As the current research of face gear drive cannot realize fluctuating gear ratio, a design method of orthogonal fluctuating gear ratio face gear drive is proposed. The mathematical model of orthogonal fluctuating gear ratio face gear drive is found based on the space engagement theory. The equation of the pitch curve, addendum curve and dedendum curve of face gear are derived. The design method of tooth surface of the face gear is available based on the envelope method. The conversion relationship of enveloping coordinate systems is obtained during the enveloping process of orthogonal fluctuating gear ratio face gear drive after the establishment of enveloping coordinate systems. Then combining with equation of generating surface, the tooth surface equation of the face gear is obtained. The three-dimensional model of orthogonal fluctuating gear ratio face gear is acquired on the basis of a modeling program, which is developed under the environment of VB and Solidworks (API). Furthermore, localization of the bearing contact is achieved by the manufacturing method and it is justified by the finite element method analysis result. Finally, the kinematics of the orthogonal fluctuating gear ratio face gear drive is analyzed, and the change laws of transmission ratio, angular displacement and angular acceleration of the face gear are acquired.

The Empirical Interpolation Method (EIM) and its generalized version (GEIM) can be used to approximate a physical system by combining data measured from the system itself and a reduced model representing the underlying physics. In presence of noise, the good properties of the approach are blurred in the sense that the approximation error no longer converges but even diverges. We propose to address this issue by a least-squares projection with constrains involving a some a priori knowledge of the geometry of the manifold formed by all the possible physical states of the system. The efficiency of the approach, which we will call Constrained Stabilized GEIM (CS-GEIM), is illustrated by numerical experiments dealing with the reconstruction of the neutron flux in nuclear reactors. A theoretical justification of the procedure will be presented in future works.

This paper proposes an approach that combines reduced-order models with machine learning in order to create physics-informed digital twins to predict high-dimensional output quantities of interest, such as neutron flux and power distributions in nuclear reactor cores. The digital twin is designed to solve forward problems given input parameters, as well as to solve inverse problems given some extra measurements. Offline, we use reduced-order modeling, namely, the proper orthogonal decomposition (POD) to assemble physics-based computational models that are accurate enough for fast predictive digital twin. The machine learning techniques, namely, k-nearest-neighbors (KNN) and decision trees (DT) are used to formulate the input-parameterdependent coefficients of the reduced basis, whereafter the high-fidelity fields are able to be reconstructed. Online, we use the real time input parameters to rapidly reconstruct the neutron field in the core based on the adapted physics-based digital twin. The effectiveness of the framework is illustrated through a real engineering problem in nuclear reactor physics -reactor core simulation in the life cycle of HPR1000 governed by the two-group neutron diffusion equations affected by input parameters, i.e., burnup, control rod inserting step, power level and temperature of the coolant, which shows potential applications for on-line monitoring purpose.

In this paper, we apply the so-called generalized empirical interpolation method (GEIM) to address the problem of sensor placement in nuclear reactors. This task is challenging due to the accumulation of a number of difficulties like the complexity of the underlying physics and the constraints in the admissible sensor locations and their number. As a result, the placement, still today, strongly relies on the know-how and experience of engineers from different areas of expertise. The present methodology contributes to making this process become more systematic and, in turn, simplify and accelerate the procedure.