Chapter 4
Hybrid Substructure Assembly Techniques for Efficient
and Robust Optimization of Additional Structures in Late Phase
NVH Design: A Comparison
Benjamin Kammermeier, Johannes Mayet, and Daniel J. Rixen
Abstract In certain circumstances, not all desired NVH properties of a given mechanical structure, e.g. a vehicle, are
satisfied at the end of a development process. In this situation, NVH properties of an existing structure must be improved
while extensive changes of this structure are not practicable. Consequently, additional components such as mass dampers are
included to improve the NVH properties. The arising task is to determine the optimal configuration of these additional
components. If one assumes that no valid or accurate simulation model of the underlying structure exists, a hybrid
substructuring approach is essential. The existing structure is measured at the required positions, the additional structures are
modeled virtually, subsequently they are combined to a hybrid assembly. The optimization includes the repeated evaluation
of such an hybrid assembly. In this contribution two major strategies are regarded: frequency based substructuring (FBS) and
state-space substructuring (SSS). The possibly large number of evaluations imposes a greater demand on the computational
efficiency compared to onetime assemblies. Furthermore, properties concerning the robustness towards measurement noise
of the assembly technique play an important role. Based on a common notation for both assembly techniques, the relevant
properties—efficiency and robustness—are compared on a numerical example.
Keywords Hybrid substructuring · Frequency-based substructuring · State-space substructuring · System identification ·
Frequency response estimation
4.1 Related Work and Outline
The paradigm of hybrid substructuring is straightforward: the assembled substructures are represented by models which
are obtained from both—measurement and numerical modeling. In the measurement process, time series of inputs and
outputs, e.g. forces and accelerations, are recorded. The process to obtain a model from measured data is called system
identification. Besides system identification, numerical methods, e.g. FEM, can be used to derive a model. Therefore, the
results of both processes will be referred to as identified and numerical model. In this contribution, a certain practical
example for hybrid substructuring, rooted in vehicle NHV design, is anticipated: determine one (or more) (sub)optimal
configuration(s) of additional substructures on a vehicle for a given objective. The vehicle can be measured and identified; the
additional structures are available as numerical models. Such a hybrid substructuring task can be achieved by two strategies—
Frequency-Based Substructuring (FBS) and State-Space Substructuring (SSS).
The FBS technique was widely used during the last few years. One application case which is often considered in the NVH
context is the Transfer Path Analysis. The framework set up in [18] is foremost based on FBS. A general framework for
substructuring, including FBS is given in [8]. In case of FBS, the assembly process is achieved in the frequency domain. The
B. Kammermeier ()
Faculty of Mechanical Engineering, Technical University of Munich, Garching, Germany
Forschungs- und Innovationszentrum FIZ, BMW Group, München, Germany
e-mail: benjamin.kammermeier@tum.de; Benjamin.Kammermeier@bmw.de
J. Mayet
Forschungs- und Innovationszentrum FIZ, BMW Group, München, Germany
e-mail: Johannes.Mayet@bmw.de
D. J. Rixen
Faculty of Mechanical Engineering, Technical University of Munich, Garching, Germany
e-mail: rixen@tum.de
© Society for Experimental Mechanics, Inc. 2020
A. Linderholt et al., Dynamic Substructures, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series,
https://doi.org/10.1007/978-3-030-12184-6_4
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