A new tracking algorithm of PIV and removal of spurious vectors using Delaunay tessellation

 A new algorithm of Delaunay Tessellation Particle Tracking Velocimetry (DT-PTV in abbreviation) is proposed for tracking particles in images of a PIV system by making use of the Delaunay tessellation (DT). The algorithm is tested by using numerically simulated particle images. The calculation results based on DT are compared with those obtained by a conventional algorithm of Binary Image Cross-correlation method (BICC). The new algorithm shows higher performance of obtaining more identical particles in two consecutive images correctly with shorter computation time even if the images contain many particles. A further application of DT to elimination of spurious vectors is also discussed. Received: 24 November 1997/Accepted: 7 August 1998     

Efficient detection of spurious vectors in particle image velocimetry data

A statistical model is introduced that describes the occurence of spurious vectors in PIV data. This model is used to investigate the performance of three different post-interrogation procedures: the global-mean, the local-mean and the local-median test. The model is also used to optimize the performance of these procedures. Predicted performances agree very well with those obtained from an artificially generated PIV record. It is demonstrated that the detectability as the conventional measure for the reliability of a measured displacement vector is very inefficient, compared to the three tests described here. The local-median test has the highest efficiency.     

An artificial neural network for double exposure PIV image analysis

 This note presents a back propagation neural network for PIV image analysis. Unlike the conventional auto-correlation method that identifies one pair of image out of the picture, the proposed network distinguishes all the image pairs in the measurement area and provides different labels for each pair. Experimental investigations show good agreement with the auto-correlation process for the uniform flow measurement, and a 78.1% success ratio for the stagnation flow. Received: 9 January 1997/Accepted: 10 September 1997     

Navier–Stokes simulations in gappy PIV data

Velocity measurements conducted with particle image velocimetry (PIV) often exhibit regions where the flow motion cannot be evaluated. The principal reasons for this are the absence of seeding particles or limited optical access for illumination or imaging. Additional causes can be laser light reflections and unwanted out-of-focus effects. As a consequence, the velocity field measured with PIV contains regions where no velocity information is available, that is gaps. This work investigates the suitability of using the unsteady incompressible Navier–Stokes equations to obtain accurate estimates of the local transient velocity field in small gaps; the present approach applies to time-resolved two-dimensional experiments of incompressible flows. The numerics are based on a finite volume discretization with partitioned time-stepping to solve the governing equations. The measured velocity distribution at the gap boundary is taken as time-varying boundary condition, and an approximate initial condition inside the gap is obtained via low-order spatial interpolation of the velocity at the boundaries. The influence of this I.C. is seen to diminish over time, as information is convected through the gap. Due to the form of the equations, no initial or boundary conditions on the pressure are required. The approach is evaluated by a time-resolved experiment where the true solution is known a priori. The results are compared with a boundary interpolation approach. Finally, an application of the technique to an experiment with a gap of complex shape is presented.     

Application of an acoustic analogy to PIV data from rectangular cavity flows

The present paper describes a method to derive information about the acoustic emission of a flow using particle image velocimetry (PIV) data. The advantage of the method is that it allows studying sound sources, the related flow phenomena and their acoustic radiation into the far field, simultaneously. In a first step the time history of two-dimensional instantaneous pressure fields is derived from planar PIV data. In a successive step the Curle’s acoustic analogy is applied to the pressure data to obtain the acoustic radiation of the flow. The test cases studied here are two rectangular cavity flows at very low Mach number with different aspect ratios L/H. The main sound source is located at the cavity trailing edge and it is due to the impingement of vortices shed in the shear layer. It is shown that the flow emits sound with a main directivity in the upstream direction for the smaller aspect ratio and the directivity is more uniform for the larger aspect ratio. In the latter case the acoustic pressure spectra has a broader character due to the impact of the downstream recirculation zone onto the shear layer instabilities, destroying their regular pattern and alternating the main sound source.     

Correction for viewing angle applied to PIV data obtained in aerodynamic blade vortex interaction studies

The paper describes the corrections required to velocimetry data obtained in PIV studies where the illuminated light sheet is viewed obliquely. The condition where the mean flow is principally normal to the sheet is considered and the non-linear transformation equations required to obtain measurements derived. An example is presented where the viewing corrections were applied to images obtained in an aerodynamic blade-vortex-interaction study.The authors would like to acknowledge the support of the British Ministry of Defence, the Defence Research Agency (formerly RAE) and the Department of Industry. The help of Westland Helicopters, in particular T Beddes, during the design and execution of the experiment was appreciated. The authors would also like to thank Dr M Luttges and Dr M Robinson of the Department of Aerospace Engineering Sciences of the University of Colorado, Boulder for their support. The invaluable work of staff Mr M Horner (now University of Colorado) in the experimental program is also acknowledged.     

Physics-constrained bayesian neural network for fluid flow reconstruction with sparse and noisy data

In many applications, flow measurements are usually sparse and possibly noisy. The reconstruction of a high-resolution flow field from limited and imperfect flow information is significant yet challenging. In this work, we propose an innovative physics-constrained Bayesian deep learning approach to reconstruct flow fields from sparse, noisy velocity data, where equationbased constraints are imposed through the likelihood function and uncertainty of the reconstructed flow can be estimated. Specifically, a Bayesian deep neural network is trained on sparse measurement data to capture the flow field. In the meantime, the violation of physical laws will be penalized on a large number of spatiotemporal points where measurements are not available. A non-parametric variational inference approach is applied to enable efficient physicsconstrained Bayesian learning. Several test cases on idealized vascular flows with synthetic measurement data are studied to demonstrate the merit of the proposed method.     

Assessment of dual plane PIV measurements in wall turbulence using DNS data

Experimental dual plane particle image velocimetry (PIV) data are assessed using direct numerical simulation (DNS) data of a similar flow with the aim of studying the effect of averaging within the interrogation window. The primary reason for the use of dual plane PIV is that the entire velocity gradient tensor and hence the full vorticity vector can be obtained. One limitation of PIV is the limit on dynamic range, while DNS is typically limited by the Reynolds number of the flow. In this study, the DNS data are resolved more finely than the PIV data, and an averaging scheme is implemented on the DNS data of similar Reynolds number to compare the effects of averaging inherent to the present PIV technique. The effects of averaging on the RMS values of the velocity and vorticity are analyzed in order to estimate the percentage of turbulence intensity and enstrophy captured for a given PIV resolution in turbulent boundary layers. The focus is also to identify vortex core angle distributions, for which the two-dimensional and three-dimensional swirl strengths are used. The studies are performed in the logarithmic region of a turbulent boundary layer at z ⁺ = 110 from the wall. The dual plane PIV data are measured in a zero pressure gradient flow over a flat plate at Re _τ = 1,160, while the DNS data are extracted from a channel flow at Re _τ = 934. Representative plots at various wall-normal locations for the RMS values of velocity and vorticity indicate the attenuation of the variance with increasing filter size. Further, the effect of averaging on the vortex core angle statistics is negligible when compared with the raw DNS data. These results indicate that the present PIV technique is an accurate and reliable method for the purposes of statistical analysis and identification of vortex structures.     

Assessment of tomographic PIV in wall-bounded turbulence using direct numerical simulation data

Simulations of tomographic particle image velocimetry (Tomo-PIV) are performed using direct numerical simulation data of a channel flow at Reynolds number of Re _τ = 934, to investigate the influence of experimental parameters such as camera position, seeding density, interrogation volume size and spatial resolution. The simulations employ camera modelling, a Mie scattering illumination model, lens distortion effects and calibration to realistically model a tomographic experiment. Results are presented for camera position and orientation in three-dimensional space, to obtain an optimal reconstruction quality. Furthermore, a quantitative analysis is performed on the accuracy of first and second order flow statistics, at various voxel sizes normalised using the viscous inner length scale. This enables the result to be used as a general reference for wall-bounded turbulent experiments. In addition, a ratio relating seeding density and the interrogation volume size is proposed to obtain an optimal reference value that remains constant. This can be used to determine the required seeding density concentration for a certain interrogation volume size.     

Combined neural network and reduced FRF techniques for slight damage detection using measured response data

Summary  This paper deals with structural damage detection using measured frequency response functions (FRF) as input data to artificial neural networks (ANN). A major obstacle, the impracticality of using full-size FRF data with ANNs, was circumvented by applying a data-reduction technique based on principal component analysis (PCA). The compressed FRFs, represented by their projection onto the most significant principal components, were used as the ANN input variables instead of the raw FRF data. The output is a prediction of the actual state of the specimen, i.e. healthy or damaged. A further advantage of this particular approach is its ability to deal with relatively high measurement noise, which is a common occurrence when dealing with industrial structures. The methodology was applied to detect three different states of a space antenna: reference, slight mass damage and slight stiffness damage. About 600 FRF measurements, each with 1024 spectral points, were included in the analysis. Six 2-hidden layer networks, each with an individually-optimised architecture for a specific FRF reduction level, were used for damage detection. The results showed that it was possible to distinguish between the three states of the antenna with good accuracy, subject to using an adequate number of principal components together with a suitable neural network configuration. It was also found that the quality of the raw FRF data remained a major consideration, though the method was able to filter out some of the measurement noise. The convergence and detection properties of the networks were improved significantly by removing those FRFs associated with measurement errors. Received 9 March 2000; accepted for publication 12 December 2000     

Evaluation of the performance of high-speed PIV compared to standard PIV in a turbulent jet

In this paper, a comparison between two particle image velocimetry (PIV) systems, one based on a standard cross-correlation charge coupled device (CCD) camera with pulsed laser and another using high-speed complementary metal oxide semiconductor (CMOS) camera with continuous laser is performed. The objective of the paper is to point out advantages and disadvantages of the two systems when computing large and small flow scale statistics. The comparison is performed on velocity measurements in the near and far fields of a circular water jet: on this flow several experimental data and empirical self-similarity laws are available for comparisons. The results show that both systems are suitable for measurements with a preference for the standard one when investigating small-scale statistics. This result depends on the lower number of effectively independent samples acquired by a high-speed system and on the higher noise levels of CMOS sensors in comparison to CCDs.     

A novel data based control method based upon neural network and simultaneous perturbation stochastic approximation

A novel data based control method is proposed by modifying the cost function of a model-free control method based on Simultaneous Perturbation Stochastic Approximation (SPSA). The controller is constructed through use of a Function Approximator (FA), which is fixed as a neural network here. In the novel approach, the ability of the controller has been greatly improved. At last, the proposed modified control method is applied to solve non-linear tracking problems. Simulation comparison tests were done on typical non-linear plants, through which, the effectiveness of the novel data based control method is fully illustrated.     

An investigation of the performance of multi layer,neural networks applied to the analysis of PIV images

An experimental investigation of freely rising spherical bubbles through a quiescent liquid is presented. The objective of the experiments is to examine the validity of a recently proposed history force expression for clean, spherical bubbles at finite Reynolds number (Mei et al. 1994). Excellent agreement between the measured and predicted bubble trajectory is obtained when using the proposed history force expression; the data presented herein thus provide an indirect validation of the history force expression. The range of Reynolds number and Weber Number based on the terminal velocity are 13 to 212 and 0.03 to 0.69, respectively. The history force expression is only applicable when the quiescent liquid is free of contaminants. Otherwise, both the steady and unsteady forces are difficult to predict because the liquid/ vapor interface is partially immobilized.The NACA aerofoils were manufactured in the Glasgow University Department of Aerospace and the measurements on the aerofoils obtained jointly with Glasgow with the support of the British Ministry of Defence, the Defence Research Agency (formerly RAE) and the Department of Industry     

神经网络算法及其在GPS导航中的应用

GPS导航解算中常采用最小二乘算法。由于导航解算中存在观测异常（粗差），采用的模型精度很难满足用户需求，而高动态用户需求的精度却不断提高，为此文中提出一种利用神经网络的非线性逼近能力，在顾及观测信息权阵的条件下，利用Hopfieid神经网络进行GPS导航解算的新算法。该算法具有很好的抗差性和自适应性，能较好地抑制观测粗差对导航解的影响。计算结果证明了该算法的有效性。     

On hyperchaos in a small memristive neural network

This paper studies a small Hopfield neural network with a memristive synaptic weight. We show that the previous stable network after one weight replaced by a memristor can exhibit rich complex dynamics, such as quasi-periodic orbits, chaos, and hyperchaos, which suggests that the memristor is crucial to the behaviors of neural networks and may play a significant role. We also prove the existence of a saddle periodic orbit, and then present computer-assisted verification of hyperchaos through a homoclinic intersection of the stable and unstable manifolds, which gives a positive answer to an interesting question that whether a 4D memristive system with a line of equilibria can demonstrate hyperchaos.     

Bifurcation in two-dimensional neural network model with delay

A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic equation associated with the model, a bifurcation diagram was drawn in an appropriate parameter plane. It is found that a line is a pitchfork bifurcation curve. Further more, the stability of each fixed point and existence of Hopf bifurcation were obtained. Finally, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined by using the normal form method and centre manifold theory. Foundation item: the National Natural Science, Foundation of China (19831030) Biography: WEI Jun-jie, Professor, Doctor, E-mail: weijj@hit.edu.cn     

Hopf-zero bifurcation in a generalized Gopalsamy neural network model

In this paper, we study Hopf-zero bifurcation in a generalized Gopalsamy neural network model. By using multiple time scales and center manifold reduction methods, we obtain the normal forms near a Hopf-zero critical point. A comparison between these two methods shows that the two normal forms are equivalent. Moreover, bifurcations are classified in two-dimensional parameter space near the critical point, and numerical simulations are presented to demonstrate the applicability of the theoretical results.     

Chaotic dynamics in a neural network under electromagnetic radiation

In this paper, a small Hopfield neural network with three neurons is studied, in which one of the three neurons is considered to be exposed to electromagnetic radiation. The effect of electromagnetic radiation is modeled and considered as magnetic flux across membrane of the neuron, which contributes to the formation of membrane potential, and a feedback with a memristive type is used to describe coupling between magnetic flux and membrane potential. With the electromagnetic radiation being considered, the previous steady neural network can present abundant chaotic dynamics. It is found that hidden attractors can be observed in the neural network under different conditions. Moreover, periodic motion and chaotic motion appear intermittently with variations in some system parameters. Particularly, coexistence of periodic attractor, quasiperiodic attractor, and chaotic strange attractor, coexistence of bifurcation modes and transient chaos can be observed. In addition, an electric circuit of the neural network is implemented in Pspice, and the experimental results agree well with the numerical ones.     

Stability in a model of a delayed neural network

The stability of the null solution in a system of coupled cells is investigated. Each cell evolves according to Hopfield's equation for an analog circuit, with a delay incorporated to account for finite switching speed of amplifiers. A necessary and sufficient condition on the connection matrix is obtained for delay-induced oscillations to be possible in a general (not necessarily symmetric) network.