An enhanced adaptive notch filtering method for online multi-frequency estimation from contaminated signals of a mechanical control system

Abstract

Real-time frequency information is extremely important in many fields of mechanical engineering, such as fault diagnosis, noise and vibration control, underwater acoustic detection, vehicle communication, etc. However, sometimes frequencies cannot be directly detected, making it important to quickly and accurately estimate the frequencies from contaminated signals of a mechanical system. An adaptive notch filter (ANF) is one of the most popular methods for online frequency estimation due to its simple structure and low computational complexity. However, ANF is a biased estimation if the signal contains uncorrelated noise. An enhanced adaptive notch filtering (EANF) method, which is able to reduce the frequency estimation bias and improve the estimation speed from contaminated signals, is proposed in this paper. Firstly, the limitations of the traditional ANF method are theoretically and numerically analyzed. Then, the principles of the proposed EANF method are formulated, including key parameter optimization and uncorrelated noise compensation in the update process. Afterwards, a multiple extension of the proposed EANF method is constructed using the adaptive simultaneous structure. The results of the numerical simulation show that the proposed method is superior to traditional ones. Finally, a two-stage vibration isolation system is established for experimental validation. The experimental results also demonstrate the effectiveness of the proposed method.

Autocorrelation energy and aquila optimizer for MED filtering of sound signal to detect bearing defect in Francis turbine

“…n (t) indicates the noise and R n (t) is strenuous about τ = 0 as shown in figure 4. The signal in R s (τ ) has the same angular frequency ω 0 as that of s (t) from equation (9). When τ gets greater, R x (τ ) solely reflects R s (τ ), hence R x (τ ) may be used to calculate the amplitude and frequency of s (t), as illustrated in figure 5.…”

“…Thus, the contactless method is preferred in this scenario to acquire the data. The sound-based technique [9][10][11][12] is one of the contactless techniques that can help in detecting the bearing defects of the Francis turbine. The extraction of periodic fault characteristics from acoustic signals is the vital in the diagnosis procedure.…”