Effect of linear image processing on the depth of correlation in micro PIV

This work investigates the effect of selected linear image processing methods on the depth of correlation (DoC) in micro particle image velocimetry using a single camera. In practice, band-pass and high-pass filters (background subtraction) are commonly applied to micro particle image velocimetry images. This work provides analytical models describing the effect of the parameters of low-, high-, and band-pass filters on the DoC and verifies the models by experiments. Furthermore, we propose a scheme that allows computing the weighting function and DoC for more complicated cases numerically.     

Improvement of measurement accuracy in micro PIV by image overlapping

Micro PIV uses volume illumination; therefore, the velocity measured at the focal plane is a weighted average of the velocities within the measurement volume. The contribution of out-of-focus particles to the PIV correlation can generate significant measurement errors particularly in near wall regions. We present a new application of image overlapping, which is shown to be very effective in improving the accuracy of time-averaged velocity measurements by effectively reducing the measurement depth. The performance of image overlapping and correlation averaging were studied using synthetic and experimental images of micro channel flow, both with and without image pre-processing. The results show that for flows without particle clumping, image overlapping provides the best measurement accuracy without any need for image pre-processing. For flows with particle clumping, image overlapping combined with band-pass filtering provides the best measurement accuracy. When overlapped images are saturated with particles due to a large number of image pairs, image overlapping measurement still does not show any visible pixel-locking effect. Image overlapping was found to have comparable or slightly reduced pixel-locking effects compared to correlation averaging. In addition, image overlapping utilizes significantly fewer computational resources than the other techniques.     

Volumetric correlation PIV: a new technique for 3D velocity vector field measurement

A method is proposed that allows three-dimensional (3D) two-component measurements to be made by means of particle image velocimetry (PIV) in any volume illuminated over a finite thickness. The method is based on decomposing the cross-correlation function into various contributions at different depths. Because the technique is based on 3D decomposition of the correlation function and not reconstruction of particle images, there is no limit to particle seeding density as experienced by 3D particle tracking algorithms such as defocusing PIV and tomographic PIV. Correlations from different depths are differentiated by the variation in point spread function of the lens used to image the measurement volume over that range of depths. A number of examples are demonstrated by use of synthetic images which simulate micro-PIV (μPIV) experiments. These examples vary from the trivial case of Couette flow (linear variation of one velocity component over depth) to a general case where both velocity components vary by different complex functions over the depth. A final validation—the measurement of a parabolic velocity profile over the depth of a microchannel flow—is presented. The same method could also be applied using a thick light sheet in macro-scale PIV and in a stereo configuration for 3D three-component PIV.     

Effects of particle migration on suspension flow in a hydraulic fracture

An asymptotic model of a hydraulic-fracture flow of a sedimenting concentrated suspension is formulated on the basis of the two-fluid approach with account of transverse particle migration. In the thin-layer approximation, a two-dimensional system of equations averaged across the fracture is constructed with account for a nonuniform distribution of the particle concentration. As compared to the similar model without particle migration, the averaged two-dimensional equations contain modified coefficients which explicitly depend on the width of the flow core occupied by the particles. Using the model constructed, a numerical simulation is performed, which shows that the particle migration towards the fracture center results in the increase in the depth of particle penetration into the fracture and the suppression of gravitational convection in the vicinity of the leading front. The calculations are compared with available experimental data and an analytical formula for the height of the dense packed sediment. A good agreement between the analytical theory, the experiments, and the two-dimensional calculations is attained.     

Phase correlation processing for DPIV measurements

A novel digital particle image velocimetry (DPIV) correlation method is presented, the Gaussian transformed phase correlation (GTPC) estimator, using nonlinear filtering techniques coupled with the phase-transform (PHAT) generalized cross-correlation filter. The use of spatial windowing is shown to be ideally suited for the use of phase correlation estimators, due to their invariance to the loss of correlation effects. Error analysis demonstrates the increased valid vector detection and measurement accuracy of the windowed GTPC over the traditional Fourier based estimator in a series of uniform displacement Monte Carlo simulations. Analysis of the GTPC performance in the PIV standard image sets shows error reductions on the order of 15–45% over the range of simulations. Experimental DPIV images from a turbulent rib roughened channel flow are used to validate the use of the GTPC, which shows a strong reduction in peak locking effects, background noise errors, and erroneous vectors. Together, these results demonstrate the coupled benefits provided by the use of advanced filtering techniques applied to the phase correlation estimator. With the correct implementation of these filters, the GTPC is able to provide substantial improvements to the robustness of DPIV estimation.     

抗差自适应插值粒子滤波及其在组合导航中的应用

针对粒子滤波存在的粒子退化和重要性密度函数难以选取的问题,在吸收抗差自适应滤波、二阶插值滤波和粒子滤波算法优点的基础上,提出了一种新的抗差自适应插值粒子滤波算法。该算法利用二阶插值滤波算法得到重要性密度函数,通过抗差自适应因子实时控制动力学模型误差及观测异常对导航解的影响。将该算法应用于SINS/CNS/SAR组合导航系统进行计算仿真,并与经典的粒子滤波算法进行比较分析。结果表明,提出的滤波算法得到的姿态误差控制在[-0.3′,+0.3′],速度误差控制在[-0.4 m/s,+0.4 m/s],位置误差控制在[-5 m,+5 m],性能明显优于经典的粒子滤波算法。新的滤波算法不但能够有效地抑制粒子退化,而且能够有效地控制动力学模型误差及观测异常的影响,提高了组合导航的滤波精度。     

Vision-based measurement of spatio-temporal deformation of excavated soil for the estimation of bucket resistive force

This paper reports a vision-based technique of measuring the spatio-temporal deformation of excavated soil for estimating the bucket resistive force. The proposed measurement technique uses two depth cameras to determine three-dimensional soil-surface displacement. The technique consists of the following two processes: the first is related to image correlation between the two cameras, and the second involves data filtering and smoothing for generating soil deformation as a continuously curved surface. The proposed technique delivers measurement accuracy to the nearest centimeter. Typical experimental results of the three-dimensional measurement of soil deformation using the proposed technique are presented in the paper. Further, this study updates an interaction model for the resistive-force estimation while a bucket excavates soil. The model introduces a correction variable that changes with the bucket wrist angle by exploiting the experimental measurement of soil deformation. The model estimates the resistive force with an error of less than one quarter of the maximum force. These updates also exhibit the effectiveness of the proposed technique.     

Particle imaging techniques for microfabricated fluidic systems

This paper presents the design and implementation of velocimetry techniques applicable to the analysis of microfluidic systems. The application of both micron-resolution particle image velocimetry (micro-PIV) and particle tracking velocimetry (PTV) to the measurement of velocity fields within micromachined fluidic channels is presented. The particle tracking system uses epifluorescent microscopy, CCD imaging, and specialized image interrogation algorithms to provide microscale velocity measurement resolution. The flow field in a straight channel section is measured using cross-correlation micro-PIV and compared to the analytical solution for a measured mass flow rate. Velocity field measurements of the flow at the intersection of a cross-channel are also presented and compared with simulations from a commercially available flow solver, CFD-ACE+. Discussions regarding flow seeding, imaging optics, and the flow setup for measuring flows in microfabricated fluidic devices are presented. A simple process for estimating measurement uncertainty of the in-plane velocity measurements caused by three-dimensional Brownian motion is described. A definition for the measurement depth for PTV measurements is proposed. The agreement between measured and predicted values lends further support to the argument that liquid microflows with characteristic dimensions of order 50-μm dimension channels follow macroscale flow theory.     

Deep field noise in holographic particle image velocimetry (HPIV): numerical and experimental particle image field modelling

 Holographic recording overcomes the limits in 2-D particle image velocimetry (PIV) to cover a 3-D flow field volume. Interrogation by focusing on single planes in a reconstructed particle field is disturbed by noise from out-of-focus particles. A numerical simulation models image reconstruction and shows how validation rates depend on aperture and volume depth. An experimental model environment of scattering particles in moveable plastic slices gives support to the numerical results. Simulations and tests are carried out for interrogation by autocorrelation and crosscorrelation techniques and furnish guidelines for system design. Received: 27 December 1996 / Accepted: 14 August 1997     

权值自适应调整Unscented粒子滤波及其在组合导航中的应用

针对粒子滤波存在的重要性密度函数难以选取和粒子退化问题,提出了一种新的权值自适应调整Unscented粒子滤波算法。该算法在Unscented粒子滤波的采样过程中吸收权值自适应调整的优点,考虑最新量测影响,通过欧氏距离和反映量测噪声统计特性的精度因子来自适应的调整粒子对应权值分布,增加有用粒子的权值,降低粒子退化程度,保持粒子多样性。同时Unscented变换提高了滤波精度,使该算法能更好地适用于非线性、非高斯系统模型的计算。将提出的算法应用于GPS/DR组合导航系统进行仿真验证,结果表明,提出的权值自适应调整Unscented粒子滤波算法得到的东向定位误差控制在±5.5 m附近,北向定位误差则在±5.2 m附近,滤波性能明显优于扩展卡尔曼滤波和Unscented粒子滤波,能提高GPS/DR组合导航系统解算精度。     

On the effect of particle image intensity and image preprocessing on the depth of correlation in micro-PIV

The depth of correlation (DOC) is an experimental parameter, introduced to quantify the thickness of the measurement volume and thus the depth resolution in microscopic particle image velocimetry (μPIV). The theory developed to estimate the value of the DOC relies on some approximations that are not always verified in actual experiments, such as a single thin-lens optical system. In many practical μPIV experiments, a deviation of the actual DOC from its nominal value can be expected, due for instance to additional components present in the optical path of the microscope or to the use of image preprocessing before the PIV evaluation. In the presented paper, the effect of real particle image intensity distribution and image preprocessing on the thickness of the measurement volume is investigated. This is performed studying the defocusing of tracer particles and the DOC-related bias error present in μPIV measurements in a Poiseuille flow. The analysis shows that the DOC predicted using the conventional formulas can be significantly smaller than its actual value. To overcome this problem, the use of an effective NA determined experimentally from the curvature of the image autocorrelations is proposed. The accuracy of this approach to properly predict the actual size of DOC is discussed and validated on the experimental data. The effectiveness of image preprocessing to reduce the DOC-related bias error is tested and discussed as well.     

激光捷联惯导系统/地形辅助导航系统中卡尔曼/粒子组合滤波算法设计及仿真

粒子滤波技术是近几年出现的一种非线性滤波技术，它适用于非线性系统以及非高斯噪声模型。结合粒子滤波和卡尔曼滤波各自的优点，给出了一种卡尔曼／粒子组合滤波器，并将这种滤波器应用到激光捷联惯导（LSINS）／地形辅助导航（TAN）数据融合过程中，避免了地形复杂的线性化问题。仿真结果表明，系统的定位精度得到了明显提高。应用粒子滤波器及其改进算法解决了导航系统中存在的强非线性问题。     

New tracking algorithm for particle image velocimetry

The cross correlation tracking technique is widely used to analyze image data, in Particle Image Velocimetry (PIV). The technique assumes that the fluid motion, within small regions of the flow field, is parallel over short time intervals. However, actual flow fields may have some distorted motion, such as rotation, shear and expansion. Therefore, if the distortion of the flow field is not negligible, the fluid motion can not be tracked well using the cross correlation technique. In this study, a new algorithm for particle tracking, called the Spring Model technique, has been proposed. The algorithm can be applied to flow fields which exhibit characteristics such as rotation, shear and expansion.The algorithm is based on pattern matching of particle clusters between the first and second image. A particle cluster is composed of particles which are assumed to be connected by invisible elastic springs. Depending on the deformation of the cluster pattern (i.e., the particle positions), the invisible springs have some forces. The smallest force pattern in the second image is the most probable pattern match to the correspondent original pattern in the first image. Therefore, by finding the best matches, particle movements can be tracked between the two images. Three-dimensional flow fields can also be reconstructed with this technique.The effectiveness of the Spring Model technique was verified with synthetic data from both a two-dimensional flow and three-dimensional flow. It showed a high degree of accuracy, even for the three-dimensional calculation. The experimental data from a vortex flow field in a cylinder wake was also measured by the Spring model technique.     

ANALYTICAL MODEL OF CERAMIC/METAL ARMOR IMPACTED BY DEFORMABLE PROJECTILE

A new analytical model was established to describe the complex behavior of ceramic/metal armor under impact of deformable projectile by assuming some hypotheses. Three aspects were taken into account: the mushrooming deformation of the projectile, the fragment of ceramic tile and the formation and change of ceramic conoid and the deformation of the metal backup plate. Solving the set of equations, all the variables were obtained for the different impact velocities: the extent and particle velocity in rigid zone; the extent, cross-section area and particle velocity in plastic zone; the velocity and depth of penetration of projectile to the target; the reduction in volume and compressive strength of the fractured ceramic conoid; the displacement and movement velocity of the effective zone of backup plate. Agreement observed among analytical result, numerical simulation and experimental result confirms the validity of the model, suggesting the model developed can be a useful tool for ceramic/metal armor design.     

The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings

 This paper describes how the accuracy for estimating the location of the displacement-correlation peak in (digital) particle image velocimetry (PIV) can be optimized by the use of a window offset equal to the integer-pixel displacement. The method works for both cross-correlation analysis of single-exposure image pairs and multiple-exposure images. The effect is predicted by an analytical model for the statistical properties of estimators for the displacement, and it is observed in the analysis of synthetic PIV images of isotropic turbulence, and in actual measurements of grid-generated turbulence and of fully-developed turbulent pipe flow. Received: 29 April 1996/Accepted: 29 October 1996     

Measurement of instantaneous Eulerian acceleration fields by particle image accelerometry: method and accuracy

Acceleration is a fundamental quantity in fluid mechanics because it reflects the sum of all forces (pressure and viscous) present within the flow. However, measurements of acceleration have been difficult to achieve relative to the ease with which fluid velocity can be measured. A particle image accelerometer (PIA) has been developed to measure Eulerian acceleration fields by time-differencing successive measurements of the Eulerian velocity field as measured by particle image velocimetry (PIV). The measurements can also be made in uniformly translating frames. With current video camera technology, it is often not possible to measure the two velocity fields with a time separation sufficiently small enough to permit accurate finite difference approximation of the time derivative. A two-CCD-camera system has been developed to alleviate this limitation. Polarization filtering is utilized to separate the particle images viewed by each camera. The polarization filtering is achieved using cross-polarized light-sheets and a polarization filter just upstream of the imaging optics of the cameras. In this manner, PIV measurements can be achieved easily at time delays several orders of magnitude smaller than the shutter-time of the CCD cameras. The accuracy of the acceleration measurements is determined by numerical finite differencing errors and random noise and bias errors associated with the measurement of velocity. These errors, and methods of compensating for them, are studied.     

Accuracy of correlation-based image registration for pressure-sensitive paint

The accuracy of correlation-based image registration (CBIR) in the analysis of pressure-sensitive paints (PSP) was investigated. CBIR has been developed to perform accurate image registration without the need for control points, even for model motions containing nonlinear local deformations. In the present study, the influence of displacement errors and their sensitivity on the accuracy of pressure measurement was examined by uncertainty analysis. The error sources in image registration were classified and several factors affecting the accuracy of image registration were examined. The performances of image registration were evaluated under several artificial model motions. Local intensity variations due to speckles, which enhance the image correlation in CBIR, may act as a source of image noise. The local pressure sensitivity in the presence and absence of speckles was investigated through pixel-by-pixel calibration. A spatial filtering was employed to reduce the local intensity variations. It was found that application of a median filter decreased the fluctuations in the local pressure sensitivity and significantly reduced the sensitivity of the intensity error to misregistration.     

混合粒子联邦滤波在多信息组合导航系统中的应用

在组合导航多信息滤波系统的应用中,会遇到部分子滤波器为非线性系统的情况。提出了一种混合粒子联邦滤波方法,把高斯粒子滤波获取多维高斯分布的计算过程融入到联邦卡尔曼滤波结构框架中,并采用该滤波框架解决混合系统的多信息融合问题,该算法在滤波模型的适应性方面要优于传统的联邦滤波。以组合导航多信息融合问题为例,建立了混合粒子联邦滤波模型,对该算法进行了仿真,仿真结果验证了混合粒子联邦滤波的有效性。     

Development of Gas-Particle Euler-Euler LES Approach: A Priori Analysis of Particle Sub-Grid Models in Homogeneous Isotropic Turbulence

A new large eddy simulation (LES) approach for particle-laden turbulent flows in the framework of the Eulerian formalism for inertial particle statistical modelling is developed. Local instantaneous Eulerian equations for the particle cloud are first written using the mesoscopic Eulerian formalism (MEF) proposed by Février et al. (J Fluid Mech 533:1–46, 2005), which accounts for the contribution of an uncorrelated velocity component for inertial particles with relaxation time larger than the Kolmogorov time scale. Second, particle LES equations are obtained by volume filtering the mesoscopic Eulerian ones. In such an approach, the particulate flow at larger scales than the filter width is recovered while sub-grid effects need to be modelled. Particle eddy-viscosity, scale similarity and mixed sub-grid stress (SGS) models derived from fluid compressible turbulence SGS models are presented. Evaluation of such models is performed using three sets of particle Lagrangian results computed from discrete particle simulation (DPS) coupled with fluid direct numerical simulation (DNS) of homogeneous isotropic decaying turbulence. The two phase flow regime corresponds to the dilute one where two-way coupling and inter-particle collisions are not considered. The different particle Stokes number (based on Kolmogorov time scale) are initially equal to 1, 2.2 and 5.1. The mesoscopic field properties are analysed in detail by considering the particle velocity probability function (PDF), correlated velocity power spectra and random uncorrelated velocity moments. The mesoscopic fields measured from DPS+DNS are then filtered to obtain large scale fields. A priori evaluation of particle sub-grid stress models gives comparable agreement than for fluid compressible turbulence models. It has been found that the standard Smagorinsky eddy-viscosity model exhibits the smaller correlation coefficients, the scale similarity model shows very good correlation coefficient but strongly underestimates the sub-grid dissipation and the mixed model is on the whole superior to pure eddy-viscosity model.     

粒子滤波及其在导航系统中的应用综述

传统的扩展卡尔曼滤波方法要求对非线性系统近似线性化,有可能会引入较大的模型误差.应用粒子滤波解决了这一问题.该算法可以直接应用于原系统的非线性模型当中,并且不需考虑系统噪声和量测噪声是否为高斯白噪声,都能得到很好的滤波效果.文中介绍了粒子滤波的理论基础-贝叶斯估计及具体的实现方式-蒙特卡罗方法;指出粒子滤波存在的退化问题,并从减小退化现象入手将重要性采样和再采样方法引入到算法之中;最后阐述了粒子滤波在导航系统中的一些应用.