We propose a globally convergent numerical method, called the convexification, to numerically compute the viscosity solution to first-order Hamilton-Jacobi equations through the vanishing viscosity ...process where the viscosity parameter is a fixed small number. By convexification, we mean that we employ a suitable Carleman weight function to convexify the cost functional defined directly from the form of the Hamilton-Jacobi equation under consideration. The strict convexity of this functional is rigorously proved using a new Carleman estimate. We also prove that the unique minimizer of this strictly convex functional can be reached by the gradient descent method. Moreover, we show that the minimizer well approximates the viscosity solution of the Hamilton-Jacobi equation as the noise contained in the boundary data tends to zero. Some interesting numerical illustrations are presented.
Data-driven condition monitoring and fault diagnosis of bearings.
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•An efficient bearing condition monitoring index is presented.•A novel hybrid optimization algorithm for discrete ...hidden Markov model parameters is proposed.•Bearing condition monitoring and fault diagnosis is performed effectively.•The superiority of presented method over conventional methods is demonstrated.
Efficient condition monitoring and fault diagnosis of bearings are of great practical significance since bearings are key elements in most rotating manufacturing machineries. In this study, a condition monitoring index of bearings is developed based on self-organizing map (SOM) in order to detect incipient bearing faults quickly. It requires low computation cost and is robust to the change of load level and motor speed, hence is quite suitable for online condition monitoring of bearings. Furthermore, a novel hybrid algorithm combining diversified gradient descent (DGD) method and Bayesian model selection (BMS) called DGD-BMS for the optimization of discrete hidden Markov model (DHMM) parameters is formulated under a general Bayesian framework. The flexibility of the DGD-BMS consists in that the algorithm can increase the diversity of the searching paths generated for DHMM parameters so that the true underlying parameters are more likely to be found out. Thus it provides an effective way to avoid trapping in one local maximum. Both simulation and industrial case study are presented to validate the proposed approach. Results show that the monitoring index can detect incipient bearing faults efficiently with 100% accuracy even under varying load levels, and the DGD-BMS method achieves on average the classification rate of 99.58%. The proposed method exhibits excellent performance compared to the conventional gradient descent (GD) and Baum-Welch (BW) methods.
The effective management of human bloodstream remains to be the prime focus for the clinicians over years and it impose greater challenges when it comes to real-time solution. In particular managing ...hypoxemia and detection of blood clots is most pertinent. One major challenge faced is the existence of limited training data generated from real-world scenarios. On the other hand, creating an efficient model is often time consuming and expensive. This paper focusses on effective convergence of artificial intelligence and nanorobotics technologies to design and implement autonomous intelligent nanorobots to deal with blood related diseases. The major contribution of the research is two-fold, first we define an efficient architecture of the nanorobotics system with appropriate design parameter. Next, we develop a novel semi-supervised learning model using stochastic gradient descent method and kernel space that efficiently control and manage the nanorobots and helps in earlier prognosis and treatment of blood related diseases. The proposed model is novel and efficient as it enables working at nanoscale, providing resourceful understanding on physical and chemical properties associated with human body. The use of artificial intelligence techniques further makes the system to work more intelligently and independently. COSMOL with integrated MATLAB environment is used for experimental setup and simulation. MNIST dataset is compared with online RP tree method and other conventional batch related techniques. The performance analysis is compared based on performance, error rates and risk related factors. The proposed approach provides significant improvement in terms of performance with minimal error rate and improved accuracy measures.
This research presents a novel method for energy-efficient path planning, aiming to enhance the endurance of unmanned surface vehicle (USV). The proposed method combines the locking sweeping (LS) ...method, gradient descent method, coastline expansion method, and energy consumption functions. The efficiency of constructing the energy consumption potential map was improved by optimising the LS structure. Moreover, maintaining a user-configurable distance between the USV and the coastline ensures safe paths with minimal energy consumption. The performance of the proposed method was evaluated using multiple simulations involving high-resolution electronic nautical charts and a historical time-variant sea current dataset. The results demonstrate the practicality of the method, and effectively address path planning challenges in a time-variant maritime environment.
•Locking sweeping, gradient descent, coastline expanding methods are integrated for USV path planning with complex maritime environments.•High-resolution and complex electronic nautical charts dataset and historic time-varying sea current dataset are used. This feature can improve the practicability of the method.•Adjustable sweep initial point, sweep area and gradient descent step size are proposed as part of locking sweeping method. It can improve the path search efficiency in a time-variant maritime environment.•The proposed method was compared with the three related methods and showed the best performance in energy efficiency.•The research included an analysis of computational time, showcasing its scalability and practicality for real-world applications.
•Abnormal magnetometer data need to be considered.•The existing algorithm is improved.•Establish a dynamic adaptive step size model and constrain the attitude angle.•Improved algorithm mitigates the ...shortcomings of the existing algorithm.•The attitude accuracy of inertial sensor is improved.
Aiming at the problems of angle oscillation, slow convergence speed, and low accuracy of traditional algorithms in low cost inertial element attitude determination, this study proposes an improved attitude algorithm based on geomagnetic correction robust model assisted adaptive step gradient descent. Firstly, a robust ellipsoid fitting algorithm is proposed to correct the geomagnetic anomaly data. Then, an adaptive step size model is established based on the momentum gradient descent method, and the iterative optimization parameters are automatically adjusted according to the error function. At the same time, the dynamic limiting mean filter is used to constrain the attitude angle, to calculate the optimal attitude information of the sensor. Finally, the algorithm is verified by static and dynamic experimental data. The results show that the improved algorithm can effectively suppress the angle oscillation, optimize the attitude convergence effect, and improve the accuracy of low cost inertial sensor attitude calculation.
The establishment of an industrial benefit distribution mechanism for reservoir migrants in water conservancy and hydropower projects is a crucial part. This paper establishes the logistic regression ...model with gradient descent by deriving the objective function and using the gradient descent method to solve its approximate solution. Then, the model is applied to predict the total income and total expenditure of reservoir migrants before and after agricultural resettlement and tertiary resettlement, and the criteria for benefit compensation distribution are given based on the comparison before and after relocation. In the case of agricultural resettlement, the average share of equal compensation in the first 5 years accounts for 54.67% of the predicted income, and the predicted average annual growth rate of net income per capita is 17.86% with a discount rate of 3.12%. In the tertiary placement case, the predicted growth rates of wage income in the first 5 years are 7.49%, 4.84%, 10.56%, and 1.15%, respectively, and the average annual growth rate of transfer income is 7.01%, and the average annual growth rate of government subsidies is 0.80%. The prediction accuracy of the logistic regression model based on gradient decline reached 84.14%, and the analysis of the distribution of industrial benefits for reservoir migrants was credible. To let the living standard of migrants recover and exceed the level of non-relocation as soon as possible, it is necessary to give migrants certain compensation for production and life recovery based on the living standard measurement index.
With the popularization of higher education, the competition in the employment market of college students is becoming increasingly intense. To enhance the employment efficiency and satisfaction of ...college students. The study first analyzes college students’ employment unit selection, attribute preference, and location preference through an employment recommendation algorithm. The collaborative filtering algorithm is utilized to complete personalized modeling and output the final recommendation results based on the acquired employment preferences and relevant data collection. Finally, the gradient descent method is used to evaluate the accuracy of college students’ employment recommendations. The results show that the overall educational requirements of enterprises for the three significant positions of short video production, account operation and anchor are not high, and the percentage of those with education of high school or below or master’s degree or above is meager, neither exceeding 3.5%. The personalized employment recommendation algorithm can provide scientific and reasonable guidance for graduates’ employment, with an accuracy rate of up to 50% and a recommendation list length of N=30. When α=0.75, the personalized employment recommendation algorithm can obtain better recommendation performance with smaller recommendation list length. This paper provides new solutions for college students’ employment and valuable references and lessons for research in related fields.
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