This paper presents a simple DFT-based golden section searching algorithm (DGSSA) for the single tone frequency estimation. Because of truncation and discreteness in signal samples, Fast Fourier Transform (FFT) and Discrete Fourier Transform (DFT) are inevitable to cause the spectrum leakage and fence effect which lead to a low estimation accuracy. This method can improve the estimation accuracy under conditions of a low signal-to-noise ratio (SNR) and a low resolution. This method firstly uses three FFT samples to determine the frequency searching scope, then – besides the frequency – the estimated values of amplitude, phase and dc component are obtained by minimizing the least square (LS) fitting error of three-parameter sine fitting. By setting reasonable stop conditions or the number of iterations, the accurate frequency estimation can be realized. The accuracy of this method, when applied to observed single-tone sinusoid samples corrupted by white Gaussian noise, is investigated by different methods with respect to the unbiased Cramer-Rao Low Bound (CRLB). The simulation results show that the root mean square error (RMSE) of the frequency estimation curve is consistent with the tendency of CRLB as SNR increases, even in the case of a small number of samples. The average RMSE of the frequency estimation is less than 1.5 times the CRLB with SNR = 20 dB and N = 512.

The inspection of railway fasteners to assess their clamping force can be used to evaluate the looseness of the fasteners and improve railway safety. Although there are various methods for inspecting railway fasteners, there is still a need for non-contact, fast inspection without installing additional devices on fasteners. In this study, a system that uses digital fringe projection technology to measure the 3D topography of the fastener was developed. This system inspects the looseness through a series of algorithms, including point cloud denoising, coarse registration based on fast point feature histograms (FPFH) features, fine registration based on the iterative closest point (ICP) algorithm, specific region selection, kernel density estimation, and ridge regression. Unlike the previous inspection technology, which can only measure the geometric parameters of fasteners to characterize the tightness, this system can directly estimate the tightening torque and the bolt clamping force. Experiments on WJ-8 fasteners showed a root mean square error of 9.272 N·m and 1.94 kN for the tightening torque and clamping force, demonstrating that the system is sufficiently precise to replace manual measurement and can substantially improve inspection efficiency while evaluating railway fastener looseness.

Continuous monitoring of pathological motor features is vital for post-stroke rehabilitation but remains challenged by power reliance and low sensitivity of wearable sensors. Here, we develop a high-sensitivity, self-powered breathable nanogenerator (BN-TENG) utilizing fish-scale-derived biological hydroxyapatite/carbon (Bio-HAp/C) fillers within electrospun polyvinylidene fluoride (PVDF) nanofibers. The Bio-HAp/C enhances electron-trapping capability, while a high-resilience ethylene-vinyl acetate (EVA) spacer optimizes contact-separation dynamics. The BN-TENG achieves a superior sensitivity of 16.28 V·N⁻¹ and remarkable stability over 10,000 cycles. By implementing a multi-node sensing strategy, the sensor successfully captures complex hemiplegic patterns, including compensatory shoulder hiking, distal muscle spasticity, and postural asymmetry. By resolving subtle micro-vibrations missed by traditional electronics, this work provides a sustainable, autonomous interface for characterizing pathological motor features and assessing rehabilitation progress in hemiplegic patients.