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Unbalanced data with very few samples for special abnormal conditions frequently occur in actual production processes, which can make accurate monitoring of the process state challenging. This paper proposes a multi-modal few-shot learning method (MMFSL) within a fault diagnosis framework for unbalanced data modelling of industrial bearings. MMFSL can handle two modes of data and therefore contains two data generation channels. The first channel deals with time series data and the second deals with images. The two modes of generated data are then evaluated using the MMFSL evaluation modules, IEI (image evaluation index) and TEI (time series evaluation index), to guarantee the quality of the generated data. In addition, the time series data are analyzed in the time-frequency domain to ensure the consistency of the frequency distribution. Original unbalanced and insufficient data samples are expanded so that the fault diagnosis model can be trained adequately. Through experiments using data from Case Western Reserve University(CWRU) and Pardborn University(PU), generated data by using the MMFSL model can increase fault detection accuracy from 80.9% to 97.5%. At the same time, false alarms rate can be reduced significantly from 4.6% to 0.1%. Moreover, fault classification model accuracy can reach 98.1% compared to 95.4% for the original time series dataset, and 99.3% compared with 96.5% for the image data extension. Various visualizations of comparison results are also provided to show the reliability of the MMFSL framework.

Surface material classification has attracted a lot of attention from the academic and industrial communities. The surface material classification methods are for static object material data. However, in real industrial production, data cannot be generated overnight. It is generated continuously. In this work, we propose an algorithm named Multi-Scale Local Receptive Field Based Online Sequential Extreme Learning Machine (MSLRF-OSELM) for material classification, which not only can make dynamic training of networks by using data that are generated online of material images, but also can extract highly representative features from complex texture by multi-scale local receptive field. We conduct experiments on the public texture ALOT dataset and MNIST dataset. Experimental results verify the effectiveness of our algorithm and has good generalization performance.

Multipath is one of the dominant error sources for high-precision positioning systems, such as global navigation satellite systems (GNSS). The minimum mean square error (MSE) criterion is usually employed for multipath estimation under the assumption of Gaussian noise. For non-Gaussian noise as appeared in most practical applications, alternative solutions are required for multipath estimation. In this work, a multipath estimation algorithm is proposed based on the minimum error entropy (MEE) criterion under Gaussian or non-Gaussian noises. A key advantage of using MEE is that it can minimize the randomness of error signals, however, the shift-invariance characteristics in MEE may lead to a bias of the estimation result. To mitigate such a bias, an improved estimation strategy is proposed by integrating the second-order central moment of the estimation error together with the prior information of multipath parameters as a constraint. The multipath estimation problem is thus formulated as a constrained optimization problem. A modified ε-constrained rank-based differential evolution (εRDE) algorithm is developed to find the optimal solution. The effectiveness of the proposed algorithm, in terms of reducing the multipath estimation error and minimizing the randomness in the error signal, has been examined through case studies with Gaussian and non-Gaussian noises.

Multipath is the dominant error source for high-accuracy positioning systems. It is significant for eliminating the multipath error and improving the positioning accuracy to estimate multipath parameters. The existing multipath estimation algorithms are usually designed for Gaussian noise, and their performances degrade dramatically in non-Gaussian noise. To solve the problem, a multipath estimation algorithm based on kernel minimum error entropy filter (KMEEF) is proposed. In KMEEF, the minimum error entropy (MEE) criterion instead of mean square error (MSE) criterion is applied, which is not limited to the assumption of Gaussian and linearity. According to the stochastic information gradient (SIG) method, an optimal filer gain matrix is obtained by minimizing the error entropy. Furthermore, the learning rate is suggested by a convergence analysis. The simulation results show the effectivity of the proposed algorithm for multipath estimation.