NN Estimator Research Articles

Robust kernel regression function with uncertain scale parameter for high dimensional ergodic data using $ k $-nearest neighbor estimation

<abstract><p>In this paper, we consider a new method dealing with the problem of estimating the scoring function $ \gamma_a $, with a constant $ a $, in functional space and an unknown scale parameter under a nonparametric robust regression model. Based on the $ k $ Nearest Neighbors ($ k $NN) method, the primary objective is to prove the asymptotic normality aspect in the case of a stationary ergodic process of this estimator. We begin by establishing the almost certain convergence of a conditional distribution estimator. Then, we derive the almost certain convergence (with rate) of the conditional median (scale parameter estimator) and the asymptotic normality of the robust regression function, even when the scale parameter is unknown. Finally, the simulation and real-world data results reveal the consistency and superiority of our theoretical analysis in which the performance of the $ k $NN estimator is comparable to that of the well-known kernel estimator, and it outperforms a nonparametric series (spline) estimator when there are irrelevant regressors.</p></abstract>

Learning-Based 6-DOF Control for Autonomous Proximity Operations Under Motion Constraints

This article proposes areinforcement learning (RL)-based six-degree-of-freedom (6-DOF) control scheme for the final-phase proximity operations of spacecraft. The main novelty of the proposed method are from two aspects: 1) The closed-loop performance can be improved in real-time through the RL technique, achieving an online approximate optimal control subject to the full 6-DOF nonlinear dynamics of spacecraft; 2) nontrivial motion constraints of proximity operations are considered and strictly obeyed during the whole control process. As a stepping stone, the dual-quaternion formalism is employed to characterize the 6-DOF dynamics model and motion constraints. Then, an RL-based control scheme is developed under the dual-quaternion algebraic framework to approximate the optimal control solution subject to a cost function and a Hamilton–Jacobi–Bellman equation. In addition, a specially designed barrier function is embedded in the reward function to avoid motion constraint violations. The Lyapunov-based stability analysis guarantees the ultimate boundedness of state errors and the weight of NN estimation errors. Besides, we also show that a PD-like controller under dual-quaternion formulation can be employed as the initial control policy to trigger the online learning process. The boundedness of it is proved by a special Lyapunov strictification method. Simulation results of prototypical spacecraft missions with proximity operations are provided to illustrate the effectiveness of the proposed method.

The functional kNN estimator of the conditional expectile: Uniform consistency in number of neighbors

Abstract The main purpose of the present paper is to investigate the problem of the nonparametric estimation of the expectile regression in which the response variable is scalar while the covariate is a random function. More precisely, an estimator is constructed by using the k Nearest Neighbor procedures (kNN). The main contribution of this study is the establishment of the Uniform consistency in Number of Neighbors (UNN) of the constructed estimator. The usefulness of our result for the smoothing parameter automatic selection is discussed. Short simulation results show that the finite sample performance of the proposed estimator is satisfactory in moderate sample sizes. We finally examine the implementation of this model in practice with a real data in financial risk analysis.

K-NEAREST NEIGHBOR AND LINEAR REGRESSION IN THE PREDICTION OF THE ARTIFICIAL FORM FACTOR

k-nearest neighbor and linear regression in the prediction of the artificial form factor . T he proposal of this study was to test whether the performance of the non parametric approach k -Nearest Neighbor ( k -NN), would improve estimates of individual artificial form factor ( f 1.3 ) of trees of the hybrid Eucalyptus urophylla x Eucalyptus grandis compared to the O rdinary L east S quares method. A total of 149 sample-trees were selected , felled , and diameter was measured along the trunk at 10% (d 0. 1 ), 30% (d 0. 3 ), 50% (d 0. 5 ) and 70% (d 0. 7 ) of commercial height and posteriorly at 2m intervals . Mathematical models recognized in the literature for predicting the form factor were adjusted for comparison . The hyperparameter k of optimum adjust ment for the k -NN estimator was obtained by repeated cross-validation. The training data of the k -NN regression model were identical to those used in the adjustment of the linear regression models since m ost multiple linear regression models present problems of collinearity or multicollinearity. The use of the covaria te (d0.3.d0.7)/d1.32 and k = 15 made it possible to construct k -NN models with better generalization capacity. The potential of the k -NN estimator to predict the artificial form factor and thus to obtain less biased estimates of individual tree volumes was demonstrated and considered to be superior to the use of linear regression and average form factors. The k -NN approach can be considered more generic for predicti on of the tree form factor , and its use is recommended when classical linear regression models or other simpler methods do not yield good results.

Tool Condition Monitoring While Using Vegetable Based Cutting Fluids During Milling of Inconel 625

This investigation has designed a tool condition monitoring system (TCM) while milling of Inconel 625 based on sound and vibration signatures. The experiments were carried out based on response surface methodology (RSM) central composite design, design of experiments. The process parameters such as speed, feed, depth of cut and vegetable-based cutting fluids were optimized based on surface roughness, flank wear. It was found that the sound pressure and vibration signatures have the direct relation with flank wear. The statistical features like root mean square, skewness, kurtosis and mean values were extracted from the experimental data. From the designed NN estimator, the cutting tool flank wear was predicted with the mean square error (MSE) of 0.084212.

Novel neural network based speed estimator for multilevel inverter fed sensorless field oriented controlled IM drive

In this paper, a new reference model adaptive system based speed estimator is proposed for multilevel inverter fed sensorless field oriented controlled induction motor drive. The proposed scheme employs 2-neural network models which is novel in this paper. The proposed speed estimator is shown to overcome low speed problems. One of the FPGA implementation issues of NN model is the identification of appropriate bit precision. The performance of reference NN estimator is studied for various bit precision and the suitable bit precision is identified compromising the memory size (resource) and the accuracy. Further the suitability of multicarrier pulse width modulation techniques for multilevel inverter is also studied. The performance is compared in terms of magnitude of the output voltage and total harmonics distortion and suitable modulation technique is identified. The encouraging results obtained are presented.

Forest inventory attribute prediction using airborne laser scanning in low-productive forestry-drained boreal peatlands

Nearly 30% of Finland’s land area is covered by peatlands. In Northern parts of the country there is a significant amount of low-productive drained peatlands (LPDPs) where the average annual stem volume growth is less than 1 m ha. The re-use of LPDPs has been considered thoroughly since Finnish forest legislation was updated and the forest regeneration prerequisite was removed from LPDPs in January 2014. Currently, forestry is one of the re-use alternatives, thus detailed forest resource information is required for allocating activities. However, current forest inventory practices have not been evaluated for sparse growing stocks (e.g., LPDPs). The purpose of our study was to evaluate the suitability of airborne laser scanning (ALS) for mapping forest inventory attributes in LPDPs. We used ALS data with a density of 0.8 pulses per m, 558 field-measured reference plots (500 from productive forests and 58 from LPDPs) and nearest neighbour (-NN) estimation. Our main aim was to study the sensitivity of predictions to the number of LPDP reference plots used in the -NN estimation. When the reference data consisted of 500 plots from productive forest stands, the root mean square errors (RMSEs) for the prediction accuracy of Lorey’s height, basal area and stem volume were 1.4 m, 2.7 m ha and 13.7 m ha in LPDPs, respectively. When 30 additional reference plots were allocated to LPDPs, the respective RMSEs were 1.1 m, 1.7 m ha and 10.0 m ha. Additional reference plot allocation did not affect the predictions in productive forest stands.3–12kkk2–13–12–13–1

Nearest Neighbor Estimators for Random Fields

Generalizing the random sequence case, this study defines a k - NN density estimator for random variables with multidimensional lattice points serving as index values. The central result is that under random field stationary and mixing assumptions, as well as standard smoothness postulates, our k - NN estimate is found to be asymptotically normal. This result readily extends to NN-type estimates for jointly distributed random variables. For illustration, a simplified version of the k - NN estimator is applied to obtain the density estimate for a soil-moisture data set selected from the geostatistical literature.