High Fidelity Mathematical Model Research Articles

Computational evaluation of PEMFC performance based on bipolar plate material types

Materials used in bipolar plates are essential for addressing the challenges associated with the large-scale commercialization of Proton Exchange Membrane Fuel Cells (PEMFCs). Therefore, it is necessary to develop effective performance evaluation approaches to evaluate the performance of materials. This work has presented a high-fidelity mathematical model that includes electrochemical, fluid flow, energy, species transport, water formation, and transport aspects to simulate the conditions in a PEMFC system and to theoretically assess the performances of commercial bipolar plate materials. Accordingly, the effects of metallic (aluminum) and carbon-based (graphite and graphite composite) bipolar plate materials on the current collection performance, thermal management, water management, and overall efficiency of PEMFCs are analyzed. The findings suggest that the current density, power density, and operating voltage of each PEMFC are greatly affected by the bipolar plate material used. When compared to graphite bipolar plates, the aluminum and graphite composite bipolar plates have exhibited 16.5 % and 7.5 % higher power densities, respectively. The change in operating conditions and thermal environments caused by a change of bipolar plate materials gives rise to distinct water transport phenomena according to their respective capabilities in the balancing of liquid water movements across the membrane, which in turn affects the species distribution pattern. Specifically, the high imbalance between the electro-osmotic drag and back diffusion in the case of aluminum bipolar plate leads to a severe membrane dry-out on the anode side, limiting the hydrogen concentration in the region.

A Mathematical Model for Simulation of Vasoplegic Shock and Vasopressor Therapy

To develop a high-fidelity mathematical model intended to replicate the cardiovascular (CV) responses of a critically ill patient to vasoplegic shock-induced hypotension and vasopressor therapy. The mathematical model consists of a lumped-parameter CV physiology model with baroreflex modulation feedback and a phenomenological dynamic dose-response model of a vasopressor. The adequacy of the proposed mathematical model was investigated using an experimental dataset acquired from 10 pigs receiving phenylephrine (PHP) therapy after vasoplegic shock induced via sodium nitroprusside (SNP). Upon calibration, the mathematical model could (i) faithfully replicate the effects of PHP on dynamic changes in blood pressure (BP), cardiac output (CO), and systemic vascular resistance (SVR) (root-mean-squared errors between measured and calibrated mathematical responses: mean arterial BP 2.5+/-1.0 mmHg, CO 0.2+/-0.1 lpm, SVR 2.4+/-1.5 mmHg/lpm; r value: mean arterial BP 0.96+/-0.01, CO 0.65+/-0.45, TPR 0.92+/-0.10) and (ii) predict physiologically plausible behaviors of unmeasured internal CV variables as well as secondary baroreflex modulation effects. This mathematical model is perhaps the first of its kind that can comprehensively replicate both primary (i.e., direct) and secondary (i.e., baroreflex modulation) effects of a vasopressor drug on an array of CV variables, rendering it ideally suited to pre-clinical virtual evaluation of the safety and efficacy of closed-loop control algorithms for autonomous vasopressor administration once it is extensively validated. This mathematical model architecture incorporating both direct and baroreflex modulation effects may generalize to serve as part of an effective platform for high-fidelity in silico simulation of CV responses to vasopressors during vasoplegic shock.

Hybrid Modeling Method of SDR Interstage Valve Based on Mechanism and Data-Driven

Variable-throat adjustment is the most practical flow regulation method of solid ducted rocket ramjet (SDR). The high-fidelity mathematical model of the interstage valve is the basis for realizing high-precision gas flow and thrust regulation. In this paper, the complex effect of gas was divided into load and throat deformation effect. The load was mainly determined by the clearance, friction torque, and pneumatic torque that the valve was subjected to during operation. And the throat deformation was determined primarily by the deposition and ablation of the valve faced in the gas. Therefore, we could divide the valve model into three parts: the servo motor model, the load characteristic model, and the deformation model of the actual acting throat (referred to as the throat). Given, we have designed a cold-air experiment program, using cold air to equalize the valve load. Furthermore, we analyzed its mechanism of action and established the load model using the experimental data and neural network. Finally, the deformation mechanism of the throat was investigated, and simultaneously, the deformation model was shown based on the flight test data. Compared with the traditional interstage valve model, the model established in this paper is closer to the actual working conditions, which is helpful to carry out the more comprehensive and practical ground simulation. It has essential reference value for further realizing the precise regulation of gas flow.

Parameter Identification for Bernoulli Serial Production Line Model

Model-based analysis of production systems is one of the main areas in manufacturing research. The foundation of the successful application of these theoretical studies is the availability of valid and high-fidelity mathematical models that are capable of capturing the behavior of job flow in production systems. The modeling process of a production system, however, may require a significant amount of nonstandardized work that can only be done properly by someone with solid training in the area and extensive experience through real case studies. This poses a critical challenge in the effective implementation of these valuable theoretical results in the Industry 4.0 era. To overcome this, we propose a new production systems modeling paradigm inspired by system identification: calculate production system model parameters that best match the standard system performance metrics measured on the factory floor. Specifically, in this article, we consider production lines characterized by the Bernoulli serial line model and develop algorithms that identify model parameters to fit the system throughput and work-in-process. Analytical algorithms are derived to solve this problem in a two-machine line case and then extended to multi-machine lines. The accuracy and computational efficiency of the algorithms are demonstrated through extensive numerical experiments. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —A high-fidelity mathematical model is of critical importance to the implementation of any model-based production system analysis method. Currently, the construction of such models is carried out in an ad hoc manner. The quality of the resulting models may heavily depend on the training, experience, intuition, and personal preference of the modeler. The proposed model parameter identification method focuses on standard key performance indices commonly measured on the factory floor. The advantage is twofold. First, these standard performance metrics are consistently defined regardless of industry, thus avoiding any data-ambiguity issue that may occur when using complex machine/equipment status data. Second, measuring these performance metrics in real time is typically convenient and cost effective, even for manufacturing plants without high-end IT infrastructure, thus making the technology accessible to not only large but also small- and mid-sized manufacturers. Using the algorithms developed in this article, a practitioner can quickly construct a serial production line model and then utilize it to access the rich library of production analysis, design, and control methods available in the literature.

Baseline architecture design for a turboelectric distributed propulsion system using single turboshaft engine operational scenario

Abstract Reducing the carbon footprints of aerial transportation became a major target for both industries and academia. Various solutions have been proposed to develop cleaner alternative methods for green transportation. Full electric, hybrid electric, and turboelectric propulsion system architectures intend to reduce greenhouse gas emissions and fuel consumption of today’s aero gas turbine engines. In this study, a turboelectric propulsion system, which is considered as the most promising technology for future aviation is selected for modelling and simulation. As the main power supply, a high fidelity mathematical model of GE T700 turboshaft engine is constructed in MATLAB/Simulink to emulate the technology of today. Selected aero gas turbine’s mathematical model is combined with NASA’s Baseline electrical power distribution architecture which is firstly designed for N-3X turboelectric aircraft. MATLAB/Simulink model is utilized to analyses a single-engine operational scenario of twin-engine aircraft which is a major design consideration due to single-engine failure. Power requirements, distribution percentages, preliminary power assessment for power electronic systems and nominal power capacities of each electrical unit of a turboelectric propulsion system are obtained using GE T700 as the main power supply.

Baseline architecture design for a turboelectric distributed propulsion system using single turboshaft engine operational scenario

Abstract Reducing the carbon footprints of aerial transportation became a major target for both industries and academia. Various solutions have been proposed to develop cleaner alternative methods for green transportation. Full electric, hybrid electric, and turboelectric propulsion system architectures intend to reduce greenhouse gas emissions and fuel consumption of today’s aero gas turbine engines. In this study, a turboelectric propulsion system, which is considered as the most promising technology for future aviation is selected for modelling and simulation. As the main power supply, a high fidelity mathematical model of GE T700 turboshaft engine is constructed in MATLAB/Simulink to emulate the technology of today. Selected aero gas turbine’s mathematical model is combined with NASA’s Baseline electrical power distribution architecture which is firstly designed for N-3X turboelectric aircraft. MATLAB/Simulink model is utilized to analyses a single-engine operational scenario of twin-engine aircraft which is a major design consideration due to single-engine failure. Power requirements, distribution percentages, preliminary power assessment for power electronic systems and nominal power capacities of each electrical unit of a turboelectric propulsion system are obtained using GE T700 as the main power supply.

Parametric optimization and control for a smart Proton Exchange Membrane Water Electrolysis (PEMWE) system

Hydrogen production from Proton Exchange Membrane Water Electrolysis (PEMWE) system is attracting attention due to its ability to circumvent the effect of the intermittent nature of variable renewal energy. However, the relatively high operating temperatures of the PEMWE system exacerbates the degradation of polymer membranes in PEMWE system. This paper describes the development of an optimal thermal management strategy for a PEMWE system that can attenuate the long-term effects of high operating temperatures or rapid temperature changes on the polymer membranes. The thermal management strategy is tested on a laboratory scale smart PEMWE system. First, a high fidelity mathematical model of the smart PEMWE is developed and validated based on which the application of the PARameteric Optimization and Control (PAROC) framework results in the design of an explicit model predictive controller which is deployed into the laboratory PEMWE system. It is shown that the smart PEMWE prototype system empowered with the embedded control policy achieves effective temperature control across the electrolyzer maintaining the integrity of the membrane electrode assembly.

Stabilization of compressor surge in systems with uncertain equilibrium flow

The adaptive correction of uncertain equilibrium states in feedback controlled systems is studied in this paper, with application to the active control of compressor surge with uncertainty in the characteristic curves. Adaptive compensation methods are introduced to correct for the uncertainty in the equilibrium state in both the state and the output feedback control cases, using information from the feedback control signal to determine the true equilibrium of the nonlinear plant. In particular, our proposed solutions overcome the odd-number condition, or parity condition, which appears as a recurring limitation in comparable solutions reported in the literature. Conditions for the existence of the adaptive solutions are presented, and the stability of the closed-loop system is demonstrated. The effectiveness of the proposed adaptation mechanism is verified using a high fidelity mathematical model of a compression system, commissioned to test active surge control methods by active magnetic bearings.

Online Tissue Conductivity Estimation in Deep Brain Stimulation

Deep brain stimulation (DBS) is an established therapy that consists of sending electrical pulses to specific brain areas via chronically implanted electrodes. DBS is used to alleviate symptoms of neurological conditions such as Parkinson's disease and essential tremor. However, the stimulation effect is patient-specific and hard to predict. In addition, electrical properties of the brain tissue around the lead change over time thus influencing the therapeutical effect. This paper proposes an approach to online conductivity estimation by applying a specially designed electrical probing signal to one contact of the DBS electrode and measuring the response on another one. A conductivity estimate is then obtained from the estimated parameters of a linear time-invariant model. Both voltage-controlled and current-controlled DBS systems are treated. Continuous least squares and the Laguerre domain identification are employed to estimate the model parameters. Results suggest that a smooth Gaussian-shaped signal is sufficient to identify the model in a noise-free situation, but the resulting excitation might be not enough for accurate estimation in the face of disturbances, e.g., local field potential deviations due to neuron firings. Better excitation is produced by input signals with designed Laguerre spectra. Due to the infeasibility of assigning electrical properties to the surroundings of the lead in vivo, synthetic data from an individualized high-fidelity mathematical model of DBS are used instead. The latter model is validated against clinically measured impedance values.

Optimal Design of Validation Experiments Based on Area Metric Factor and Fuzzy Expert System

Experiments used for model validation constitute a new type of experiments, whose primary goal is to determine the ability of a high-fidelity mathematical model in simulating a well-characterized physical process. Considering the importance of the credibility of the validation experiment, in this paper, a methodology for the optimal design of validation experiments based on the area metric factor and the fuzzy expert system is presented to obtain the test scheme with low cost and satisfactory credibility. First, the concept of area metric factor is proposed, which is a dimensionless validation metric. Then, a criterion for qualitative assessment of the predictive model accuracy is developed based on the fuzzy expert system, in which the inconsistency among the different expert groups is considered. Subsequently, an optimization model of the validation experiment design is constructed, in which the sample size of the experiments is designed variable, while the credibility of the validation experiment is a constraint. Meanwhile, a novel method is developed to solve the optimization model, in which the Latin hypercube sampling is used to obtain the location of each validation experiment. Finally, two simulation examples are adopted to validate the proposed methods. The simulation results show that the randomness of the experimental scheme significantly affects the credibility of the evaluation results in the case of small sample sizes. The proposed method for the validation experiment design can reduce the impact of the selection of the testing programs on the credibility of model validation.

Comparative studies of CO2 capture solvents for gas-fired power plants: Integrated modelling and pilot plant assessments

Natural gas accounts for 21.3% of the total primary energy supply. In particular, with the shale gas boom, its application has experienced an exponential growth rate. Nevertheless, natural gas has the highest hydrogen to carbon ratio among all hydrocarbons and the dilute (with respect to CO2) exhausts of its combustion pose considerable thermodynamic challenges for carbon capture. Solvent-based carbon capture can potentially mitigate the carbon emissions. Nonetheless, minimizing the penalties associated with the costs of carbon capture requires detailed understanding of the underlying physical and chemical phenomena. The present research exploits a rigorous methodology based on rate-based distributed modelling and statistical associating fluid theory (SAFT). The important characteristics of this modelling approach include abstract formulation in conjunction with high predictability. The present research aims at establishing the performance of a new solvent (an amine-promoted buffer salt, APBS) in comparison to the baseline solvent, i.e., monoethanolamine (MEA). The features of interest include: (i) developing a high fidelity mathematical model of the carbon capture process, (ii) validating the model with pilot plant data, (iii) quantification of the energetic and technical performances of the solvents using key process indicators (KPIs), and (iv) employing optimization programming for further solvent performance improvement.

Flight Dynamics Analyses of a Propeller-Driven Airplane (II): Building a High-Fidelity Mathematical Model and Applications

This paper is the second in a series and aims to build a high-fidelity mathematical model for a propeller-driven airplane using the propeller's aerodynamics and inertial models, as developed in the first paper. It focuses on aerodynamic models for the fuselage, the main wing, and the stabilizers under the influence of the wake trailed from the propeller. For this, application of the vortex lattice method is proposed to reflect the propeller's wake effect on those aerodynamic surfaces. By considering the maneuvering flight states and the flow field generated by the propeller wake, the induced velocity at any point on the aerodynamic surfaces can be computed for general flight conditions. Thus, strip theory is well suited to predict the distribution of air loads over wing components and the viscous flow effect can be duly considered using the 2D aerodynamic coefficients for the airfoils used in each wing. These approaches are implemented in building a high-fidelity mathematical model for a propeller-driven airplane. Flight dynamic analysis modules for the trim, linearization, and simulation analyses were developed using the proposed techniques. The flight test results for a series of maneuvering flights with a scaled model were used for comparison with those obtained using the flight dynamics analysis modules to validate the usefulness of the present approaches. The resulting good correlations between the two data sets demonstrate that the flight characteristics of the propeller-driven airplane can be analyzed effectively through the integrated framework with the propeller and airframe aerodynamic models proposed in this study.

A Method for Predicting Minimum-Time Capability of a Motorcycle on a Racing Circuit

Prediction by simulation of the minimum-time lap of a flat and level racing circuit by a high-performance motorcycle is treated. A novel method is described. Constituents of the method comprise: (i) a high-fidelity mathematical model of the vehicle; (ii) a rider model with control of throttle/brake position, steering torque, and upper-body lean torque. The rider model uses linear quadratic optimal preview control with adaptation to variations in running conditions by gain scheduling; (iii) a circuit model; and (iv) a learning process through which the rider arrives at the best speed target. The constituents are discussed in turn. Then, systematic reduction of lap times for each of two circuits is demonstrated. Aspects of the performance of the motorcycle in very fast laps of the circuits are shown, providing evidence of the effectiveness of the method established.

The methodology for developing the kinematic model of selected CPR-a system as a necessity for the development of a dynamic model

The authentic form or general form of Cable Suspended Parallel Robot type A, CPR-A mathematical model is defined. The proper definition of the system kinematic model which includes trajectory, velocity and acceleration is a prerequisite for the formulation of a dynamic model. These three components represent the basic functional criteria of the real system which is described by the corresponding geometric relations and differential equations. Kinematic model is defined for the CPR-A system via the Jacobian matrix. An adequate choice of generalized coordinates (in this paper, the internal coordinates), provides a mathematical model that illuminates the mapping of internal (resultant forces in the ropes) and external forces (acting on a camera carrier) over the Jacobian matrix on motion dynamics of each motor. Software packages AIRCAMA are formed and used for individual and comparative analysis of the CPR-A system from various aspects. The impact of changing any parameter of the system (workspace dimensions, the mass of a camera carrier, change the size and dynamics of power disturbances, the choice of control law, the reference trajectory, and the presence of singularity avoidance system and a number of other characteristics) can be analyzed through these software packages. Different examples of the CPR-A system motion are analyzed and their results are presented. The aim of this study is to define really the characteristics of CPR-A system, all this for the purpose of modernization and wider application of the same. This would be reflected in the implementation of highly-automated systems that would lead the camera precisely in space with the minimum participation of human labor. Setting and achieving this goal provide much wider possibilities for its future use. The sophisticated operation of this system can be provided only with the application of its high-fidelity mathematical model during the synthesis and analysis, which would further enable the development and application of modern control laws. Application possibilities are certainly much broader than it may be assumed at this moment, especially for sports, cultural, military or police purposes.

High fidelity mathematical model building with experimental data: A Bayesian approach

Mathematical models of physicochemical systems are usually built in an iterative fashion during the course of an experimental investigation. In this paper, a novel Bayesian approach to model building is presented. This approach is now feasible because of breakthroughs in Monte Carlo sampling procedures and high performance computing, that make it possible to deal directly with the nonlinear mathematical models themselves instead of their linear approximations. By including an error model for experimental data, it is further possible to use nonlinear statistical concepts to test a given model for adequacy against experimental data and prior knowledge, and to place realistic confidence limits on the resulting model parameters. In this paper a model building work flow that takes advantage of these recent advances to enable high fidelity mathematical modeling is proposed. A set of models and their parameters are needed to initiate the process. Probability distributions for the models and their parameters based on available quantitative and subjective information must also be supplied. Finally, an error model describing the heteroscedasticity in the data along with probability distributions for the error model parameters must be generated from exploratory data. Then experiments are designed and data collected. Using Bayes’ theorem, Monte Carlo (MC) or Markov Chain Monte Carlo (MCMC) methods are used to generate a sequence of samples of parameter values for each postulated model. These sets of samples are then used to discriminate among the models using the criteria introduced in this paper. Once discrimination is achieved, a global lack of fit test is introduced to determine model adequacy. After a single adequate model is selected, highest probability density (HPD) intervals are determined for the individual parameters and HPD density regions are constructed for all model parameter pairs. Experiments are then designed to reduce the uncertainty in the joint posterior probability HPD regions. Finally, a sampling procedure is described to properly represent uncertainties in predictions made from the model. The proposed approach is demonstrated by an illustrative problem where three simple models are discriminated and the parameters in the most suitable ones are estimated rigorously.

Validation of the Harshness Problem of Automotive Active Suspensions

SUMMARY The advantages of an automotive fully active suspension system have been promised for many years. Among them, simultaneously achieving good body and wheel mode damping is of the most fundamental. However, implementations of such concepts with hydraulic actuators have generally exhibit worse-than-passive harshness performance when such vehicles are driven through small irregularities on the road. Additional forces are transmitted through the hydraulic active suspension to the vehicle body at high frequencies. Conventional wisdom blames the non-ideal actuator in practice for the problem since most analytical papers assume it an ideal force-producing element. However, the mechanism of generating such excessive force as well as the methodology of solving it has not been systematically demonstrated in the literature. In this paper, a high fidelity mathematical quarter vehicle model is first developed and identified with vehicle test data. This model captures realistic dynamic behaviors of the hydraulic active suspension. The mechanism of creating such harshness problem is then explained with this model. To validate such mechanism, a frequency domain methodology that yields an equal-to-passive high frequency performance while maintaining a good active body behavior was developed based on this model and demonstrated with a test vehicle. The model predicts the test results almost exactly.