## 5 An Engineering Mechanics Experimental Method Based on the Wireless Sensor Network
### The Design of the Wireless Sensor Algorithm Model in an Engineering Mechanics Experiment  
(1) The initial dataset partitioning algorithm based on wireless sensor density sensing  
We assumed that the dataset of the designed mechanical test was \(X=\{x_{1},x_{2},\ldots,x_{\text{N}}\}\), and each data point within the dataset was \(x_{i}=\{x_{i1},\,x_{i2},\,\ldots,\,x_{\text{M}}\}\), where M represents the number of data test traits. The cluster center of the data is ordinarily determined by a neighbor test focused on the density, and the data centers with a high neighborhood density maintain a large distance between them. The local density of sample data \(x_{i}\) is expressed as \(\rho_{i}\):  
\[\rho_{i}=\sum_{j=1}^{N}\exp\left[-\left(\frac{\parallel\mathbf{x}_{i}-\mathbf{x}_{j} \parallel}{d_{c}}\right)^{2}\right], \tag{22}\]  
where \(\parallel x_{i}-x_{j}\parallel\) represents the Euclidean distance between \(x_{i}\) and \(x_{j}\); \(d_{c}\) is a predefined truncation distance, usually the first 1\(\sim\)2% of the truncation distance of all samples. The local density pi represents the number of data points whose distance from the sample data \(x_{i}\) is less than \(d_{c}\). The more data points that are less than \(d_{c}\) from the sample data \(x_{i}\), the greater the density value \(\rho_{i}\). The characteristic distance represents the minimum distance between the engineering mechanics test sample data \(x_{i}\) and the sample data with higher local density:  
\[\delta_{i}=\underset{x_{j}\
eq\rho_{i}}{\min}\big{(}\parallel\mathbf{x}_{i}-\mathbf{x }_{j}\parallel\big{)}\, \tag{23}\]  
where \(\delta_{i}\) represents the shortest distance between the engineering mechanics test sample data \(x_{i}\) and the other high-density engineering mechanics test sample data. The sample data with high local density and large feature distance are more likely to become the cluster center. The direct neighbor \(q\) represents the direct neighbor of the engineering mechanics test sample data \(p\), which is defined as:  
\[q=\arg\underset{j\
eq\rho_{p}>\rho_{i}}{\min}\big{(}\parallel\mathbf{x}_{i}-\mathbf{x }_{p}\parallel\big{)}. \tag{24}\]  
The engineering mechanics test sample data \(x_{i}\) with the highest density has no direct neighbor, and the characteristic distance of such sample data is:  
\[\delta_{s}=\underset{s\
eq i}{\max}(\parallel\mathbf{x}_{i}-\mathbf{x}_{s}\parallel). \tag{25}\]  
To build a directed acyclic graph (DAG) based on the wireless sensor networks, the test dataset of the construction machinery was divided into several levels according to the characteristic distance. If the dataset has a small feature distance, the data samples and their neighbors belong to the same category, while the feature points with a large feature distance and their neighbors do not belong to the same category. Therefore, after several iterations, the engineering mechanics test sensor dataset was divided into several temporary categories, as shown in Figure 6.  
Finally, we clustered the number of remote sensor hubs C according to the fuzzy clustering calculation and intertwined the M temporary classes created to create the starting density-based parcel of the dataset. The clustering was conducted according to the following steps:  
Step 1 Using the formula \(\gamma\)i = \(\rho\)i\(\delta\)i, we calculated the \(\gamma\). The M transitory cluster centers were \(\gamma\) in descending order;  
Step 2 After calculating the \(\gamma\), we selected the cluster center of the primary C temporary classes as the introductory cluster center of the fuzzy clustering;  
Step 3 We merged the tests within the remaining temporary classes into the primary C temporary classes where their neighbors were found, totaled the combination of the temporary classes, and framed the beginning parcel of the dataset. (2) The fuzzy clustering algorithm based on sensor node density perception  
The wireless strain sensor based on a fuzzy clustering algorithm was used to test the loading strain of reinforced concrete beams.