Generalized Random Decrement Method for Analysis of Vibration Data

1998 ◽  
Vol 120 (3) ◽  
pp. 806-813 ◽  
Author(s):  
P. D. Spanos ◽  
B. A. Zeldin
Keyword(s):  
Correlation Function ◽  
Random Vibration ◽  
Gaussian Random Process ◽  
White Noise Process ◽  
Vibration Data ◽  
Auto Correlation ◽  
Random Decrement ◽  
Auto Correlation Function ◽  
Random Decrement Method ◽  
Theoretical Developments

The Random Decrement method used in system identification for analysis of random vibration data is considered from a rigorous mathematical perspective. It is shown that the Random Decrement signature deviates from the system free vibration curve of an associated linear system, unless the corresponding input excitation is white. The error induced by approximating the system excitation by a white noise process is examined. Further, a generalized Random Decrement signature is introduced; it is used to estimate efficiently the auto-correlation function of an ergodic Gaussian random process. Several examples are discussed to elucidate the theoretical developments.

Fast Detection of Chatter in End-Milling Using Pseudo Auto-Correlation Function

2012 ◽  
Vol 6 (6) ◽  
pp. 728-735 ◽  
Author(s):  
Kenji Shimana ◽  
◽  
Eiji Kondo ◽  
Hiroko Karashima ◽  
Norio Kawagoishi ◽  
...  
Keyword(s):  
Correlation Function ◽  
High Speed ◽  
End Milling ◽  
Machined Surface ◽  
Tool Vibration ◽  
Fast Detection ◽  
Vibration Data ◽  
Auto Correlation ◽  
Chatter Vibrations ◽  
Auto Correlation Function

The chatter vibrations cause problems, such as the reduction of tool life, tool fracture, and a deterioration in the quality of the machined surface. This paper presents a fast detection method for expected chatter in high-speed end-milling. In this study, a pseudo auto-correlation function is applied to tool vibration data sampled at intervals as the spindle rotated at a constant angle. The calculation time for the pseudo auto-correlation function is expected to be shorter than that of the FFT method. As a result, it was indicated that detection reliability under the proposed method was approximately equal to the detection reliability by the previous methods by using tool vibration data sampled at constant intervals of time.

scholarly journals New Orthogonal Small Set Kasami Code Sequence

2015 ◽  
Vol 14 (1) ◽  
Author(s):  
I Nyoman Pramaita ◽  
I G.A.G.K. Diafari ◽  
DNKP Negara ◽  
Agus Dharma
Keyword(s):  
Correlation Function ◽  
Cross Correlation ◽  
Code Sequence ◽  
Cross Correlation Function ◽  
Auto Correlation ◽  
M Sequence ◽  
Auto Correlation Function ◽  
Small Set

In this paper, the authors propose the design of a new orthogonal small set Kasami code sequence generated using combination of non-orthogonal m-sequence and small set Kasami code sequence. The authors demonstrate that the proposed code sequence has comparable auto-correlation function (ACF), cross- correlation function (CCF), peak cross-correlation values with that of the existing orthogonal small set Kasami code sequence. Though the proposed code sequence has less code sequence sets than that of the existing orthogonal small set Kasami code sequence, the proposed code sequence possesses one more numbers of members in each code sequence set. The members of the same code set of the proposed code sequence are orthogonal to each other.

scholarly journals Mapping input noise to escape noise in integrate-and-fire neurons: a level-crossing approach

2021 ◽  
Author(s):  
Tilo Schwalger
Keyword(s):  
Correlation Function ◽  
Hazard Rate ◽  
Second Order ◽  
Level Crossing ◽  
Input Noise ◽  
Integrate And Fire ◽  
Auto Correlation ◽  
Auto Correlation Function ◽  
Decoupling Approximation ◽  
Crossing Theory

AbstractNoise in spiking neurons is commonly modeled by a noisy input current or by generating output spikes stochastically with a voltage-dependent hazard rate (“escape noise”). While input noise lends itself to modeling biophysical noise processes, the phenomenological escape noise is mathematically more tractable. Using the level-crossing theory for differentiable Gaussian processes, we derive an approximate mapping between colored input noise and escape noise in leaky integrate-and-fire neurons. This mapping requires the first-passage-time (FPT) density of an overdamped Brownian particle driven by colored noise with respect to an arbitrarily moving boundary. Starting from the Wiener–Rice series for the FPT density, we apply the second-order decoupling approximation of Stratonovich to the case of moving boundaries and derive a simplified hazard-rate representation that is local in time and numerically efficient. This simplification requires the calculation of the non-stationary auto-correlation function of the level-crossing process: For exponentially correlated input noise (Ornstein–Uhlenbeck process), we obtain an exact formula for the zero-lag auto-correlation as a function of noise parameters, mean membrane potential and its speed, as well as an exponential approximation of the full auto-correlation function. The theory well predicts the FPT and interspike interval densities as well as the population activities obtained from simulations with colored input noise and time-dependent stimulus or boundary. The agreement with simulations is strongly enhanced across the sub- and suprathreshold firing regime compared to a first-order decoupling approximation that neglects correlations between level crossings. The second-order approximation also improves upon a previously proposed theory in the subthreshold regime. Depending on a simplicity-accuracy trade-off, all considered approximations represent useful mappings from colored input noise to escape noise, enabling progress in the theory of neuronal population dynamics.

Generalized spot auto-focusing method with a high-definition auto-correlation function in transmission electron microscopy

Microscopy ◽  
2019 ◽  
Vol 68 (5) ◽  
pp. 395-412
Author(s):  
Shigeto Isakozawa ◽  
Misuzu Baba ◽  
Junpei Amano ◽  
Shohei Sakamoto ◽  
Norio Baba
Keyword(s):  
Correlation Function ◽  
Yeast Cell ◽  
Thin Section ◽  
High Definition ◽  
Auto Correlation ◽  
Transmission Electron ◽  
Wide Range ◽  
Auto Correlation Function ◽  
Spot Image ◽  
Auto Focusing

Abstract The spot auto-focusing (AF) method with a unique high-definition auto-correlation function (HD-ACF) proposed in the previous paper is improved and is now applicable to general specimens at a wide range of magnifications. According to the definition where the AF is defocused to obtain the highest resolution, the proposed method achieves the sharpest HD-ACF profile in the AF spot image. The relationship where the sharpest HD-ACF profile gives the highest resolution is theoretically explained, and practical AF examples for different specimens and magnifications are experimentally demonstrated. Specimens include a yeast cell thin section at 10-k magnification, a standard grating replica used as a ruler at 50-k, a crystal lattice of graphitized carbon at 400-k and a 60°-tilted thin section (yeast cell) at 10-k. Different procedures are prepared to actively identify the defocus position that gives the sharpest HD-ACF profile. Every AF result demonstrates the highest-resolution image.

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