# Non-Destructive Methodology to Determine Modulus of Elasticity in Static Bending of Quercus mongolica Using Near-Infrared Spectroscopy

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## Abstract

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_{p}) and the root mean square error of prediction (RMSEP) and in the prediction set. In comparison with the predicted results of the models, BPNN performed better results with the higher r

_{p}of 0.91 and lower RMSEP of 0.76. The results indicate that it is feasible to accurately determine the MOE of wood by using the NIR spectroscopy technique.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Specimen Preparation

#### 2.2. NIR Spectra Measurements

#### 2.3. Detemination of MOE in Static Bending

#### 2.4. Calibration Set and Predition Set Partitioning Using Improved Kennard-Stone Method

_{p}(j) and x

_{q}(j) were the absorbance of sample p and q at the j wavelength, respectively, m was the number of wavelengths in a spectrum, and n was the total number of samples.

#### 2.5. Pretreatment of NIR Spectra

#### 2.6. Characteristic Spectrum Extraction

#### 2.6.1. SiPLS

#### 2.6.2. SPA

#### 2.7. Model Evaluation Standard

_{c}of calibration set, r

_{p}of prediction set), the standard error of cross-validation (SECV), the root mean square error of prediction (RMSEP), and the ratio of performance to deviation (RPD). The type of cross-validation was leave-one-out RPD, which was the quotient of standard deviation (SD) of the true value of prediction set and the RMSEP of prediction set. The selection of the final model was based on its predictability following a procedure which has already been successfully applied [27]. Generally, a good model should have higher values of r

_{c}, r

_{p}, and RPD, but a lower value of RMSEC and RMSEP.

## 3. Results and Discussion

#### 3.1. Determination of the MOE and Dataset Partitioning

#### 3.2. Near-Infrared Spectra of Specimens and Spectral Pretreatment

#### 3.3. Characteristic Spectrum Selection

#### 3.3.1. Optimal Spectra Intervals Selected by SiPLS

#### 3.3.2. Characteristic Wavelengths Selected by SPA

#### 3.4. Analysis of the Predictive Models

_{p}of 0.91 and lower RMSEP of 0.76. Furthermore, the RPD of BPNN was between 2.5 and 3.0, which suggested that the model met the needs of quantitative prediction [26]. The experimental results indicated that BPNN was capable of quantitative analysis and prediction of the MOE of Quercus mongolica specimens without defects. Figure 7 shows the relationship between measured and predicted MOE of Quercus mongolica specimens with BPNN as the prediction model. Figure 7 shows a clear separation of high and lower MOE values in the calibration set; this is because in order to ensure the integrity and representativeness of the calibration set, the improved K-S put the biggest different sample into the calibration set and the closing samples into the prediction set, and led the number of specimens in the high MOE value and low MOE value were more than the others.

## 4. Conclusions

- (1)
- The improved K-S method can make the sample distribution uniform, and ensure that the calibration set is widely distributed
- (2)
- By pretreating with MSC and the SG smoothing and differentiation filter, the overall variation trend of spectra was more consistent, and the contour of spectra was more clear. Moreover, the absorption peak is more obvious. When the window size of SG was of 11, the effect of pretreatment was the best
- (3)
- SiPLS combined with SPA could extract characteristic wavelengths that had the closest relevance with the MOE of Quercus mongolica. It reduced the dimensions of the original data, decreasing the computation and reducing the complexity of the modelling process.
- (4)
- Compared with the prediction results, BPNN was better capable of predicting the MOE of the specimens by using the characteristic wavelengths to establish the calibration model. The r
_{p}, RMSEP, and RPD of BPNN were 0.91, 0.76, and 2.93, respectively. The quantitative prediction effects of the model can meet the needs of actual industrial activities.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 4.**Pretreated spectra: (

**a**) Pretreated by MSC; (

**b**) Pretreated by MSC combined with SG convolution smoothing and differentiation filter.

**Figure 6.**The results of characteristic wavelengths selection by SPA: (

**a**) The variation of RMSE with SPA; (

**b**) Final selected wavelengths.

**Figure 7.**Relationships between the measured and predicted MOE of Quercus mongolica in the (

**a**) calibration set and (

**b**) prediction set.

Sample Set | Serial Number of Samples | ||||||
---|---|---|---|---|---|---|---|

Calibration set | 2 | 3 | 4 | 6 | 9 | 11 | 12 |

15 | 16 | 17 | 18 | 19 | 20 | 21 | |

22 | 23 | 25 | 26 | 27 | 28 | 29 | |

30 | 32 | 35 | 36 | 37 | 40 | 41 | |

43 | 44 | 45 | 47 | 48 | 49 | 50 | |

52 | 53 | 54 | 56 | 60 | 63 | 64 | |

66 | 67 | 69 | 72 | 74 | 75 | 76 | |

77 | 78 | 79 | 80 | 82 | 83 | 84 | |

85 | 86 | 87 | 88 | 92 | 93 | 94 | |

95 | 96 | 97 | 98 | 100 | 101 | 104 | |

105 | 106 | 107 | 108 | 111 | 112 | 113 | |

114 | 115 | 118 | 120 | 122 | 123 | 125 | |

Prediction set | 1 | 5 | 7 | 8 | 10 | 13 | 14 |

24 | 31 | 33 | 34 | 38 | 39 | 42 | |

46 | 51 | 55 | 57 | 58 | 59 | 61 | |

62 | 65 | 68 | 70 | 71 | 73 | 81 | |

89 | 90 | 91 | 99 | 102 | 103 | 109 | |

110 | 116 | 117 | 119 | 121 | 124 |

Samples | Maximum (GPa) | Minimum (GPa) | Mean (GPa) | Standard Deviation (GPa) |
---|---|---|---|---|

Calibration set (n = 84) | 19.25 | 10.43 | 16.00 | 3.05 |

Prediction set (n = 41) | 18.96 | 11.22 | 16.41 | 2.23 |

Number of Intervals | PCs | Selected Subintervals | RMSECV |
---|---|---|---|

5 | 8 | [1 3 5] | 1.439 |

6 | 7 | [1 2 3 6] | 1.431 |

7 | 6 | [1 5 7 9] | 1.354 |

8 | 8 | [1 6 7] | 1.388 |

9 | 8 | [1 2 6 8] | 1.355 |

10 | 6 | [1 5 7 9] | 1.354 |

11 | 7 | [1 2 8 10] | 1.374 |

12 | 8 | [1 2 9 11] | 1.360 |

13 | 6 | [1 6 9 11] | 1.387 |

14 | 7 | [1 7 10 12] | 1.388 |

15 | 7 | [1 7 12 13] | 1.389 |

Types of model | r_{c} | RMSEC | SECV | r_{p} | RMSEP | RPD |
---|---|---|---|---|---|---|

PLSR | 0.90 | 1.35 | 1.34 | 0.84 | 1.08 | 2.06 |

BPNN | 0.94 | 1.00 | 1.04 | 0.89 | 0.76 | 2.93 |

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**MDPI and ACS Style**

Liang, H.; Zhang, M.; Gao, C.; Zhao, Y.
Non-Destructive Methodology to Determine Modulus of Elasticity in Static Bending of *Quercus mongolica* Using Near-Infrared Spectroscopy. *Sensors* **2018**, *18*, 1963.
https://doi.org/10.3390/s18061963

**AMA Style**

Liang H, Zhang M, Gao C, Zhao Y.
Non-Destructive Methodology to Determine Modulus of Elasticity in Static Bending of *Quercus mongolica* Using Near-Infrared Spectroscopy. *Sensors*. 2018; 18(6):1963.
https://doi.org/10.3390/s18061963

**Chicago/Turabian Style**

Liang, Hao, Meng Zhang, Chao Gao, and Yandong Zhao.
2018. "Non-Destructive Methodology to Determine Modulus of Elasticity in Static Bending of *Quercus mongolica* Using Near-Infrared Spectroscopy" *Sensors* 18, no. 6: 1963.
https://doi.org/10.3390/s18061963