Data binning

Abstract: In the modern industry, the information has been sufficiently shared among the production equipment, intelligent subsystems, and mobile devices via advanced network technology. For this purpose, many challenges on plant-wide performance evaluation such as product quality prediction have been received considerable attention in complex industrial Internet of Things systems. In this article, an efficient and effective soft sensor based on the semisupervised parallel deepFM model is proposed for the product quality prediction. First, a label broadcasting method is presented to augment labeled samples from unlabeled samples. Then, a data binning method is introduced to discretize process variables for an unbiased estimation. Based on the modified deepFM model, quality information can be separately extracted from different components of the model while high- and low-dimensional features can be obtained. Manifold regularization is embedded into the back propagation algorithm, in which unlabeled samples issue can be further resolved. Experiments on a real-world dataset demonstrate the effectiveness and performance of the proposed methods.

Abstract: Summary Fragility functions that define the probabilistic relationship between structural damage and ground motion intensity are an integral part of performance-based earthquake engineering or seismic risk analysis. This paper introduces three approaches based on kernel smoothing methods for developing analytical and empirical fragility functions. A kernel assigns a weight to each data that is inversely related to the distance between the data value and the input of the fragility function of interest. The kernel smoothing methods are, therefore, non-parametric forms of data interpolation. These methods enable the implicit treatment of uncertainty in either or both of ground motion intensity and structural damage without making any assumption about the shape of the resulting fragility functions. They are particularly beneficial for sparse, noisy, or non-homogeneous data sets. For illustration purposes, two types of data are considered. The first is a set of numerically simulated responses for a four-story steel moment-resisting frame, and the second is a set of field observations collected after the 2010 Haiti earthquake. The results demonstrate that these methods can develop continuous representations of fragility functions without specifying their functional forms and treat sparse data sets more efficiently than conventional data binning and parametric curve fitting methods. Moreover, various uncertainty analyses are conducted to address the issues of over-fitting, bias, and confidence intervals. Copyright © 2014 John Wiley & Sons, Ltd.

Abstract: We present a filtered backprojection algorithm for reconstructing the Wigner function of a system of large angular momentum j from Stern–Gerlach-type measurements. Our method is advantageous over the full determination of the density matrix in that it is insensitive to experimental fluctuations in j, and allows for a natural elimination of high-frequency noise in the Wigner function by taking into account the experimental uncertainties in the determination of j, its projection m and the quantization axis orientation. No data binning and no arbitrary smoothing parameters are necessary in this reconstruction. Using recently published data (Riedel et al 2010 Nature 464 1170), we reconstruct the Wigner function of a spin-squeezed state of a Bose–Einstein condensate of about 1250 atoms, demonstrating that measurements along quantization axes lying in a single plane are sufficient for performing this tomographic reconstruction. Our method does not guarantee positivity of the reconstructed density matrix in the presence of experimental noise, which is a general limitation of backprojection algorithms.

Abstract: (ABRIDGED) We present a new Schwarzschild orbit-superposition code designed to model discrete datasets composed of velocities of individual kinematic tracers in a dynamical system. This constitutes an extension of previous implementations that can only address continuous data in the form of (the moments of) velocity distributions, thus avoiding potentially important losses of information due to data binning. Furthermore, the code can handle any combination of available velocity components, i.e., only line-of-sight velocities, only proper motions, or a combination of both. It can also handle a combination of discrete and continuous data. The code finds the distribution function (DF, a function of the three integrals of motion E, Lz, and I3) that best reproduces the available kinematic and photometric observations in a given axisymmetric gravitational potential. The fully numerical approach ensures considerable freedom on the form of the DF f(E,Lz,I3). This allows a very general modeling of the orbital structure, thus avoiding restrictive assumptions about the degree of (an)isotropy of the orbits. We describe the implementation of the discrete code and present a series of tests of its performance based on the modeling of simulated datasets generated from a known DF. We find that the discrete Schwarzschild code recovers the original orbital structure, M/L ratios, and inclination of the input datasets to satisfactory accuracy, as quantified by various statistics. The code will be valuable, e.g., for modeling stellar motions in Galactic globular clusters, and those of individual stars, planetary nebulae, or globular clusters in nearby galaxies. This can shed new light on the total mass distributions of these systems, with central black holes and dark matter halos being of particular interest.