Linear Mathematical Model Research Articles

Experimental Analysis of the Influence of Carrier Layer Material on the Performance of the Control System of a Cantilever-Type Piezoelectric Actuator.

The subject of this article is an experimental analysis of the control system of a composite-based piezoelectric actuator and an aluminum-based piezoelectric actuator. Analysis was performed for both the unimorph and bimorph structures. To carry out laboratory research, two piezoelectric actuators with a cantilever sandwich beam structure were manufactured. In the first beam, the carrier layer was made of glass-reinforced epoxy composite (FR4), and in the second beam, it was made of 1050 aluminum. A linear mathematical model of both actuators was also developed. A modification of the method of selecting weights in the LQR control algorithm for a cantilever-type piezoelectric actuator was proposed. The weights in the R matrix for the actuator containing a carrier layer made of stiffer material should be smaller than those for the actuator containing a carrier layer made of less stiff material. Additionally, regardless of the carrier layer material, in the case of a bimorph, the weight in the R matrix that corresponds to the control voltage of the compressing MFC patch should be smaller than the weight corresponding to the control voltage of the stretching MFC patch.

Mathematical models for determining and analyzing thermal regimes in mining industry mechanism structures

Purpose. To develop linear and nonlinear mathematical models of heat conduction for isotropic heterogeneous media with internal heating. This will allow for an increased accuracy in determining temperature fields, which will subsequently impact the effectiveness of designing mechanisms, devices, and individual components of structures that have a layered structure and are subjected to heat stress. Methodology. For the development of linear and nonlinear mathematical models of the temperature field and the analysis of temperature regimes in layered media with internal thermal heating, the coefficient of thermal conductivity is described as a whole using asymmetric unit functions. This makes it possible to solve a differential equation with singular coefficients in both linear and nonlinear boundary value problems of heat conduction with appropriate boundary conditions. Findings. Quadratic equations are obtained to determine the analytical solutions of linear and nonlinear boundary problems of heat conduction for a layered plate with internal heat load. Originality. The scientific novelty lies in the given method of linearization of the nonlinear mathematical model of heat conduction and obtaining analytical solutions, in a closed form, of the corresponding linear and nonlinear boundary value problems for isotropic layered media subjected to internal heating. Practical value. The developed linear and nonlinear mathematical models for determining the temperature distribution in layered structures with internal heating make it possible to analyze heat exchange processes and ensure the thermal stability of such structures. This also makes it possible to increase the heat resistance of structures and protect them from overheating, which can lead to damage to individual components and elements of mechanisms, as well as to the entire structure as a whole. The resulting analytical solutions can be used to predict temperature fields in mine shafts, underground environments and mechanisms of mining equipment, in particular, in drilling and underground compressor stations, ventilation systems and other equipment, which improves work efficiency and reduces useful energy consumption.

Estimating Circular Economic Potential of Organic Fraction of Municipal Solid Waste in Small City

The current waste management paradigm leads to a circular economic approach. To implement it, it is necessary to know the potential for resource recovery from waste, including organic fraction of municipal solid waste (OFMSW). This research aims to investigate the potential for resource recovery from OFMSW generated in Buleleng Regency, Bali Province, Indonesia. Five technologies were assessed for their potential to transform OFMSW into resources, namely anaerobic decomposition (AD), densification and drying to produce solid fuel, composting, processing with black soldier fly (BSF), and processing for eco-enzymes production. The potential for resource recovery is estimated using a simple linear relationship mathematical model using data available from the literature and secondary data of waste generation in Buleleng Regency. The study estimated 37,489.08 tons OFMSW is generated in Buleleng in 2023. The estimate shows that revenue potential from densification and drying about 9,336 million IDR, followe by composting about 2,471 million IDR, anaerobic digestion about 1,939 million IDR, BSF about 145 million IDR, and eco-enzyme about 13 million IDR. Finally, by estimating the quantity of resources available in OFMSW and their potential market value, it can be taken into consideration in planning and managing the circularity of OFMSW.

METHOD OF ESTIMATING THE DANGEROUS RANGE OF TRANSONIC NUMBERS M OF THE FLIGHT OF SUPERSONIC AIRCRAFT AND AEROSPACE SYSTEMS

Ensuring flight safety of supersonic aircraft and aerospace systems in the transonic range of flight M numbers still remains an ac- tual scientific and applied problem. This is due to the occurrence of various dangerous aeroelasticity phenomena in these flight modes. Such phenomena include transonic flutter, the occurrence of which has repeatedly resulted in the destruction of aircraft structural elements and, first of all, of aerodynamic control surface structural elements. Many publications are devoted to the theoretical and experimental research of this phenomenon, in which various approaches are proposed to substantiate the causes of intense oscillations of the aerodynamic control surfaces of modern supersonic aircraft in these flight modes, the conditions of their occurrence, the influence of various factors on the level of oscillations. It is noted that there are still no reliable theoretical methods for estimating the non-stationary forces of aerodynamic control surfaces that oscillate in a transonic flow, so the use of linear mathematical similarity models does not always allow transferring the results of blowing models in wind tunnels to full-scale aircraft designs. The paper proposes a method for estimating the dangerous range of M numbers in which transonic flutter of the aerodynamic control surfaces of supersonic aircraft and aerospace systems is possible. The method is based on the analysis of regularities of the adiabatic expansion of the local supersonic air flow on the surface of the airfoil in the range of transonic numbers M. Calculations have proven that for typical aerodynamic surfaces of modern supersonic aircraft, the occurrence of transonic flutter is possible in a narrow range of numbers M = 0.9…0.94. The obtained results can be used to substantiate the safe flight modes of supersonic aircraft both at the stage of flight tests and at the stage of operation. Further studies of this problem should be devoted to the analysis of methods for reducing the level of oscillations of aerodynamic control surfaces when transonic flutter occurs.

Experimental and optimization of die casting parameters on Al-Si alloy with snail shell reinforcing agent

The demand for aluminum in various fields continuously grows, including in the automotive industry. In this industry, aluminum is used as the material for the spare part. Therefore, aluminum with high mechanical properties and low casting defects is required. One of the available alternatives for producing excellent aluminum is through aluminum casting, including die casting. Die casting offers low cost in mass manufacturing of complex shaped components with acceptable casting results. Further, the selection of die-casting parameters and the addition of reinforcing elements can also improve the mechanical properties of aluminum. In this study, we strengthened the Al-Si matrix using High Pressure Die Casting process with particles from snail shell powder (calcium carbonate). Further, this study also explores the mechanical properties and microstructure of the product produced through experiment and optimization. The optimization was adopted to identify the optimum parameter. For the optimization, we used the Taguchi method. Our analysis results suggested that the reinforcing agent from the snail shell powder has the CaO and Ca(OH)2 phases, with a crystallite size of 106.59 nm. The morphology of the shell powder reinforcing agent showed the presence of agglomeration and interconnected structures, such as skeletons, with average particle size of 0.4 micro. The functional group of the shell powder reinforcing agent showed the OH band during the water absorption by CaO, along with asymmetric C–O with vibration from the carbonate group and Ca–O bound. The most excellent hardness level was identified from T8, with 86.33 HRB and die casting parameters of 0.15% reinforce agents, 750 °C temperature injection, and 50 MPa pressure. Meanwhile, the best tensile strength was found from the T9 sample, with 109,95 MPa and die casting parameters of 0.15% reinforce agents, 800 °C temperature injection, and 60 MPa pressure. Microstructure on the used piston die casting sample with snail shell powder reinforcing agent showed the presence of Al, Si, dendrite, and Al4Ca phases. The multiple response analysis on the three factors indicated that the reinforcing agent presented the most significant effects toward the tensile strength and hardness, followed by pressure and temperature injection. Meanwhile, the Taguchi method and ANOVA results showed the optimal parameter die casting was obtained from a combination of 0.15 wt% reinforce agent, 800 °C injection temperature, and 50 MPa pressure. A multiple linear regression mathematical model for tensile strength and hardness was developed from the observed data. In regression model, the value of R2 of tensile strength 74.02% and R2 of the hardness is 95,18% Thus, the developed model can be effectively used to predict the tensile strength and hardness

A Generalized Linear Mathematical Model of Cutting Part Movement in Deep Hole Machining

A Generalized Linear Mathematical Model of Cutting Part Movement in Deep Hole Machining

Minimization Implementation of Fuzzy Logic to Optimize a Cashew Nut Production using Simpleks-Duality Theory

Production control of cashew nuts greatly affects the profits earned by the company. When cashew nut raw materials exceed production needs, it results in storing cashews for an extended period, causing the cashew products to lose freshness, and the quality of processed cashews deteriorates. If the raw materials are damaged, the manufacturer must acquire additional costs to procure raw materials again. Another issue is that cashew nut raw materials are seasonal products and are not always available.To solve these problems, a calculation method is needed to control optimal production inventory to minimize the company's expenditures. The method used is to formulate the problem into a Fuzzy Linear Programming mathematical model using a combination of methods: the Simplex algorithm and Duality Theory. The case implementation focuses on the uncertainty of cashew nut production quantities outside the harvest season. Moreover, the calculation of an optimal production quantity to minimize resulting losses is needed. The output generated is an optimal production prediction using the combination of the Simplex Algorithm and Duality Theory in solving Fuzzy Linear Programming.

Optimization of production planning using integer linear programming method (case study of bakpia menik)

Bakpia Menik is a Small and Medium Enterprise (UKM) which operates in the field of bakpia production. Bakpia is one of the local cakes which is the main souvenir from Yogyakarta, so there is a big potential for increasing production. However, SMEs still lack production management planning to optimize resource use. So it is difficult to capture this big opportunity to maximize profits for SMEs. Seeing these problems, this research designed an integer linear programming mathematical model to optimize profits by using existing resources. Integer Linear Programming (ILP) is a mathematical model for maximizing profit and minimizing cost based on a mathematical model involving integer variables represented in a linear relationship. This research produces an integer linear programming model that presents the variables, resources, and constraints of Bakpia Menik. The model output shows that the optimal production amount by maximizing resource use is 31232 units and the maximum profit is IDR 33,431,750. From the model output, it can also show the advantages and disadvantages of Bakpia resources, so that resource availability planning can be carried out which can minimize holding costs.

On-site workshop investment problem: A novel mathematical approach and solution procedure

In real-world construction sites, On-Site Workshops (OSW) are installed to accelerate construction activities and facilitate the material handling process. These temporary OSWs are cost-effective, leading to decreasing the material handling cost and project makespan, which indicates their important role as a part of a construction project. However, considering the OSW, which has not been addressed in the project scheduling problems, requires the construction site to have a space capacity constraint while considering the workshop size, availability level, and other project-related constraints. In the present work, by considering the OSWs, a real construction project scheduling problem is studied as a Multi-Mode On-Site Workshop Investment Problem with Tardiness (MOSWIPT) while finding the installation/dismantling time of the OSWs. Two new (linear) mathematical programming models are proposed for MOSWIPT. Next, due to the NP-hardness of the problem, an enhanced Genetic Algorithm (GA)-based metaheuristic with efficient problem-specific improvement rules as local search and effective crossover and mutation operators is proposed. Computational experiments show that the proposed method has solved most of the instances of the addressed problem to optimality and outperformed the existing metaheuristics, e.g., Simulated Annealing (SA) and Particle Swarm Optimization (PSO). Finally, conclusions and suggestions for future studies are stated.

Designing a virtual cellular manufacturing system with route selection and workers’ considerations: A multi-objective robust possibilistic model

In today’s economy, the necessity for responsiveness to variations in customers’ permanent requirements is increasing significantly. Achieving immediate response or success in the competitive market requires boosting flexibility, agility, and efficiency in utilizing available production equipment and workforce. Implementing a Virtual Cellular Manufacturing System (VCSM) prevents the reconfiguration costs and is suitable for many systems where the machines are not removable. Owing to the significant role of human resources in VCMS, this paper assigns the workers based on their skills, interest in cooperation, and workload balancing among cells. The considerable novelty is balancing physical and time workloads simultaneously. Another strength of this research is the consideration of various routes to process each part. A comprehensive linear multi-objective mathematical model is developed for a virtual cellular manufacturing system. This paper develops the model by stating social and technical dimensions, which minimize exceptional elements and voids, maximize the workers' interest in cooperation, and minimize workload deviation. Stemming from uncertain parameters, a robust possibilistic approach is addressed. Due to the multi-objective model, the multi-choice meta-goal programming with the utility function is applied. Afterward, a real-case study is presented to validate the model. Eventually, the outcomes and sensitivity analysis are brought up.

Phenomenological modeling of wear mechanisms between nickel-based superalloy blades and ceramic-based abradable coatings in turbomachines

The tribological behavior and wear mechanism between K417G nickel-based superalloy blades and 8 wt% yttria-stabilized zirconia poly-p-hydroxybenzoate ceramic-based abradable coatings were investigated using a high-speed rubbing test machine simulating actual operating conditions. Two main influencing factors (linear velocity and incursion rate) were varied, and their effects on the system were determined. The wear mechanism of the system was attempted to be characterized. A significant correlation was found between all test results and the linear velocity, indicating that the linear velocity was the primary influence driving the friction. The incursion rate became a secondary factor. A linear mathematical model based on the proposed wear mechanism was developed to explain the wear mechanism and to predict the test results. The excellent fit and normally distributed residual results indicated the excellent performance of the model. This work can be used as an aid to understanding the present results and as a basis for further research on these phenomena in the future.

Application of the method of insignificant divergences to diagnose the technical aircraft gas turbine engine state under the transient-state conditions of its operation

The article deals with issues related to the use of parametric information of the transient-state gas turbine engines (GTE) operation conditions for diagnosing their technical condition during the operation. A review of general approaches to computational algorithms for the recognition and classification of the condition applicable to aircraft GTE has been carried out. The significance of analytical models in modern algorithms for assessing the technical GTE condition is emphasized. The construction of a linearized mathematical model for the transient-state condition of the generalized-scheme aircraft GTE operation has been considered. It represents a system of equations analytically combining the relative parameter divergences measured during the engine operation with the relative divergences of unmeasured thermogasdynamic parameters and geometric gas-air flow duct parameters allowing for the technical condition of gas-air channel elements to be classified. A method for constructing mathematical and diagnostic engine models, using the transient response data, has been formulated. The capability of employing a method of insignificant divergences, used to build linear (linearized) mathematical and diagnostic GTE models for the steady-state conditions of its operation, has been demonstrated as well. It is shown that, despite the structural similarity of linear models of the steady and transient-state processes, diagnostics by means of the stated above processes is based on completely different principles – under the steady-state condition, the classification of a technical condition is determined by the variation in the value of the group of controlled responses, and under the transient-state condition, this operation is based on correlating the change in the transient-state behavior. To ensure the versatility of employing proposed methods regarding various GTE designs installed on modern civil aircraft, a generalized-design aircraft GTE model – a three-shaft bypass turbojet engine with mixing flows in a common jet nozzle, has been considered.

Critical Velocity, Maximal Lactate Steady State, and Muscle MCT1 and MCT4 after Exhaustive Running in Mice.

Although the critical velocity (CV) protocol has been used to determine the aerobic capacity in rodents, there is a lack of studies that compare CV with maximal lactate steady state intensity (iMLSS) in mice. As a consequence, their physiological and molecular responses after exercise until exhaustion at CV intensity remain unclear. Thus, we aimed to compare and correlate CV with iMLSS in running mice, following different mathematical models for CV estimation. We also evaluated their physiological responses and muscle MCT1 and MCT4 after running until exhaustion at CV. Thirty C57BL/6J mice were divided into two groups (exercised-E and control-C). Group E was submitted to a CV protocol (4 days), using linear (lin1 and lin2) and hyperbolic (hyp) mathematical models to determine the distance, velocity, and time to exhaustion (tlim) of each predictive CV trial, followed by an MLSS protocol. After a running effort until exhaustion at CV intensity, the mice were immediately euthanized, while group C was euthanized at rest. No differences were observed between iMLSS (21.1 ± 1.1 m.min-1) and CV estimated by lin1 (21.0 ± 0.9 m.min-1, p = 0.415), lin2 (21.3 ± 0.9 m.min-1, p = 0.209), and hyp (20.6 ± 0.9 m.min-1, p = 0.914). According to the results, CV was significantly correlated with iMLSS. After running until exhaustion at CV (tlim = 28.4 ± 8,29 min), group E showed lower concentrations of hepatic and gluteal glycogen than group C, but no difference in the content of MCT1 (p = 0.933) and MCT4 (p = 0.123) in soleus muscle. Significant correlations were not found between MCT1 and MCT4 and tlim at CV intensity. Our results reinforce that CV is a valid and non-invasive protocol to estimate the maximal aerobic capacity in mice and that the content of MCT1 and MCT4 was not decisive in determining the tlim at CV, at least when measured immediately after the running effort.

Research and concept design of wave energy converter on ocean squid jigging ship

Wave power capture applied on a squid jigging ship is assessed in this paper; this would decrease the operating cost of ships and reduce carbon emissions. Firstly, the history of wave energy devices and wave energy generation on ships are briefly reviewed. Then, a new wave energy device on an ocean squid jigging ship is designed. The linear mathematical system model of the device, and WAMIT software are used to calculate wave energy captured. The floating bodies of the device is designed to take advantage of resonance. By comparing wave capture width ratio of the float with arm hinged on the ship, it is found that wave capture width ratio of the device is highest when the arm length is half a wavelength. The numerical method is validated by experimental tests which are presented in details from setup, data treatment to wave energy capture ratio calculated. Based on a resonance criterion, 20 wave energy device layouts of the ocean squid jigging ship are designed. From numerical simulation the optimum radius of the floating body is 2 m, and the maximum annual average power among these devices is 136 kW at Northwest Pacific fishery ground, which can provide about 10 % of the power consumption for the ocean squid jigging ship.

Linear mathematical models for yield estimation of baby corn (Zea mays L.)

Linear mathematical models have been developed for predicting baby corn yield in terms of cob volume for two cycles of maize (Zea mays L.). Cob volume is directly proportional to morphological parameters such as length, weight, and girth; hence, linear mathematical models have been developed. Primary data for a random selection of 60 cobs for each cycle were collected, and lab work was carried out to measure the corn ears and cob growth parameters. An irregular distribution was observed among all six growth parameters examined in the study. Descriptive statistical measures were employed to facilitate the description of growth parameters. The final volume of the baby corn cob was used for crop yield estimation. The water displacement method was employed to measure the actual volume of cobs, which was then compared with the volumes estimated using the developed mathematical models. For both cycles, similar trends were observed in both estimated and actual volumes of cobs, providing numerical confirmation for the validity of the developed mathematical models. The theoretical validity of these models was also established using statistical measures such as R2, adjusted R2, F-test, P-value, and correlation coefficient. Any deviations between estimated and actual volumes would indicate changes in the dependent variables of the model, attributed to the effects of climate change, as other internal and external factors are held constant. These models offer a critical predictive tool for stakeholders, enabling improved yield predictions and optimized resource allocation. As a result, they facilitate strategic planning for increased profitability.

Resistive Sensing of Seed Cotton Moisture Regain Based on Pressure Compensation.

The measurement of seed cotton moisture regain (MR) during harvesting operations is an open and challenging problem. In this study, a new method for resistive sensing of seed cotton MR measurement based on pressure compensation is proposed. First, an experimental platform was designed. After that, the change of cotton bale parameters during the cotton picker packaging process was simulated through the experimental platform, and the correlations among the compression volume, compression density, contact pressure, and conductivity of seed cotton were analyzed. Then, support vector regression (SVR), random forest (RF), and a backpropagation neural network (BPNN) were employed to build seed cotton MR prediction models. Finally, the performance of the method was evaluated through the experimental platform test. The results showed that there was a weak correlation between contact pressure and compression volume, while there was a significant correlation (p < 0.01) between contact pressure and compression density. Moreover, the nonlinear mathematical models exhibited better fitting performance than the linear mathematical models in describing the relationships among compression density, contact pressure, and conductivity. The comparative analysis results of the three MR prediction models showed that the BPNN algorithm had the highest prediction accuracy, with a coefficient of determination (R2) of 0.986 and a root mean square error (RMSE) of 0.204%. The mean RMSE and mean coefficient of variation (CV) of the performance evaluation test results were 0.20% and 2.22%, respectively. Therefore, the method proposed in this study is reliable. In addition, the study will provide a technical reference for the accurate and rapid measurement of seed cotton MR during harvesting operations.

Sustainable aquafeed development: Incorporating select fruit wastes into Zebrafish diets using mathematical model-based approach

Expensive aquafeed is a major problem in aquaculture, creating the need for a low-cost feed that provides ideal nutritional requirement to maximize growth performances. This study aims to formulate and evaluate two new optimized Zebrafish feeds (F1 and F2) using linear programming mathematical model, one of which incorporates two pigment rich fruit wastes (Pitaya peel and Roselle calyx) in the formulation. The model represents nutritional content and cost of each ingredient into linear equations, with the goal of finding ideal combination that satisfies the specific nutrient requirements. By systematically evaluating ingredient proportions, linear programming ensures that Zebrafish receives adequate nutrients at the lowest possible cost, making the feed development process more efficient and cost-effective. The novel feed formulations derived from the mathematical model were tested on the growth and pigmentation of Zebrafish in comparison to a commercial feed (control). Feed intake of F1 and F2 were generally found to be similar to the control feed, indicating the acceptability of the formulated feeds by the Zebrafish. Body weight and length of Zebrafish fed with F1 and F2 were comparable to Zebrafish fed with control feed (p > 0.05). Similarly, Zebrafish fed with F1 and F2 showed no significant differences in pigment intensity compared to Zebrafish fed with control feed (p > 0.05). The survival rate of fishes in all feeding groups were greater than 70 % with no significant differences (p > 0.05). Results obtained in this study illustrated the potential of mathematic linear programming and effectiveness of utilising pigment-rich fruit wastes in formulating an optimized economic aquafeed.

Математичні моделі температурного поля у елементах електронних пристроїв із чужорідним включенням

Linear and non-linear mathematical models for the determination of the temperature field, and subsequently for the analysis of temperature regimes in isotropic media with semi-transparent foreign inclusions that are also subject to external heat load, have been developed. To solve the nonlinear boundary-value problem, a linearizing function was introduced, using which the original nonlinear heat conduction equation and nonlinear boundary conditions were linearized, and as a result, a partially linearized second-order differential equation with partial derivatives and discontinuous and singular coefficients relative to the linearizing function and partially linearized boundary conditions was obtained. For the final linearization of the partially linearized differential equation and boundary conditions, the approximation of the temperature according to one of the spatial coordinates on the boundary surfaces of the inclusion was performed by piecewise constant functions. To solve the obtained linear boundary value problem, the Hankel integral transformation method was used, as a result of which an analytical solution was obtained, which determines the introduced linearizing function. For the numerical analysis of temperature behavior and heat exchange processes caused by external heat load, software tools have been developed, which are used to create a geometric image of temperature distribution depending on spatial coordinates. The obtained results indicate the correspondence of the developed mathematical models of the analysis of heat exchange processes in heterogeneous media with external heating to a real physical process. The obtained results indicate the correspondence of the developed mathematical models of the analysis of heat exchange processes in heterogeneous media with external heating to a real physical process. The developed models make it possible to analyze environments with foreign elements under external thermal loads regarding their thermal resistance. As a result, it becomes possible to increase it and protect it from overheating, which can cause the destruction of not only individual elements, but also the entire structure.

Distributed risk-constrained strategy management of cloud energy storage for residential and electricity market services provision

Energy storage systems can improve the performance of home energy management systems and also provide ancillary services in electricity markets. However, the economic and technical insufficiency of individual home storage units, makes employing them inefficient for domestic storage and market applications, respectively. Therefore, central storage units with capacity sharing capability to small consumers as Cloud Energy Storages (CESs) are becoming a promising solution, and are also potentially able to contribute to ancillary service provision in the market. In this context, this paper aims to develop a novel stochastic day-ahead distributed management framework for CES to simultaneously adopt the optimal strategy of storage allocation for photovoltaic-integrated homes and participation in energy and ancillary service markets. The developed distributed framework is formulated within the Benders decomposition approach in which CES strategy and home energy management systems are optimized through master and subproblems based on linear mathematical models, respectively. Furthermore, the uncertainty of market prices is handled by the Conditional Value at Risk (CVaR) method. The developed model is assessed through real-world case studies of ERCOT. The results highlight the effectiveness of the collaborative service framework for both CES and households. Energy arbitrage through local storage services compensates for CES's challenges such as degradation and low power rating in the provision of energy services. These improvements benefit CES owners with higher net revenues and households with reduced cost of electricity supply.

Retracted: Application of Linear Regression Mathematical Model in the Evaluation of Teachers’ Informatization Quality

Retracted: Application of Linear Regression Mathematical Model in the Evaluation of Teachers’ Informatization Quality