Mathematical Signal Processing Research Articles

Current Status of Research on Fault Diagnosis Using Machine Learning for Gear Transmission Systems

Gear transmission system fault diagnosis is crucial for the reliability and safety of industrial machinery. The combination of mathematical signal processing methods with deep learning technology has become a research hotspot in fault diagnosis. Firstly, the development and status of gear transmission system fault diagnosis are outlined in detail. Secondly, the relevant research results on gear transmission system fault diagnosis are summarized from the perspectives of time-domain, frequency domain, and time-frequency-domain analysis. Thirdly, the relevant research progress in shallow learning and deep learning in the field of fault diagnosis is explained. Finally, future research directions for gear transmission system fault diagnosis are summarized and anticipated in terms of the sparsity of signal analysis results, separation of adjacent feature components, extraction of weak signals, identification of composite faults, multi-factor combinations in fault diagnosis, and multi-source data fusion technology.

Feasibility of ultrasonic non-destructive testing of ancient funerary urns: Experimental and analytical parametric model

Non-invasive modalities are being developed as the computer tools and industrial non-destructive testing capabilities become more widespread. Using the same investigation methods as those applied to modern objects, we seek to study ancient funerary urns containing human bones. The exploration of ancient urns is key to increasing our understanding of the practices of burial and cremation in archaeo-anthropology. But those urns present at archaeological sites are exposed to diversified environments (wet, temperate or dry environment), and can be subjected to chemical or mechanical destructive actions over time. As ancient funeral urns containers are sometimes made of lead, stone or ceramic, the use of X-ray scanners is difficult or even impossible for in situ control. In this work, we propose an engineering technique based on ultrasonic non-destructive testing and wave propagation in urns. An analytical parametric model is developed using mathematical signal processing tools and validated by means of laboratory experiments under controlled conditions of propagation through reproductions of ancient urns for two ultrasonic frequencies (500 kHz and 1 MHz). The aim is to characterise an ancient urn by creating an analytical model, and to use a parametric identification algorithm to determine the presence or absence of bone fragments. The parametric identification algorithm based on the Levenberg–Marquardt method makes it possible to determine the geometrical (thickness) and physical (wave velocity and attenuation, mass density) parameters when the urn is filled with water, with water and bones, and with water, bones and sand. We show that the model makes it readily (processing time ≈15 sec) possible to find the different times of flight between the transducer and the different walls of the urn and the parameters with an accuracy less than 10%.

A modified algebraic method of mathematical signal processing in radar problems

A new method for approximate solution of ill-posed inverse problems of reconstructing images of objects with angular resolution exceeding the Rayleigh criterion is proposed and justified, i.e. with super resolution. Angular super-resolution allows you to obtain images of objects with increased clarity and distinguish previously invisible details of images of complex objects. In addition, on this basis, the probability of correct solutions to problems of object recognition and identification increases. Mathematically, the problem is reduced to solving the linear Fredholm integral equation of the first kind of convolution type. Solutions are sought with additional conditions in the form of restrictions on the location and size of the desired radiation source, which makes it possible to regularize the problem. The method is a development of one of the parameterization methods the algebraic method. The solution is sought in the form of a representation of the desired function in the area where the source is located in the form of a series expansion over the input sequence of orthogonal functions with unknown coefficients. Thus, the inverse problem is parameterized and reduced to searching for expansion coefficients. The presented method is based on the use of a priori information about the localization area of the radiation source, or on an estimate of the location and size of this area obtained by scanning the viewing sector with a goniometer system. Using zero values of the function describing the source outside this region, for systems based on antenna arrays it is possible to find tens and even hundreds of expansion coefficients of the desired function in a Fourier series. The solution is constructed in the form of an iterative process with a consistent increase in the number of functions used in the expansion until the solution remains stable. The adequacy and stability of the solutions was verified during numerical experiments using a mathematical model. The results of numerical studies show that the presented methods of digital processing of received signals make it possible to achieve an effective angular resolution 3–10 times higher than the Rayleigh criterion. The proposed method makes it possible to miniaturize the antenna system without degrading its characteristics. Compared to known ones, it is relatively simple, which allows it to be used by systems in real time.

Audio signal transmission method in network-based audio analytics system

The subject matter of the article is аudio signal transmission method in network-based audio analytics system. The creation of a network-based audio analytics system leads to the emergence of new classes of load sources that transmit packetized sound data. Therefore, without constructing adequate mathematical models, it is impossible to build a well-functioning network-based audio analytics system. A fundamental question in traffic theory is the question of load source models. The development of an method for transmitting audio signals in a network-based audio analytics system becomes necessary. Based on this, the goal of the work is to create methods an method for transmitting audio signals in a network-based audio analytics system to ensure efficiency and accuracy in audio analytics. The following tasks were solved in the article: the formation of a model for the system's load sources, investigation of connection and traffic management, implementation of control and traffic monitoring functions in the network, research of methods to ensure the quality of audio signal transmission and the development of a method of transmitting an audio signal by virtual routes switching. To achieve these goals, the following methods are used: mathematical signal processing, data compression algorithms, optimization of network protocols, and the use of high-speed network connections. The obtained results include modeling of the system's load sources, examination of connection and traffic management, investigation of methods to ensure the quality of audio signal transmission and a method of transmitting an audio signal by virtual routes switching was proposed. In conclusion, the possibilities of using simulation modeling of nodes in the network-based audio analytics system are highly limited. This is explained by the fact that the acceptable level of information loss in data centers is very low. The use of the developed method enables effective control and processing of sound information in real-time. This method can find broad applications in various fields, including security, healthcare, management systems, and other industries where the analysis of audio signals is a crucial element.

Peculiarities of measuring fluorescence decay times by a streak camera for ps-TALIF experiments in reactive plasmas

We present a detailed methodology for (i) correctly configuring a streak camera to capture raw picosecond two-photon absorption laser induced fluorescence signals (ps-TALIF) of H-atom in low- and atmospheric-pressure plasmas, and (ii) properly processing the recorded raw experimental data with a dedicated mathematical signal processing method to infer actual ps-TALIF signals of H-atom. The goal is the accurate determination of the decay time of the recorded ps-TALIF signals of H-atom. A ps-laser is used to excite atomic hydrogen produced in both plasmas and the raw fluorescence signals are detected by the streak camera using different time windows/ranges (TR). It is shown that the choice of the TR affects the shapes and the decay times of the recorded raw TALIF signals. This is defined as the instrumental function of the streak camera and has a Gaussian profile as determined by recording the ultrafast laser pulse at different TR. To remove this instrumental distortion and extract the actual shape of the TALIF signals, the captured raw TALIF signals were fitted using the mathematical procedure developed in this study, which involved an exponentially modified Gaussian function. The application of our methodology leads to more reliable measurements of hydrogen atoms decay times after respecting the following acquisition conditions: (i) the TR of the streak camera should be sufficiently large to capture the complete (raw) TALIF signal, and (ii) the time width of the instrumental function of the streak camera should be as small as possible compared to the actual decay time of the fluorescence, while ensuring an optimal signal-to-noise ratio. This work demonstrates the remarkable potential of the combination of ps-TALIF and streak cameras in state-of-the-art optical plasma diagnostics.

Robust neural network filtering in the tasks of building intelligent interfaces

Objectives. In recent years, there has been growing scientific interest in the creation of intelligent interfaces for computer control based on biometric data, such as electromyography signals (EMGs), which can be used to classify human hand gestures to form the basis for organizing an intuitive human-computer interface. However, problems arising when using EMG signals for this purpose include the presence of nonlinear noise in the signal and the significant influence of individual human characteristics. The aim of the present study is to investigate the possibility of using neural networks to filter individual components of the EMG signal.Methods. Mathematical signal processing techniques are used along with machine learning methods.Results. The overview of the literature on the topic of EMG signal processing is carried out. The concept of intelligent processing of biological signals is proposed. The signal filtering model using a convolutional neural network structure based on Python 3, TensorFlow and Keras technologies was developed. Results of an experiment carried out on an EMG data set to filter individual signal components are presented and discussed.Conclusions. The possibility of using artificial neural networks to identify and suppress individual human characteristics in biological signals is demonstrated. When training the network, the main emphasis was placed on individual features by testing the network on data received from subjects not involved in the learning process. The achieved average 5% reduction in individual noise will help to avoid retraining of the network when classifying EMG signals, as well as improving the accuracy of gesture classification for new users.

РАЗРАБОТКА МЕТОДА НЕИНВАЗИВНОГО ИЗМЕРЕНИЯ РАСХОДА ЖИДКОСТИ И ГАЗА ЧЕРЕЗ СТЕНКУ ТРУБОПРОВОДА

In connection to methods developed for determining “liquid-gas” volume-mass parameters, carried out at South Ural State University, this article presents a new method for measuring liquid and gas flow rates. The method makes it possible to measure a turbulent flow’s convective velocity through a pipeline wall and the volumetric flow rate of a liquid or gas. A brief description of Taylor's “frozen turbulence” hypothesis, which forms the basis of the method, is given, and the main problems associated with its proof in relation to the problem of determining the convection velocity of turbulence are identified. A mathematical signal processing method is presented based on two-dimensional frequency-wave number spectral processing and spatiotemporal signal filtering. A functional scheme and the input signal processing algorithm of the proposed device is presented. Mathematical modeling was performed in the ANSYS CFD computational fluid dynamics package using the hybrid eddy-resolving turbulence model SBES to determine the optimal configuration of the experimental setup. A brief description is given of the non-invasive sonar flow meter “K-Omega P1” prototype based on method presented and of numerical simulation results. Tests were performed on the METRAN-UPA-2000 flow test workbench which is a secondary standard. Full-scale test results on the flow test workbench for five flow rates are presented. Conclusions are drawn about the research results to date and further steps to improve the measurement method using the k-omega beamforming processing method.

Mathematically assisted UV-spectrophotometry as a greener alternative to HPLC-UV for quality control analysis of free-drug combinations

Here we introduce a novel and a comprehensive evaluation of the eco-friendliness of UV-spectrophotometry versus HPLC-UV, as used for the quality control testing of free-drug combinations. We offer a new perspective to improve the sustainability of quality control testing of pharmaceuticals, through utilization of UV-spectrophotometry coupled to mathematical signal processing as means to improve selectivity of analysis of multicomponent pharmaceutical samples. First, we developed two novel analytical methods based on UV-spectrophotometry and HPLC-UV, for the simultaneous determination of antidiabetic free-drug combination consisting of dapagliflozin (DAPA) and saxagliptin (SAXA), in the form of active pharmaceutical ingredients or finished pharmaceutical products. Furthermore, we perform qualitative and quantitative evaluation of methods’ greenness employing five reported tools namely: National Environmental Methods Index (NEMI), Raynie and Driver’s assessment tool, Green Analytical Procedure Index (GAPI), Eco-scale and Analytical GREEnness Metric (AGREE). Our results indicate that both methods were equally efficient in quantifying target analytes in the studied forms, however, UV-spectrophotometry was found to be superior to HPLC-UV from a green analytical chemistry perspective, with more than 20 folds reduction in organic solvent consumption, ~ 10 folds reduction in energy consumption and ~4 folds reduction in analysis time, making it a safer alternative to consider.

Diffuse reflectance spectroscopy in dental caries detection and classification

Machine learning and augmented reality form very important computational tools in biomedicine, neurology and stomatology as well. The present paper is devoted to a novel method of spectroscopic detection of caries lesions that changes the optical properties of the affected tissue. This method of the diffuse reflectance spectroscopy is used in many biomedical areas even though the analysis of associated data suffers from a large variance of acquired signals’ shape and their properties. The proposed methodology of measured spectra analysis is based upon general methods of signal feature evaluation and the use of computational intelligence for their classification. The paper compares properties of dental feature clusters for the set of 578 tissues with different levels of their changes. Classification results of selected features by the support vector machine, Bayesian method, k-nearest neighbour method and neural network enable to distinguish the healthy tissue and caries lesions with the accuracy from 94.1 to 98.4% and the cross-validation error lower than 8.3%. These results suggest how the augmented reality and general mathematical signal processing methods can be beneficial for diagnostic purposes in dental research and possibly in the clinical practice as well.

Frequency Shift Chirp Modulation: The LoRa Modulation

Low power wide area networks (LPWAN) are emerging as a new paradigm, especially in the field of Internet of Things (IoT) connectivity. LoRa is one of the LPWAN and it is gaining quite a lot of commercial traction. The modulation underlying LoRa is patented and has never been described theoretically. The aim of this letter is to give the first rigorous mathematical signal processing description of the modulation and demodulation processes. We provide as well a theoretical derivation of the optimum receiver entailing a low-complexity demodulation process, resorting to the Fast Fourier Transform. We compare then the performance of the LoRa modulation and the frequency-shift keying modulation both in an additive white gaussian noise channel and a frequency selective channel, showing the superiority of the LoRa modulation in the frequency selective channel. The results of this letter will enable a further assessment of the LoRa based networks, much more rigorous than what has been done until now.

Kernel Theorems for Modulation Spaces

We deal with kernel theorems for modulation spaces. We completely characterize the continuity of a linear operator on the modulation spaces $M^p$ for every $1\leq p\leq\infty$, by the membership of its kernel to (mixed) modulation spaces. Whereas Feichtinger's kernel theorem (which we recapture as a special case) is the modulation space counterpart of Schwartz' kernel theorem for temperate distributions, our results do not have a couterpart in distribution theory. This reveals the superiority, in some respects, of the modulation space formalism upon distribution theory, as already emphasized in Feichtinger's manifesto for a post-modern harmonic analysis, tailored to the needs of mathematical signal processing. The proof uses in an essential way a discretization of the problem by means of Gabor frames. We also show the equivalence of the operator norm and the modulation space norm of the corresponding kernel. For operators acting on $M^{p,q}$ a similar characterization is not expected, but sufficient conditions for boundedness can be sated in the same spirit.

P842A novel mathematical signal processing application which automates and improves the accuracy of FFR assessment

P842A novel mathematical signal processing application which automates and improves the accuracy of FFR assessment

Reconstruction of target image from inhomogeneous degradations through backscattering medium images using self-calibration.

Target images recorded with range-gated laser imaging systems and conventional passive imaging systems through rapidly changing turbid mediums inevitably suffer from inhomogeneous degradations. Consequently, this makes the images partly or entirely different from their true targets and eventually has adverse effects on target identification. To date, the inhomogeneous degradations are still not finely eliminable despite utilizing adaptive optical methods and pure mathematical signal improvement techniques. Herein, we demonstrate an image restoration method involving intrinsic physical evolution of light beams based on the backscattering images of a turbid medium. The corresponding mathematical signal processing algorithms are applied for restoring the true target images in the presence of rapidly changing inhomogeneous degradations. This technique would benefit target imaging through moving cloud/mist in air and flowing muddy masses under water.

Agricultural chemical export dynamics in a watershed

Understanding how agricultural chemicals filter through a catchment is important for managing water quality. Using a concept of the catchment as a physicochemical filter, Guan et al. examined nitrate, phosphate, and atrazine loads in the Little Vermillion River watershed, a tile‐drained watershed in Illinois. They analyzed a 10‐year data set using mathematical signal processing to investigate spatial and temporal patterns in chemical concentrations and discharge rate. They found that export of these chemicals had a linear relationship with streamflow at annual scales—the higher the streamflow, the more these chemicals were exported from the watershed. The researchers' approach helps identify the roles of different hydrological flow paths in controlling chemical export at different spatial and temporal scales and reveals that chemical inputs overwhelm normal biogeochemical processing in these agricultural systems, leading to high long‐term average rates of export. (Water Resources Research, doi:10.1029/2010WR009997, 2011)

Measuring and processing technique of complex conduction current of 110–750 kV high-voltage equipment basic insulation at diagnostics under operating voltage

The developed technique of complex conduction current measurement during on-line testing of 110 –750 kV high-voltage equipment basic insulation is described. The algorithm of mathematical signal processing for operating noise minimization is proposed. The technique can be used for diagnostics of high-voltage current transformers, bushings, nonlinear voltage limiters and other equipment in operating conditions.

CoSaMP

Compressive sampling (CoSa) is a new paradigm for developing data sampling technologies. It is based on the principle that many types of vector-space data are compressible , which is a term of art in mathematical signal processing. The key ideas are that randomized dimension reduction preserves the information in a compressible signal and that it is possible to develop hardware devices that implement this dimension reduction efficiently. The main computational challenge in CoSa is to reconstruct a compressible signal from the reduced representation acquired by the sampling device. This extended abstract describes a recent algorithm, called, <code>CoSaMP</code>, that accomplishes the data recovery task. It was the first known method to offer near-optimal guarantees on resource usage.

Advances in signal processing technology for electronic warfare

The denial of effective communications by enemy forces during hostile military operations has been a primary concern for military commanders since the inception of radio communications on the battlefield before World War II. Since then, the electromagnetic environment has been in a constant state of evolution toward more sophisticated jam-resistant and convert forms of modulation. For example, exotic modulation techniques employing spread spectrum (SS) signaling are routinely used by our adversaries to provide their communication links an advantage over US and Allied jammers. These same spread spectrum modulation techniques are being refined to provide convert, low probability-of-intercept (LPI) features to the unintended interceptor. The thrust of this paper focuses on developments in the theory and algorithms for detection, characterization, and exploitation of advanced waveforms using new mathematical signal processing tools. Specifically, quadratic time-frequency signal representations, wavelet transforms, and cyclostationary signal processing are introduced. This overview demonstrates the importance of these advanced techniques in a clear and concise manner. Applications and future research activities are described.

Computer-assisted breast cancer grading

Morphological tumour differentiation has been shown in numerous studies to give a good prognosis in breast cancer, but as histological grading is based upon a subjective assessment of microscopical appearances, difficulities in consistency and reproducibility are inevitable. A review of the many conventional methods served to highlight a common limitation in their approach; lack of structure. We introduce a new approuch which seeks to overcome the problem, by formalizing the methods and identifying aspects which are well suited to computer aided analysis, these being incorporated into a microcomputer system facilitating the collection and appraisal of morphometric data. Within the Information Technology Institute (ITRI) at Brighton Polytechnic a research team is carrying out multidisciplinary work into the elucidation of biological systems. This programme, entitled ‘Intelligent Medical Systems’, used methods of mathematical signal processing and artificial intelligence, applied to a number of areas, one of which is decribed in this paper. The aim has been to utilize the inherent skill exercised by the histopathologist in interpreting microscopical images, whilst making quantilization more accurate and reproducible. the system has been developed within a highly structured framework and will have applications in teaching and routine histological analysis. The value of artificial intelligence techniques in the wider issues of this area is discussed.

Remarks on Mathematical Signal Processing by the Brain During Rhythmic Neurophysiological Stimulation

In order to study information transfer in physiological systems, one method is used very frequently. This method consists in the determination of systems frequency characteristics on application of sinusoidal stimulation signals. Unfortunately a biological systems theory does not exist yet and the application of the methods of general systems theory to biological systems is limited and not always satisfactory. Generally biological systems are frequency-dependent nonlinear systems and a big number of biological systems, especially the brain system exhibit spontaneous rhythmic activities which makes the problem much more complicated.The aim of this study is to try to find some approaches which will offer new possibilities for interpretation in the analysis of brain systems (or biological systems in general).