Parameter estimation for externally simulated thermal network models

Brastein, Ole Magnus; Lie, Bernt; Sharma, Roshan; Skeie, Nils-Olav

doi:10.1016/j.enbuild.2019.03.018

Cited by 19 publications

(9 citation statements)

References 21 publications

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“…(3) is obtaining reasonable estimates for process and noise covariance matrices, respectively W and V . In (Brastein et al, 2019) V was obtained from data, while W was found by manual experimentation. A better approach is to estimate them from data, by including them in θ .…”

Section: Resultsmentioning

confidence: 99%

“…Observe also that while the model is linear, the algorithm is not restricted to linear models. The choice of Kalman Filter implementation is determined by the type of model being used (Brastein et al, 2019). Table 1 lists a set of experimentally obtained nominal parameters, which are used as initial guesses for model calibration, and min/max limits which corresponds to the bounds of the constrained parameter space Θ.…”

Section: Modelmentioning

confidence: 99%

“…However, if parameters R b and R w are interdependent, the projection of the likelihood function for the parameter space Θ onto R b will be affected by R w , and subsequently by the constraint imposed by Θ. This type of constraints, in the presence of parameter interdependence, is known to produce such breaks in the computed profiles (Brastein et al, 2019), as discussed in Section 2.1.…”

Section: Profile Likelihoodmentioning

confidence: 99%

See 2 more Smart Citations

Sensor placement and parameter identi?ability in grey-box models of building thermal behaviour

Brastein¹,

Sharma²,

Skeie³

2019

Linköping Electronic Conference Proceedings

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Building Energy Management systems can reduce energy consumption for space heating in existing buildings, by utilising Model Predictive Control. In such applications, good models of building thermal behaviour is important. A popular method for creating such models is creating Thermal networks, based cognitively on naive physical information about the building thermal behaviour. Such models have lumped parameters which must be calibrated from measured temperatures and weather conditions. Since the parameters are calibrated, it is important to study the identifiability of the parameters, prior to analysing them as physical constants derived from the building structure. By utilising a statistically founded parameter estimation method based on maximising the likelihood function, identifiability analysis can be performed using the Profile Likelihood method. In this paper, the effect of different sensor locations with respect to the buildings physical properties is studied by utilising likelihood profiles for identifiability analysis. The extended 2D profile likelihood method is used to compute two-dimensional profiles which allows diagnosing parameter inter-dependence, in addition to analysing the identifiability. The 2D profiles are compared with confidence regions computed based on the Hessian.

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Section: Resultsmentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Section: Profile Likelihoodmentioning

confidence: 99%

See 1 more Smart Citation

Sensor placement and parameter identi?ability in grey-box models of building thermal behaviour

Brastein¹,

Sharma²,

Skeie³

2019

Linköping Electronic Conference Proceedings

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“…We wish to combine the measurements (y) with the state space model to estimate the unmeasured rotor copper temperature T r and air gap temperature T δ a . To do that, we use two different Kalman Filter algorithms: the Unscented Kalman Filter (UKF) is presented in (Simon, 2006), while the Ensemble Kalman Filter (EnKF) is succinctly described in (Brastein et al, 2019). A summary of the UKF and EnKF algorithms are given in Tables 5 and 6, respectively.…”

Section: State Estimationmentioning

confidence: 99%

State Estimation of a Thermal Model of Air-cooled Synchronous Generator

Pandey¹,

Øyvang²,

Lie³

2020

Linköping Electronic Conference Proceedings

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In this paper, we extend a previous study on a totally enclosed thermal model of a synchronous generator, with temperature state estimation using experimental data. The extension includes a new formulation of the system model, with four different model variations with and without temperature dependence in the metal, air, and water heat capacities and the copper resistances, where temperature variation in water and/or air requires a non-standard heat exchanger model. In the former study, the Unscented Kalman Filter (UKF) was used for state estimation. Here, we include both the UKF as well as the Ensemble Kalman Filter (EnKF) in the comparison. UKF and EnKF are compared based on estimation accuracy and computational speed. Results show that EnKF exhibits lower RMSE for the innovation process and thus is more accurate than the UKF even with a "minimum" of 50 particles, but the UKF with 6 sigma points (3 states) is faster. It is too early to conclude which of 4 models is more accurate, as they need to be tuned individually wrt. parameter fitting.

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“…The choice of KF implementation, either the standard linear KF for linear models, or a non-linear variant such as the Extended KF (EKF) or the Unscented KF (UKF), depends on the model equations Brastein et al [2019a]. Equation (6) is further simplified by conditioning on knowing y 0 , taking the negative logarithm, and eliminating the factor 1 2 .…”

Section: Stochastic Parameter Estimationmentioning

confidence: 99%

Estimating uncertainty of model parameters obtained using numerical optimisation

Brastein¹,

Lie²,

Pfeiffer³

et al. 2019

MIC

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Obtaining accurate models that can predict the behaviour of dynamic systems is important for a variety of applications. Often, models contain parameters that are difficult to calculate from system descriptions. Hence, parameter estimation methods are important tools for creating dynamic system models. Almost all dynamic system models contain uncertainty, either epistemic, due to simplifications in the model, or aleatoric, due to inherent randomness in physical effects such as measurement noise. Hence, obtaining an estimate for the uncertainty of the estimated parameters, typically in the form of confidence limits, is an important part of any statistically solid estimation procedure. Some uncertainty estimation methods can also be used to analyse the practical and structural identifiability of the parameters, as well as parameter inter-dependency and the presence of local minima in the objective function. In this paper, selected methods for estimation and analysis of parameters are reviewed. The methods are compared and demonstrated on the basis of both simulated and real world calibration data for two different case models. Recommendations are given for what applications each of the methods are suitable for. Further, differences in requirements for system excitation are discussed for each of the methods. Finally, a novel adaption of the Profile Likelihood method applied to a moving window is used to test the consistency of dynamic information in the calibration data for a particular model structure.

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Parameter estimation for externally simulated thermal network models

Cited by 19 publications

References 21 publications

Sensor placement and parameter identi?ability in grey-box models of building thermal behaviour

Sensor placement and parameter identi?ability in grey-box models of building thermal behaviour

State Estimation of a Thermal Model of Air-cooled Synchronous Generator

Estimating uncertainty of model parameters obtained using numerical optimisation

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