Recursive Integration Research Articles

Real-time dynamic displacement monitoring with double integration of acceleration based on recursive least squares method

Due to the difficulty of establishing fixed reference points, it is difficult to monitor displacement of a civil engineering structure in the field for long term. Although to integrate acceleration signals numerically is a common and low-cost displacement measurement method, the schemes proposed in the field of seismology are not suitable for long-term structural monitoring environment because of batch calculations of existing algorithms. In this paper, combining a baseline correction technique based on recursive least squares, a recursive high-pass filter and a recursive integrator, through multi-round baseline correction, filtering and integration, the authors develop an online and real-time acceleration integral scheme. This scheme is then applied to a numerical simulation case and a shaking table test, where the accuracy and reliability are proved. Finally, the applicability of the scheme in real monitoring environment is confirmed through utilizing it to monitor displacement of a real bridge.

3D2SeqViews: Aggregating Sequential Views for 3D Global Feature Learning by CNN With Hierarchical Attention Aggregation.

Learning 3D global features by aggregating multiple views is important. Pooling is widely used to aggregate views in deep learning models. However, pooling disregards a lot of content information within views and the spatial relationship among the views, which limits the discriminability of learned features. To resolve this issue, 3D to Sequential Views (3D2SeqViews) is proposed to more effectively aggregate the sequential views using convolutional neural networks with a novel hierarchical attention aggregation. Specifically, the content information within each view is first encoded. Then, the encoded view content information and the sequential spatiality among the views are simultaneously aggregated by the hierarchical attention aggregation, where view-level attention and class-level attention are proposed to hierarchically weight sequential views and shape classes. View-level attention is learned to indicate how much attention is paid to each view by each shape class, which subsequently weights sequential views through a novel recursive view integration. Recursive view integration learns the semantic meaning of view sequence, which is robust to the first view position. Furthermore, class-level attention is introduced to describe how much attention is paid to each shape class, which innovatively employs the discriminative ability of the fine-tuned network. 3D2SeqViews learns more discriminative features than the state-of-the-art, which leads to the outperforming results in shape classification and retrieval under three large-scale benchmarks.

Dynamic stiffness matrix for free vibration analysis of flexure hinges based on non-uniform Timoshenko beam

As a typical non-uniform beam with complex varying cross-section and large curvature, free vibration analysis of flexure hinges in the state-of-the-art compliant mechanisms is challenging due to their complicated and even unsolvable governing differential equation. Investigation on the free vibration analysis of non-uniform beams was attractive in the past but still with a few types of specific beams or approximate solutions. The contribution of this paper is to formulate the dynamic stiffness matrix for generic non-uniform beams and applied for the first time to the free vibration analysis of flexure hinges. Firstly, the vibration solution of general non-uniform Timoshenko beam is derived by using a recursive integral in power series of circular frequency but not the traditional way in the well-known method of Frobenious. Then, the dynamic stiffness matrix of non-uniform Timoshenko beam is derived based on the variational principle. At last, the new method is applied for the free vibration analysis of flexure hinges and flexure-based compliant mechanisms. Several case studies demonstrate the advantage of the proposed approach in terms of high accuracy, generality and high efficiency (only one element is needed). The obtained results are useful for dynamic design of flexure hinges and can serve as a benchmark to examine the accuracy of other numerical solutions. Due to the closed form and universality of the proposed method, it is also of benefit for free vibration analysis of other non-uniform beams with all kinds of varying cross-section or functionally graded beams.

The detection of abandoned mineshafts by railway track bed using transmitted seismic waves using broadside shot gathers

The practical challenges of mineshaft detection under railway embankments are discussed, together with typical mineshaft properties over the centuries. The paper focuses on the broadside shot seismic transmission method to detect abandoned mineshafts, with the potential to be used in the vicinity of embankments. A numerical model was developed, using a new type of absorbing boundary condition, which is referred to as the Recursive Integration Perfectly Matched Layer. From a series of simulations using this model, a series of practical outcomes were identified regarding the feasibility of the broadside seismic transmission method. These include the layout of the geophones, the frequency of the shot source together with ways of improving the signal to noise ratio. The results from a field trail in East Lothian, Scotland are compared with the output from the numerical model and good agreement was identified.

Multipole Perfectly Matched Layer for Finite-Difference Time-Domain Electromagnetic Modeling

A new multipole perfectly matched layer (PML) formulation is presented. Based on the stretched-coordinate approach, the formulation that utilizes a recursive integration concept in its development, introduces a PML stretching function that is created as the sum of any given number of complex-frequency shifted (CFS) constituent poles. Complete formulae for up to a three-pole formulation, to facilitate its implementation in finite-difference time-domain codes, are developed. The performance of this new multipole formulation compares favorably with existing higher order PMLs that instead utilize stretching functions that are developed as the product of elementary CFS constituent poles. It is argued that the optimization of the new multipole PML (MPML) could be more straightforward when compared to that of a higher order PML due to the absence of extra terms generated by the process of multiplication used in the development of the overall PML stretching function in higher order PMLs. The new MPML is found to perform very well when compared to standard CFS-PMLs requiring equivalent computational resources.

Application of Linear Viscoelastic Properties in Semianalytical Finite Element Method with Recursive Time Integration to Analyze Asphalt Pavement Structure

Traditionally, asphalt pavements are considered as linear elastic materials in finite element (FE) method to save computational time for engineering design. However, asphalt mixture exhibits linear viscoelasticity at small strain and low temperature. Therefore, the results derived from the elastic analysis will inevitably lead to discrepancies from reality. Currently, several FE programs have already adopted viscoelasticity, but the high hardware demands and long execution times render them suitable primarily for research purposes. Semianalytical finite element method (SAFEM) was proposed to solve the abovementioned problem. The SAFEM is a three‐dimensional FE algorithm that only requires a two‐dimensional mesh by incorporating the Fourier series in the third dimension, which can significantly reduce the computational time. This paper describes the development of SAFEM to capture the viscoelastic property of asphalt pavements by using a recursive formulation. The formulation is verified by comparison with the commercial FE software ABAQUS. An application example is presented for simulations of creep deformation of the asphalt pavement. The investigation shows that the SAFEM is an efficient tool for pavement engineers to fast and reliably predict asphalt pavement responses; furthermore, the SAFEM provides a flexible, robust platform for the future development in the numerical simulation of asphalt pavements.

LC-HRMS Data Processing Strategy for Reliable Sample Comparison Exemplified by the Assessment of Water Treatment Processes.

The behavior of micropollutants in water treatment is an important aspect in terms of water quality. Nontarget screening by liquid chromatography coupled to high-resolution mass spectrometry (LC-HRMS) offers the opportunity to comprehensively assess water treatment processes by comparing the signal heights of all detectable compounds before and after treatment. Without preselection of known target compounds, all accessible information is used to describe changes across processes and thus serves as a measure for the treatment efficiency. In this study, we introduce a novel LC-HRMS data processing strategy for the reliable classification of signals based on the observed fold changes. An approach for filtering detected features was developed and, after parameter adjustment, validated for its recall and precision. As proof of concept, the fate of 411 target compounds in a 0.1 μg/L standard mix was tracked throughout the data processing stages, where 406 targets were successfully recognized and retained during filtering. Potential pitfalls in signal classification were addressed. We found the recursive peak integration to be a key point for the reliable classification of signal changes across a process. For evaluating the repeatability, a combinatorial approach was conducted to verify the consistency of the final outcome using technical replicates of influent and effluent samples taken from an ozonation process during drinking water treatment. The results showed sufficient repeatability and thus emphasized the applicability of nontarget screening for the assessment of water treatment processes. The developed data processing strategies may be transferred to other research fields where sample comparisons are conducted.

Nonlinear thermomechanical response and constitutive modeling of viscoelastic polyethylene membranes

Thin films of linear low-density polyethylene show a significant time-dependent behavior, strongly reliant on temperature and strain rate effects. A constitutive nonlinear thermo-viscoelastic relation is developed to characterize the response of thin membranes up to yielding, in a wide range of temperatures, strain rates, and mechanical loading conditions. The presented plane stress orthotropic formulation involves the free volume theory of viscoelasticity and the time-temperature superposition principle, necessary to describe non-linearities and non-isothermal conditions. Uniaxial tension tests at constant strain rate and long-duration biaxial inflation experiments have been employed in the calibration of the material parameters. The model has been implemented in the Abaqus finite element code by means of a user-defined subroutine based on a recursive integration algorithm. The accuracy of the constitutive relation has been validated against experimental data of full field diaphragm inflation tests and uniaxial tension, relaxation and cyclic experiments, covering sub-ambient temperatures and strain rate ranges observed during the operation of stratospheric balloons.

Prescreening and efficiency in the evaluation of integrals over ab initio effective core potentials.

New, efficient schemes for the prescreening and evaluation of integrals over effective core potentials (ECPs) are presented. The screening is shown to give a rigorous, and close bound, to within on average 10% of the true value. A systematic rescaling procedure is given to reduce this error to approximately 0.1%. This is then used to devise a numerically stable recursive integration routine that avoids expensive quadratures. Tests with coupled clusters with single and double excitations and perturbative triple calculations on small silver clusters demonstrate that the new schemes show no loss in accuracy, while reducing both the power and prefactor of the scaling with system size. In particular, speedups of roughly 40 times can be achieved compared to quadrature-based methods.

Design of Second Order Recursive Digital Integrators with Matching Phase and Magnitude Response

Design of Second Order Recursive Digital Integrators with Matching Phase and Magnitude Response

A Neumann series of Bessel functions representation for solutions of perturbed Bessel equations

A new representation for a regular solution of the perturbed Bessel equation of the form is obtained. The solution is represented as a Neumann series of Bessel functions uniformly convergent with respect to . For the coefficients of the series, explicit direct formulas are obtained in terms of the systems of recursive integrals arising in the spectral parameter power series (SPPS) method, as well as convenient for numerical computation recurrent integration formulas. The result is based on application of several ideas from the classical transmutation (transformation) operator theory, recently discovered mapping properties of the transmutation operators involved and a Fourier–Legendre series expansion of the transmutation kernel. For convergence rate estimates, asymptotic formulas, a Paley–Wiener theorem, and some results from constructive approximation theory were used. We show that the analytical representation obtained among other possible applications offers a simple and efficient numerical method able to compute large sets of eigendata with a nondeteriorating accuracy.

GprMax: Open source software to simulate electromagnetic wave propagation for Ground Penetrating Radar

gprMax is open source software that simulates electromagnetic wave propagation, using the Finite-Difference Time-Domain (FDTD) method, for the numerical modelling of Ground Penetrating Radar (GPR). gprMax was originally developed in 1996 when numerical modelling using the FDTD method and, in general, the numerical modelling of GPR were in their infancy. Current computing resources offer the opportunity to build detailed and complex FDTD models of GPR to an extent that was not previously possible. To enable these types of simulations to be more easily realised, and also to facilitate the addition of more advanced features, gprMax has been redeveloped and significantly modernised. The original C-based code has been completely rewritten using a combination of Python and Cython programming languages. Standard and robust file formats have been chosen for geometry and field output files. New advanced modelling features have been added including: an unsplit implementation of higher order Perfectly Matched Layers (PMLs) using a recursive integration approach; diagonally anisotropic materials; dispersive media using multi-pole Debye, Drude or Lorenz expressions; soil modelling using a semi-empirical formulation for dielectric properties and fractals for geometric characteristics; rough surface generation; and the ability to embed complex transducers and targets. Program summaryProgram title: gprMaxCatalogue identifier: AFBG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBG_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU GPL v3No. of lines in distributed program, including test data, etc.: 627180No. of bytes in distributed program, including test data, etc.: 26762280Distribution format: tar.gzProgramming language: Python.Computer: Any computer with a Python interpreter and a C compiler.Operating system: Microsoft Windows, Mac OS X, and Linux.RAM: Problem dependentClassification: 10.External routines: Cython[1], h5py[2], matplotlib[3], NumPy[4], mpi4py[5]Nature of problem: Classical electrodynamicsSolution method: Finite-Difference Time-Domain (FDTD)Running time: Problem dependent

Rank constrained distribution and moment computations

Consider a set of independent random variables with specified distributions or a set of multivariate normal random variables with a product correlation structure. This paper shows how the distributions and moments of these random variables can be calculated conditional on a specified ranking of their values. This can be useful when the ordering of the variables can be determined without observing the actual values of the variables, as in ranked set sampling, for example. Thus, prior information on the distributions and moments from their individual specified distributions can be updated to provide improved posterior information using the known ranking. While these calculations ostensibly involve high dimensional integral expressions, it is shown how the previously developed general recursive integration methodology can be applied to this problem so that they can be evaluated in a straightforward manner as a series of one-dimensional or two-dimensional integral calculations. Furthermore, the proposed methodology possesses a self-correction mechanism in the computation that prevents any serious growth of the errors. Examples illustrate how different kinds of ranking information affect the distributions, expectations, variances, and covariances of the variables, and how they can be employed to solve a decision making problem.

Integral Representation of Vega for American Put Options

There is an inaccurate formula in Huang et al. (1996) [Huang J., M. Subrahmanyam, and G. Yu (1996) Pricing and Hedging American Options: A Recursive Integration Method. Review of Financial Studies 9 (1):277–300]. In fact, a substantial term is missing in their equation (14) for computing the value of an important option hedging parameter, i.e., the vega. We fix it in this note by providing its correct form and characterizing an associated (new) integral equation. Some related explanations and arguments are also corrected.

Distribution of Discrete Time Delta-Hedging Error via a Recursive Relation

AbstractWe introduce a new method to compute the approximate distribution of the Delta-hedging error for a path-dependent option, and calculate its value over various strike prices via a recursive relation and numerical integration. Including geometric Brownian motion and Merton's jump diffusion model, we obtain the approximate distribution of the Delta-hedging error by differentiating its price with respect to the strike price. The distribution from Monte Carlo simulation is compared with that obtained by our method.

A Dynamic Programming Track‐Before‐Detect Algorithm Based on Local Linearization for Non‐Gaussian Clutter Background

The Dynamic programming track before detect (DP-TBD) algorithm has been widely used for detection and tracking of weak targets. The selection of the merit function has an immediate influence on the performance of the DP-TBD. The amplitude merit function is easy to calculate, but the performance of which will decrease in the presence of non-Gaussian clutter. The likelihood ratio merit function in closed analytical form is difficult to derive under non-Gaussian background without target signal parameters. To solve this problem, a novel DPTBD algorithm based on local linearization is proposed. Taking maximum of the state conditional probability ratio of the target as the optimal criteria, a recursive integration equation is derived. The equation is locally linearized by Taylor series expansion and a suboptimal multi-frame test statistic is developed. The calculation of new merit function in the statistic needs only clutter distribution model, and heavy clutter peak can be restrained by making use of clutter distribution characters. So the proposed algorithm can efficiently extract weak target in strong non-Gaussian clutter. Numerical simulations are provided to assess and compare the performance of the proposed algorithm. It turns out that the proposed algorithm has better detection and tracking performance than the widely used DPTBD algorithm at present and is resilient to various clutter distribution models.

Free Vibration Analysis of Integrally Stiffened Plates with Plate-Strip Stiffeners

We investigated the natural frequencies and mode shapes of a freely vibrating, integrally stiffened and/or stepped plate. The stiffeners used here were plate-strip stiffeners as opposed to the normally employed rib stiffeners. Both the plate and stiffeners were analyzed using the first-order shear deformation theory. The deflections and rotations were assumed as a tensor product of Timoshenko beam functions, chosen appropriately according to the given boundary conditions. Unlike Navier and Levy solution techniques, the approach used in this paper can also be applied to fully clamped, free, and cantilever supported stiffened plates. The governing differential equations were solved using the Rayleigh–Ritz method. The development of the stiffness and the mass matrices in the Ritz analysis was found to consume a huge amount of CPU time due to recursive integration of Timoshenko beam functions. An approach is suggested to greatly decrease this amount of CPU time, by replacing the recursive integration in a loop structure in the computer program, with the analytical integration of the integrand in the loop. The numerical results were compared with the solutions available in the literature as well as the commercially available finite-element software ABAQUS®, and the results were found to be highly satisfactory.

An integral equation representation approach for valuing Russian options with a finite time horizon

In this paper, we first describe a general solution for the inhomogeneous Black–Scholes partial differential equation with mixed boundary conditions using Mellin transform techniques. Since Russian options with a finite time horizon are usually formulated into the inhomogeneous free-boundary Black–Scholes partial differential equation with a mixed boundary condition, we apply our method to Russian options and derive an integral equation satisfied by Russian options with a finite time horizon. Furthermore, we present some numerical solutions and plots of the integral equation using recursive integration methods and demonstrate the computational accuracy and efficiency of our method compared to other competing approaches.

Design of half sample delay recursive digital integrators using trapezoidal integration rule

This paper describes the design of half sample delay recursive digital integrators. For this, a half sample delay is applied on trapezoidal integration rule, then a modified FIR fractional delay filter is used to design recursive digital integrators. The modified FIR fractional delay filter is less complex and more efficient than original one. In this way lower order recursive digital integrators have been designed and compared with existing half sample delay and conventional recursive digital integrators. The results show the effectiveness of the proposed integrators with low percentage absolute magnitude relative error (PARE) and linear phase response over almost 0% to 80% of the entire Nyquist frequency range.

A Generalization of the Recursive Integration Method for the Analytic Valuation of American Options

This article provides a general accelerated recursive integration method for pricing American options based on stochastic volatility and double jump processes. Our proposed model is a generalization of the recursive integral representation method. American option prices can be evaluated by the sum of a corresponding European option price and an early exercise premium integral. Numerical results show that our proposed method is efficient and accuracy in pricing American options with stochastic volatility and double jump processes. © 2015 Wiley Periodicals, Inc. Jrl Fut Mark 36:887–901, 2016