Formulation Of Mathematical Model Research Articles

Experimental analysis of ON/OFF and variable speed drive controlled industrial chiller towards energy efficient operation

This study demonstrates thermodynamic and energy effects of a Variable Speed Drive (VSD), powering compressor in a partially loaded chiller system. The proposed work fits the gap in the existing literature, which mostly addresses VSD applications in chiller’s auxiliary pumps and fans. The goals of this work are defined by four Research Problems (RP’s): RP1. comparison of thermodynamic extensive parameters, for ON/OFF and VSD controlled systems, RP2. load ranges in which VSD control systems are energy efficient, RP 3. potential energy savings in VSD controlled compressor, and RP 4. mathematical model formulation, useful in energy audit conditions, estimating potential benefits of VSD implementation, based on measurement data from existing ON-OFF controlled chiller. To address these aspects, a set of measurements have been performed on a fully equipped experimental chiller system (UW Oshkosh Teaching and Energy Research Industrial Lab). All data have been collected for a wide spectrum of loads in both control configurations. Data analysis showed significant differences in a chiller operation. VSD operated chiller eliminates fluctuations in all measured thermodynamic parameters (RP1.). The accomplished work demonstrated that the most energy efficient effects can be achieved for a partially loaded, VSD-controlled chiller, working at ∼55–75% of its nominal capacity (RP 2.). The implementation of a Variable Speed Drive for such load levels allows for achieving up to 25% of energy savings (RP 3.) Finally, proposed mathematical model have been experimentally verified as useful in the range of 50–100% of nominal load (RP 4.).

Parameter estimation techniques for a chemotaxis model inspired by Cancer-on-Chip (COC) experiments

The present work is inspired by laboratory experiments, investigating the cross-talk between immune and cancer cells in a confined environment given by a microfluidic chip, the so called Organ-on-Chip (OOC). Based on a mathematical model in form of coupled reaction–diffusion-transport equations with chemotactic functions, our effort is devoted to the development of a parameter estimation methodology that is able to use real data obtained from the laboratory experiments to estimate the model parameters and infer the most plausible chemotactic function present in the experiment. In particular, we need to estimate the model parameters representing the convective and diffusive regimes included in the PDE model, in order to evaluate the diffusivity of the chemoattractant produced by tumor cells and its biasing effect on immune cells.The main issues faced in this work are the efficient calibration of the model against noisy synthetic data, available as macroscopic density of immune cells. A calibration algorithm is derived based on minimization methods which applies several techniques such as regularization terms and multigrids application to improve the results, which show the robustness and accuracy of the proposed algorithm.

Unmanned Aerial Vehicles Motion Control with Fuzzy Tuning of Cascaded-PID Gains

One of the main challenges of maneuvering an Unmanned Aerial Vehicle (UAV) to keep a stabilized flight is dealing with its fast and highly coupled nonlinear dynamics. There are several solutions in the literature, but most of them require fine-tuning of the parameters. In order to avoid the exhaustive tuning procedures, this work employs a Fuzzy Logic strategy for online tuning of the PID gains of the UAV motion controller. A Cascaded-PID scheme is proposed, in which velocity commands are calculated and sent to the flight control unit from a given target desired position (waypoint). Therefore, the flight control unit is responsible for the lower control loop. The main advantage of the proposed method is that it can be applied to any UAV without the need of its formal mathematical model. Robot Operating System (ROS) is used to integrate the proposed system and the flight control unit. The solution was evaluated through flight tests and simulations, which were conducted using Unreal Engine 4 with the Microsoft AirSim plugin. In the simulations, the proposed method is compared with the traditional Ziegler-Nichols tuning method, another Fuzzy Logic approach, and the ArduPilot built-in PID controller. The simulation results show that the proposed method, compared to the ArduPilot controller, drives the UAV to reach the desired setpoint faster. When compared to Ziegler-Nichols and another different Fuzzy Logic approach, the proposed method demonstrates to provide a faster accommodation and yield smaller errors amplitudes.

Modeling Performance of Butterfly Valves Using Machine Learning Methods

Control of airflow of activated sludge systems has significant challenges due to the non-linearity of the control element (butterfly valve). To overcome this challenge, some valve manufacturers developed valves with linear characteristics. However, these valves are 10–100 times more expensive than butterfly valves. By developing models for butterfly valves installed characteristics and utilizing these models for real-time airflow control, the authors of this paper aimed to achieve the same accuracy of control using butterfly valves as achieved using valves with linear characteristics. Several approaches were tested to model the installed valve’s characteristics, such as a formal mathematical model utilizing Simscape/Matlab software, a semi-empirical model, and several machine learning methods (MLM), including regression, support vector machine, Gaussian process, decision tree, and deep learning. Several versions of the airflow-valve position models were developed using each machine learning method listed above. The one with the smallest forecast error was selected for field testing at the 55.5×103 m3/day 12 MGD City of Chico activated sludge system. Field testing of the formal mathematical model, semi-empirical model, and the regularized gradient boosting machine model (the best among MLMs) showed that the regularized gradient boosting machine model (RGBMM) provided the best accuracy. The use of the RGBMMs in airflow control loops since 2019 at the City of Chico wastewater treatment plant showed that these models are robust and accurate (2.9% median error).

Parametric Investigation of Photochemical Machining of SS- 430 for Manufacturing of Micromesh

Photochemical machining (PCM) is an emerging method for machining of very thin and difficult-to-cut material with complex geometrical profile. PCM is one of recommended method for machining of aerospace components, biomedical appliances, electronics part and decorative items. High corrosion resistance, better life, good appearance and strength recommend SS-430 as suitable material for various applications. In the current investigation, the parametric investigations of process parameters in photochemical machining for concentration and temperature of etchant, time of etching is done through ANOVA analysis. Grey Relational Analysis is performed to estimate the optimum machining parameters during PCM of SS-430. Formulation of mathematical model is done for prediction of results. Taguchi (L27) experimental array is used for Design of Experiments (DoE). The significance process parameters are estimated to govern the process with F-Values. Confirmatory test is conducted to observe the improvement in the responses. ANN predictive model is built up for investigation of error between predictive and experimental values. The obtained optimum set is used for manufacturing of micromesh typically used in smoke detector to safeguard human life.

Stochastic optimization for vaccine and testing kit allocation for the COVID-19 pandemic

We present a formal mathematical modeling framework for a multi-agent sequential decision problem during an epidemic. The problem is formulated as a collaboration between a vaccination agent and learning agent to allocate stockpiles of vaccines and tests to a set of zones under various types of uncertainty. The model is able to capture passive information processes and maintain beliefs over the uncertain state of the world. We designed a parameterized direct lookahead approximation which is robust and scalable under different scenarios, resource scarcity, and beliefs about the environment. We design a test allocation policy designed to capture the value of information and demonstrate that it outperforms other learning policies when there is an extreme shortage of resources (information is scarce). We simulate the model with two scenarios including a resource allocation problem to each state in the United States and another for the nursing homes in Nevada. The US example demonstrates the scalability of the model and the nursing home example demonstrates the robustness under extreme resource shortages.

Adaptation and parametrization of an iron loss model for rotating magnetization loci in NO electrical steel

PurposeThe magnetic characterization of electrical steel is typically examined by measurements under the condition of unidirectional sinusoidal flux density at different magnetization frequencies. A variety of iron loss models were developed and parametrized for these standardized unidirectional iron loss measurements. In the magnetic cross section of rotating electrical machines, the spatial magnetic flux density loci and with them the resulting iron losses vary significantly from these unidirectional cases. For a better recreation of the measured behavior extended iron loss models that consider the effects of rotational magnetization have to be developed and compared to the measured material behavior. The aim of this study is the adaptation, parametrization and validation of an iron loss model considering the spatial flux density loci is presented and validated with measurements of circular and elliptical magnetizations.Design/methodology/approachThe proposed iron loss model allows the calculation and separation of the different iron loss components based on the measured iron loss for different spatial magnetization loci. The separation is performed in analogy to the conventional iron loss calculation approach designed for the recreation of the iron losses measured under unidirectional, one-dimensional measurements. The phenomenological behavior for rotating magnetization loci is considered by the formulation of the different iron loss components as a function of the maximum magnetic flux density Bm, axis ratio fAx, angle to the rolling direction (RD) θ and magnetization frequency f.FindingsThe proposed formulation for the calculation of rotating iron loss is able to recreate the complicated interdependencies between the different iron loss components and the respective spatial magnetic flux loci. The model can be easily implemented in the finite element analysis of rotating electrical machines, leading to good agreement between the theoretically expected behavior and the actual output of the iron loss calculation at different geometric locations in the magnetic cross section of rotating electrical machines.Originality/valueBased on conventional one-dimensional iron loss separation approaches and previously performed extensions for rotational magnetization, the terms for the consideration of vectorial unidirectional, elliptical and circular flux density loci are adjusted and compared to the performed rotational measurement. The presented approach for the mathematical formulation of the iron loss model also allows the parametrization of the different iron loss components by unidirectional measurements performed in different directions to the RD on conventional one-dimensional measurement topologies such as the Epstein frames and single sheet testers.

Design of a robust active fuzzy parallel distributed compensation anti-vibration controller for a hand-glove system.

Undesirable vibrations resulting from the use of vibrating hand-held tools decrease the tool performance and user productivity. In addition, prolonged exposure to the vibration can cause ergonomic injuries known as the hand-arm vibration syndrome (HVAS). Therefore, it is very important to design a vibration suppression mechanism that can isolate or suppress the vibration transmission to the users’ hands to protect them from HAVS. While viscoelastic materials in anti-vibration gloves are used as the passive control approach, an active vibration control has shown to be more effective but requires the use of sensors, actuators and controllers. In this paper, the design of a controller for an anti-vibration glove is presented. The aim is to keep the level of vibrations transferred from the tool to the hands within a healthy zone. The paper also describes the formulation of the hand-glove system’s mathematical model and the design of a fuzzy parallel distributed compensation (PDC) controller that can cater for different hand masses. The performances of the proposed controller are evaluated through simulations and the results are benchmarked with two other active vibration control techniques-proportional integral derivative (PID) controller and active force controller (AFC). The simulation results show a superior performance of the proposed controller over the benchmark controllers. The designed PDC controller is able to suppress the vibration transferred to the user’s hand 93% and 85% better than the PID controller and the AFC, respectively.

Geometric forming and mechanical performance of reciprocal frame structures assembled using fibre reinforced composites

Reciprocal frame (RF) structures were developed in this work using pultruded glass fibre reinforced polymer (GFRP) members and the formulation of mathematical model for geometric forming and capacity design of such structures were presented. Firstly, governing geometric relationships are identified for the height, span and slope of the RF structure and its overall geometry can be formed accordingly. Once the geometry is determined, the structure can be analysed to calculate the internal forces of each component and connections under given loads. GFRP pultruded members were used to assemble the RF structure due to their high strength and lightweight. Considering the closed shape of the tubular section and the anisotropy of the materials, an innovative connection configuration was developed to facilitate the assembly and minimise the requirement of tools in the construction. Both the conceptual design and modelling analysis are supported with experimental results at connection and structural levels. The load-drift relationships of the connections were experimentally examined. Subsequently, A GFRP reciprocal frame structure was then assembled with a span of 4.5 m and subjected to multi-point bending to verify the proposed evaluation method and to study its mechanical performance. Verified by experimental results, a two-dimensional numerical model of the RF structure was developed and analysed using the finite element (FE) approach where different structural boundary conditions and connection stiffnesses were discussed. Finally, the geometrical nonlinear analysis was also studied for the structure through FE modelling.

Formulation of mathematical model using dimensional analysis approach for plastic shredding process through Human powered flywheel Motor (HPFM)

The practical feasibility and productive viability of a Human-powered flywheel machine (HPFM) system having the capacity to produce 3 to 5 Horse Power (H.P) is preferred over motorized machines for rural-based applications. The present work deals to establish precise dimensionless equations for four parameters i.e. Duration of Energy consumption, Quantity of Material Processed/Time, Quality of shredding parts, Process Horse Power (H.P), and Instantaneous Load Torque using the Buckingham Pi-theorem technique for the waste monomer plastic shredding operation using HPFM. The independent and dependent variables affecting the shredding operation have been identified to form the experimental data-based model equations for the above-mentioned response variables. These equations will further help to understand the phenomenon of shredding plastic using HPFM in the rural sector and they will also help in developing the capacity of the machine according to the various requirements. A distinct experimental plan has been established for calculating the kinetic energy of the system and the different variables identified for the process.

Synthesis of stable coalitions in the economy based on fundamental criteria of the portfolio theory

Subject. The article outlines basic principles of a mathematical model for formation of stable coalitions in the economy at the interstate level. Objectives. We focus on developing a mathematical model to build such coalitions. Methods. The study employs the portfolio theory, risk-return model, correlation and regression analysis, technical and fundamental analysis. The proposed model rests on fundamental provisions of creating a multicomponent, widely diversified investment portfolio. The model uses the key concepts, like expected profitability, risk level, industry diversification and hedging, in combination with the synthesis of a diversified group of leading commodity indices. Results. We show possibilities of using internal (based on the country’s indices) and external (based on other countries’ indices) correlation analysis, according to data on trends in economic indices, to ensure sectoral diversification within the country and maximize the international level of sectoral diversification, respectively. We performed a fundamental analysis of the condition of economies of the countries included in the coalition, and of the countries, which are considered to be included in the coalition as appropriate. The paper assesses positive and negative factors of joint functioning of the economies of the coalition countries, from the point of view of their geographic location. Conclusions. The model makes it possible to build new optimal coalitions in the economy, to analyze the practicability of further existence of previously formed coalitions, and to update the composition of coalitions, according to trends in the world economy development.

SARS-CoV-2 adsorption on suspended solids along a sewerage network: mathematical model formulation, sensitivity analysis, and parametric study

Accounting for SARS-CoV-2 adsorption on solids suspended in wastewater is a necessary step towards the reliable estimation of virus shedding rate in a sewerage system, based on measurements performed at a terminal collection station, i.e., at the entrance of a wastewater treatment plant. This concept is extended herein to include several measurement stations across a city to enable the estimation of spatial distribution of virus shedding rate. This study presents a pioneer general model describing the most relevant physicochemical phenomena with a special effort to reduce the complicated algebra. This is performed both in the topology regime, introducing a discrete-continuous approach, and in the domain of independent variables, introducing a monodisperse moment method to reduce the dimensionality of the resulting population balance equations. The resulting simplified model consists of a large system of ordinary differential equations. A sensitivity analysis is performed with respect to some key parameters for a single pipe topology. Specific numerical techniques are employed for the integration of the model. Finally, a parametric case study for an indicative—yet realistic—sewerage piping system is performed to show how the model is applied to SARS-CoV-2 adsorption on wastewater solids in the presence of other competing species. This is the first model of this kind appearing in scientific literature and a first step towards setting up an inverse problem to assess the spatial distribution of virus shedding rate based on its concentration in wastewater.

Chaotic dynamics driven by particle-core interactions

High-intensity beams in modern linacs are frequently encircled by diffuse halos, which drive sustained particle losses and result in the gradual degradation of accelerating structures. In large part, the growth of halos is facilitated by internal space-charge forces within the beams, and detailed characterization of this process constitutes an active area of ongoing research. A partial understanding of dynamics that ensue within space-charge dominated beams is presented by the particle-core interaction paradigm—a mathematical model wherein single particle dynamics, subject to the collective potential of the core, is treated as a proxy for the broader behavior of the beam. In this work, we investigate the conditions for the onset of large-scale chaos within the framework of this model and demonstrate that the propensity toward stochastic evolution is strongly dependent upon the charge distribution of the beam. In particular, we show that while particle motion within a uniformly charged beam is dominantly regular, rapid deterministic chaos readily arises within space-charge dominated Gaussian beams. Importantly, we find that for sufficiently high values of the beam's space charge and beam pulsation amplitude, enhanced chaotic mixing between the core and the halo can lead to an enhanced radial diffusion of charged particles. We explain our results from analytic grounds by demonstrating that chaotic motion is driven by the intersection of two principal resonances of the system and derives the relevant overlap conditions. Additionally, our analysis illuminates a close connection between the mathematical formulation of the particle-core interaction model and the Andoyer family of integrable Hamiltonians.

A spiking central pattern generator for the control of a simulated lamprey robot running on SpiNNaker and Loihi neuromorphic boards

Central pattern generator (CPG) models have long been used to investigate both the neural mechanisms that underlie animal locomotion, as well as for robotic research. In this work we propose a spiking central pattern generator (SCPG) neural network and its implementation on neuromorphic hardware as a means to control a simulated lamprey model. To construct our SCPG model, we employ the naturally emerging dynamical systems that arise through the use of recurrent neural populations in the neural engineering framework (NEF). We define the mathematical formulation behind our model, which consists of a system of coupled abstract oscillators modulated by high-level signals, capable of producing a variety of output gaits. We show that with this mathematical formulation of the CPG model, the model can be turned into a spiking neural network (SNN) that can be easily simulated with Nengo, an SNN simulator. The SCPG model is then used to produce the swimming gaits of a simulated lamprey robot model in various scenarios. We show that by modifying the input to the network, which can be provided by sensory information, the robot can be controlled dynamically in direction and pace. The proposed methodology can be generalized to other types of CPGs suitable for both engineering applications and scientific research. We test our system on two neuromorphic platforms, SpiNNaker and Loihi. Finally, we show that this category of spiking algorithms displays a promising potential to exploit the theoretical advantages of neuromorphic hardware in terms of energy efficiency and computational speed.

6DOF manoeuvring model of KCS with full roll coupling

In the present article a novel mathematical model formulation is introduced to account for the effect of heeling of the ship while manoeuvring in calm water, harbour conditions. The mathematical model is based on a comprehensive captive manoeuvring test program, carried out with the well-known benchmark hull KCS, where the roll motion was forced with a newly installed harmonic roll actuator.The new mathematical model was implemented in the ship manoeuvring simulator and compared against free running model tests. The simulator model, after slight tuning, seems capable of capturing the manoeuvring motion of the ship in 6 DOF, however, additional research is planned with respect to the effect of the transverse stability and the draft of the ship.

A systematic comparison of community detection algorithms for measuring selective exposure in co-exposure networks

The use of community detection techniques for understanding audience fragmentation and selective exposure to information has received substantial scholarly attention in recent years. However, there exists no systematic comparison, that seeks to identify which of the many community detection algorithms are the best suited for studying these dynamics. In this paper, I address this question by proposing a formal mathematical model for audience co-exposure networks by simulating audience behavior in an artificial media environment. I show how a variety of synthetic audience overlap networks can be generated by tuning specific parameters, that control various aspects of the media environment and individual behavior. I then use a variety of community detection algorithms to characterize the level of audience fragmentation in these synthetic networks and compare their performances for different combinations of the model parameters. I demonstrate how changing the manner in which co-exposure networks are constructed significantly improves the performances of some of these algorithms. Finally, I validate these findings using a novel empirical data-set of large-scale browsing behavior. The contributions of this research are two-fold: first, it shows that two specific algorithms, FastGreedy and Multilevel are the best suited for measuring selective exposure patterns in co-exposure networks. Second, it demonstrates the use of formal modeling for informing analytical choices for better capturing complex social phenomena.

Modeling and prediction of the transmission dynamics of COVID-19 based on the SINDy-LM method.

The transmission dynamics of COVID-19 is investigated in this study. A SINDy-LM modeling method that can effectively balance model complexity and prediction accuracy is proposed based on data-driven technique. First, the Sparse Identification of Nonlinear Dynamical systems (SINDy) method is used to discover and describe the nonlinear functional relationship between the dynamic terms in the model in accordance with the observation data of the COVID-19 epidemic. Moreover, the Levenberg–Marquardt (LM) algorithm is utilized to optimize the obtained model for improving the accuracy of the SINDy algorithm. Second, the obtained model, which is consistent with the logistic model in mathematical form with small errors and high robustness, is leveraged to review the epidemic situation in China. Otherwise, the evolution of the epidemic in Australia and Egypt is predicted, which demonstrates that this method has universality for constructing the global COVID-19 model. The proposed model is also compared with the extreme learning machine (ELM), which shows that the prediction accuracy of the SINDy-LM method outperforms that of the ELM method and the generated model has higher sparsity.

Индивидуально-типологические особенности руководителей региональных медицинских учреждений санаторно-курортного профиля

Sanatorium complexes are a special direction related to the health care system, their heads are required to have specialized knowledge. However, there are different views on this, some experts believe that a professional manager can productively perform duties in an institution of any profile. Others believe that the head of a medical institution must have a medical education, otherwise difficulties may arise. Currently, there is a lack of research focused on the identification, assessment and consistency of personality traits with the direction of work. The article examines the individual-typological features of the heads of regional medical institutions of a sanatorium-resort profile. There were revealed clearly expressed individual-typological features that distinguish managers with medical education in cognitive, personal and motivational components from leaders of a different educational profile, which affects professional efficiency. Psychological basic features that determine the activity and behavioral activity of employees within the profession were identified. A formal-mathematical model has been developed, which makes it possible to comprehensively assess the level of effectiveness of professional management activities of managers. In addition, regional specificity was identified, which proves the influence of climatic and economic conditions on the mental and behavioral characteristics of a specialist.

A Practical Model of Hole Effective Mass of Si on Si1−x Ge x Modulated by External Electric Field and External Strain

This paper reconsiders the mathematical formulation of the conventional nonparabolic band dispersion model of holes of Si on SiGe materials, and proposes a practical model of hole effective mass of covalent semiconductors modulated by the external electric field and external strain. This paper also discusses how the nonparabolicity of the valence band impacts the effective masses of holes that are confined within the barriers. Since the conventional simplified model for band nonparabolicity does not include the external potential effect as a perturbation, it is examined whether this perturbation can be implemented into the conventional model to enhance its usefulness. This consideration is also applied to the impact of strain on the effective mass of holes. The conventional dispersion model for the nonparabolic hole band is examined on the basis of the Hamiltonian operator representation because the insertion of perturbation energy must be validated mathematically. When the perturbation energy is smaller than the unperturbed energy, the insertion of the perturbation energy term into the conventional expression for the nonparabolic band dispersion model is reasonably valid. For example, it is anticipated that this approximation is accurate for a sub-10 nm thick Si physically confined on the SiGe layer, so this study contributes to the analysis of nano-scale devices.

Matrix-Based Formulation of Heterogeneous Individual-Based Models of Infectious Diseases: Using SARS Epidemic as a Case Study.

Heterogeneities of individual attributes and behaviors play an important role in the complex process of epidemic spreading. Compared to differential equation-based system dynamical models of infectious disease transmission, individual-based epidemic models exhibit the advantage of providing a more detailed description of realities to capture heterogeneities across a population. However, the higher granularity and resolution of individual-based epidemic models comes with the cost of increased computational complexities, which result in difficulty in formulating individual-based epidemic models with mathematics. Furthermore, it requires great effort to understand and reproduce existing individual-based epidemic models presented by previous researchers. We proposed a mathematical formulation of heterogeneous individual-based epidemic models using matrices. Matrices and vectors were applied to represent individual attributes and behaviors. We derived analytical results from the matrix-based formulations of individual epidemic models, and then designed algorithms to force the computation of matrix-based individual epidemic models. Finally, we used a SARS epidemic control as a case study to verify the matrix-based formulation of heterogeneous individual-based epidemic models.