营养液紫外LED杀菌模组仿真与响应面法优化

doi:10.13304/j.nykjdb.2022.1068

摘要/Abstract

摘要：

为了研究营养液紫外LED杀菌（ultraviolet LED nutrient solution sterilization， UV-NSS）模组内紫外辐照分布并优化其关键结构参数，采用Tracepro光学仿真软件对UV-NSS模组进行建模和光线追迹，并以模组管道内径、管壁厚度、管灯距离及灯条内表面双向反射分布函数（bidirectional reflectance distribution function， BRDF）为参数因子，以有效紫外辐照比例（effective UV radiation ratio， EURR）和辐照离散度（irradiance dispersion， ID）为响应值进行响应面法参数优化。结果表明，当UV-NSS模组管道内径28 mm、管壁厚度2 mm、管灯距离4 mm、BRDF为0时，其模型EURR为12.14%，ID为0.320 6，模型中心位置紫外辐照度模拟值与实测值仅相差3.68%，可准确反映模组内辐照分布情况。基于上述模型开展中心复合有界设计，以响应面法拟合EURR和ID的二次回归方程，其决定系数分别为0.962 0和0.967 8，拟合显著（P<0.05）。以EURR最大化、ID最小化为目标，结合响应面法与实际情况确定参数因子的最优组合为管道内径50 mm、管壁厚度3 mm、管灯距离0.6 mm、BRDF为0.55。代入模型后EURR为32.11%，较优化前提升了164.50%；ID为0.317 8，较优化前降低了0.87%。采用该参数制造UV-NSS模组，其紫外辐照度实测值与模拟值仅相差1.73%。

关键词: 紫外杀菌, Tracepro, 模型, 中心复合有界设计, 参数优化

Abstract:

In order to reveal the influence of structural parameters on distribution of ultraviolet radiation in the ultraviolet LED nutrient solution sterilization （UV-NSS） module and optimize key structural parameters， the engineering software Tracepro was used to model and ray-trace the UV-NSS module. The inner diameter of tube， the thickness of tube wall， the tube-lamp distance and the bidirectional reflectance distribution function （BRDF） of the inner surface of light bar were the parameter factors， the effective UV radiation ratio （EURR） and the irradiance dispersion （ID） were the response. The results showed that when the UV-NSS module model had the tube inner diameter of 28 mm， the tube wall thickness of 2 mm， the tube-lamp distance of 4 mm， and the BRDF of 0， its EURR was 12.14%， ID was 0.320 6， and the difference between the simulated value and the measured value of ultraviolet irradiance was only 3.68%， which meaned that the model could accurately show the irradiance distribution in the module. Based on the model， the central composite bounded design was carried out， and the response surface method was used to analyze the quadratic regression equations of EURR and ID. Their determination coefficients were 0.962 0 and 0.967 8， respectively， which meaned the fitting was significant （P<0.05）. With the goal of maximizing EURR and minimizing ID， the optimal combination of parameter factors was determined with response surface method under the consideration of actual situation： the inner diameter of tube was 50 mm， the thickness of tube wall was 3 mm， the tube-lamp distance was 0.6 mm， BRDF was 0.55. After being substituted into model， its EURR and ID were 32.11% and 0.317 8， which increased and decreased by 164.50% and 0.87% compared with before optimization， respectively. Using these parameters to manufacture the UV-NSS module， the difference between the measured value and the simulated value of the ultraviolet irradiance was only 1.73%.

Key words: UV sterilization, Tracepro, model, central composite inscribed design, parameter optimization

中图分类号:

S221

柯昊纯, 李琨, 程瑞锋. 营养液紫外LED杀菌模组仿真与响应面法优化[J]. 中国农业科技导报, 2023, 25(4): 132-146.

Haochun KE, Kun LI, Ruifeng CHENG. Simulation and Optimization on Ultraviolet LED Nutrient Solution Sterilization Module Based on Response Surface Method[J]. Journal of Agricultural Science and Technology, 2023, 25(4): 132-146.

图/表 22

图1 UV-NSS模组A：UV-NSS模组正面；B：UV-NSS模组斜侧面。1—UV-LED灯条；2—UV-LED灯珠；3—石英管；4—固定装置

Fig. 1 Pictures of UV-NSS moduleA：Front of UV-NSS module； B：Oblique side of UV-NSS module. 1—UV-LED bar； 2—UV-LED beads； 3—Quartz tube； 4—Fixtures

图 2 UV-LED光谱图

Fig. 2 Spectrum of UV-LED

图3 石英管透过率测定A：UV-LED测量灯板；B：石英管紫外透过率测量装置。1—UV-LED测量灯板；2—与试验用石英管规格相同的半圆形石英片；3—紫外光谱仪的测量探头

Fig. 3 Measurement of transmittance for quartz tubeA：UV-LED measurement board； B：UV transmittance measurement device for quartz tube. 1—UV-LED measurement board； 2—Semicircular quartz plate with the same specifications as quartz tube； 3—Measurement probe of ultraviolet spectrometer

表1 石英片遮盖前后紫外辐照度及透过率

Table 1 UV irradiance before and after covering the quartz plate and its transmittance

指标Index	遮盖前Before covering	遮盖后After covering	透过率Transmittance
辐照度Irradiance/（μW·cm^-2）	123.5	115.7	0.937
	133.9	125.4	0.937
	144.8	136.9	0.945
	157.1	146.2	0.931
	194.9	175.5	0.900

图4 UV-LED灯珠模型光线追迹

Fig. 4 Lighting of UV-LED bead model

图5 UV-LED灯条模型光线追迹

Fig. 5 Lighting of UV-LED bar model

图6 UV-NSS模组模型注：1—UV-LED灯珠模型；2—UV-LED灯条模型；3—石英管模； 4—液体模型。

Fig. 6 UV-NSS module modelNote：1—UV-LED bead model； 2—UV-LED bar model； 3—Quartz tube model； 4—Liquid model.

图7 参考面在模型中的位置

Fig. 7 Position of the reference surface in the model

图8 UV-NSS模组辐照度实测注：1—光谱仪探头受光面；2—探头固定件；3—UV-LED灯条；4—石英管。

Fig. 8 Measurement of UV-NSS module irradianceNote：1—Light-receiving surface of spectrometer probe； 2—Probe fixture； 3—UV-LED bar； 4—Quartz tube.

图9 单侧发光下参考面紫外辐照分布及光谱仪探头受光面对应位置

Fig. 9 Ultraviolet irradiance distribution of the reference surface and the corresponding position of the light-receiving surface of the spectrometer probe under unilateral lighting

表2 参数因子水平及其编码表

Table 2 Parameter factor level and code

因子Factor	编码Coding	水平Level
因子Factor	编码Coding	-2	-1	0	1	2
管道内径Inner diameter of tube/mm	A	24.00	30.50	37.00	43.50	50.00
管壁厚度Thickness of tube wall/mm	B	0.00	0.75	1.50	2.25	3.00
管灯距离Tube-lamp distance/mm	C	0.00	1.25	2.50	3.75	5.00
双向反射分布函数BRDF	D	0.00	0.25	0.50	0.75	1.00

图10 UV-NSS模组模型参考面紫外辐照分布

Fig. 10 Ultraviolet radiation distribution on the UV-NSS module model reference surface

表3 仿真试验设计方案及结果

Table 3 Design scheme and results of simulation experiments

试验序号Number of experiment	试验设计组合Experiment design combination				试验结果Experiment result
试验序号Number of experiment	A	B	C	D	EURR/%	ID
1	-1	-1	-1	-1	18.94	0.381 2
2	1	-1	-1	-1	24.66	0.387 9
3	-1	1	-1	-1	18.60	0.303 3
4	1	1	-1	-1	24.09	0.325 7
5	-1	-1	1	-1	15.96	0.312 4
6	1	-1	1	-1	21.30	0.314 8
7	-1	1	1	-1	15.30	0.272 6

表3 仿真试验设计方案及结果 (续表Continued)

Table 3 Design scheme and results of simulation experimentsxu

试验序号Number of experiment	试验设计组合Experiment design combination				试验结果Experiment result
试验序号Number of experiment	A	B	C	D	EURR/%	ID
8	1	1	1	-1	20.58	0.280 1
9	-1	-1	-1	1	33.20	0.342 9
10	1	-1	-1	1	37.88	0.358 5
11	-1	1	-1	1	31.36	0.279 5
12	1	1	-1	1	35.00	0.305 8
13	-1	-1	1	1	27.40	0.303 8
14	1	-1	1	1	31.31	0.307 9
15	-1	1	1	1	24.73	0.261 8
16	1	1	1	1	29.36	0.271 5
17	-2	0	0	0	17.43	0.274 2
18	2	0	0	0	29.12	0.310 6
19	0	-2	0	0	28.01	0.357 4
20	0	2	0	0	23.18	0.263 6
21	0	0	-2	0	28.85	0.412 3
22	0	0	2	0	19.56	0.294 9
23	0	0	0	-2	17.94	0.314 0
24	0	0	0	2	49.78	0.298 9
25	0	0	0	0	24.61	0.304 7

表4 以有效紫外辐照比例为考察指标的回归系数检验表

Table 4 Analysis of regression coefficient test of the effective ultraviolet radiation ratio

来源Source	和方差Sum of squares	自由度Degree of freedom	均方Mean square	F值F value	P值P value
模型 Model	1 461.900 0	14	104.420 0	27.710 0	<0.000 1
A	160.530 0	1	160.530 0	42.600 0	<0.000 1
B	18.890 0	1	18.890 0	5.010 0	0.049 1
C	132.400 0	1	132.400 0	35.130 0	0.000 1
D	994.470 0	1	994.470 0	263.900 0	<0.000 1
AB	0.023 3	1	0.023 3	0.006 2	0.938 9
AC	0.008 6	1	0.008 6	0.002 3	0.962 9
AD	1.540 0	1	1.540 0	0.409 7	0.536 5
BC	0.008 6	1	0.008 6	0.002 3	0.962 9
BD	3.110 0	1	3.110 0	0.824 3	0.385 3
CD	8.250 0	1	8.250 0	2.190 0	0.169 7
A²	3.080 0	1	3.080 0	0.816 6	0.387 4
B²	0.038 0	1	0.038 0	0.010 1	0.922 0
C²	0.946 4	1	0.946 4	0.251 2	0.627 1
D²	50.970 0	1	50.970 0	13.520 0	0.004 3
残差Residual	37.680 0	10	3.770 0	—	—
总和Cor total	1 499.580 0	24	—	—	—

表5 以辐照离散度为考察指标的回归系数检验表

Table 5 Analysis of regression coefficient test of the irradiance dispersion

来源Source	和方差Sum of squares	自由度Degree of freedom	均方Mean square	F值F value	P值P value
模型 Model	0.037 6	14	0.002 7	45.42	<0.000 1
A	0.001 2	1	0.001 2	19.77	0.001 2
B	0.014 8	1	0.014 8	250.84	<0.000 1
C	0.014 7	1	0.014 7	249.16	<0.000 1
D	0.001 3	1	0.001 3	21.95	0.000 9
AB	8.6E-05	1	8.6E-05	1.45	0.255 6
AC	0.000 1	1	0.000 1	2.36	0.155 2
AD	1.74E-05	1	1.74E-05	0.29	0.599 1
BC	0.000 7	1	0.000 7	11.28	0.007 3
BD	2.53E-05	1	2.53E-05	0.43	0.528 2
CD	0.000 4	1	0.000 4	6.18	0.032 2
A²	0.000 1	1	0.000 1	2.36	0.155 7
B²	1.16E-05	1	1.16E-05	0.20	0.667 9
C²	0.001 6	1	0.001 6	26.53	0.000 4
D²	1.23E-11	1	1.23E-11	2.07E-07	0.999 6
残差Residual	0.000 6	10	5.91E-05	—	—
总和Cor total	0.038 2	24	—	—	—

表6 重新拟合后有效紫外辐照比例和辐照离散度的二次回归方程拟合统计指标

Table 6 Fitting statistics of the quadratic regression equation of effective ultraviolet radiation ratio and irradiance dispersion after refitting

拟合统计指标Fit statistic index	有效紫外辐照比例EURR	辐照离散度ID
标准差Standard deviation	1.730 0	0.008 5
均值Mean	25.930 0	0.313 6
变异系数Coefficient of variation/%	6.680 0	2.710 0
决定系数R²	0.962 0	0.967 8
调整后决定系数Adjusted R²	0.952 0	0.954 5
预测拟合度Predicted R²	0.885 6	0.919 5
精度值Adequate precision	37.878 5	31.003 3

图11 有效紫外辐照比例和辐照离散度的单因素效应曲线注：A—管道内径；B—管壁厚度；C—管灯距离；D—双向反射分布函数。

Fig. 11 Effect of single factors on effective ultraviolet radiation ratio and irradiance dispersionNote：A—Inner diameter of tube；B—Thickness of tube wall；C—Tube-lamp distance；D—Bidirectional reflectance distribution function.

图12 管壁厚度与管灯距离的交互效应对辐照离散度的响应面图及等高线图

Fig. 12 Response surface for the interaction of tube wall thickness and tube-lamp distance on irradiance dispersion

图13 管灯距离与BRDF的交互效应对辐照离散度的响应面图及等高线图

Fig. 13 Response surface for the interaction of tube-lamp distance and BRDF on irradiance dispersion

表7 优化后的参数组合及响应面法预测结果

Table 7 Optimized parameter combinations and prediction results of response surface method

序号 Number	管道内径 Inner diameter of tube/mm	管壁厚度Thickness of tube wall/mm	管灯距离Tube-lamp distance/mm	双向反射分布函数 BRDF	有效紫外辐照比例 EURR/%	辐照离散度ID	复合合意度 Composite desirability
1	50.00	3.000	0.556	1	52.955 9	0.284 957	0.058 412 8
2	50.00	3.000	0.009	1	53.982 4	0.305 335	0.057 210 2
3	49.42	2.268	0.000	1	54.633 0	0.341 957	0.046 972 4
4	50.00	2.951	3.828	1	46.865 1	0.263 957	0.038 111 3
5	50.00	0.043	3.988	1	50.003 4	0.333 833	0.035 034 1
6	39.83	3.000	2.557	1	45.147 4	0.240 142	0.035 022 2
7	24.09	3.000	0.000	1	43.690 6	0.277 902	0.026 365 7
8	27.54	0.000	4.026	1	41.046 3	0.310 753	0.016 768 1
9	27.95	2.882	3.944	1	37.956 7	0.244 203	0.014 896 7

图14 UV-LED灯条内表面铝箔覆盖前后对比

Fig. 14 Comparison of the inner surface of UV-LED bar before and after covered by aluminum foil

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