First-order Moment Research Articles

Assessing measurement uncertainty on trihalomethanes prediction through kinetic models in water supply systems

Disinfection of drinking water through chlorine is commonly used in many countries for reducing pathogenic infection problems, but it may pose a risk to human health due to the formation of some by-products, such as trihalomethanes (THMs). For an adequate management of the disinfection process, it is useful to have models capable of simulating THMs concentrations in water supply systems. However, a crucial aspect is the reliability of their performances when used on real systems and the knowledge of the uncertainty of their predictions. The objective of the present paper is to investigate the simulation of THMs formation through calibrated kinetic models, along with the assessment of the measurement uncertainty on the parameters' estimate and on the model predictions. In particular, a first-order, a second-order and a two-phase kinetic model are considered, while the effect of measurement uncertainty is mainly investigated through the first-order second moment (FOSM) method. The analysis performed on a real case study shows that the three considered models have similar performances in terms of predicted concentrations, which suggests using the simplest first-order one. Moreover, the FOSM results reveal that the first-order model is less affected by measurement uncertainty.

An Improved Algorithm Based on First-order Cyclostationarity for Recognition of M-FSK Signals

This paper proposes an improved algorithm based on Piecewise Auto Correlation Accumulation (PACA) and first-order cyclostationarity for recognition of M-ary frequency shift keying (M-FSK, M = 2/4/8) signals in communication systems. Theoretical analysis indicates that the number of first-order Cycle Frequencies (CFs) is equal to the modulation order of M-FSK signals. Therefore, by estimating the first-order cyclic moment of the autocorrelation of M-FSK signals and detecting the number of CFs, the modulation order of M-FSK signals can be identified. Based on its multicarrier characteristics, the proposed algorithm does not require a priori information and is not significantly influenced by factors such as timing delay and frequency offset. Further, PACA suppresses noise, and thereby helps to improve the antinoise performance of the algorithm’s modulation recognition. The results of simulations conducted confirm the efficacy of the proposed algorithm.

Quantum state tomography of the microwave field

We propose a new method for reconstructing the density matrix of a single-mode field of photons in the cavity using the discrete photodetection, which allows studying the quantum field in the microwave range. For reconstruction it is necessary to know the phase quadrature moments of all orders. A method of obtaining the first-order moment is discussed here.

A result on precise asymptotics for largest eigenvalues of β ensembles

The paper focuses on the precise asymptotics of the largest eigenvalues of β-Hermite ensemble and β-Laguerre ensemble. In particular, we obtain a general law on the precise moment convergence rates for a type of weighted series constructed by the first-order conditional moment of the largest eigenvalues of β ensembles. The results are motivated by the complete convergence for partial sums of independent random variables. The proofs depend on the small deviations for largest eigenvalue of β ensembles and non-asymptotic tail probability inequalities of the general β Tracy-Widom law.

Mean-value first-order saddlepoint approximation based collaborative optimization for multidisciplinary problems under aleatory uncertainty

Reliability-based multidisciplinary design optimization (RBMDO) has received increasing attention in engineering design for achieving high reliability and safety in complex and coupling systems (e.g., multidisciplinary systems). Mean-value first-order saddlepoint approximation (MVFOSA) is introduced in this paper and is combined with the collaborative optimization (CO) method for reliability analysis under aleatory uncertainty in RBMDO. Similar to the mean-value first-order second moment (MVFOSM) method, MVFOSA approximated the performance function with the first-order Taylor expansion at the mean values of random variables. MVFOSA uses saddlepoint approximation rather than the first two moments of the random variables to estimate the probability density and cumulative distribution functions. MVFOSA-based CO (MVFOSA-CO) is also formulated and proposed. Two examples are provided to show the accuracy and efficiency of the MVFOSA-CO method.

The impact of twine/mesh ratio on the flow dynamics through a porous cylinder

The impact of the twine/mesh ratio on the flow through a porous hollow cylinder of diameter D has been experimentally investigated at Reynolds number Re = 800 with a surface porosity varying from 0.67 to 0.90. Our porous cylinder models are inspired by aquaculture pens in that they have similar geometries, and porosities, to those nets commonly used within the aquaculture industry. We show that the surface porosity alone is not the key parameter determining the flow topology of the model, but rather a non-dimensional parameter \(\alpha =t^{0.5}D^{0.5}/m\) (based upon twine thickness t, mesh void m and cylinder diameter D) effectively collapses first-order moments. Three different wake regimes are observed in the flow for different twine/mesh ratios: a laminar flow regime where streamlines pass through the model without significant deformation; a partially occluded flow, where the mean flow is decelerated, and a flow with a fully developed recirculation zone exhibiting a von Karman vortex street similar to that produced in the wake of a solid cylinder. Our observation that the flow structure depends upon the parameter \(\alpha \), rather than simply the surface porosity, is supported by calculated dispersion times of virtual particles released both inside the model and within the wake. The particle distributions display three distinct dispersion behaviours, from nearly linear to a logarithmic decay slower than that of a solid cylinder, thus emphasising the existence of multiple flow regimes and the importance of the relative twine/mesh ratio.

Crystal growth, characterization and theoretical studies of alkaline earth metal-doped tetrakis(thiourea)nickel(II) chloride

The influence of Sr(II)-doping on the properties of tetrakis(thiourea)nickel(II) chloride (TTNC) has been described. The reduction in the intensity observed in powder X-ray diffraction of doped specimen and slight shifts in vibrational frequencies of doped specimens confirm the lattice stress as a result of doping. Surface morphological changes due to doping of the Sr(II) are observed by scanning electron microscopy. The incorporation of metal into the host crystal lattice was confirmed by energy dispersive X-ray spectroscopy. Lattice parameters are determined by single crystal XRD analysis. The thermogravimetric and differential thermal analysis studies reveal the purity of the materials and no decomposition is observed up to the melting point. The nonlinear optical properties of the doped and undoped specimens were studied. Theoretical calculations were performed using the Density functional theory (DFT) method with B3LYP/LANL2DZ as the basis set. The molecular geometry and vibrational frequencies of TTNC in the ground state were calculated and the observed structural parameters of TTNC are compared with parameters obtained from single crystal X-ray studies. The atomic charge distributions are obtained by Mulliken charge population analysis. The first-order molecular hyperpolarizability, polarizability and dipole moment were derived.

A Gini-based unit root test

A Gini-based statistical test for a unit root is suggested. This test is based on the well-known Dickey–Fuller test, where the ordinary least squares (OLS) regression is replaced by the semi-parametric Gini regression in modeling the AR process. A residual-based bootstrap is used to find critical values. The Gini methodology is a rank-based methodology that takes into account both the variate values and the ranks. Therefore, it provides robust estimators that are rank-based, while avoiding loss of information. Furthermore, the Gini methodology relies on first-order moment assumptions, which validates its use for a wide range of distributions. Simulation results validate the Gini-based test and indicate its superiority in some design settings in comparison to other available procedures. The Gini-based test opens the door for further developments such as a Gini-based cointegration test.

Semi-fragile self-recoverable watermarking algorithm based on wavelet group quantization and double authentication

Semi-fragile self-recoverable watermarking algorithms are important to meet various requirements such as security, robustness, localization, and image recovery. However, current approaches are not adequate for this importance. Thus, we propose a novel semi-fragile and self-recoverable watermarking algorithm based on a group quantization and double authentication method. In the proposed algorithm, a target image is first split into 16 ×16 image blocks. For each image block, a five-bit authentication watermark is generated from the first-order statistical moment of the block and then is embedded into the mid-frequency band of another image block by a novel group-based wavelet quantization method. With the generated watermarks, image security is enhanced by randomly permuting coefficients among a group and image robustness is improved by embedding the watermark in the largest coefficient inside a sub-group by significant difference parity quantization. The proposed double authentication ring structure effectively improves the image localization accuracy. Recovered image is a better approximate to the original image. Experimental comparisons of ours with other algorithms shows the effectiveness of the proposed self-recoverable and semi-fragile watermarking algorithm.

Novel Structures for Cyclic Convolution Using Improved First-Order Moment Algorithm

This paper first presents a decomposition scheme to reduce the computation time and make the first-order moment- based cyclic convolution well suited for hardware implementation. By decomposing the fixed convolution kernel into similar subparts and using their preprocessing results as control signals, each sub- part of cyclic convolution can be calculated with a basic computing substructure. Due to the flexibility of decomposition, a trade-off between computation time and hardware complexity exists. And for a pair of fixed decomposition coefficients, the similarity among subparts leads to the time-efficient structure and the area-efficient structure for cyclic convolution without limitation on the convolu- tion length and the word length . Since the basic computing substructure only contains a simple control module, several circu- larly right-shift registers and accumulation units, there is no requirement for multipliers and large memory. Comparisons in terms of area-delay product, area-time product and power con- sumption with the existing memory-based structures have been made to demonstrate the efficiency and effectiveness of the pro- posed structures. Using the same metrics, the comparison results further show significant improvement of theproposed designs over the previous first-order moment-based structure.

Application of Gaussian Moment Closure to Microscale Flows with Moving Embedded Boundaries

The application of the Gaussian moment closure to continuum and microscale flows with embedded, and possibly moving, boundaries is considered. The Gaussian moment closure is briefly reviewed, as is an extension that allows for the treatment of flow of diatomic gases. A parallel upwind, finite volume scheme with adaptive mesh refinement using a Roe-type numerical flux function is described for solving the hyperbolic system of partial differential equations arising from this closure on multiblock meshes with embedded and possibly moving boundaries. The purely hyperbolic nature of moment equations makes them particularly insensitive to discretizations involving grids with irregularities. Typical of adaptive mesh-refinement, embedded-boundary, and Cartesian cut-cell treatments, mesh irregularities are difficult to deal with when second derivatives are required by the physical model. Such is the case for the Navier–Stokes equations. Numerical solutions to mathematical descriptions involving second derivatives show significantly degraded solution quality as compared to solutions of first-order quasi-linear moment equations. Solid-wall boundary conditions are implemented via a Knudsen-layer approximation. Comparisons are made between numerical solutions of the Gaussian model on both body-fitted meshes and meshes with embedded boundaries, as well as to experimental and approximate analytic results for a variety of flow problems. The benefits and potential of the proposed approach for unsteady microscale flow applications having complex geometries are clearly demonstrated.

Regional Variance for Multi-Object Filtering

Recent progress in multi-object filtering has led to algorithms that compute the first-order moment of multi-object distributions based on sensor measurements. The number of targets in arbitrarily selected regions can be estimated using the first-order moment. In this work, we introduce explicit formulae for the computation of the second-order statistic on the target number. The proposed concept of regional variance quantifies the level of confidence on target number estimates in arbitrary regions and facilitates information-based decisions. We provide algorithms for its computation for the probability hypothesis density (PHD) and the cardinalized probability hypothesis density (CPHD) filters. We demonstrate the behaviour of the regional statistics through simulation examples.

Multi-target Bayesian filter for propagating marginal distribution

The Bayesian filter and its approximation, the probability hypothesis density (PHD) filter, propagate joint distribution of the multi-target state and the first-order moment of the joint distribution, respectively. However, these two filters fail to distinguish multiple distinct targets when these targets are closely spaced. To efficiently distinguish closely spaced targets according to a sequence of measurements, we (1) use the individual state distributions to model the uncertainties of individual target states caused by the target dynamic uncertainty and measurement uncertainty, (2) use the existence probabilities of individual targets to characterize the randomness of target appearance and disappearance, and (3) propose a novel multi-target Bayesian filter. Instead of maintaining the joint state distribution, the proposed filter jointly propagates the marginal distributions and existence probabilities of each target. An implementation of the proposed filter for linear and Gaussian models is also presented to deal with an unknown and variable number of targets. The simulation results demonstrate that the proposed filter is better at distinguishing distinct targets and tracking multiple targets than the Gaussian mixture PHD filter.

Uncertainty Quantification in Remaining Useful Life Prediction Using First-Order Reliability Methods

In this paper, we investigate the use of first-order reliability methods to quantify the uncertainty in the remaining useful life (RUL) estimate of components used in engineering applications. The prediction of RUL is affected by several sources of uncertainty, and it is important to systematically quantify their combined effect on the RUL prediction in order to aid risk assessment, risk mitigation, and decision-making. While sampling-based algorithms have been conventionally used for quantifying the uncertainty in RUL, analytical approaches are computationally cheaper, and sometimes they are better suited for online decision-making. Exact analytical algorithms may not be available for practical engineering applications, but effective approximations can be made using first-order reliability methods. This paper describes three first-order reliability-based methods for RUL uncertainty quantification: first-order second moment method (FOSM), the first-order reliability method (FORM), and the inverse first-order reliability method (inverse-FORM). The inverse-FORM methodology is particularly useful in the context of online health monitoring, and this method is illustrated using the power system of an unmanned aerial vehicle, where the goal is to predict the end of discharge of a lithium-ion battery.

Simplicial Homology of Random Configurations

Given a Poisson process on a d-dimensional torus, its random geometric simplicial complex is the complex whose vertices are the points of the Poisson process and simplices are given by the C̆ech complex associated to the coverage of each point. By means of Malliavin calculus, we compute explicitly the three first-order moments of the number of k-simplices, and provide a way to compute higher-order moments. Then we derive the mean and the variance of the Euler characteristic. Using the Stein method, we estimate the speed of convergence of the number of occurrences of any connected subcomplex as it converges towards the Gaussian law when the intensity of the Poisson point process tends to infinity. We use a concentration inequality for Poisson processes to find bounds for the tail distribution of the Betti number of first order and the Euler characteristic in such simplicial complexes.

Simplicial Homology of Random Configurations

Given a Poisson process on a d-dimensional torus, its random geometric simplicial complex is the complex whose vertices are the points of the Poisson process and simplices are given by the C̆ech complex associated to the coverage of each point. By means of Malliavin calculus, we compute explicitly the three first-order moments of the number of k-simplices, and provide a way to compute higher-order moments. Then we derive the mean and the variance of the Euler characteristic. Using the Stein method, we estimate the speed of convergence of the number of occurrences of any connected subcomplex as it converges towards the Gaussian law when the intensity of the Poisson point process tends to infinity. We use a concentration inequality for Poisson processes to find bounds for the tail distribution of the Betti number of first order and the Euler characteristic in such simplicial complexes.

Central Difference Kalman-probability Hypothesis Density Filter for Multiple Speakers Tracking

Aiming at nonlinear system model in multiple speakers tracking, a central difference Kalman-probability hypothesis density filter for multiple speakers tracking is proposed in this paper. Time difference of arrival for microphone array is taken as measurement, Stirling interpolation formula is utilized to derive polynomial approximations of nonlinear functions, central difference Kalman filter and Gaussian mixture probability hypothesis density filter are applied to estimate first-order statistical moment of posterior multiple speakers states, and finally multiple speakers tracking of nonlinear Gaussian system is realized while the speakers states are extracted by recursive updating. Simulation results show that the robustness of the algorithm is enhanced, and estimation accuracy of multiple speakers number and states is improved.

Unit root vector autoregression with volatility induced stationarity

Abstract We propose a discrete-time multivariate model where lagged levels of the process enter both the conditional mean and the conditional variance. This way we allow for the empirically observed persistence in time series such as interest rates, often implying unit-roots, while at the same time maintain stationarity despite such unit-roots. Specifically, the model bridges vector autoregressions and multivariate ARCH models in which residuals are replaced by levels lagged. An empirical illustration using recent US term structure data is given in which the individual interest rates are found to have unit roots, have no finite first-order moments, but remain strictly stationary and ergodic. Moreover, they co-move in the sense that their spread has no unit root. The model thus allows for volatility induced stationarity, and the paper shows conditions under which the multivariate process is strictly stationary and geometrically ergodic. Interestingly, these conditions include the case of unit roots and a reduced rank structure in the conditional mean, known from linear co-integration. Asymptotic theory of the maximum likelihood estimators for a particular structured case (so-called self-exciting) is provided, and it is shown that T -convergence to Gaussian distributions apply despite unit roots as well as absence of finite first and higher order moments. Monte Carlo simulations illustrate the asymptotic theory.

Principal resonance responses of SDOF systems with small fractional derivative damping under narrow-band random parametric excitation

The principal resonance responses of nonlinear single-degree-of-freedom (SDOF) systems with lightly fractional derivative damping of order α (0<α<1) subject to the narrow-band random parametric excitation are investigated. The method of multiple scales is developed to derive two first order stochastic differential equation of amplitude and phase, and then to examine the influences of fractional order and intensity of random excitation on the first-order and second-order moment. As an example, the stochastic Duffing oscillator with fractional derivative damping is considered. The effects of detuning frequency parameter, the intensity of random excitation and the fractional order derivative damping on stability are studied through the largest Lyapunov exponent. The corresponding theoretical results are well verified through direct numerical simulations. In addition, the phenomenon of stochastic jump is analyzed for parametric principal resonance responses via finite differential method. The stochastic jump phenomena indicates that the most probable motion is around the larger non-trivial branch of the amplitude response when the intensity of excitation is very small, and the probable motion of amplitude responses will move from the larger non-trivial branch to trivial branch with the increasing of the intensity of excitation. Such stochastic jump can be considered as bifurcation.

A Novel Approach to Compute Discrete W Transform

The discrete W transform (DWT) is widely used in digital signal processing. This paper proposes a novel approach to compute DWT via computation of the first-order moments without multiplications. A scalable and efficient systolic array is designed to implement this approach. Compared with the other existing methods, the proposed algorithms are simpler and more applicable.