Sensitivity performance prediction and optimisation of flexible pressure sensing unit based on RSM and SVR-IDBO
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摘要: 为优化柔性压力传感单元制备工艺，提升传感器灵敏度特性。本研究通过建立灵敏度解析模型，确定了影响其性能表现的主要因素，采用机械共混的方式，通过调节碳纳米管(CNT)、多层石墨烯(MLG)、搅拌时间(Mixing time)、成型温度(Molding temperature)等参数优化了柔性传感单元的灵敏度性能。首先在单因素分析的基础上，应用实验设计(DOE)中的中心复合实验方法(CCD)进行多因素实验设计，通过响应面法(RSM)和支持向量机(SVR)对多因素的交互影响进行了分析，并分别建立了灵敏度预测模型。其次根据决定系数($ {R}^{2} $)、均方根误差(Rmse)和平均误差率(Mae)对两种模型进行评估与定型，模型性能对比结果表明，通过超参优化后的SVR模型表现出更高水平的准确性和可预测性。然后基于改进的蜣螂优化算法(IDBO)对模型进行迭代优化，得到了比早期实验更好的灵敏度性能。仿真结果显示在0~30kPa的单轴压力下，当CNTs含量为2.3wt%、MLG含量为1.9wt%、混合时间15 min、成型温度78℃时，灵敏度达到0.5512 kPa−1，经过实验验证，与实际灵敏度(0.5371 kPa−1)的相对误差为2.625%，且与同类型研究相比较，本研究的传感单元灵敏度性能也处较高水平。证明该方法有助于寻找最佳的传感器含量配比与制备工艺，提升实验效率，节约实验成本，为快速制备高性能电容式柔性压力传感单元提供了新思路。Abstract: To enhance the preparation process of flexible pressure sensors and improve their sensitivity characteristics, objective measures must be taken. This study identified the main factors affecting performance through a sensitivity analysis model. The sensitivity performance of the flexible sensing unit was optimized by adjusting the parameters of multi-walled carbon nanotubes (MWCNTs), multilayered graphene (MLGs), mixing time, and molding temperature using mechanical co-mingling. The study utilized the central combinatorial method (CCD) in design of experiments (DOE) for multi-factor experimental design. The interaction effects of the multi-factors were analyzed using response surface methodology (RSM) and support vector machine (SVR), based on single-factor analysis. Sensitivity prediction models were established accordingly. The two models were evaluated and finalized based on the coefficient of determination ($ {R}^{2} $), root mean square error (Rmse), and mean error rate (Mae). The results indicate that the SVR model, optimized by hyperparameterization, exhibits a higher level of accuracy and predictability. The model was then iteratively optimized using the Improved Dung Beetle Optimization (IDBO) algorithm, which yielded better sensitivity performance than earlier experiments. The simulation results show a sensitivity of 0.5512 kPa−1 at a uniaxial pressure of 0-30 kPa when the CNTs content is 2.3 wt%, the MLG content is 1.9 wt%, the mixing time is 15 min, and the molding temperature is 78°C. The experimentally verified relative error to the actual sensitivity (0.5371 kPa−1) is 2.625% and the sensitivity performance of the sensing unit in this study is also at a high level when compared with similar studies. It is proved that this method helps to find the optimal sensor content ratio and preparation process, improve the experimental efficiency, save the experimental cost, and provide a new idea for the rapid preparation of high-performance capacitive flexible pressure sensing units.
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图 3 触觉敏感单元改性前后对比
Figure 3. Comparison between before and after modification of the tactile sensitivity unit
图 5 渗滤复合材料作为介电层的柔性电容式压力传感器的工作原理图
Figure 5. Working principle diagram of flexible capacitive pressure sensor with percolation composite as dielectric layer
图 6 输入参数的单因素影响：(a) CNTs单因素影响；(b) MLGs单因素影响；(c) 搅拌时间单因素影响；(d) 成型温度单因素影响
Figure 6. Single factor effect of input parameter：(a) single-factor effect of CNTs; (b) single-factor effect of MLGs; (c) single-factor effect of mixing time; (d) single-factor effect of molding temperature
图 12 灵敏度三维响应面图：(a)碳纳米管(CNT)/石墨烯(MLG)相互作用；(b)CNT/搅拌时间相互作用；(c)CNT/成型温度相互作用；(d)MLG/搅拌时间相互作用；(e)MLG/成型温度相互作用；(f)搅拌/成型温度相互作用
Figure 12. Three-dimensional response surface plots of sensitivity: (a) Interaction between CNT/MLG content; (b) Interaction between CNT/mixing time; (c) Interaction between CNT/molding temperature; (d) Interaction between MLG/mixing time; (e) Interaction between MLG/molding temperature; (f) Interaction between mixing time/molding temperature
图 14 SVR和RSM模型的5折交叉验证的雷达图
Figure 14. Radar diagrams of SVR and RSM models with 5 fold cross validation
图 15 改进蜣螂优化算法(IDBO)收敛过程
Figure 15. Dung beetle optimization algorithm (IDBO) convergence process
表 1 单因素实验方案
Table 1. Single-factor protocol
Index Content of CNTs/g Content of MLGs/g Mixing time/min Molding temperature/℃ Analysis of factors affecting 1 0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.1 0.6 15 80 CNT 2 0.7 0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.1 15 80 MLG 3 0.7 0.6 10,15,20,25,30 80 Mixing time 4 0.7 0.6 15 40,60,80,100,120 Molding temperature 
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表 2 四个因素的水平和编码
Table 2. Level and code of four factors
Code Levels Factor CNTs/g MLGs/g Mixing time/min Molding temperature/℃ −2 0.7 0.6 10 40 −1 0.8 0.7 15 60 0 0.9 0.8 20 80 1 1.0 0.9 25 100 2 1.1 1.0 30 120
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表 3 多因素中心组合实验设计(CCD)与结果
Table 3. Multifactorial central combinatorial experimental design (CCD) and results
Run Factors Sensitivity CNT MLG Mixing time Molding temperature 1 1 −1 −1 1 0.227 2 0 0 2 0 0.13 3* 0 0 0 0 0.118 4 −1 −1 −1 1 0.058 5 1 1 1 1 0.191 6 1 −1 −1 −1 0.208 7 −1 1 1 1 0.025 8* 0 0 0 0 0.145 9 −1 1 −1 1 0.05 10 −1 −1 1 −1 0.125 11 −2 0 0 0 0.05 12 0 −2 0 0 0.185 13 0 0 −2 0 0.193 14 −1 1 1 −1 0.164 15 1 1 −1 −1 0.375 16 1 −1 1 −1 0.18 17* 0 0 0 0 0.135 18 1 1 1 −1 0.31 19 0 1 0 0 0.198 20 2 0 0 0 0.478 21 −1 1 −1 −1 0.178 22 0 0 0 0 0.154 23 1 1 −1 1 0.326 24 0 0 0 −2 0.124 25* 0 0 0 0 0.117 26* 0 0 0 0 0.112 27 −1 −1 −1 −1 0.078 28 1 −1 1 1 0.248 29 −1 −1 1 1 0.09 30 0 0 0 2 0.073 Note: *indicates the central repeated trials.
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表 4 灵敏度响应的方差分析
Table 4. Analysis of variance for sensitivity response
Source Sum of squares df Mean square F-value P-value Status Model 0.2877 14 0.0205 32.91 < 0.0001 Significant $ {x}_{1} $-CNT 0.1931 1 0.1931 309.36 < 0.0001 $ {x}_{2} $-MLG 0.0117 1 0.0117 18.789 0.0006 $ {x}_{3} $-Mixing time 0.0036 1 0.0036 5.73 0.0302 $ {x}_{4} $-Temperature 0.0106 1 0.0106 17.02 0.0009 $ {x}_{1}{x}_{2} $ 0.0047 1 0.0047 7.46 0.0155 $ {x}_{1}{x}_{3} $ 0.0038 1 0.0038 6.11 0.0259 $ {x}_{1}{x}_{4} $ 0.0036 1 0.0036 5.81 0.0292 $ {x}_{2}{x}_{3} $ 0.0060 1 0.0060 9.68 0.0071 $ {x}_{2}{x}_{4} $ 0.0136 1 0.0136 21.83 0.0003 $ {x}_{3}{x}_{4} $ 0.0001 1 0.0001 0.2211 0.6449 $ {{x}_{1}}^{2} $ 0.0267 1 0.0267 42.79 < 0.0001 $ {{x}_{2}}^{2} $ 0.0085 1 0.0085 13.65 0.0022 $ {{x}_{3}}^{2} $ 0.0008 1 0.0008 1.26 0.2795 $ {{x}_{4}}^{2} $ 0.0030 1 0.0030 4.88 0.0432 Residual 0.0094 15 0.0006 Lack of fit 0.0079 10 0.0008 2.70 0.1422 Not significant Pure error 0.0015 5 0.0003 Cor total 0.2970 29 $ {R}^{2} $ 0.9685 $ {R}_{\mathrm{A}\mathrm{d}\mathrm{j}}^{2} $ 0.9390 $ {R}_{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{d}}^{2} $ 0.8311 C.V% 14.86 Adeq precision 23.8126 Notes: Cor total refers to the total number of correlation coefficients;$ {R}_{\mathrm{A}\mathrm{d}\mathrm{j}}^{2} $indicates adjusted coefficient of determination;$ {R}_{\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{d}}^{2} $ indicates predicted R-squared; Adeq precision is an important statistical metric for evaluating the predictive ability of response surface models.
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表 5 SVR模型的5折交叉验证预测性能评价指标
Table 5. Performance evaluation index of SVR model by cross validation
Index 1 2 3 4 5 Average $ {R}^{2} $ 0.9893 0.9841 0.9735 0.9769 0.9882 0.9824 Rmse 0.0253 0.0328 0.0354 0.0389 0.0188 0.0320 Mae 0.0193 0.0301 0.0231 0.0321 0.0151 0.0239
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表 6 RSM模型的5折交叉验证预测性能评价指标
Table 6. Performance evaluation index of RSM model by cross validation
Index 1 2 3 4 5 Average R2 0.9563 0.9642 0.9778 0.9669 0.9782 0.96868 Rmse 0.04002 0.02701 0.03103 0.04731 0.03312 0.035698 Mae 0.03623 0.02443 0.02671 0.03113 0.02608 0.028916
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表 7 传感单元灵敏度性能对比
Table 7. Comparison of sensitivity performance of sensing units
Reference Method Sensitivity /k$ \mathrm{P}{\mathrm{a}}^{-1} $ Pressure range /$ \mathrm{k}\mathrm{P}\mathrm{a} $ Comparison /k$ \mathrm{P}{\mathrm{a}}^{-1} $ [12] Microstructure design 0.451 0-25 0.7665 [42] Microstructure design 0.69 0-10 1.7531 [43] Microstructure design 1.01 0-25 0.7665 [44] mechanical blending 0.3850 0-30 0.5371 [45] Microstructure design 0.341 0-5 1.9698 This study mechanical blending 0.5371 0-30 -
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