Aiming at the problems of nonlinearity and serious confusion of fault characteristics in analog circuits, this paper proposed a fault diagnosis method for an analog circuit based on ensemble empirical pattern decomposition (EEMD) and improved multifractal detrended fluctuations analysis (MF-DFA). This method consists of three steps: preprocessing, feature extraction, and fault classification identification. First, the EEMD decomposition preprocesses (denoises) the original signal; then, the appropriate IMF components are selected by correlation analysis; then, the IMF components are processed by the improved MF-DFA, and the fault feature values are extracted by calculating the multifractal spectrum parameters, and then the feature values are input to a support vector machine (SVM) for classification, which enables the diagnosis of soft faults in analog circuits. The experimental results show that the proposed EEMD-improved MF-DFA method effectively extracts the features of soft faults in nonlinear analog circuits and obtains a high diagnosis rate.

It is difficult for traditional circuit-fault feature-extraction methods to accurately distinguish between nonlinear analog-circuit faults and analog-circuit faults with high fault rates and high diagnostic costs. To solve this problem, this paper proposes a method of mathematical morphology fractal dimension (VMD-MMFD) based on variational mode decomposition for soft-fault feature extraction in analog circuits. First, the signal is decomposed into variational modes to suppress the influence of environmental noise, and multiple high-dimensional eigenmode functions with different center frequencies are obtained. The fractal dimension of the signal feature information component IMF is calculated, and then, KPCA (Kernel Principal Component Analysis) is used to remove the overlapping and redundant parts of the data. The fault set obtained is used as the basis for judging the working state and the fault type of the circuit. The experimental results of the simulation circuits show that this method can be effectively used for circuit-fault diagnosis.

Aiming at the problems of low reconstruction rate and poor reconstruction precision when reconstructing sparse signals in wireless sensor networks, a sparse signal reconstruction algorithm based on the Limit-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) quasi-Newton method is proposed. The L-BFGS quasi-Newton method uses a two-loop recursion algorithm to find the descent direction dk directly by calculating the step difference between m adjacent iteration points, and a matrix Hk approximating the inverse of the Hessian matrix is constructed. It solves the disadvantages of BFGS requiring the calculation and storage of Hk, reduces the algorithm complexity, and improves the reconstruction rate. Finally, the experimental results show that the L-BFGS quasi-Newton method has good experimental results for solving the problem of sparse signal reconstruction in wireless sensor networks.

The improvement of coverage is a critical issue in the coverage hole patching of sensors. Traditionally, VOPR and VORCP algorithms improve the coverage of the detection area by improving the original VOR algorithm, but coverage hole patching algorithms only target homogeneous networks. In the real world, however, the nodes in the wireless sensor network (WSN) are often heterogeneous, i.e., the sensors have different sensing radii. The VORPH algorithm uses the VOR in a hybrid heterogeneous network and improves the original algorithm. The patched nodes are better utilized, and the detection range is enlarged. However, the utilization rate of the patched nodes is not optimized, making it impossible to patch the coverage holes to the maximum degree. In the environment of hybrid heterogeneous WSN, we propose a coverage hole patching algorithm with a priority mechanism. The algorithm determines the patching priority based on the size of the coverage holes, thereby improving network coverage, reducing node redundancy, and balancing resource allocation. The proposed algorithm was compared under the same environment by simulation and analysis. The results show that our algorithm is superior to the traditional coverage hole patching algorithms in coverage rate, and can reduce node redundancy.

Aiming at the problems of data loss and uneven energy consumption in wireless sensor networks during data transmission, this paper proposes a ReInForM transmission fault-tolerant routing algorithm based on energy selection and erasure code fault-tolerant machines (E-ReInForMIF). The E-ReInForMIF algorithm improves the multi-path routing algorithm by combining an erasure coding fault-tolerant machine and node residual energy sorting selection. First, the erasure coding fault-tolerant machine is used to encode the signal, determine the number of transmission paths through multi-path routing, and then select the specific node of the next hop by sorting the residual energy of the node. The E-ReInForMIF routing algorithm effectively solves the problems of uneven energy consumption and data loss in data transmission, improving network lifespan and transmission reliability. Finally, the signal is decoded. The simulation results show that the E-ReInForMIF routing algorithm is superior to the ReInForM routing algorithm in improving the reliability of data transmission.