Computation, Volume 9, Issue 3 (March 2021) – 14 articles

Wind turbine gearboxes are known to be among the weakest components in the system and the possibility to study and understand the behavior of geared transmissions when subject to several types of faults might be useful to plan maintenance and eventually reduce the costs by preventing further damage. The aim of this work is to develop a high-fidelity numerical model of a single-stage planetary gearbox selected as representative and to evaluate its behavior in the presence of surface fatigue and tooth-root bending damage, i.e., pits and cracks. The planetary gearbox is almost entirely modelled, including shafts, gears as well as bearings with all the rolling elements. Stresses and strains in the most critical areas are analyzed to better evaluate if the presence of such damage can be somehow detected using strain gauges and where to place them to maximize the sensitivity of the measures to the damage. Several simulations with different levels, types and positions of the damage were performed to better understand the mutual relations between the damaged and the stress state. The ability to introduce the effect of the damage in the model of a gearbox represents the first indispensable step of a Structural Health Monitoring (SHM) strategy. The numerical activity was performed taking advantage of an innovative hybrid numerical–analytical approach that ensures a significant reduction of the computational effort. The developed model shows good sensitivity to the presence, type and position of the defects. For the studied configuration, the numerical results show clearly show a relation between the averaged rim stress and the presence of root cracks. Moreover, the presence of surface defects seems to produce local stress peaks (when the defects pass through the contact) in the instantaneous rim stress. Full article

In this work, mathematical models are formulated in order to investigate the effect of the additional order on the expected total profit of a two-stage supply chain. A multi-period buyback contract between a supplier and a retailer under the demand uncertainty is considered. Under the contract, an advance order is submitted to the supplier in advance when the demand is unknown, and an additional order can be made at the beginning of each period after the previous period demand is realized. The impact of the coordination on the supply chain’s expected total profit is also considered. The results show that the additional order does not always increases the supply chain profit. The additional order increases the supply chain profit only when both the retailer and supplier are coordinated. Under the decentralized system with the buyback contract, the retailer tends to order less in an advance order to reduce the risk. This leads to the higher cost due the additional order after the demand is realized. As a result, it is lowers the supply chain profit. Moreover, the sensitivity analysis is performed using numerical studies in order to observe the behavior of the expected total profit of the supply chain. Full article

The sugar industry is of great importance to the Thai economy. In general, the government sets sugarcane prices at the beginning of each harvesting season based on type (fresh or fired), sweetness (sugar content) and gross weight. The main aim of the present research is to use optimal control to find optimal sugarcane harvesting policies for fresh and fired sugarcane for the four sugarcane producing regions of Thailand, namely North, Central, East and North-east, for harvesting seasons 2012/13, 2013/14, 2014/15, 2017/18 and 2018/19. The optimality problem is to determine the harvesting policy which gives maximum profit to the farmers subject to constraints on the maximum amount that can be cut in each day, where a harvesting policy is defined as the amount of each type of sugarcane harvested and delivered to the sugar factories during each day of a harvesting season. The results from the optimal control methods are also compared with results from three optimization methods, namely bi-objective, linear programming and quasi-Newton. The results suggest that discrete optimal control is the most effective of the five methods considered. The data used in this paper were obtained from the Ministry of Industry and the Ministry of Agriculture and Co-operatives of the Royal Thai government. Full article

Accurate, fast, and automatic detection and classification of animal images is challenging, but it is much needed for many real-life applications. This paper presents a hybrid model of Mamdani Type-2 fuzzy rules and convolutional neural networks (CNNs) applied to identify and distinguish various animals using different datasets consisting of about 27,307 images. The proposed system utilizes fuzzy rules to detect the image and then apply the CNN model for the object’s predicate category. The CNN model was trained and tested based on more than 21,846 pictures of animals. The experiments’ results of the proposed method offered high speed and efficiency, which could be a prominent aspect in designing image-processing systems based on Type 2 fuzzy rules characterization for identifying fixed and moving images. The proposed fuzzy method obtained an accuracy rate for identifying and recognizing moving objects of 98% and a mean square error of 0.1183464 less than other studies. It also achieved a very high rate of correctly predicting malicious objects equal to recall = 0.98121 and a precision rate of 1. The test’s accuracy was evaluated using the F1 Score, which obtained a high percentage of 0.99052. Full article

Until recently, traditional machine learning techniques (TMLTs) such as multilayer perceptrons (MLPs) and support vector machines (SVMs) have been used successfully for churn prediction, but with significant efforts expended on the configuration of the training parameters. The selection of the right training parameters for supervised learning is almost always experimentally determined in an ad hoc manner. Deep neural networks (DNNs) have shown significant predictive strength over TMLTs when used for churn predictions. However, the more complex architecture of DNNs and their capacity to process huge amounts of non-linear input data demand more time and effort to configure the training hyperparameters for DNNs during churn modeling. This makes the process more challenging for inexperienced machine learning practitioners and researchers. So far, limited research has been done to establish the effects of different hyperparameters on the performance of DNNs during churn prediction. There is a lack of empirically derived heuristic knowledge to guide the selection of hyperparameters when DNNs are used for churn modeling. This paper presents an experimental analysis of the effects of different hyperparameters when DNNs are used for churn prediction in the banking sector. The results from three experiments revealed that the deep neural network (DNN) model performed better than the MLP when a rectifier function was used for activation in the hidden layers and a sigmoid function was used in the output layer. The performance of the DNN was better when the batch size was smaller than the size of the test set data, while the RemsProp training algorithm had better accuracy when compared with the stochastic gradient descent (SGD), Adam, AdaGrad, Adadelta, and AdaMax algorithms. The study provides heuristic knowledge that could guide researchers and practitioners in machine learning-based churn prediction from the tabular data for customer relationship management in the banking sector when DNNs are used. Full article

In the finance market, the Black–Scholes equation is used to model the price change of the underlying fractal transmission system. Moreover, the fractional differential equations recently are accepted by researchers that fractional differential equations are a powerful tool in studying fractal geometry and fractal dynamics. Fractional differential equations are used in modeling the various important situations or phenomena in the real world such as fluid flow, acoustics, electromagnetic, electrochemistry and material science. There is an important question in finance: “Can the fractional differential equation be applied in the financial market?”. The answer is “Yes”. Due to the self-similar property of the fractional derivative, it can reply to the long-range dependence better than the integer-order derivative. Thus, these advantages are beneficial to manage the fractal structure in the financial market. In this article, the classical Black–Scholes equation with two assets for the European call option is modified by replacing the order of ordinary derivative with the fractional derivative order in the Caputo type Katugampola fractional derivative sense. The analytic solution of time-fractional Black–Scholes European call option pricing equation with two assets is derived by using the generalized Laplace homotopy perturbation method. The used method is the combination of the homotopy perturbation method and generalized Laplace transform. The analytic solution of the time-fractional Black–Scholes equation is carried out in the form of a Mittag–Leffler function. Finally, the effects of the fractional-order in the Caputo type Katugampola fractional derivative to change of a European call option price are shown. Full article

Buruli ulcer caused by Mycobacterium ulcerans (M. ulcerans) is identified by a pain-free cyst or edema which develops into a massive skin ulcer if left untreated. There are reports of chemoresistance, toxicity, noncompliance, and poor efficacy of current therapeutic options. Previously, we used cheminformatics approaches to identify potential antimycobacterial compounds targeting major receptors in M. ulcerans. In this paper, we sought to identify potential bioactive compounds by targeting Cystathionine gamma-synthase (CGS) MetB, a key receptor involved in methionine synthesis. Inhibition of methionine synthesis restricts the growth of M. ulcerans. Two potent inhibitors Juglone (IC₅₀ 0.7 +/− 0.7 µmol/L) and 9-hydroxy-alpha-lapachone (IC₅₀ 0.9 +/− 0.1 µmol/L) were used to generate 3D chemical feature pharmacophore model via LigandScout with a score of 0.9719. The validated model was screened against a pre-filtered library of 2530 African natural products. Compounds with fit scores above 66.40 were docked against the structure of CGS to generate hits. Three compounds, namely Gentisic 5-O glucoside (an isolate of African tree Alchornea cordifolia), Isoscutellarein (an isolate of Theobroma plant) and ZINC05854400, were identified as potential bioactive molecules with high binding affinities of −7.1, −8.4 and −8.4 kcal/mol against CGS, respectively. Novel structural insight into the binding mechanisms was elucidated using LigPlot+ and molecular dynamics simulations. All three molecules were predicted to possess antibacterial, anti-ulcerative, and dermatological properties. These compounds have the propensity to disrupt the methionine synthesis mechanisms with the potential of stagnating the growth of M. ulcerans. As a result of reasonably good pharmacological profiling, the three drug-like compounds are potential novel scaffolds that can be optimized into antimycobacterial molecules. Full article

The objective of this present paper is to utilize an auxiliary equation method for constructing exact solutions associated with variable coefficient function forms for certain nonlinear partial differential equations (NPDEs) in the sense of the conformable derivative. Utilizing the specific fractional transformations, the conformable derivatives appearing in the original equation can be converted into integer order derivatives with respect to new variables. As for applications of the method, we particularly obtain variable coefficient exact solutions for the conformable time (2 + 1)-dimensional Kadomtsev–Petviashvili equation and the conformable space-time (2 + 1)-dimensional Boussinesq equation. As a result, the obtained exact solutions for the equations are solitary wave solutions including a soliton solitary wave solution and a bell-shaped solitary wave solution. The advantage of the used method beyond other existing methods is that it provides variable coefficient exact solutions covering constant coefficient ones. In consequence, the auxiliary equation method based on setting all coefficients of an exact solution as variable function forms can be more extensively used, straightforward and trustworthy for solving the conformable NPDEs. Full article

Porcine reproductive and respiratory syndrome virus (PRRSV) causes reproductive failure in sows and respiratory disease in piglets and growing pigs. The disease rapidly spreads in swine populations, making it a serious problem causing great financial losses to the swine industry. However, past mathematical models used to describe the spread of the disease have not yielded sufficient understanding of its spatial transmission. This work has been designed to investigate a mathematical model for the spread of PRRSV considering both time and spatial dimensions as well as the observed decline in infectiousness as time progresses. Moreover, our model incorporates into the dynamics the assumption that some members of the infected population may recover from the disease and become immune. Analytical solutions are derived by using the modified extended hyperbolic tangent method with the introduction of traveling wave coordinate. We also carry out a stability and phase analysis in order to obtain a clearer understanding of how PRRSV spreads spatially through time. Full article

In this article a sincere effort has been made to address the origin of the incommensurability/irrationality of numbers. It is folklore that the starting point was several unsuccessful geometric attempts to compute the exact values of $\sqrt{2}$ and $\pi .$ Ancient records substantiate that more than 5000 years back Vedic Ascetics were successful in approximating these numbers in terms of rational numbers and used these approximations for ritual sacrifices, they also indicated clearly that these numbers are incommensurable. Since then research continues for the known as well as unknown/expected irrational numbers, and their computation to trillions of decimal places. For the advancement of this broad mathematical field we shall chronologically show that each continent of the world has contributed. We genuinely hope students and teachers of mathematics will also be benefited with this article. Full article

In this paper, we consider an important problem for modeling complex coupled phenomena in porous media at multiple scales. In particular, we consider flow and transport in the void space between the pores when the pore space is altered by new solid obstructions formed by microbial growth or reactive transport, and we are mostly interested in pore-coating and pore-filling type obstructions, observed in applications to biofilm in porous media and hydrate crystal formation, respectively. We consider the impact of these obstructions on the macroscopic properties of the porous medium, such as porosity, permeability and tortuosity, for which we build an experimental probability distribution with reduced models, which involves three steps: (1) generation of independent realizations of obstructions, followed by, (2) flow and transport simulations at pore-scale, and (3) upscaling. For the first step, we consider three approaches: (1A) direct numerical simulations (DNS) of the PDE model of the actual physical process called BN which forms the obstructions, and two non-DNS methods, which we call (1B) CLPS and (1C) LP. LP is a lattice Ising-type model, and CLPS is a constrained version of an Allen–Cahn model for phase separation with a localization term. Both LP and CLPS are model approximations of BN, and they seek local minima of some nonconvex energy functional, which provide plausible realizations of the obstructed geometry and are tuned heuristically to deliver either pore-coating or pore-filling obstructions. Our methods work with rock-void geometries obtained by imaging, but bypass the need for imaging in real-time, are fairly inexpensive, and can be tailored to other applications. The reduced models LP and CLPS are less computationally expensive than DNS, and can be tuned to the desired fidelity of the probability distributions of upscaled quantities. Full article

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions. Full article

In turbulent premixed flames, for the mixing at a molecular level of reactants and products on the flame surface, it is crucial to sustain the combustion. This mixing phenomenon is featured by the scalar dissipation rate, which may be broadly defined as the rate of micro-mixing at small scales. This term, which appears in many turbulent combustion methods, includes the Conditional Moment Closure (CMC) and the Probability Density Function (PDF), requires an accurate model. In this study, a mathematical closure for the conditional mean scalar dissipation rate, $<N_c|\zeta >$, in Reynolds, Averaged Navier–Stokes (RANS) context is proposed and tested against two different Direct Numerical Simulation (DNS) databases having different thermochemical and turbulence conditions. These databases consist of lean turbulent premixed V-flames of the CH4-air mixture and stoichiometric turbulent premixed flames of H2-air. The mathematical model has successfully predicted the peak and the typical profile of $<N_c|\zeta >$with the sample space ζ and its prediction was consistent with an earlier study. Full article

Within the context of structure deterioration studies, we propose a new numerical method based on the use of fragility curves. In particular, the present work aims to theoretically study the degradation of concrete bridge structures subjected to aggressive environments. A simple probabilistic method based on fragility curves is presented which allows the forecasting of the lifetime of the considered structural system and the best monitoring time. The method was applied to investigate the degradation of a concrete bridge used as a case study. A Monte Carlo numerical procedure was used to simulate the variation over time of the residual resistant section and the ultimate bending moment of the deck of the case study. Within this context, fragility curves are used as reliable indicators of possible monitoring scenarios. In comparison with other methods, the main advantage of the proposed approach is the small amount of computing time required to obtain rapid assessment of reliability and deterioration level of the considered structure. Full article