Kernel Regression Coefficients for Practical Significance

Quantitative researchers often use Student’s t-test (and its p-values) to claim that a particular regressor is important (statistically significantly) for explaining the variation in a response variable. A study is subject to the p-hacking problem when its author relies too much on formal statistical significance while ignoring the size of what is at stake. We suggest reporting estimates using nonlinear kernel regressions and the standardization of all variables to avoid p-hacking. We are filling an essential gap in the literature because p-hacking-related papers do not even mention kernel regressions or standardization. Although our methods have general applicability in all sciences, our illustrations refer to risk management for a cross-section of firms and financial management in macroeconomic time series. We estimate nonlinear, nonparametric kernel regressions for both examples to illustrate the computation of scale-free generalized partial correlation coefficients (GPCCs). We suggest supplementing the usual p-values by “practical significance” revealed by scale-free GPCCs. We show that GPCCs also yield new pseudo regression coefficients to measure each regressor’s relative (nonlinear) contribution in a kernel regression.

IMPACT OF DOWNSTREAM POTENTIAL PERTURBATIONS ON THE NONLINEAR STABILITY OF A GENERIC FAN

The dependence of the aerodynamic stability of fan blades with amplitude and nodal diameter of potential perturbations associated with the presence of pylons is studied. The analysis is conducted using a novel block-wise spatial Fourier decomposition of the reduced-passages to reconstruct the full-annulus solution. The method represents very efficiently unsteady flows generated by outlet static pressure non-uniformities. The explicit spatial Fourier approximation is exploited to characterize the relevance of each nodal diameter of outlet perturbations in the fan stall process, and its nonlinear stability is studied in a harmonic by harmonic basis filtering the nonlinear contribution of the rest. The methodology has been assessed for the NASA rotor 67. The maximum amplitude of the downstream perturbation at which the compressor becomes unstable and triggers a stall process has been mapped. It is concluded that the fan stability dependence with the amplitude of the perturbation is weaker than in the case of intake distortion. For perturbations with an odd number of nodal diameters, the nonlinear stability analysis leads to the same conclusions as to the small amplitude linear stability analysis. However, if the perturbations have an even number nodal diameters, the flow exhibits a supercritical bifurcation and have a stabilizing effect.

Особенности когерентной спиновой динамики двумерного электронного газа в режиме холловского ферромагнетика

By means of the time-resolved Kerr rotation technique, a spin-depolarized electron system at a filling factor ν = 1 in a GaAs quantum well was studied. At temperatures above 5 K, a transition from a new spin-correlated state to a state with low spin stiffness characteristic of a single-particle electron system was found. A nonlinear contribution to the decay of Larmor oscillations arising at low temperatures, when spin-spin correlations determine the ground state of a two-dimensional electron system, is highlighted. The parameters of the fluctuating magnetic field acting on individual electron spins are estimated.

KECA Similarity-Based Monitoring and Diagnosis of Faults in Multi-Phase Batch Processes

Multiple phases with phase to phase transitions are important characteristics of many batch processes. The linear characteristics between phases are taken into consideration in the traditional algorithms while nonlinearities are neglected, which can lead to inaccuracy and inefficiency in monitoring. The focus of this paper is nonlinear multi-phase batch processes. A similarity metric is defined based on kernel entropy component analysis (KECA). A KECA similarity-based method is proposed for phase division and fault monitoring. First, nonlinear characteristics can be extracted in feature space via performing KECA on each preprocessed time-slice data matrix. Then phase division is achieved with the similarity variation of the extracted feature information. Then, a series of KECA models and slide-KECA models are established for steady and transitions phases respectively, which can reflect the diversity of transitional characteristics objectively and preferably deal with the stage-transition monitoring problem in multistage batch processes. Next, in order to overcome the problem that the traditional contribution plot cannot be applied to the kernel mapping space, a nonlinear contribution plot diagnosis algorithm is proposed, which is easier, more intuitive and implementable compared with the traditional one. Finally, simulations are performed on penicillin fermentation and industrial application. Specifically, the proposed method detects the abnormal agitation power and the abnormal substrate supply at 47 h and 86 h, respectively. Compared with traditional methods, it has better real-time performance and higher efficiency. Results demonstrate the ability of the proposed method to detect faults accurately and effectively in practice.

Critical Assessment of Geoengineering Strategies using Response Theory

We investigate in an intermediate-complexity climate model (I) the applicability of linear response theory to assessing a geoengineering method, and (II) the success of the considered method. The geoengineering problem is framed here as a special optimal control problem, which leads mathematically to the following inverse problem. A given rise in carbon dioxide concentration [CO2] would result in a global climate change with respect to an appropriate ensemble average of the surface air temperature . We are looking for a suitable modulation of solar forcing which can cancel out the said global change, or modulate it in some other desired fashion. It is rather straightforward to predict this solar forcing, considering an infinite time period, by linear response theory, and we will spell out an iterative procedure suitable for numerical implementation that applies to finite time periods too. Regarding (I), we find that under geoengineering, i.e. the combined greenhouse and solar forcing, the actual response Δ asymptotically is not zero, indicating that the linear susceptibility is not determined correctly. This is due to a significant quadratic nonlinearity of the response under system identification achieved by a forced experiment. This nonlinear contribution can in fact be easily removed, which results in much better estimates of the linear susceptibility, and, in turn, in a five-fold reduction in Δ under geoengineering. Regarding (II), however, we diagnose this geoengineering method to result in a considerable spatial variation of the surface temperature anomaly, reaching more than 2 [K] at polar/high latitude regions upon doubling the [CO2] concentration, even in the ideal case when the geoengineering method was successful in canceling out the response in the global mean. In the same time, a new climate is realised also in terms of e.g. an up to 4 [K] cooler tropopause or drier/disrupted Tropics, relative to unforced conditions.

Tomographic-PIV Survey of the Near-Field Hydrodynamic and Hydroacoustic Characteristics of a Marine Propeller

This article deals with a pioneering application of tomographic particle image velocimetry (tomographic PIV) for the hydrodynamic and hydroacoustic analysis of a marine propeller. The hydrodynamic study was mainly focused on the topological analysis of the propeller wake characteristics in the near field based on the vorticity field and on the tilting and stretching terms of the vorticity transport equation. Hydroacoustic analysis concerned the use of tomographic PIV in combination with the Powell's acoustic analogy. Tomographic PIV proved to be a valid tool for the detailed quantitative reconstruction of the complex vortex topology in the propeller wake and provided an accurate description of the source terms of the Powell's analogy. In particular, it was shown that the tip vortex perturbation represents the dominant nonlinear contribution to the radiated far-field noise in non-cavitating flow conditions.

A Model of Predicting Corrosion Rate for Substation Grounding Grid Based on the Similarity and Support Vector Regression

In this paper, we proposed a training model to predict the corrosion rate for substation grounding grid based on the Similarity and Support Vector Regression (SSVR). In the proposed model, the effect of grounding grid corrosion rate was acted as a feature vector and processed by a dimensionless treatment. Then, the similarity between the feature vector of training terminal and index vector of actual site would be calculated. In the prediction of corrosion rate, the traditional Linear Average Method (LAM) to describe the nonlinear contribution has some fault defects. Therefore, we proposed the training model named SSVR. From the experimental results, the proposed SSVR can obtain better predicting performance than the traditional LAM.

On the Relation between NARX Clusters and Even/Odd Nonlinearities through Frequency-Domain Analysis

Although polynomial NARX models have been intensively used in nonlinear system identification, few papers discussed how to relate the inner nonlinearities to specific types of clusters and regressors. The objective of this paper is to discuss this relationship for a class of systems that contain even or odd nonlinearities. This class covers block-structured models (Hammerstein, Wiener, and others) and systems with dynamic nonlinearities. To achieve the paper’s aim, a deep frequency-domain analysis is performed. For each type of nonlinearity, all the NARX clusters are investigated and the results show that each regressor type provides specific nonlinear contribution. The investigation is based on an output power spectra analysis when a specific multisinusoidal excitation is applied. According to the spectral contributions in some of the frequency lines, the nonlinearity classification is possible. By applying the same procedure to the clusters, one interprets how these clusters can (or not) contribute to explain the system nonlinearity. The paper findings have two major impacts: (i) one gains deep knowledge on how the nonlinearities are coded by the clusters, and (ii) this information can be used, for instance, to aid a structure selection procedure (ERR, term clustering, etc.) during the discarding of the clusters which are not able to explain the system nonlinear behavior. Some practical and experimental aspects are discussed, while numerical examples are presented to show the validity of the theoretical analysis.