This article proposes a software fusion processing method for multi-sensor monitoring the Internet of Things based on the fractional differential filtering algorithm. The purpose is to solve the difference between the detection data caused by the difference in each production information sampling node's equipment performance and working environment. The article applies the above algorithm to the remote detection data fusion processing experiment of the discrete manufacturing system of the Internet of Things. The research found that the algorithm realizes the remote high-precision measurement of the Internet of Things sensor information. The fractional integral operator has high fusion accuracy in remote detection data fusion processing.

#### Keywords

- Integral discrete guidance
- Fractional differential equations
- Internet of things
- Differentiated data fusion
- Modeling

#### MSC 2010

- 34A08

The Internet of Things connects all objects through perception technology and identification technology and the Internet for information exchange and communication [1]. This provides universal data analysis and services based on heterogeneous Internet infrastructure and ubiquitous sensors and networks. It finally realizes the one-to-one mapping relationship between data and objects and provides query interfaces [2]. This paper proposes a discrete system differential data fusion guided by integral discrete in the Internet of Things. We first adopt the Internet of Things technology to uniformly collect and integrate the terminal data of each discrete manufacturing system under the distributed system. In addition, after summarizing all the information, we use the integral discrete guidance method to process all the differentiated data obtained to achieve the effective fusion of all data [3]. Finally, we use a set of 6 types of data of 100 nodes to test the system's performance.

An integral discrete guidance algorithm is an algorithm that uses the calculus method to fuse and uniformly process the distributed and differentiated data in the system network. We use the integration idea under the distributed system to organically combine various data in the network system [4]. Finally, the efficient integration of differentiated data is realized. The system model of the integral discrete guidance algorithm is defined as:

We need to adopt the minimization thought processing method in the integral discrete guidance algorithm [5]. Therefore, we use the variational nature of the integral discrete guided algorithm to construct the corresponding differential data guiding function, which we define as:

We need to eliminate arbitrary functions to get the final difference data guide model. Therefore,

Processing the difference data fusion algorithm guided by integral discrete can get:

The transformation properties of the difference data fusion algorithm guided by integral discrete are:

We substitute formula (6) into formula (5) and eliminate the coefficients to obtain:

The arbitrariness of the function

We use the inverse transformation of the differential data fusion algorithm guided by integral discreteness to get the partial differential equation of the corresponding differential data fusion algorithm as:

Finally, the gradient descent method of the differential data fusion algorithm can be used to obtain the model of the differential data fusion algorithm based on discrete integral guidance:

Then the difference fusion of the difference data fusion algorithm guided by discrete integral guidance in each direction is defined as:

Therefore, according to the nature of the differential data fusion algorithm guided by integral discrete, the corresponding relationship between the spatial domain and the frequency domain of the first-order difference is defined as:

In the same way, it can be seen that the corresponding relationship between the spatial domain and the frequency domain of the differential data fusion algorithm guided by integral discrete is:

We extend the integer-order

In this way, the difference data fusion algorithm guided by the integral discrete can obtain the conjugate operator of the differential operator:

There is known difference data

We use the different data fusion algorithm guided by integral discreteness to fuse the original data in different directions to form new fused output data. This can greatly improve the difference between different data of different sensor nodes in the discrete manufacturing system [7]. The flow chart of the differential data fusion algorithm guided by integral discrete is shown in Figure 1. It can be seen from Figure 1 that the differential data fusion algorithm using discrete integral guidance first needs to integrate all the data. Then judge the difference of all the data. The integration method is used to process the different data and fuse the different data. Finally, it is judged whether the system algorithm is over according to the quality of the data fusion effect.

The basic characteristics of the Internet of Things technology are mainly reflected in the following aspects [8]:

(1) Comprehensive perception. Signal detection and perception are carried out through sensors, detectors, two-dimensional codes, and even transducers. This provides preconditions for intelligent analysis and network resource sharing.

(2) Reliable delivery. Through the establishment of the Internet of a Things technology platform and the integration with the Internet, the transmission of parameter information, the sharing of information resources, and real-time processing are realized.

(3) Intelligent processing. Through modern signal and information processing technology (data mining technology, cloud processing technology, neural network system technology, pattern recognition technology), information processing and analysis of massive data and extraction of useful information [9]. In this way, the object-oriented operation and control are implemented, and the user's purpose is finally achieved.

The objective function of the differentiated data fusion system under the Internet of Things based on discrete integral guidance is defined as:

Assume that the differentiated data fusion function ^{υ(x)} satisfies:

Therefore, the system of differentiated data fusion can be expressed as:

So we use the function of the ^{υ}(Ω) space of differentiated data fusion to obtain the differentiated data fusion under the Internet of Things based on discrete integral guidance as:

In:

We get the expression of the differentiated data. It satisfies the following formula:

We still use the basic properties of the functional extremum. Let

Because when the differentiated data in the system (^{2} is:

According to the differential data equation, the final transformation form of the objective function of the differential data fusion system under the Internet of Things guided by integral discreteness can be obtained as:

The differentiated data fusion algorithm under the Internet of Things guided by integral discreteness can continuously collect data information in the Internet of Things system. It merges the differences of the differentiated data [10].

The hardware equipment used in the experiment is brand

Description of experimental parameters.

Project | Parameter Description |
---|---|

Number of difference data nodes | 100 |

Number of different data types | 6 |

Differential data distribution type | Random distribution difference |

Difference tolerance | Within the set range, a standard deviation of 1 |

Difference processing method | Equal treatment |

The system experiment is carried out under the system experiment environment constructed in Table 1. The distribution of the original data is shown in Figure 2.

It can be seen from Figure 2 that the data of each discrete manufacturing system in the original state presents the characteristics of the individual combination. It shows strong clustering nder the same rule [12]. The article uses a differentiated data fusion algorithm based on discrete integral guidance to process the above data under the Internet of Things. The result is shown in Figure 3.

Through the comparison of Figure 2 and Figure 3, it can be seen that the original data has obvious partition characteristics due to the differences in equipment and sources [13]. We use a differentiated data fusion algorithm under the Internet of Things based on discrete integral guidance to process the data, and the data distribution characteristics are more random. The data spectrum before and after the differential data fusion is shown in Figure 4.

It can be seen from Figure 4 that the spectral characteristics of the original data show a situation where six peaks are merged. The original data distribution is relatively regular, so the data peak characteristic is very strong. After the differential fusion algorithm processes the data, the data spectrum becomes a uniformly distributed random spectrum. This shows that the differences between the data have been merged.

A discrete system differential data fusion in the Internet of Things guided by integral discrete is studied. The data of each node needs to be processed separately. This article proposes a discrete system differential data fusion in the Internet of Things guided by integral discrete. Then treat all data as research objects for unified processing. Then, the method of discrete integral guidance is used to process all the obtained differential data. We integrate the data we have to judge the differences of all the data. We use the integration method to process the different data and fuse the different data to combine effectively. Finally, a set of 6 types of data of 100 nodes is used for experiments. The results show that the discrete system differential data fusion in the Internet of Things is guided by integral discreteness and the average distribution of the data spectrum. So the algorithm has a very good application value.

#### Description of experimental parameters.

Project | Parameter Description |
---|---|

Number of difference data nodes | 100 |

Number of different data types | 6 |

Differential data distribution type | Random distribution difference |

Difference tolerance | Within the set range, a standard deviation of 1 |

Difference processing method | Equal treatment |

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