Figure 11 - uploaded by Péter Zoltán Csurcsia
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The BLA FRF estimations and their coherences components. The pink line shows the classical multiple coherence estimate. The dashed line refers to the transient coherence component. The red line refers to the nonlinear coherence component. The thin black line refers to the noise coherence component.
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PurposeThis paper provides a novel method to split up the multiple coherence function into noise, nonlinear distortion, and transient components.Method
The method relies on the nonparametric estimation framework called the Best Linear Approximation (BLA) where vibro-acoustic systems are excited by special so-called multisines (pseudo-random noise)...
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Citations
... This information will be later used at the building stage of the nonlinear models (see Sections 4.3 and 5. 2-5.3). An in-depth modal analysis of the F-16 aircraft can be found at [33], while the nonparametric modeling is described in [35]. Preliminary FRF Analysis Figure 7 shows the FRFs at the driving points. ...
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.
... The complex aerodynamic lift force for a harmonically pitching wing can also be seen as a classical nonlinear signal processing problem, not unlike a nonlinear vibro-acoustic system [36,46]. We explore that viewpoint in the present section to determine what (datadriven) model would be required to capture such nonlinear dynamics. ...
... The complex aerodynamic lift force for a harmonically pitching wing can also b as a classical nonlinear signal processing problem, not unlike a nonlinear vibro-ac system [36,46]. We explore that viewpoint in the present section to determine what driven) model would be required to capture such nonlinear dynamics. ...
This work discusses the experimental challenges and processing of unsteady experiments for a pitching wing in the low-speed wind tunnel of the Vrije Universiteit Brussel. The setup used for unsteady experiments consisted of two independent devices: (a) a position control device to steer the pitch angle of the wing, and (b) a pressure measurement device to measure the aerodynamic loads. The position control setup can pitch the wing for a range of frequencies, amplitude, and offset levels. In this work, a NACA-0018 wing profile was used with an aspect ratio of 1.8. The position control and the pressure measurement setups operate independently of each other, necessitating advanced signal processing techniques to synchronize the pitch angle and the lift force. Furthermore, there is a (not well-documented) issue with the (sampling) clock frequency of the pressure measurement setup, which was resolved using a fully automated spectral analysis technique. The wing was pitched using a simple harmonic sine excitation signal at eight different offset levels (between 6° and 21°) for a fixed amplitude variation (std) of 6°. At each offset level, the wing was pitched at five different frequencies between 0.1 Hz and 2 Hz (that correspond to reduced frequencies k ranging from 0.006 to 0.125). All the experiments were conducted at a fixed chord-based Reynolds number of 2.85 × 105. The choice of operating parameters invokes the linear and nonlinear behavior of the wing. The linear unsteady measurements agreed with the analytical results. The unsteady pressure measurements at higher offset levels revealed the nonlinear aerodynamic phenomenon of dynamic stall. This confirms that a nonlinear and dynamic model is required to capture the salient characteristics of the lift force on a pitching wing.
