This paper proposes a novel data-driven adaptive decomposition method named broadband mode decomposition (BMD) for analyzing complex signals containing broadband components, such as square signals and sawtooth signals. For effective broadband signals with “sharp corners”, an unavoidable error occurs when applying former methods, such as variational mode decomposition (VMD) and ensemble empirical mode decomposition (EEMD), due to the Gibbs phenomenon and the interpolation of extreme points. Therefore, we propose BMD for separating the broadband modes, narrowband modes and noise in a complex nonstationary signal. First, an associative dictionary library consisting of typical broadband signals and narrowband signals is established. Second, a smoothness function is employed as the optimization objective function, and the amplitude, frequency and phase of the broadband signals and the filter parameters of the narrowband signals are applied as optimization parameters. Third, the sparsest decomposition results are obtained by searching the dictionary using an artificial chemical reaction optimization algorithm (ACROA). The simulation and experimental signal analyses indicate that BMD is more accurate than EEMD and VMD in extracting broadband components from a noisy signal and that BMD is suitable for quality evaluations of welding inverter power source signals.

The application of photovoltaic power is becoming more and more extensive presently, when the existing time-frequency analysis methods are used to analyze photovoltaic mutation signals such as transient rise and transient fall, the cornered signal will produce Gibbs phenomenon and leads to errors. Thus, the Broadband Mode Decomposition (BMD) method is proposed. The main idea of BMD is to search in the associated dictionary that contains the wideband and narrowband signals. However, the BMD algorithm may treat the wideband signal as several narrowband components, when applied to a wideband signal interfered by strong noise, because the relative bandwidth is not sufficiently small. Therefore, a modulated broadband modal decomposition (MBMD) based on the modulation differential operator is proposed. By multiplying a high-frequency single-frequency signal, the relative bandwidth of the effective wideband signal is much smaller than 1, and the wideband signal is processed as an approximate wideband signal. Meanwhile, because the errors of the traditional dot product sum algorithm in DC energy measurement cannot be positive and negative offset, while the compound Simpson integral algorithm has small error and high calculation accuracy. Therefore, a photovoltaic DC power calculation method based on the MBMD and compound Simpson integration is proposed.

A lot of adaptive signal decomposition methods have been applied for nonstationary DPMIG electrical signals as they are always affected by noise. Recently, to solve the problems of former methods caused by the Gibbs phenomenon and the calculation of extremas when dealing with broadband electrical signals such as square signals and sawtooth signals with “sharp corners”, broadband mode decomposition (BMD) method was proposed and the application of the algorithm showed a good performance. The main idea of BMD is searching in the associative dictionary contains both broadband and narrowband signals using a regulated differential operator as the optimal object. However, when applied to a broadband signal interfered by strong noise, as the relative bandwidth is not small enough, the BMD algorithm may treat the broadband signal to be several narrowband components. Therefore, modulated broadband mode decomposition (MBMD) is proposed in this paper to denoise broadband electrical signals based on modulated differential operator. By multiplying a high frequency mono-frequency signal, the relative bandwidth of the effective broadband signal is translated to be far less than 1, and the broadband signals are treated as approximate broadband signals to get more accurate decomposition results. For the further feature extraction of the electrical signals, locality preserving projection (LPP) is applied combined with MBMD. The effectiveness of the proposed method is testified by simulation and experimental signals, results show that it is effective when drawing broadband feature from noise, as well as is adaptive for the feature extraction of double pulse metal inert gas welding.

There are two difficulties in the remaining useful life prediction of rolling bearings. First, the vibration signals are always interfered by noise signals. Second, some of the extracted features include useless information which may decrease the prediction accuracy. In order to solve the problems above, corresponding methods are employed in this article. First, adaptive sparsest narrow-band decomposition is utilized for extracting the degradation information from noise. Compared with the commonly used empirical mode decomposition method, problems including mode mixture and boundary effect caused by the calculation of extremas is not required. Second, locality-preserving projection is applied for merging the meaningful information from the original data and reduces the dimension of features. Based on adaptive sparsest narrow-band decomposition and locality preserving projection, a novel approach is employed for the remaining useful life prediction. The prediction procedure is as follows. First, the signals are analyzed by adaptive sparsest narrow-band decomposition and the feature vectors are constructed. Afterwards, the features are fused by locality preserving projection to merge useful information from the features. Least squares support vector machine is applied for the remaining useful life prediction in the end. The analysis results indicate that the proposed approach is reliable for rolling bearing remaining useful life prediction.

A novel adaptive signal decomposition algorithm, broadband mode decomposition (BMD), is proposed for analyzing nonstationary broadband signals. Unavoidable error will occur when applying former time-frequency methods to broadband signals, which is caused by Gibbs phenomenon and the calculation of extrema. To overcome that problem, BMD is proposed by searching in the associative dictionary that contains both broadband and narrowband signals. The procedure of the proposed method is as follows: First, the collected datasets are analyzed by BMD and the composite multiscale fuzzy entropies (CMFEs) of the obtained effective components are calculated. Then, locality preserving projection (LPP) is applied for further feature extraction. Analysis results show BMD is more effective when drawing broadband feature from noise and BMD is adaptive for the quality monitoring of DPMIG welding.

As a core transmission component of rotating machinery, gearboxes require effective health monitoring and fault diagnosis. To obtain a feature that directly characterizes the dynamic relationship between the two shafts while modeling correlations over the entire frequency band, this paper proposes a gear fault diagnosis method based on the shaft-to-shaft transmissibility and Vision Transformer (TF-ViT). An on-shaft vibration test rig was constructed, where sensors were mounted directly on the input and output shafts, with conductive slip rings ensuring signal transmission under rotating conditions. Modeling the gearbox as a dynamic system whose two measured responses are the input- and output-shaft vibrations, the shaft-to-shaft transmissibility $T\left(f\right)$ is estimated from the responses via Welch’s method (the H1 cross-spectral ratio) to characterize the inter-shaft dynamic relationship. The transmissibility magnitude sequence was partitioned into equal-length patches and fed into a Transformer encoder after linear embedding and positional encoding; multi-head self-attention models dependencies between arbitrary positions across the entire frequency band, extracting global frequency-domain fault features. Experimental results over ten paired random-seed evaluations show that TF-ViT achieves the highest mean test accuracy among the compared dual-channel CNN, TCN, and ViT models.