The confidence limit is a standard measure of the accuracy of the result in any statistical analysis. Most of the confidence limits are derived as follows. The data are first divided into subsections and then, under the ergodic assumption, the temporal mean is substituted for the ensemble mean. Next, the confidence limit is defined as a range of standard deviations from this mean. However, such a confidence limit is valid only for linear and stationary processes. Furthermore, in order for the ergodic assumption to be valid, the subsections have to be statistically independent. For non‐stationary and nonlinear processes, such an analysis is no longer valid. The confidence limit of the method here termed EMD/HSA (for empirical mode decomposition/Hilbert spectral analysis) is introduced by using various adjustable stopping criteria in the sifting processes of the EMD step to generate a sample set of intrinsic mode functions (IMFs). The EMD technique acts as a pre‐processor for HSA on the original data, producing a set of components (IMFs) from the original data that equal the original data when added back together. Each IMF represents a scale in the data, from smallest to largest. The ensemble mean and standard deviation of the IMF sample sets obtained with different stopping criteria are calculated, and these form a simple random sample set. The confidence limit for EMD/HSA is then defined as a range of standard deviations from the ensemble mean. Without evoking the ergodic assumption, subdivision of the data stream into short sections is unnecessary; hence, the results and the confidence limit retain the full‐frequency resolution of the full dataset. This new confidence limit can be applied to the analysis of nonlinear and non‐stationary processes by these new techniques. Data from length‐of‐day measurements and a particularly violent recent earthquake are used to demonstrate how the confidence limit is obtained and applied. By providing a confidence limit for this new approach, a stable range of stopping criteria for the decomposition or sifting phase (EMD) has been established, making the results of the final processing with HSA, and the entire EMD/HSA method, more definitive.

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A confidence limit for the empirical mode decomposition and Hilbert spectral analysis

To improve the performance of particle image velocimetry in measuring instantaneous velocity fields, direct cross-correlation of image fields can be used in place of auto-correlation methods of interrogation of double- or multiple-exposure recordings. With improved speed of photographic recording and increased resolution of video array detectors, cross-correlation methods of interrogation of successive single-exposure frames can be used to measure the separation of pairs of particle images between successive frames. By knowing the extent of image shifting used in a multiple-exposure and by a priori knowledge of the mean flow-field, the cross-correlation of different sized interrogation spots with known separation can be optimized in terms of spatial resolution, detection rate, accuracy and reliability.

Theory of cross-correlation analysis of PIV images : Image analysis as measuring technique in flows

Two circular cylinders in cross-flow: A review

Instantaneous frequency (IF) is necessary for understanding the detailed mechanisms for nonlinear and nonstationary processes. Historically, IF was computed from analytic signal (AS) through the Hilbert transform. This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing IF. The first approach is to compute the quadrature (defined here as a simple 90° shift of phase angle) directly. The second approach is designated as the normalized Hilbert transform (NHT), which consists of applying the Hilbert transform to the empirically determined FM signals. Additionally, we have also introduced alternative methods to compute local frequency, the generalized zero-crossing (GZC), and the teager energy operator (TEO) methods. Through careful comparisons, we found that the NHT and direct quadrature gave the best overall performance. While the TEO method is the most localized, it is limited to data from linear processes, the GZC method is the m...

/pdf/on-instantaneous-frequency-2cyyzahk31.pdf

On instantaneous frequency

random data analysis and measurement procedures is available in our digital library an online access to it is set as public so you can get it instantly. Our book servers spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the random data analysis and measurement procedures is universally compatible with any devices to read.

Random Data Analysis And Measurement Procedures

Wind driven natural ventilation through multiple windows of a building: A computational approach

In this study spanwise correlation measurements and smoke flow visualization were performed on vortex shedding behind a normal plate. For Reynolds numbers in a range between 1800 and 27000, the hot-wire signals measured were analysed by a wavelet transformation, from which the instantaneous properties of vortex shedding were obtained and examined. Results show that the phase difference of vortex shedding detected at two spanwise locations, separated by twice the characteristic length, can be as high as 35. A correlation analysis further shows that large spanwise phase differences occur when small fluctuating amplitudes in the vortex shedding signals are measured. Smoke-wire visualization performed at Reynolds number 1800 indicates that the formation of shedding vortex can be divided into two distinct situations, namely, one featuring a long formation region, called Mode L; and the other featuring a short formation region, called Mode S. In Mode S, the three-dimensionality of vortex formation appears to be very pronounced, and the secondary vortices are clearly present in the separated shear layer. The events of Mode S occupy less than 5% of the total time measured, and are called the burst events in this study.

On low-frequency modulations and three-dimensionality in vortex shedding behind a normal plate

Experiments were performed for individual reali- zations of the vortex shedding process behind a circular disk at Reynolds numbers of 103—105, at which periodic vortex shedding prevails in the wake. The phase differences regarding the individual vortex shedding structures detected at multiple circumferential locations in the wake were obtained by analyzing the hot-wire signals with a conditional-sampling scheme. The phase differences of vortex shedding detected at circumferential positions 90i apart show a wide scatter, but the anti-phase character is largely preserved in the individual vortex shedding process as detected at circumferential loca- tions 180i apart. The randomness of phase differences involved in the vortex shedding process is noted to be essential in order to satisfy the axisymmetric property of the global flow.

On vortex shedding behind a circular disk

Control of separated flow behind a backward-facing step using a two-dimensional oscillating fence installed upstream has been investigated in this work. Parameters of the flow considered included the reduced frequency of the oscillating fence, the distance from the oscillating to the backward-facing step, the ratio of the maximum height of the oscillating fence to the step height, and the Reynolds number. It was found that with the experimental parameters properly selected the time-mean reattachment length of the separation region could be reduced over 40%, compared to the case without the presence of an oscillating fence. The evolution of unsteady flow behind a backward-facing step was further studied in detail by a phase-averaging measurement technique. The results obtained indicate that suppression of the separated flow behind the step is mainly due to the downwash motion induced by the vortical structure released upstream from the oscillating fence, when it convects over the step.

Control of separated flow by a two-dimensional oscillating fence

The characteristics of flow developments above 50-deg sweep delta wings with different leading-edge profiles are shown by flow visualizations and velocity measurements. The Reynolds number based on freestream velocity and root chord is about 7 x 103. The leading-edge profiles studied include the shapes of square, round, windward surface beveling, leeward surface beveling, and wedge. Based on the velocity data obtained along the leading edges of the delta wings it is noted that the flow angles associated with the separated shear layers vary with the leading-edge profiles studied. This finding infers that varying the leading-edge profile has an impact on the initial development of the separated shear layer, consequently, the formation of leading-edge vortex. Furthermore, it is shown that the leading edge of windward beveling causes the largest leading-edge flow angle and produces the most organized leading-edge vortex.

Jiun-Jih Miau

Papers

Wind driven natural ventilation through multiple windows of a building: A computational approach

On low-frequency modulations and three-dimensionality in vortex shedding behind a normal plate

On vortex shedding behind a circular disk

Control of separated flow by a two-dimensional oscillating fence

Flow developments above 50-deg sweep delta wings with different leading-edge profiles