Approaches are being considered to transform the given time-domain experimental input-output data into a frequency-domain transform function model description along with the associated noise error characterization. Both second-order spectrum and cross-spectrum of the data record as well as higher-order integrated polyspectrum of the data record is being exploited for such purposes.

This allows for far fewer a priori assumptions; rather such modeling is dictated by the acquired data. The case of noisy input measurements is also being considered. A stochastic embedding approach is being followed for quantifying modeling errors. Katayama and S.

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Cooperative Agreement Conditions. Special Conditions. Federal Demonstration Partnership. Policy Office Website. Jitendra Tugnait tugnajk eng. It has been shown that the Hanning window or Von-Hann window given by. The upper time limit t u and the lower time limit t l determine the borders of the window function. Due to the slowly increasing ramp shown in Fig. The dotted—dashed line green represents the measured vibration angle of the 6th engine order on a test bench. The black line with the triangle symbol shows the vibration angle of the 6th engine order with the identified TVD parameters.

Hence, a significant improvement can be seen in this range compared to the simulation utilizing the initial parameters of the torsional vibration damper. On the one hand, the engine orders of the simulation with the initial parameters and, on the other hand, the engine orders of a simulation with the identified parameters of the TVD are shown. As expected, the spectra of the orders other than the 6th are only slightly affected.

The present paper shows a new method for parameter identification using the amplitude response of oscillations in multibody system dynamics.

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The proposed method combines the classical Fourier analysis with the adjoint sensitivity analysis for the gradient computation in an optimization problem. Using the spectrum of a system output helps in understanding the behavior of a system whereas the interpretation of the time domain data is not always promising because of excessive time ranges, noisy signals, or systematic errors.

The method is applied to a nonlinear cart—pendulum system. In order to demonstrate that the method copes with system uncertainties in the example, one parameter, which is not part of the identification, is set to a value different from the one used for generating the measurement. Therefore, the desired spectrum cannot be obtained to its full extent, but only in the given frequency range.

In the time domain this would lead to an optimization problem that is not well-posed. Further, an identification is performed using the model of a four-cylinder engine. Here, the robustness of the method and also the capability to deal with larger systems are pointed out.

The equations of motion of the four-cylinder engine are summarized here. As mentioned in Sect.

## System identification of flexible aircraft in frequency domain | Emerald Insight

Note that we have canceled the degree of freedom of the secondary side of the dual mass flywheel, because its motion is given by a function q runup t. Hence, we exchange the degree of freedom of the dual mass flywheel q 23 by the given function q runup t. The crankshaft, conrods, and the pistons are described with redundant coordinates. Hence, we introduce four algebraic constraint equations for each cylinder, where r c s is the radius of the crankshaft, l c r is the length of the conrod, and s c r is the distance to the center of mass.

Finally, the vector of constraint equations C q is given by.

## System Identification: A Frequency Domain Approach, 2nd Edition

From Fig. The first constraint equation describes the x -component of the big end bearing. Using the Hanning window function. It has been shown that more than one period is required when using a Hanning window. National Center for Biotechnology Information , U. Multibody System Dynamics. Multibody Syst Dyn. Published online Nov 3. Author information Article notes Copyright and License information Disclaimer. Stefan Oberpeilsteiner, Email: ta. Corresponding author. Received Apr 25; Accepted Aug Abstract The adjoint method shows an efficient way to incorporate inverse dynamics to engineering multibody applications, as, e.

Introduction Applications of the adjoint method to solve a variety of optimization problems in engineering sciences are widespread. The adjoint gradient computation Following the basic idea presented in Nachbagauer et al. Numerical examples Cart pendulum system In order to present the performance of the identification method, we study a system of pendula connected to a cart performing a one-dimensional motion.

Open in a separate window. Identification of torsional vibration damper TVD parameters In this section the presented method is applied to a model of a four-cylinder engine, shown in Fig. Model structure Crankshaft The torsional vibration modes of the crankshaft are crucial for the parameter identification process. Piston In the used model, each piston features only one translational degree of freedom.

Dual mass flywheel The primary side of the dual mass flywheel DMF is mounted on the right end of the crankshaft see Fig. Torsional vibration damper The torsional vibration damper TVD is installed for reducing the internal torsional vibrations of the crankshaft. Cylinder pressures The cylinder pressure is given by a two-dimensional map depending on the rotational speed and the crankshaft angle. Run-up of the engine In order to simulate the run-up performed on the real test bench, the rotational speed of the secondary side of the DMF is increased up to the final rotational speed.

Conclusions The present paper shows a new method for parameter identification using the amplitude response of oscillations in multibody system dynamics. Appendix A: The model equations The equations of motion of the four-cylinder engine are summarized here. References 1. Bottasso C.

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On the solution of inverse dynamics and trajectory optimization problems for multibody systems. Multibody Syst.