Four-point Algorithm Research Articles

One-stage extraction four-point algorithm for rainflow cycle counting in fatigue life estimation

PurposeIn order to improve the computation efficiency of the four-point rainflow algorithm, a one-stage extraction four-point rainflow algorithm is proposed based on a novel data preprocessing method.Design/methodology/approachIn this new algorithm, the procedure of cycle counting is simplified by introducing the data preprocessing method. The high efficiency of new algorithm makes it a preferable candidate in fatigue life online estimation of structural health monitoring systems.FindingsAccording to the data preprocessing method, in the process of cycle extraction, all equivalent cycles can be extracted at just one stage instead of two stages in the four-point rainflow algorithm, where the cycle extraction has to be performed from the doubled residue. Besides, there are no residues in the new algorithm. The extensive numerical simulation results demonstrate that the accuracy of new algorithm is the same as that of the four-point rainflow algorithm. Moreover, a comparative study based on a long input data sequence shows that the computation efficiency of the new algorithm is 42% higher than that of the four-point rainflow algorithm.Originality/valueThis merit of new algorithm makes it preferable in some application scenarios where fatigue life estimation needs to be accomplished online based on massive measured data. And it may attribute to preprocessing of input data sequence before data processing, which provides beneficial guidance to improve the efficiency of existing algorithms.

A comparative study of three methods to detect the upper atmospheric wind speed by DASH

The DASH (Doppler asymmetric spatial heterodyne) is used to detect the upper atmospheric wind speed by its imaging Fizeau interference fringes. There are two wind measurement methods: Fourier series method (FSM) and popular Fourier transform method (FTM). However, the wind speed measurement accuracy of FTM is greatly influenced by window function, and the calculation is relatively complicated. The Four-point algorithm (FPA) for DASH’s wind speed measurement is proposed in this paper. The contents of wind speed measurement principle, forward modeling, noise and inversion by the FSM, FTM and FPA are wholly compared and studied. The three wind speed measurement methods are all derived from the phase difference transformation of DASH Fizeau interference fringes. The Fizeau interference fringes with wind speed of 0–100 m/s at the interval of 10 m/s are simulated, and the forward wind speeds are obtained by FSM, FTM and FPA, and the corresponding wind measurement errors are 2.93%, 4.67% and 3.00%, respectively. After artificially adding Gaussian noise with a mean value of 0 and a standard deviation of 0.1, FSM, FTM and FPA are used to forward the Fizeau interference fringes after flat field, and the corresponding relative errors are 2.30%, 11.66% and 2.27%, respectively. After artificially adding Gaussian noise, the Fizeau interference fringes of wind speeds of 31–39 m/s with 1 m/s interval and 30.1–30.9 m/s with 0.1 m/s interval are simulated, and the forward wind speeds are obtained by FSM and FPA. In both cases, the wind speed measurement errors of FSM are 3.55% and 4.15% higher than those of FPA. The O(<sup>1</sup>S) 557.7 nm airglow at peak altitude of 98 km in Xi’an was photographed by using our GBAII (ground based airglow imaging interferometer)-DASH, and the imaging interferograms with zenith angles of 0° and 45° were obtained. Then by the methods of Fourier series, Fourier transform and FPA are used to obtain the inversion wind speed of 32.21 m/s, 43.55 m/s and 32.17 m/s, respectively. From the forward and inversion results of DASH, we can see that the FPA has a better result for detecting the upper atmospheric wind due to its simple calculation and smaller wind measurement error.

A compact static birefringent interferometer for the measurement of upper atmospheric winds: concept, design and lab performance

Abstract. A new compact static wind imaging interferometer, called the Birefringent Doppler Wind Imaging Interferometer (BIDWIN), has been developed for the purpose of observing upper atmospheric winds using suitably isolated airglow emissions. The instrument combines a field-widened birefringent delay plate placed between two crossed Wollaston prisms with an imaging system, waveplates and polarizers to produce four fixed 90∘ phase-stepped images of the interference fringes conjugate to the scene of interest. A four-point algorithm is used to extract line-of-sight Doppler wind measurements across the image of the scene. The arrangement provides a similar throughput to that of a field-widened Michelson interferometer; however, the interferometric component of BIDWIN is smaller, simpler to assemble and less complicated to operate. Consequently, the instrument provides a compact, lightweight and robust alternative that can be constructed and operated with lower cost. In this paper, the instrument concept is presented, and the design and optimization of a prototype version of the instrument are discussed. Characterization of the lab prototype is presented, and the performance of the instrument is examined by applying the instrument to measure a low-velocity two-dimensional Doppler wind field with a high precision (5 m s−1) in the lab.

On One Solution of the Numerical Problem Differentiation in Calculation Vertical Speed of Aircraft

To ensure safety and improve the efficiency of flight missions, reliable information about the altitude and speed parameters of the aircraft (AC) is required. Therefore, improving the algorithm for calculating the vertical speed used as part of the algorithmic support for air signal systems (ASS) is a very urgent task. Purpose of the study. The problem of calculating the vertical speed of an aircraft in the ASS is considered. Materials and methods. The analysis of literature data on the use of numerical differentiation procedures to solve this problem is carried out, it is noted that the methods used are based on different ideas and approaches. It is indicated that two-point algorithms are significantly worse than multi-point algorithms in terms of the achieved accuracy, howe¬ver, they are characterized by significant simplicity and speed. Various versions of multipoint algorithms are used, differing in complexity, the amount of information used, and the accuracy achieved. The features of the regularizing algorithms, which are essentially filters of a low-frequency useful signal, suppressing the high-frequency component of the error in measuring the altitude signal or, what is the same, atmospheric pressure, are noted. The data on systems with hardware differentiation of the height signal are given. Results. A fairly simple four-point algorithm for numerical differen¬tiation is proposed and substantiated. Due to the averaging of both the measurement results themselves and the estimates of the derivatives, significant filtering of noise is realized, which is an important advantage of the algorithm. For greater accuracy in estimating the vertical speed, it is envisa¬ged to include a preliminary filtering algorithm in the experimental data processing scheme. The filtering algorithm is found from the solution of the optimization problem; it is shown that this algorithm is structurally similar to the filtering algorithms constructed according to the well-known approaches of R. Kalman. The results of computational experiments on the study of the features and characteristics of the proposed algorithms are presented, illustrating their advantages, performance and the possibility of further use in ASS. It is shown that preliminary filtering significantly increases the accuracy of the vertical velocity estimation. Conclusion. The developed algorithms can be used to improve the algorithmic support of the ASS.

Four-Point Regulation Algorithm for an End-Effector of a Flexible Drilling Robot

A new four-point algorithm for orientation and position regulation of an end-effector for a flexible drilling robot is presented in this paper．Four non-coplanar points in three-dimensional space can determine a unique sphere tangent to them, we can find out this sphere’s center point and radii and regard the shape of a workpiece surface in machining area approximately as such a sphere. A vector from the machining point to the center point is regarded as the one normal to the workpiece surface. By this principle, the algorithm firstly measured and calculated a vector normal to drilling machining area on curved surface by four points，and then calculated the difference between this normal vector and the axis of the spindle. If there is difference, the algorithm further figures out the angles of two revolving axes on end-effector and the displacements of three linear axes on robot main body, which should be adjusted．Simulation results of two kinds of curved surface show that the accuracy and efficiency satisfy the practical requirements using this algorithm．

Equivalence of four-point and three-point rainflow cycle counting algorithms

Two forms of the rainflow cycle counting algorithm for fatigue damage prediction are shown to be equivalent, namely the three-point algorithm as presented by Bannantine et al. [Bannantine JA, Comer JJ, Handrock JL. Fundamentals of metal fatigue analysis. Englewood Cliffs, NJ: Prentice-Hall; 1990], and the four-point algorithm as presented by Amzallag et al. [Amzallag C, Gerey JP, Robert JL, Bahuaud J. Standardization of the rainflow counting method for fatigue analysis. Int J Fatigue 1994;16:287–293]. While it can be demonstrated by example that the same result is obtained by the two algorithms, no generalised proof of their equivalence has previously been presented. The proof is built on several identified properties of the four-point algorithm, including that certain modifications to the stress series being analysed do not alter the outcome.

A new approach using a phase-measuring algorithm in detector-width-compensated displacement-measuring interferometer

Use of spatial phase measurement techniques in a displacement-measuring grating interferometer using detector width compensation becomes impractical due to the highly sensitive nature of the phase spectrum at the wrapped edges (−π and π) to the noise in the system. A usual unwrapping mechanism to accumulate phase fails to avoid any false jump of phase cycle near these edges and results in unwanted errors in displacement data. A new way of using such algorithms is proposed, which avoids these edges during accumulation of phase and hence reduces errors in displacement measurements. A conventional 90° phase step, four-point algorithm can be used simultaneously with a modified three-point phase algorithm, which gives a similar phase incremental value except the difference in instantaneous phase value. We have implemented this shift in origin to avoid the wrapped edges and have used a sequence of incremental phase values to generate cumulative phase and therefore displacement data by simultaneously using both algorithms in our detector-width-compensated displacement-measuring grating interferometer. Simulation results are introduced to show the usefulness and accuracy of this approach compared to a conventional phase unwrapping mechanism.