Interval arithmetic operations for uncertainty analysis with correlated interval variables

A new interval arithmetic method is proposed to solve interval functions with correlated intervals through which the overestimation problem existing in interval analysis could be significantly alleviated. The correlation between interval parameters is defined by the multidimensional parallelepiped model which is convenient to describe the correlative and independent interval variables in a unified framework. The original interval variables with correlation are transformed into the standard space without correlation,and then the relationship between the original variables and the standard interval variables is obtained. The expressions of four basic interval arithmetic operations, namely addition, subtraction, multiplication, and division, are given in the standard space. Finally, several numerical examples and a two-step bar are used to demonstrate the effectiveness of the proposed method.

Reliability analysis of urban gas transmission and distribution system based on FMEA and correlation operator

In order to improve the safety management of urban gas transmission and distribution system, failure mode and effects analysis （FMEA） was used to construct the reliability analysis system of the pipeline network. To solve the problem of subjectivity and uncertainty of the multi-expert decision making, the correlation operator was introduced into the calculation of the risk priority number （RPN）. Using FMEA along with weight analysis and expert investigation approach, the FMEA evaluation table was given, including five failure modes, risk priority numbers, failure causes and effects, as well as corrective actions. The results show that correlation operator can directly process the linguistic terms and quantify the priority of the risks.

Damage localization for beams based on the wavelet correlation operator

The continuous wavelet transform(CWT) is one of the crucial damage identification tools in the vibration-based damage assessment. Because of the vanishing moment property, the CWT method is capable of featuring damage singularity in the higher scales, and separating the global trends and noise progressively. In the classical investigations about this issue, the localization property of the CWT is usually deemed as the most critical point. The abundant information provided by the scale-domain information and the corresponding effectiveness are, however, neglected to some extent. Ultimately, this neglect restricts the sufficient application of the CWT method in damage localization, especially in noisy conditions. In order to address this problem,the wavelet correlation operator is introduced into the CWT damage detection method as a post-processing. By means of the correlations among different scales, the proposed operator suppresses noise, cancels global trends, and intensifies the damage features for various mode shapes. The proposed method is demonstrated numerically with emphasis on characterizing damage in noisy environments, where the wavelet scale Teager-Kaiser energy operator is taken as the benchmark method for comparison.Experimental validations are conducted based on the benchmark data from composite beam specimens measured by a scanning laser vibrometer. Numerical and experimental validations/comparisons present that the introduction of wavelet correlation operator is effective for damage localization in noisy conditions.

No-core Monte Carlo shell model calculations with unitary correlation operator method and similarity renormalization group

The unitary correlation operator method （UCOM） and the similarity renormalization group theory （SRG） are compared and discussed in the framework of the no-core Monte Carlo shell model （MCSM） calculations for ^3H and ^4He. The treatment of spurious center-of-mass motion by Lawson＇s prescription is performed in the MCSM calculations. These results with both transformed interactions show good suppression of spurious center-of-mass motion with proper Lawson＇s prescription parameter βc.m. values. The UCOM potentials obtain faster convergence of total energy for the ground state than that of SRG potentials in the MCSM calculations, which differs from the cases in the no-core shell model calculations （NCSM）. These differences are discussed and analyzed in terms of the truncation scheme in the MCSM and NCSM, as well as the properties of the potentials of SRG and UCOM.

Three‑Dimensional Nano‑displacement Measurement by Four‑Beam Laser Interferometry

A 3D nano-displacement measurement method,where the difference in phase between the beams in a four-beam laser interference is changed,is proposed.Simulation results demonstrate that the variation of phase difference causes the deviation of the interference pattern in the laser interference system.Based on this theory,we design and build a four-beam laser interference system.The corner cube prism in the optical path is shifted,and the phase of the beam is changed by applying different voltages to a piezoelectric stage.The phase difference is obtained by analyzing the lattice pattern with subpixel precision,and then the displacement is determined by correlation operation.The experimental measurement results are consistent with the theoretical analysis,thereby verifying the feasibility of this measurement method.