Mathematical Problems in Engineering

Any company must constantly innovate if they want to maintain its market share in the present cutthroat and unstable industry. Innovation has a big influence on consumer behavior, yet it goes against the principles of sustainability. The issue of sustainability has become crucial to their company’s growth. In order to evaluate a business firm’s sustainability performance statistically, a new and effective fuzzy logic tool is created. Evolution and assessment are performed by a novel interval type-2 fuzzy logic inference system. The judgment of the inference system is carried out on the basis of type-2 fuzzy logic (T2FL), principal component analysis (PCA), and statistical data analysis. The main input variables include corporate environmental performance (CEP) and corporate financial performance (CFP). The suggested approach can effectively examine a corporation’s sustainable performance, according to experimental findings. A unique approach that makes use of language variables and if-then logic to assist quantitative business sustainability events is the link between CEP and CFP. The recommended test will provide senior administrative leaders with useful information to supervise natural concerns correctly and gauge their commitment to company success.

The world is having a vast collection of text with abandon of knowledge. However, it is a difficult and time-taking process to manually read and recognize the text written in numerous regional scripts. The task becomes more critical with Gurmukhi script due to complex structure of characters motivated from the challenges in designing an error-free and accurate classification model of Gurmukhi characters. In this paper, the author has customized the convolutional neural network model to classify handwritten Gurmukhi words. Furthermore, dataset has been prepared with 24000 handwritten Gurmukhi word images with 12 classes representing the month’s names. The dataset has been collected from 500 users of heterogeneous profession and age group. The dataset has been simulated using the proposed CNN model as well as various pretrained models named as ResNet 50, VGG19, and VGG16 at 100 epochs and 40 batch sizes. The proposed CNN model has obtained the best accuracy value of 0.9973, whereas the ResNet50 model has obtained the accuracy of 0.4015, VGG19 has obtained the accuracy of 0.7758, and the VGG16 model has obtained value accuracy of 0.8056. With the current accuracy rate, noncomplex architectural pattern, and prowess gained through learning using different writing styles, the proposed CNN model will be of great benefit to the researchers working in this area to use it in other ImageNet-based classification problems.

For the hyperspectral image (HSI) denoising problem, a symmetric proximal alternating direction method multiplier (spADMM) is proposed to solve the sparse optimization problem which cannot be solved accurately by traditional ADMM. The proposed method finds a high-quality recovery method using the traditional low-rank Tucker decomposition method, which can fully take into account the overall spatial and spectral correlation between HSI bands by using the Tucker decomposition. By choosing appropriate steps to update the Lagrange multipliers twice, it makes the selection and use of variables more flexible and better for solving sparsity problems. To maintain stability, we also add appropriate proximity terms to solve the problem during the computation. Experiments have shown that the spADMM has better results than the traditional ADMM. The final experimental results on the dataset demonstrate the effectiveness of the method.

Researchers have developed a range of methods and strategies to decrease wireless sensor network energy consumption. Mote clustering is one of the competent topological control approaches to boost the networks’ energy efficiency, scalability, and performance. Energy is dissipated during the cluster creation, cluster head selection, routing from the head and base stations of the cluster, and data aggregation—clustering and routing emphasis on the stability and the longevity of the network. This research work provides the optimization technique for the wireless sensor network to optimize the energy through NN-LEACH. The main goal is to extend network life and reduce power consumption by clustering and routing sensor nodes using the two-step NN-LEACH protocol, which is suggested. An additional goal might be to establish the appropriate course of action for the suggested approach for this network.

One of the most challenging next-generation issues is examining a novel and sustainable aircraft to reduce emissions and fuel burn. IATA addressed these issues in collaboration with the EU, GARDEN, and Clean Sky programs to tackle the challenges using retrofit design and upgraded systems. This study aims to create a sustainable aircraft design to solve the fuel burn issue by minimizing the maximum take-off weight (MTOW). An optimized wide-body aircraft is established by selecting twelve aerodynamic design variables and fourteen flight mission constraints (retrofit, operational performance, and stability). To develop a sustainable wide body aircraft structure, this study proposes a hybrid design optimization algorithm combined with the multicriteria decision-making (MCDM) technique. The CRITIC-WASPAS technique is used to obtain the baseline aircraft, and the optimal design of the baseline aircraft is achieved by solving the proposed nonlinear constrained optimization model. The selected baseline aircraft was compared with the optimized result to validate and determine the robustness of the objective function. The findings reflect that the formulation has improved the MTOW, empty weight fraction, fuel weight, and performance by 3.75%, 28.38%, 2.06%, and 8.63%, respectively.

In order to meet the optimization needs of physical education curriculum resource allocation, the author proposes a deep belief-based physical education curriculum resource allocation technology. The efficient feature abstraction and feature extraction capabilities of deep belief technology fully explore the interests and preferences of learners on course resources. Because deep belief has strong capabilities in feature detection and feature extraction, it has unique and efficient feature abstraction capabilities for different dimensional attributes of input data; the author proposes a DBN-MCPR model optimization method based on deep belief classification in the MOOC environment. Experimental results show that when the number of iterations reaches about 80, the RMSE of DBN-MCPR trained with the training dataset without learner feature vector is 77.94%, while the RMSE of DBN-MCPR trained with the dataset with learner feature vector is 77.01; DBN-MCPR with full eigenvectors tends to converge after about 40 iterations, while DBN-MCPR without learner eigenvectors starts to converge after about 15 iterations; this result is in line with the characteristics of the internal network structure of DBN. Conclusion. This application proves that the technical research based on deep belief can effectively meet the needs of the optimization of physical education curriculum resource allocation.