Vector-valued Functions Research Articles

Enhanced square root CKF with mixture correntropy loss for robust state of charge estimation of lithium-ion battery

The measurement data of lithium-ion battery collected in complex operating conditions may be contaminated by non-Gaussian noises (or outliers), a novel robust state of charge (SOC) estimation approach that enhances the robustness of square-root cubature Kalman filter (SRCKF) by incorporating a mixture correntropy loss (MCL) is proposed to overcome the issue of non-Gaussian measurement noise interference. Although the SRCKF can perform non-destructive state estimation for nonlinear system, it is sensitive to the non-Gaussian noises (or outliers) due to the use of mean square error (MSE) loss. To overcome this limitation, the MCL is used as a cost to replace the MSE in CKF framework, which is constructed by mixture of two Gaussian kernel functions with different kernel widths and has outstanding robustness. Moreover, we establish an effective nonlinear regression model that incorporates noise and state error information into the MCL function, and then a fixed-point iteration method is utilized to update the posterior state estimation. Additionally, to further suppress the influence of abnormal noise on the posterior state estimation, we introduce the exponential function of the innovation vector to adjust the measurement covariance matrix in real-time. Accordingly, an enhanced MCL-SRCKF is developed for SOC estimation considering the measurement noises with non-Gaussian distribution. Results from various simulation environments demonstrate that the proposed method achieves high estimation accuracy in different cases.

Reduction of supernova light curves by vector Gaussian processes

ABSTRACT Bolometric light curves play an important role in understanding the underlying physics of various astrophysical phenomena, as they allow for a comprehensive modelling of the event and enable comparison between different objects. However, constructing these curves often requires the approximation and extrapolation from multicolour photometric observations. In this study, we introduce vector Gaussian processes as a new method for reduction of supernova light curves. This method enables us to approximate vector functions, even with inhomogeneous time-series data, while considering the correlation between light curves in different passbands. We applied this methodology to a sample of 29 superluminous supernovae (SLSNe) assembled using the Open Supernova Catalog. Their multicolour light curves were approximated using vector Gaussian processes. Subsequently, under the blackbody assumption for the SLSN spectra at each moment of time, we reconstructed the bolometric light curves. The vector Gaussian processes developed in this work are accessible via the python library gp-multistate-kernel on GitHub. Our approach provides an efficient tool for analysing light curve data, opening new possibilities for astrophysical research.

A Banach—Stone Type Theorem for Space of Vector-Valued Differentiable Maps

A Banach—Stone Type Theorem for Space of Vector-Valued Differentiable Maps

Making Waves

We study linear PDE constraints for vector-valued functions and distributions. Our focus lies on wave solutions, which give rise to distributions with low-dimensional support. Special waves from vector potentials are represented by syzygies. We parametrize all waves by projective varieties derived from the support of the PDE. These include determinantal varieties and Fano varieties, and they generalize wave cones in analysis.

A High-Accuracy-Light-AI Data-Driven Diagnosis Method for Open-Circuit Faults in Single-Phase PWM Rectifiers

Data-driven solutions like artificial intelligence (AI) are more upright and effectual for fault diagnosis in the power converter system. To decrease computing load and improve the diagnosis speed of the intelligent algorithm, a high-accuracy-light-AI data-driven open-circuit diagnosis method is proposed to diagnose single or multiple IGBT open-circuit faults in the single-phase pulse width modulation (PWM) rectifiers. Firstly, the fault characteristics of three fault scenarios are analyzed to seek the most critical features and provide prior knowledge for developing the intelligent diagnostic algorithm. Then, a fast-learning algorithm named random vector function link network (RVFL) is utilized to extract the mapping knowledge between the well-selected features and fault modes. To balance the testing accuracy and calculation time of the diagnostic algorithm, the RVFL parameters are tuned to decrease the computing burden. After that, a decision-making framework is designed for identifying the faults in real-time. Finally, the effectiveness of the proposed fault diagnosis method is thoroughly verified by extensive experimental tests. A substantial comparison to state-of-the-art techniques shows the proposed scheme’s superiority in diagnostic accuracy, computing time, and diagnosis time.

Stable Distribution of Multivariate Data

The main theorem of the paper states that every stable random vector with marginal skewness parameters different from ±1 can be turned into a sub-Gaussian random vector by using an appropriately tailored transformation in multidimensional space. The theorem is used to create a formula on probability density function of stable random vector and to perform a procedure of testing the stable distribution of multivariate data. A dataset collected from the Nasdaq stock market is used to illustrate the proposed procedure.

Analysis of the impact of ADDIE education model based on logistic regression model on teaching contemporary cultural and creative product design

Abstract Exploring the influence of the ADDIE education model on teaching cultural and creative product design to promote the improvement of the quality of teaching cultural and creative product design. Starting from the ADDIE education model, this paper analyzes the five components of the model and the specific functions of each component. The logistic regression algorithm that constitutes the analysis module of the ADDIE education model is introduced, and a sparse prior factor is introduced to optimize the logistic regression algorithm; then, a sparse logistic regression algorithm is constructed to solve the likelihood function of the weight vector. Finally, the ADDIE education model is used to analyze the indicators of cultural and creative product design teaching in two aspects: the teaching objectives and teaching principles of cultural and creative product design. From the teaching objectives, the influence of cognitive, skill, and emotional objectives accounted for 47.11%, 44.41% and 51.26%, respectively. From the teaching principles, the percentages of uniqueness, practicality, and attractiveness are 51.5%, 43.7%, and 40.3%, respectively. Based on the ADDIE education model can affect the emotional goals and uniqueness in the teaching of cultural and creative product design, and it is necessary to focus on the emotional teaching of product design as well as diversified and differentiated teaching in design teaching in order to enhance better the learners’ interest degree in cultural and creative product design.

A classification of S-boxes generated by orthogonal cellular automata

Most of the approaches published in the literature to construct S-boxes via Cellular Automata (CA) work by either iterating a finite CA for several time steps, or by a one-shot application of the global rule. The main characteristic that brings together these works is that they employ a single CA rule to define the vectorial Boolean function of the S-box. In this work, we explore a different direction for the design of S-boxes that leverages on Orthogonal CA (OCA), i.e. pairs of CA rules giving rise to orthogonal Latin squares. The motivation stands on the facts that an OCA pair already defines a bijective transformation, and moreover the orthogonality property of the resulting Latin squares ensures a minimum amount of diffusion. We exhaustively enumerate all S-boxes generated by OCA pairs of diameter 4≤d≤6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4 \\le d \\le 6$$\\end{document}, and measure their nonlinearity. Interestingly, we observe that for d=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=4$$\\end{document} and d=5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=5$$\\end{document} all S-boxes are linear, despite the underlying CA local rules being nonlinear. The smallest nonlinear S-boxes emerges for d=6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=6$$\\end{document}, but their nonlinearity is still too low to be used in practice. Nonetheless, we unearth an interesting structure of linear OCA S-boxes, proving that their Linear Components Space is itself the image of a linear CA, or equivalently a polynomial code. We finally classify all linear OCA S-boxes in terms of their generator polynomials.

Necessary optimality conditions for a semivectorial bilevel optimization problem via a revisited Charnes–Cooper scalarization

In this paper, we investigate a multiobjective bilevel optimization problem with a vector-valued lower-level objective function. We revisit the Charnes–Cooper scalarization technique for multi-objective programs and use optimal value reformulation to transform the scalar problem into a one-level optimization problem. Using Mordukhovich's generalized differentiation calculus, a new subdifferential estimate and Lipschitz condition for the optimal value function of this problem are developed as a result of this reformulation. In addition, we construct first-order necessary optimality conditions in the smooth setting.

On the density of CV0(X)⊗A in CV0(X,A)

Let X be a completely regular Hausdorff space and V a Nachbin family on X. For a locally convex algebra A, let CV0(X,A) be the algebra of all weighted vector-valued continuous functions which vanish at infinity with the topology given by the uniform seminorms induced by V. In this paper we present some sufficient conditions under which CV0(X)⊗A is a dense subspace of CV0(X,A) or isomorphic to it.

Complex sparse Bayesian learning for guided wave dispersion curve estimation in plate-like structures

This paper proposes a new dispersion curve estimation method that employs the complex sparse Bayesian learning (CSBL). It is well accepted that guided wave packets are distorted because of the differences in propagation velocities at different frequencies; thus, the preceding velocity–frequency curve estimation is beneficial for wave packet recovery, feature recognition and defect localization. Conventional dispersion curve estimation methods, such as two-dimensional Fourier transform and multiple signal classification, are suitable for array signal and are restricted by the transducer aperture, leading to a small application scope. According to the frequency–response model of the guided wave, for each frequency, the responses obtained by the transducers can be sparsely represented based on an overcomplete dictionary matrix constructed using multiple discretized wavenumbers and known distances. A CSBL algorithm was developed to infer the posterior probability density function of the weight vector in the sparse representation. The non-zero elements in the sparse weight vector mean that the corresponding dictionary atoms indicated wavenumbers are contained in the frequency response, and the velocity–frequency curve can be finally derived from the wavenumber–frequency curve. The proposed CSBL method has a satisfactory capability to solve this sparse representation of the complex frequency response because a hierarchical form of the Laplace prior is employed to achieve a high degree of sparsity of the weight vector. This method effectively incorporates the real and imaginary parts of the complex frequency response by employing the same hyperparameter to integrate the known information. This method requires only a few randomly placed transducers; thus, it has a wide range of applications. The effectiveness of the proposed approach was validated using multiple guided-wave signals obtained through numerical simulations and an experimental study on a plate structure.

Жадная эвристика размещения ортогональных многогранников для оптимизированного решения задач компоновки объектов нерегулярной формы

The article deals with the cutting and packing problems of irregular shape objects, which consist in finding the most compact way to place a given set of objects of arbitrary geometry inside a certain limited space. These problems belong to the class of ­NP-hard discrete optimization problems for which there are no methods of polynomial complexity to obtain exact solutions, so in practice they are most often solved approximately using heuristic and metaheuristic optimization methods. When placing objects of irregular shape, it is additionally necessary to take into account the geometry of objects to determine the correctness of their placement relative to each other. Existing methods of analyzing the geometry of objects and the formed placement scheme, based on the use of phi-functions and the construction of a hodograph of a vector function of dense placement, theoretically provide the possibility of obtaining an accurate solution, but require the use of time-consuming methods of nonlinear optimization. Therefore, in order to increase the speed of packing a large number of irregular-shaped objects, their shape is transformed by voxelization, followed by combining the resulting set of voxels into orthogonal polyhedra. To improve the quality of the solutions obtained, the paper proposes a greedy heuristic for the placement of orthogonal polyhedra, which implements the choice of the best orientation option for the object being placed, in which the formed packing will be the densest in comparison with other available orientation options for this object. The analysis of the effectiveness of this greedy heuristic on the problems of irregular cutting and packing of three-dimensional objects is carried out. Computational experiments have shown that the proposed greedy heuristic provides very fast high-quality solutions. Additionally, the results of testing the greedy placement heuristics using a genetic algorithm to optimize solutions to the packing problem are presented.

Constraint Qualifications for Vector Optimization Problems in Real Topological Spaces

In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions by use of “linear set”. We prove that our generalized affine functions have some similar properties to generalized convex functions. We present examples to show that our generalized affinenesses are different from one another, and also provide an example to show that our definition of presubaffinelikeness is non-trivial; presubaffinelikeness is the weakest generalized affineness introduced in this article. We work with optimization problems that are defined and taking values in linear topological spaces. We devote to the study of constraint qualifications, and derive some optimality conditions as well as a strong duality theorem. Our optimization problems have inequality constraints, equality constraints, and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions.

Existence and Ulam‐type stability for impulsive oscillating systems with pure delay

In this paper, we first introduce the new concept of an impulsive delayed vector function, which helps us to build the representation of an exact solution for the linear impulsive oscillating differential delay systems (IODDSs). Second, we derive some sufficient conditions to guarantee the existence and uniqueness of solution by Schauder's and Banach's fixed point theorems for a new class of nonlinear IODDSs. Finally, we obtain the Ulam‐Hyers stability (UHs) and Ulam‐Hyers‐Rassias stability (UHRs) for nonlinear IODDSs, and two examples are presented to illustrate the main results of our study.

2-Local isometries on vector-valued differentiable functions

2-Local isometries on vector-valued differentiable functions

Multivariate Multiplicative Functions of Uniform Random Vectors in Large Integer Domains

Multivariate Multiplicative Functions of Uniform Random Vectors in Large Integer Domains

Stability and Periodic Motions for a System Coupled with an Encapsulated Nonsmooth Dynamic Vibration Absorber

The dynamic vibration absorber (DVA) is widely used in engineering models with complex vibration modes. The research on the stability and periodic motions of the DVA model plays an important role in revealing its complex vibration modes and energy transfer. The aim of this paper is to study the stability and periodic motions of a two-degrees-of-freedom system coupled with an encapsulated nonsmooth dynamic vibration absorber under low-frequency forced excitation. Based on the slow–fast method, the model is transformed into a six-dimensional piecewise smooth system coupling two time scales. The existence and stability of the admissible equilibrium points for the model are discussed under different parameter conditions. Based on the first integrals, the Melnikov vector function of the nonsmooth dynamic vibration absorber model is calculated. The existence and number of periodic orbits bifurcated from a family of periodic orbits under different parameters are discussed. The phase diagram configuration of periodic orbits is given based on numerical simulation. The results obtained in this paper offer a new perspective for vibration analysis and parameter control for nonsmooth dynamic vibration absorbers.

Improving geometric iterative approximation methods using local approximations

In this study, we propose improvements to Geometric Iterative Methods (GIM) for curve and surface approximation. Our key contributions include introducing an error vector function and deriving new error vectors, which enhance the approximation quality compared to the Least Squared Progressive and Iterative Approximation (LSPIA) methods. Additionally, we integrate parameter correction and control points update based on local approximations, achieving comparable accuracy to Geometric Approximation (GA) methods while being more computationally efficient. Extensive experiments demonstrate the superior accuracy and computational efficiency of our method.

Synthesis of an adaptive control system for unstable and deterministic chaotic processes with m-inputs and n-outputs

The paper proposes a method for solving the problem of synthesis of an adaptive control system for unstable and deterministic chaotic processes in the class of ‘dovetail’ catastrophes for objects with m-inputs and n-outputs. The synthesis problem is solved by the gradient-velocity method of Lyapunov vector functions. From the conditions of the aperiodic robust stability of the etalon model with the desired dynamics of the main control loop and the generalised configurable object, the control goal is achieved. One of the most promising ways of solving the problem of managing unstable and deterministic chaotic processes is the synthesis of a control system in the class of ‘swallowtail’ catastrophes and the use of adaptation methods. Selecting and studying a reference model, and employing the gradient-velocity method for a generalised configurable control object ensure robust stability, utilise current information effectively, and achieve desired system quality and management goals.

L-Index in Joint Variables: Sum and Composition of an Entire Function with a Function With a Vanished Gradient

The composition H(z)=f(Φ(z)) is studied, where f is an entire function of a single complex variable and Φ is an entire function of n complex variables with a vanished gradient. Conditions are presented by the function Φ providing boundedness of the L-index in joint variables for the function H, if the function f has bounded l-index for some positive continuous function l and L(z)=l(Φ(z))(max{1,|Φz1′(z)|},…,max{1,|Φzn′(z)|}),z∈Cn. Such a constrained function L allows us to consider a function Φ with a nonempty zero set. The obtained results complement earlier published results with Φ(z)≠0. Also, we study a more general composition H(w)=G(Φ(w)), where G:Cn→C is an entire function of the bounded L-index in joint variables, Φ:Cm→Cn is a vector-valued entire function, and L:Cn→R+n is a continuous function. If the L-index of the function G equals zero, then we construct a function L˜:Cm→R+m such that the function H has bounded L˜-index in the joint variables z1,…,zn. The other group of our results concern a sum of entire functions in several variables. As a general case, a sum of functions with bounded index is not of bounded index. The same is also valid for the multidimensional case. We found simple conditions proving that f1(z1)+f2(z2) belongs to the class of functions having bounded index in joint variables z1,z2. We formulate some open problems based on the deduced results and on the usage of fractional differentiation operators in the theory of functions with bounded index.