# Modeling and Application of Temporal Correlation of Grain Temperature during Grain Storage

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}), and root mean square error (RMSE) were chosen to evaluate the models, with the results showing that the effect of the model established by the threshold set by the 3σ-setting method, with SSE, R

^{2}and RMSE of 0.056, 0.9771 and 0.0748, respectively, was better than the model established using the DBSCAN method. Finally, the correlation coefficients of grain temperatures with empty warehouse, new grain addition, aeration and self-heating were analyzed. The results show that the four modes in a certain time interval (e.g., 30 days) does not meet the correlation coefficient threshold during normal storage. The result can provide a theoretical basis for grain storage condition detection when grain temperature data is intermittently missing.

## 1. Introduction

## 2. Data and Methods

#### 2.1. Grain Temperature Data Collection and Processing

#### 2.1.1. Data Collection

#### 2.1.2. Grain Temperature Plane Composition

_{ijk}, where 0 < i ≤ n, 0 < j ≤ m, 0 < k ≤ l (i, j, k are integers). The temperature sensors form three planes that are parallel to the XOY, XOZ, and YOZ planes, respectively, namely, a plane parallel to XOY (referred to as the XOY plane), a plane parallel to XOZ (referred to as the XOZ plane) and a plane parallel to YOZ (referred to as the YOZ plane), as shown in Figure 2. Among the granaries selected, l = 4, m = 4~10, and n = 6~15.

#### 2.1.3. Grain Temperature Data Preprocessing

#### 2.2. Research Methods

#### 2.2.1. Time Correlation Calculation Method for Plane Grain Temperature

_{z}of grain temperature in the XOY plane can be obtained using Equation (1). Additionally, the correlation coefficients R

_{y}and R

_{x}of the grain temperature in the XOZ plane and the YOZ plane can be obtained. During storage, the grain temperature is usually collected 1~2 times a week. To more accurately analyze grain temperature data, seven days was taken as a cycle within which to calculate the XOY-plane grain temperature correlation coefficient for 27 granaries over 3 months, that is, the time intervals between t

_{1}and t

_{2}in Equation (1) are 1, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, and 91 days. The lower limits of the distribution interval of the correlation coefficient of grain temperature from the first to the fourth layers are shown in Figure 3.

**T**and

_{ijkt1}**T**are the grain temperature data matrix at the time t1 and t2 of the XOY plane of the k

_{ijkt2}_{th}layer; $\overline{{T}_{kt1}}$ and $\overline{{T}_{kt2}}$ are the mean values of grain temperature at the time of t1 and t2 of the XOY plane of the k

_{th}layer, °C.

#### 2.2.2. Correlation Coefficient Preprocessing

**R**,

_{z}_{1}**R**

_{z}**,**

_{2}**R**

_{z}**, and**

_{3}**R**, respectively.

_{z}_{4}**R**,

_{z}_{1}**R**

_{z}**,**

_{2}**R**

_{z}**, and**

_{3}**R**represent the correlation coefficient vectors of the grain temperature in the first, second, third, and fourth XOY planes from the top layer to bottom layer, respectively. Similarly, the vectors of the correlation coefficient in the XOZ and YOZ planes are

_{z}_{4}**R**= {

_{y}**R**,

_{y}_{1}**R**,

_{y}_{2}**R**,

_{y}_{3}**R**} and

_{y}_{4}**R**= {

_{x}**R**,

_{x}_{1}**R**,

_{x}_{2}**R**,

_{x}_{3}**R**}, respectively. The correlation coefficients of storage for 1, 7, 14, 21, 28, 35, 42, 49, 56, 63, and 70 days are processed in the same way to form arrays.

_{x}_{4}#### 2.2.3. Threshold Setting Method

- (1)
- Threshold Setting Method Based on DBSCAN Clustering

**R**was divided into four vectors—

_{z}**R**,

_{z1}**R**,

_{z2}**R**, and

_{z3}**R**—for the purposes of clustering. To set the input matrix of the clustering algorithm, a constant vector of the same length (the constant is 1) was added in front of four vectors to form a matrix as the input matrix of the clustering algorithm, namely {1(x),

_{z4}**R**

_{z}**(x)}, {1(x),**

_{1}**R**

_{z}**(x)}, {1(x),**

_{2}**R**

_{z}**(x)}, {1(x),**

_{3}**R**

_{z}**(x)} (1 < x ≤ s, s represents the value of**

_{4}**R**length). Before clustering, the number of clusters k was set to two, and the criterion function is the sum of the distances of points between clusters. After the clustering had been completed, the maximum and minimum values of the ordinates in each category were taken to form threshold intervals, and the minimum value was set as the correlation coefficient threshold for the purposes of modeling analysis. The XOZ plane and the YOZ plane were handled in the same way.

_{z}_{1}- (2)
- 3σ-Threshold-Based Setting Method

**R**,

_{z1}**R**,

_{z2}**R**,

_{z3}**R**,

_{z4}**R**, etc., of the correlation coefficient sets of different storage times are calculated. A correlation coefficient threshold was obtained for each plane under each storage time, and the correlation coefficient threshold is modeled and analyzed below.

_{y1}#### 2.2.4. Model Building Method and Environment

#### 2.2.5. Relevance Rating

#### 2.2.6. Evaluation of the Model Index

^{2}), and the root mean square error (root mean square error, RMSE). The equations of each evaluation index are shown below.

## 3. Results and Discussion

#### 3.1. Mode of Correlation Coefficient Threshold

#### 3.1.1. Models of Grain Temperature Correlation Coefficient Threshold on the XOY Plane

#### 3.1.2. Models of Grain Temperature Correlation Coefficient Threshold on the XOZ Plane

#### 3.1.3. Models of Grain Temperature Correlation Coefficient Threshold on the YOZ Plane

#### 3.1.4. Evaluation of Threshold Setting Method

^{2}and RMSE were used to the established models based on the clustering results, as shown in Table 5. The SSE of the established models based on the 3$\mathsf{\sigma}$-threshold method is lower than that of the established model based on the DBSCAN clustering results, indicating that the models based on the results of the 3$\mathsf{\sigma}$-threshold method possess a slightly better fitting effect. Comparing R

^{2}and RMSE, the same conclusion can be reached. In general, the fitting effect of the model established based on the results of the 3$\mathsf{\sigma}$-threshold method is better than that of the model based on the DBSCAN clustering results.

#### 3.2. Discussion

#### 3.2.1. Influence of Empty Warehouse on Temperature Correlation

#### 3.2.2. Influence of New Grain on Temperature Correlation

#### 3.2.3. Influence of Aeration Operation on Temperature Correlation

#### 3.2.4. Influence of Self-Heating on Temperature Correlation

^{−1}, 0.15 d

^{−1}). Ref. [34] presented a method in which grain temperature statistical parameters were used to detect grain inventory modes (empty and aeration) based on DBSCAN (density-based spatial clustering of applications with noise). The statistical parameters contained the grain temperature differences between adjacent layers, the aggregation ratios of four layers of grain temperature, the change rate of grain temperature, and the standard deviation of the change rate. The above research realized the detection of some grain storage states by using the statistical characteristics of grain temperature. However, they all ensure that there is a body of grain temperature data every day through the use of interpolation, and abnormal grain temperature is detected based on continuous grain temperature data. This study used the missing grain temperature data in the time domain for the purpose of statistical analysis, verifying that abnormal grain temperature states can also be detected by reasonably setting the threshold using missing grain temperature data in the time domain, making up for the deficiencies in the practical application of the above research.

## 4. Conclusions

^{2}), and root mean square error (RMSE) were selected to evaluate the models. The indicators show that the model indicators established based on the threshold set using the 3$\mathsf{\sigma}$-threshold method were 0.056, 0.9771, and 0.0748, which is better than the values obtained for the model established using the threshold of the DBSCAN clustering method.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Layout of temperature measurement sensors in the granary. The colored circles in the figure indicates the location of the temperature measurement sensors. The green, red and purple circles in the figure form three planes parallel to XOZ.

**Figure 2.**Layout of temperature measurement in the granary. (

**a**) Plane parallel to XOY. (

**b**) Plane parallel to XOZ. (

**c**) Plane parallel to YOZ.

**Figure 3.**Model of the correlation coefficient threshold for grain temperature under different storage times.

**Figure 4.**The model of the grain temperature correlation coefficient threshold in the XOY planes: (

**a**) fitting model of clustering results with DBSCAN; (

**b**) fitting model of clustering results with 3σ.

**Figure 5.**The model of grain temperature correlation coefficient threshold on the XOZ plane. (

**a**) Fitting models of clustering results with DBSCAN. (

**b**) Fitting models of clustering results with 3$\mathsf{\sigma}$.

**Figure 6.**The model of grain temperature correlation coefficient threshold on the YOZ plane. (

**a**) Fitting models of clustering results with DBSCAN. (

**b**) Fitting models of clustering results with 3$\mathsf{\sigma}$.

**Figure 9.**Temperature field cloud map of the fourth layer on the XOY plane on 11 October 2017. The area with lower temperature in the middle is near the ventilated air duct.

**Figure 10.**Temperature field cloud map of the second layer on the XOY plane on 4 September 2018. The grain temperature in some areas of the middle exceeds 50 °C, which means that the grain is in the self-heating state.

Ranges | Levels |
---|---|

0.8~1.0 | Extremely strong correlation |

0.6~0.8 | Strong correlation |

<0.6 | Weak correlation or no correlation |

Layers | DBSCAN | 3σ | ||||
---|---|---|---|---|---|---|

p1 | P2 | q1 | p1 | P2 | q1 | |

First Layer | −780.2 | 39,970 | 39,860 | −44.64 | 1784 | 2188 |

Second Layer | −17.46 | 840.4 | 849.6 | −120.3 | 5012 | 5715 |

Third Layer | −23.89 | 1163 | 1190 | −309.1 | 13,260 | 15,480 |

Fourth Layer | −0.74 | 37.27 | 35.14 | −4.34 | 201.9 | 232.7 |

Planes | DBSCAN | 3$\mathsf{\sigma}$ | ||||
---|---|---|---|---|---|---|

p1 | P2 | q1 | p1 | P2 | q1 | |

First Layer | −23.15 | 1206 | 1247 | −984.3 | 39,150 | 47,330 |

Second Layer | −1.44 | 69.99 | 68.37 | −1038 | 42,470 | 51,250 |

Third Layer | −893 | 42,710 | 44,040 | −49.98 | 1998 | 2362 |

Fourth Layer | −1.85 | 103.1 | 106.9 | −5.81 | 246.5 | 287.5 |

Planes | DBSCAN | 3$\mathsf{\sigma}$ | ||||
---|---|---|---|---|---|---|

p1 | P2 | q1 | p1 | P2 | q1 | |

First Layer | −1.09 | 26.58 | 26.36 | −2.46 | 39.27 | 53.48 |

Second Layer | −75.52 | 2435 | 2538 | −2.55 | 39.08 | 51.47 |

Third Layer | −1.29 | 49.85 | 47.75 | −2.45 | 44.66 | 63.06 |

Fourth Layer | −5.22 | 291.8 | 292.2 | −3.28 | 93.95 | 109.1 |

Planes | DBSCAN | 3$\mathsf{\sigma}$ | ||||
---|---|---|---|---|---|---|

SSE | R^{2} | RMSE | SSE | R^{2} | RMSE | |

XOY Planes | 0.1282 | 0.9323 | 0.1223 | 0.0080 | 0.9961 | 0.0314 |

XOZ Planes | 0.1209 | 0.9306 | 0.1222 | 0.1132 | 0.9496 | 0.1188 |

YOZ Planes | 0.1723 | 0.9332 | 0.1444 | 0.0467 | 0.9857 | 0.0742 |

Means | 0.1405 | 0.9320 | 0.1296 | 0.0560 | 0.9771 | 0.0748 |

XOY Planes | 20 March 2017 and 20 April 2017 | 20 March 2017 and 20 May 2017 |
---|---|---|

First Layer | 0.133 | −0.184 |

Second Layer | 0.001 | −0.193 |

Third Layer | −0.086 | −0.257 |

Fourth Layer | −0.113 | 0.322 |

XOY Planes | 17 July 2017 and 17 August 2017 | 17 July 2017 and 28 September 2017 |
---|---|---|

First Layer | −0.216 | 0.095 |

Second Layer | −0.147 | −0.324 |

Third Layer | −0.067 | −0.113 |

Fourth Layer | 0.334 | 0.357 |

XOY Planes | 21 September 2017 and 20 October 2017 | 21 September 2017 and 31 October 2017 |
---|---|---|

First Layer | 0.176 | 0.711 |

Second Layer | −0.007 | 0.068 |

Third Layer | 0.048 | 0.067 |

Fourth Layer | −0.015 | 0.064 |

XOY Planes | 20 July 2018 and 20 August 2018 | 20 July 2018 and 20 September 2018 |
---|---|---|

First Layer | 0.234 | 0.574 |

Second Layer | 0.149 | 0.186 |

Third Layer | 0.974 | 0.911 |

Fourth Layer | 0.975 | 0.946 |

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**MDPI and ACS Style**

Cui, H.; Zhang, Q.; Wu, W.; Zhang, H.; Ji, J.; Ma, H.
Modeling and Application of Temporal Correlation of Grain Temperature during Grain Storage. *Agriculture* **2022**, *12*, 1883.
https://doi.org/10.3390/agriculture12111883

**AMA Style**

Cui H, Zhang Q, Wu W, Zhang H, Ji J, Ma H.
Modeling and Application of Temporal Correlation of Grain Temperature during Grain Storage. *Agriculture*. 2022; 12(11):1883.
https://doi.org/10.3390/agriculture12111883

**Chicago/Turabian Style**

Cui, Hongwei, Qu Zhang, Wenfu Wu, Haolei Zhang, Jiangtao Ji, and Hao Ma.
2022. "Modeling and Application of Temporal Correlation of Grain Temperature during Grain Storage" *Agriculture* 12, no. 11: 1883.
https://doi.org/10.3390/agriculture12111883