Secant-type iteration for nonlinear ill-posed equations in Banach space

In this paper, we study secant-type iteration for nonlinear ill-posed equations involving 𝑚-accretive mappings in Banach spaces. We prove that the proposed iterative scheme has a convergence order at least 2.20557 using assumptions only on the first Fréchet derivative of the operator. Further, using a general Hölder-type source condition, we obtain an optimal error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter.

A boundary division guiding synchrosqueezed wave packet transform method for rolling bearing fault diagnosis

Synchrosqueezed wave packet transform (SSWPT) can effectively reconstruct the band-limited components of the signal by inputting the specific reconstructed boundaries and it provides an alternative bearing fault diagnosis method. However, the selection of reconstructed boundaries can significantly affect the fault feature extraction performance of SSWPT. Accordingly, this paper presents a boundary division guiding SSWPT (BD-SSWPT) method. In this method, an adaptive boundary division method is developed to effectively determine the reconstructed boundaries of SSWPT. Firstly, the marginal spectrum of SSWPT, more robust to noise than the Fourier spectrum, is defined for the scale-space division to obtain the initial boundaries. Secondly, the inverse transform of SSWPT is conducted based on the initial boundaries to obtain the initial reconstructed components. Thirdly, a boundary redefinition scheme, composed of clustering and combination, is conducted to redefine the boundaries. Finally, the potential components are extracted by the inverse transform of SSWPT based on the redefined boundaries. The validity of BD-SSWPT is verified by simulated and experimental analysis, and the superiority of BD-SSWPT is highlighted through comparison with singular spectrum decomposition (SSD) and an adaptive parameter optimized variational mode decomposition (AVMD). The results demonstrate that BD-SSWPT identifies more significant fault features and has higher computational efficiency than SSD and AVMD.

Adaptive neural network–based fault estimation for nonlinear systems with actuator faults in simultaneous multiplicative and additive forms

Non-linearities and actuator faults often exist in practical systems which may degrade system performance or even lead to catastrophic accidents. In this article, a fault-tolerant compensation control strategy is proposed for a class of non-linear systems with actuator faults in simultaneous multiplicative and additive forms. First, radial basis function neural network is employed to approximate the system non-linearity. The approximation is achieved by only one adaptive parameter, which simplifies the computation burden. Then, by means of the backstepping technique, an adaptive neural controller is developed to cope with the adverse effects brought by the system non-linearity and actuator faults in multiplicative and additive forms. Meanwhile, the proposed control design scheme can guarantee that the considered closed-loop system is stable. The novelty of the article lies in that the system non-linearity, the additive actuator faults, and the multiplicative actuator faults that often exist in practical engineering are catered for simultaneously. Furthermore, compared with some existing works, the approximation of the system non-linearity is achieved by only one adaptive parameter for the purpose of reducing the computation burden. Therefore, its applicability is more general. Finally, a numerical simulation and a comparative simulation are carried out to show the effectiveness of the developed controller.

An Adaptive-Parameter Pixel Unmixing Method for Mapping Evergreen Forest Fractions Based on Time-Series NDVI: A Case Study of Southern China

Spectral unmixing remains the most popular method for estimating the composition of mixed pixels. However, the spectral-based unmixing method cannot easily distinguish vegetation with similar spectral characteristics (e.g., different forest tree species). Furthermore, in large areas with significant heterogeneity, extracting a large number of pure endmember samples is challenging. Here, we implement a fractional evergreen forest cover-self-adaptive parameter (FEVC-SAP) approach to measure FEVC at the regional scale from continuous intra-year time-series normalized difference vegetation index (NDVI) values derived from moderate resolution imaging spectroradiometer (MODIS) imagery acquired over southern China, an area with a complex mixture of temperate, subtropical, and tropical climates containing evergreen and deciduous forests. Considering the cover of evergreen forest as a fraction of total forest (evergreen forest plus non-evergreen forest), the dimidiate pixel model combined with an index of evergreen forest phenological characteristics (NDVIann-min: intra-annual minimum NDVI value) was used to distinguish between evergreen and non-evergreen forests within a pixel. Due to spatial heterogeneity, the optimal model parameters differ among regions. By dividing the study area into grids, our method converts image spectral information into gray level information and uses the Otsu threshold segmentation method to simulate the appropriate parameters for each grid for adaptive acquisition of FEVC parameters. Mapping accuracy was assessed at the pixel and sub-pixel scales. At the pixel scale, a confusion matrix was constructed with higher overall accuracy (87.5%) of evergreen forest classification than existing land cover products, including GLC 30 and MOD12. At the sub-pixel scale, a strong linear correlation was found between the cover fraction predicted by our method and the reference cover fraction obtained from GF-1 images (R2 = 0.86). Compared to other methods, the FEVC-SAP had a lower estimation deviation (root mean square error = 8.6%). Moreover, the proposed method had greater estimation accuracy in densely than sparsely forested areas. Our results highlight the utility of the adaptive-parameter linear unmixing model for quantitative evaluation of the coverage of evergreen forest and other vegetation types at large scales.

Attentive 3D-Ghost Module for Dynamic Hand Gesture Recognition with Positive Knowledge Transfer

Hand gesture recognition is a challenging topic in the field of computer vision. Multimodal hand gesture recognition based on RGB-D is with higher accuracy than that of only RGB or depth. It is not difficult to conclude that the gain originates from the complementary information existing in the two modalities. However, in reality, multimodal data are not always easy to acquire simultaneously, while unimodal RGB or depth hand gesture data are more general. Therefore, one hand gesture system is expected, in which only unimordal RGB or Depth data is supported for testing, while multimodal RGB-D data is available for training so as to attain the complementary information. Fortunately, a kind of method via multimodal training and unimodal testing has been proposed. However, unimodal feature representation and cross-modality transfer still need to be further improved. To this end, this paper proposes a new 3D-Ghost and Spatial Attention Inflated 3D ConvNet (3DGSAI) to extract high-quality features for each modality. The baseline of 3DGSAI network is Inflated 3D ConvNet (I3D), and two main improvements are proposed. One is 3D-Ghost module, and the other is the spatial attention mechanism. The 3D-Ghost module can extract richer features for hand gesture representation, and the spatial attention mechanism makes the network pay more attention to hand region. This paper also proposes an adaptive parameter for positive knowledge transfer, which ensures that the transfer always occurs from the strong modality network to the weak one. Extensive experiments on SKIG, VIVA, and NVGesture datasets demonstrate that our method is competitive with the state of the art. Especially, the performance of our method reaches 97.87% on the SKIG dataset using only RGB, which is the current best result.