Search Results

Experimentalists are familiar with the aliasing that happens in data acquisition when the sampling rate is less than twice the highest frequency of energy in the signal to be sampled. Much effort has been made over the years using a combination of analog and digital filters to make sure that the higher frequencies are filtered out to avoid or minimize the effect of this aliasing. Much less talked about is the aliasing that occurs in modal parameter estimation, or curvefitting, when the residual effects of out of band modes violate the assumptions of the finite dimensional parametric model that the experimentalist uses to curvefit the acquired digitized data. While the out of band energy has been filtered out of the now band limited data, the tails, sometimes called residual flexibility and inertial restraint of the out of band modes are still present in the data.

Vold and Leuridan [1] introduced in 1993 an algorithm for high resolution, slew rate independent order tracking based on the concepts of Kalman filters [5, 6]. The algorithm has been highly successful as implemented in a commercial software system in solving data analysis problems previously intractable with other analysis methods. At the same time certain deficiencies have surfaced, prompting the development of an improved formulation. This paper presents for the first time the second generation algorithm and its theoretical foundations. The new algorithm allows for the simultaneous estimation of multiple orders, effectively decoupling close and crossing orders. This is especially important for acoustics applications, where order crossings cause transient beating events. The algorithm now allows for a much wider range of filter shapes, such that signals with sideband modulations are processed with high fidelity.

The use of Kalman filter methods for high-performance order tracking of noise and vibration signals was introduced in 1993. Based on experience with that original formulation, further work has produced significant enhancements which greatly extend the ability of these methods to deal with several practical issues of concern in vehicle testing. This paper reports on advances in the areas of: RPM estimation accuracy, even for fast-changing events such as gear shifts; Higher order Kalman filters, with improved shapes for extracting modulated orders; Decoupling of close and even crossing orders by use of multiple RPM references; Significant speed improvement over the original algorithm. Besides obtaining the magnitude and phase of selected orders as a function of time or RPM, the harmonic content may be extracted as time-histories, with no phase or leakage distortion.