Grey-box model for pipe temperature based on linear regression

Kicsiny, Richárd

doi:10.1016/j.ijheatmasstransfer.2016.11.033

Cited by 16 publications

(25 citation statements)

References 18 publications

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“…Eqn. (31) reveals a similar structure as the heuristic DDE-model (10). 4 Apart from the different constants k i there is an additional term involving input temporal derivative, which is induced by a feedthrough of the input temperature in the physical based approach.…”

Section: Approximation As Delay-differential Equationmentioning

confidence: 90%

“…As a consequence, the overall structure of the transfer function is similar to the structure of the DDE-model (10) discussed in Section 2.3. The main difference is constituted by the filter part G 3 (z, s) replacing the simple first-order low-pass filter in the DDE-model (10). In order to compute the impulse response of this filter, i.e., transforming the input-output relation associated with G 3 (z, s) into the time domain, the transfer function is expanded into a power series:…”

Section: Constant Flow Rate and Perfect Isolationmentioning

confidence: 99%

“…For the sake of simplicity, these computations are discussed for constant flow rates only, i.e., for (30). The simplest approximation of the DPDE-model (30) with n = 1 provides the link to the DDE-model (10). It corresponds to a discretization of the spatial derivative by the difference…”

Section: Approximation As Delay-differential Equationmentioning

confidence: 99%

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On delay partial differential and delay differential thermal models for variable pipe flow

Wurm

Bachler

Woittennek

2020

International Journal of Heat and Mass Transfer

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A new formulation of physical thermal models for variable plug flow through a pipe is proposed. The derived model is based on a commonly used onedimensional distributed parameter model, which explicitly takes into account the heat capacity of the jacket of the pipe. The main result of the present contribution is the constitution of the equivalence of this model with a serial connection of a pure delay or transport system and another partial-differential equation (PDE), subsequently called delay-partial-differential equation (DPDE)-model. The means for obtaining the proposed model comprise operational calculus in the Laplace domain as well as classical theory of characteristics. The finitedimensional approximation of the DPDE-model leads to a delay-differential equation (DDE)-system, which can be seen as a generalization of commonly used DDE-models consisting of a first-order low-pass filter subject to an input delay. The proposed model is compared to several alternative models in simulations and experimental studies.

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Section: Approximation As Delay-differential Equationmentioning

confidence: 90%

Section: Constant Flow Rate and Perfect Isolationmentioning

confidence: 99%

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On delay partial differential and delay differential thermal models for variable pipe flow

Wurm

Bachler

Woittennek

2020

International Journal of Heat and Mass Transfer

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“…These problems include thermodynamic analysis models (Sheng & Tu, 2013;Bolatturk, 2006;Kalema et al, 2008;Stepanov et al, 2000;Valero, 2014;Torío et al, 2009;Romero & Linares, 2014), heat power system models (Goryachikh et al, 2010;Kicsiny, 2014;Bau et al, 2015;Kicsiny, 2017), combustion models (Messerle et al, 2013;Messerle et al, 2014;;Gao et al, 2010;Karpenko et al, 2016), local heat exchange system models (e.g., solar collectors (Kaminski & Krzyzynski, 2016;Hussain et al, 2016;Bég et al, 2016;Li & Chen, 2008;Smith et al, 2012;Thianpong et al, 2012), etc.…”

Section: Introductionmentioning

confidence: 99%

“…A solution is considered as a gradient process and no direct linear dependence is given. Richard Kicsiny discusses modern mathematical models of a piped heat system in his latest studies (Kicsiny, 2014;Kicsiny, 2017) based on differential equations of the Newton's law for pipe cooling. A rather common problem is building dynamic models of municipal heat networks to improve their efficiency.…”

Section: Introductionmentioning

confidence: 99%

Solving a Sequence of Recurrence Relations for First-Order Differential Equations

Batukhtin

Batukhtina

Bass

et al. 2017

EURASIA J MATH SCI T

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A whole category of engineering and economic problems can be reduced to solving a set of differential equations. Downsides of known approaches for their solutions include limited accuracy numerical methods with stringent requirements for computational power. A direct analytical solution should be derived to eliminate such flaws. This research intends to derive such a solution for an n-dimensional set of recurrence relations for first-order differential equations, linearly dependent on the right side. The research methodology relies on successive integration of the considered set in view of the initial conditions. The overall solution was derived as a sum of products of exponential multipliers with constant coefficients that are defined through weights of a tree graph, which is a descriptor of successive integration. An analytical solution for an n-dimensional set of recurrent differential equations in view of the initial conditions has been derived for the first time in this research.

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Modified effectiveness and linear regression based models for heat exchangers under heat gain/loss to the environment

2018

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Developing mathematical models for describing heat exchanger outlet temperatures is of great importance for the practice, since heat exchangers are unavoidable elements in any applications, where heat transfer is needed between hydraulically separated fluid parts. The conventional, well-tried physically-based E model (standing for the known effectiveness-NTU approach) is recalled. This model assumes energy balance between the two sides of a heat exchanger (without any interaction with the environment). Based on studies in the literature, mathematical models with similar simplicity and usability to that of the E model, but under heat gain/loss to the environment, are still lacking in the field. This work intends to contribute to filling this gap with two proposed models, called ME and LR models. Based on measured data, all three models are accurate enough for general engineering/modelling purposes, nevertheless, the partly physically-based, partly empirical ME model is more precise than the E model if the heat gain/loss to the environment is considerable, and the empirical (black-box type) LR model is more precise than both the E and ME models if the heat gain/loss is not negligible. Furthermore, the outlet temperatures can be explicitly expressed from the simple linear algebraic relations characterizing all models alike.

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Grey-box model for pipe temperature based on linear regression

Cited by 16 publications

References 18 publications

On delay partial differential and delay differential thermal models for variable pipe flow

On delay partial differential and delay differential thermal models for variable pipe flow

Solving a Sequence of Recurrence Relations for First-Order Differential Equations

Modified effectiveness and linear regression based models for heat exchangers under heat gain/loss to the environment

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