Rigorous Mathematical Derivation Research Articles

Analyses of the performance of adaptive subspace detector on fluctuating target detection in system‐dependent clutter background

The adaptive subspace detector in system-dependent clutter background (SDC-ASD) is proved to be able to improve the detection performance for deterministic target detection in the authors' previous study. However, the exact performance of the SDC-ASD for fluctuating target detection is still unknown. In this study, with the aid of matrix decomposition theory, the analytical performance of the SDC-ASD for detecting fluctuating target is considered and assessed. At the design stage, the rigorous mathematical derivation processes for the exact theoretical detection performance of the SDC-ASD for fluctuating target detection is derived. The theoretical results, which have explicitly expressions for both the false alarm probability and the detection probability, not only provide an effective mathematical method to analyse the fluctuating target detection performance, but also can further simplify the deterministic target detection assessments. At the analysis stage, Monte Carlo simulations are resorted to validate the analytical results. Numerical experiments are conducted to assess the effectiveness of the SDC-ASD for fluctuating target detection. Results show that the SDC-ASD, by dealing separately with the clutter and the noise, performs the best in comparison with its published counterparts, i.e. the generalised likelihood ratio detectors, the adaptive matched filters, the adaptive subspace detectors and the low-rank detectors based on sample covariance matrix. (Less)

Spin dephasing in a magnetic dipole field around large capillaries: Approximative and exact results

We present an analytical solution of the Bloch-Torrey equation for local spin dephasing in the magnetic dipole field around a capillary and for ensembles of capillaries, and adapt this solution for the study of spin dephasing around large capillaries. In addition, we provide a rigorous mathematical derivation of the slow diffusion approximation for the spin-bearing particles that is used in this regime. We further show that, in analogy to the local magnetization, the transverse magnetization of one MR imaging voxel in the regime of static dephasing (where diffusion effects are not considered) is merely the first term of a series expansion that constitutes the signal in the slow diffusion approximation. Theoretical results are in agreement with experimental data for capillaries in rat muscle at 7T.

Accurate Analysis of Finite-Volume Lumped Elements in Metamaterial Absorber Design

To simulate lumped elements (LEs) more accurately in metamaterial absorber (MA) designs, a finite-volume LE (FVLE) model based on the time-domain finite-integral theorem (TDFIT) is proposed in this paper. In MA designs, lumped resistors and capacitors play an important role in dissipating electromagnetic (EM) fields, controlling resonant frequencies, and achieving an impedance matching. Through a rigorous mathematical derivation, we successfully prove that an arbitrary lumped resistor or capacitor can be modeled more accurately by modifying the conductivity or permittivity of a finite-volume model in TDFIT method. Compared with existing traditional zero-volume LE (ZVLE) solutions, the coupling effect between the circuit part and the EM part can be considered much better in the proposed FVLE model. For this reason, the numerical results of the FVLE model match the measured results much better. In addition, a result comparison is given to validate that the challenges of grid dispersion error and frequency response error in the classic ZVLE solution can be greatly overcome by the proposed FVLE model.

Generalized Theory of Phase-Shifted Carrier PWM for Cascaded H-Bridge Converters and Modular Multilevel Converters

This paper discusses the generalized theory of phase-shifted carrier pulsewidth modulation (PSC-PWM) for cascaded H-bridge (CHB) converters and modular multilevel converters (MMCs), provides a reasonable classification of the PSC-PWM, and extends the possible phase-shift angles to full range. First, the PSC-PWM for CHB converter is classified into two categories by phase-shift pattern. In addition, by rigorous mathematical derivation, the impact law of the full-range phase-shift angles on harmonic minimization is obtained. And then, it is proved that the generalized theory is equally applicable to MMC, which also merges the former proposed PSC-PWM for MMCs into itself. Moreover, the harmonic analysis of the dead-time error voltage is discussed, which is found to have the same harmonic distribution as the ideal voltage, except for the emerging of odd-order harmonics. In summary, this generalized theory offers a general perspective of the PSC-PWM for CHB converter and MMC, and builds up a scientific and comprehensive understanding for researchers from both academia and industry. Finally, the analytical findings are sufficiently validated by simulation and experimental results.

Stabilization conditions for fuzzy control of uncertain fractional order non‐linear systems with random disturbances

A novel fractional order Takagi–Sugeno (T–S) fuzzy control method for a class of fractional order non-linear systems is proposed in this study. On the basis of the fractional order interval theory, the generalised T–S fuzzy model for a class of uncertain fractional order non-linear systems is presented. By using fractional order Lyapunov stability theorem, the more relaxed and practical sufficient stability conditions which are presented as a new set of linear matrix inequalities are put forward, which are guaranteed by rigorous mathematical derivation. The proposed control scheme is developed for fractional order non-linear systems stabilisation in the presence of random disturbances. Typical instances including the fractional order three-dimensional (3D) non-linear system and the fractional order 4D non-linear Lorenz hyperchaos are implemented. Simulation results indicate the designed fractional order T–S fuzzy control scheme works well compared with the existing method.

Design criterion involving comprehensive performance characteristics of nozzle–flapper valves

The traditional parameter design rule for the nozzle–flapper valves has always followed the maximum control pressure sensitivity criterion; however, this article queries the validity of this traditional parameter design theory for the comprehensive performance characteristics of a flapper–nozzle valve. Accordingly, a new parameter design rule, which involves symmetry, linearity and sensitivity of the control pressure, was constructed from a detailed and rigorous mathematical derivation that employs a non-dimensional analysis method. Then, an effect verification of the new criterion and a comparison between the pressure–flow curves and three key valve coefficients, which are dominated by the traditional rule and the new criterion, respectively, are performed. Finally, the comprehensive performance characteristics of the flapper–nozzle valve, such as the reliability, response, accuracy, sensitivity, efficiency, anti- disturbance and control pressure range, which are produced by the two parameter design rules, are compared. The results indicate that the performance of nozzle–flapper valve followed by the new parameter design criteria is superior to the performance directed by the traditional one with respect to various indexes, such as the reliability, response, accuracy and anti-disturbance. In addition, for the design of nozzle–flapper valves, the studies have also revealed that the optimal values of the structural parameter are dependent on the actual flapper motion ranges and the priority of the above-mentioned performance indexes. All these new findings can develop and supplement the existing design theory of nozzle–flapper valve and can also be beneficial to the design of double-nozzle–flapper electro-hydraulic servo valves.

A contribution to the design of fast code converters for position encoders

ABSTRACTPseudorandom binary sequences (PRBS) are very useful in many areas of applications. Absolute position encoders based on PRBS have many advantages. However, the pseudorandom code is not directly applicable to the digital electronic systems, hence a converter from pseudorandom to natural binary code is needed. Recently, a fast pseudorandom/natural code converter based on Galois PRBS generator (much faster than previously used converter based on Fibonacci PRBS generator) was proposed. One of the main parts of the Galois code converter is an initial logic. The problem of the design of the initial logic has been solved only for some single values of resolution, but it is still not solved for any value of resolution, which significantly limits the applicability of the fast Galois code converter. This paper solves this problem presenting the solution for the design of the initial logic of the fast Galois pseudorandom/natural code converters used in the pseudorandom position encoders, in general manner, that is for any value of the resolution, allowing for a wide applicability of the fast Galois pseudorandom position encoders. Rigorous mathematical derivation of the formula for the designing of the initial logic is presented. Simulation of the proposed converter is performed in NI MultiSim software. The proposed solution, although developed for pseudorandom position encoders, can be used in many other fields where PRBS are used.

Camera self-calibration with lens distortion

Camera calibration is considered as an important issue in computer vision. One aspect of camera calibration is to estimate the intrinsic parameters of the camera. These parameters determine how the image coordinates of a point are derived. In this paper, we present an accurate and flexible method to calibrate intrinsic parameters of a camera together with lens distortion. Through rigorous mathematical derivation, we get the relationship between the distortion and perfect image points. Then we use a stratified method to calculate the intrinsic parameters optimally. We verify the efficiency and accuracy of the proposed algorithm both with simulation and real image experiments.

Analysis Of The Multi-Channel Three Dimensional Probability Csma Protocol With Monitoring Function For Wsn

Abstract For the wireless sensor networks (WSNs), MAC layer protocol, relating to system throughput, involving functions of system, concerning the consumption of system energy efficiency, etc. other system indicators, is very important. With the development of WSN, involving vary businesses, the amount and style of data which the sensor nodes detecting is large and divertive. Based on threedimensional probability CSMA protocol, the proposed protocol, multi-channel three-dimensional probability CSMA protocol with monitoring function (MATP-CSMA), is providing the sensor nodes owning different task with diversified throughput, meeting the quality of services (QoS) of diversiform business. The paper analyses the protocol from three aspects: the system throughput, system delay and energy efficiency. Through rigorous mathematical derivation, get the exact expression of relevant indicators; with the use of simulation tools, verify the accuracy of the model and expressions

The Protocol of Probability Detection CSMA with Monitoring Function Based on Isolated Type Two Cross Tree Conflict Decomposition

In the Internet of Things, the CSMA protocol of detection probability of having a monitoring function of isolated binary-based conflict resolution. Analysis methods the averaging period, through rigorous mathematical derivation of accurate mathematical expression protocol-related indicators, and compare with other similar models. Through simulation, simulation and theoretical values consistency, the collision rate is reduced, throughput is significantly improved.

Fuzzy Generalized Predictive Control for Nonlinear Brushless Direct Current Motor

Abstract In the study, a novel fuzzy generalized predictive control (GPC) scheme is proposed for the stability control of nonlinear brushless DC motor (BLDCM). First, the fuzzy predictive model of BLDCM is presented via Takagi–Sugeno fuzzy model. Then, based on the controlled autoregressive moving average (CARMA) model transformed by Takagi–Sugeno fuzzy model of BLDCM, a new fuzzy GPC scheme for the nonlinear BLDCM is designed by combining fuzzy techniques and GPC theory, and the rigorous mathematical derivation is given. Finally, numerical simulations are implemented to verify the effectiveness and superiority of the proposed scheme. It also provides reference for other nonlinear even chaos control in actual project.

Assessment of errors in Precipitable Water data derived from Global Navigation Satellite System observations

Among the new remote sensing techniques, one of the most promising is a GNSS meteorology, which provides continuous remote monitoring of the troposphere water vapor in all weather conditions with high temporal and spatial resolution. The Continuously Operating Reference Station (CORS) network and available meteorological instrumentation and models were scrutinized (we based our analysis on ASG-EUPOS network in Poland) as a troposphere water vapor retrieval system. This paper shows rigorous mathematical derivation of Precipitable Water errors based on uncertainties propagation method using all available data source quality measures (meteorological sensors and models precisions, ZTD estimation error, interpolation discrepancies, and ZWD to PW conversion inaccuracies). We analyze both random and systematic errors introduced by indirect measurements and interpolation procedures, hence estimate the PW system integrity capabilities. The results for PW show that the systematic errors can be under half-millimeter level as long as pressure and temperature are measured at the observation site. In other case, i.e. no direct observations, numerical weather model fields (we used in this study Coupled Ocean Atmospheric Mesoscale Prediction System) serves as the most accurate source of data. Investigated empirical pressure and temperature models, such as GPT2, GPT, UNB3m and Berg introduced into WV retrieval system, combined bias and random errors exceeding PW standard level of accuracy (3mm according to E-GVAP report). We also found that the pressure interpolation procedure is introducing over 0.5hPa bias and 1hPa standard deviation into the system (important in Zenith Total Delay reduction) and hence has negative impact on the WV estimation quality.

Research on Interference Model of Cooperative Cognitive Radio Networks over Rayleigh Fading Channel

Cooperative spectrum sensing technology has been identified as an effective approach to mitigate the interference generated by cognitive radio users on primary networks. In this paper, based on the rigorous mathematical derivation, we proposed an interference model of cooperative cognitive radio networks on the licensed user over Rayleigh fading wireless channel. In the case of the cognitive radio users independently and cooperatively sensing the existence of the licensed user, the proposed model analyzes the effect of some key parameters on the interference such as the missing detection probability of spectrum sensing scheme, spatial density of cognitive radio users etc. This model not only is a theoretical expression but also can be put into applications. The numerical results are given to verify the proposed model.

Stability investigation of the Generalised-α time integration method for dynamic coupled consolidation analysis

In this paper, the stability of the Generalised-α time integration method (the CH method) for a fully coupled solid-pore fluid formulation is analytically investigated for the first time and the corresponding theoretical stability conditions are proposed based on a rigorous mathematical derivation process. The proposed stability conditions simplify to the existing ones of the CH method for the one-phase formulation when the solid–fluid coupling is ignored. Furthermore, by degrading the CH method to the Newmark method, the stability conditions are in agreement with the ones proposed in previous stability investigations on coupled formulation for the Newmark method. The analytically derived stability conditions are validated with finite element (FE) analyses considering a range of loading conditions and for various soil permeability values, showing that the numerical results are in agreement with the theoretical investigation. Then, the stability characteristics of the CH method are explored beyond the limits of the theoretical investigation, assuming elasto-plastic soil behaviour which is prescribed with a bounding surface plasticity constitutive model. Since the CH method is a generalisation of a number of other time integration methods, the derived stability conditions are relevant for most of the commonly utilised time integration methods for the two-phase coupled formulation.

Comparative Analysis of Underwater Vibrating Compaction Technology and Compaction on Land

In HongKong-Zhuhai-Macao bridge project, about 4.8 kilometers stone bed underwater should be compacted to make it smooth and remove the excess settlement. Vibrating compaction method would be used to tamp the stone layer with no dead angle in a short construction period. This paper theoretical studied on vibrating compaction technology of scattering-filling rubble stone layer. Vibrating compaction system and stone layer were simplified to a mechanical model and the vibration equation was established. According to an interpolation table, a fitting formula of equivalent damping was given. Through rigorous mathematical derivation, this paper gave mathematical expressions of the vibration displacement, the vibration velocity and compaction work on stone layer. Both compaction work on land and compaction work underwater could be calculated by these mathematical expressions. Lastly, through a set of field test parameters, comparative analysis between compaction work on land and compaction work underwater was carried out. The result shows that the weakening effect of water on compaction work is poor.

Probability Detection CSMA with Monitoring Based on the Improved Binary Tree Conflict Resolution Algorithm

This paper presents a new wireless sensor network MAC protocol: the probability detection CSMA protocol with monitoring function based on the improved binary tree conflict resolution algorithm. By using the average cycle method, the paper gets the mathematical expressions of the throughput, system average delay of the probability detection CSMA protocol with monitoring function and the probability detection CSMA protocol with monitoring function based on the improved binary tree conflict resolution algorithm through complicated mathematical modeling, rigorous mathematical derivation. The computer simulation results not only confirm the correctness of the theoretical analysis but also show that the probability detection CSMA protocol with monitoring function based on the improved binary tree conflict resolution algorithm due to adding to the conflict resolution algorithm, resulting in the increases of systemic throughput but increase the time delay of the system.

Similar Structure Algorithm for Solving Boundary Value Problem of Differential Equations

Based on the similar structure theory, we conduct rigorous mathematical derivation and proof for the boundary value problem of a class of differential equation . We put forward a new algorithm------Similar Structure Algorithm to solve such boundary value problems. The similar structure algorithm only includes arithmetic and logical operation, hence it can be oriented towards computer. According to the similar structure algorithm, an example is given to conduct a simulation experiment by the application of computer software at the end of the paper. And we also observe and analysis the variational laws of the laboratory result by changing the coefficient of the boundary condition.

Homogenization of immiscible compressible two-phase flow in highly heterogeneous porous media with discontinuous capillary pressures

This paper presents a study of immiscible compressible two-phase, such as water and gas, flow through highly heterogeneous porous media with periodic microstructure. Such models appear in gas migration through engineered and geological barriers for a deep repository for radioactive waste. We will consider a domain made up of several zones with different characteristics: porosity, absolute permeability, relative permeabilities and capillary pressure curves. Consequently, the model involves highly oscillatory characteristics and internal nonlinear interface conditions. The microscopic model is written in terms of the phase formulation, i.e. where the wetting (water) saturation phase and the non-wetting (gas) pressure phase are primary unknowns. This formulation leads to a coupled system consisting of a nonlinear parabolic equation for the gas pressure and a nonlinear degenerate parabolic diffusion-convection equation for the water saturation, subject to appropriate transmission, boundary and initial conditions. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Moreover, the transmission conditions are nonlinear and the saturation is discontinuous at interfaces separating different media. Under some realistic assumptions on the data, we obtain a nonlinear homogenized coupled system with effective coefficients which are computed via a cell problem and give a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence.

The Analysis of Probability Detection CSMA Protocol for Wireless Sensor Network Based on the Request-Response Mechanism

This paper presents a new MAC protocol the probability detection CSMA protocol for wireless sensor network based on the request-response mechanism. Builds the corresponding mathematical model using the average cycle method, and get the mathematical expression of systemic throughput through a rigorous mathematical derivation and makes the computer simulations. Simulation results show the correctness of the theoretical analysis and the effectiveness of the protocol; meanwhile, the protocol this paper presents increases the reliability and stability of the system through increasing RTS-CTS request-response mechanism and ACK handshake signal, thereby improving the systems transmission quality.

Homogenization results for a coupled system modelling immiscible compressible two-phase flow in porous media by the concept of global pressure

A model for immiscible compressible two-phase flow in heterogeneous porous media is considered. Such models appear in gas migration through engineered and geological barriers for a deep repository for radioactive waste. The main feature of this model is the introduction of a new global pressure and it is fully equivalent to the original equations. The resulting equations are written in a fractional flow formulation and lead to a coupled degenerate system which consists of a nonlinear parabolic (the global pressure) equation and a nonlinear diffusion–convection one (the saturation) equation with rapidly oscillating porosity function and absolute permeability tensor. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Under some realistic assumptions on the data, we obtain a nonlinear homogenized problem with effective coefficients which are computed via a cell problem and give a rigorous mathematical derivation of the upscaled model by means of two-scale convergence.