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Abstract Background Grain count is crucial to wheat yield composition and estimating yield parameters. However, traditional manual counting methods are time-consuming and labor-intensive. This study developed an advanced deep learning technique for the segmentation counting model of wheat grains. This model has been rigorously tested on three distinct wheat varieties: ‘Bainong 307’, ‘Xinmai 26’, and ‘Jimai 336’, and it has achieved unprecedented predictive counting accuracy. Method The images of wheat ears were taken with a smartphone at the late stage of wheat grain filling. We used image processing technology to preprocess and normalize the images to 480*480 pixels. A CBAM-HRNet wheat grain segmentation counting deep learning model based on the Convolutional Block Attention Module (CBAM) was constructed by combining deep learning, migration learning, and attention mechanism. Image processing algorithms and wheat grain texture features were used to build a grain counting and predictive counting model for wheat grains. Results The CBAM-HRNet model using the CBAM was the best for wheat grain segmentation. Its segmentation accuracy of 92.04%, the mean Intersection over Union (mIoU) of 85.21%, the category mean pixel accuracy (mPA) of 91.16%, and the recall rate of 91.16% demonstrate superior robustness compared to other models such as HRNet, PSPNet, DeeplabV3+ , and U-Net. Method I for spike count, which calculates twice the number of grains on one side of the spike to determine the total number of grains, demonstrates a coefficient of determination R2 of 0.85, a mean absolute error (MAE) of 1.53, and a mean relative error (MRE) of 2.91. In contrast, Method II for spike count involves summing the number of grains on both sides to determine the total number of grains, demonstrating a coefficient of determination R2 of 0.92, an MAE) of 1.15, and an MRE) of 2.09%. Conclusions Image segmentation algorithm of the CBAM-HRNet wheat spike grain is a powerful solution that uses the CBAM to segment wheat spike grains and obtain richer semantic information. This model can effectively address the challenges of small target image segmentation and under-fitting problems in training. Additionally, the spike grain counting model can quickly and accurately predict the grain count of wheat, providing algorithmic support for efficient and intelligent wheat yield estimation.

In solving the boundary conditions of a hydrostatic motorized spindle, there are some certain errors between the boundary conditions calculated by the traditional empirical formula and the actual conditions. In order to solve this problem, an optimization algorithm based on response surface is proposed in this paper, which is based on the idea of composite experimental design. The mathematical models of air gap heat transfer coefficient between stator and rotor, forced convection heat transfer coefficient of spindle inner hole and temperature are established, which is also called the mathematical model of temperature field. By using ANSYS Workbench simulation analysis software, load the optimized convective heat transfer coefficient into the simulation model to solve the temperature field of the hydrostatic motorized spindle to solve the temperature field of the hydrostatic motorized spindle. After selecting the sensor measuring points for temperature measurement, the results are compared with the simulation results. The results show that: the maximum error between the front bearing simulation temperature measurement point and the experimental temperature point is only 9.41%, and the maximum error between the rear bearing measurement point and the experimental temperature point is 3.09%. And it verifies the effectiveness and reliability of the method to improve the simulation accuracy of the hydrostatic motorized spindle.

In this paper, the delay-dependent stability of haptic systems is studied by developing a new stability criterion. Firstly, the haptic system inevitably introduces time delays by using communication networks to transmit information between the controller and the haptic device. When discussing the stability of the haptic system near its operating point, the original nonlinear system is modeled as a linear system with the time delay mentioned above. In addition, a suitable augmented Lyapunov–Krasovskii functional (LKF) with more integral forms is constructed and an auxiliary function-based integral inequality is applied to estimate the derivative of the proposed LKF. Then, a less conservative delay-dependent criterion in terms of the linear matrix inequality (LMI) is derived to calculate the delay margin for the haptic system. Finally, case studies are carried out based on a one degree of freedom haptic system. The results show that, compared with criteria in existing works, the proposed criterion can obtain more accurate results and require less calculation complexity, and, with the increase in virtual damping in a certain range, the stable upper bound of the haptic system increases at first and then decreases.