The softmax function is widely used in deep neural networks (DNNs), its hardware performance plays an important role in the training and inference of DNN accelerators. However, due to the complexity of the traditional softmax, the existing hardware architectures are resource-consuming or have low precision. In order to address the challenges, we study a base-2 softmax function in terms of its suitability for neural network training and efficient hardware implementation. Compared to the classical base- $e$ softmax function, the base-2 softmax function is a new softmax function that uses 2 as the exponential base instead of $e$ . From the aspects of mathematical derivation and software simulation, we first demonstrate the feasibility and good accuracy of the base-2 softmax function in the application of neural network training. Then, we use the symmetric-mapping lookup table (SM-LUT) method to design a low-complexity architecture but with high precision to implement it. Under TSMC 28nm CMOS technology, an example design of our architecture has the area of $5676 ~\mu m^{2}$ and the power consumption of 13.12 mW for circuit synthesis at the frequency of 3 GHz. Compared with the latest works, our architecture achieves the best performance and efficiency.

The key to ensuring rotating machinery’s safe and reliable operation is efficient and accurate faults diagnosis. Intelligent fault diagnosis technology based on deep learning (DL) has gained increasing attention. A critical challenge is how to embed the characteristics of time series into DL to obtain stable features that correlate with equipment conditions. This study proposes a lightweight rolling bearing fault diagnosis method based on Gramian angular field (GAF) and coordinated attention (CA) to improve rolling bearing recognition performance and diagnosis efficiency. Firstly, the time domain signal is encoded into GAF images after downsampling and segmentation. This method retains the temporal relation of the time series and provides valuable features for DL. Secondly, a lightweight convolution neural network (CNN) model is constructed through depthwise separable convolution, inverse residual block, and linear bottleneck layer to learn advanced features. After that, CA is employed to capture the long-range dependencies and identify the precise position information of the GAF images with nearly no additional computational overhead. The proposed method is tested and evaluated by CWRU bearing dataset and experimental dataset. The results demonstrate that the CNN based on GAF and CA (GAF-CA-CNN) model can effectively reduce the calculation overhead of the model and achieve high diagnostic accuracy.

The track line suffers from track irregularity, subgrade settlement, rail surface defects and gauge distortion. Measuring the track geometry quality plays an important role for rail administrations to safe operation and track maintenance. In order to meet the requirements of track daily inspection, this paper describes a comprehensive detection system for the track geometry, which is designed by four cameras, an inclinometer and inertial measurement unit. Moreover, the detection system has the characteristics of simple structure, automatic detection and multiple measurement parameters. Firstly, to measure track alignment and irregularity, a multi-sensing calibration method is established to fuse visual sensors and inertial sensors. An accelerometer and a Kalman filter are used to eliminate accumulated unrealistic drifts of accelerometer and gyroscope. Secondly, to measure the rail surface defects and gauge, the model of laser and machine vision is deduced to obtain coordinate values in a unified coordinate system and an improved iterative closest point method is developed to improve the matching accuracy. Finally, a series of experiments are carried out to validate the measuring performance. The results indicate that the proposed method can accurately measure the track geometry, with the maximum deviations of track alignment, track irregularity, rail defects and gauge are less than 0.5mm, 0.4mm, 0.3mm and 0.1mm, respectively. The detection system is not only simple in structure but also has multiple detection parameters, which is especially suitable for track daily maintenance.

Softmax is a common and complex activation function in Deep Neural Networks (DNN). However, it is a challenge to apply it efficiently in DNN training hardware accelerator. Therefore, we propose a high precision calculation method and architecture based on base- $2$ softmax, which has low hardware complexity than base- $e$ softmax but can still be useful in DNN training. First, we simplify the hardware implementation complexity of calculating base- $2$ softmax. Second, we use the base-TEXPRESERVE4 hyperbolic COordinate Rotation Digital Computer (CORDIC) to implement the core computation. Finally, we show that the proposed method can be used in DNN training through experiments. Moreover, with the same order of the magnitude of high precision, our hardware cost is lower than traditional base- $e$ softmax or other alternative design methods. Under TSMC 28nm CMOS technology, an example design of our architecture has the area of $98787.43\mu m^2$ and the power consumption of $24.72$ mW for circuit synthesis at the frequency of 1GHz.

Rail surface defects will not only bring wheel rail noise during train operation, but also cause corresponding accidents. Most of the existing detection methods are manual detection, which is time-consuming, laborious, inefficient, and subjective. With the development of technology, automatic detection replaces manual detection, which reduces manual labor, improves efficiency, and objectively evaluates the surface state of rails, which is in line with the purpose of modern intelligent production. The automatic detection of a single sensor is usually not enough to complete the recognition, but multiple sensors need to be additionally installed and refitted on the service vehicle, which creates difficulty for on-site test conditions. Therefore, in order to overcome these shortages and to adapt to the actual vibration characteristics of service vehicles, a rail surface defect recognition method based on optimized VMD gray image coding and DCNN is proposed in this paper. Firstly, the optimization method of VMD mode number based on the maximum envelope kurtosis is proposed. The VMD after parameter optimization is used to decompose the four-channel axle box vibration signal, and the component with the largest correlation coefficient between each order eigenmode component and the original signal is extracted. Secondly, the filtered IMF components are arranged in sequence and encoded into grayscale images. Finally, the DCNN structure is designed, and the training set is input into the network for training, and the test set verifies the effectiveness of the network and realizes the recognition of rail surface defects. The test accuracy of railway data set measured on the serviced vehicle is 99.75%, and the results show that this method can accurately identify the category of rail surface defects. After adding Gaussian noise to the original signal, the test accuracy reaches 99.20%, which proves that the method has good generalization ability and anti-noise performance. Additionally, this method can ensure the safe operation of vehicles without adding new equipment, which reduces operation costs and improves the intelligent operation and maintenance of rails.