The research on wireless sensor networks has achieved a lot in recent years and some of the results have been put into practical applications, but with the increasing demand and requirements for wireless sensor networks, many old and new problems need to be solved urgently. In this paper, a data topology optimization algorithm based on local tree reconstruction for heterogeneous wireless sensor networks is proposed for data transmission in wireless sensor networks that are easily affected by external instabilities. This heterogeneous network can accomplish better data transmission; firstly, the nodes are divided into different layers according to the hop count of nodes in the network, and a certain proportion of relay nodes are selected for different layer nodes; then, different initial energy is set for different layer nodes, and since the data packets of different nodes have different sizes, the corresponding data aggregation coefficients are used in this paper according to the actual data requirements of the network during data transmission; finally, the topology of the tree is dynamically updated in real time during the operation of the network to extend the lifetime of the nodes. The simulation results verify that the proposed heterogeneous network topology evolution algorithm effectively extends the network lifetime and improves the utilization of nodes. This paper establishes a modified least-squares target localization model to achieve accurate 3D localization of targets in real scenes and proposes an optimal base station node selection strategy based on spectral clustering using the location distribution information of base station nodes in space. The simulation results show that the error of the terminal 3D coordinates calculated by the proposed algorithm is smaller than the real coordinates, and the error is smaller than other existing algorithms with the same simulation data.

This paper refers to the Lagrangian mathematical model and the Rackwitz-Fiessler transform model in modeling advanced mathematics applications. In this paper, the Lagrangian interpolation method and Rackwitz-Fiessler transform are used to calculate the correlation coefficient efficiently. The purpose of this algorithm is to speed up the process of probabilistic modeling. This paper uses integral probability transformation to characterize the output's uncertainty by the production's joint distribution function. The purpose of this process is to improve the reliability of the calculation. Through the algorithm analysis, it is found that the method is reasonable and efficient.

The paper analyzes the thermo-mechanical couplinag phenomenon under the condition of sliding contact, establishes the finite element analysis continuous model of thermo-mechanical coupling, and proposes the system dynamic equilibrium equation and thermodynamic equilibrium equation. The article analyzes the contact conditions between the objects in the system and obtains the objects? contact conditions? mathematical expression. On this basis, the constraint function is used to express the mathematical homogenization. We apply the variation principle to the constraint function and form a non-linear equation group with the system balance equation solve the thermal-mechanical coupling problem. The example shows that we use the constraint function method to solve the thermo-mechanical coupling problem, which has good convergence, stable algorithm, and the calculation result can reflect the actual situation.