Kernel Function Research Articles

Remaining useful life prediction of high-capacity lithium-ion batteries based on incremental capacity analysis and Gaussian kernel function optimization

Remaining useful life (RUL) is a key indicator for assessing the health status of lithium (Li)-ion batteries, and realizing accurate and reliable RUL prediction is crucial for the proper operation of battery systems. As high-capacity Li batteries have more complex chemical properties, most of the current RUL prediction methods rely mainly on a priori knowledge to make judgments. As a result, prediction accuracy is not high. In this study, we developed a health indicator-capacity (HI-C) dual Gaussian process regression (GPR) model based on incremental capacity analysis (ICA) and optimized its kernel function to achieve accurate RUL prediction for 280 Ah high-capacity Li batteries. Validation against the United States National Aeronautics and Space Administration’s four battery test datasets showed that the use of the HI-C dual GPR model resulted in a mean absolute percentage error and root mean square error of less than 0.02 and 0.04, respectively, for the four battery-rated capacity predictions. Additionally, this model achieved an absolute error of less than five battery failure turns. Compared with a single model, the HI-C dual GPR model not only had high accuracy but also solved the problem that the HI was not measurable in the actual battery operation, which made it more suitable for RUL prediction of Li batteries.

Axisymmetric Indentation of Circular Rigid Plate on Layered Elastic Halfspace with Transverse Isotropy

This paper investigates the contact problem of a layered elastic halfspace with transverse isotropy under the axisymmetric indentation of a circular rigid plate. Fourier integral transforms and a backward transfer matrix method are used to obtain the analytical solution of the contact problem. The interaction between the rigid plate and the layered halfspace can be expressed with the standard Fredholm integral equations of the second kind. The induced elastic field in the layered halfspace can be expressed as the semi-infinite integrals of four known kernel functions. The convergence and singularity of the semi-infinite integrals near or at the surface of the layered halfspace are resolved using an isolating technique. The efficient numerical algorithms are used and developed for accurately calculating the Fredholm integral equations and the semi-infinite integrals. Numerical results show the correctness of the proposed method and the effect of layering non-homogeneity on the elastic fields in layered transversely isotropic halfspace induced by the axisymmetric indentation of a circular rigid plate.

Fenton type minimax problems for sum of translates functions

Following an insightful work of P. Fenton, we investigate sum of translates functions F(x,t):=J(t)+∑j=1nνjK(t−xj), where J:[0,1]→R_:=R∪{−∞} is a “sufficiently non-degenerate” and upper-bounded “field function”, and K:[−1,1]→R_ is a fixed “kernel function”, concave both on (−1,0) and (0,1), x:=(x1,…,xn) with 0≤x1≤…≤xn≤1, and ν1,…,νn>0 are fixed. We analyze the behavior of the local maxima vector m:=(m0,m1,…,mn), where mj:=mj(x):=supxj≤t≤xj+1⁡F(x,t), with x0:=0, xn+1:=1; and study the optimization (minimax and maximin) problems infx⁡maxj⁡mj(x) and supx⁡minj⁡mj(x). The main result is the equality of these quantities, and provided J is upper semicontinuous, the existence of extremal configurations and their description as equioscillation points w, i.e., w satisfying m0(w)=m1(w)=⋯=mn(w). In our previous papers we obtained results for the case of singular kernels, i.e., when K(0)=−∞ and the field was assumed to be upper semicontinuous. In this work we get rid of these assumptions and prove common generalizations of Fenton's and our previous results, and arrive at the greatest generality in the setting of concave kernel functions.

Combining Dielectric and Hyperspectral Data for Apple Core Browning Detection

Apple core browning not only affects the nutritional quality of apples, but also poses a health risk to consumers. Therefore, there is an urgent need to develop a fast and reliable non-destructive detection method for apple core browning. To deal with the challenges of the long incubation period, strong infectivity, and difficulty in the prevention and control of apple core browning, a novel non-destructive detection method for apple core browning has been developed through combining hyperspectral imaging and dielectric techniques. To reduce the computational complexity of high-dimensional multi-view data, canonical correlation analysis is employed for feature dimensionality reduction. Then, the two low-dimensional vectors extracted from two different sensors are concatenated into one united feature vector; therefore, the information contained in the hyperspectral and dielectric data is fused to improve the detection accuracy of the non-destructive method. At last, five traditional classifiers, such as k-Nearest Neighbors, a support vector machine with radial basis function kernel and polynomial kernel, Decision Tree, and neural network, are trained on the fused feature vectors to discriminate apple core browning. The experimental results on our own constructed dataset have shown that the sensitivity, specificity, and precision of SVM with RBF kernel based on concatenated 70-dimensional feature vectors extracted via canonical correlation analysis reached 99.98%, 99.70%, and 99.70%, respectively, which achieved better results than other models. This study can provide theoretical assurance and technical support for further development of higher accuracy and lower-cost non-destructive detection devices for apple core browning.

Estimates for Certain Rough Multiple Singular Integrals on Triebel–Lizorkin Space

This paper focuses on studying the mapping properties of singular integral operators over product symmetric spaces. The boundedness of such operators is established on Triebel–Lizorkin spaces whenever their rough kernel functions belong to the Grafakos and Stefanov class. Our findings generalize, extend and improve some previously known results on singular integral operators.

Research on the prediction method of wing structure noise based on the combination of conditional generative adversarial neural network and numerical methods

This paper presents a technique for predicting noise generated by airfoil structures that combines deep learning techniques with traditional numerical methods. In traditional numerical methods, accurately predicting the noise of airfoil structures requires significant computational resources, making it challenging to perform low-noise optimization design for these structures. To expedite the prediction process, this study introduces Conditional Generative Adversarial Networks (CGAN). By replacing the generator and discriminator of CGAN with traditional regression neural network models, the suitability of CGAN for regression prediction is ensured. In this study, the data computation was accelerated by expanding the kernel function in the traditional boundary element method using a Taylor series. Based on the resulting data, an alternative predictive model for wing structure noise was developed by integrating Conditional Generative Adversarial Networks (CGAN). Finally, the effectiveness and feasibility of the proposed method are demonstrated through three case studies.

AI-Enhanced GraphoText Analysis for Tracking Counselling Therapy Progress: Integrating Multimodal Graphology and Machine Learning

Despite the robustness of existing instruments, routine manual observation in psychotherapy faces significant challenges, including lack of time, labour, high implementation costs, and potential biases such as response bias and social desirability. This study proposes a dynamic assessment approach using machine learning and multimodal features extracted from handwriting, incorporating graphology-based and content-based features. The integration of content-based and graphology-based features involves combining text and handwriting features with the Support Vector Machine (SVM) using the Radial Basis Function Kernel (RBF). The results show that this approach achieves an impressive accuracy rate of 86.25%. The proposed framework not only improves psychotherapeutic practise, but also offers new insights into human cognition and emotional dynamics by revealing intricate patterns in handwriting. This advance facilitates data-driven decision-making, improves the quality of patient care, and overcomes challenges associated with manual monitoring, including social desirability bias and response set bias. This research paves the way for innovative methods at the interface of mental health and technology, and promises a more objective and efficient approach to monitoring the progress of psychotherapy.

State of Charge Estimation of Lithium-Ion Batteries for Electric Vehicle Application Using Gaussian Process Regression Approach

For the purpose of ensuring a secure, dependable and affordable performancealong with clean energy in electric vehicles, the estimation of the precise state of charge of LIB is very important. In this article, Gaussian Process Regression with different kernel functions-based SOC prediction is proposed and their performance with good health and well-beingare evaluated and analyzed. A useful benefit of employing GPR is the ability to quantify and estimate uncertainties, allowing for the evaluation of the SOC estimate's dependability. The kernel function serves as a crucial hyperparameter that improves GPR performance. GPR considers the temperature and voltage of the battery, which are independent of one another, as their respective input parametersthat relates Industry, innovation and infrastructure where target-dependent variable is battery SOC. Initially, the training process involves determining the ideal hyperparameters of a kernel function to accurately represent the characteristics of the data. The accuracy of predicting SOC of the battery is evaluated using test data. According to the simulation outcomes, the squared exponential kernel function-based GPR estimates SOC with high accuracy and lower RMSE and MAE which ensures energy efficiency and quality education.

Extraction of agricultural plastic greenhouses based on a U-Net Convolutional Neural Network Coupled with edge expansion and loss function improvement

ABSTRACT Agricultural plastic greenhouses (APGs) are crucial for sustainable agricultural planting, and accurate spatial distribution information acquisition is crucial. Deep learning network models can extract target features from remote sensing images more effectively than traditional interpretation methods, which face challenges like high workloads and poor repeatability. In this study, we aim to enhance the inventorying of Agricultural Plastic Greenhouses (APGs) by improving the extraction accuracy of their locations and numbers through remote sensing techniques. Utilizing GF-7 satellite imagery, we propose an enhanced U-Net convolutional neural network (CNN) model that incorporates edge information expansion and a joint loss function to optimize performance. The primary objective is to provide a rapid and accurate method for mapping APGs, which is crucial for effective agricultural management and environmental monitoring. The U-Net network’s accuracy was enhanced by 1.1% after expanding 3 × 3sample edge information, and further by 1.9% by combining edge extension and loss function constraints. Our results demonstrate that the modified U-Net model significantly improves extraction accuracy compared to traditional methods, thereby facilitating better inventory management and planning for agricultural cash crops. This advancement not only supports farmers in optimizing resources but also contributes to sustainable agricultural practices by enabling precise monitoring of APG distribution. Implication Statement Compared to traditional interpretation methods, which suffer problems such as heavy workloads, small adaptation ranges and poor repeatability, deep learning network models can better extract target features from remote sensing images. In this study, we used GF-7 image data to improve the traditional U-Net convolutional neural network (CNN) model. The Canny operator and Gaussian kernel (GK) function were used for sample edge expansion, and the binary cross-entropy and GK functions were used to jointly constrain the loss. Finally, APGs were accurately extracted and compared to those obtained with the original model. The results indicated that the APG extraction accuracy of the U-Net network was improved through the expansion of sample edge information and adoption of joint loss function constraints.

Long-time behaviors of wave equations stabilized by boundary memory damping and friction damping

In this paper, we study the long-time behaviors of wave equations subject to boundary memory damping and friction damping. Different from assumptions that memory kernel is a nonnegative, monotone function in the previous literatures, we assume that the primitive of the memory kernel is a generalized positive definite kernel (abbreviated to GPDK), which may vary sign or oscillate. The key to the problem lies in establishing the connection between memory damping and energy terms. By combining the properties of the positive definite kernel with classical multiplier methods, and constructing auxiliary systems, we ultimately establish the asymptotic stability, exponential stability and polynomial stability of systems featuring boundary memory damping and friction damping. To illustrate our theoretical results, we provide some numerical simulations.

Localized negative binomial quasi maximum likelihood estimation for time varying integer-valued processes

This paper aims to study the non parametric Negative Binomial Quasi-Maximum Likelihood Estimation (NBQMLE) for locally stationary integer valued processes. So, we have considered two locally stationary integer-valued models of negative binomial type, namely: INARCH ( p ) and INGARCH ( p , q ) models. Imposing some contraction arguments, we have extended the stationary negative-binomial QMLE to a localized one in our non-stationary environment. This estimation method is based on a kernel function that achieves the convergence rates of n h n order. Under some regularity assumptions, the consistency, as well as the asymptotic normality of the obtained estimator, are established. The performances of the established estimators are evaluated via a simulation study and an application to real data set.

Optimization design of composite cap-shape pillar structure based on gaussian process of combined kernel function

Abstract To quickly realize the optimal design of the cap-shaped structure, an optimization design method of composite cap-shaped pillar structure based on combined kernel function Gaussian process was proposed. First, the shortcomings of two kernel functions representing different linear characteristics of data in model construction were analyzed, on which a new combined kernel function was constructed. Based on the finite element numerical simulation results, a database with the web thickness, web height, fiber volume, and ultimate bearing capacity of the cap-shaped structure was constructed. Then, a Gaussian process model based on the combined kernel function was established and the model parameters were trained by the maximum likelihood method. Finally, taking the ultimate bearing capacity per unit volume as the optimization objective, the artificial fish swarm algorithm was used to quickly obtain the structure design parameters under the optimal objective function, and the simulation results were compared with the initial design parameters. The results showed that the method proposed in this paper can optimize the structure performance, improve the design efficiency, and meet the engineering design requirements.

Regulation of tapioca starch 3D printability by yeast protein: Rheological, textural evaluation, and machine learning prediction

This article investigated the effects of yeast protein (YP) on gel rheology, texture, and 3D printability of tapioca starch and the feasibility of Principal component analysis (PCA) and support vector machine (SVM) algorithms for classification and prediction of printability. The results indicated that increasing YP content enhanced the viscosity, storage and loss moduli, and hardness, thereby improving extrudability and supportability of 3D printing. The addition of 15% YP exhibited the best 3D printing performance, but excessively high YP addition hindered ink extrusion. PCA analysis based on rheological and texture indices categorized the ink's 3D printing performance into four classes: poor support and low printing accuracy; good support but low printing accuracy; good support and high printing accuracy; and non-smooth extrusion. Furthermore, SVM algorithm used texture data to predict printability classification, with the highest prediction accuracy (91.67%) achieved at polynomial kernel among four different kernel functions. These results confirm that YP can serve as a potential ink for 3D printing and underscore SVM's efficacy in predicting ink's 3D printing performance.

Research on dangerous flight weather prediction based on machine learning

Abstract With the continuous expansion of the scale of air transport, the demand for aviation meteorological support also continues to grow. The impact of hazardous weather on flight safety is critical. How to effectively use meteorological data to improve the early warning capability of flight dangerous weather and ensure the safe flight of aircraft is the primary task of aviation meteorological services. In this work, support vector machine (SVM) models are used to predict hazardous flight weather, especially for meteorological conditions with high uncertainty such as storms and turbulence. SVM is a supervised learning method that distinguishes between different classes of data by finding optimal decision boundaries in a high-dimensional space. To meet the needs of this study, we chose the radial basis function (RBF) as the kernel function, which helps to deal with nonlinear problems and enables the model to better capture complex meteorological data structures. During the model training phase, we used historical meteorological observations from multiple weather stations, including temperature, humidity, wind speed, wind direction, and other meteorological indicators closely related to flight safety. From this data, the SVM model learns how to distinguish between normal and dangerous flight weather conditions.

A generalized refined Moore–Gibson–Thompson thermoelastic model based on the concept of memory-dependent higher-order derivatives

The inclusion of memory-dependent derivatives (MDD) in constitutive models improves the ability to predict and analyze time-dependent responses of materials, providing a more detailed depiction of their mechanical properties and structural changes. In this paper, a new thermoelasticity model is created that combines the Moore-Gibson-Thompson (MGT) equation with higher-order memory-dependent derivatives (MDD), any optional kernel function, and time delay. The objective of this model is to provide a more accurate mathematical depiction of the thermal and mechanical reactions of materials, particularly those that exhibit complex behaviors over time. A theoretical study was conducted to provide additional clarification of the proposed concept. For this purpose, thermal-mechanical waves were studied in a semi-infinite region, surrounded by a magnetic field, and exposed to a direct heat source uniformly distributed on its outer surface. To solve the coupled partial differential equations governing the system, the Laplace transform methodology was used. The effects of different kernel functions, time delays, and higher-order (HO) derivatives on the behavior of thermoelastic materials are discussed and illustrated using figures and tables.

Adaptive indefinite kernels in hyperbolic spaces

Learning embeddings in hyperbolic space has gained increasing interest in the community, due to its property of negative curvature, as a way of encoding data hierarchy. Recent works investigate the improvement of the representation power of hyperbolic embeddings through kernelization. However, existing developments focus on defining positive definite (pd) kernels, which may affect the intriguing property of hyperbolic spaces. This is due to the structures of hyperbolic spaces being modeled in indefinite spaces (e.g., Kreĭn space). This paper addresses this issue by developing adaptive indefinite kernels, which can better utilize the structures in the Kreĭn space. To this end, we first propose an adaptive embedding function in the Lorentz model and define indefinite Lorentz kernels (iLks) via the embedding function. Due to the isometric relationship between the Lorentz model and the Poincaré ball, these iLks are further extended to the Poincaré ball, resulting in the development of what are termed indefinite Poincaré kernels (iPKs). We evaluate the proposed indefinite kernels on a diversity of learning scenarios, including image classification, few-shot learning, zero-shot learning, person re-identification, knowledge distillation, etc. We show that the proposed indefinite kernels can bring significant performance gains over the baselines and enjoy better representation power from RKKSs than pd kernels.

TCAD‐enabled machine learning framework for DC and RF performance evaluation of InGaAs sub‐channel DG‐HEMTs

AbstractThis research presents a machine learning (ML)‐based model that determines the DC and RF characteristics of InGaAs sub‐channel double gate high electron mobility transistors (DG‐HEMTs) to optimize the device structure. We employ technology computer‐aided design (TCAD) simulations to analyze the DC and RF performance of InGaAs sub‐channel DG‐HEMTs, generating a range of datasets by varying the material composition, layer width, and thickness of different layers in the device structure. We then train and optimize support vector regression (SVR) models using 5‐fold cross‐validation, varying the kernel function and degree parameters, and achieve better performance with the radial basis function (RBF) kernel. The simulated results indicate that the ML model predicts physical parameters more effectively than experimental analysis, offering a compact modeling solution that requires fewer computing resources than traditional methods.

Developing some models to predict the uniaxial compressive strength of various sedimentary rocks (Case studies: Large dam site and mine in Southeast China)

Direct determination of uniaxial compressive strength (UCS) is time-consuming, expensive, and challenging. Therefore, this study aims to indirectly predict UCS using statistical and machine learning methods. First, laboratory measurements were conducted to determine carbonate percentage, water absorption percentage, moisture content, porosity percentage, P-wave velocity, and UCS of sandstone, dolomite, dolomitic limestone, marl limestone, and limestone samples. Subsequently, various models were established to predict UCS using multivariate linear regression (MVLR), random forest regression (RFR), Gaussian process regression (GPR) based on squared exponential kernel function, and adaptive neuro-fuzzy inference system (ANFIS). The influence of Jurassic limestone texture on physical and mechanical properties in stable and unstable slopes in the Three Gorges Dam site and reservoir (TGDSR) showed that the percentage of mudstone texture in unstable slopes is higher than in stable slopes. The UCS, density, compressional wave velocity, and percentage of carbonate in unstable slopes is less than stable slopes. The results indicated that the average measured UCS is 60.60 MPa. Moreover, the average predicted UCS based on the three intelligent methods was 60.55 MPa. The percentage difference between the measured and predicted UCS was −0.09 %, demonstrating that the average error of the three employed methods is less than one percent, highlighting the high accuracy of these methods in estimating rock UCS. Notably, based on error level, Taylor diagram, Wilmot agreement index (WAI), A10 and A20 indices, Nash-Sutcliffe efficiency (NSE), and PM (performance metric) criteria the RFR exhibited superior precision (R2=99 %, and RMSE= 0.06 MPa) compared to the other used methods. The Kruskal-Wallis test (KWT) results showed that there is no significant difference between the measured and predicted values.

Fuzzy robust regression based on exponential-type kernel functions

The least squares method is a frequently used technique in fuzzy regression analysis. However, it is highly sensitive to outliers in the dataset. To address this challenge, we propose a novel robust fuzzy regression model based on exponential-type kernel functions. This approach effectively mitigates the influence of poorly fitted observations on the predicted results by reducing their weights. Furthermore, we use the gh-transformation to guarantee the nonnegativity of the spreads of the predicted response variable. In order to evaluate the performance of our method, a simulation study and three real data sets were considered. The experimental results demonstrate that the proposed method outperforms several popular robust methods in almost all cases. Furthermore, a sensitivity analysis of the estimated parameters provides further evidence of the superior efficiency of the proposed method.

Polynomial-based kernel reproduced gradient descent for stochastic optimization

Stochastic gradient descent (SGD) is widely applied to machine learning tasks. However, the existence of gradient variance degrades the convergence performance of SGD, which cannot be tackled well for tasks with one-time data sampling per sample. In this paper, a kernel reproduced gradient descent algorithm is proposed where the gradient of the risk function is estimated by utilizing the Reproducing Kernel Hilbert Space (RKHS) theory. Meanwhile, to ensure a low storage requirement, a kernel function linearization strategy is used to design the polynomial form of the kernel learning algorithm. It is shown that the error resulting from linearization decreases as the model parameter size increases, and the proposed polynomial-like kernel reproduced gradient descent (PKRGD) algorithm can converge faster than SGD. From experiments on models such as the latest image matching model, LightGlue, it is verified that the reproduced gradients have lower variances, and existing optimizers using the reproduced gradients can further accelerate model training.