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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 lea...
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... 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. ...
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... The excitation profile contains a random selection of odd-frequency sine waves; leakage into the response of other frequency content can then be treated as an indicator of nonlinearity in the structure. 22 The ORPM tests were carried out with the Hawk in its undamaged condition, and also with some single-site mass additions. Initial ORPM tests were conducted in a single-input multipleoutput (SIMO) configuration, considering each input location separately, with following tests carried out as previously in a MIMO configuration. ...
The use of measured vibration data from structures has a long history of enabling the development of methods for inference and monitoring. In particular, applications based on system identification and structural health monitoring have risen to prominence over recent decades and promise significant benefits when implemented in practice. However, significant challenges remain in the development of these methods. The introduction of realistic, full-scale datasets will be an important contribution to overcoming these challenges. This article presents a new benchmark dataset capturing the dynamic response of a decommissioned BAE Systems Hawk T1A. The dataset reflects the behaviour of a complex structure with a history of service that can still be tested in controlled laboratory conditions, using a variety of known loading and damage simulation conditions. As such, it provides a key stepping stone between simple laboratory test structures and in-service structures. In this article, the Hawk structure is described in detail, alongside a comprehensive summary of the experimental work undertaken. Following this, key descriptive highlights of the dataset are presented, before a discussion of the research challenges that the data present. Using the dataset, non-linearity in the structure is demonstrated, as well as the sensitivity of the structure to damage of different types. The dataset is highly applicable to many academic enquiries and additional analysis techniques which will enable further advancement of vibration-based engineering techniques.
... This is a popular input design method to enable non-linear system identification (SYSID) in the frequency domain. The excitation profile contains a random selection of odd-frequency sine waves; leakage into the response of other frequency content can then be treated as an indicator of non-linearity in the structure [17]. The ORPM tests were carried out with the Hawk in its undamaged condition, and also with some single-site mass additions. ...
The use of measured vibration data from structures has a long history of enabling the development of methods for inference and monitoring. In particular, applications based on system identification and structural health monitoring have risen to prominence over recent decades and promise significant benefits when implemented in practice. However, significant challenges remain in the development of these methods. The introduction of realistic, full-scale datasets will be an important contribution to overcoming these challenges. This paper presents a new benchmark dataset capturing the dynamic response of a decommissioned BAE Systems Hawk T1A. The dataset reflects the behaviour of a complex structure with a history of service that can still be tested in controlled laboratory conditions, using a variety of known loading and damage simulation conditions. As such, it provides a key stepping stone between simple laboratory test structures and in-service structures. In this paper, the Hawk structure is described in detail, alongside a comprehensive summary of the experimental work undertaken. Following this, key descriptive highlights of the dataset are presented, before a discussion of the research challenges that the data present. Using the dataset, non-linearity in the structure is demonstrated, as well as the sensitivity of the structure to damage of different types. The dataset is highly applicable to many academic enquiries and additional analysis techniques which will enable further advancement of vibration-based engineering techniques.
... The proposed procedure is to generate independent random excitations for every input channel [26] [27], as opposed to the classical Hadamard technique [4]. A freeware implementation of a multisine toolbox can be found in [28]. The essence of a Best Linear Approximation (BLA) [4] is to minimize the mean squared error between the measured nonlinear response of a system and the response of a linear nonparametric frequency response function model (the BLA), for a given level of excitation. ...
A known challenge when building nonlinear models from data is to limit the size of the model in terms of the number of parameters. Especially for complex nonlinear systems, which require a substantial number of state variables, the classical formulation of the nonlinear part (e.g. through a basis expansion) tends to lead to a rapid increase in the model size. In this work, we propose two strategies to counter this effect: 1) The introduction of a novel nonlinear-state selection algorithm. The method relies on the non-parametric nonlinear distortion analysis of the Best Linear Approximation framework to identify the state variables which are the most impacted by nonlinearities. Pre-selecting only the most appropriate states when constructing the nonlinear terms results in a considerable reduction of the model size. 2) The use of so-called 'decoupled' functions directly in the model estimation procedure. While it is known that function decoupling can reduce the model size in a secondary step, we show how a decoupled formulation can be imposed to advantage from the start. The results of this approach are benchmarked with the state-of-the-art a posteriori decoupling technique. Our strategies are demonstrated on real-life data of a multiple-input, multiple-output (MIMO) ground vibration test of an F-16 aircraft, a prime complex and nonlinear dynamic system. 1 INTRODUCTION Engineers and scientists want mathematical models of the observed system for understanding, design and control. Modeling nonlinear systems is essential because many systems are inherently nonlinear. The challenge lies in the fact that there are several differently behaving nonlinear structures and therefore modeling is very involved. As it becomes increasingly important to cope with nonlinear analysis and modeling, various approaches have been proposed; for a detailed overview we refer to [1] [2] and [3]. In this work, we propose a data-driven nonlinear modeling procedure where we build upon a number of well-known, matured, system identification techniques, and add two novel tools in order to overcome some of the drawbacks of the classical approach. In doing so, we provide a complete modeling strategy which allows retrieving compact nonlinear state-space models from data. The procedure combines both nonparametric and parametric nonlinear modeling techniques and is particularly useful when dealing with complex nonlinear systems, such as dynamic structures with many resonances. An important domain of application is found in the modeling of multiple-input, multiple-output (MIMO) real-life vibro-acoustic measurements. We illustrate the methodologies on a ground vibration test of an F-16 aircraft. The recommended nonlinear modeling procedure is listed below and illustrated in Figure 1. ▪ In the experiment design step, systems are excited by broadband (multisine) signals at multiple excitation levels. The recommended multisine (also known as pseudo-random noise) excitation signal consists of a series of periodic multisines that are mutually independent over the experiments. The main advantage of the recommended signals is that there is no problem with spectral leakage or transients. They deliver excellent linear models while providing useful information about the level and type of nonlinearities. ▪ In the second step, the measured signals are (nonparametrically) analyzed by applying the (multisine-driven) Best Linear Approximation (BLA) framework of MIMO systems as a generalization of the conceptual work [4]. Even though the technique works best with the recommended multisines, (with some loss of accuracy) any (orthogonal) signal can be applied. This (multisine-driven) BLA analysis differs from the classical H 1 Frequency Response Function (FRF) estimation process [5]. The key idea is to make use of the statistical features of the excitation signal. The outcome of the BLA analysis results in a series of nonparametric FRFs together with noise and nonlinear distortion estimates.
... where ω 1 is the fundamental frequency, the user-defined amplitude of the k th harmonic is a k , ϕ k represents the phase, k max is the highest excited harmonic component. Interested users are referred to the free multisine generation toolbox (optimized for multiple input systems) [15]. ...
... The acquired output signal, which is shown in Fig. 13, is processed using the SAMI toolbox [15]. The first attempt in our work was to use the flexible LPM method. ...
Electrochemical impedance spectroscopy (EIS) is one of the most widely used techniques for battery monitoring and characterization. However, EIS measurement is a time-consuming process, since it must be performed after the battery relaxation time interval. In this paper, a method for performing fast broadband EIS during battery relaxation by compensating for the effect of the transient is proposed. The approach is based on the local rational method (LRM), which is a nonparametric frequency-domain system identification technique, and eliminates the need for long waiting time before starting the measurement process. The proposed approach is validated by numerical simulations and experiments, proving its capability of compensating the effect of the transient and outperforming other nonparametric techniques, such as the local polynomial method. In particular, experimental tests performed on a 18650 lithium-ion battery show that the proposed flexible LRM approach is capable of compensating the transient behavior and providing usable EIS estimates immediately after the battery discharge is finished. This behavior is demonstrated using a broadband multisine excitation signal of 20 s duration, spanning a frequency range from 50 mHz to 100 Hz.
This paper introduces a user-friendly estimation toolbox for (industrial) measurements of (vibro-acoustic) systems with multiple inputs. The vibration testing methods are very important because they help to improve the product quality and to avoid safety and comfort issues. The time-consuming testing procedures are nowadays fully substituted by techniques that evaluates the frequency response functions (FRFs).
The toolbox provides a user-friendly nonparametric estimation method that uses a special combined Local Polynomial/Rational approach. The toolbox can be used even in case of multiple inputs with only one measured period – that would be not possible with the classical FRF estimator frameworks.
