Mathematical Problems in Engineering
ISSN / EISSN: 1024123X / 15635147
Published by: Hindawi Limited
Total articles ≅ 20,800
Latest articles in this journal
Published: 30 May 2023
Mathematical Problems in Engineering, Volume 2023, pp 1-12; https://doi.org/10.1155/2023/2139906
Hard turning has replaced conventional grinding in production processes in recent years as an emerging technique. Nowadays, coated carbide tools are replacing expensive CBN inserts in turning. Wear is a significant concern when turning with coated carbide; it immediately affects the acceptability of the machined surface, which causes machine downtime and loss due to wastage in machined parts. Online tool condition monitoring (TCM) is required to prevent such critical conditions. Hard turning differs from conventional turning in energy balance during metal cutting, resulting in greater thrust force; hence, the TCM model presented for conventional turning may not be suitable for hard turning. Hence, tool wear prediction for turning is projected based on thrust force using an artificial neural network (ANN). All of the tests were done using a design of experiments called full factorial design (FFD). The specimens were made of AISI 4140 steel that had been hardened to 47 HRC, and the inserts were made of coated carbide. The most impactful input features for wear, selected based on experimental outputs, were given to the neural network and trained. Tool wear is an estimated output from the training set that has been validated with satisfactory results for random conditions. The 5101 network structure with the LevenbergMarquardt (LM) learning algorithm, R2 values of 0.996602 and 0.969437 for the training and testing data, and mean square error values of 0.000133152 and 0.004443 for the training and testing data, respectively, gave the best results. The MEP values of 0.575407 and 2.977617 are very low (5). The LM learning algorithm-based ANN is good at predicting tool wear based on how well it predicts tool wear for both the testing set and the training set.
Published: 27 May 2023
Mathematical Problems in Engineering, Volume 2023, pp 1-13; https://doi.org/10.1155/2023/5748824
The problem of infinite horizon H∞ control for general delayed nonlinear stochastic Markov jump systems with the infinite jumping parameters is considered in this paper, in which the noise is dependent on the state, control, and external disturbance. The coupled HamiltonJacobi inequalities (HJIs)-based sufficient condition is given to ensure the existence of the H∞ controller. As a corollary, infinite horizon H∞ controllers are designed for nonlinear stochastic time-delay systems without jumps by solving a series of coupled HJIs. Besides, the effectiveness of the proposed method is verified by a numerical example.
Published: 24 May 2023
Mathematical Problems in Engineering, Volume 2023, pp 1-15; https://doi.org/10.1155/2023/6350647
In this paper, an off-policy model-free algorithm is presented for solving the cooperative optimal output regulation problem for linear discrete-time multi-agent systems. First, an adaptive distributed observer is designed for each follower to estimate the leader’s information. Then, a distributed feedback-feedforward controller is developed for each follower to solve the cooperative optimal output regulation problem utilizing the follower’s state information and the adaptive distributed observer. Based on the reinforcement learning method, an adaptive algorithm is presented to find the optimal feedback gains via online data collection from system trajectory. By designing a Sylvester map, the solution to the regulator equations is calculated via data collected from the optimal feedback gain design steps, and the feedforward control gain is found. Finally, an off-policy model-free algorithm is proposed to design the distributed feedback-feedforward controller for each follower to solve the cooperative optimal output regulation problem. A numerical example is given to verify the effectiveness of this proposed approach.
Published: 23 May 2023
Mathematical Problems in Engineering, Volume 2023, pp 1-8; https://doi.org/10.1155/2023/2919259
This study determined the value of mixed-reality (MR) technology for doctor-patient communication, preoperative planning, intraoperative navigation, and tumor localization in treating patients with breast cancer. Fifty-eight patients with breast space-occupying lesions (16 benign and 42 malignant) who underwent breast lumpectomy at the People’s Liberation Army General Hospital of China were included in this study. The patients were randomly divided into the MR group and the computed tomography (CT) group. In the MR group, a 3D reconstruction of whole-breast ultrasound was used to localize the spatial position of the breast lesion and was combined with the 3D reconstruction of breast MRI to determine the lesion boundaries. To improve the preciseness of surgery, a postoperative survey was conducted. The MR group exhibited a higher level of patient knowledge regarding the disease, treatment, and diagnosis (26.207 ± 1.698 points) than the CT group (19.228 ± 4.889 points) (T = 7.033; ), and patient satisfaction with surgical results, treatment confidence, and communication methods (4.448 ± 0.572) was also higher than that of the CT group (3.172 4.448 ± 0.572) 0.602) . In addition, doctors were significantly more satisfied with surgical planning and intraoperative localization when the MR technique was used (T = 8.273; ). The use of MR technology in lumpectomy has improved patients’ understanding of surgical procedures and surgical results and has achieved positive results. This technique may provide clinical benefits.
Published: 22 May 2023
Mathematical Problems in Engineering, Volume 2023, pp 1-20; https://doi.org/10.1155/2023/7795246
We investigate a discrete-time Chen system. First, we give the topological classifications of the fixed points of this system. Then, we analytically show that the discrete Chen system underlies a Neimark–Sacker (NS) bifurcation and period doubling (PD) under specific parametric circumstances. We confirm the existence of a PD and NS bifurcation via the explicit PD-NS bifurcation criterion and determine the direction of both bifurcations with the help of center manifold theory. We performed numerical simulations to confirm our analytical results. Furthermore, we use the 0-1 chaos test to quantify whether there is chaos in the system or not. At the end, the hybrid control strategy and the OGY (Ott, Grebogi, and Yorke) method are applied to eliminate chaotic trajectories of the system.
Published: 22 May 2023
Mathematical Problems in Engineering, Volume 2023, pp 1-13; https://doi.org/10.1155/2023/6955772
With the development of smart classrooms, analyzing students’ emotions for classroom learning is an effective means of accurately capturing their learning process. Although facial expression-based emotion analysis methods are effective in analyzing classroom learning emotions, current research focuses on facial expressions and does not consider the fact that expressions in different postures do not represent the same emotions. To provide a continuous and deeper understanding of students’ learning emotions, this study proposes an algorithm to characterize learning emotions based on classroom time-series image data. First, face expression data for classroom scenarios are established to address the lack of expression databases in real teaching environments. Second, to improve the accuracy of facial expression recognition, a residual channel cross transformer masking net expression recognition model is proposed in this paper. Finally, to address the problem that the existing research dimension of learning emotion is too single, this paper uses the facial expression and head posture data obtained from deep learning models for fusion analysis and innovatively proposes a Dempster–Shafer evidence-theoretic fusion model to characterize the learning emotion within the lecture duration of knowledge points. The experiments show that both the proposed expression recognition model and the learning sentiment analysis algorithm have good performance, with the expression recognition model achieving an accuracy of 73.58% on the FER2013 dataset. The proposed learning emotion analysis method provides technical support for holistic analysis of student learning effects and evaluation of students’ level of understanding of the knowledge points.
Published: 19 May 2023
Mathematical Problems in Engineering, Volume 2023, pp 1-30; https://doi.org/10.1155/2023/3516707
Complex picture fuzzy set is a special picture fuzzy set where the truth, abstinence, and falsity grades are shown by a complex number and can effortlessly illustrate the problem and inconsistency in the genuine world. T-norm and t-conorm play an essential and beneficial role in the environment of fuzzy set theory; similarly, Archimedean t-norm and t-conorm have massive flexibility and dominancy in the information fusion procedure. The major contribution of this analysis is to explore the algebraic, Einstein, Hamacher, and Frank operational laws under the complex picture fuzzy set. Moreover, the principle of complex picture fuzzy Archimedean Heronian aggregation operator and complex picture fuzzy weighted Archimedean Heronian aggregation operator are also elaborated by using Archimedean t-norm and t-conorm. Additionally, by using the elaborated operators, a multiattribute decision-making technique is presented to elaborate the consistency and reliability of the explored works. Finally, many examples are illustrated for discussing the advantages and sensitive analysis and graphical representation of the investigated works.
Published: 18 May 2023
Mathematical Problems in Engineering, Volume 2023, pp 1-13; https://doi.org/10.1155/2023/2003724
Everybody wants to maintain solitariness to some extent or entirely in his dealings with other people during different modes of communication. To retain privacy, researchers materialized distinct image encryption algorithms using chaotic maps. Due to their extraordinary features, most researchers employed multidimensional chaotic maps to barricade clandestine information or digital images from potential invaders. Still, multidimensional chaotic maps have many impediments conferred in the literature review. In this paper, we developed a cryptosystem utilizing multiple chaotic maps to mitigate the shortcoming of multidimensional chaotic maps. A distinctive approach is adopted to sire a key stream using a combination of chaotic maps and create a sequence of random integers linked with the pixels of the plain image to shatter the association between neighboring pixels of a plain image. Finally, diffusion is accomplished using the previously diffused pixels at a decimal level. Security and statistical analysis demonstrate that the presented encryption algorithm is robust against well-known attacks. An ample key space indicates that it is best suited for secure communication.
Published: 18 May 2023
Mathematical Problems in Engineering, Volume 2023, pp 1-10; https://doi.org/10.1155/2023/7335443
Location-routing problem (LRP) thoroughly considers location allocation problem (LAP) and vehicle routing problem (VRP) which has been an integral part applied in modern logistics. A number of researchers at home and aboard have put forward their views by establishing fine models. On the basis of studying the previous research results by classification, summary, and comparative analysis, this study hence proposes a new solution-fuzzy clustering model and algorithm to resolve two-layer location-routing problem based on a heuristic hybrid algorithm: Designing a hybrid genetic and simulated annealing algorithm (GASA) to optimize the initial value of the fuzzy C-means clustering algorithm (FCM); considering the roving visit characteristics of vehicles to design the path by employing a special VRP problem—the multiple traveling salesman problem (MTSP). Theoretical analysis and experimental results show that the algorithm used in this study has the advantages of fast convergence speed and less iterations, which significantly improve the quality of the initial solution of FCM in LAP, shorten the vehicle patrol cycle in VRP to a great extent, improve the vehicle utilization, and save the vehicle patrol costs. A specific example is programmed by MATLAB to verify the feasibility of this method.
Published: 16 May 2023
Mathematical Problems in Engineering, Volume 2023, pp 1-19; https://doi.org/10.1155/2023/1647844
In this paper, we consider a two-commodity stochastic perishable inventory system of the multiqueue Jackson network at a service facility with reneging and jockeying of the customers. The waiting room capacity of the first queue is and the second queue is , where . In this network, different queues have different service rates. Service times are exponentially distributed. Customers join the system at a rate of using a Poisson process. We assumed that some customers maybe impatient due to the long waiting time in the queue and can leave the system without service or may switch from the longest queue to the shortest queue to reduce the waiting time. If the inventory levels of the items from the warehouse at any time reaches below or reorder level , an order units is placed to bring the inventory level up to . The joint probability distribution of...