Design Method of High-Order Kalman Filter for Strong Nonlinear System Based on Kronecker Product Transform

In this paper, a novel design idea of high-order Kalman filter based on Kronecker product transform is proposed for a class of strong nonlinear stochastic dynamic systems. Firstly, those augmenting systems are modeled with help of the Kronecker product without system noise. Secondly, the augmented system errors are illustratively charactered by Gaussian white noise. Thirdly, at the expanded space a creative high-order Kalman filter is delicately designed, which consists of high-order Taylor expansion, introducing magical intermediate variables, representing linear systems converted from strongly nonlinear systems, designing Kalman filter, etc. The performance of the proposed filter will be much better than one of EKF, because it uses more information than EKF. Finally, its promise is verified through commonly used digital simulation examples.

Component-scaled signal reconstruction for enhanced noise filtration

This research introduces a procedure for signal denoising based on linear combinations of intrinsic mode functions (IMFs) extracted using empirical mode decomposition (EMD). The method, termed component-scaled signal reconstruction, employs the standard EMD algorithm, with no enhancements to decompose the signal into a set of IMFs. The problem of mode mixing is leveraged for noise removal by constructing an optimal linear combination of the potentially mixed IMFs. The optimal linear combination is determined using an optimization routine with an objective function that maximizes and minimizes the information and noise, respectively, in the denoised signal. The method is demonstrated by applying it to a computer-generated voice sample and the displacement response of a cantilever beam with local stiffness nonlinearity. In the first application, the noise is introduced into the sample manually by adding a Gaussian white-noise signal to the signal. In the second application, the response of the entire beam is filmed using two 1-megapixel cameras, and the three-dimensional displacement field is extracted using digital image correlation. The noise in this application arises entirely from the images captured. The proposed method is compared to existing EMD, ensemble EMD, and LMD based denoising approaches and is found to perform better.

Toward Real-time Microseismic Event Detection using the YOLOv3 Algorithm

Real-time microseismic monitoring is essential for understanding fractures associated with underground fluid injection in unconventional reservoirs. However, microseismic events recorded on monitoring arrays are usually contaminated with strong noise. With a low signal-to-noise ratio (S/R), the detection of microseismic events is challenging using conventional detection methods such as the short-term average/long-term average (STA/LTA) technique. Common machine learning methods, e.g., feature extraction plus support vector machine (SVM) and convolutional neural networks (CNNs), can achieve higher accuracy with strong noise, but they are usually time-consuming and memory-intensive to run. We propose the use of YOLOv3, a state-of-art real-time object detection system in microseismic event detection. YOLOv3 is a one-stage deep CNN detector that predicts class confidence and bounding boxes for images at high speed and with great precision. With pre-trained weights from the ImageNet 1000-class competition dataset, physics-based training of the YOLOv3 algorithm is performed on a group of forward modeled synthetic microseismic data with varying S/R. We also add randomized forward-modeled surface seismic events and Gaussian white noise to generate ``semi-realistic'' training and testing datasets. YOLOv3 is able to detect weaker microseismic event signals with low signal-to-noise ratios (e.g., S/N=0.1) and achieves a mean average precision of 88.71\% in near real time. Further work is required to test YOLOv3 in field production settings.

Research and application of tristable stochastic resonance based on harmonic and pinning potential model

In view of the unique potential barrier and complex potential function of the pining model, as well as the lack of researches on two-dimensional stochastic resonance, two new potential tristable models are proposed: one-dimensional tristable model and two-dimensional tristable model. The stochastic resonance mechanism and application of two potential systems under Gaussian white noise and weak external driving force are discussed and the differences and advantages of the two systems are analyzed in detail for the first time. First, the potential function and mean first passage time are analyzed. Second, according to the linear response theory, the probability flow method is used to calculate the spectral amplification. The effects of system parameters on spectral amplification of the two models are studied, and the two models are compared. Finally, the two models are applied to the detection of actual bearing fault signals together with the classical tristable system and the performance is compared. Both algorithms can detect fault signals effectively, but the two-dimensional model has better amplitude and difference, and the one-dimensional model has less interference burrs. The theoretical basis and reference value of the system are provided for further application in practical engineering testing.

Frequency transfer of the ventriloquism aftereffect

The ventriloquism aftereffect (VAE) describes the persistent shift of perceived sound location after having been adapted to a ventriloquism condition, in which the sound was repeatedly paired with a displaced visual stimulus. In the latter case, participants consistently mislocalize the sound in the direction of the visual stimulus (ventriloquism effect, VE). Previous studies provide conflicting reports regarding the strength of the VAE, ranging from 0 to nearly 100%. Moreover, there is controversy about its generalization to different sounds than the one inducing the VE, ranging from no transfer at all, to full transfer across different sound spectra. Here, we imposed the VE for three different sounds: a low-frequency and a high-frequency narrow-band noise, and a broadband Gaussian white noise (GWN). In the adaptation phase, listeners generated fast goal-directed head movements to localize the sound, presented across a 70 deg range in the horizontal plane, while ignoring a visual distracter that was consistently displaced 10 deg to the right of the sound. In the post-adaptation phase, participants localized narrow-band sounds with center frequencies from 0.5 to 8 kHz, as well as GWN, without the visual distracter. Our results show that the VAE amounted to approximately 40% of the VE and generalized well across the entire frequency domain. We also found that the strength of the VAE correlated with the pre-adaptation sound-localization performance. We compare our results with previous reports and discuss different hypotheses regarding optimal audio-visual cue integration.

Three-dimensional tomographically reconstructed optical emission profiles of Hall thruster plasmas

A diagnostic system was developed for spectrally resolved, three-dimensional tomographic reconstruction of Hall thruster plasmas, and local intensity profiles of Xe I and Xe II emissions were reconstructed. In this diagnostic system, 28 virtual cameras were generated using a single, fixed charge-coupled device (CCD) camera by rotating the Hall thruster to form a sufficient number of lines of sight. The Phillips-Tikhonov regularization algorithm was used to reconstruct local emission profiles from the line-integrated emission signals. The reconstruction performance was evaluated using both azimuthally symmetric and asymmetric synthetic phantom images including 5% Gaussian white noise, which resulted in a root-mean-square error of the reconstruction within an order of 10-3 even for a 1% difference in the azimuthal intensity distribution. Using the developed system, three-dimensional local profiles of Xe II emission (541.9 nm) from radiative decay of the excited state 5p4(3P2)6p2[3]˚5/2 and Xe I emission (881.9 nm) from 5p5(2P˚3/2)6p2[5/2]3 were obtained, and two different shapes were found depending on the wavelength and the distance from the thruster exit plane. In particular, a stretched central jet structure was distinctively observed in the Xe II emission profile beyond 10 mm from the thruster exit, while gradual broadening was found in the Xe I emission. Approximately 10% azimuthal nonuniformities were observed in the local Xe I and Xe II intensity profiles in the near-plume region (< 10 mm), which could not be quantitatively distinguished by analysis of the frontal photographic image. Three-dimensional Xe I and Xe II intensity profiles were also obtained in the plume region, and the differences in the structures of both emissions were visually confirmed.

Lévy noise-induced self-induced stochastic resonance in a memristive neuron

All previous studies on self-induced stochastic resonance (SISR) in neural systems have only considered the idealized Gaussian white noise. Moreover, these studies have ignored one electrophysiological aspect of the nerve cell: its memristive properties. In this paper, first, we show that in the excitable regime, the asymptotic matching of the deterministic timescale and mean escape timescale of an $$\alpha $$ α -stable Lévy process (with value increasing as a power $$\sigma ^{-\alpha }$$ σ - α of the noise amplitude $$\sigma $$ σ , unlike the mean escape timescale of a Gaussian process which increases as in Kramers’ law) can also induce a strong SISR. In addition, it is shown that the degree of SISR induced by Lévy noise is not always higher than that of Gaussian noise. Second, we show that, for both types of noises, the two memristive properties of the neuron have opposite effects on the degree of SISR: the stronger the feedback gain parameter that controls the modulation of the membrane potential with the magnetic flux and the weaker the feedback gain parameter that controls the saturation of the magnetic flux, the higher the degree of SISR. Finally, we show that, for both types of noises, the degree of SISR in the memristive neuron is always higher than in the non-memristive neuron. Our results could guide hardware implementations of neuromorphic silicon circuits operating in noisy regimes.

A Novel Feature-Based Detector for Underwater Acoustic Beacon Signals Using Superimposed Envelope Spectrum of Multi-Pulses

For tackling the challenge of in-time searching a sea-crashed plane, it is critical to develop a convenient and reliable detector for the underwater beacon signal. In the application of signal detection, a conventional detector such as linear correlation (LC) is used based on the assumption of Gaussian white noise, but it has turned out to be a poor choice in a sophisticated underwater environment. To address this issue, a novel feature-based detector using superimposed envelope spectrum (SES) of multi-pulses is proposed in this paper. The proposed detector firstly extracts the envelopes of the received multi-pulse signals and superimposes the envelopes according to the known period. Then, the harmonic features of the SES are derived and utilized in the feature judgment to make the final decision. The proposed method is evaluated together with several existing state-of-the-art detectors, including the matched filter (MF), the generalized likelihood ratio test (GRLT) detector, and the periodogram of the directly dislocation superposition (PDDS) detectors with constant false alarm probability. Compared with the conventional detectors, it is found that the proposed SES detector is more robust against the colored noise, the random phase, and the channel distortions caused by the sophisticated underwater environment. Simulation results show that, given a detection probability value of 90% and a false alarm probability value of 1%, the proposed detector shows a gain of 3–12 dB compared with the best one of the MF, GRLT, and the PDDS detectors under distorted channels in terms of signal-to-noise ratio (SNR) requirements, respectively. Experimental results based on lake trial data have also verified the validity and feasibility of the proposed feature-based detector.

Novel anomalous diffusion phenomena of underdamped Langevin equation with random parameters

The diffusion behavior of particles moving in complex heterogeneous environment is a very topical issue. We characterize particle's trajectory via an underdamped Langevin system driven by a Gaussian white noise with a time dependent diffusivity of velocity, together with a random relaxation timescale $\tau$ to parameterize the effect of complex medium. We mainly concern how the random parameter $\tau$ influences the diffusion behavior and ergodic property of this Langevin system. Besides, the comparison between the fixed and random initial velocity $v_0$ is conducted to show the effect of different initial ensembles. The heavy-tailed distribution of $\tau$ with finite mean is found to suppress the decay rate of the velocity correlation function and promote the diffusion behavior, playing a competition role to the time dependent diffusivity. More interestingly, a random $v_0$ with a specific distribution depending on random $\tau$ also enhances the diffusion. Both the random parameters $\tau$ and $v_0$ influence the dynamics of the Langevin system in an non-obvious way, which cannot be ignored even they has finite moments.