Scientia Agricultura Sinica ›› 2019, Vol. 52 ›› Issue (15): 2695-2705.doi: 10.3864/j.issn.0578-1752.2019.15.013

• FOOD SCIENCE AND ENGINEERING • Previous Articles     Next Articles

Response Surface Design and Multi-Objective Optimization of Apple Slices Dried by Air-Impingement

JIA MengKe,WU Zhong,ZHAO WuQi(),LU Dan,ZHANG QingAn,ZHANG BaoShan,SONG ShuJie   

  1. College of Food Engineering and Nutritional Science, Shaanxi Normal University, Xi’an 710119
  • Received:2019-02-13 Accepted:2019-04-09 Online:2019-08-01 Published:2019-08-06
  • Contact: WuQi ZHAO E-mail:zwq65@163.com

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Abstract:

【Objective】 In order to obtain the drying process parameters of apple slices with high quality and low energy consumption, the effects of air temperature, slice thickness, air velocity and their interaction on the vitamin C (VC) content, rehydration ratio and energy consumption were investigated during the air-impingement drying of apple slices. 【Method】 With the air temperature, slice thickness and air velocity as the factors, and the three-factor response surface Box-Behnken response surface design was carried out with the VC content, rehydration ratio and unit energy consumption of apple slices as the response. The factors and their interactions between the various factors were analyzed, and a quadratic regression model of VC content, rehydration ratio and unit energy consumption was established and verified by applying three optimization methods, including genetic algorithm, fgoalattain function method and membership degree comprehensive evaluation method, were applied respectively. 【Result】 The factors’ order of influencing on the Vc content was as the follows: Air temperature, slice thickness and air velocity. Regarding the air temperature, both the interactions between the slice thickness and the air velocity were extremely significant, respectively. The factors’ influencing rehydration ratio ordered as the air temperature, air velocity and slice thickness, and all these factors had an extremely significant effect; the interactions between slice thickness and air velocity were significant. The orders influencing on the energy consumption were the slice thickness, air temperature and air velocity. And the air temperature, slice thickness and the interactions between air temperature and air velocity were extremely significant, air velocities and the interactions between air temperature and slice thickness were significant. The established regression model of VC content, rehydration ratio and energy consumption was statistically significant (P<0.05), suggesting that the model could be used to analyze and predict air-impingement drying parameters. The optimal drying parameters analyzed by genetic algorithm were of 63.24℃ air temperature, 2.00 mm slice thickness and 12.00 m·s -1air velocity, respectively. Under these conditions, the VC content, rehydration ratio and energy consumption of apple slices were 66.96 μg/100 g, 3.83 and 26.49 kJ·g -1, respectively; the optimal process parameters obtained by fgoalattain function were as: air temperature 71.62℃, slice thickness 2.37 mm, air velocity 11.18 m·s -1, and VC content was 64.90 μg/100 g, rehydration ratio was 3.41, and unit energy consumption was 25.85 kJ·g -1; the optimal process parameters obtained by the comprehensive evaluation method of membership degree were as: air temperature 63.57℃, slice thickness 2.00 mm, air velocity 12.00 m·s -1, and VC content was 66.94 μg/100 g, rehydration ratio was 3.79, unit energy consumption was 26.53 kJ·g -1. With the fitness value as the index, it could be concluded that the genetic algorithm optimized results were the best. 【Conclusion】The genetic algorithm could be used for the multi-objective optimization in air-impingement drying apple slices. The optimum parameters were of 63℃ air temperature, 2 mm slice thickness, and 12 m·s -1air velocity. With these parameters, the VC content, rehydration ratio and unit energy consumption under this parameter were 66.85 μg/100 g, 3.78, and 26.59 kJ·g -1, respectively. In conclusion, the air-impingement technique could be applied in the drying of apple slices with high VC content, high rehydration ratio and low energy consumption.

Key words: apple slice, air-impingement drying, quality evaluation, response surface, comprehensive optimization

Table 1

Response surface design and parameters"

因素
Factor		 水平 Level
-1 0 1
A风温 Air temperature (℃) 60 70 80
B切片厚度 Slice thickness (mm) 2 4 6
C风速 Air velocity (m·s-1) 10 11 12

Table 2

The results of response surface method"

编号
Code		 风温
Air
temperature
(℃)		 切片厚度
Slice
thickness
(mm)		 风速
Air velocity
(m·s-1)		 VC
(μg/100 g)		 复水比
Rehydration ratio		 能耗
Energy consumption
(kJ·g-1)		 VC含量
隶属度值Membership value of VC		 复水比
隶属度值
Membership
value of RR		 能耗隶属值
Membership value of energy consumption		 综合评价S Comprehensive evaluation
1 80 6 11 54.63 2.58 33.76 0.02 0.02 0.39 0.09
2 60 6 11 67.23 3.42 38.64 0.98 0.65 0.00 0.72
3 70 6 10 66.18 3.81 37.41 0.90 0.95 0.10 0.75
4 70 4 11 66.12 3.28 27.64 0.90 0.55 0.88 0.82
5 70 6 12 63.44 3.05 35.47 0.69 0.38 0.25 0.54
6 60 2 11 63.48 3.83 28.19 0.70 0.96 0.83 0.78
7 60 4 12 67.45 3.47 29.68 1.00 0.69 0.72 0.88
8 70 2 12 65.51 3.56 26.11 0.85 0.76 1.00 0.86
9 70 4 11 65.20 3.18 28.16 0.83 0.47 0.84 0.76
10 60 4 10 63.23 3.78 33.85 0.68 0.92 0.38 0.67
11 80 4 10 60.51 2.96 28.15 0.47 0.31 0.84 0.51
12 70 4 11 66.10 3.42 27.11 0.90 0.65 0.92 0.85
13 80 4 12 54.42 2.55 30.64 0.00 0.00 0.64 0.13
14 70 2 10 64.86 3.88 28.73 0.80 1.00 0.79 0.84
15 70 4 11 63.89 3.27 28.88 0.73 0.54 0.78 0.70
16 80 2 11 60.25 2.83 26.64 0.45 0.21 0.96 0.50
17 70 4 11 64.59 3.33 27.45 0.78 0.59 0.89 0.76

Table 3

Three indicators regression coefficient significance test results"

变异来源
Source		 自由度
Free degree		 P值 P value
y1 y2 y3
模型Model 9 <0.0001 <0.0001 <0.0001
A 1 <0.0001 <0.0001 0.0007
B 1 0.0459 0.0012 <0.0001
C 1 0.103 0.0001 0.0151
AB 1 0.0004 0.3716 0.0465
AC 1 0.0002 0.5696 0.0019
BC 1 0.0576 0.0342 0.6371
A2 1 <0.0001 0.0004 0.006
B2 1 0.8042 0.0171 <0.0001
C2 1 0.8144 0.0074 0.0038
失拟项 Lack of fit 3 0.9791 0.5606 0.4814

Table 4

Result of single targets’ optimization"

目标
Target		 风温
Air temperature (℃)		 切片厚度
Slice thickness (mm)		 风速
Air velocity (m·s-1)		 目标优化值
The optimal value of target
VC (y1) (μg/100 g) 60.10 4.37 11.99 67.63
复水比Rehydration ratio (y2) 60.65 2.58 10.13 3.91
能耗Energy consumption (y3) (kJ·g-1) 71.04 2.40 10.85 26.05

Fig. 1

Effects of AB mutual interactions and AC mutual interactions on the content of Vc"

Fig. 2

Effects of AB mutual interactions and AC mutual interactions on the content of energy consumption"

Fig. 3

Effects of BC mutual interactions on the RR"

Table 5

Comparison of three optimization methods"

优化方法
Optimization methods		 工艺参数 Process parameter 考察指标Index 适应度值
Fitness value
风温
Air temperature
(℃)		 风速
Air velocity
(m·s-1)		 切片厚度
Slice thickness
(mm)		 VC
(μg/100 g)		 复水比
Rehydration ratio		 单位能耗
Energy consumption (kJ·g-1)
遗传算法
Genetic algorithm		 63.24 2.00 12.00 66.96 3.83 26.49 0.000198
Fgoalattain函数法
Fgoalattain function method		 71.62 2.37 11.18 64.90 3.41 25.85 0.004298
隶属度综合评分法
Membership degree comprehensive
evaluation method		 63.57 2.00 12.00 66.94 3.80 26.53 0.000298

Table 6

Analysis of variance of membership degree comprehensive score response surface regression model"

平方和
Sum of squares		 自由度
Free degree		 均方差
Mean square deviation		 F值
F value		 P值
P value		 显著性
Significance
模型Model 0.88 9 0.098 48.5 <0.0001 显著
Significant
气流温度 Air temperature (℃) 0.41 1 0.41 204.4 <0.0001
切片厚度 Slice thickness (mm) 0.097 1 0.097 47.79 0.0002
C-气流速度 Air velocity (m·s-1) 0.016 1 0.016 8 0.0255
AB 0.031 1 0.031 15.12 0.006
AC 0.087 1 0.087 42.96 0.0003
BC 0.013 1 0.013 6.53 0.0378
A2 0.22 1 0.22 107.81 <0.0001
B2 0.00324 1 0.00324 1.6 0.2463
C2 0.0000318 1 0.0000318 0.016 0.9038
残基Residual 0.014 7 0.00203
失拟项 Lack of Fit 0.0005 3 0.000167 0.049 0.9838 不显著
Not significant
纯误差 Pure Error 0.014 4 0.00342
总和 Total 0.9 16
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