Multidimensional Filter Research Articles

Nonlinear convolutional sparse filtering with Gaussian fitting for rolling bearings compound fault diagnosis

The operational precision, stability, and lifespan of servo motors are directly influenced by the healthy operation of rolling bearings. Early diagnosis of bearing faults holds significant importance in enhancing the reliability of servo motors and preventing substantial economic losses and personal injuries. However, strong noise interference in industrial environments poses challenges to bearing fault diagnosis. Additionally, the difficulty in detecting single faults in bearings often leads to the occurrence of compound faults. To achieve compound fault diagnosis under intense noise interference in industrial environments, this paper proposes the nonlinear convolutional sparse filtering (NCSF). First, generalized sigmoid and Z-score normalization are utilized to amplify fault features and reduce the influence of irrelevant interference. Subsequently, multidimensional filters are learned based on a nonlinear objective function to achieve the separation of compound faults. Then, the Gaussian function is utilized to fit the trained filters, reducing the impact of low-frequency noise. Finally, the filtered signals are envelope demodulated to analyze fault types. The capability of NCSF to distinguish compound faults amid noise interference is confirmed by both experimental and simulation results. The proposed NCSF is an effective method to realize compound fault diagnosis under strong noise interference.

Algorithm for ocean surface pollution detection based on the results of video surveillance image processing

The problems of timely detection of environmental disturbances caused by the consequences of various man-made disasters on land and on the water surface of water areas of seas and oceans are based on imperfect methods of control and monitoring of large spaces. Therefore, it is relevant to search for approaches for learning procedures used in the construction of monitoring systems. The aim of article to consider approaches to the formation of feature spaces based on the processing of multiple-scale distributions of signals from drone cameras and the application of discrete series of continuous-time wavelets. An approach to the formalization of the recognition task is proposed. The results of using discrete series of continuous-time wavelets are presented, which allows obtaining a result similar to the use of a multi-dimensional filter bank loaded on integrators. Results of a practical experiment are presented, which showed that increasing the dimensionality of feature vectors reduces their contrast. The directions of further research are formed. The presented results open new possibilities for realization of recognition systems at the software level.

Adaptive algorithm for detecting and evaluating the parameters of ultra-wideband signals against the background of interference in sub-bands based on a multidimensional biorthogonalizer filter

Adaptive algorithm for detecting and evaluating the parameters of ultra-wideband signals against the background of interference in sub-bands based on a multidimensional biorthogonalizer filter

Time-domain extended-source full-waveform inversion: Algorithm and practical workflow

Extended-source full-waveform inversion (ES-FWI) first computes wavefields with data-driven source extensions such that the simulated data in inaccurate velocity models match the observed counterpart sufficiently well to prevent cycle skipping. Then, the source extensions are minimized to update the model parameters toward the true medium. This two-step workflow is iterated until data and sources are matched. It has been recently indicated that the source extensions are the least-squares solutions of the scattered data-fitting problem. As a result, the source extensions are computed by propagating backward in time the deconvolved data residuals by the damped data-domain Hessian of the scattered data-fitting problem. Estimating these weighted data residuals is the main computational bottleneck of time-domain ES-FWI. To mitigate this burden, we approximate the inverse data-domain Hessian by mono- and multidimensional matching filters with two simulations per source. We implement time-domain ES-FWI with the alternating-direction method of multipliers and total-variation regularization. Moreover, we apply ES-FWI with a multiscale approach involving frequency continuation and layer stripping, with the latter being implemented with an offset-time-dependent weighting operator. In this framework, we further regularize the inversions while mitigating their computational burden by matching the grid interval to the frequency bandwidth. Finally, the overall workflow combines ES-FWI and classical FWI during the early and late stages of the multiscale approach, respectively. We illustrate that the sensitivity of ES-FWI to the accuracy of the approximated inverse data-domain Hessian depends on the complexity of the targeted model, the data anatomy, and the accuracy of the starting model. In the case of the 2004 BP salt model, we determine that the layer stripping is necessary when the inverse data-domain Hessian is approximated by a 2D Gabor matching filter and the starting model is crude, whereas this feature is not necessary with the Marmousi II model.

Logarithmic Learning Differential Convolutional Neural Network

Convolutional Neural Networks (CNNs) have revolutionized image classification through their innovative design and training methodologies in computer vision. Differential convolutional neural network with simultaneous multidimensional filter realization improved the performance of the convolutional neural network with calculation cost drawback. This paper introduces logarithmic learning integration into the differential Convolutional neural network to overcome the drawback by supplying faster error minimization and convergence. This task is done by incorporating LogRelu activation, a Logarithmic Cost Function, and unique logarithmic learning method. The effectiveness of the proposed approaches are evaluated by using various datasets and SGD/Adam optimizers. The first step is the adaptation of LogRelu activation function to convolutional and differential convolutional neural networks. The experiment results show that LogRelu integration to convolutional neural network and differential convolutional neural network yields performance improvements ranging from 1.61% to 5.44%. The same integration on ResNet-18, ResNet-34, and ResNet-50 enhances top-1 accuracy in the range of 3.07% and 9.96%. In addition to LogRelu activation function, a Logarithmic Cost Function with logarithmic learning method is also proposed and adapted to differential convolutional neural network. These improvements lead to a new differential convolutional neural network named as Logarithmic Differential Convolutional Neural Network (LDiffCNN), It consistently outperforms standard CNN by increasing the accuracy up to 3.02%. Notably, Logarithmic Differential Convolutional Neural Network demonstrates reduced training iterations up to 38% with faster convergence. The experimental results proved the efficiency of the proposed approach.

AAK Theorem and a Design of Multidimensional BIBO Stable Filters

AAK Theorem and a Design of Multidimensional BIBO Stable Filters

Estimating the selection function of Gaia DR3 subsamples

Context. Understanding the intricacies behind the presence and absence of sources in an astronomical catalogue is crucial for the accurate interpretation of astronomical data. In particular, for the multi-dimensional Gaia data, filters and cuts on different parameters or measurements introduce a selection function that may unintentionally alter scientific conclusions in subtle ways. Aims. We aim to develop a methodology to estimate the selection function for different subsamples of stars in the Gaia catalogue. Methods. Comparing the number of stars in a given subsample to that in the overall Gaia catalogue provides an estimate of the subsample membership probability as a function of sky position, magnitude, and colour. The method used to make this estimate must differentiate the stochastic absence of subsample stars from selection effects. When multiplied with the overall Gaia catalogue selection function, this provides the total selection function of the subsample. Results. We present our new method for estimating the selection function by applying it to the sources in Gaia DR3 with heliocentric radial velocity measurements. We also compute the selection function for the stars in the Gaia-Sausage/Enceladus sample, confirming that the apparent asymmetry of its debris across the sky is merely caused by selection effects. Conclusions. The method we have developed estimates the selection function of the stars present in a subsample of Gaia data, given that the subsample is completely contained in the Gaia parent catalogue (for which the selection function is known). This tool is made available in a GaiaUnlimited Python package.

A Well-Posed Multidimensional Rational Covariance and Generalized Cepstral Extension Problem

In the present paper we consider the problem of estimating the multidimensional power spectral density which describes a second-order stationary random field from a finite number of covariance and generalized cepstral coefficients. The latter can be framed as an optimization problem subject to multidimensional moment constraints, i.e., to search a spectral density maximizing an entropic index and matching the moments. In connection with systems and control, such a problem can also be posed as finding a multidimensional shaping filter (i.e., a linear time-invariant system) which can output a random field that has identical moments with the given data when fed with a white noise, a fundamental problem in system identification. In particular, we consider the case where the dimension of the random field is greater than two for which a satisfying theory is still missing. We propose a multidimensional moment problem which takes into account a generalized definition of the cepstral moments, together with a consistent definition of the entropy. We show that it is always possible to find a rational power spectral density matching exactly the covariances and approximately the generalized cepstral coefficients, from which a shaping filter can be constructed via spectral factorization. In plain words, our theory allows us to construct a well-posed spectral estimator for any finite dimension.

Multidimensional Particle Filter for Long-Term Visual Teach and Repeat in Changing Environments

When a mobile robot is asked to navigate intelligently in an environment, it needs to estimate its own and the environment's state. One of the popular methods for robot state and position estimation is particle filtering (PF). Visual Teach and Repeat (VT&R) is a type of navigation that uses a camera to navigate the robot along the previously traversed path. Particle filters are usually used in VT&R to fuse data from odometry and camera to estimate the distance traveled along the path. However, in VT&R, there are other valuable states that the robot can benefit from, especially when moving through changing environments. We propose a multidimensional particle filter to estimate the robot state in VT&R navigation. Apart from the traveled distance, our particle filter estimates lateral and heading deviation from the taught path as well as the current appearance of the environment. This appearance is estimated using maps created across various environmental conditions recorded during the previous traversals. The joint state estimation is based on contrastive neural network architecture, allowing self-supervised learning. This architecture can process multiple images in parallel, alleviating the potential overhead caused by computing the particle filter over the maps simultaneously. We conducted experiments to show that the joint robot/environment state estimation improves navigation accuracy and robustness in a continual mapping setup. Unlike the other frameworks, which treat the robot position and environment appearance separately, our PF represents them as one multidimensional state, resulting in a more general uncertainty model for VT&R.

An octonion-based nonlinear echo state network for speech emotion recognition in Metaverse

While the Metaverse is becoming a popular trend and drawing much attention from academia, society, and businesses, processing cores used in its infrastructures need to be improved, particularly in terms of signal processing and pattern recognition. Accordingly, the speech emotion recognition (SER) method plays a crucial role in creating the Metaverse platforms more usable​ and enjoyable for its users. However, existing SER methods continue to be plagued by two significant problems in the online environment. The shortage of adequate engagement and customization between avatars and users is recognized as the first issue and the second problem is related to the complexity of SER problems in the Metaverse as we face people and their digital twins or avatars. This is why developing efficient machine learning (ML) techniques specified for hypercomplex signal processing is essential to enhance the impressiveness and tangibility of the Metaverse platforms. As a solution, echo state networks (ESNs), which are an ML powerful tool for SER, can be an appropriate technique to enhance the Metaverse’s foundations in this area. Nevertheless, ESNs have some technical issues restricting them from a precise and reliable analysis, especially in the aspect of high-dimensional data. The most significant limitation of these networks is the high memory consumption caused by their reservoir structure in face of high-dimensional signals. To solve all problems associated with ESNs and their application in the Metaverse, we have come up with a novel structure for ESNs empowered by octonion algebra called NO2GESNet. Octonion numbers have eight dimensions, compactly display high-dimensional data, and improve the network precision and performance in comparison to conventional ESNs. The proposed network also solves the weaknesses of the ESNs in the presentation of the higher-order statistics to the output layer by equipping it with a multidimensional bilinear filter. Three comprehensive scenarios to use the proposed network in the Metaverse have been designed and analyzed, not only do they show the accuracy and performance of the proposed approach, but also the ways how SER can be employed in the Metaverse platforms.

РАДІОЛОКАЦІЙНІ ХАРАКТЕРИСТИКИ ОПАДІВ, ЩО ВПЛИВАЮТЬ НА СУПРОВОДЖЕННЯ ОБ'ЄКТІВ СУДНОВОЮ РЛС

In this paper, we consider the possibility of using the radar characteristics under precipitation conditions in order to reduce the echo signal’s negative impact on the object tracking performed by the ship’s radar. Precipitation particles’ size, state (solid or liquid phase), shape, and the factors that determine their combined action play an important role in echo signal formation. The rain particles’ size in comparison with the wavelength of the ship’s radar may contribute to the creation of a larger or smaller noise echo signal on the ship’s radar display. This signal’s power in the Rayleigh scattering area towards the radar is characterized by the effective scattering area. Raindrops represent a combination of randomly located reflectors. Their scattering properties depend on spatial distribution and movement regularity. At the same time, the radar characteristics of clouds with precipitation generated by them can be used in ship radars to determine the intensity of the atmospheric process along the ship’s route. The uncertainty in determining the power attenuation of an electromagnetic wave emitted by a ship’s radar antenna and passing through the precipitation zone can be reduced by the simultaneous use of two wavelengths on which a ship’s radars operate. The presented uncertainty function characterizes a narrow-band polarized scattered signal in regard to radar information about the distance to the sea object and the scatterer's speed. It characterizes the matched multidimensional coherent filter’s properties. This filter provides optimal echo reception against the background of an uncorrelated precipitation echo signal. The matched filter belongs to the class of optimal linear filters according to the criterion of the maximum signalto-noise ratio and is the main element for radar detection devices in the ship radar, which is optimal according to the Neyman-Pearson criteria. Keywords: radar characteristics of precipitation, precipitation intensity, effective scattering area, precipitation particle diameter, dielectric constant, energy attenuation, radio waves, wavelength.

Multi-dimensional particle filter-based estimation of phase line biases for single-differenced ambiguity resolution in GNSS-based attitude determination

Global navigation satellite systems (GNSSs) have been widely used to provide real-time and high-precision attitude information for land vehicles, ships and aircraft over the past few decades. With the joint use of emerging multi-GNSS common-clock receivers and the single-differenced (SD) model, the accuracy of pitch and roll can be significantly improved to the same level as that of yaw. However, the prerequisite is that the frequency-dependent phase line biases (LBs) in multiple GNSS systems and frequencies are accurately and rapidly estimated. In this contribution, we intend to solve this problem by using a multi-dimensional particle filter (PF)-based approach. We first investigate the relationship between the ratio value and the multi-dimensional phase LBs. Results have revealed that the ratio value can be used to judge the quality of multi-dimensional phase LBs and represent the likelihood function of the observations. We then present the procedure of multi-dimensional PF-based phase LBs estimation for SD ambiguity resolution and attitude determination. An improved strategy is also proposed to reduce the computation time. Finally, we take the two-dimensional case as a representative example to evaluate the performance of the proposed method in aspects of the convergence and accuracy of phase LB estimates, the attitude determination accuracy, and the computation time. Experimental results from two static datasets have demonstrated that the two-dimensional phase LBs basically rapid converge within 20 epochs. Moreover, compared with the double-differenced method, the proposed multi-dimensional PF-based SD method could provide comparable yaw accuracy and much better pitch accuracy. The pitch accuracy is improved to the same level as yaw by approximately 42.9%–50.0%. With regard to the computation time, it is found that with the proposed modification strategy, the single-epoch computation times are significantly reduced by approximately 90.7%–93.5%, and they are mostly within 0.05 s for most of the epochs on a personal computer.

Multidimensional projection filters via automatic differentiation and sparse-grid integration

The projection filter is a technique for approximating the solutions of optimal filtering problems. In projection filters, the Kushner–Stratonovich stochastic partial differential equation that governs the propagation of the optimal filtering density is projected to a manifold of parametric densities, resulting in a finite-dimensional stochastic differential equation. Despite the fact that projection filters are capable of representing complicated probability densities, their current implementations are limited to Gaussian family or unidimensional filtering applications. This work considers a combination of numerical integration and automatic differentiation to construct projection filter algorithms for more generic problems. Specifically, we provide a detailed exposition of this combination for the manifold of the exponential family, and show how to apply the projection filter to multidimensional cases. We demonstrate numerically that based on comparison to a finite-difference solution to the Kushner–Stratonovich equation and a bootstrap particle filter with systematic resampling, the proposed algorithm retains an accurate approximation of the filtering density while requiring a comparatively low number of quadrature points. Due to the sparse-grid integration and automatic differentiation used to calculate the expected values of the natural statistics and the Fisher metric, the proposed filtering algorithms are highly scalable. They therefore are suitable to many applications in which the number of dimensions exceeds the practical limit of particle filters, but where the Gaussian-approximations are deemed unsatisfactory.

Performance evaluation of MDKF based on state estimations for path tracking applications

One of the most difficult tasks for tracking in control systems in the presence of uncertainty is estimating the accuracy and efficiency of hidden variables. For tracking applications, the Kalman filter is the most extensively used estimation algorithm. However, tracking several objects remains a difficult effort in order to improve prediction and corrective results. For tracking several objects, a multi-dimensional Kalman filter (MDKF) based on state estimations is offered as a solution. This research also includes a performance analysis of the MDKF for tracking paths by modifying co-efficients of the steady-state and covariance equations. For linear dynamic systems, MDKF is evaluated. Path tracking using the Kalman filter and MDKF is also investigated. The true and filtered responses of MDKF filtering algorithm for path tracking are observed. After four trials, the output covariance yields steady state values. The simulation results reveal that our proposed filtering algorithm performs 2x better than a typical Kalman filter for objects moving in linear motion, indicating that it is suitable for real-time implementation.

Prediction of petrophysical characteristics of deposits in Kurovdagh field by use of attribute analysis of 3D data

The paper is devoted to predicting petrophysical parameters of productive series of Kurovdagh field by use of attribute analysis of seismic data to define the direction of reconnaissance works in this field. The paper considers geographical position of the study area, its cover by geological and geophysical studies and underlines, in particular, the importance of 3D seismic data acquisition for more detailed study of Kurovdagh structure. Lithological and stratigraphic characteristics of the section is also given in the paper with detailed description of Productive Series deposits. In addition, tectonics of the area is considered in more detail. It is noted that the area is attributed to the Low Kur basin — the compound of the large tectonic unit. The tectonic zone of the south-eastern Shirvan is embracing four anticlinal zones: Pirsaat-Khamamdagh; Kharami—Mishovdag—Kalmas—Khydirly—Aghaevir-Byandovan; Kursangya; Padar—Kurovdagh—Karabaghly—Babazanan—Duzdagh-Neftchala. The latter anticlinal zone is characterized by a significant length. In the north-western part between the folds of Padar and Karabaghly the brachyanticline of Kurovdagh is located. In the north it has the border with M. Kharami uplift, in the north-east with Mishovdagh fold, it borders with Kursyanga anticline in the south-east and in the south-west with wide Salyan trough. In the Near-Kur depression the existence of two tectonic stripes has been established. One of them embraces the south-eastern Shirvan, the other covers the eastern Mughan and the western portion of Salyan steppe. The detailed description of fold setting is given on the basis of 3D seismic survey data. It has been indicated that the results of 3D data interpretation made it possible to study in more detail and make changes in the scheme of faults location accepted earlier. The other problem considered in the paper is the oil-and-gas presence in Kurovdagh field, which is related to the Absheron stage of Pleistocene, Akchagyl stage and Productive series (horizons of PS01—PS20) of Neogene, with lithology represented by sandy-clay rocks with various degrees of calcareousness. The structure of each of indicated horizons is rather complicated and variable in lateral. The most complicated of them is the Middle Absheron sub-stage, with identified 11 oil-bearing layers. Study results are given in the end of the paper. For prediction purposes within the study area we have prepared normalized curves of relative parameter of SP-ASP, gamma-log — dGR and resistivity by use of well logging data. The analysis of dependence of seismic attributes on petrophysical parameters within target interval, identified the low information bearing ability of SP method and gamma-log across the study area and established a good correlation between resistivity curve and instantaneous amplitudes, frequencies and dip angles. The clay cubes have been designed. To outline productive layers, we have applied multidimensional filters with cut offs for reservoir and as a result we have acquired a cube for supposed distribution of productive layers. It is emphasized that the conducted studies led to the conclusion that due to the complexity and interference nature of the observed wave pattern in some parts of the Kurovdagh structure, it was not possible to reliably convert the attributes of the seismic wave field into petrophysical parameters.

A novel multi-dimensional zero-phase IIR notch filter with independently-tunable multiple notches

A novel multi-dimensional zero-phase IIR notch filter with independently-tunable multiple notches

FPGA implementation of multi-dimensional Kalman filter for object tracking and motion detection

Object tracking and motion detection are the major challenges in the real-time image and video processing applications. There are several tracking and prediction algorithms available to estimate and predict the state of a system. Kalman filter is the most widely used prediction algorithm as it is very simple, efficient and easy to implement for linear measurements. However, these types of filter algorithms are customized on hardware platforms such as Field-Programmable Gate Arrays (FPGAs) and Graphic Processing Units (GPUs) to achieve design requirements for embedded applications. In this work, a multi-dimensional Kalman filter (MDKF) algorithm is proposed for object tracking and motion detection. The numerical analysis of proposed tracking algorithm achieves competitive tracking performance in contrast with state-of-the-art tracking algorithms trained on standard benchmarks. Furthermore, MDKF is implemented on Xilinx Zynq™-7000 System-on-a chip (SoC). The implementation of MDKF on SoC performs 2× times tracking speed than that of software approach. The experimental results provide resource utilization of about 61.43% of Block RAMs (BRAMs), 90.09% of DSPs, 83.27% of Look-up tables (LUTs) and 82.35% of logic cells operating at 140 MHz with power consumption of 780 mW which outperforms previous related methods.

Supergraph Topology Feature Index for Personalized Interesting Subgraph Query in Large Labeled Graphs

Interesting subgraph query aims to find subgraphs that are isomorphic to the given query graph from a data graph and rank the subgraphs according to their interestingness scores. However, the existing subgraph query approaches are inefficient when dealing with large-scale labeled data graph. This is caused by the following problems: (i) the existing work mainly focuses on unweighted query graphs, while ignoring the impact of query constraints on query results. (ii) Excessive number of subgraph candidates or complex joins between nodes in the subgraph candidates reduce the query efficiency. To solve these problems, this paper proposes an intelligent solution. Firstly, an Isotype Structure Graph Compression (ISGC) strategy is proposed to compress similar nodes in a graph to reduce the size of the graph and avoid unnecessary matching. Then, an auxiliary data structure Supergraph Topology Feature Index (STFIndex) is designed to replace the storage of the original data graph and improve the efficiency of an online query. After that, a partition method based on Edge Label Step Value (ELSV) is proposed to partition the index logically. In addition, a novel Top-K interest subgraph query approach is proposed, which consists of the multidimensional filtering (MDF) strategy, upper bound value (UBV) (Size-c) matching, and the optimizational join (QJ) method to filter out as many false subgraph candidates as possible to achieve fast joins. We conduct experiments on real and synthetic datasets. Experimental results show that the average performance of our approach is 1.35 higher than that of the state-of-the-art approaches when the query graph is unweighted, and the average performance of our approach is 2.88 higher than that of the state-of-the-art approaches when the query graph is weighted.

A modified filter nonmonotone adaptive retrospective trust region method

In this paper, aiming at the unconstrained optimization problem, a new nonmonotone adaptive retrospective trust region line search method is presented, which takes advantages of multidimensional filter technique to increase the acceptance probability of the trial step. The new nonmonotone trust region ratio is presented, which based on the convex combination of nonmonotone trust region ratio and retrospective ratio. The global convergence and the superlinear convergence of the algorithm are shown in the right circumstances. Comparative numerical experiments show the better effective and robustness.

Sparse grid-based adaptive noise reduction strategy for particle-in-cell schemes

We propose a sparse grid-based adaptive noise reduction strategy for electrostatic particle-in-cell (PIC) simulations. By projecting the charge density onto sparse grids we reduce the high-frequency particle noise. Thus, we exploit the ability of sparse grids to act as a multidimensional low-pass filter in our approach. Thanks to the truncated combination technique [1–3], we can reduce the larger grid-based error of the standard sparse grid approach for non-aligned and non-smooth functions. The truncated approach also provides a natural framework for minimizing the sum of grid-based and particle-based errors in the charge density. We show that our approach is, in fact, a filtering perspective for the noise reduction obtained with the sparse PIC schemes first introduced in [4]. This enables us to propose a heuristic based on the formal error analysis in [4] for selecting the optimal truncation parameter that minimizes the total error in charge density at each time step. Hence, unlike the physical and Fourier domain filters typically used in PIC codes for noise reduction, our approach automatically adapts to the mesh size, number of particles per cell, smoothness of the density profile and the initial sampling technique. It can also be easily integrated into high performance large-scale PIC code bases, because we only use sparse grids for filtering the charge density. All other operations remain on the regular grid, as in typical PIC codes. We demonstrate the efficiency and performance of our approach with two test cases: the diocotron instability in two dimensions and the three-dimensional electron dynamics in a Penning trap. Our run-time performance studies indicate that our approach can provide significant speedup and memory reduction to PIC simulations for achieving comparable accuracy in the charge density.