The joint time–frequency (TF) distribution is a critical method of describing the instantaneous frequency that changes with time. To eliminate the errors caused by strong modulation and noise interference in the process of time-varying fault feature extraction, this paper proposes a novel approach called second-order time–frequency sparse representation (SOTFSR), which is based on convex optimization in the domain of second-order short-time Fourier transform (SOSTFT) where the TF feature manifests itself as a relative sparsity. According to the second-order local estimation of the phase function, SOSTFT can provide a sparse TF coefficient in the short-time Fourier transform (STFT) domain. To obtain the optimal TF coefficient matrix from noisy observations, it is innovatively formulated as a typical convex optimization problem. Subsequently, a multivariate generalized minimax concave penalty is employed to maintain the convexity of the least-squares cost function to be minimized. The aim of the proposed SOTFSR is to obtain the optimal STFT coefficient in the TF domain for extraction of time-varying features and for perfect signal reconstruction. To verify the superiority of the proposed method, we collect the multi-component simulation signals and the signals under variable speed from a rolling bearing with an inner ring fault. The experimental results show that the proposed method can effectively extract the time-varying fault characteristics.

Ultrasonic testing is a useful approach for quantifying the flaws in mechanical components. The height of the flaws in ultrasonic angle beam testing is closely related to the calibration value of the probe refraction angle. In order to reduce the calibration error, some ignored data during the traditional calibration process are reanalyzed and fused to determine the refraction angle. Both arithmetical measurement fusion method and weighted measurement fusion method are applied and compared. Monte Carlo simulation is used to estimate the probability distribution of the refraction angle and obtain the optimal refraction angle weights. Experiments were carried out to verify the results of Monte Carlo simulation. The applicability of data fusion on refraction angles is investigated. It was found in the study that the data fused with the refraction angle is helpful for measuring the height of flaws.

Two disputes about the metallographic testing of welding joints of the high alloy steel on-site installation welding of the current power plant boiler are discussed. This thesis analyzes the reasons for the two dispute. On this basis, the accordance for the detection, detection method, qualification assessment standard and the ratio of detected parts to quantity are defined. This paper can provide reference for strengthening the quality of welding joints for high alloy steel installation welding of power station boilers.