# Modeling and Optimization for Konjac Vacuum Drying Based on Response Surface Methodology (RSM) and Artificial Neural Network (ANN)

^{*}

## Abstract

**:**

^{2}> 0.928; MSE < 1.46; MAE < 1.04; RMSE < 1.21) than the ANN model. The main results may provide some theoretical and technical basis for the konjac vacuum drying and the designing of related equipment.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sample Preparation

#### 2.2. Equipment and Procedure Description

#### 2.3. The Key Indexes of the Konjac Vacuum Drying

#### 2.3.1. Drying Time

#### 2.3.2. Konjac Glucomannan

#### 2.3.3. Whiteness Index

#### 2.4. Experimental Design

#### 2.4.1. Response Surface Methodology

_{i}and X

_{j}are the independent variables affecting the response, β

_{0}, β

_{0}and β

_{ij}are the regression coefficients for intercept quadratic liner and interaction terms.

#### 2.4.2. Artificial Neural Network Modeling

#### 2.5. Statistical Analysis

_{i}= (x − x

_{min})/(x

_{max}− x

_{min}), where, x

_{i}is the normalized value, x is experimental value, x

_{max}is the maximal value and x

_{min}is the minimum value. The experimental value and the normalized value were tabulated in the Table 2. The performance of the prediction models (RSM models and ANN models) were statistically evaluated by the determination coefficient (R

^{2}), mean absolute error (MAE), mean square error (MSE) and root mean square (RMSE), which can be, respectively, calculated followed by the Equations (5)–(8) [34,35]:

_{pred,i}is the value predicted by the models, Y

_{exp,i}is the experimental value, Y

_{exp}is the mean of the experimental values and n is the number of the data points.

## 3. Results

^{2}), Adj R

^{2}, Pred R

^{2}, Adep Precision, PRESS and residuals obtained by the ANOVA were adopted to determine the significance of the terms or the models. A regression equation coefficient of the proposed models with statistical significance of the main responses was calculated for each response and their significance values (p ≤ 0.05) were judged, as tabulated in Table 3. The interactions of any two independent variables that effect t, KGM and WI were visualized with the response 3D surface plots for the fitted model as the function of two independent variables. The main results of the effect of the drying parameters on responses are as follows:

#### 3.1. Drying Time

^{2}, Adj R

^{2}, Pred R

^{2}, Adep Precision, C.V.% and PRESS shown in Table 3 are used to check the suitability of the model. It was found that the p-value of the model for the drying time is 0.0015, indicating that the model is significant. The value of the determination coefficient (R

^{2}) is 0.9337, which implies that 93.37% of the variations can be explained by the fitted model. The Adj R

^{2}of 0.8485 is close to the R

^{2}of 0.9337. The lack of fit for the model is not significant and a relatively low value of C.V. (5.63%) also indicates a good reliability of the experiment’s data. In conclusion, the fitted model demonstrates good suitability and can be adopted to describe the variation of the drying time.

^{2}) significantly affected the drying time. The combined effect of DT and MT affected the drying time was analyzed with the help of the response surface shown in Figure 3a. It can be obviously observed that drying time reduces with the increase in DT, while the drying time reduces with the reduction in the MT when the DT is under 65 °C. However, as shown in Figure 3b, when the DT is above 65 °C, interestingly the drying time reaches the minimum value (5.12 h), where the MT is 3 mm instead of the thinnest MT (2 mm), which might be caused by the material surface hardening shrinkage phenomenon, as reported by Fengying et al. in Litchi chinensis Sonn vacuum and selective far-infrared radiation superheat drying process [37], and similar findings were also reported by Xingyi et al. for shiitake mushroom [38], and Li Biansheng et al. for candied prunes [39].

#### 3.2. Konjac Glucomannan Content

^{2}and MT

^{2}terms. The values of evaluation indexes including R

^{2}, Adj R

^{2}, Pred R

^{2}, Adep Precision, C.V.% and PRESS are 0.9347, 0.8508, 0.1168, 13.693, 3.41% and 299.53, respectively. The indexes indicate that the model is significant and can be used for further analysis.

#### 3.3. Whiteness Index

^{2}, the p-value (0.0004) of the model shows that the model is significant. Additionally, the significance of the model is also judged by the evaluation indexes mentioned above, and all the behaviors indicate that the model shows good suitability.

#### 3.4. Optimization of Process Parameters

#### 3.5. ANN Modeling for Konjac Vacuum Drying

#### 3.6. Comparison of the Established RSM Models and the ANN Model

^{2}, MAE, MSE and RMSE), and the results are tabulated in Table 6.

^{2}for the three RSM models vary from 0.929 to 0.959, while the values of R

^{2}for the ANN model are all greater than 0.980. However, the values of MAE, MSE and RMSE for RSM models are smaller than the values of corresponding responses predicted by the ANN model. The same behavior was reported by Thyagarajan, et al. [49], who introduced a comparable performance of ANN and RSM models in phytase production modeling. Above all, it can be concluded that the predicting ability of the RSM model is better than the ANN model in the present work and the established RSM models may provide some practical guidance for the konjac vacuum drying process.

## 4. Conclusions

- (1)
- Three second order polynomial models (KGM, t, WI) were established in this study, though the models show good predicting performance, the results at the significance level showed that the WI performs a better performance than the KGM and t.
- (2)
- The results of the interaction analysis indicated that the drying temperature and the material thickness of the konjac should be, respectively, under 60 °C and 4 mm for quality and efficiency purposes.
- (3)
- The optimal drying conditions obtained based on the given criteria are 60.34 °C, 0.06 MPa and 2.00 mm. For the optimized combination of drying parameters, the t, KGM and WI are 5 h, 61.96% and 82, respectively. In order to facilitate the practical production, the optimal drying parameters were adjusted as 60.00 °C, 0.06 MPa and 2.00 mm.
- (4)
- Though both models provided good quality predictions, the results confirmed that the established RSM models in this work are superior in predicting capacity compared (R
^{2}> 0.928; MSE < 1.46; MAE < 1.04; RMSE < 1.21) with the ANN model. Such a result may suggest that the performance may be a problem-specific issue and might provide some theoretical and technical basis for guiding the konjac vacuum drying and the designing of related equipment.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Response surface (

**a**) and contour (

**b**) for drying time with respect to interaction term DT•MT at a constant vacuum degree of 0.06 MPa.

**Figure 4.**Response surface and (

**a**) contour (

**b**) for KGM content with respect to interaction term DT•DV at a constant initial material thickness of 2 mm.

**Figure 5.**Response surface and (

**a**) contour (

**b**) for KGM content with respect to interaction term DT•MT at a constant DV of 0.05 MPa.

**Figure 6.**Response surface and (

**a**) contour (

**b**) for KGM content with respect to interaction term DV•MT at a constant DT of 60 °C.

**Figure 7.**Response surface (

**a**) and contour (

**b**) for WI with respect to interaction term of DT•MT at a constant drying vacuum of 0.06 MPa.

**Figure 8.**Response surface (

**a**) and contour (

**b**) for W with respect to interaction term of DT•DV at a constant MT of 2 mm.

**Figure 10.**The comparison of experimental values and predicting results for the t (

**a**), KMG (

**b**) and WI (

**c**). RSM: response surface methodology.

Variables | Code Levels | ||
---|---|---|---|

−1 | 0 | 1 | |

Natural Levels | |||

DT (Drying temperatures,°C) | 50 | 60 | 70 |

MT (Konjac Thicknesses, mm) | 2 | 4 | 6 |

DV (Vacuum Degrees, MPa) | 0.04 | 0.05 | 0.06 |

Run | Std | Experimental Design | Results | ||||
---|---|---|---|---|---|---|---|

DT (°C) | DV (MPa) | MT (mm) | t (h) | KGM (%) | WI | ||

1 | 10 | 60(0.5) | 0.06(1) | 2(0) | 5.42(0.06) | 62.5(0.99) | 81.4(0.97) |

2 | 16 | 60(0.5) | 0.05(0.5) | 4(0.5) | 6.62(0.34) | 52.8(0.43) | 75.9(0.70) |

3 | 12 | 60(0.5) | 0.06(1) | 6(1) | 7.32(0.50) | 49.5(0.24) | 66.2(0.24) |

4 | 3 | 50(0) | 0.06(1) | 4(0.5) | 6.75(0.37) | 46.8(0.09) | 65.8(0.22) |

5 | 4 | 70(1) | 0.06(1) | 4(0.5) | 5.15(0.00) | 52.1(0.39) | 73.8(0.60) |

6 | 17 | 60(0.5) | 0.05(0.5) | 4(0.5) | 6.68(0.35) | 52.9(0.44) | 76.2(0.72) |

7 | 11 | 60(0.5) | 0.04(0) | 6(0.5) | 6.95(0.41) | 51.06(0.33) | 68.7(0.36) |

8 | 6 | 70(1) | 0.05(0.5) | 2(0) | 5.99(0.19) | 51.2(0.34) | 70.6(0.45) |

9 | 15 | 60(0.5) | 0.05(0.5) | 4(0.5) | 7.08(0.44) | 53.2(0.45) | 76.2(0.72) |

10 | 8 | 70(1) | 0.05(0.5) | 6(1) | 6.35(0.28) | 48.2(0.17) | 63.6(0.11) |

11 | 2 | 70(1) | 0.04(0) | 4(0.5) | 6.54(0.32) | 45.32(0.00) | 61.3(0.00) |

12 | 13 | 60(0.5) | 0.05(0.5) | 4(0.5) | 6.65(0.34) | 50.8(0.32) | 73.5(0.59) |

13 | 7 | 50(0) | 0.05(0.5) | 6(1) | 9.5(1.00) | 48.74(0.20) | 65.4(0.20) |

14 | 5 | 50(0) | 0.05(0.5) | 2(0) | 7.12(0.45) | 62.7(1.00) | 82.1(1.00) |

15 | 1 | 50(0) | 0.04(0) | 4(0.5) | 7.67(0.58) | 51.51(0.36) | 71.8(0.50) |

16 | 9 | 60(0.5) | 0.04(0) | 2(0) | 6.05(0.21) | 54.2(0.51) | 78.2(0.81) |

17 | 14 | 60(0.5) | 0.05(0.5) | 4(0.5) | 6.52(0.31) | 54.2(0.51) | 76.4(0.73) |

**Table 3.**ANOVA evaluation of linear, quadratic and interaction terms for response and coefficient of prediction models.

Source | Drying Time | Konjac Glucomannan Content | Whiteness Index | ||||||
---|---|---|---|---|---|---|---|---|---|

Sum of Squares | Coefficient | p-Value | Sum of Squares | Coefficient | p-Value | Sum of Squares | Coefficient | p-Value | |

Model | 13.68 | 3.832 | 0.0023 * | 316.99 | 52.29 | 0.0022 * | 591.03 | 5.1375 | 0.0004 * |

DT | 6.14 | −0.28217 | 0.0003 * | 20.90 | 0.96962 | 0.037 * | 31.20 | 3.38 | 0.0203 * |

DV | 0.83 | 498.125 | 0.0448 * | 9.70 | −129.125 | 0.1233 | 6.48 | −287.5 | 0.2157 |

MT | 3.84 | 0.83075 | 0.0012 * | 136.95 | −9.69875 | 0.0003 * | 292.82 | −7.0125 | <0.0001 * |

DT•DV | 0.055 | −1.175 | 0.5482 | 33.01 | 28.725 | 0.0178 * | 85.56 | 46.25 | 0.0017 * |

DT•MT | 1.02 | −0.02525 | 0.0301 * | 30.03 | 0.137 | 0.0144 * | 23.52 | 0.12125 | 0.0358 * |

DV•MT | 0.25 | 12.5 | 0.2214 | 24.30 | −123.25 | 0.0276 * | 8.12 | −71.25 | 0.1714 |

DT^{2} | 0.37 |
2.9525 × 10
^{−3} | 0.1479 | 28.38 | −0.025962 | 0.0201 * | 118.83 | −0.053125 | 0.0006 * |

DV^{2} | 1.09 | −5097.5 | 0.0262 * | 4.14 | −9912.5 | 0.2903 | 18.79 | −21125 | 0.0536 |

MT^{2} | 0.17 | 0.050687 | 0.3009 | 32.69 | 0.69656 | 0.0148 * | 0.08 | 0.034375 | 0.8844 |

Residual | 0.97 | 22.14 | 24.49 | ||||||

Lack of Fit | 0.83 (NS) | 18.35 (NS) | 18.91(NS) | ||||||

Pure Error | 0.15 | 3.79 | 5.58 | ||||||

Std. Dev | 0.37 | 1.78 | 1.87 | ||||||

Mean | 6.74 | 52.14 | 72.17 | ||||||

R^{2} | 0.9337 | 0.9347 | 0.9602 | ||||||

Adj R^{2} | 0.8485 | 0.8508 | 0.9091 | ||||||

Pred R^{2} | 0.0825 | 0.1168 | 0.4943 | ||||||

Adep Pre | 14.499 | 13.693 | 14.865 | ||||||

C.V.% | 5.53 | 3.41 | 2.59 | ||||||

PRESS | 13.44 | 299.53 | 311.28 |

Solution Number | Parameters | Responses | Desirability | ||||
---|---|---|---|---|---|---|---|

DT | MT | DV | t | KGM | WI | ||

1 | 60.34 | 2.00 | 0.06 | 5 | 61.96 | 82 | 0.984 |

2 | 59.92 | 2.00 | 0.06 | 5 | 62.03 | 82 | 0.983 |

3 | 60.99 | 2.00 | 0.06 | 5 | 61.82 | 82 | 0.981 |

4 | 60.37 | 2.02 | 0.06 | 5 | 61.85 | 82 | 0.980 |

5 | 58.73 | 2.00 | 0.06 | 5 | 62.17 | 82 | 0.980 |

Weight | Matrix |
---|---|

$iw\{1,1\}$ | ${\left[\begin{array}{llllllllll}-\mathit{1.5485}& -\mathit{1.1896}& \mathit{1.2995}& -\mathit{0.1283}& \mathit{0.88355}& -\mathit{1.8239}& -\mathit{1.0092}& \mathit{1.4292}& \mathit{2.3875}& \mathit{1.5284}\\ -\mathit{2.2486}& -\mathit{1.6935}& -\mathit{2.3644}& -\mathit{0.16251}& -\mathit{2.8041}& \mathit{1.7806}& -\mathit{2.2935}& -\mathit{2.0127}& -\mathit{0.1276}& \mathit{1.6143}\\ -\mathit{1.0057}& -\mathit{1.705}& -\mathit{1.1219}& -\mathit{2.883}& \mathit{0.22473}& \mathit{1.4881}& \mathit{0.49466}& -\mathit{1.8236}& -\mathit{1.1918}& -\mathit{2.2426}\end{array}\right]}^{T}$ |

$iw\{2,1\}$ | $\left[\begin{array}{llllllllll}0.11719& -0.20031& -0.92857& 0.24623& 0.25743& 0.50884& 1.1206& -0.16612& 0.87807& 0.12095\\ -0.24653& 0.28233& 0.44907& 1.1557& -0.2302& 0.46417& 0.42098& -0.55108& -0.6603& 0.801\\ 0.19157& 0.4472& 0.93092& 0.97381& -1.0095& 0.6018& -0.017862& 0.097757& -0.30043& -0.15305\end{array}\right]$ |

$b\{1\}$ | ${\left[\begin{array}{llllllllll}\mathit{3.1099}& \mathit{2.5969}& -\mathit{1.7251}& \mathit{1.1526}& \mathit{0.52729}& -\mathit{0.82056}& -\mathit{1.0568}& \mathit{1.5445}& \mathit{2.8732}& \mathit{2.869}\end{array}\right]}^{T}$ |

$b\{2\}$ | ${\left[\begin{array}{lll}-\mathit{0.415334}& \mathit{0.70893}& \mathit{0.32821}\end{array}\right]}^{T}$ |

Parameters | RSM Models | ANN Model | ||||
---|---|---|---|---|---|---|

t (h) | KGM (%) | WI | t (h) | KGM (%) | WI | |

Determination coefficient (R^{2}) | 0.9312 | 0.9286 | 0.9591 | 0.9796 | 0.9982 | 0.9896 |

Mean-square error (MSE) | 0.0595 | 1.4399 | 1.4648 | 0.2116 | 2.5676 | 6.2089 |

Mean absolute error (MAE) | 0.2092 | 1.0262 | 1.0427 | 0.1823 | 0.6773 | 1.2922 |

Root-mean-square error (RMSE) | 0.2439 | 1.1999 | 1.2103 | 0.4600 | 1.6024 | 2.4918 |

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## Share and Cite

**MDPI and ACS Style**

Zeng, Z.; Chen, M.; Wang, X.; Wu, W.; Zheng, Z.; Hu, Z.; Ma, B.
Modeling and Optimization for Konjac Vacuum Drying Based on Response Surface Methodology (RSM) and Artificial Neural Network (ANN). *Processes* **2020**, *8*, 1430.
https://doi.org/10.3390/pr8111430

**AMA Style**

Zeng Z, Chen M, Wang X, Wu W, Zheng Z, Hu Z, Ma B.
Modeling and Optimization for Konjac Vacuum Drying Based on Response Surface Methodology (RSM) and Artificial Neural Network (ANN). *Processes*. 2020; 8(11):1430.
https://doi.org/10.3390/pr8111430

**Chicago/Turabian Style**

Zeng, Zhiheng, Ming Chen, Xiaoming Wang, Weibin Wu, Zefeng Zheng, Zhibiao Hu, and Baoqi Ma.
2020. "Modeling and Optimization for Konjac Vacuum Drying Based on Response Surface Methodology (RSM) and Artificial Neural Network (ANN)" *Processes* 8, no. 11: 1430.
https://doi.org/10.3390/pr8111430