Algorithms for Digital Processing of Measurement Data Providing Angular Superresolution

Incorrect one- and two-dimensional inverse problems of reconstructing images of objects with angular resolutionexceeding the Rayleigh criterion are considered. The technique is based on the solution of inverse problems of source reconstruction signals described Fredholm integral equations. Algebraic methods and algorithms for processing dataobtained by measuring systems in order to achieve angular superresolution are presented. Angular superresolution allows you to detail images of objects, solve problems of their recognition and identification on this basis. The efficiency of using algorithms based on developed algebraic methods and their modifications in parameterization the inverse problems under study and further reconstructing approximate images of objects of various types is shown. It is shown that the noise immunity of the obtained solutions exceeds many known approaches. The results of numerical experiments demonstrate the possibility of obtaining images with a resolution exceeding the Rayleigh criterion by 2-6 times at small values of the signal-to-noise ratio. The ways of further increasing the degree of superresolution based on the intelligent analysis of measurement data are described. On the basis of the preliminary information on a source of signals algorithms allow to increase consistently the effective angular resolution before achievement greatest possible for a solved problem. Algorithms of secondary processing of the information necessary for it are described. It is found that the proposed symmetrization algorithm improves the quality of solutions to the inverse problems under consideration and their stability. The examples demonstrate the successful application of modified algebraic methods and algorithms for obtaining images of the objects under study in the presence of a priori information about the solution. The results of numerical studies show that the presented methods of digital processing of received signals allow us to restore the angular coordinates of individual objects under study and their elements with super-resolution with good accuracy. The adequacy and stability of the solutions were verified by conducting numerical experiments on a mathematical model. It was shown that the stability of solutions, especially at a significant level of random components, is higher than that of many other methods. The limiting possibilities of increasing the effective angular resolution and the accuracy of image reconstruction of signal sources, depending on the level of random components in the data utilized, are found. The effective angular resolution achieved in this case is 2—10 times higher than the Rayleigh criterion. The minimum required signal-to-noise ratio for obtaining adequate solutions with super-resolution is 13—16 dB for the described methods, which is significantly less than for the known methods. The relative simplicity of the presented methods allows you to use inexpensive computing devices and work in real time.

Experimental Study on Dynamic Combustion Characteristics in Swirl-Stabilized Combustors

An experimental study was performed to investigate the combustion instability characteristics of swirl-stabilized combustors. A premixed gas composed of ethylene and air was burned under various flow and geometric conditions. Experiments were conducted by changing the inlet mean velocity, equivalence ratio, swirler vane angle, and combustor length. Two dynamic pressure sensors, a hot-wire anemometer, and a photomultiplier tube were installed to detect the pressure oscillations, velocity perturbations, and heat release fluctuations in the inlet and combustion chambers, respectively. An ICCD camera was used to capture the time-averaged flame structure. The objective was to understand the relationship between combustion instability and the Rayleigh criterion/the flame structure. When combustion instability occurred, the pressure oscillations were in-phase with the heat release oscillations. Even if the Rayleigh criterion between the pressure and heat release oscillations was satisfied, stable combustion with low pressure fluctuations was possible. This was explained by analyzing the dynamic flow and combustion data. The root-mean-square value of the heat release fluctuations was observed to predict the combustion instability region better than that of the inlet velocity fluctuations. The bifurcation of the flame structure was a necessary condition for combustion instability in this combustor. The results shed new insight into combustion instability in swirl-stabilized combustors.

A synthetic study of tidal analysis for satellite altimeter in shallow water

<p>Tidal constituents obtained from satellite radar altimeter derived water levels are widely used for ocean-related applications. However, in coastal waters, the tidal signal's complexity increases due to non-linear interactions between tidal constituents and other dynamics such as surge, giving rise to higher harmonics. A higher number of constituents increases the chance of pairwise frequency proximity, which creates retrieval time constraints using the typical series' length requirement criterion (Rayleigh criterion). Another issue is that with the lower observation frequency of altimeters, aliasing frequencies have to be considered. These lead to more challenges in shallow waters than its ocean counterpart since it is currently unfeasible to meet the series's time length requirements. In tidal analysis software, the Rayleigh criterion is often defined as fixed default harmonic selection condition. Therefore, many potentially important harmonics are left-out of the satellite radar altimeter based tidal analysis in shallow-waters, limiting derived usage.</p><p>To gain more insight into the accuracy of altimeter-derived tidal analysis, we extended the tidal analysis to include a more realistic correlation model for the surge. This model is implemented as a Kalman filter allowing us to obtain information about how the estimates' accuracy improves as more data becomes available. The improved correlation model aims to obtain realistic accuracy estimates for various strategies using synthetic data, i.e., before applying the method. An analysis of the condition number of the covariance information matrix was carried out alongside a twin experiment with simulated data. We demonstrated that the Rayleigh criterion is associated with the condition number of the information matrix and the effects of noise in the retrieval times. It shows that the accumulation of information is constant and proportional to the decrease of uncertainty. Depending on the amount of certainty one is after, the Rayleigh criterion is dispensable. Careful consideration has to be made for the signal to noise ratio of retrievals, especially when a constituent's amplitude is smaller than the variability introduced by noise, in our case, non-tidal variability. Overall, the analysis brings benefits on-top of traditional tidal analysis because it allows testing theoretical retrieval times and tidal analysis accuracy with multiple pairwise proximity issues and aliasing considerations. It also gives a straightforward way of analyzing the retrieval characteristics of semi-regular and irregular observation periods.</p>

Time-domain topological energy imaging with ultrasonic Lamb waves considering multiple defects

This study presents a fast imaging approach with ultrasonic Lamb waves based on time-domain topological energy to identify multiple defects with defect spacing smaller than the threshold of the Rayleigh criterion in terms of imaging resolution. The direct acoustical field and time-domain topological energy of the two fields are used as imaging functions when considering the calculation of direct and adjoint acoustical fields in a non-defective reference medium on the basis of topological theory. The functions are not limited by acoustic diffraction and can achieve super-resolution imaging with multiple defects. First, a 3D finite element model is established. Transient acoustic field diagrams at different moments are used to show the focusing process of direct and adjoint acoustical fields clearly with multiple defects, thereby revealing the physical mechanism of time-domain topological energy imaging. Second, the effectiveness of the proposed approach to characterise multiple defects when the defect spacing is smaller than the imaging resolution threshold is verified through numerical simulation. Finally, the feasibility of super-resolution imaging considering multiple defects is proven by conducting experiments on aluminium plate samples with multiple defects under different defect spacing conditions. Numerical simulation and experimental results show that the proposed approach can overcome the problem of multiple defects with defect spacing smaller than the imaging resolution threshold by breaking the Rayleigh criterion constraint, while the accuracy presented is higher than that of the traditional delay-and-sum method.

Three-dimensional axisymmetric sources for Majumdar–Papapetrou type spacetimes

From Newtonian potential-density pairs, we construct three-dimensional axisymmetric relativistic sources for a Majumdar–Papapetrou type conformastatic spacetime. As simple examples, we build two families of relativistic thick disks from the first two Miyamoto–Nagai potential-density pairs used in Newtonian gravity to model flat galaxies, and a three-component relativistic model of galaxy (bulge, disk and dark matter halo). We study the equatorial circular motion of test particles around such structures. Also the stability of the orbits is analyzed for radial perturbation using an extension of the Rayleigh criterion. In all examples, the relativistic effects are analyzed and compared with the Newtonian approximation. The models are considered satisfying all the energy conditions.