MUMI: Multisine for multiple input systems: A user-friendly excitation toolbox for physical systems

Abstract

Scientists and engineers want accurate mathematical models of physical systems for understanding, design, and control. To obtain accurate models, persistently exciting rich signals are needed. The MUMI Matlab toolbox creates multisine signals to assess the underlying systems in a time efficient, user-friendly way. In order to avoid any spectral leakage, to reach full nonparametric characterization of the noise, and to be able to detect nonlinearities and time-variations, multisine signals can be used. By the use of the toolbox, inexperienced users can easily create state-of-the-art excitation signals to be used to perturbate almost any physical systems.

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MUMI: Multisine for multiple input systems: A user-friendly excitation
toolbox for physical systems
Péter Zoltán Csurcsia
PII: S2665-9638(21)00083-X
DOI: https://doi.org/10.1016/j.simpa.2021.100192
Reference: SIMPA 100192
To appear in: Software Impacts
Received date : 19 November 2021
Accepted date : 26 November 2021
Please cite this article as: P.Z. Csurcsia, MUMI: Multisine for multiple input systems: A
user-friendly excitation toolbox for physical systems, Software Impacts (2021), doi:
https://doi.org/10.1016/j.simpa.2021.100192.
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license (http://creativecommons.org/licenses/by/4.0/).

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Title / name of your software
MUMI: Multisine for multiple input systems: a user-friendly excitation toolbox for physical systems
Names of authors / main developers (incl. affiliations, addresses, email)
Péter Zoltán Csurcsia
Department of Engineering Technology,
Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Elsene, Belgium
peter.zoltan.csurcsia@vub.be
Abstract
Scientists and engineers want accurate mathematical models of physical systems for understanding,
design, and control. To obtain accurate models, persistently exciting rich signals are needed. The MUMI
Matlab toolbox creates multisine signals to assess the underlying systems in a time efficient, user-friendly
way. In order to avoid any spectral leakage, to reach full nonparametric characterization of the noise, and
to be able to detect nonlinearities and time-variations, multisine signals can be used. By the use of the
toolbox, inexperienced users can easily create state-of-the-art excitation signals to be used to perturbate
almost any physical systems.
Keywords
Multisine excitation
Nonlinearity and time-variations
Multiple input systems
Structural testing
Signal processing
Code metadata
Nr
Code metadata description
Please fill in this column
C1
Current code version
V1.8
C2
Permanent link to code/repository used
for this code version
https://github.com/commodos/-MUMI
C3
Permanent link to reproducible capsule
https://codeocean.com/capsule/8587971
C4
Legal code license
GNU General Public License (GPL) 3
C5
Code versioning system used
none
C6
Software code languages, tools and
services used
Matlab c
C7
Compilation requirements, operating
environments and dependencies
Matlab 2011 or higher
C8
If available, link to developer
documentation/manual
C9
Support email for questions
peter.zoltan.csurcsia@vub.be
Manuscript Click here to view linked References

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Body of the article (excluding metadata, tables, figures, references)
1. Introduction
This work presents a user-friendly signal generation Matlab toolbox for real-life (industrial) experiments of physical
systems with multiple inputs. Many structures are inherently time-varying and nonlinear. This toolbox addresses the
questions related to the user-friendly design of experiment. When the proposed signals are used, it is easily possible
a) to decide, if the underlying system is linear or not, b) to decide if the linear framework is still accurate (safe)
enough to be used, and c) to tell the inexperienced (non-expert) user how much can be gained using an advanced
time-varying or nonlinear framework. For detailed information w.r.t. estimation techniques, see [1] [2].
In modern system identification special excitation signals are available to assess the underlying systems in a user-
friendly, time efficient way. To avoid any spectrum leakage, to reach full nonparametric characterization of the noise,
and to be able to detect nonlinearities and time-variations, an advanced excitation signal is needed. Many users
prefer noise excitations, because they seem simple to implement – and randomness is usually needed to fulfill silent
assumptions on estimation framework applied in the work – but in this case the nonlinearities and time-variations
are not identifiable, and there is a possible leakage error. One of the (best) possibilities is the usage of special
multisines because they can avoid spectral leakage, inconsistency, non-persistency, and they provide a handy, robust
solution to build linear models and to detect the level and type of nonlinearities and time-variations.
Most structures can be excited by the so-called random phase multisines that are a sum of harmonically related
sinusoids. These signals generated in the frequency domain such that the magnitude characteristic is set by the user
(i.e., it is customizable), the phases of the cosines are chosen randomly from a uniform distribution, and defined as
follows:
   

  (1)
where  is the fundamental angular frequency (that sets the frequency resolution),  is the amplitude of the
harmonic and  is the highest harmonic component.
If the multisine contains all/only odd or even harmonics, then it is called full/odd or even multisine. The toolbox also
allows users to create other types of multisine with linear and Schroeder phase, for details on these types of signals,
see [3].
2. The usage
The MUMI toolbox is a user-friendly Matlab based toolbox. It supports command line and graphical user interfaces.
The signal generation toolbox has been tested with many simulations, real-life industrial measurements, and it is
optimized for MIMO (multiple input, multiple output) experiments. The GUI of the multisine toolbox is shown in
Figure 1, a signal illustration is shown in Figure 2.
The GUI of the toolbox can be started by calling running the ‘mumi.m’ file (or double clicking on the ‘mumi.fig’ file).
The starting screen of GUI begins with a simplified view where the most common parameters can be quickly adjusted.
By clicking on the ‘advanced settings button’ more interactive setting-sensitive options can be adjusted. If someone
wants to explore the command line possibilities, the parametrization and examples can be found by typing ‘help
GenerateSignal’. This also implicitly implies that the GUI – which contains many contradiction check-ups – is calling
the ‘GenerateSignal.m’ file in the background to create the actual signal.
Basically, there are three supported multisines modes in the toolbox (reading the rest of the article will make clear
the choices listed here):
1) combined (default, multiple  random realizations and  periods of missing odd multisines),
2) fast (one realization, multiple  periods of missing odd multisines), and
3) robust (multiple  realization of full) multisines.
The toolbox can be used straightway – without setting any parameters – but of course the intended use that the
user sets these parameters according to the system under test and the instrumentation setup. The default values
can be amended (see the ‘Test_settings.m’ file in the ‘sources folder’) that gives the user the freedom to easily tailor
the code according to the actual needs. Such parameters are, for instance,
 The sampling frequency (
), this is usually determined by the components of the instrumentation and the
system under test.
 The number of input channels, determined by the system and/or experiment.

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 The maximum power/amplitude level of excitation: determined by the safety margins of the
system/instrumentation.
 The frequency resolution (
) or the number of samples in one period  (the relationship is 
 
).
The following sections will make sure that the basic choices of the toolbox (e.g. parameter choices and their effect)
are adequality described for the novice users.
Figure 1: GUI of the multisine generation toolbox. The left figure shows the opening screen where the default
values are set from the user-defined profile.
Figure 2: An example of the generated signal using the toolbox.
2.1. Multisines for nonlinearity evaluation
In general, when a small excitation level is used, the effects of nonlinearities can be hidden in the noise. If the
excitation level is higher, the effect of the nonlinearities become visible. If a full-band multisine excitation is used,
then the details of the nonlinear behavior are not directly separable from the linear part. Figure 3 shows an example,
how the system response consists of the linear and nonlinear part. When an excitation set of only even harmonics
is used, the odd nonlinearities are not detectable. The solution to detect both even and odd nonlinear contributions
is to use an excitation set only with odd harmonics, e.g. odd random phase multisine. To examine the odd
frequencies, it is needed to skip several odd harmonics in the multisine. The experiences show that the odd, random
phase multisine with randomly skipped harmonics is the best what can be used because when a fixed odd harmonic
is missing then certain type of nonlinearities can be hidden. A random skipping is recommended to be done within
a fixed group of harmonics (
). The author recommends using a group of three or four, i.e. in each series of
three/four odd harmonics, one odd harmonic is skipped randomly. The disadvantage of the missing harmonics
multisine is that the effective frequency resolution (that is displayed in GUI) becomes coarser, but on the other hand,
at the same power level of the excitation system, the frequency components can be more excited. A further
minimal user-
interaction
predefined
values
state-of-the art
MIMO signals
optimized for
nonlinear
detection
See Figure 2

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advantage is to mention that using band-limited multisines allows the user to detect in-band and out-band
nonlinearities, i.e. to detect that the nonlinearities are limited to the band of excitation or not.
It is important to highlight that it is possible to use multiple  periods and  realizations of multisines. Using multiple
periods, the SNR (signal-to-noise ratio) will be improved. Using multiple realizations will improve the SNLR (signal-
to-nonlinearity ratio).
Figure 3: System response originating from linear and nonlinear part of excited system
2.2. Multisines for detection of time-variations
Due to the properties of the spectral output of linear time-varying systems, multisines can be used to detect time-
variations. The recommended excitation signal is (the default) odd random phase multisines. A measurement is
shown in Figure 4. Observe that around the excited frequencies skirt-like shapes appear, which could be interpreted
as a spectral leakage. Since the usage of multisines will prevent leakage, these skirts are due to time-variations.
Figure 4: The figure on the left shows the magnitude spectrum of the excitation signal. The figure on the right
shows the measured output of a time-varying system.
2.3. Multisines for multiple input measurements
When considering a MIMO measurement setup, input channel-wise independent experiments are needed. In
classical MIMO identification, one of the most often applied solution to this problem is the use of Hadamard
decorrelation technique (known as +- technique as well [4]: a square matrix (whose entries are either +1 or −1) is
elementwise multiplied with one single realization of the signal. The restriction is that the order of the Hadamard
exist for certain dimensions only. Further, it is very important to highlight that a measurement using Hadamard
structure unnecessarily “stretches” the structure. For example, think of the vibration testing of a symmetric structure,
for instance, an airplane where the wings are excited. The “stretch” appears by applying inputs of opposite sign at
certain time instances. In order to overcome the issues with the classical solutions, author recommends using the
orthogonal random multisines (default setting), extending the idea of the orthogonal inputs proposed for linear
MIMO measurements in [5]. The available options are shown in the GUI under ‘MIMO structure’ options.
3. Impact
The proposed toolbox has been used in various research related works.
0 0.1 0.2 0.3 0.4
0
0.05
0.1
normalized frequency (f/fs)
input magnitude [V]
0 0.1 0.2 0.3 0.4
0
0.05
0.1
normalized frequency (f/fs)
output magnitude [V]

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Typical applications include, for instance:
 ground vibration testing of aircrafts where the wings of the airplane are simultaneously excited [6] [7] [8]
[9] [10];
 identification and measurement of tire suspension systems [11] [12];
 satellite testing using loudspeakers [13] ;
 blade testing of a wind turbine [14];
 valve control of cascaded control’s system [15] [16];
 wind tunnel experiments to control the angle of attack or the freestream velocity: [17] [18] [19] [20] [21];
 in time-varying system identification [22] [23] [24] [25] [26] [27] cases;
 prediction of inputs cases of autonomous systems [28] [29];
 input generation for local module identification task [30].
4. Future development
Author plans to make in the near future a Python implementation of the toolbox thus untethering the
need to have Matlab license needed to run the code.
Declaration of competing interest
The author declares that he has no known competing financial interests or personal relationships that
could have appeared to influence the work reported in this paper.
Acknowledgement
This work was funded by the VLAIO Innovation Mandate project number HBC.2016.0235 and by the SRP
project 60 of the Vrije Universiteit Brussel.
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[6]
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Vibration Engineering and USD 2018 - International Conference on Uncertainty in Structural Dynamics,
Leuven, Belgium, 2018.
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P. Csurcsia, J. Schoukens and B. Peeters, "First Results on Regularized Time-Varying Operational Modal
Analysis," IFAC-PapersOnLine, vol. 51, no. 15, pp. 162-167, 2018.
[21]
M. F. Siddiqui, T. D. Troyer, J. Decuyper, P. Z. Csurcsia, J. Schoukens and M. C. Runacres, "A data-driven
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2022.
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P. Csurcsia, J. Schoukens, I. Kollár and J. Lataire, "Nonparametric time-domain identification of linear slowly
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P. Csurcsia, B. Peeters and J. Schoukens, "Tracking the modal parameters of time-varying structures by
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[25]
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spline algorithm," in IEEE I2MTC - International Instrumentation and Measurement Technology Conference,
Graz, Austria, 2012.
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144, 2020.
[30]
K. Ramaswamy, P. Csurcsia, J. Schoukens and P. Van Den Hof, "A frequency domain approach for local module
identification in dynamic networks," Automatica, 2022.

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User-friendly generaon of excitaon signal
A novel Matlab toolbox for advanced mulsine signals
Orthogonal excitaon for mulple inputs systems

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Declaraon of interests
☒ The authors declare that they have no known compeng nancial interests or personal relaonships
that could have appeared to inuence the work reported in this paper.
☐The authors declare the following nancial interests/personal relaonships which may be considered
as potenal compeng interests: