To address the contradiction between the convergence error and convergence rate in the LMS algorithm, this study proposes a variable-step-size adaptive filter algorithm with a momentum term based on the logistic function. First, the normalization LMS algorithm is obtained by seeking the extremum under the Lagrange function constraint. Second, to reduce the convergence error of the algorithm, the logistic model is used as a function model of step size variation with error, resulting in a variable-step normalization LMS algorithm. Our experimental results demonstrate that this algorithm achieves smaller convergence errors compared to those of the traditional LMS algorithm. Finally, to further improve the convergence rate of the algorithm, a momentum term is introduced into the weight coefficient update process of the LMS algorithm. This leads to the development of a variable-step adaptive filter algorithm with a momentum term based on the logistic function. The impact of different parameters on the algorithm performance is also investigated. In order to verify the rationality of the proposed algorithm, a dynamic system mathematical model was identified using the proposed algorithm. The results showed that the proposed algorithm had an identification accuracy of over 97% for the mathematical model parameters and a suppression of over 99% for noise. In order to verify the engineering application value of the proposed algorithm, real-time vibration data fitting experiments were conducted in the Aeroelasticity Laboratory of the China Aerodynamics Research and Development Center, and their results were compared with three algorithms: ARMAX, N4SID, and LMS. The results showed that the proposed algorithm had a higher fitting accuracy than the three others. Through simulations and experiments, it is demonstrated that this study has value both theoretically and in engineering applications, promoting engineering applications of adaptive filtering algorithms and providing strong support for the research of adaptive control.

A new type of gust generator generates the airflow oscillation in the wind tunnel through the Coanda effect of the unsteady trailing edge blowing, which has been shown to have strong potential for accurately simulating discrete gusts. It is necessary to study the relationship between the generated gust characteristics and the control parameters of such devices in order to optimize the design performance and improve gust simulation capabilities. By solving the compressible unsteady Reynolds-averaged Navier–Stokes (URANS) equations, the computational fluid dynamics model of the subsonic airflow past the gust generator in the wind tunnel was presented. The effects of jet momentum, frequency, and spanwise blowing ratio on gust intensity, shape, and spatial uniformity were investigated. Results indicate that the intensity of gusts is positively correlated with jet momentum and frequency. The gust shape matches well with the normalized jet momentum coefficient curve. However, when the frequency increases to above 10 Hz, the gust shape differs significantly from expectation due to the appearance of reverse wave peaks. In addition, the mechanism of the impact of the sidewall and partial spanwise blowing on gusts was revealed. In the three-dimensional situation, streamwise vortices are formed on the sidewall and at the spanwise position where the blowing stops, respectively. This results in an increase and noticeable nonuniformity in gust amplitude. When the blowing with a 15% spanwise length near the sidewall is turned off, the gust amplitude at the symmetry plane increases by nearly 40% due to the main vortex being closer to the main flow. The result provides a physical explanation for the availability of this operation to reduce gust attenuation.