A four parallel laser-based simultaneous measurement method for 6-degrees-of-freedom errors of rigid body with translational motion.

The measurement of six-degrees-of-freedom (6-DOF) errors of rigid bodies can show the real and accurate spatial pose of those rigid bodies. It plays a major role in precision calibration, spacecraft docking, machining, assembly, etc. In this paper, a four parallel laser-based simultaneous measurement (FPL-SM) method is proposed for measuring 6-DOF errors of rigid bodies with translational motion. First, a FPL-SM device is introduced. Its four laser heads form a rectangle, which is perpendicular to the movement direction of the measured linear displacement. Second, identification formulas for all geometrical errors in rigid bodies with translational motion are presented based on the relative positions of the four lasers. Based on the readings of the four lasers, angular errors and corresponding straightness errors are calculated for the direction of motion around the other two linear motions. As the two parallel sides of the rectangle are in different planes, the straightness errors of the two planes are different. The rolling angular error in the direction is expressed as the difference between the straightness errors of the two planes divided by the distance between the two planes. Six fundamental errors for rigid bodies with translational motion are obtained by four lasers in a single setting of the device. For multiple rigid bodies with mutually perpendicular translational motion, the squareness error is calculated by fitting to the actual direction of motion. Finally, experiments were carried out on the SmartCNC_DRDT five-axis machine tool and 21 geometric errors were determined for three translational axes. Error compensation was carried out using the generated machine tool geometric error data to verify the effectiveness of the proposed FPL-SM method. In addition, geometric errors and thermal errors of the Z axis of the GTI-2740 machine tool are measured based on the FPL-SM method.

Acoustic signal analysis for detecting defects inside an arc magnet using a combination of variational mode decomposition and beetle antennae search.

An accurate, rapid signal analysis is crucial in the acoustic-based detection for internal defects in arc magnets. Benefiting from the adaptive decomposition without the mode mixing, variational mode decomposition (VMD), has emerged as a promising technology for processing and analyzing acoustic signals. However, improper parameter settings are the root cause of inaccurate VMD results, while existing optimization methods for VMD parameters are only applicable to a single signal with exclusive signal characteristics, rather than different signals with similar features. Therefore, we developed a new acoustic signal analysis method combining VMD, beetle antennae search (BAS), and naive Bayes classification (NBC), and then applied it for detecting internal defects of arc magnets. In this method, multiple optimizations for different signals are simplified to a one-time optimization for the whole signal group by a specially designed parameter-related fitness function. Since the coordinates of the function maximum value in a parameter space correspond to the unified parameter setting generating the overall optimal processing effect for all signals, BAS is introduced to achieve a rapid search of coordinates. With the obtained unified parameter setting, each acoustic signal of arc magnets can be consistently processed by VMD. Next, two modes stemmed from VMD are screened out by an energy threshold, and their specific frequency information is extracted as features representing the internal defects. NBC is carried out to learn and identify the extracted features. The experimental validation of the proposed method was conducted by detecting various arc magnets. Experimental results indicate that the identification accuracy reaches 100% and the detection speed per a single arc magnet approximately ranges between 1.7 and 4.5 s. This work provides not only a new strategy for the parameter optimization of VMD, but also a practical solution for the internal defect detection of arc magnets.

Modeling counter-current chromatography with non-ideal injection.

In general counter-current chromatography systems, there are several off-column fittings between injector and column inlet, such as bends, valves, connecting tubes and joints. Due to these off-column fittings, the sample will diffuse in the mobile phase and form an irregular distribution when it flows from the injector to the column inlet. Thus, the concentration distribution of the solutes at the column inlet is a continuous curve (called the injection profile). As some previous research reveals, it is necessary to input actual injection profile into the simulation model to mimic elution profile. Therefore, we built a non-ideal CCC model whose initial value is from the actual injection profile, and validated the rationality of this model with iteration method. The simulation analysis of different injection profiles shows the conditions whereby a discrete injection profile can replace the actual injection profile in the non-ideal CCC model for accurate simulation elution. Simulation elution under such conditions reveal that non-ideal injection model can reflect the relationship between the injection profile and elution profile, and help to explain the reasons of irregular change in elution profile, like the tailed peak and flat peak.

Low-Rank Sparse Preserving Projections for Dimensionality Reduction.

Learning an efficient projection to map high-dimensional data into a lower dimensional space is a rather challenging task in the community of pattern recognition and computer vision. Manifold learning is widely applied because it can disclose the intrinsic geometric structure of data. However, it only concerns the geometric structure and may lose its effectiveness in case of corrupted data. To address this challenge, we propose a novel dimensionality reduction method by combining the manifold learning and low-rank sparse representation, termed low-rank sparse preserving projections (LSPP), which can simultaneously preserve the intrinsic geometric structure and learn a robust representation to reduce the negative effects of corruptions. Therefore, LSPP is advantageous to extract robust features. Because the formulated LSPP problem has no closed-form solution, we use the linearized alternating direction method with adaptive penalty and eigen-decomposition to obtain the optimal projection. The convergence of LSPP is proven, and we also analyze its complexity. To validate the effectiveness and robustness of LSPP in feature extraction and dimensionality reduction, we make a critical comparison between LSPP and a series of related dimensionality reduction methods. The experimental results demonstrate the effectiveness of LSPP.