Search Results (10)

This article investigates the effects of roof opening and closure conditions on the mean and fluctuating wind pressure coefficient of the roof surface through rigid model wind tunnel tests and further explores the non-Gaussian characteristics of wind pressure (skewness, kurtosis, and wind pressure probability density) under the two conditions. Then, based on the non-Gaussian characteristics under two working conditions, this paper constructs a Hermite moment model to solve the peak factor of the roof surface to evaluate the impact of roof opening and closure on the most unfavorable extreme wind pressure. The research results show that under the two working conditions of roof opening and closure, the windward leading edge’s mean and fluctuating wind pressure coefficients change most significantly, leading to an increase in the degree of flow separation at the windward leading edge. This causes the skewness, kurtosis, and probability density function of the wind pressure at the windward leading edge of the roof to deviate significantly from the standard Gaussian distribution, exhibiting strong non-Gaussian characteristics. Meanwhile, based on the Hermite moment model, it is found that the peak factor of most measuring points is concentrated between 3.5 and 5.0 under both roof opening and closure conditions, significantly higher than the recommended value of 2.5 in GB 50009-2012. In addition, under roof opening, the most unfavorable negative pressure coefficient is −4.54, and the absolute value of its most unfavorable negative pressure extreme is 1.3% higher than the roof opening closure condition. Full article

We studied theoretically and experimentally the propagation of structured Laguerre–Gaussian (sLG) beams through an optical system with general astigmatism based on symplectic ABCD transforms involving geometry of the second-order intensity moments symplectic matrices. The evolution of the coordinate submatrix ellipses accompanying the transformation of intensity patterns at different orientations of the cylindrical lens was studied. It was found that the coordinate submatrix W and the twistedness submatrix M of the symplectic matrix P degenerate in the astigmatic $\mathrm{sLG}$ beam with simple astigmatism, which sharply reduces the number of degrees of freedom, while general astigmatism removes the degeneracy. Nevertheless, degeneracy entails a simple relationship between the coordinate element $W_{xy}$ and the twistedness elements $M_{xy}$ and $M_{yx}$ of the submatrix M, which greatly simplifies the measurement of the total orbital angular momentum (OAM), reducing the full cycle of measurements of the Hermite–Gaussian (HG) mode spectrum (amplitudes and phases) of the structured beam to the only measurement of the intensity moment. Moreover, we have shown that Fourier transform by a spherical lens enables us to suppress the astigmatic OAM component and restore the original free-astigmatic $\mathrm{sLG}$ beam structure. However, with further propagation, the $\mathrm{sLG}$ beam restores its astigmatic structure while maintaining the maximum OAM. Full article

The non-Gaussian property and its influence on peak factors and extreme wind pressures on the long-span cylindrical roof are studied in this paper. Firstly, the moment-based Hermite polynomial model (HPM), which is used to determine peak factors of non-Gaussian processes, is briefly introduced. Then, wind tunnel tests for the scaled rigid roof model are carried out to measure wind pressures on the roof surface. The statistical and spatial distribution of non-Gaussian properties of wind pressure on the roof is demonstrated. Regions around curved edges along the span of the roof exhibiting strong non-Gaussian properties are found. Peak factors determined by the HPM are examined by wind tunnel results and then calculated for the entire roof. According to their distribution, the regions with considerable peak factors are found. Results indicate that the peak factor of constant 2.5 or peak factor following the Gaussian process assumption is far smaller than that determined by the HPM, leading to extreme wind pressures being underestimated by 40–50%. Hence, it is necessary to include the non-Gaussian properties of wind pressure when calculating their extreme values for such long-span cylindrical roofs. Full article

Large-span open prefabricated spatial grid structures are characterized by light mass, high flexibility, low self-oscillation frequency, and low damping, resulting in wind-sensitive structures. Meanwhile, their height tends to be relatively low, located in the wind field with a large wind speed gradient and high turbulence area. Therefore, surface airflow is complex, and many flow separations, reattachment, eddy shedding, and other phenomena occur, causing damage to local areas. This paper took the Evergrande Stadium in Guiyang, China, as the research object and used the random number cyclic pre-simulation method to study its surface extreme wind pressure. Firstly, five conventional distributions (Gaussian, Weibull, three-parameter gamma, generalized extreme value, and lognormal distribution) were fitted to the wind pressure probability densities at different measurement points on the surface of the open stadium. It is found that the same distribution could not be chosen to describe the probability density distribution of wind pressure at all measurement points. Hence, based on the simulation results, the Gaussian and non-Gaussian regions of this structure were divided to determine where to apply which distribution. Additionally, the accuracy of the peak factor, improved peak factor, and modified Hermite moment model method were compared to check their applicability. Finally, the effect of roughness on the extreme wind pressure distribution on the open stadium surface was also investigated according to the highest accuracy method above. The findings of this study will provide a reference for engineers in designing large-span open stadiums for wind resistance to minimize the occurrence of wind damage. Full article

Previous studies show that the largest wind-induced response of a square section fixed-base high-rise building occurs when the strong wind is blowing perpendicular onto a building face, and the greatest translational response is likely to occur in the crosswind direction. When it comes to a square section base-isolated high-rise building that allows the isolation system to yield under strong wind excitation, the inelastic response shows distinctive non-Gaussian characteristics under fluctuating wind excitation and mean drift phenomenon under non-zero mean wind load. These characteristics may lead to a quite different result when determining the most unfavorable wind direction. Thus, the influence of wind direction on the inelastic response of a square base-isolated high-rise building is discussed in this study based on synchronous pressure measurement. The multi-story superstructure is modeled as a linear elastic shear building, while the isolation system is represented in a bilinear hysteresis restoring force model. The peak value of the inelastic response is estimated through a moment-based Hermit model from an underlying standard Gaussian process. The results show that when the strong wind blows perpendicular onto a building face, the greatest inelastic displacement, both at the top and isolation level, occurs in the along-wind direction, which is different from the elastic response. With the change of wind direction, the largest combined inelastic displacement still occurs when the wind inclination angle is 0°, while the combined displacement in other directions is also very large, which is worthy of concern. Full article

Copyright protection of medical images is a vital goal in the era of smart healthcare systems. In recent telemedicine applications, medical images are sensed using medical imaging devices and transmitted to remote places for screening by physicians and specialists. During their transmission, the medical images could be tampered with by intruders. Traditional watermarking methods embed the information in the host images to protect the copyright of medical images. The embedding destroys the original image and cannot be applied efficiently to images used in medicine that require high integrity. Robust zero-watermarking methods are preferable over other watermarking algorithms in medical image security due to their outstanding performance. Most existing methods are presented based on moments and moment invariants, which have become a prominent method for zero-watermarking due to their favorable image description capabilities and geometric invariance. Although moment-based zero-watermarking can be an effective approach to image copyright protection, several present approaches cannot effectively resist geometric attacks, and others have a low resistance to large-scale attacks. Besides these issues, most of these algorithms rely on traditional moment computation, which suffers from numerical error accumulation, leading to numerical instabilities, and time consumption and affecting the performance of these moment-based zero-watermarking techniques. In this paper, we derived multi-channel Gaussian–Hermite moments of fractional-order (MFrGHMs) to solve the problems. Then we used a kernel-based method for the highly accurate computation of MFrGHMs to solve the computation issue. Then, we constructed image features that are accurate and robust. Finally, we presented a new zero-watermarking scheme for color medical images using accurate MFrGHMs and 1D Chebyshev chaotic features to achieve lossless copyright protection of the color medical images. We performed experiments where their outcomes ensure the robustness of the proposed zero-watermarking algorithms against various attacks. The proposed zero-watermarking algorithm achieves a good balance between robustness and imperceptibility. Compared with similar existing algorithms, the proposed algorithm has superior robustness, security, and time computation. Full article

This paper develops an approach based on Gram–Charlier-like expansions for modeling financial series to take in due account features such as leptokurtosis. A Gram–Charlier-like expansion adjusts the moments of interest of a given distribution via its own orthogonal polynomials. This approach, formerly adopted for univariate series, is here extended to a multivariate context by means of spherical densities. Previous works proposed the Gram–Charlier of the multivariate Gaussian, obtained by using Hermite polynomials. This work shows how polynomial expansions of an entire class of spherical laws can be worked out with the aim of obtaining a wide set of leptokurtic multivariate distributions. A Gram–Charlier-like expansion is a distribution characterized by an additional parameter with respect to the parent spherical law. This parameter, which measures the increase in kurtosis due to the polynomial expansion, can be estimated so as to make the resulting distribution capable of describing the empirical kurtosis found in the data. An application of the Gram–Charlier-like expansions to a set of financial assets proves their effectiveness in modeling multivariate financial series and assessing risk measures, such as the value at risk and the expected shortfall. Full article

We propose a local feature descriptor based on moment. Although conventional scale invariant feature transform (SIFT)-based algorithms generally use difference of Gaussian (DoG) for feature extraction, they remain sensitive to more complicated deformations. To solve this problem, we propose MIFT, an invariant feature transform algorithm based on the modified discrete Gaussian-Hermite moment (MDGHM). Taking advantage of MDGHM’s high performance to represent image information, MIFT uses an MDGHM-based pyramid for feature extraction, which can extract more distinctive extrema than the DoG, and MDGHM-based magnitude and orientation for feature description. We compared the proposed MIFT method performance with current best practice methods for six image deformation types, and confirmed that MIFT matching accuracy was superior of other SIFT-based methods. Full article

We treat the non-equilibrium evolution of an open one-particle statistical system, subject to a potential and to an external “heat bath” (hb) with negligible dissipation. For the classical equilibrium Boltzmann distribution, W_c,eq, a non-equilibrium three-term hierarchy for moments fulfills Hermiticity, which allows one to justify an approximate long-time thermalization. That gives partial dynamical support to Boltzmann’s Wc_,eq, out of the set of classical stationary distributions, Wc;st, also investigated here, for which neither Hermiticity nor that thermalization hold, in general. For closed classical many-particle systems without hb (by using W_c,eq), the long-time approximate thermalization for three-term hierarchies is justified and yields an approximate Lyapunov function and an arrow of time. The largest part of the work treats an open quantum one-particle system through the non-equilibrium Wigner function, W. Weq for a repulsive finite square well is reported. W’s (< 0 in various cases) are assumed to be quasi-definite functionals regarding their dependences on momentum (q). That yields orthogonal polynomials, H_Q,n(q), for Weq (and for stationary W_st), non-equilibrium moments, W_n, of W and hierarchies. For the first excited state of the harmonic oscillator, its stationary W_st is a quasi-definite functional, and the orthogonal polynomials and three-term hierarchy are studied. In general, the non-equilibrium quantum hierarchies (associated with Weq) for the W_n’s are not three-term ones. As an illustration, we outline a non-equilibrium four-term hierarchy and its solution in terms of generalized operator continued fractions. Such structures also allow one to formulate long-time approximations, but make it more difficult to justify thermalization. For large thermal and de Broglie wavelengths, the dominant W_eq and a non-equilibrium equation for W are reported: the non-equilibrium hierarchy could plausibly be a three-term one and possibly not far from Gaussian, and thermalization could possibly be justified. Full article

We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb) at thermal equilibrium at temperature T (either with ab initio dissipation or without it). Boltzmann’s classical equilibrium distributions generate, as Gaussian weight functions in momenta, orthogonal polynomials in momenta (the position-independent Hermite polynomialsHn’s). The moments of non-equilibrium classical distributions, implied by the Hn’s, fulfill a hierarchy: for long times, the lowest moment dominates the evolution towards thermal equilibrium, either with dissipation or without it (but under certain approximation). We revisit that hierarchy, whose solution depends on operator continued fractions. We review our generalization of that moment method to classical closed many-particle interacting systems with neither a hb nor ab initio dissipation: with initial states describing thermal equilibrium at T at large distances but non-equilibrium at finite distances, the moment method yields, approximately, irreversible thermalization of the whole system at T, for long times. Generalizations to non-equilibrium quantum interacting systems meet additional difficulties. Three of them are: (i) equilibrium distributions (represented through Wigner functions) are neither Gaussian in momenta nor known in closed form; (ii) they may depend on dissipation; and (iii) the orthogonal polynomials in momenta generated by them depend also on positions. We generalize the moment method, dealing with (i), (ii) and (iii), to some non-equilibrium one-particle quantum interacting systems. Open problems are discussed briefly. Full article