Abstract: Nonlinear evolution of broadband ultrasonic pulses
passed through the rock specimens is studied using the apparatus
“GEOSCAN-02M”. Ultrasonic pulses are excited by the pulses of Qswitched
Nd:YAG laser with the time duration of 10 ns and with the
energy of 260 mJ. This energy can be reduced to 20 mJ by some light
filters. The laser beam radius did not exceed 5 mm. As a result of the
absorption of the laser pulse in the special material – the optoacoustic
generator–the pulses of longitudinal ultrasonic waves are excited with
the time duration of 100 ns and with the maximum pressure
amplitude of 10 MPa. The immersion technique is used to measure
the parameters of these ultrasonic pulses passed through a specimen,
the immersion liquid is distilled water. The reference pulse passed
through the cell with water has the compression and the rarefaction
phases. The amplitude of the rarefaction phase is five times lower
than that of the compression phase. The spectral range of the
reference pulse reaches 10 MHz. The cubic-shaped specimens of the
Karelian gabbro are studied with the rib length 3 cm. The ultimate
strength of the specimens by the uniaxial compression is (300±10)
MPa. As the reference pulse passes through the area of the specimen
without cracks the compression phase decreases and the rarefaction
one increases due to diffraction and scattering of ultrasound, so the
ratio of these phases becomes 2.3:1. After preloading some horizontal
cracks appear in the specimens. Their location is found by one-sided
scanning of the specimen using the backward mode detection of the
ultrasonic pulses reflected from the structure defects. Using the
computer processing of these signals the images are obtained of the
cross-sections of the specimens with cracks. By the increase of the
reference pulse amplitude from 0.1 MPa to 5 MPa the nonlinear
transformation of the ultrasonic pulse passed through the specimen
with horizontal cracks results in the decrease by 2.5 times of the
amplitude of the rarefaction phase and in the increase of its duration
by 2.1 times. By the increase of the reference pulse amplitude from 5
MPa to 10 MPa the time splitting of the phases is observed for the
bipolar pulse passed through the specimen. The compression and
rarefaction phases propagate with different velocities. These features
of the powerful broadband ultrasonic pulses passed through the rock
specimens can be described by the hysteresis model of Preisach-
Mayergoyz and can be used for the location of cracks in the optically
opaque materials.
Abstract: Extended Kalman Filter (EKF) is probably the most
widely used estimation algorithm for nonlinear systems. However,
not only it has difficulties arising from linearization but also many
times it becomes numerically unstable because of computer round off
errors that occur in the process of its implementation. To overcome
linearization limitations, the unscented transformation (UT) was
developed as a method to propagate mean and covariance
information through nonlinear transformations. Kalman filter that
uses UT for calculation of the first two statistical moments is called
Unscented Kalman Filter (UKF). Square-root form of UKF (SRUKF)
developed by Rudolph van der Merwe and Eric Wan to
achieve numerical stability and guarantee positive semi-definiteness
of the Kalman filter covariances. This paper develops another
implementation of SR-UKF for sequential update measurement
equation, and also derives a new UD covariance factorization filter
for the implementation of UKF. This filter is equivalent to UKF but
is computationally more efficient.
Abstract: This paper introduces a new signal denoising based on the Empirical mode decomposition (EMD) framework. The method is a fully data driven approach. Noisy signal is decomposed adaptively into oscillatory components called Intrinsic mode functions (IMFs) by means of a process called sifting. The EMD denoising involves filtering or thresholding each IMF and reconstructs the estimated signal using the processed IMFs. The EMD can be combined with a filtering approach or with nonlinear transformation. In this work the Savitzky-Golay filter and shoftthresholding are investigated. For thresholding, IMF samples are shrinked or scaled below a threshold value. The standard deviation of the noise is estimated for every IMF. The threshold is derived for the Gaussian white noise. The method is tested on simulated and real data and compared with averaging, median and wavelet approaches.
Abstract: Convergence of power series solutions for a class of
non-linear Abel type equations, including an equation that arises
in nonlinear cooling of semi-infinite rods, is very slow inside their
small radius of convergence. Beyond that the corresponding power
series are wildly divergent. Implementation of nonlinear sequence
transformation allow effortless evaluation of these power series on
very large intervals..
Abstract: Recent research result has shown that two multidelay
feedback systems can synchronize each other under different
schemes, i.e. lag, projective-lag, anticipating, or projectiveanticipating
synchronization. There, the driving signal is significantly
complex due that it is constituted by multiple nonlinear transformations
of delayed state variable. In this paper, a secure communication
model is proposed based on synchronization of coupled multidelay
feedback systems, in which the plain signal is mixed with a complex
signal at the transmitter side and it is precisely retrieved at the receiver
side. The effectiveness of the proposed model is demonstrated and
verified in the specific example, where the message signal is masked
directly by the complex signal and security is examined under the
breaking method of power spectrum analysis.