction.
To improve the accuracy of the syrup brix calculation model, this paper studies an SVR-based syrup brix calculation model, optimizes the SVR using improved particle swarm optimization (PSO), and establishes a one-to-one mapping relationship between the resonant parameters and syrup brix. Compared with other calculation models, the PSO–SVR model could obtain the best performance using different evaluation indexes.