Deep belief network (DBN) is an effective deep learning model, which can learn the complex data by extracting features hierarchically. However, the successful application of DBN depends on the suitable size of the structure (the number of hidden neurons), which is still an open problem. Currently, the network structure size is basically determined by experience with a time-consuming process. In this article, a complexity-based structural optimization (CBSO) algorithm, based on multiobjective ordinal optimization (MOO), is developed for designing the DBN structure. First, the problem formulation of structural optimization of DBN is given, where the multiple objectives are to minimize the fitting error and complexity. Second, the lower bound for alignment probability in optimizing DBN structure is developed according to MOO. Finally, an effective method to maximize the probability of correct select is given to pursue the good tradeoff between the complexity and the performance. The performance of proposed CBSO algorithm is demonstrated via predicting and controlling water quality of wastewater treatment process (WWTP) using the CBSO-DBN-based model predictive control (MPC) strategy. The simulation results show that the resulting CBSO-DBN can find the better structure design by using CBSO algorithm with smaller fitting error and limited computational complexity, and thereby achieve the better performance in WWTP than its peers. Especially, the CBSO-DBN-MPC improves the control accuracy by 76.16% and computational complexity by 50.45%, respectively.

Globally, wind power plays a leading role in the renewable energy industry. In order to ensure the normal operation of a wind farm, the staff will regularly check the equipment of the wind farm. However, manual inspection has some disadvantages, such as heavy workload, low efficiency and easy misjudgment. In order to realize automation, intelligence and high efficiency of inspection work, inspection robots are introduced into wind farms to replace manual inspections. Path planning is the prerequisite for an intelligent inspection robot to complete inspection tasks. In order to ensure that the robot can take the shortest path in the inspection process and avoid the detected obstacles at the same time, a new path-planning algorithm is proposed. The path-planning algorithm is based on the chaotic neural network and genetic algorithm. First, the chaotic neural network is used for the first step of path planning. The planning results are encoded into chromosomes to replace the individuals with the worst fitness in the genetic algorithm population. Then, according to the principle of survival of the fittest, the population is selected, hybridized, varied and guided to cyclic evolution to obtain the new path. The shortest path obtained by the algorithm can be used for the robot inspection of the wind farms in remote areas. The results show that the proposed new algorithm can generate a shorter inspection path than other algorithms.

Aiming at the problem that the global search performance of a transiently chaotic neural network is not ideal, a multiple frequency conversion sinusoidal chaotic neural network (MFCSCNN) model is proposed based on the biological mechanism of the brain, including multiple functional modules and sinusoidal signals of different frequencies. In this model, multiple FCS functions and Sigmoid functions with different phase angles were used to construct the excitation function of neurons in the form of weighted sum. In this paper, the inverted bifurcation diagram, Lyapunov exponential diagram and parameter range of the model are given. The dynamic characteristics of the model are analyzed and applied to function optimization and combinatorial optimization problems. Experimental results show that the multiple frequency conversion sinusoidal chaotic neural network has better global search performance than the transient chaotic neural network and other related models.

Bearing fault diagnosis under varying operating conditions faces speed and data-source shifts that can make models unreliable outside their development regime. Record-level diagnosis therefore requires both fault classification and an automatic accept-or-defer decision. This study proposes Support-Bounded Confidence-First Selective Evidence Diagnosis (CSED), which separates evidence applicability from selective acceptance. CSED combines a frequency-domain logistic regression anchor with an acceleration-only WaveCNN expert. A prespecified support gate and calibration criterion admit waveform evidence; otherwise, the frequency anchor is retained. Records are ranked by a fixed confidence-risk score and accepted at prespecified coverage levels without a learned router or evaluation-label tuning. On the primary HUST (Huazhong University of Science and Technology) held-speed profile, five predeclared seed pairs yielded 270 pooled descriptive model-record predictions from 54 held record identifiers. Full-coverage Macro-F1/error was 0.8701/0.1333; at the prespecified 80% target, accepted Macro-F1/error was 0.9406/0.0602 and deferred error was 0.4259. Removing the support boundary increased observed accepted error, but the paired record-identifier-cluster bootstrap interval included zero, so this result is directional rather than statistically established. Additional variable-speed, cross-source, and frequency-anchor tests assess behavior beyond the primary profile. The results support the selective-diagnosis policy only under the evaluated record-wise protocol, not cross-source waveform transfer or bearing-wise generalization.