In an effort to overcome the problem that the traditional stochastic resonance system cannot adjust the structural parameters adaptively in bearing fault-signal detection, this article proposes an adaptive-parameter bearing fault-detection method. First of all, the four strategies of Sobol sequence initialization, exponential convergence factor, adaptive position update, and Cauchy–Gaussian hybrid variation are used to improve the basic grey wolf optimization algorithm, which effectively improves the optimization performance of the algorithm. Then, based on the multistable stochastic resonance model, the structure parameters of the multistable stochastic resonance are optimized through improving the grey wolf algorithm, so as to enhance the fault signal and realize the effective detection of the bearing fault signal. Finally, the proposed bearing fault-detection method is used to analyze and diagnose two open-source bearing data sets, and comparative experiments are conducted with the optimization results of other improved algorithms. Meanwhile, the method proposed in this paper is used to diagnose the fault of the bearing in the lifting device of a single-crystal furnace. The experimental results show that the fault frequency of the inner ring of the first bearing data set diagnosed using the proposed method was 158 Hz, and the fault frequency of the outer ring of the second bearing data set diagnosed using the proposed method was 162 Hz. The fault-diagnosis results of the two bearings were equal to the results derived from the theory. Compared with the optimization results of other improved algorithms, the proposed method has a faster convergence speed and a higher output signal-to-noise ratio. At the same time, the fault frequency of the bearing of the lifting device of the single-crystal furnace was effectively diagnosed as 35 Hz, and the bearing fault signal was effectively detected.

In light of the problem of difficult model parameter selection and poor resonance effects in traditional bearing fault detection, this paper proposes a parameter-adaptive stochastic resonance algorithm based on an improved whale optimization algorithm (IWOA), which can effectively detect bearing fault signals of rotating machinery. First, the traditional WOA was improved with respect to initial solution distribution, global search ability and population diversity generalization, effectively improving the global convergence of the WOA. Then, the parameters of the bistable stochastic resonance model were optimized using the improved WOA, and adaptive adjustment of the stochastic resonance parameters was realized. Finally, the Case Western Reserve University bearing data set and the XJTU-SY bearing data set were used as fault data for the actual bearing to be tested for experimental verification. The signal-to-noise ratios of the detected fault frequencies for the above two data sets were −20.5727 and −21.1289, respectively. Among the algorithms compared, the IWOA proposed in this paper had the highest signal-to-noise ratio of the detected fault frequencies. The experimental results show that the proposed method can effectively detect a weak bearing fault signal in enhanced noise.

To solve the problem of the common unsteady inverse heat conduction problem in the industrial field, a real-time solution method of improving the whale optimization algorithm (IWOA) and parameter-adaptive proportional-integral-differential (PID) is proposed in the paper. A feedback control system with IWOA-PID, which can inversely solve the boundary heat flux, is established. The deviation between the calculated temperature and the measured temperature of the measured point obtained by solving the direct heat conduction problem (DHCP) is used as the system input. The heat flux which is iteration-solved by IWOA-PID is used as system output. The method improves the initial solution distribution, global search capability and population diversity generalization of the traditional whale optimization algorithm (WOA), which effectively improves the parameter-adaptive capability of PID. The experimental results show that the solution method of inverse heat transfer proposed in the paper can accurately retrieve the variation of the boundary heat flux in real time and has good resistance and self-adaptability.

Aiming at the poor effect of traditional denoising algorithms on image enhancement with strong noise, an image denoising algorithm based on improved whale optimization algorithm and parameter adaptive array stochastic resonance is proposed in the paper. In this algorithm, through dimensionality reduction scanning, coding, modulation and other processing, the noise-containing gray image becomes a one-dimensional aperiodic binary pulse amplitude modulation signal suitable for a bistable stochastic resonance model. Then, the traditional whale optimization algorithm is improved in the initial solution distribution, global search ability and population diversity generalization. The improved whale optimization algorithm is applied to select the parameters of the stochastic resonance, which effectively improves the parameters self-adaptive of the array stochastic resonance model. Finally, the denoised image is obtained by demodulating, decoding and anti-scanning the stochastic resonance output. The experimental results show that compared with the array stochastic resonance method with fixed parameters and the classical image denoising method, the algorithm proposed in this paper has better performance in terms of visual effect and peak signal-to-noise ratio index, which proves the advantages and effective application of the method in image denoising.

Conditions are investigated in this paper for uniquely determining parameters of a descriptor system from time-domain noise-free input/output data, in which system matrices depend on its parameters through a linear fractional transformation. This model includes networked dynamic systems as its special cases. A bilinear matrix equality based necessary and sufficient condition has been derived, which can be verified in principle for a low dimensional system. Moreover, a computationally attractive condition is derived under the orthogonality of some transfer function matrices. These results completely remove the full rank assumption required in the available studies. A circuit example is given to illustrate their properties.

The object tracking algorithm TransT, based on Transformer, achieves significant improvements in accuracy and success rate by fusing the extracted features of convolutional neural networks with the structure of Transformer. However, when dealing with the deformation of the object’s appearance, the algorithm exhibits issues such as insufficient tracking accuracy and drift, which directly affect the stability of the algorithm. In order to overcome this problem, this paper demonstrates how to expand scene information at the scale level during the fusion process and, on this basis, achieve accurate recognition and positioning. The predicted results are promptly fed back to the subsequent tracking process, from which temporal templates are embedded. Starting from both location and time can effectively improve the adaptive ability of the tracking model. In the final experimental comparison results, the algorithm proposed in this paper can adapt well to the situation of object deformation, and the overall performance of the tracking model has also been improved.