Search results for: multi-phase nonlinear wiener process

Authors: Hao Chen, Bo Guo, Ping Jiang

Abstract:

Residual life (RL) estimation based on multi-phase nonlinear Wiener process was studied in this paper, which is significant for complicated products with small samples. Firstly, nonlinear Wiener model with random parameter was introduced and multi-phase nonlinear Wiener model was proposed to model degradation process of products that were nonlinear and separated into different phases. Then the multi-phase RL probability density function based on the presented model was derived approximately in a closed form and parameters estimation was achieved with the method of maximum likelihood estimation (MLE). Finally, the method was applied to estimate the RL of high voltage plus capacitor. Compared with the other three different models by log-likelihood function (Log-LF) and Akaike information criterion (AIC), the results show that the proposed degradation model can capture degradation process of high voltage plus capacitors in a better way and provide a more reliable result.

Keywords: multi-phase nonlinear wiener process, residual life estimation, maximum likelihood estimation, high voltage plus capacitor

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Authors: A. Brouri, F. Giri, A. Mkhida, A. Elkarkri, M. L. Chhibat

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Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. Presently, the linear subsystem is allowed to be parametric or not, continuous- or discrete-time. The input and output nonlinearities are polynomial and may be noninvertible. A two-stage identification method is developed such the parameters of all nonlinear elements are estimated first using the Kozen-Landau polynomial decomposition algorithm. The obtained estimates are then based upon in the identification of the linear subsystem, making use of suitable pre-ad post-compensators.

Keywords: nonlinear system identification, Hammerstein-Wiener systems, frequency identification, polynomial decomposition

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Authors: U. Mary

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Let be a graph with a finite, nonempty set of objects called vertices together with a set of unordered pairs of distinct vertices of called edges. The vertex set is denoted by and the edge set by. Given two graphs and the wiener index of, wiener index for the splitting graph of a graph, the first Zagreb index of and its splitting graph, the 3-steiner wiener index of, the 3-steiner wiener index of a special graph are explored in this paper.

Keywords: complementary prism graph, first Zagreb index, neighborhood corona graph, steiner distance, splitting graph, steiner wiener index, wiener index

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Authors: Leili Esmaeilani, Jafar Ghaisari, Mohsen Ahmadian

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Hammerstein–Wiener model is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output and could be used to model various processes. This paper contains an optimization approach method for analysing the problem of Hammerstein–Wiener systems identification. The method relies on reformulate the identification problem; solve it as constraint quadratic problem and analysing its solutions. During the formulation of the problem, effects of adding noise to both input and output signals of nonlinear blocks and disturbance to linear block, in the emerged equations are discussed. Additionally, the possible parametric form of matrix operations to reduce the equation size is presented. To analyse the possible solutions to the mentioned system of equations, a method to reduce the difference between the number of equations and number of unknown variables by formulate and importing existing knowledge about nonlinear functions is presented. Obtained equations are applied to an instance H–W system to validate the results and illustrate the proposed method.

Keywords: identification, Hammerstein-Wiener, optimization, quantization

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Authors: Brouri Adil, Giri Fouad

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The problem of identifying Wiener-Hammerstein systems is addressed in the presence of two linear subsystems of structure totally unknown. Presently, the nonlinear element is allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method such a set of points of the nonlinearity are estimated first. Then, the frequency gains of the two linear subsystems are determined at a number of frequencies. The method involves Fourier series decomposition and only requires periodic excitation signals. All involved estimators are shown to be consistent.

Keywords: Wiener-Hammerstein systems, Fourier series expansions, frequency identification, automation science

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Authors: Abdul Jalil M. Khalaf, Esraa M. Kadhim

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The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x= 1 is equal to the Wiener index and second derivative at x=1 is equal to the Hyper-Wiener index. In this paper we study the Hosoya polynomial of zero-divisor graphs.

Keywords: Hosoya polynomial, wiener index, Hyper-Wiener index, zero-divisor graphs

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Authors: Vikram Saini, Lillie Dewan

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This paper presents the iterative schemes based on Least square, Hierarchical Least Square and Stochastic Approximation Gradient method for the Identification of Wiener model with parametric structure. A gradient method is presented for the parameter estimation of wiener model with noise conditions based on the stochastic approximation. Simulation results are presented for the Wiener model structure with different static non-linear elements in the presence of colored noise to show the comparative analysis of the iterative methods. The stochastic gradient method shows improvement in the estimation performance and provides fast convergence of the parameters estimates.

Keywords: hard non-linearity, least square, parameter estimation, stochastic approximation gradient, Wiener model

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Authors: Joon-Hyung Kim, Him-Chan Lee, Jin-Hyuk Kim, Yong-Kab Lee, Young-Seok Choi

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The crude oil in an oil well exists in various phases such as gas, seawater, and sand, as well as oil. Therefore, a phase separator is needed at the front of a single-phase pump for pressurization and transfer. On the other hand, the application of a multiphase pump can provide such advantages as simplification of the equipment structure and cost savings, because there is no need for a phase separation process. Therefore, the crude oil transfer method using a multiphase pump is being applied to recently developed oil wells. Due to this increase in demand, technical demands for the development of multiphase pumps are sharply increasing, but the progress of research into related technologies is insufficient, due to the nature of multiphase pumps that require high levels of skills. This study was conducted to verify the reliability of pump performance evaluation using numerical analysis, which is the basis of the development of a multiphase pump. For this study, a model was designed by selecting the specifications of the pump under study. The performance of the designed model was evaluated through numerical analysis and experiment, and the results of the performance evaluation were compared to verify the reliability of the result using numerical analysis.

Keywords: multiphase pump, numerical analysis, experiment, performance evaluation, reliability verification

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Authors: Soudabeh Shemehsavar

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In this paper, we consider the situation under a life test, in which the failure time of the test units are not related deterministically to an observable stochastic time varying covariate. In such a case, the joint distribution of failure time and a marker value would be useful for modeling the step stress life test. The problem of accelerating such an experiment is considered as the main aim of this paper. We present a step stress accelerated model based on a bivariate Wiener process with one component as the latent (unobservable) degradation process, which determines the failure times and the other as a marker process, the degradation values of which are recorded at times of failure. Parametric inference based on the proposed model is discussed and the optimization procedure for obtaining the optimal time for changing the stress level is presented. The optimization criterion is to minimize the approximate variance of the maximum likelihood estimator of a percentile of the products’ lifetime distribution.

Keywords: bivariate normal, Fisher information matrix, inverse Gaussian distribution, Wiener process

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Authors: Hossein Javidnia, Salehe Taheri

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The Electrocardiogram (ECG) is the recording of the heart’s electrical potential versus time. ECG signals are often contaminated with noise such as baseline wander and muscle noise. As these signals have been widely used in clinical studies to detect heart diseases, it is essential to filter these noises. In this paper we compare performance of Wiener Filtering and Median Filtering methods to filter Additive White Gaussian (AWG) noise with the determined signal to noise ratio (SNR) ranging from 3 to 5 dB applied to long-term ECG recordings samples. Root mean square error (RMSE) and coefficient of determination (R2) between the filtered ECG and original ECG was used as the filter performance indicator. Experimental results show that Wiener filter has better noise filtering performance than Median filter.

Keywords: ECG noise filtering, Wiener filtering, median filtering, Gaussian noise, filtering performance

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Authors: Ajish K. Abraham

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Hearing aid is the most fundamental technology employed towards rehabilitation of persons with sensory neural hearing impairment. Hearing in noise is still a matter of major concern for many hearing aid users and thus continues to be a challenging issue for the hearing aid designers. Several techniques are being currently used to enhance the speech at the hearing aid output. Most of these techniques, when implemented, result in reduction of intelligibility of the speech signal. Thus the dissatisfaction of the hearing aid user towards comprehending the desired speech amidst noise is prevailing. Multichannel Wiener Filter is widely implemented in binaural hearing aid technology for noise reduction. In this study, Wiener filter based noise reduction approach is experimented for a single microphone based hearing aid set up. This method checks the status of the input speech signal in each frequency band and then selects the relevant noise reduction procedure. Results showed that the Wiener filter based algorithm is capable of enhancing speech even when the input acoustic signal has a very low Signal to Noise Ratio (SNR). Performance of the algorithm was compared with other similar algorithms on the basis of improvement in intelligibility and SNR of the output, at different SNR levels of the input speech. Wiener filter based algorithm provided significant improvement in SNR and intelligibility compared to other techniques.

Keywords: hearing aid output speech, noise reduction, SNR improvement, Wiener filter, speech enhancement

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Authors: Sanju Vaidya, Aihua Li

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Vulnerability measures and topological indices are crucial in solving various problems such as the stability of the communication networks and development of mathematical models for chemical compounds. In 1947, Harry Wiener introduced a topological index related to molecular branching. Now there are more than 100 topological indices for graphs. For example, Hosoya polynomials (also called Wiener polynomials) were introduced to derive formulas for certain vulnerability measures and topological indices for various graphs. In this paper, we will find a relation between the Hosoya polynomials of any graph and its Mycielskian graph. Additionally, using this we will compute vulnerability measures, closeness and betweenness centrality, and extended Wiener indices. It is fascinating to see how Hosoya polynomials are useful in the two diverse fields, cybersecurity and chemistry.

Keywords: hosoya polynomial, mycielskian graph, graph vulnerability measure, topological index

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Authors: P. Sathyathas, H. M. I. S. W. Herath, T. Amalraj, U. J. M. A. L. Jayasinghe

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Over two thirds of medical radiation can now be attributed to Computed Tomography (CT). There is little information on amount of radiation received from multiphase CT scan of abdomen- pelvic region in clinical practice. We sought to estimate the radiation dose and associated exposure parameters in the multiphase abdomen - pelvic scan of Multideteror Computed Tomography (MDCT) studies in clinical practice. This was a retrospective cross sectional studies describing radiation dose associated with main exposure parameters in diagnostic multiphase abdomen - pelvic scans performed on 152 consecutive patients by two different sixteen slice CT scanners. Patient information, exposure parameters of CTDI (volume), DLP, kVp, mAs and pitch were recorded for every phases of abdomen- a pelvic study from dose report of MDCT scanners (MDCTs). Age of patients range from 14 years to 87 years in both MDCT scanners. Overall CTDI (volume) median was 63.8 (±10.4) mGy for a multiphase abdominal-pelvic scan with scanner A while it was 35.4 (±15.6) mGy for scanner B. Patients' effective dose for multiphase abdomen - pelvic CT scan range from 8.2 mSv to 58 mSv. Median effective dose for patients, who underwent multiphase abdomen- pelvis scan with scanner A and B were 38.5 (± 8.2) mSv and 21.3 (± 8.6) mSv respectively. Median value of exposure parameters of mAs, kVp and pitch, were 150 (±29.7), 130 (±15.3) and 1.3 (±0.1) respectively in scanner A. In scanner B; they were 60 (±14.5), 120 and 1. The median effective dose for patients between multiphase abdomen-pelvic scan of both MDCT, a significant different (P<0.05) was observed. Multiphase abdomen – pelvic scan of clinical study shows significant different of effective dose with reference level of phantom studies (8-14mSv) and it depends on the type of vendors.

Keywords: abdomen-pelvic region, computed tomography, exposure parameters, radiation dose

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Authors: Aydin Azizi, Ahmed Al. Azizi

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Mechanical seals are essential components in centrifugal pumps since they help in controlling leaking out of the liquid that is pumped under pressure. Unlike the common types of packaging, mechanical seals are highly efficient and they reduce leakage by a great extent. However, all multiphase mechanical seals leak and they are subject to failure. Some of the factors that have been recognized to their failure include excessive heating, open seal faces, as well as environment related factors that trigger failure of the materials used to manufacture seals. The proposed research study will explore the failure of multiphase mechanical seal in centrifugal pumps. The objective of the study includes how to reduce the failure in multiphase mechanical seals and to make them more efficient.

Keywords: mechanical seals, centrifugal pumps, multi phase failure, excessive heating

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Authors: Mohamad R. Moshtagh, Ahmad Bagheri

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Accurate fault detection in rotating machinery is of utmost importance to ensure optimal performance and prevent costly downtime in industrial applications. This study presents a robust fault detection system based on vibration data collected from rotating gears under various operating conditions. The considered scenarios include: (1) both gears being healthy, (2) one healthy gear and one faulty gear, and (3) introducing an imbalanced condition to a healthy gear. Vibration data was acquired using a Hentek 1008 device and stored in a CSV file. Python code implemented in the Spider environment was used for data preprocessing and analysis. Winner features were extracted using the Wiener feature selection method. These features were then employed in multiple machine learning algorithms, including Convolutional Neural Networks (CNN), Multilayer Perceptron (MLP), K-Nearest Neighbors (KNN), and Random Forest, to evaluate their performance in detecting and classifying faults in both the training and validation datasets. The comparative analysis of the methods revealed the superior performance of the Wiener-CNN approach. The Wiener-CNN method achieved a remarkable accuracy of 100% for both the two-class (healthy gear and faulty gear) and three-class (healthy gear, faulty gear, and imbalanced) scenarios in the training and validation datasets. In contrast, the other methods exhibited varying levels of accuracy. The Wiener-MLP method attained 100% accuracy for the two-class training dataset and 100% for the validation dataset. For the three-class scenario, the Wiener-MLP method demonstrated 100% accuracy in the training dataset and 95.3% accuracy in the validation dataset. The Wiener-KNN method yielded 96.3% accuracy for the two-class training dataset and 94.5% for the validation dataset. In the three-class scenario, it achieved 85.3% accuracy in the training dataset and 77.2% in the validation dataset. The Wiener-Random Forest method achieved 100% accuracy for the two-class training dataset and 85% for the validation dataset, while in the three-class training dataset, it attained 100% accuracy and 90.8% accuracy for the validation dataset. The exceptional accuracy demonstrated by the Wiener-CNN method underscores its effectiveness in accurately identifying and classifying fault conditions in rotating machinery. The proposed fault detection system utilizes vibration data analysis and advanced machine learning techniques to improve operational reliability and productivity. By adopting the Wiener-CNN method, industrial systems can benefit from enhanced fault detection capabilities, facilitating proactive maintenance and reducing equipment downtime.

Keywords: fault detection, gearbox, machine learning, wiener method

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Authors: Minas Balyan

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Nowadays X-ray nonlinear diffraction and nonlinear effects are investigated due to the presence of the third generation synchrotron sources and XFELs. X-ray third order nonlinear dynamical diffraction is considered as well. Using the nonlinear model of the usual visible light optics the third-order nonlinear Takagi’s equations for monochromatic waves and the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses are obtained by the author in previous papers. The obtained equations show, that even if the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero (forbidden reflection), the dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus, in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well-known Renninger effect takes place. In this work, the 'third order nonlinear Renninger effect' is considered theoretically.

Keywords: Bragg diffraction, nonlinear Takagi’s equations, nonlinear Renninger effect, third order nonlinearity

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Authors: Juliette Harper, Yu Yang

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Biofuels have gained significant attention recently due to the new regulations and agreements regarding fossil fuels and greenhouse gases being made by countries around the globe. One of the most common types of biofuels is biodiesel, primarily made via the transesterification reaction. We model this nonlinear process in MATLAB using the standard kinetic equations. Then, a nonlinear Model predictive control (NMPC) was developed to regulate this process due to its capability to handle process constraints. The feeding flow uncertainty and kinetic disturbances are further incorporated in the model to capture the real-world operating conditions. The simulation results will show that the proposed NMPC can guarantee the final composition of fatty acid methyl esters (FAME) above the target threshold with a high chance by adjusting the process temperature and flowrate. This research will allow further understanding of NMPC under uncertainties and how to design the computational strategy for larger process with more variables.

Keywords: NMPC, biodiesel, uncertainties, nonlinear, MATLAB

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Authors: Bououden Soraya

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This paper aims to study the existence of the change of coordinates which permits to transform a class of nonlinear dynamical systems into the so-called nonlinear observer canonical form (NOCF). Moreover, an algorithm to construct such a change of coordinates is given. Based on this form, we can design an observer with a linear error dynamic. This enables us to estimate the state of a nonlinear dynamical system. A concrete example (biological model) is provided to illustrate the feasibility of the proposed results.

Keywords: nonlinear observer canonical form, observer, design, gene regulation, gene expression

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Authors: Sandy Black, Calum McLaughlin, Alessandro Pranzitelli, Marc Laing

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Multiphase flow structures of two-phase multicomponent fluids were experimentally investigated in a large diameter high-pressure pipeline up to 130 bar at TÜV SÜD’s National Engineering Laboratory Advanced Multiphase Facility. One of the main objectives of the experimental test campaign was to evaluate the impact of pressure on multiphase flow patterns as much of the existing information is based on low-pressure measurements. The experiments were performed in a horizontal and vertical orientation in both 4-inch and 6-inch pipework using nitrogen, ExxsolTM D140 oil, and a 6% aqueous solution of NaCl at incremental pressures from 10 bar to 130 bar. To visualise the detailed structure of the flow of the entire cross-section of the pipe, a fast response X-ray tomography system was used. A wide range of superficial velocities from 0.6 m/s to 24.0 m/s for gas and 0.04 m/s and 6.48 m/s for liquid was examined to evaluate different flow regimes. The results illustrated the suppression of instabilities between the gas and the liquid at the measurement location and that intermittent or slug flow was observed less frequently as the pressure was increased. CFD modellings of low and high-pressure simulations were able to successfully predict the likelihood of intermittent flow; however, further tuning is necessary to predict the slugging frequency. The dataset generated is unique as limited datasets exist above 100 bar and is of considerable value to multiphase flow specialists and numerical modellers.

Keywords: computational fluid dynamics, high pressure, multiphase, X-ray tomography

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Authors: Margarita Mayoral-Villa, J. Klapp, L. Di G. Sigalotti, J. E. V. Guzmán

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Automated learning techniques are widely applied in the energy sector to address challenging problems from a practical point of view. To this end, we discuss the implementation of a Message Passing algorithm (MPNN)within a Graph Neural Network(GNN)to leverage the neighborhood of a set of nodes during the aggregation process. This approach enables the characterization of multiphase diffusion processes in the reservoir, such that the flow paths underlying the interconnections between multiple wells may be inferred from previously available data on flow rates and bottomhole pressures. The results thus obtained compare favorably with the predictions produced by the Reduced Order Capacitance-Resistance Models (CRM) and suggest the potential of MPNNs to enhance the robustness of the forecasts while improving the computational efficiency.

Keywords: multiphase diffusion, message passing neural network, well interconnection, interwell connectivity, graph neural network, capacitance-resistance models

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Authors: Hyun-Woo Cho

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Unexpected events may occur with serious impacts on industrial process. This work utilizes a data representation technique to model and to analyze process data pattern for the purpose of diagnosis. In this work, the use of triangular representation of process data is evaluated using simulation process. Furthermore, the effect of using different pre-treatment techniques based on such as linear or nonlinear reduced spaces was compared. This work extracted the fault pattern in the reduced space, not in the original data space. The results have shown that the non-linear technique based diagnosis method produced more reliable results and outperforms linear method.

Keywords: process monitoring, data analysis, pattern modeling, fault, nonlinear techniques

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Authors: Hyun-Woo Cho

Abstract:

Unexpected operational events or abnormalities of industrial processes have a serious impact on the quality of final product of interest. In terms of statistical process control, fault detection and diagnosis of processes is one of the essential tasks needed to run the process safely. In this work, nonlinear representation of process measurement data is presented and evaluated using a simulation process. The effect of using different representation methods on the diagnosis performance is tested in terms of computational efficiency and data handling. The results have shown that the nonlinear representation technique produced more reliable diagnosis results and outperforms linear methods. The use of data filtering step improved computational speed and diagnosis performance for test data sets. The presented scheme is different from existing ones in that it attempts to extract the fault pattern in the reduced space, not in the original process variable space. Thus this scheme helps to reduce the sensitivity of empirical models to noise.

Keywords: fault diagnosis, nonlinear technique, process data, reduced spaces

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Authors: Kwame Sarkodie, William Cheung, Andrew R. Fergursson

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The characterization of multiphase flow has gained enormous attention for most petroleum and chemical industrial processes. In order to fully characterize fluid phases in a stream or containment, there needs to be a profound knowledge of the existing composition of fluids present. This introduces a problem for real-time monitoring of fluid dynamics such as fluid distributions, and phase fractions. This work presents a simple technique of correlating absorbance spectrums of water, oil and air bubble present in containment. These spectra absorption outputs are derived by using an Fourier Infrared spectrometer. During the testing, air bubbles were introduced into static water column and oil containment and with light absorbed in the infrared regions of specific wavelength ranges. Attenuation coefficients are derived for various combinations of water, gas and oil which reveal the presence of each phase in the samples. The results from this work are preliminary and viewed as a build up to the design of a multiphase flow rig which has an infrared sensor pair to be used for multiphase flow characterization.

Keywords: attenuation, infrared, multiphase, spectroscopy

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Authors: Nacera YASSA, Abdelmalek saidoune, GHania ouadfel, Hamza Houassine

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The rapid advancement in electrical technologies has underscored the increasing importance of multiphase machines across various industrial sectors. These machines offer significant advantages in terms of efficiency, compactness, and reliability compared to their single-phase counterparts. However, early detection and diagnosis of electrical faults remain critical challenges to ensure the durability and safety of these complex systems. This paper presents an advanced analytical model for multiphase machines, with a particular focus on dual stator asynchronous machines. The primary objective is to develop a robust diagnostic tool capable of effectively detecting and locating electrical faults in these machines, including short circuits, winding faults, and voltage imbalances. The proposed methodology relies on an analytical approach combining electrical machine theory, modeling of magnetic and electrical circuits, and advanced signal analysis techniques. By employing detailed analytical equations, the developed model accurately simulates the behavior of multiphase machines in the presence of electrical faults. The effectiveness of the proposed model is demonstrated through a series of case studies and numerical simulations. In particular, special attention is given to analyzing the dynamic behavior of machines under different types of faults, as well as optimizing diagnostic and recovery strategies. The obtained results pave the way for new advancements in the field of multiphase machine diagnostics, with potential applications in various sectors such as automotive, aerospace, and renewable energies. By providing precise and reliable tools for early fault detection, this research contributes to improving the reliability and durability of complex electrical systems while reducing maintenance and operation costs.

Keywords: faults, diagnosis, modelling, multiphase machine

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Authors: Zhao Tianxu, Cui Shumei

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This paper proposes a novel multiphase motor structure. The armature winding consists of several independent multiphase windings that have different rating rotate speed and power. Compared to conventional motor, the novel motor structure has more operation mode and fault tolerance mode, which makes it adapt to high-reliability requirement situation such as electric vehicle, aircraft and ship. Performance of novel motor structure varies with winding match. In order to find optimum control strategy, motor torque character, efficiency performance and fault tolerance ability under different operation mode are analyzed in this paper, and torque distribution strategy for efficiency optimization is proposed. Simulation analyze is taken and the result shows that proposed structure has the same efficiency on heavy load and higher efficiency on light load operation points, which expands high efficiency area of motor and cruise range of vehicle. The proposed structure can improve motor highest speed.

Keywords: multiphase motor, armature winding match, torque distribution strategy, efficiency

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Authors: Hilal Naimi, Amelbahahouda Adamou-Mitiche, Lahcene Mitiche

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The main problem in the area of medical imaging has been image denoising. The most defying for image denoising is to secure data carrying structures like surfaces and edges in order to achieve good visual quality. Different algorithms with different denoising performances have been proposed in previous decades. More recently, models focused on deep learning have shown a great promise to outperform all traditional approaches. However, these techniques are limited to the necessity of large sample size training and high computational costs. This research proposes a denoising approach basing on LDTCWT (Lifting Dual Tree Complex Wavelet Transform) using Hybrid Thresholding with Wiener filter to enhance the quality image. This research describes the LDTCWT as a type of lifting wavelets remodeling that produce complex coefficients by employing a dual tree of lifting wavelets filters to get its real part and imaginary part. Permits the remodel to produce approximate shift invariance, directionally selective filters and reduces the computation time (properties lacking within the classical wavelets transform). To develop this approach, a hybrid thresholding function is modeled by integrating the Wiener filter into the thresholding function.

Keywords: lifting wavelet transform, image denoising, dual tree complex wavelet transform, wavelet shrinkage, wiener filter

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Authors: Abdullah Eqal Al Mazrooei

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In this work, a new nonlinear model will be introduced. The model is in the state-space form. The nonlinearity of this model is in the state equation where the state vector is multiplied by its self. This technique makes our model generalizes many famous models as Lotka-Volterra model and Lorenz model which have many applications in the real life. We will apply our new model to estimate the wind speed by using a new nonlinear estimator which suitable to work with our model.

Keywords: nonlinear systems, state-space model, Kronecker product, nonlinear estimator

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Authors: Hassan Manouzi

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We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: least squares, wick product, SPDEs, finite element, wiener chaos expansion, gradient method

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Authors: Swapan Maiti, Dipanwita Roy Chowdhury

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Nonlinear functions are essential in different cryptoprimitives as they play an important role on the security of the cipher designs. Rule 30 was identified as a powerful nonlinear function for cryptographic applications. However, an attack (MS attack) was mounted against Rule 30 Cellular Automata (CA). Nonlinear rules as well as maximum period CA increase randomness property. In this work, nonlinear rules of maximum period nonlinear hybrid CA (M-NHCA) are studied and it is shown to be a better crypto-primitive than Rule 30 CA. It has also been analysed that the M-NHCA with single nonlinearity injection proposed in the literature is vulnerable against MS attack, whereas M-NHCA with multiple nonlinearity injections provide maximum length cycle as well as better cryptographic primitives and they are also secure against MS attack.

Keywords: cellular automata, maximum period nonlinear CA, Meier and Staffelbach attack, nonlinear functions

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In the paper, our purpose is to enhance the ability to solve a nonlinear differential equation which is about the motion of an incompressible fluid flow going down of an inclined plane without thermal effect with a simple and innovative approach which we have named it new method. Comparisons are made amongst the Numerical, new method, and HPM methods, and the results reveal that this method is very effective and simple and can be applied to other nonlinear problems. It is noteworthy that there are some valuable advantages in this way of solving differential equations, and also most of the sets of differential equations can be answered in this manner which in the other methods they do not have acceptable solutions up to now. A summary of the excellence of this method in comparison to the other manners is as follows: 1) Differential equations are directly solvable by this method. 2) Without any dimensionless procedure, we can solve equation(s). 3) It is not necessary to convert variables into new ones. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison to the other methods.

Keywords: viscos fluid, incompressible fluid flow, inclined plane, nonlinear phenomena

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