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The authors wish to make the following corrections to the original paper [...]

In high dynamic scenes, fringe projection profilometry (FPP) may encounter fringe saturation, and the phase calculated will also be affected to produce errors. This paper proposes a saturated fringe restoration method to solve this problem, taking the four-step phase shift as an example. Firstly, according to the saturation of the fringe group, the concepts of reliable area, shallow saturated area, and deep saturated area are proposed. Then, the parameter A related to the reflectivity of the object in the reliable area is calculated to interpolate A in the shallow and deep saturated areas. The theoretically shallow and deep saturated areas are not known in actual experiments. However, morphological operations can be used to dilate and erode reliable areas to produce cubic spline interpolation (CSI) areas and biharmonic spline interpolation (BSI) areas, which roughly correspond to shallow and deep saturated areas. After A is restored, it can be used as a known quantity to restore the saturated fringe using the unsaturated fringe in the same position, the remaining unrecoverable part of the fringe can be completed using CSI, and then the same part of the symmetrical fringe can be further restored. To further reduce the influence of nonlinear error, the Hilbert transform is also used in the phase calculation process of the actual experiment. The simulation and experimental results validate that the proposed method can still obtain correct results without adding additional equipment or increasing projection number, which proves the feasibility and robustness of the method.

An improved three-frequency heterodyne synthesis phase unwrapping method is proposed to improve the measurement accuracy through phase difference and phase sum operations. This method can reduce the effect of noise and increase the equivalent phase frequency. According to the distribution found in the phase difference calculation process, the Otsu segmentation is introduced to judge the phase threshold. The equivalent frequency obtained from the phase sum is more than those of all projected fringe patterns. In addition, the appropriate period combinations are also studied. The simulations and related experiments demonstrate the feasibility of the proposed method and the ability to improve the accuracy of the measurement results further.

The extraction of rolling bearings’ degradation features has been developed for decades. However, the degradation features always present different trends of different run-to-failure data. To find a consistent indicator of different data will be helpful to establish a general model and explore the nature of bearings’ degradation. In this study, we have found there is a trend of similarity between the energy and complexity features. By using the cointegration test, we found the two kinds of features exhibit a certain degree of cointegration relationship. Fused by the cointegration method, we have obtained a novel health indicator which can depict different run-to-failure data in a unified way. The difference between the energy features and complexity features can be explained by the novel health indicator. The indicator has “two-stage” characters. The first stage is the zero-line stage and the second stage is the quickly raise stage, which presents like an exponential function. It is easy to think about using an exponential degradation model to model this indicator. Next, we have compared the indicator to root mean square (RMS) by using the exponential degradation model. It shows that the indicator is more suitable for the exponential degradation model. In this paper, we used eleven run-to-failure data to verify the generality and “two-stage” characters of the proposed indicator. The result shows that the novel indicator is general and effective and that it will promote the development of bearings’ prognostics.

First purchases of fruit are mainly dependent on aspects of appearance such as color. However, repeat buys of fruit are determined by internal quality traits such as flavor-related volatiles. Differences in volatile profiles in white- and red-fleshed peach fruit are not well understood. In the present study, peach cultivars with white- and red-fleshed fruit were subjected to sensory analysis using electronic nose (e-nose) to evaluate overview volatile profiles. Approximately 97.3% of the total variation in peach color-volatiles was explained by the first principle component 1 (PC1) and PC2. After analyzing sensory differences between peach fruit samples, 50 volatile compounds were characterized based on GC-MS. Multivariate analysis such as partial least squares discriminant analysis (PLS-DA) was applied to identify volatile compounds that contribute to difference in white- and red-fleshed peach fruit cultivars. A total of 18 volatiles that could separate peach fruit cultivars with different colors in flesh during ripening were identified based on variable importance in projection (VIP) score. Fruity note latone γ-hexalactone had higher contents in red-fleshed cultivars, while grassy note C6 compounds such as hexanal, 2-hexenal, (E)-2-hexenal, 1-hexanol, and (Z)-2-hexen-1-ol showed great accumulation in white-fleshed peach fruit.