Control Model Research Articles

Stability analysis of flying wing layout aircraft based on radial basis function neural network model

Purpose To ensure the stability of the flying wing layout unmanned aerial vehicle (UAV) during flight, this paper uses the radial basis function neural network model to analyse the stability of the aforementioned aircraft. Design/methodology/approach This paper uses a linear sliding mode control algorithm to analyse the stability of the UAV's attitude in a level flight state. In addition, a wind-resistant control algorithm based on the estimation of wind disturbance with a radial basis function neural network is proposed. Through the modelling of the flying wing layout UAV, the stability characteristics of a sample UAV are analysed based on the simulation data. The stability characteristics of the sample UAV are analysed based on the simulation data. Findings The simulation results indicate that the UAV with a flying wing layout has a short fuselage, no tail with a horizontal stabilising surface and the aerodynamic focus of the fuselage and the centre of gravity is nearby, which is indicative of longitudinal static instability. In addition, the absence of a drogue tail and the reliance on ailerons and a swept-back angle for stability result in a lack of stability in the transverse direction, whereas the presence of stability in the transverse direction is observed. Originality/value The analysis of the stability characteristics of the sample aircraft provides the foundation for the subsequent establishment of the control model for the flying wing layout UAV.

Machine learning regression-based prediction model for the autonomous control of coagulant dosing in smart water purification plants

ABSTRACT The global issue of water scarcity is escalating due to urbanization and increased demand. This paper proposes a machine learning (ML) regression-based model for automatic coagulant dosing control in smart water purification plants (SWPPs).1 The model uses random forest (RF), light gradient boosting machine (LGBM), extreme gradient boosting (XGB), and k-nearest neighbors (KNN) algorithms. Performance metrics include MAE, MSE, RMSE, MAPE, and R2. The RF algorithm showed superior performance, with MAE of 0.005, MSE of 0.002, RMSE of 0.05, and MAPE of 0.000 for anion-poly aluminum chloride dosing, and MAE of 0.007, MSE of 0.00, RMSE of 0.02, and MAPE of 0.000 for Polymax dosing. The RF model's performance is due to its robust handling of large datasets and ensemble learning approach. Limitations include testing only two coagulants and reliance on historical data. These findings suggest integrating advanced water management, energy systems, and facility management to make SWPPs feasible and efficient, establishing a foundation for future applications of ML in chemical processes.

Comparative analysis of tardigrade locomotion across life stage, species, and disulfiram treatment.

Animal locomotion requires coordination between the central and peripheral nervous systems, between sensory inputs and motor outputs, and between nerves and muscles. Analysis of locomotion thus provides a comprehensive and sensitive readout of nervous system function and dysfunction. Tardigrades, the smallest known walking animals, coordinate movement of their eight legs with a relatively simple nervous system, and are a promising model for neuronal control of limb-driven locomotion. Here, we developed open-source tools for automated tracking of tardigrade locomotion in an unconstrained two-dimensional environment, for measuring multiple parameters of individual leg movements, and for quantifying interleg coordination. We used these tools to analyze >13,000 complete strides in >100 tardigrades, and identified preferred walking speeds and distinct step coordination patterns associated with those speeds. In addition, the rear legs of tardigrades, although they have distinct anatomy and step kinematics, were nonetheless incorporated into overall patterns of interleg coordination. Finally, comparisons of tardigrade locomotion across lifespan, between species, and upon disulfiram treatment suggested that neuronal regulation of high-level aspects of walking (e.g. speed, turns, walking bout initiation) operate independently from circuits controlling individual leg movements and interleg coordination.

Реформа контрольно-надзорной деятельности в России: анализ процесса и возникающие проблемы

The paper offers an analysis of control and supervision activities in Russia. Starting with systematic properties of the analyzed process, authors accentuate the introduction of risk-analysis as the key subject of current reform phase. Dominant issues of risk-management are theoretical (coping with essential characteristics of it) and practical (mechanisms and methods of applying the one) as well. The methodic and normative regulation of control and supervision activities are scarce, which creates limitations for efficient application of risk-oriented approaches in the field. Actual reform of control and supervision activities in Russia belongs to overall systematic reform of state management in the context of digitalization. Arguing the process approach, we evaluate digitalization as the key factor touching actual model of control and supervision activities that are linked to essential aspects of management in general.

A Privacy-Preserving Electromagnetic-Spectrum-Sharing Trading Scheme Based on ABE and Blockchain

The electromagnetic spectrum is a limited resource. With the widespread application of the electromagnetic spectrum in various fields, the contradiction between the demand for the electromagnetic spectrum and electromagnetic spectrum resources has become increasingly prominent. Spectrum sharing is an effective way to improve the utilization of the electromagnetic spectrum. However, there are many challenges in existing distributed electromagnetic spectrum trading based on blockchain technology. Since a blockchain does not provide privacy protection, the risk of privacy leakage during the trading process makes electromagnetic spectrum owners unwilling to share. In addition, a blockchain only guarantees integrity, and the imperfect trading dispute resolution mechanism causes electromagnetic spectrum owners to be afraid to share. Therefore, we propose a privacy-preserving electromagnetic-spectrum-sharing trading scheme based on blockchain and ABE. The scheme not only designs an ABE fine-grained access control model in ciphertext form but also constructs a re-encryption algorithm that supports trading arbitration to achieve privacy protection for electromagnetic spectrum trading. Finally, we experimentally evaluated the efficiency of the proposed electromagnetic spectrum trading scheme. The experimental results show that the electromagnetic spectrum trading scheme we propose was highly efficient.

Artificial neural network-based control of powered knee exoskeletons for lifting tasks: design and experimental validation

Abstract This study introduces a hybrid model that utilizes a model-based optimization method to generate training data and an artificial neural network (ANN)-based learning method to offer real-time exoskeleton support in lifting activities. For the model-based optimization method, the torque of the knee exoskeleton and the optimal lifting motion are predicted utilizing a two-dimensional (2D) human–exoskeleton model. The control points for exoskeleton motor current profiles and human joint angle profiles from cubic B-spline interpolation represent the design variables. Minimizing the square of the normalized human joint torque is considered as the cost function. Subsequently, the lifting optimization problem is tackled using a sequential quadratic programming (SQP) algorithm in sparse nonlinear optimizer (SNOPT). For the learning-based approach, the learning-based control model is trained using the general regression neural network (GRNN). The anthropometric parameters of the human subjects and lifting boundary postures are used as input parameters, while the control points for exoskeleton torque are treated as output parameters. Once trained, the learning-based control model can provide exoskeleton assistive torque in real time for lifting tasks. Two test subjects’ joint angles and ground reaction forces (GRFs) comparisons are presented between the experimental and simulation results. Furthermore, the utilization of exoskeletons significantly reduces activations of the four knee extensor and flexor muscles compared to lifting without the exoskeletons for both subjects. Overall, the learning-based control method can generate assistive torque profiles in real time and faster than the model-based optimal control approach.

Enhanced classification and severity prediction of major depressive disorder using acoustic features and machine learning

BackgroundPrevious studies have classified major depression and healthy control groups based on vocal acoustic features, but the classification accuracy needs to be improved. Therefore, this study utilized deep learning methods to construct classification and prediction models for major depression and healthy control groups.Methods120 participants aged 16–25 participated in this study, included 64 MDD group and 56 HC group. We used the Covarep open-source algorithm to extract a total of 1200 high-level statistical functions for each sample. In addition, we used Python for correlation analysis, and neural network to establish the model to distinguish whether participants experienced depression, predict the total depression score, and evaluate the effectiveness of the classification and prediction model.ResultsThe classification modelling of the major depression and the healthy control groups by relevant and significant vocal acoustic features was 0.90, and the Receiver Operating Characteristic (ROC) curves analysis results showed that the classification accuracy was 84.16%, the sensitivity was 95.38%, and the specificity was 70.9%. The depression prediction model of speech characteristics showed that the predicted score was closely related to the total score of 17 items of the Hamilton Depression Scale(HAMD-17) (r=0.687, P<0.01); and the Mean Absolute Error(MAE) between the model’s predicted score and total HAMD-17 score was 4.51.LimitationThis study’s results may have been influenced by anxiety comorbidities.ConclusionThe vocal acoustic features can not only effectively classify the major depression and the healthy control groups, but also accurately predict the severity of depressive symptoms.

Image based Modeling and Control for Batch Processes

This manuscript addresses the problem of leveraging thermal images for modeling and feedback control, specifically tailored for terminal quality control of batch processes. The primary objective, common in many batch processes, is to produce products with quality variables aligning with user specifications, available for measurement only at batch termination, precluding the direct use of classical control strategies. Furthermore, in many instances, traditional online sensors such as thermocouples may not be available, but instead spectral inputs like thermal images or acoustic data may be more readily available for feedback control. The challenge is to not only use the non-traditional sensor data for building a dynamic model but also to use that model for terminal quality control. The proposed approach involves a multi-layered modeling strategy. Initially, a dimensionality reduction technique is employed to condense the high-dimensional image into a set of representative outputs. Subsequently, subspace identification (SSID) is applied to develop a Linear Time-Invariant (LTI) State Space (SS) model between the inputs and the reduced outputs. Finally, a Partial Least Squares (PLS) model is constructed linking the terminal states of a batch (identified using SSID) with the product qualities obtained for that specific batch. This model is then incorporated into a Model Predictive Control (MPC) formulation. The effectiveness of the MPC is illustrated by showcasing its capability to generate products of high quality by deploying the MPC on a bi-axial lab-scale rotational molding setup.

A cross domain access control model for medical consortium based on DBSCAN and penalty function

BackgroundGraded diagnosis and treatment, referral, and expert consultations between medical institutions all require cross domain access to patient medical information to support doctors’ treatment decisions, leading to an increase in cross domain access among various medical institutions within the medical consortium. However, patient medical information is sensitive and private, and it is essential to control doctors’ cross domain access to reduce the risk of leakage. Access control is a continuous and long-term process, and it first requires verification of the legitimacy of user identities, while utilizing control policies for selection and management. After verifying user identity and access permissions, it is also necessary to monitor unauthorized operations. Therefore, the content of access control includes authentication, implementation of control policies, and security auditing. Unlike the existing focus on authentication and control strategy implementation in access control, this article focuses on the control based on access log security auditing for doctors who have obtained authorization to access medical resources. This paper designs a blockchain based doctor intelligent cross domain access log recording system, which is used to record, query and analyze the cross domain access behavior of doctors after authorization. Through DBSCAN clustering analysis of doctors’ cross domain access logs, we find the abnormal phenomenon of cross domain access, and build a penalty function to dynamically control doctors’ cross domain access process, so as to reduce the risk of Data breach. Finally, through comparative analysis and experiments, it is shown that the proposed cross domain access control model for medical consortia based on DBSCAN and penalty function has good control effect on the cross domain access behavior of doctors in various medical institutions of the medical consortia, and has certain feasibility for the cross domain access control of doctors.

ENHANCED MODEL-FREE PREDICTIVE CONTROL FOR VOLTAGE SOURCE INVERTERS USING AN ADAPTIVE OBSERVER

In this paper, a free model predictive control based on the active vector execution time (AVET-MFPC) using an adaptive observer is proposed for two-level voltage source inverters. The traditional model-free predictive control (MFPC) uses the sampling period to select one voltage vector for all candidate vectors according to the minimizing cost function principle. With the proposed control, two vectors are selected at one sampling period. The first vector is an active vector that uses the execution time of the active vector to select it, while the second one is a zero vector as it is applied after the active vector. The execution time is calculated using the ultra-local model (ULM) equation. In the traditional MFPC, the factor in the ULM is chosen with approximate values ranging between ±50 % of the nominal value. This paper proposes an adaptive sliding mode observer (ASMO) with an improved design to observe the variation of this factor, especially in case of mismatch parameters and during a step change in the reference signal. Combining the proposed ASMO observer and the AVET-MFPC controller gives faster system response, good tracking results, and less computational burden. Finally, the effectiveness of the proposed control model is approved and confirmed under various conditions, as well as the simulations carried out and the results obtained.

Abstract B019: Sensitivity and specificity of detecting premalignant pancreatic lesions by hyperpolarized magnetic resonance

Abstract Introduction: The high mortality rate of pancreatic cancer (PC) results from a lack of methods for early detection. The progression of PC occurs primarily via two precursor pathways, either through microscopic pancreatic intraepithelial neoplasias (PanINs) or macroscopic cystic lesions, of which intraductal papillary mucinous neoplasms (IPMNs) are the most common. The progression from either PanIns or IPMN to PC, provides an opportunity for early detection of this lethal disease. PC cells have extensively reprogrammed metabolism and we have successfully employed hyperpolarized 1-13C pyruvate metabolic imaging (HP MR) to measure non-invasively the metabolic plasticity as the disease initiates and evolves. Concurrently, the specificity of HP MR of detecting premalignant lesions will be determined by imaging pancreatitis induced mice at different timepoints and compare them to the premalignant models. Methods: HP 1-13C Pyruvate MRS was employed to study the metabolic processes in tamoxifen inducible GEM models (P48CreERT2;LSL-KrasG12D (iKC)) with pre-invasive PanIN precursor lesions, invasive PC model (P48CreERT2;LSL-KrasG12D;LSL-p53R172H (iKPC)) and control animals (P48CreERT2 (iC)). These mice were imaged at different time points, before tamoxifen induction, 10-, 20-, and 30-weeks post induction. HP MR was also employed on IPMN mouse model (p48Cre;LSL- KrasG12D;Rosa26R-LSL-rtTA-TetO-GnasR201C) that develop premalignant cystic lesions, that progresses to PC on doxycycline diet (Dox+) for 15 weeks and control mice on normal diet (Dox-). These mice were imaged after 15 weeks of (Dox±) treatment. Simultaneously, wildtype, iC and iKC mice were treated with caerulein for three weeks for the development of pancreatitis and imaged 24 hours after treatment. Results: In the PanIN model, the lactate-to-pyruvate (lac/pyr) ratio increased in the PC models compared to the control model. For the aggressive iKPC mouse model, at the 20-week post induction imaging there was a significant increase of the lac/pyr ratio (0.28±0.04) compared to the 10-week time point (0.22±0.03). At the 20-week time point, the iKPC ratio was higher than the iKC and control ratios, (0.28±0.04 compared to 0.23±0.03 and 0.22±0.02 respectively) indicating the invasive nature of the cancer. Even in the iKC model there is a slight increase of the lac/pyr ratio at 20-weeks (0.23±0.03) compared to control (0.22±0.02). Mice treated with caerulein developed pancreatitis as demonstrated by tissue histology. Surprisingly, the lac/pyr ratio remained constant in both iC and iKC mice that developed pancreatitis, around 0.15±0.03 for both groups. In the IPMN model, IPMN mice feed with doxycycline showed increase pancreatic lesions and an increased lac/pyr ratio (0.43±0.05) compared to mice on normal diet (0.24±0.05). Conclusion: HP MR can detect metabolic shift to lactate in two different models of PC premalignancy representing two different pathways of PC progression. This finding can be potentially translated to the clinic for detection of premalignant pancreatic lesions in high-risk populations. Citation Format: José S Enriquez, Rian M Howell, Olivereen Le Roux, Shivanand Pudakalakatti, Prasanta Dutta, Florencia McAllister, Pratip K Bhattacharya. Sensitivity and specificity of detecting premalignant pancreatic lesions by hyperpolarized magnetic resonance [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Advances in Pancreatic Cancer Research; 2024 Sep 15-18; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2024;84(17 Suppl_2):Abstract nr B019.

Adaptive Curve Passing Control in Autonomous Vehicles with Integrated Dynamics and Camera-Based Radius Estimation

Autonomous vehicles frequently encounter performance degradation during high-speed cornering due to excessive speed and lateral acceleration, potentially leading to collisions or rollovers. This paper proposes a novel curve-passing control approach that first estimates the curve radius and then controls the steer and speed for smooth and comfortable handling. In particular, the curve radius is innovatively estimated using a combination of a camera-based lane detection model and a steering wheel dynamic model. The curve-passing control approach is validated on high-speed ramps and curves, demonstrating its robustness and intelligence to adapt to dynamic changes in curve curvature. The model effectively prevents vehicles from entering curves at dangerously high speeds from straight roads and mitigates sudden accelerations or decelerations when entering curves. Experimental results indicate that the vehicle speed is reduced to around 50 km/h and the corresponding acceleration is −0.6 m/s2 upon entering curves with a minimum radius of 150 m. This demonstrates that the proposed control model can ensure a comfortable and safe driving experience by autonomously decelerating the vehicle before entering various types of curves.

Novel additive lamination manufacturing system for rapid fabrication of large-scale reinforced structural members

Purpose Additive lamination manufacturing (ALM), as a novel additive manufacturing technology, builds up the geometry via the lamination of fiber-reinforced polymer (FRP) fabric laterally, rendering it suitable for fabricating large-scale Stay-in-Place concrete formwork. This paper aims to investigate the control parameters and structure performance of ALM and assess its application for the fabrication of large-scale concrete formwork. Design/methodology/approach Based on previous feasibility studies, this research systematically investigates the control and material parameters that influence horizontal and vertical extrusion speeds, as well as the overall quality of ALM. Once the system parameters are established, a series of prototypes are fabricated and tested to validate the tensile strength of the formwork and its reinforcement capabilities. In addition, this study assesses the potential geometric freedom and implementation constraints of ALM. Findings This research identifies the essential control parameters for path planning in ALM and examines their impact on fabrication. In addition, this paper evaluates ALM’s strengths and limitations in producing concrete formwork for large-scale concrete structures, comparing these to industry benchmarks. Originality/value A critical challenge in additive manufacturing lies in its scalability and compatibility with existing construction processes. In comparison to concrete, FRP offers advantages such as being lighter, easier to handle and providing surface protection and reinforcement. These qualities make FRP superior for formwork and compatible with existing building standards. Despite its advantages and potential, the current path planning and control model in 3D printing do not apply to ALM due to its novel build-up process. Also, the performance of fabricated parts as part of integrated large-scale structures is yet to be studied.

Design and development of a flexible-rigid Triglide sorting manipulator

Flexible manipulators have been widely applied in various tasks involving grasping and manipulation, and their unique characteristics in terms of lightweight design and adaptability make them particularly suitable for tackling complex spatial pick-and-place operations. In this work, a Triglide flexible manipulator is presented and developed, based on the parallel Biglide mechanism and dual leaf springs in parallelogram structure, which features adjustable stiffness by changing the transverse configuration of the leaf springs. To analyze the deflections of the leaf springs efficiently, a segmented approach is deployed, to calculate large deflection within the plane of the leaf-springs parallelogram structure. The adopted approach uses classical bending deformation formulas from mechanics of materials. Consequently, the static models of the manipulator are derived for analyzing bending deformation and workspace by means of numerical calculations. Finite element analysis is adopted to investigate the mechanical characteristics of the manipulator. A prototype of the variable stiffness manipulator is built, and an experimental setup is established for static testing. The obtained results align with the previously observed mechanical characteristics. The main advantages of the flexible robotic manipulator lie in its simple structure, small footprint, and simple kinematic model for control.

Modeling environmental-born melioidosis dynamics with recurrence: An application of optimal control

Melioidosis is a significant health problem in tropical and subtropical regions, especially in Southeast Asia and Northern Australia. Recurrent melioidosis is a major obstacle to eliminating the disease from the community in these nations. This work aims to propose and analyze a human melioidosis model with recurrent phenomena and an optimal control model by incorporating time-dependent control functions. The basic reproduction number (R0) of the uncontrolled model is derived using the method of the next-generation matrix. Using the construction of a Lyapunov functional, we present the global asymptotic dynamics of the autonomous model in the presence of recurrent for both disease-free and endemic equilibria. The global asymptotic stability of the model’s equilibria shows the absence of a backward bifurcation for the model in both cases, whether in the absence or presence of relapse. The sensitivity analysis aims to identify the parameters that have the most significant impact on the model’s dynamics. Furthermore, qualitative analysis of the model’s global dynamics and the changing effect of the most influential parameters on R0 are supported by numerical experiments, with the results being illustrated graphically. The model with time-dependent controls is analyzed using optimal control theory to assess the impact of various intervention strategies on the spread of the epidemic. The numerical results of the optimality system are carried out using the Forward–Backward Sweep method in Matlab. We also conducted a cost-effectiveness analysis using two approaches: the average cost-effectiveness ratio and the incremental cost-effectiveness ratio.

The state as a model for AI control and alignment

The state as a model for AI control and alignment

Coupling Electrochemical Leaching with Solvent Extraction for Recycling Spent Lithium-Ion Batteries.

We propose coupling electrochemical leaching with solvent extraction to separate and recover Li and Co from spent lithium-ion batteries (LIBs). Electrochemical leaching occurs in the aqueous electrolyte for converting solid LiCoO2 into soluble Li+ and Co2+, in which electrons act as reductants to reduce Co(III) to Co(II). Simultaneously, solvent extraction occurs at the interface of aqueous and organic phases to separate Co2+ and Li+. By capturing and utilizing the protons from P507, leaching yields for both Co and Li exceed ∼7 times than acid leaching without solvent extraction. The extraction efficiency of Co2+ reaches 86% at 60 °C, 3.5 V, while simultaneously retaining the majority of Li+ in the H2SO4 solution. The total leaching amount was improved because the organic phase provides protons to help the leaching of Co2+, and the continuous extraction process of Co(II) maintains the low Co2+ concentration in the aqueous solution. The synergistic interaction between electrochemical leaching and solvent extraction processes significantly reduces the consumption of chemicals, enhances the utilization efficiency of protons, and simplifies the recovery process. The leaching kinetics of Li and Co both conforms well to the residue layer diffusion control model and the activation energy (Ea) values of the leaching for Li and Co are 4.03 and 7.80 kJ/mol, respectively. Lastly, the economic and environmental assessment of this process also demonstrates the advantages of this method in reducing inputs, lowering environmental pollution, and enhancing economic benefits.

‘Six of one’: conflict vs control in the policing of intimate partner violence

ABSTRACT Challenging the historical attitude that intimate partner violence (IPV) is not police business has been identified as key to effective police response. This attitude draws on the wider cultural assumption that IPV is situational and based on interpersonal conflict – a belief compounded by media coverage and certain theoretical approaches. The coercive control model counters this view, framing the majority of IPV as a power differential established through a deliberate pattern of threat and control. Coercive and controlling behaviour (CCB) was criminalised in England and Wales in the Serious Crime Act 2015. The offence describes a pattern of behaviour – rather than the discrete incidents – and subverts ingrained beliefs about the causes of IPV. This qualitative research draws on in-depth interviews with officers and victim-survivors in a force in the north of England. Critical discourse analysis examines police attitudes and culture as embedded within the wider context. A key finding is that police response officers commonly approach IPV as situational and arising from mutual conflict rather than investigating for evidence of CCB. The lack of nuanced understanding of control mechanisms and their effects often leads to exasperation with repeat callers and failure to ‘dig deeper’. However, officers who recognise the subtleties of CCB contribute to an empowering effect on victim-survivors, an outcome not formally recognised by policing processes. To equip officers for effective and supportive response, officer development should address the embedded assumption of conflict and focus on CCB as underlying the majority of IPV rather than existing as a distinct offence.

Formalization of Elements and Control Schemes in Intelligent System Models

The purpose of the work is to formalize the concepts and principles that form the basis of the mathematical model for controlling the life cycles of intelligent systems. The controlling elements formal description is part of a universal model of such systems. This model part is important for implementing complex intelligent systems with a large amount and diversity of knowledge flows and knowledge processing schemes performed simultaneously. The other two areas of this model are associated with a unified logical-algebraic description of the concept of knowledge representation formalism, as well as concepts related to the architecture of intelligent systems. Formalization of ideas about control in intelligent systems is carried out according to the principle of a hierarchy of controlling elements and processes. The elements of the mathematical model that implements this principle correspond to event-controlled automata with infinite memory and associated algorithms for the automata simulation in specific systems. The objectives of the research include the development of formats for describing the hierarchy of diagrams and assemblies of control elements in a universal model of an intelligent system, and diagrams of algorithms for the functioning of intelligent systems based on the processing of model descriptions. Models of intelligent system control elements hierarchy and execution algorithms for the sets of activated control elements for the implementation time of life cycles of intelligent systems are described by extending the special ontological structures. These structures implement customizations of universal control model

Ideal Arrival and Service Control Model Policy Based on Fuzzy Queuing System of Uncertainty Measure

In this work, we investigate how to optimize costs for a single-server queuing system operating in a fuzzy, unpredictable environment. Constructing the overall optimal cost and cost function of the queuing system under uncertainty in the fuzzy paradigm is the aim of the inquiry. The fuzzy analysis is carried out to offer a more practical answer to the issues at hand, as opposed to the model's usual crisp responses. The model's crisp and fuzzy systems have different theoretical advances that have been determined, and the estimated costs are easily verifiable and comparable. Lastly, sensitivity analysis has also been carried out utilising numerical analysis to evaluate the theoretical conclusions of the model that is being studied.