Typical Kernel Research Articles

A Kernel-Based Calibration Algorithm for Chromatic Confocal Line Sensors.

In chromatic confocal line sensors, calibration is usually divided into peak extraction and wavelength calibration. In previous research, the focus was mainly on peak extraction. In this paper, a kernel-based algorithm is proposed to deal with wavelength calibration, which corresponds to the mapping relationship between peaks (i.e., the wavelengths) in image space and profiles in physical space. The primary component of the mapping function is depicted using polynomial basis functions, which are distinguished along various dispersion axes. Considering the unknown distortions resulting from field curvature, sensor fabrication and assembly, and even the inherent complexity of dispersion, a typical kernel trick-based nonparametric function element is introduced here, predicated on the notion that similar processes conducted on the same sensor yield comparable distortions.To ascertain the performance with and without the kernel trick, we carried out wavelength calibration and groove fitting on a standard groove sample processed via glass grinding and with a reference depth of 66.14 μm. The experimental results show that depths calculated by the kernel-based calibration algorithm have higher accuracy and lower uncertainty than those ascertained using the conventional polynomial algorithm. As such, this indicates that the proposed algorithm provides effective improvements.

An equivalent formulation of Sonine condition

Sonine kernel is characterized by the Sonine condition (denoted by SC) and is an important class of kernels in nonlocal differential equations and integral equations. This work proposes a SC with a more general form (denoted by gSC), which is more convenient than SC to accommodate complex kernels and equations. A typical kernel is given, and the first-kind Volterra integral equation under gSC is accordingly transformed and then analyzed. Based on these results, it is finally proved that the gSC is indeed equivalent to the original SC, which indicates that the Sonine kernel may be essentially characterized by the behavior of its convolution with the associated kernel at the starting point.

BENK: The Beran Estimator with Neural Kernels for Estimating the Heterogeneous Treatment Effect

A method for estimating the conditional average treatment effect under the condition of censored time-to-event data, called BENK (the Beran Estimator with Neural Kernels), is proposed. The main idea behind the method is to apply the Beran estimator for estimating the survival functions of controls and treatments. Instead of typical kernel functions in the Beran estimator, it is proposed to implement kernels in the form of neural networks of a specific form, called neural kernels. The conditional average treatment effect is estimated by using the survival functions as outcomes of the control and treatment neural networks, which consist of a set of neural kernels with shared parameters. The neural kernels are more flexible and can accurately model a complex location structure of feature vectors. BENK does not require a large dataset for training due to its special way for training networks by means of pairs of examples from the control and treatment groups. The proposed method extends a set of models that estimate the conditional average treatment effect. Various numerical simulation experiments illustrate BENK and compare it with the well-known T-learner, S-learner and X-learner for several types of control and treatment outcome functions based on the Cox models, the random survival forest and the Beran estimator with Gaussian kernels. The code of the proposed algorithms implementing BENK is publicly available.

A novel global RBF direct collocation method for solving partial differential equations with variable coefficients

Conventional radial basis function (RBF) approximation techniques face two fundamental challenges: determining the optimal shape parameter and solving the ill-conditioned linear system, which result from the use of typical kernel functions such as the Multiquadric (MQ) RBF. The objective of this study is to address these challenges by employing a novel RBF kernel, termed the coupled MQ RBF (CMQ-RBF). The new kernel combines the MQ with an m-order conical spline, where m denotes the optimal value determined by the so-called back check method (BCM) introduced in this study. Leveraging the CMQ-RBF kernel, we present a novel global RBF collocation method that generates a well-conditioned linear system, enabling direct solver utilization and delivering highly accurate numerical results without the need for laborious shape parameter selection. Consequently, the previously challenging issues can be effectively circumvented by switching to the "better kernel" offered by the CMQ-RBF. The proposed methodology is characterized by its mathematical simplicity and ease of numerical implementation. Several benchmark examples are investigated to verify its performance.

KELL: A Kernel-Embedded Local Learning for Data-Intensive Modeling

Kernel methods are widely used in machine learning. They introduce a nonlinear transformation to achieve a linearization effect: using linear methods to solve nonlinear problems. However, typical kernel methods like Gaussian process regression suffer from a memory consumption issue for data-intensive modeling: the memory required by the algorithms increases rapidly with the growth of data, limiting their applicability. Localized methods can split the training data into batches and largely reduce the amount of data used each time, thus effectively alleviating the memory pressure. This paper combines the two approaches by embedding kernel functions into local learning methods and optimizing algorithm parameters including the local factors, model orders. This results in the kernel-embedded local learning (KELL) method. Numerical studies show that compared with kernel methods like Gaussian process regression, KELL can significantly reduce memory requirements for complex nonlinear models. And compared with other non-kernel methods, KELL demonstrates higher prediction accuracy.

Multi-dimensional research on brown rice fracture characteristics and mechanism under quasi-static compression

The microscopic and macroscopic structure of brown rice kernel determines that it is a complex bio-material. Therefore, revealing kernel structural characteristics and fracture mechanisms can provide a reference for related processing application situations. In this study, an in-situ observation method with the multi-layer structure optical platform was developed to better understand the kernel fracture behavior. SEM images show that the starch structure distribution inside the endosperm layer could be divided into core, transition and outer layers. Meanwhile, kernel interior crack formation mechanism was revealed under quasi-static compression and verified from the perspective of fracture and structural mechanics. Typical kernel contact surface expansion behavior under compression conditions was analyzed. The results indicate that the compressive strength of glutinous kernel (56.3 MPa) larger than indica (48.1 MPa), and it was affected by kernel surface dimension and microscopic structure. The study aims to in-depth analysis fracture mechanism of brown rice kernel during the processing, providing a methodological reference for bio-material fracture.

Hybrid metaheuristic method of ABC kernel filtering for nonlinear acoustic echo cancellation

This research work uses nonlinear kernel adaptive filtering to eliminate echo, a type of voice that is undesirable and communicated over the microphone. Adaptive filters enable the detection of time-varying potentials and the tracking of the signal’s dynamic changes. In this work, a hybrid metaheuristic technique that combines the Artificial Bee Colony (ABC) with the Kernel Adaptive Improved Proportionate and Normalized Least Mean Square (KIPNLMS) filter is developed to significantly boost echo cancellation efficiency. The unique adaptive filter based on sub-filter and proportionate adaptation is combined in the advanced technique, which presents an improved Non-linear Acoustic Echo Cancellation (NAEC) framework. An essential part of kernel techniques is that they translate the information on to a high-dimensional feature space, where linear filtering is performed. In the initial space, the arithmetic operations are carried out by evaluating inner products among pairs of input patterns, also known as kernels. Along with the ABC step size regulation technique, kernel-based adaptive filtering improves Signal to Noise Ratio (SNR) and accelerates convergence. The algorithm's effectiveness is assessed through simulation using signal Echo Return Loss Enhancement (ERLE). The performance of Kernel LMS, Kernal Normalized LMS (KNLMS), Kernal Proportionate NLMS, and KIPNLMS algorithms are compared. In contrast to typical kernel adaptive filters, the suggested ABC-KIPNLMS increases the ERLE more than 10 dB compared to other algorithms.

Multiple Video Frame Interpolation via Enhanced Deformable Separable Convolution.

Generating non-existing frames from a consecutive video sequence has been an interesting and challenging problem in the video processing field. Typical kernel-based interpolation methods predict pixels with a single convolution process that convolves source frames with spatially adaptive local kernels, which circumvents the time-consuming, explicit motion estimation in the form of optical flow. However, when scene motion is larger than the pre-defined kernel size, these methods are prone to yield less plausible results. In addition, they cannot directly generate a frame at an arbitrary temporal position because the learned kernels are tied to the midpoint in time between the input frames. In this paper, we try to solve these problems and propose a novel non-flow kernel-based approach that we refer to as enhanced deformable separable convolution (EDSC) to estimate not only adaptive kernels, but also offsets, masks and biases to make the network obtain information from non-local neighborhood. During the learning process, different intermediate time step can be involved as a control variable by means of an extension of coord-conv trick, allowing the estimated components to vary with different input temporal information. This makes our method capable to produce multiple in-between frames. Furthermore, we investigate the relationships between our method and other typical kernel- and flow-based methods. Experimental results show that our method performs favorably against the state-of-the-art methods across a broad range of datasets. Code will be publicly available on URL: https://github.com/Xianhang/EDSC-pytorch.

A Quality-Related Fault Detection Method Based on the Dynamic Data-Driven Algorithm for Industrial Systems

For nearly a decade, quality-related fault detection algorithms have been widely used in industrial systems. However, the majority of these detection strategies rely on static assumptions of the operating environment. In this paper, taking the time series of variables into consideration, a dynamic kernel entropy component regression (DKECR) framework is proposed to address the instability of quality-related fault detection due to the existing dynamic characteristics. Compared with the typical kernel entropy component analysis method, the proposed method constructs the relationship between process states and quality states to further interpret the direct effect on the product taken by the fault. In the proposed approach, process measurements are converted to a lower-dimensional subspace with a specific angular structure that is more comprehensive than traditional subspace approaches. In addition, the angular statistics and their relevant thresholds are exploited to enhance the quality-related fault detection performance. Finally, the proposed method will be compared with three methods by means of a numerical example and two industrial scenarios to demonstrate its practicality and effectiveness. Note to Practitioners—This paper studies a quality-related fault detection problem for the dynamic nonlinear industrial system. Controlling and measuring the quality state is challenging for the high-level monitoring system of the manufacturing process due to the nonlinear dynamic feature in states. This paper proposes a new data-driven method based on the kernel entropy component analysis method to assess the correlation between the quality and fault in the industrial system, reducing unnecessary overhaul and maintenance. Based on the autoregressive moving average exogenous algorithm, the proposed method captures the dynamic interaction between the process states to decrease false alarms. In the experimental section, the DKECR method outperforms the compared approaches, which can provide stable fault detection results. Additionally, the unique angle structure of the proposed method can supply more information for engineers’ monitoring needs.

Image signal denoising method of grating linear displacement sensor based on NLM

To improve the measurement resolution and accuracy of the grating displacement sensor, this paper proposes an image signal denoising method of grating linear displacement sensors based on NLM. Firstly, the optical system is designed to load the displacement information into the fringe image based on the grating pitch; Then, the principle of NLM image denoising is studied, and the inverse ratio kernel NLM denoising algorithm is designed; Thirdly, the effect of denoising algorithm is compared with the typical kernel function; Finally, the optimized image is used for displacement demodulation. The experimental results show that the SNR of the image is 30.1370db after denoising by this algorithm, and the high-precision displacement stage is set at 20 nm, 40 nm, and, 60 nm. Using the method in this paper, the positioning can be calculated to 22.7 nm, 38.2 nm, and 63.3 nm, and the sub-pixel positioning of the image and the nanopositioning measurement of the displacement are completed.

A hierarchical prediction method based on hybrid-kernel GWO-SVM for metal tube bending wrinkling detection

Metal bending tube is widely used in industry while its forming defects extremely affect the bending quality. Among all defects, the bending-inside wrinkling caused by the non-uniform compressive stress is a zero-tolerated defect, particularly when the tube is for transportation. However, the current wrinkling detection approach, suffering from the lack of insight into wrinkling mechanism, is normally posteriori. To obtain the priori wrinkling condition for a certain go-to-bend tube, we put forward a metal tube bending wrinkling hierarchical prediction method based on hybrid-kernel gray wolf optimizer (GWO) support vector machine (SVM). Three typical kernel combinations are utilized for the GWO-SVM prediction model. To verify the proposed wrinkling prediction method, aluminum alloy series tubes are tested. By constructing the 12 typical designations of aluminum alloy tubes’ finite element bending simulation case base, the prediction model is trained through three hybrid-kernel GWO-SVMs, respectively. The results are compared with the traditional SVM and GWO-SVM, which show that the proposed hybrid-kernel GWO-SVM model has the best performance for hierarchically predicting bending wrinkling. Analysis of the predicted results shows that when the relative wall thickness is less than 0.015, wrinkling is very likely to occur with any relative bending radius within the range. On the contrary, there is less tendency to wrinkle. At the same time, the smaller the R/D, the higher the hierarchy of wrinkling. This proposed prediction method lays the foundation for metal tube bending wrinkling detection and prevention.

Numerical Solution of a One-Dimensional Nonlocal Helmholtz Equation by Perfectly Matched Layers

We consider the computation of a nonlocal Helmholtz equation by using Perfectly Matched Layer (PML). We first derive the nonlocal PML equation by extending PML modifications from the local operator to the nonlocal operator of integral form. We then give stability estimates of some weighted average value of the nonlocal Helmholtz solution and prove that (i) the weighted average value of the nonlocal PML solution decays exponentially in PML layers in one case; (ii) in the other case, the weighted average value of the nonlocal Helmholtz solution itself decays exponentially outside some domain. Particularly for a typical kernel function $\gamma_1(s)=\frac12 e^{-| s|}$, we obtain the Green's function of the nonlocal Helmholtz equation, and use the Green's function to further prove that (i) the nonlocal PML solution decays exponentially in PML layers in one case; (ii) in the other case, the nonlocal Helmholtz solution itself decays exponentially outside some domain. Based on our theoretical analysis, the truncated nonlocal problems are discussed and an asymptotic compatibility scheme is also introduced to solve the resulting truncated problems. Finally, numerical examples are provided to verify the effectiveness and validation of our nonlocal PML strategy and theoretical findings.

Optimization and Development of Existing Corn Sheller Machine

Abstract: In our country, most of the land use for the agriculture purpose that manufacture semi-finish product or product. Farmers in developing country like Republic of India grows little scale maze. Corn is sold-out by farmer with cob. the typical kernel value is just about double the value of cob. maze is extremely helpful plant for man and animal. it's a serious material for business particularly for production of starch, oil, protein, food sweeteners and bio fuels. it's process is effortful and time intense. This mobile machine was designed to shell maize and to separate the cob from the grain. The additional financial gain is generated by farmers if corns is embellished and kernels area unit sold-out on the market themselves. however this needs a worker of low cost operated by hand and economical maize. the shortage of little maize process machine i.e, maize worker is that the major maize production downside, particularly in our country Republic of India.

Parameterized Resampling Time-Frequency Transform

Many signals contain multiple components with time-varying instantaneous frequencies (IFs) which share a common trajectory trend, such as machinery vibration signals, speech signals, and biomedical signals. To analyze this kind of signals and achieve high time-frequency resolution, we propose a method called parameterized resampling time-frequency transform (PRTF transform) in this paper. Adapting the idea of the general parameterized time-frequency transform (GPTF transform), we use a parameterized kernel to represent a resampling function and further construct time-varying and time-invariant resampling operators to eliminate IF variations and relocate IF positions. These operators can improve the energy concentration of multiple components simultaneously in the time-frequency representation (TFR). Typical kernel functions containing the polynomial function and Fourier series are provided for different kinds of signals. A corresponding kernel estimation method is proposed to detect the shared trend of IFs by utilizing multiple components and to recursively approximate kernel parameters. Both numerical simulations and practical experiments show the effectiveness of the proposed method in improving the time-frequency resolution of TFRs for non-stationary multi-component signals.

Random Error in Strain Calculation using Regularized Polynomial Smoothing (RPS) and Point-wise Least Squares (PLS) in Digital Image Correlation

The strain error analysis is greatly concerned recently as digital image correlation (DIC) is used to measure the heterogeneous deformation. This paper focuses on the estimation of random error and under-matched error caused by two strain calculation methods, i.e. the point-wise least squares (PLS) and the regularized polynomial smoothing method (RPS). Two assumptions are put forward on the noise error of the calculated displacement that are: a) it is pure random error without bias and b) in each strain window, it is the independent Gaussian white noise with zero-mean. Based on the assumptions, the random error of displacement and strain is estimated, and the under-matched error of displacement and strain is theoretically analyzed by the aid of Laplacian operator. These two error solutions are verified by some stimulated experiments. Then for the typical kernel function of 3rd order polynomial, a self-adaptive algorithm minimizing the total error is proposed to choose the optimal parameters, i.e. window size and parameter λ. Experiments show that when the original displacement noise conforms to the assumptions strictly, 1) the estimated random error and under-matched error agrees very well with the experimental value, 2) the self-adaptive algorithm can give the optimal parameters in restoring the displacement and strain field, and 3) the estimation of random error and under-matched error is affected by DIC noise greatly, and it is better to use low-pass Gaussian filter before utilizing self-adaptive algorithm.

A Generic Design of Driver Drowsiness and Stress Recognition Using MOGA Optimized Deep MKL-SVM.

Driver drowsiness and stress are major causes of traffic deaths and injuries, which ultimately wreak havoc on world economic loss. Researchers are in full swing to develop various algorithms for both drowsiness and stress recognition. In contrast to existing works, this paper proposes a generic model using multiple-objective genetic algorithm optimized deep multiple kernel learning support vector machine that is capable to recognize both driver drowsiness and stress. This algorithm simplifies the research formulations and model complexity that one model fits two applications. Results reveal that the proposed algorithm achieves an average sensitivity of 99%, specificity of 98.3% and area under the receiver operating characteristic curve (AUC) of 97.1% for driver drowsiness recognition. For driver stress recognition, the best performance is yielded with average sensitivity of 98.7%, specificity of 98.4% and AUC of 96.9%. Analysis also indicates that the proposed algorithm using multiple-objective genetic algorithm has better performance compared to the grid search method. Multiple kernel learning enhances the performance significantly compared to single typical kernel. Compared with existing works, the proposed algorithm not only achieves higher accuracy but also addressing the typical issues of dataset in simulated environment, no cross-validation and unreliable measurement stability of input signals.

A boundary-condition-transfer method for shell-to-solid submodeling and its application in high-speed trains

The boundary-condition-transfer method for a shell-to-solid submodeling is fundamental for analyzing local or weak regions of a complex structure accurately. In this paper, a novel method is presented for transferring displacement boundaries based on hypothetical nodes. By considering the invariable volume of an element as a constraint, the interpolation through conventional methods using 6-degrees-of-freedom (DOFs) nodal translations and rotations is converted into a 3-DOF translational interpolation at the cut boundary of a submodel. To demonstrate this method, a radial basis function (RBF) was employed for interpolation. For validating the accuracy of the proposed method, a square plate with a hole under tensile and bending load were designed as examples. By considering global and local errors, three typical kernel functions with respect to mesh density ratios were analyzed to fix the optimal parameter in RBF. The examples showed that the proposed method significantly improves the accuracy in shell-to-solid submodeling problems compared to conventional solutions such as ANSYS. For structural analysis of a high-speed train car body under combined mechanical and aerodynamic loads, the submodeling method was implemented on the solid-element-based local model with a welding seam, with which a more detailed stress state was obtained compared with that computed by shell elements. The accurate and reliable results illustrate that the proposed method is the core for the global–local analysis of large complex structures, which also is used for the design and evaluation of the mechanical properties.

Efficient Algorithms for Kernel Aggregation Queries

Kernel functions support a broad range of applications that require tasks like density estimation, classification, regression or outlier detection. For these tasks, a common online operation is to compute the weighted aggregation of kernel function values with respect to a set of points. However, scalable aggregation methods are still unknown for typical kernel functions (e.g., Gaussian kernel, polynomial kernel, sigmoid kernel and additive kernels) and weighting schemes. In this paper, we propose a novel and effective bounding technique, by leveraging index structures, to speed up the computation of kernel aggregation. In addition, we extend our technique to additive kernel functions, including X2, intersection, JS and Hellinger kernels, which are widely used in different communities, e.g., computer vision, medical science, Geoscience etc. To handle the additive kernel functions, we further develop the novel and effective bound functions to efficiently evaluate the kernel aggregation. Experimental studies on many real datasets reveal that our proposed solution KARL achieves at least one order of magnitude speedup over the state-of-the-art for different types of kernel functions.

Privacy-Preserving Support Vector Machine Computing Using Random Unitary Transformation

A privacy-preserving support vector machine (SVM) computing scheme is proposed in this paper. Cloud computing has been spreading in many fields. However, the cloud computing has some serious issues for end users, such as the unauthorized use of cloud services, data leaks, and privacy being compromised. Accordingly, we consider privacy-preserving SVM computing. We focus on protecting visual \red{information} of images by using a random unitary transformation. Some properties of the protected images are discussed. The proposed scheme enables us not only to protect images, but also to have the same performance as that of unprotected images even when using typical kernel functions such as the linear kernel, radial basis function(RBF) kernel and polynomial kernel. Moreover, it can be directly carried out by using well-known SVM algorithms, without preparing any algorithms specialized for secure SVM computing. In an experiment, the proposed scheme is applied to a face-based authentication algorithm with SVM classifiers to confirm the effectiveness.

Distribution-free uncertainty quantification for kernel methods by gradient perturbations

We propose a data-driven approach to quantify the uncertainty of models constructed by kernel methods. Our approach minimizes the needed distributional assumptions, hence, instead of working with, for example, Gaussian processes or exponential families, it only requires knowledge about some mild regularity of the measurement noise, such as it is being symmetric or exchangeable. We show, by building on recent results from finite-sample system identification, that by perturbing the residuals in the gradient of the objective function, information can be extracted about the amount of uncertainty our model has. Particularly, we provide an algorithm to build exact, non-asymptotically guaranteed, distribution-free confidence regions for ideal, noise-free representations of the function we try to estimate. For the typical convex quadratic problems and symmetric noises, the regions are star convex centered around a given nominal estimate, and have efficient ellipsoidal outer approximations. Finally, we illustrate the ideas on typical kernel methods, such as LS-SVC, KRR, varepsilon -SVR and kernelized LASSO.