Parameter optimization of double‐blade normal milk processing and mixing performance based on RSM and BP‐GA

Abstract Temperature stability was taken as the evaluation index of processing performance, and the three factors that influence normal milk processing and mixing performance were optimized by response surface analysis and BP‐GA neural network algorithm. Analysis results showed the influence order of the factors on temperature stability was as follows: shape > height > rotating speed. In the optimization by response surface methodology (RSM), when rotating speed was 30 r/min, height was 31 mm, and blade shape was a full trapezoid, predicted value and actual value of variable coefficient were 0.0046 and 0.0044 respectively, with relative error of 4.5%. In the optimization by BP‐GA neural network algorithm, when rotating speed was 34 r/min, height was 25 mm, and blade shape was a full trapezoid, the predicted value and actual value of variable coefficient were 0.0036 and 0.0035 respectively, with relative error of 2.9%. The predicted root‐mean‐square error of the model by the BP‐GA neural network algorithm was 0.0013, determination coefficient was 0.9960, and relative percent deviation was 8.4961, which showed better performance than the RSM model. Thus, the BP‐GA neural network algorithm has better fitting performance, and then, the optimal working parameter combination was confirmed, which could provide reference to improving double‐blade normal milk processing and mixing device design and milk processing quality.


Response surface methodology (RSM) and Artificial Neural
Network (ANN) as nonlinear optimization methods are frequently applied in structural optimization design of machine components and optimization of working parameter combination. For example,  and Winiczenko, Górnicki, Kaleta, Martynenko, et al. (2018) optimized the ANN topology for predicting the rehydrated apple cubes color change using RSM and GA. The result turned out that the optimal ANN topology can be considered as more precise for predicting color change in the rehydrated apple cubes. Samuel and Okwu (2019) simulated and optimized the productive rate conditional parameter of coconut oil ethyl esters and did test verification by using RSM and ANN. Pilkington, Preston, and Gomes (2014) extracted artemisinin from artemisia annua using RSM and ANN and optimized combination of extraction temperature, extraction time, and solvent parameters. Sinha, Chowdhury, Saha, and Datta (2013) established a prediction model for simulation and optimization of dye extraction by RSM and ANN. Muthusamy, Manickam, Murugesan, Muthukumaran, and Pugazhendhi (2019) extracted pectin from helianthus annuus (sunflower) heads using RSM and ANN modeling by a genetic algorithm approach. Yu, Huang, Lin, Kuo, and Shieh (2019) used Artificial Neural Networks and Response Surface Methodology to compare the effection of ultrasound-assisted extraction of chlorogenic acid from lonicera japonica. The above research showed that RSM and ANN can establish the extraction process model very well, and the optimization effect of the ANN is better in the process of optimizing the extraction condition parameters. In addition, some scholars used the response surface method and the artificial neural network to finish the research on the machining performance of martensitic stainless steel, surface roughness of keyway milling, surface finish analysis of wire electric discharge machined specimens and cutting parameters in turning of gray cast iron. On the basis of modeling, the machining performance of mechanical materials was analyzed and optimized, and the experimental verification was carried out (Bhupinder & Misra, 2019;Ghosh, Mandal, & Mondal, 2019;Laouissi, Yallese, Belbah, Belhad, & Haddad, 2019;Zerti, Yallese, Zerti, Nouioua, & Khettabi, 2019). Tang, Huang, and Fang (2011) did optimal design on face plate structure of the numerical control rotary table by applying genetic algorithm and BP neural network. Yang, Zhan, Wu, Wang, and Bao (2015) did optimal design on the cold extrusion dies of bearing inner race on automobile hubs based on orthogonal test, BP neural network, and genetic algorithm. Du, Li, Wang, Wu, and Lin (2017) did size optimization on chief bars of small-wing flank-type forest fruit collection device using genetic algorithm. Chen, Xue, et al. (2015) optimized the shape of boom truss and the cross-sectional dimensions of spray boom by multi-island genetic algorithm. Chen, Li, Cao, and Zheng (2015) established a multi-objective optimization mathematical model taking vertical vibration acceleration and elevation angular acceleration as indexes by applying genetic algorithm. Ma, Li, He, Meng, and Liang (2006) studied the performance of stripping elements on sugarcane harvester based on BP neural network.  studied the performance parameters of black tea fermentation using extreme learning machine algorithm. Yang et al. (2018) optimized the root-lifting speed of cassava harvester based on improving spider cluster algorithm. Wang, Dong, Wu, and Fang (2017) optimized corn planting density and fertilization quantity based on BP neural network. Gao et al. (2017) optimized the vacuum freeze-drying process of bitter melon slices based on genetic algorithm. The above research showed that the neural network algorithm could complete the optimization of the mechanism parameters and the working performance parameters combination. Therefore, based on the research methods mentioned above, taking the designed double-blade ordinary milk processing and mixing device as test platform, and temperature stability as evaluation index for processing performance, the parameters of the ordinary processing and mixing device, such as rotating speed of agitator blades, height from agitator blades from barrel bottom, shape of the blades, were optimized by using RSM and BP-GA. At last the optimal parameter combination was obtained and the optimization method for the device was determined, through comparison analysis, which offered reference to improving design of normal milk processing and mixing device and quality of processed milk.

| Materials and equipment
2.1.1 | Overall structure of the normal milk processing and mixing device and working principle The overall structure of the normal milk processing and mixing device is shown in Figure 1. The device is mainly composed of an F I G U R E 1 Schematic diagram of the structure of mixing device for normal milk processing. The main components are as follows: 1. Water pump, 2. Solenoid valve, 3. Liquid level meter, 4. Water outlet, 5. Cleaning nozzle, 6. Interior barrel for processing and storage, 7. Mixing electric motor, 8. Mixing shaft, 9. Electric cabinet, 10. Exterior barrel for water circulation, 11. Milk supply pipeline, and 12. Body frame interior barrel for processing and storage, an exterior barrel for water circulation, a mixing electric motor, a mixer and a water pump.
The device can accomplish milk pasteurization through heating and cooling by water circulation.
In working process, the mixing device for constant milk processing mainly mixes normal milk through a motor-driven mixer and improves temperature conductivity, including heating and cooling of normal milk. Water bath is adopted in heating: first, raw milk is poured into the interior barrel, and then, the water pump pumps water to the exterior barrel, in which the heating rod heats the water. Temperature is transferred to milk through barrel wall, when the detected milk temperature by temperature sensor reaches the set value, the heating process is stopped. The cooling process adopts the method of water circulation, after pumping water to the exterior barrel, water temperature gradually reduces and cools the milk through barrel wall, and then, the discharged hot water flows into water storage tank through water outlet for reutilization; when milk temperature reduces to the set value, the normal milk processing is finished.

| Temperature detection system
Normal milk processing testing platform is composed of temperature detection module, single-chip microcomputer minimum system and human-computer interaction module, as is shown in Figure 2. It mainly measures temperature at different positions during normal milk processing, with sampling frequency of 1 Hz and 12 collection points, temperature measurement range of −55 to 125°C. Collected data are stored by a USB flash disk. A touch screen is used in operation system.
The system microprocessor is an 8-bit STC89C54RD+ microprocessor produced by STC micro Technology Co., Ltd. By considering precision of temperature measuring in processing and collection of temperature data at different heights, there were three groups of temperature sensors, each group having four sensors. The length of the first group sensors was 436 mm, that of the second group sensors was 287 mm, and that of the third group sensors was 138 mm.
Temperature sensors were DS18B20 monobus temperature sensors. In order to improve the anti-interference ability of the system, an opto-isolator unit was added in the testing platform by using Omron optocoupler relay G3VM-402C; and the TK6071iQ type touch screen produced by WEINVIEW CO., LTD was adopted to display and store temperature data. RS-485 communication network was used to connect the touch screen and single-chip microcomputer. Configuration software was used to make "project files," which can be downloaded to the touch screen through PC and communication port of the touch screen; the programming software of the touch screen was EB8000 and the collected data can be transferred to Excel and stored to the USB flasher disk.
The software system is a distributed structure, in which the single-chip microcomputer mainly realizes reading of real-time temperature data, the touch screen stores and displays data, and

| Sample collection and equipment
The milk used in the test was produced in the third cattle farm of 121

regiment, Eighth Division of Xinjiang Production and Construction
Corps, the mixing device for constant milk processing (self-designed), temperature detection system (self-designed), laptop (win10), agitator blades of three shapes (full trapezoid, full rectangular, and trapezoid frame, which were self-designed).

| Test design
A three-factor and three-level test was designed by taking rotating speed of agitator blades, height from agitator blades to barrel bottom, shape of agitator blades as level factors, and temperature stability as the evaluation index. The code table of test factors are shown in Table 1.
F I G U R E 2 Block diagram of milk processing testing platform. It is composed of temperature detection module, single-chip microcomputer minimum system and human-computer interaction module

| Evaluation index
Temperature stability in this test is described by variable coefficient.
The smaller the variable coefficient is, the less the degree of variation of data under this level combination would be, showing better heating and cooling stability of the material processing system.

Variable coefficient is calculated by Equation 1.
where CV is variable coefficient; S is the standard deviation of samples; V is the mean value of samples.

| Establishment of BP-GA integrated optimization algorithm
Back Propagation (BP) neural network algorithm is a kind of neural network of feedforward learning algorithm and back propagation algorithm, which can effectively solve the problem of connection weight of hidden layer in the multi-layer neural networks and improve the self-learning and organization ability of neural network (Liu, Wu, Wang, Tan, & Wang, 2012;Zhang et al., 2014). Genetic The specific steps of the BP-GA integration optimization algorithm are as follows:

Population initialization
The individual coding method is a real code, and each individual is a real string, which is composed of input layer and hidden layer connection weight, hidden layer threshold, hidden layer and output layer connection weight, and an output layer threshold. The individual weight and the threshold value of the individual are initialized.

Fitness function
According to the initial weight and threshold of BP neural network obtained by individuals, the output of BP neural network is trained with training data, and the absolute value of error between prediction output and expected output is taken as individual fitness value F. The formula is as follows: where n is output points for the network; y i is the expected output of the i node. o i is the predicted output of the i node, k is the coefficient.

Selection operation
The genetic algorithm operation selection roulette method, which is a selection strategy based on fitness ratio. The selection probability p i of each individual i is as follows: where F i is the fitness value of individual i, N is the number of population individuals.

Cross operation
The cross operation method adopts real number cross operation, chromosomal a k of position k, and chromosomal a l of position l cross operation at the position j is as follows: where b is a random number between [0, 1]. where a max is the upper bound of the gene, a min is the lower bound of the gene, r 2 is a random number, g is the number of iterations, G max is the maximum number of evolution, and r is the random number be-

| RE SULTS AND ANALYS IS
A three-factor and three-level test was designed by taking rotating speed of agitator blades, height between agitator blades and barrel bottom, shape of agitator blades as level factors, and temperature stability as the evaluation index. There were 17 test points, including 12 analytic factors, and 5 zero errors of estimate. Based on the principle of milk pasteurization, in this test, the milk with volume of 90 L and normal temperature as initial temperature was heated to 80°C and cooled to 39°C. In the process, the designed temperature detection system was used to obtain the real-time temperature. In the process of data processing, the temperature values on the 12 sensors of the temperature detection system were exported, and 20 time points were randomly selected and the data of 12 sensors corresponding to each time point were extracted, namely a data matrix of 20 × 12 was extracted. The extraction process requires that every two time intervals should be equal, and the 20 sets of data include the whole process of temperature rise and fall. The data of 12 sensors corresponding to each time point were processed to calculate the coefficient of variation, and the 12 coefficients of variation were averaged to obtain the coefficient of variation, and the stability of temperature change was evaluated. Test scheme and response values are shown in Table 2.

| Analysis on influence effect of factors
In order to directly show the influence of the three factors on variable coefficient, the horizontal index relationship shown in (as is shown in Figure 7), and the color of the slice and grids describes the values of variable coefficient. Table 2 and Figure 5 show that the overall influence trend within the set parameters is: as the stirring paddle speed increases, the coefficient of variation first decreases and then increases. When the speed is 30-40 r/min, the coefficient of variation is small, namely the temperature of the milk is stable.
The coefficient of variation is better; when the height of the paddle blade is 25-35 mm from the bottom of the barrel, the coefficient of variation is small; when the shape of the paddle blade is trapezoidal full face and rectangular face, the coefficient of variation is small.
The regression model reflects the influence of rotating speed, height, blade shape on variable coefficient (temperature stability), the higher the variable coefficient is, the greater temperature change would be, and that is not good for pasteurization of normal milk. Table 3 shows that the influence order of all factors on variable coefficient is as follows: shape > height > rotating speed. The response surface of influence of the interaction among factors on variable coefficient is shown in Figure 8a,b,c. The interaction effect between rotating speed and height was significant, while the interaction effects between height and shape, shape and rotating speed were not significant.
F I G U R E 6 Relationship between factor levels and coefficients of variation. X 1 means rotating speed of agitator blades; X 2 means height from agitator blades to barrel bottom; X 3 means shape of agitator blades Cor total 2.098 × 10 -3 16 *p < .05 (significant). **p < .01 (highly significant).
TA B L E 3 Variance analysis results of response surface model Figure 8a shows that, with the increase of height from 20 to 40 mm, the variable coefficient reduced before an increase; when the height reached 30 mm, the variable coefficient presented the minimum, at this time, the temperature had best stability; when rotating speed increased from 25 to 45 r/min, the variable coefficient reduced before an increase; when rotating speed reached 35 r/min, the variable coefficient reached the maximum value, and at this time, the temperature difference in the temperature field of the mixing system was the least, showing best temperature stability; Figure 8b,c shows the response surface of interaction effects between blade shape, rotating speed, and height, which were consistent in variation tendency. It can be seen that, among the three kinds of blades, the trapezoid frame had greatest influence on temperature stability, full trapezoid showed best effects, and with the increase of rotating speed and height, the variable coefficient presented a tendency of a decrease before an increase.

| Optimization results of the RSM
To ensure the stability of temperature difference in the temperature field of the mixing system, namely small value of variable coefficient, the Optimization-Numerical module in the software Design-Expert 9 was applied for optimized solution on the regression equation model, and the constraint condition for optimization was as follows: objective function min Y (X 1 , X 2 , X 3 ); variable range 25 ≤ X 1 ≤ 45, 20 ≤ X 2 ≤ 40, −1 ≤ X 3 ≤ 1. The optimal parameter combination was obtained after optimization as follows: rotating speed was 30.28 r/min, height was 30.98 mm, the blade shape was −0.92, and the theoretical coefficient of variation after optimization was 0.0046, which is lower than 0.0054 of the No. 10 test in Table 2. The optimal parameter combination after rounding was as follows: rotating speed was 30 r/ min, the height was 31 mm, and blade shape was 1 (full trapezoidal). the best number of neurons in the hidden layer was finally determined to be 7. According to test arrangement, rotating speed, blade shape, and height were input values, and variable coefficient was the output value (the topological diagram is shown in Figure 9). As the program ran, the X 3 blade shapes of full trapezoidal, full rectangular, and trapezoid frame were numbered 1, 2, and 3 for replacement.

| Optimization results of the BP-GA model
where N is the number of nodes in the hidden layer, L in is the number of nodes of input layer, and L out is the number of nodes in the output layer.
The predicted output of trained BP neural network was taken as the individual fitness value for genetic algorithm optimization calculation, and the optimal values and corresponding input values of the function were found through selection, interlace operation, and mutation operations. The number of evolutionary parameters of genetic algorithm optimization is 150, the population size is 20, the crossover probability is 0.4, the mutation probability is 0.2, the floating point number is encoded, the individual length is 3, the individual parameters mainly include the individual fitness function trained by BP neural network, the population size evolution algebra, the variable function, the optimal fitness value, and the optimal individual of each generation of the population. In the process of BP-GA algorithm, the curve of fitness value with change of evolutionary parameters is shown in Figure 10. It can be seen that after 130 iterations, the fitness value has basically reached stability. The optimal fitness value obtained by BP-GA grid optimization is 0.0036. The corresponding function position is (33.8175, 25.3945, 1.0202), that is, when the rounded variable factor level value is the speed of 34 r/min, the height of 25 mm, and the shape is 1 (trapezoidal full face), the minimum coefficient of variation of temperature change stability is 0.0036.

| Comparison of RSM and BP-GA optimization methods
The prediction ability of models can be evaluated by predicting rootmean-square error RMSEP, determination coefficient R 2 , and relative percent difference (RPD; Dai, Cheng, Sun, Zhu, & Pu, 2016;Dong, (9) Figure 11 show that the rootmean-square error predicted by BP-GA neural network prediction model was 0.0013, determination coefficient was 0.9960, and relative percent difference was 8.4961, which were better than the evaluation indexes of RSM model, showing that the prediction ability of BP-GA neural network model was better than the RSM model. In addition, Table 4 shows that the variable coefficient value predicted by BP-GA neural network was 0.0036, test value was 0.0035, with relative error of 2.9%. The optimal value of the response surface method after quadratic polynomial fitting was 0.0046, the test value was 0.0044, and the relative error was 4.5%, indicating that the extreme value predicted by the response surface method was not really the minimum coefficient of variation, and the optimized value predicted by BP-GA neural network algorithm was more closer to the extreme value.

| CON CLUS IONS
In this paper, temperature stability was taken as the evaluation index for processing performance. Taking the rotating speed of agitator blades, the height from blades to the barrel bottom and shape of the agitator blades as variables, a test design was conducted to study the influence order of the factors on temperature stability, which was shape > height > rotating speed. The comparison between the optimization results of RSM and BP-GA neural network algorithms showed that, in the optimization process by RSM, when rotating speed was 30 r/min, height was 31 mm, blade shape was a full trapezoid, and the predicted value and actual value of variable coefficient were 0.0046 and 0.0044, respectively, with relative error of 4.5%. In the optimization by BP-GA neural network algorithm, when rotating speed was 34 r/min, height was 25 mm, blade shape was a full trapezoid, and the predicted value and actual value of variable coefficient were 0.0036 and 0.0035, respectively, with relative error of 2.9%.
It is feasible to optimize parameter combination by applying RSM and BP-GA neural network algorithm. The predicted rootmean-square error of the model by the BP-GA neural network algorithm was 0.0013, determination coefficient was 0.9960, and relative percent deviation was 8.4961, which showed better performance than the RSM model. Therefore, in the parameter optimization of the mixing device for constant milk processing, the BP-GA neural network algorithm has better fitting performance than the RSM, and then, the optimal working parameter combination in the range of global variable was as follows: rotating speed was 34 r/min, height was 25 mm, and blade shape was a full trapezoid, which could provide reference to improving normal milk processing and mixing device design and normal milk processing quality.
F I G U R E 11 Predicted scatter diagram of RSM and BP-GA models.