We propose and analyze two locking-free three-field virtual element methods for Biot’s consolidation model in poroelasticity. One is a high-order scheme, and the other is a low-order scheme. For time discretization, we use the backward Euler scheme. The proposed methods are well-posed, and optimal error estimates of all the unknowns are obtained for fully discrete solutions. The generic constants in the estimates are uniformly bounded as the Lamé coefficient λ tends to infinity, and as the constrained specific storage coefficient is arbitrarily small. Therefore the methods are free of both Poisson locking and pressure oscillations. Numerical results illustrate the good performance of the methods and confirm our theoretical predictions.

To address the challenges of real-time insulation monitoring and accurate partial discharge (PD) location in cable joints. A distributed Optical Fiber sensing system with polarization compensation module is established to detect the ultrasonic signal of partial discharge. The locating range of optical time-domain reflectometer (Φ-OTDR) is analyzed, and a variance variable mathematical model based on Rayleigh scattering coherent light signals is established to denote weak ultrasonic characteristic signals of partial discharge in cable joints. The polarizing beam splitter (PBS) is devised in the Φ-OTDR detection circuit to improves the stability of polarization states. Four Optical Fiber ring sensors are wound on the cable joint to locate and detect the partial discharge point of the cable joint. Then, the signal characteristics of partial discharge measured by electrical measurement method and Optical Fiber acoustic measurement method are compered, and the positions of four Optical Fiber ring sensors are calibrated based on piezoelectric sensors. It shows that when the test fiber length is 600m or 1125m respectively, the locating deviation is less than 1.9m, which is verified a high accuracy of Optical Fiber sensing system in detecting partial discharge. It provides a feasible monitoring method for real-time sensing of insulation status of transmission equipment.

In order to solve the problem that the dual Mach Zehnder (M-Z) interferometer system is easily affected by external environmental noise, a data signal-processing scheme based on Hilbert–Huang transform (HHT) is proposed to achieve high-precision location with distributed optical fibers. The polarization compensation module has a built-in dual Sagnac interferometer system which is used to stabilize the polarization state of the Sagnac interferometer. The eigenmode function is obtained by empirical mode decomposition of the received two optical signals, and then the Hilbert spectrum is obtained by superimposing the Hilbert transform, so that the high-similarity curve caused by the vibration signal can be clearly and intuitively extracted. The optical signal information can be calculated based on the cross-correlation and delay estimation algorithm to accurately obtain the vibration position information. The experimental results show that the positioning accuracy can reach ±11 m, with a sensing fiber length of 15 km and a sampling rate of 10 MHz. It is proven that the distributed optical fiber sensing technology based on the dual Sagnac interferometer system has high practical application value.

Homogeneous parameters of a mathematical nuclear core full power steady state were built based on the equivalence theory upon the Canada Pickering a CANDU reactor. The reactor core neutronics is based on a two energy group formulation and a typical spatial discretization employs one node per fuel assembly, each of the assemblies is further subdivided into 12 to 30 axial slices which is sufficiently detailed to account for the non-uniform aspect of reactor core composition. This provides us a good reference solution from which all the nodal nuclear parameters can be calculated. The detailed homogeneous parameters are got which can be a reference as the nodal diffusion methods to resolve the homogeneous parameters problem.