A prototype of a solar ground-layer adaptive optics (GLAO) system, which consists of a multi-direction correlating Shack–Hartmann wavefront sensor with 30 effective subapertures and about a 1 arcmin field of view (FoV) in each subaperture, a deformable mirror with 151 actuators conjugated to the telescope entrance pupil, and a custom-built real-time controller based on field-programmable gate array and multi-core digital signal processor (DSP), is implemented at the 1 m New Vacuum Solar Telescope at Fuxian Solar Observatory and saw its first light on January 12th, 2016. The on-sky observational results show that the solar image is apparently improved in the whole FoV over 1 arcmin with the GLAO correction.

In solar observations, the vertical distribution of turbulence can be detected with a multidirectional Shack–Hartmann wavefront sensor, based on SLODAR or S-DIMM+. By expressing the measured cross-correlation as a linear combination of theoretical correlation functions for various height layers, the distribution of turbulence intensity can be obtained through fitting. The theoretical correlation functions in different heights are employed to describe the slope correlation and calculated based on the phase structure function corresponding to classical turbulence statistical theories such as Kolmogorov or von Karman. However, for turbulence that does not obey classical theory, this deviation of the statistical characteristics would result in the measurement accuracy degradation of seeing profiles. A method, so-called AutoCorrelation-SLODAR (AC-SLODAR), is proposed. The feasibility of transforming cross-correlation into autocorrelation is analysed theoretically. Then, the autocorrelation function is calculated based on the actual data to avoid the deviation introduced by the theoretical turbulence statistical model. Extracting statistical characteristics from data also simplifies measurements, without requiring the evaluation of whether the data conforms to a particular classical statistical model. AC-SLODAR was validated with simulation data generated by the open-source emulator SOAPY. The measured error was reduced by 10 per cent compared with SLODAR for the situation of turbulence model deviation. The performance of AC-SLODAR was further compared with those of SLODAR based on the actual data collected in 2016 and 2017 on the New Vacuum Solar Telescope. The corresponding results of AC-SLODAR are consistent with those of SLODAR using a pre-evaluated turbulent model.

The tuning of fractional-order proportional-integral-derivative (FOPID) controllers for automatic voltage regulator (AVR) systems presents a complex challenge, necessitating the solution of real-order integral and differential equations. This study introduces the Dumbo Octopus Algorithm (DOA), a novel metaheuristic inspired by machine learning with animal behaviors, as an innovative approach to address this issue. For the first time, the DOA is invented and employed to optimize FOPID parameters, and its performance is rigorously evaluated against 11 existing metaheuristic algorithms using 23 classical benchmark functions and CEC2019 test sets. The evaluation includes a comprehensive quantitative analysis and qualitative analysis. Statistical significance was assessed using the Friedman’s test, highlighting the superior performance of the DOA compared to competing algorithms. To further validate its effectiveness, the DOA was applied to the FOPID parameter tuning of an AVR system, demonstrating exceptional performance in practical engineering applications. The results indicate that the DOA outperforms other algorithms in terms of convergence accuracy, robustness, and practical problem-solving capability. This establishes the DOA as a superior and promising solution for complex optimization problems, offering significant advancements in the tuning of FOPID for AVR systems.