The problem of aircraft engine condition monitoring based on vibration signals is addressed. To do so, we compare two estimators of the Frequency Response Function of an aircrat engine which input is its shaft angular position and which output is an accelerometric signal that measures vibrations. It is shown that this problem can be seen as a smoothing problem, and that linear kernel smoothing ...

In this paper, we develop a fast algorithm for a smoothing spline estimator in multivariate regression. To accomplish this, we employ general concepts associated with roughness penalty methods in conjunction with the theory of radial basis functions and reproducing kernel Hilbert spaces. It is shown that through the use of compactly supported radial basis functions it becomes possible to recove...

We extend the spectrum estimation method of Thomson to non-stationary signals by formulating a multiple window spectrogram. The traditional spectrogram can be represented as a member of Cohen’s class of time-frequency distributions (TFDs), where the smoothing kernel is the Wigner distribution of the signal temporal window. We show the unusual shape of the Cohen’s class smoothing kernels corresp...

Mesh smoothing is an important algorithm for the improvement of element quality in unstructured mesh finite element methods. A new optimisation based mesh smoothing algorithm is presented for anisotropic mesh adaptivity. It is shown that this smoothing kernel is very effective at raising the minimum local quality of the mesh. A number of strategies are employed to reduce the algorithm’s cost wh...

We address two practical issues, namely smoothing factor selection and efficient implementation of thresholding with hysteresis, in implementing Canny’s edge detector. The smoothing factor of the Gaussian kernel should be chosen to maximize the discrete version of Canny’s original criteria. Thresholding with hysteresis should be implemented using an efficient connected component analysis algori...

Nonparametric regression techniques are often sensitive to the presence of correlation in the errors. The practical consequences of this sensitivity are explained, including the breakdown of several popular data-driven smoothing parameter selection methods. We review the existing literature in kernel regression, smoothing splines and wavelet regression under correlation, both for short-range an...

Voxel-based analysis (VBA) methods are increasingly being used to compare diffusion tensor image (DTI) properties across different populations of subjects. Although VBA has many advantages, its results are highly dependent on several parameter settings, such as those from the coregistration technique applied to align the data, the smoothing kernel, the statistics, and the post-hoc analyses. In ...

In earlier work with Gabor Lugosi, we introduced a method to select a smoothing factor for kernel density estimation such that, for all densities in all dimensions, the L1 error of the corresponding kernel estimate is not larger than 3 + e times the error of the estimate with the optimal smoothing factor plus a constant times Ov~--~-n/n, where n is the sample size, and the constant only depends...

A method of counts-in-cells analysis of galaxy distribution is investigated with arbitrary smoothing functions in obtaining the galaxy counts. We explore the possiblity of optimizing the smoothing function, considering a series of m-weight Epanechnikov kernels. The popular top-hat and Gaussian smoothing functions are two special cases in this series. In this paper, we mainly consider the second...

Smoothing (say by a Guassian kernel) has been a very popular technique for optimizing a nonconvex objective function. The rationale behind smoothing is that the smoothed function has less spurious local minima than the original one. This technique has seen tremendous success in many real world tasks such as those arising in machine learning and computer vision. Despite its empirical success, th...