Approaches to Parameter Identiﬁcation for
Hybrid Multilinear Time Invariant Systems
Aadithyan Sridharan
1 a
, Gerwald Lichtenberg
1 b
, Antonio Correcher Salvador
2 c
and Carlos Vargas Salgado
3 d
1
Faculty of Life Sciences, University of Applied Sciences, Ulmenliet 20, 21033 Hamburg, Germany
2
Instituto Universitario de Autom
´
atica e Inform
´
atica Industrial (ai2),
Universitat Polit
`
ecnica de Val
`
encia, 46022, Valencia, Spain
3
Department of Electrical Engineering, Universitat Polit
`
ecnica de Val
`
encia, 46022, Valencia, Spain
Keywords:
Multilinear Systems, Parameter Identiﬁcation, Tensor Decomposition, Industrial Building Modelling.
Abstract:
Industrial buildings often have interacting continuous- and discrete-valued signals. Hybrid multilinear time
invariant (MTI) models have been shown to be able to describe this hybrid dynamics appropriately for many
cases. White box modelling methods from ﬁrst principles have been used in this application domain before.
The parameters of these models can be efﬁciently represented by higher order tensors. This paper introduces
as alternatives black and grey box approaches for the parameter identiﬁcation of MTI models from data. The
methods are tested with the help of simulation data produced from a multilinear model of an industrial hall. It
is assumed that all state variables are measured with additative noise and the input and disturbances are exactly
measured, too. Two black box methods obtain either the full parameter tensor or a rank-r decomposition of it.
Numerical examples using the industrial building model show the principle applicability of these approaches
for real data.
1 INTRODUCTION
Systems in many application areas as buildings engi-
neering show discrete-valued as well as continuous-
valued signals, e.g. if a continuous state like a temper-
ature depends on the switching ON/OFF of a binary
input like a gas heater. This example can be sufﬁ-
ciently good described by multilinear time invariant
(MTI) models, as well as many more from other ap-
plication areas, (Lichtenberg, 2011).
There are three traditional approaches in order to
obtain a state space model depending on the avail-
able information about the system. If no sufﬁcient
prior knowledge about the system is available, then
the black box identiﬁcation approach is chosen (Cha-
van and Talange, 2018), (Tayamon, Zambrano, Wi-
gren and Carlsson, 2011), (Royer, Thil, Talbert and
Polit, 2014). On the contrary, in some cases through
ﬁrst principles like laws of physics, sufﬁcient infor-
a
https://orcid.org/0000-0002-1237-3125
b
https://orcid.org/0000-0001-6032-0733
c
https://orcid.org/0000-0002-2443-9857
d
https://orcid.org/0000-0002-9259-8374
mation about the system can be obtained. In these
cases, white box techniques are used. However, if the
information through ﬁrst principles is incomplete, in
the sense that there are unknown parameters in the
system, the grey box identiﬁcation approach is used
(Bacher and Madsen, 2011).
In (Batselier, Ko, Phan, Cichoki and Wong, 2018),
the system identiﬁcation problem of multilinear state
space models has been considered. In this work, the
coefﬁcients of the state space matrices have been es-
timated by representing them as tensor train matrices.
The computational complexity is reduced by repre-
sentation as tensor train matrices. The contribution of
this paper are different methods for parameter identi-
ﬁcation of an MTI state space model. In order to solve
the identiﬁcation problem, both the grey and black
box methods are considered. The grey box problem
involves ﬁnding the unknown physical parameters of
the system. In this case the structure of the model is
known beforehand.
On the other hand, the black box problem involves
no prior knowledge about the system. The identiﬁ-
cation problem is to ﬁnd parameters of a multilinear
state space model, given a set of input state data and
Sridharan, A., Lichtenberg, G., Salvador, A. and Salgado, C.
Approaches to Parameter Identiﬁcation for Hybrid Multilinear Time Invariant Systems.
DOI: 10.5220/0009887502550262
In Proceedings of the 10th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2020), pages 255-262
ISBN: 978-989-758-444-2
Copyright
c
2020 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
255