Model-based analysis and simulation of airflow control systems of ventilation units in building environments

Wu, Zhuang; Melnik, Roderick V. N.; Borup, Finn

doi:10.1016/j.buildenv.2005.08.031

Cited by 26 publications

(7 citation statements)

References 4 publications

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“…Mathematical modelling provides a powerful tool in solving a wide range of problems in industrial applications [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60] and interdisciplinary approaches play an indispensable role in formulating state-of-the-art mathematical models in such applications [61]. For some of these applications it is often the case that a degree of uncertainty about the corresponding system, process, or phenomenon under the study needs to be incorporated into the model.…”

Section: Developing Multi-dimensional Models With Jumpsmentioning

confidence: 99%

First passage time for multivariate jump‐diffusion processes in finance and other areas of applications

Zhang

Melnik

2008

Appl Stoch Models Bus & Ind

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The first passage time (FPT) problem is an important problem with a wide range of applications in science, engineering, economics, and industry. Mathematically, such a problem can be reduced to estimating the probability of a stochastic process first to reach a boundary level. In most important applications in the financial industry, the FPT problem does not have an analytical solution and the development of efficient numerical methods becomes the only practical avenue for its solution. Most of our examples in this contribution are centered around the evaluation of default correlations in credit risk analysis, where we are concerned with the joint defaults of several correlated firms, the task that is reducible to a FPT problem. This task represents a great challenge for jump-diffusion processes (JDP). In this contribution, we develop further our previous fast Monte Carlo method in the case of multivariate (and correlated) JDP. This generalization allows us, among other things, to evaluate the default events of several correlated assets based on a set of empirical data. The developed technique is an efficient tool for a number of financial, economic, and business applications, such as credit analysis, barrier option pricing, macroeconomic dynamics, and the evaluation of risk, as well as for a number of other areas of applications in science and engineering, where the FPT problem arises.Many applications in science, engineering, finance, economics, and industry require the solution of the first passage problem. Examples range from population genetics and other applications in biology, to neurobiology and neurophysiology, to molecule kinetics and problems in chemistry and physics, to rare events modelling and quantum information, and to aerospace engineering applications (e.g. [1][2][3][4]). This problem also arises in financial applications. Although methodologies developed in this paper are applicable to a number of other areas, we exemplify our discussion here with problems from finance.In the financial world, individual companies are usually linked together via economic conditions, so default correlation, defined as the risk of multiple companies' default together, has been an important area of research in credit analysis with applications to joint defaults, credit derivatives, asset pricing, and risk management.Currently, there are two dominant groups of theoretical models used in default correlation. One is a reduced form model, such as in [5] that uses a Copula function to parameterize the default correlation. In this context, it is worthwhile noting that Chen and Sopranzetti [6] have translated the joint default probability into a bivariate normal probability function, making the analysis and applications of such models potentially more convenient.The second group of models for default correlation is a structural form model. Zhou [7] and Hull and White [8] were the first to incorporate default correlation into the Black-Cox first passage structural model. They obtained similar closed-form solutions for two ...

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Section: Developing Multi-dimensional Models With Jumpsmentioning

confidence: 99%

First passage time for multivariate jump‐diffusion processes in finance and other areas of applications

Zhang

Melnik

2008

Appl Stoch Models Bus & Ind

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“…As a real case study, it is assumed that the physical parameters of air-handling unit are varied around their nominal values. For instance, for the amount of c percent uncertainty in the quantity d, it is described by a varying value in the assumed variation range: ð1 À cÞ d < d < ð1 þ cÞ d (6) where the quantity d can be any parameters given in Table 1; while their nominal values (d) are given in Table 2.…”

Section: Uncertain Dynamics Of the Ahumentioning

confidence: 99%

“…By implementation of the thermodynamics rules, heat and mass transfer laws, differential equations describing dynamic behavior of the AHU are determined as follows [6,27,28]:…”

Section: Nonlinear Multivariable Dynamics Of the Air-handling Unitmentioning

confidence: 99%

“…Many control strategies have been implemented to improve the dynamic behavior of air conditioners. Model based analysis and simulation of airflow control of AHUs using PI and adaptive self-tuning PI controllers [6], model predictive control [7], optimal control [8,9], feedback linearization control and robust observer of VAV-AHU [10], energy optimization of HVAC system [11], a hybrid MPC optimization [12], improving the robust performance of air-conditioning systems [13], regulation of building temperature via MPC [14], handling of the model uncertainties in buildings via MPC [15], flatness control of a fractional thermal system [16], adaptive and robust control for nonlinear HVAC system [17] and robust path tracking using flatness for fractional linear MIMO thermal system [18] have been presented.…”

Section: Introductionmentioning

confidence: 99%

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PID-Fuzzy control of air handling units in the presence of uncertainty

Moradi

Setayesh

Alasty

2016

International Journal of Thermal Sciences

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“…Ghodsipour [4] estimated the maximum regenerator effectiveness as a function of rotational speed as well as hot and cold air velocities. Wu et al [5], developed a mathematical model to simulate ventilation air flow control system of an air-conditioning unit including a rotary regenerator. Sanaye et al [6] obtained optimum operational conditions of air-to-air rotary regenerator for airconditioning applications considering thermal effectiveness as a single objective function.…”

Section: Introductionmentioning

confidence: 99%