The mean correcting martingale measures for exponential additive processes

The mean correcting martingale measure for the stochastic process defined as the exponential of an additive process is constructed. Necessary and sufficient conditions for the existence of mean correcting martingale are also obtained. The investigation of this paper will establish a unified way that is applicable both to the case of Ldvy processes and that of the sums of independent random variables. As an application, we present the necessary and sufficient conditions that the discounted stock price process is a martingale.

Parameter-independent error correction for potential measurements by reference electrode in lithium-ion batteries

The safety monitoring of lithium-ion batteries(LIBs) is of great significance for realizing all-climate and full-lifespan battery management. In-situ measurement of anode potential with implanted reference electrodes(REs) has proven to be effective to monitor and avoid the occurrence of severe side reactions like Li plating to ensure the safe and fast charging. However, the intrinsic measurement errors caused by local blocking effects, which also can be referred to as potential artefacts, are seldom taken into consideration in existing studies, yet they highly dominate the correctness of conclusions inferred from REs. In this study, aiming at exploring the physical origin of the measurement errors and ensure reliable potential monitoring, electrochemical and post-mortem tests are conducted using commercial pouch cells with implanted REs. Corresponding electrochemical model which describes the blocking effects, is established to validate the abnormal absence of lithium plating that predicted by measured anode potentials under various charging rates. Theoretical derivation is further presented to explain the error sources, which can be attributed to increased local liquid potential of the RE position. Most importantly, with the guidance of error analysis, a novel parameter-independent error correction method for RE measurements is proposed for the first time, which is proven to be adequate to estimate the real anode potentials and deduce the critical C-rate of Li plating with extra safety margin. After error correction, the resulting critical C-rates are all within the range of 0.55 ± 0.03 C, which is close to the C-rate of 0.6–0.7 C obtained from experiments. In addition, this error correction method can be performed conveniently with only some simple RE measurements of polarization voltages, totally independent of battery electrochemical and geometric parameters. This study provides highly practical error correction method for RE measurements in real LIBs, substantially facilitating the fast diagnosis and safety evaluation of Li plating during charging of LIBs.

Differential correction method applied to measurement of the FAST reflector

The Five-hundred-meter Aperture Spherical radio Telescope （FAST） adopts an active deformable main reflector which is composed of 4450 triangular panels. During an observation, the illuminated area of the reflector is deformed into a 300-m diameter paraboloid and directed toward a source. To achieve accurate control of the reflector shape, positions of 2226 nodes distributed around the entire reflector must be measured with sufficient precision within a limited time, which is a challenging task because of the large scale. Measurement of the FAST reflector makes use of stations and node targets. However, in this case the effect of the atmosphere on measurement accuracy is a significant issue. This paper investigates a differen- tial correction method for total stations measurement of the FAST reflector. A multi-benchmark differential correction method, including a scheme for benchmark selection and weight assignment, is proposed. On- site evaluation experiments show there is an improvement of 70%-80% in measurement accuracy compared with the uncorrected measurement, verifying the effectiveness of the proposed method.

Online Pattern Recognition and Data Correction of PMU Data Under GPS Spoofing Attack

Smart grids are increasingly dependent on data with the rapid development of communication and measurement.As one of the important data sources of smart grids,phasor measurement unit(PMU)is facing the high risk from attacks.Compared with cyber attacks,global position system(GPS)spoofing attacks(GSAs)are easier to implement because they can be exploited by portable devices,without the need to access the physical system.Therefore,this paper proposes a novel method for pattern recognition of GSA and an additional function of the proposed method is the data correction to the phase angle difference(PAD)deviation.Specifically,this paper analyzes the effect of GSA on PMU measurement and gives two common patterns of GSA,i.e.,the step attack and the ramp attack.Then,the method of estimating the PAD deviation across a transmission line introduced by GSA is proposed,which does not require the line parameters.After obtaining the estimated PAD deviations,the pattern of GSA can be recognized by hypothesis tests and correlation coefficients according to the statistical characteristics of the estimated PAD deviations.Finally,with the case studies,the effectiveness of the proposed method is demonstrated,and the success rate of the pattern recognition and the online performance of the proposed method are analyzed.

Correction of the second-order degree of coherence measurement

The measurement of the second-order degree of coherence [g（2）（t）] is one of the important methods used to study the dynamical evolution of photon-matter interaction systems. Here, we use a nitrogen-vacancy center in a diamond to compare the measurement of g（2） （t） with two methods. One is the prototype measurement process with a tunable delay. The other is a start-stop process based on the time-to-amplitude conversion （TAC） and multichannel analyzer （MCA） system, which is usually applied to achieve efficient measurements. The divergence in the measurement results is observed when the delay time is comparable with the mean interval time between two neighboring detected photons. Moreover, a correction function is presented to correct the results from the TAC-MCA system to the genuine g（2）（t）. Such a correction method will provide a way to study the dynamics in photonic systems for quantum information techniques.

Beam transmission efficiency of the HIRFL-SSC

In this paper we address the problem of the low beam transmission efficiency of the HIRFL-SSC. The influence of the SFC-SSC energy match, the SSC RF voltage, and harmonic field in the injection area of the SSC, and the SSC central trajectory on the beam transmission efficiency have been analyzed both from the theoretical side and from the actual operating data. The main reason is that the soft-edge approximation of the magnet field （the so-called theoretical field） and the simplified calculation programs were adopted when calculating the beam center trajectory and designing the injection and extraction system, and the measured magnetic field was not used to correct the calculation results. These led to large deviations of the calculated center trajectory, and then resulted in low efficiency of the SSC beam transmission. Therefore, the re-calculation of SSC beam center trajectory and injection and extraction system, as well as the measured magnet field correction are the key points required to solve the problem.

Recalculation of the HIRFL-SSC injection and extraction system

In order to further improve beam transmission efficiency at the SSC, the beam center trajectory and injection and extraction system are recalculated based on the program group used in the final design of the GANIL accelerator, with some necessary changes and the addition of some auxiliary programs. The two different types of injection and extraction elements （the bending magnet and the inductive septum） are distinguished, and their interaction with the ambient field is considered. More focus is placed on considering the differences in the magnet field inhomogeneity of the ambient field in the located area of the inductive septum where the ends are situated in the ambient field （between the main magnet poles）. Thus the gradient magnetic field problem of the inductive septum is solved perfectly. As well as preparing the necessary auxiliary programs and taking the structural integration of the SSC magnetic field maps, the measured magnet field correction is completed. Therefore, the trajectory and a variety of injection and extraction system parameters are obtained. According to the recalculation results, the SSC beam transmission efficiency will be enhanced significantly.

3D shape measurement of larger complex objects based on fringe cycle correction

The grating fringe on the reference plane is broadened in the intersecting axis system because of oblique-angle projection. In order to solve this problem, we study the theoretical model of the temporal phase unwrapping method based on the fringe cycle correction. We also study the 3D shape measurement theoretical model of the larger complex objects after considering the coordinate deviation and lens distortion. Experimental results demonstrate that the fringe cycle on the reference plane can be corrected to a constant value, the lens distortion can be corrected, and 3D shape of larger complex objects can be accurately measured.