Identifying linear models of systems suffering nonlinear distortions

The Saint Venant equations are two nonlinear partial differential equations (PDE) which are used to describe the dynamics of one-dimensional flow in open water channels. Despite being nonlinear PDEs, the Saint Venant equations seem to exhibit linear behaviour in response to sinusoidal input signals. It is therefore of interest to determine "how nonlinear" the Saint Venant equations are. In this paper, we investigate the nonlinearity in the Saint Venant equations using several commonly used nonlinearity tests suggested in the literature. Five different open water channels are considered, and the results from the nonlinearity tests show that the Saint Venant equations are nearly linear in an operating region from at least half the nominal flow to twice the nominal flows, and many of the channels display linear behaviour in a larger operating region. This finding is useful as it further justifies the use of linear control design methodologies for open water channels.

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“…By obtaining the magnitude and phase at each frequencies using Eqns. (12) and (13), the Bode plot can be constructed. Fig.…”

Section: A Sine Sweeping Methodsmentioning

confidence: 99%

“…The idea originated from [12], where a signal that contains only certain harmonics is used to excite the system. One example of such a signal is the odd-odd multisines signal.…”

Section: Broadband Periodic Excitationmentioning

confidence: 99%

Nonlinearity tests of the Saint Venant equations

Foo

Weyer

2013

52nd IEEE Conference on Decision and Control

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“…This technique (which is known also as the "broadband" excitation method) has been previously used for many problems where the influence of nonlinear distortions on the linear system behavior is to be evaluated and measured [10][11][12][13][14][15][16][17]. By using properly selected periodic excitations, called random multisines, it is possible not only to detect but also to quantify these distortions.…”

Section: Introductionmentioning

confidence: 99%

Multisine excitation technique for rotor crack detection

Kulesza

2013

Proceedings of the 14th International Carpathian Control Conference (ICCC)

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Rotordynamic systems have had many applications for decades. Well known examples include gas turbines and compressors used intensively in many important industry fields. Driven by rotating shafts transmitting large amounts of kinetic energy and utilized with continuous heavy loads, these machines very often suffer from sudden unpredicted failures. Such failure usually results in abrupt release of the transmitted energy, machine damage and a catastrophic accident.Propagating fatigue cracks are dangerous malfunctions, which had been recognized as the most frequent causes of similar accidents in the past. The fatigue shaft crack initiates from a small surface imperfection or a micro-crack due to a combination of corrosive, thermal, loading and other processes. Advancing slowly yet continuously the crack may achieve the critical depth at which an immediate shaft fracture occurs. Therefore the fatigue shaft crack, and especially the methods for its early detection and warning have a great deal of attention.It is widely known that a developing shaft crack manifests itself in the appearance of nonlinear effects resulting in higher harmonics in a vibration spectrum. However, such symptoms are characteristic not only for developing shaft cracks but also for other malfunctions such as a shaft bow, a coupling misalignment, etc. That is why novel shaft crack detection methods introduce a specially designed diagnostic force applied to the shaft in order to amplify the particular symptoms of the crack. Most often a simple harmonic force is used for such purposes, yet the results may not be very reliable.The present paper analyzes the possible application of the multisine excitation technique for an early shaft crack detection problem. This technique has been previously used for many problems where the influence of nonlinear distortions on the linear system behavior is to be evaluated and measured. By using well chosen periodic excitations, called random multisines, it is possible not only to detect but also to quantify these distortions.In the present paper the multisine technique is adopted for the rotating cracked shaft. The approach is illustrated with the numerical results of the flexible rotating shaft modeled with the rigid finite element method. In order to asses the effectiveness of the proposed method the numerical results obtained for the uncracked and cracked rotors are compared. The robustness of the method to additional disturbances is checked by introducing some noise to the system. The results demonstrate a potential of the presented method. Possible problems of its practical implementation are briefly discussed.

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