Proposed Extrapolation Method Research Articles

A Novel Load Extrapolation Method for Multiple Non-Stationary Loads on the Drill Pipe of a Rotary Rig

The drill pipe of a rotary rig is subject to the dynamic influence of non-stationary loads, including rotation torque and applied force. In order to address the challenge of simultaneously extrapolating multiple non-stationary loads, a novel extrapolation framework is proposed. This framework utilizes rainflow counting to obtain mean and amplitude sequences of the loads. The extreme values of the amplitude sequence are fitted using the Generalized Pareto Distribution (GPD), while the median values are fitted using the Double Kernel Density Estimation (DKDE). By extrapolating the Inverse Cumulative Distribution Function (ICDF) based on the fitted distribution, a new amplitude sequence can be derived. The combination of this extrapolated amplitude sequence with the original mean sequence forms a new load spectrum. The results of applying the proposed extrapolation method to the drill pipe of a rotary rig demonstrate the ability of the method to yield conservative extrapolation results and accurately capture the variations in damage under the original working conditions.

A double load spectrum extrapolation for drill pipe of rotary drilling rig considering load sequence

The load spectrum of rotary drilling rig’s drill pipe is used for drill pipe design, simulated fatigue testing, and reliability assessment. However, the proper extrapolation of the drill pipe double load is challenging, especially to meet the requirements of both load sequence and load strengthening. In this paper, an extrapolation technique for a double load of drill pipe is proposed. The time sequence rainflow counting technique is proposed to keep the torque and pressure sequence. Meanwhile, the individual distributions of the loads are accurately estimated. Finally, the torque and pressure are simulated and extrapolated by the percentile extrapolation method. The results show that the proposed extrapolation method for maintaining the load sequence enriches the dynamics and diversity of the loads while ensuring the load sequence.

Fermionic physics from abinitio path integral Monte Carlo simulations of fictitious identical particles.

The abinitio path integral Monte Carlo (PIMC) method is one of the most successful methods in statistical physics, quantum chemistry and related fields, but its application to quantum degenerate Fermi systems is severely hampered by an exponential computational bottleneck: the notorious fermion signproblem. Very recently, Xiong and Xiong [J. Chem. Phys. 157, 094112 (2022)] have suggested to partially circumvent the signproblem by carrying out simulations of fictitious systems guided by an interpolating continuous variable ξ ∈ [-1, 1], with the physical Fermi- and Bose-statistics corresponding to ξ = -1 and ξ = 1. It has been proposed that information about the fermionic limit might be obtained by calculations within the bosonic sector ξ > 0 combined with an extrapolation throughout the fermionic sector ξ < 0, essentially bypassing the signproblem. Here, we show how the inclusion of the artificial parameter ξ can be interpreted as an effective penalty on the formation of permutation cycles in the PIMC simulation. We demonstrate that the proposed extrapolation method breaks down for moderate to high quantum degeneracy. Instead, the method constitutes a valuable tool for the description of large Fermi-systems of weak quantum degeneracy. This is demonstrated for electrons in a 2D harmonic trap and for the uniform electron gas (UEG), where we find excellent agreement (∼0.5%) with exact configuration PIMC results in the high-density regime while attaining a speed-up exceeding 11 orders of magnitude. Finally, we extend the idea beyond the energy and analyze the radial density distribution (2D trap), as well as the static structure factor and imaginary-time density-density correlation function (UEG).

Actuation Arrangement of Rigid Foldable Waterbomb Origami

Abstract A novel approach is proposed to arrange the actuations of rigid foldable waterbomb origami with multiple facet loops such that the number of actuations equaled the degrees-of-freedom (DOF) of the origami. In this approach, the rigid waterbomb origami was regarded as a combination of three types of six-crease origami units, which is equivalent to spherical 6R mechanisms with three DOF. Then, clear, target, and arrangement parts were created to define the facets of the origami pattern in the proposed extrapolation method. The actuation arrangement for a waterbomb origami pattern, which extended outwards circumferentially from a six-crease origami unit, was completed, and adams software was used to verify the correctness of the arrangement. Finally, an intuitive mathematical method was used to arrange the actuations for this type of waterbomb origami. The proposed approach provided DOF for the rigid foldable waterbomb origami and facilitated an actuation design such that the origami exhibits unique motion and can be normally actuated.

Piecewise Iterative Extrapolation Method for Bandlimited Signal

In some high spectrally efficient communication structures, the Gerchberg-Papoulis extrapolation algorithm can be used to reconstruct nonorthogonal signals. However, the extrapolation efficiency and accuracy degrades when the energy of known signal is small or the iterative filter bandwidth is large. Focused on these drawbacks, a piecewise iterative extrapolation method is proposed to extrapolate bandlimited signals with higher extrapolation efficiency and accuracy. In this paper, the amplitude change of the unknown part over iterations is analyzed and the feasibility of the proposed extrapolation method is discussed. Numerical simulation shows the accuracy superiority of proposed method with the frequency offset compared to the GP algorithm with fixed computational complexity. Besides, the feasibility of the proposed method is verified in fractional Fourier domain with performance advantages.

Generative Adversarial CT Volume Extrapolation for Robust Small-to-Large Field of View Registration

Intraoperative Computer Tomographs (iCT) provide near real time visualizations which can be registered with high-quality preoperative images to improve the confidence of surgical instrument navigation. However, intraoperative images have a small field of view making the registration process error prone due to the reduced amount of mutual information. We herein propose a method to extrapolate thin acquisitions as a prior step to registration, to increase the field of view of the intraoperative images, and hence also the robustness of the guiding system. The method is based on a deep neural network which is trained adversarially using self-supervision to extrapolate slices from the existing ones. Median landmark detection errors are reduced by approximately 40%, yielding a better initial alignment. Furthermore, the intensity-based registration is improved; the surface distance errors are reduced by an order of magnitude, from 5.66 mm to 0.57 mm (p-value = 4.18×10−6). The proposed extrapolation method increases the registration robustness, which plays a key role in guiding the surgical intervention confidently.

Low- and High-Frequency Extrapolation of Band-Limited Frequency Responses to Extract Delay Causal Time Responses

Frequency responses, such as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> parameters, can be utilized to analyze the time-domain characteristics of circuit components and systems using the hybrid time–frequency-domain approach [1]. However, most frequency responses have a limited frequency range and no low-frequency data due to the limitations of the bandwidth of instruments and the computational resource of simulators. Using these frequency responses, the accuracy and delay causality of the extracted time responses cannot be guaranteed, occurring an inaccurate time-domain analysis. Therefore, this article presents a low- and high-frequency extrapolation method to extract the delay causal time responses from the band-limited frequency responses. Unlike previous methods, the proposed extrapolation method can accurately estimate a propagation delay for improving the accuracy of the overall extrapolated frequency response, even if the applied band-limited frequency response has no low-frequency data. Moreover, in this method, the coefficients of both the low- and high-frequency extrapolation functions can be extracted precisely without an intensive iteration. To verify the proposed method, a two-port network using a multisection band-stop filter and a four-port differential channel using coupled transmission lines were designed. In both cases, the proposed method had a higher accuracy than previous methods, such as the delay-based macromodeling scheme and noniterative extrapolation for the high-frequency range. Furthermore, the computational efficiency of the proposed method was also higher than the delay-based macromodeling while maintaining a similar efficiency as with the noniterative extrapolation method.

Accelerated image reconstruction using extrapolated Tikhonov filtering for photoacoustic tomography.

Development of simple and computationally efficient extrapolated Tikhonov filtering reconstruction methods for photoacoustic tomography. The model-based reconstruction algorithms in photoacoustic tomography typically utilize Tikhonov regularization scheme for the reconstruction of initial pressure distribution from the measured boundary acoustic data. The automated choice of regularization parameter in these cases is computationally expensive. Moreover, the Tikhonov scheme promotes the smooth features in the reconstructed image due to the smooth regularizer, thus leading to loss of sharp features. The proposed extrapolation method estimates the solution at zero regularization assuming the solution being a function of regularization parameter and thus posing it as a zero value problem. Thus, the numerically computed zero regularization solution is expected to have better features compared to standard Tikhonov solution, with an added advantage of removing the necessity of automated choice of regularization. The reconstructed results using this method were shown in three variants (Lanczos, traditional, and exponential) of Tikhonov filtering and were compared with the standard error estimate technique. Four numerical (including realistic breast phantom) and two experimental phantom data were utilized to show the effectiveness of the proposed method. It was shown that the proposed method performance was superior than the standard error estimate technique, being at least four times faster in terms of computation, and provides an improvement as high as 2.6 times in terms of standard figures of merit. The developed extrapolated Tikhonov filtering methods overcome the difficulty of obtaining a suitable regularization parameter and shown to be reconstructing high-quality photoacoustic images with additional advantage of being computationally efficient, making it more appealing in real-time applications.

Experimental Investigation of Roughness Effect on Ship Resistance Using Flat Plate and Model Towing Tests

Towing tests on a thin flat plate of 3-mm thickness and on a ship model in smooth and rough condition were performed and extrapolation to ship scale was attempted. A newly designed experimental setup was constructed for the examination of the thin plate. The experiments on smooth flat plate included examination of a series of trip wires for flow stimulation, among which the optimum was 1.3 mm. In rough condition, the plate was covered with sandpapers of 40 and 80 grit. Both calculated roughness functions exhibited Nikuradse behavior, verifying the validity of the experiments. The equivalent sand roughness height was 1.7 times the average sandpaper roughness, as calculated by the Schlichting diagram for sand-roughened plates. Both roughness functions indicated transitionally rough regime, except for the last two data of the rougher sandpaper that lay on the fully rough regime. The results were extrapolated to ship scale using Granville method. Extrapolation of smooth model results in ship scale revealed that the traditional Froude method predicts higher resistance coefficient compared to the International Towing Tank Conference (ITTC) 78 method. Rough model results were extrapolated to ship scale by applying a newly proposed extrapolation method, using Schlichting resistance formula for rough plates as the friction correlation line, according to Froude method and for two length scales, namely the plate and ship length. The two versions of the proposed extrapolation method provided an upper and lower limit for the predicted rough hull total resistance coefficient.

Simplified Effective Notch Stress calculation for non-overlapping circular hollow section K-Joints

This paper presents two simplified procedures for the calculation of the Effective Notch Stress (ENS) on non-overlapping circular hollow section (CHS) K-joints. The proposed procedures aim to alleviate the modeling challenges associated with the traditional ENS calculation on joints with complex geometry, such as the CHS joints. The first procedure is an extension of the recently proposed extrapolation method, similar to the extrapolation in the widely-used Structural Hot-Spot Stress (SHSS) approach. The second procedure provides ENS estimations based on the parametric relationship between the ENS and SHSS. Through an extensive numerical study, this investigation develops parametric equations supporting each procedure, covering practical geometric range for CHS K-joints under balanced brace axial load. Both simplified procedures demonstrate close agreement with the traditional ENS calculation and provide reasonable fatigue life assessments with a substantial number of experimental data, based on the S-N framework.

An extrapolation method to determine the effective notch stress in circular hollow section X‐joints

AbstractThis paper presents an extrapolation method to determine the effective notch stress (ENS) on the weld toes of welded circular hollow section (CHS) X‐joints in‐line with the extrapolation method to determine the structural hot‐spot stress in existing design guidelines. This investigation verifies and extends the recently proposed ENS extrapolation scheme to CHS X‐joints, which elevates significantly the difficulty in generating a weld toe radius along the brace‐to‐chord intersection as required in existing guidelines. An extensive numerical study then investigates the ENS extrapolation for CHS X‐joints under three loading conditions, namely, the brace axial load, the brace in‐plane bending load, and the brace out‐of‐plane bending load. The numerical study derives a set of recommended extrapolation parameters that ensures accurate ENS estimation for each loading condition. This paper demonstrates that the proposed extrapolation method for the CHS X‐joints yields good agreement with the standard ENS calculation procedure described in the International Institute of Welding (IIW) guideline.

An extrapolation method to determine the effective notch stress in welded joints

AbstractThis paper presents the development of an extrapolation method to estimate the notch stress in welded steel joints, in line with the effective notch stress concept described in the International Institute of Welding guideline. The proposed approach provides a convenient method to determine the local notch stress at the weld toes without the need to model a finite notch radius as required in engineering guidelines, which creates significant modeling challenges in the numerical procedure, especially for 3‐D joints with a complex topology. An experimental study validates the feasibility of this extrapolation method through strain measurements on cruciform joints. The numerical study then investigates two types of welded connections: (1) cruciform joints with full‐penetration welds and (2) tube‐to‐plate joints. The proposed extrapolation method provides accurate effective notch stress estimations on both joint types, compared with the effective notch stress calculated following the mesh requirement in the existing guidelines.

Determination of ice content in hardened concrete by low-temperature calorimetry

Low-temperature calorimetry has been used to determine the ice content in concrete at different temperatures when exposed to low-temperature environments. However, the analysis of the ice content from the measured data of heat flow is not straightforward. In this study, two important factors influencing the ice content calculation are discussed. The importance of the baseline determination for the calculation of the ice content is realized. Two different methods of generating the baseline are discussed. First, the ‘J-baseline’ is discussed which is a recently proposed extrapolation method based on the accumulated heat curves measured in the freezing and the melting process. Second, the ‘C-baseline’ is discussed in which a calculated baseline is used where the heat capacity of both water and ice and the phase changing behaviour under different testing temperatures are considered. It turns out that both the ‘J-baseline’ method and the ‘C-baseline’ method can be used to calculate the approximate baseline. The heat of fusion of the water confined in small pores is another important parameter to be considered in ice content calculation. This property must be carefully analyzed in order to accurately calculate the ice contents at different temperatures in the freezing and melting process. It should be noted that there is no general agreement on how to obtain the important temperature dependence of the heat of fusion of water confined in small pores. By performing comparison studies, the present study shows the influence of the different values of the heat of fusion commonly adopted on the calculated ice content for the studied concrete samples. The importance and necessity to use an accurate value of the heat of fusion is emphasized. Based on the calculation of the baseline proposed in this work and by carefully selecting the values for the heat of fusion, the ice content in a hardened concrete sample is expected to be estimated with an acceptable accuracy.

A Method of Map Extrapolation for Unequal and Partial Admission in a Double Entry Turbine

This paper presents a method for prediction of the unequal admission performance of a double entry turbine based on the full admission turbine maps and a minimal number of unequal admission points. The double entry turbine has two separate inlet ports which feed a single turbine wheel: this arrangement can be beneficial in a turbocharger application; however the additional entry does add complexity in producing a complete turbine map which includes unequal admission behavior. When a double entry turbine is operated under full admission conditions, with both entries feeding the turbine equally, this will act effectively as a single entry device and the turbine performance can be represented by a standard turbine map. In reality a multiple entry turbine will spend the majority of time operating under varying degrees of unequal admission, with each entry feeding the turbine different amounts; the extent of this inequality can have a considerable impact on turbine performance. In order to produce a full map which extends from full admission through to the partial admission case (where one inlet has no flow) a large number of unequal admission data points are required. The paper starts by discussing previous attempts to describe the partial and unequal admission performance of a double entry turbine. The full unequal admission performance is then presented for a nozzled, double entry turbine. The impact of unequal admission on turbine performance is demonstrated. Under some conditions of operation, the turbine efficiency may be less than half that of the equivalent full admission case based on the average turbine velocity ratio. A method of using the steady, equal admission maps, with a limited number of unequal admission data points, to predict the full unequal admission behavior is presented. A good agreement is found when the map extension method is validated against the full unequal admission turbine performance measured on a test stand. In the prediction of efficiency a mean error of approximately 0.39% is found between the test stand data and the proposed extrapolation method, with a standard deviation of 2.79%. A better agreement is generally found at conditions of higher power.

Load Spectrum Compilation Based on Nonparametric Statistical Extrapolation

Considering the special load characteristics of the wheel loader, thispaper focus on compiling the load spectrum of the transmission of the wheelloader using the nonparametric statistical extrapolation method (NSEM). In thisprocess, the determination of the kernel function shape is the critical issue,which has been discussed in detail. Before extrapolating the sample loadspectrum, the signal denoising of the field-tested time-history load signals isperformed. After that, the sample load cycles are obtained using the rainflowcounting method and the corresponding kernel function shape is determined. Thenthe NSEM of rainflow matrix is proposed, by which the whole-life load spectrumis estimated. The proposed extrapolation method can well realize the estimationof the load cycles that do not appear in sample load cycles but may exist inthe whole-life load history.

Short‐term extreme response analysis of a jacket supporting an offshore wind turbine

ABSTRACTWind turbines must be designed in such a way that they can survive in extreme environmental conditions. Therefore, it is important to accurately estimate the extreme design loads. This paper deals with a recently proposed method for obtaining short‐term extreme values for the dynamic responses of offshore fixed wind turbines. The 5 MW NREL wind turbine is mounted on a jacket structure (92 m high) at a water depth of 70 m at a northern offshore site in the North Sea. The hub height is 67 m above tower base or top of the jacket, i.e. 89 m above mean water level. The turbine response is numerically obtained by using the aerodynamic software HAWC2 and the hydrodynamic softwareUSFOS. Two critical responses are discussed, the base shear force and the bending moment at the bottom of the jacket. The extreme structural responses are considered for wave‐induced and wind‐induced loads for a 100 year return‐period harsh metocean condition with a 14.0 m significant wave height, a 16 s peak spectral period, a 50 m s − 1(10 min average) wind speed (at the hub) and a turbulence intensity of 0.1 for a parked wind turbine. After performing the 10 min nonlinear dynamic simulations, a recently proposed extrapolation method is used for obtaining the extreme values of those responses over a period of 3 h. The sensitivity of the extremes to sample size is also studied. The extreme value statistics are estimated from the empirical mean upcrossing rates. This method together with other frequently used methods (i.e. the Weibull tail method and the global maxima method) is compared with the 3 h extreme values obtained directly from the time‐domain simulations. Copyright © 2012 John Wiley &amp; Sons, Ltd.

An improved ITU-R rain attenuation prediction model over terrestrial microwave links in tropical region

AbstractAn improved approach of predicting rain attenuation cumulative distribution (CD) over terrestrial microwave links operating in tropical regions is presented in this article. The proposed method offers a better extrapolation approach for determining the values of rain attenuation at different exceedance probability from the measured attenuation at 0.01% of the time. The experimental data consist of measured rainfall rates and rain attenuation over six geographically spread DIGI MINI-LINKs operating at 15 GHz in Malaysia. A new set of numerical coefficients was derived for improved rain attenuation CD predictions in the Malaysian tropical climate. In order to test the applicability of the proposed extrapolation method, a validation was performed using rain rate and rain attenuation measurements from five Brazilian and seven Nigerian tropical locations. When tested against measurements, the proposed method seems to provide a significant improvement over the current extrapolation method adopted by ITU-R Recommendations P.530-14, for the prediction of rain attenuation CD over tropical regions.

Efficient Low-Delay Distributed Video Coding

Distributed video coding (DVC) is a video coding paradigm that allows for a low-complexity encoding process by exploiting the temporal redundancies in a video sequence at the decoder side. State-of-the-art DVC systems exhibit a structural coding delay since exploiting the temporal redundancies through motion-compensated interpolation requires the frames to be decoded out of order. To alleviate this problem, we propose a system based on motion-compensated extrapolation that allows for efficient low-delay video coding with low complexity at the encoder. The proposed extrapolation technique first estimates the motion field between the two most recently decoded frames using the Lucas-Kanade algorithm. The obtained motion field is then extrapolated to the current frame using an extrapolation grid. The proposed techniques are implemented into a novel architecture featuring hybrid block-frequency Wyner-Ziv coding as well as mode decision. Results show that having references from both temporal directions in interpolation provides superior rate-distortion performance over a single temporal direction in extrapolation, as expected. However, the proposed extrapolation method is particularly suitable for low-delay coding as it performs better than H.264/AVC intra, and it is even able to outperform the interpolation-based DVC codec from DISCOVER for several sequences.

Extrapolation of Wideband Electromagnetic Response Using Sparse Representation

Wideband electromagnetic response can be extrapolated using combined low frequency and early time information, which can substantially reduce the computational load. Most existing extrapolation methods are based on orthogonal polynomials, but selecting optimal parameters of orthogonal polynomials is not straightforward. This work proposes to extrapolate wideband electromagnetic response using sparse representation. The electromagnetic response is expressed as linear combination of atoms from an overcomplete dictionary. Optimal linear combination of atoms is then sought through the affine scaling transformation and the support vector regression. By increasing the data length step by step, convergence of the sparse solution is used as a criterion to determine the sufficient data length. Performance analysis shows that our proposed extrapolation method retains lower computational complexity and renders more flexibility in reconstructing a signal. Numerical examples are presented to show the efficacy and advantages of the proposed extrapolation method.

The singular stress field and stress intensity factors of a crack terminating at a bimaterial interface

For the fracture evaluation of inclined cracks terminating at the dissimilar material interface, not only the singularities, but also the detailed stress field and its stress intensity factors are necessary. However, though there are many researches reported on the singularity analysis, the stress field and its stress intensity factors are still not clear. This paper has deduced theoretically the singular stress and displacement fields near the tip of a crack terminating at the interface between bonded dissimilar materials, for both cases of real and oscillatory singularities. From the deduced singular stress field, the stress intensity factors are defined for such a crack, and the corresponding numerical extrapolation methods are also proposed. Through the numerical examinations, it is found that the theoretical stress distributions agree well with the numerical results obtained by the finite element method. Moreover, the proposed extrapolation method shows a good linearity, thus it can be used as an efficient way to determine the characteristics of the stress and displacement fields near the tip of a crack terminating at interface.