Multiscale regression on unknown manifolds

<abstract><p>We consider the regression problem of estimating functions on $ \mathbb{R}^D $ but supported on a $ d $-dimensional manifold $ \mathcal{M} ~~\subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear approximation, we construct low-dimensional coordinates on $ \mathcal{M} $ at multiple scales, and perform multiscale regression by local polynomial fitting. We propose a data-driven wavelet thresholding scheme that automatically adapts to the unknown regularity of the function, allowing for efficient estimation of functions exhibiting nonuniform regularity at different locations and scales. We analyze the generalization error of our method by proving finite sample bounds in high probability on rich classes of priors. Our estimator attains optimal learning rates (up to logarithmic factors) as if the function was defined on a known Euclidean domain of dimension $ d $, instead of an unknown manifold embedded in $ \mathbb{R}^D $. The implemented algorithm has quasilinear complexity in the sample size, with constants linear in $ D $ and exponential in $ d $. Our work therefore establishes a new framework for regression on low-dimensional sets embedded in high dimensions, with fast implementation and strong theoretical guarantees.</p></abstract>

On one method of numerical modeling of piezoconductive processes of a two-phase fluid system in a fractured-porous reservoir

A method of numerical modeling based on splitting by physical processes of two-phase fluid transfer in a formation with fractured-porous reservoirs is described. Reservoirs of this type have a natural fracture system and are described by the dual porosity model. A four-block mathematical model of the fluid redistribution between a pore-type matrix and a natural fracturing pattern is proposed and studied. The resulting system is complex and entails a number of difficulties associated with a large number of variables and the absence of important properties of a linearized system of equations, such as self-adjointness and symmetry, which are present in the description of piezoconductive processes. The complete splitting by physical processes is carried out to solve this problem. The resulting split model is differentially equivalent to the discrete initial balance equations of the system (conservation of the mass components of the fluids and the total energy of the system), written in divergent form. This approach is associated with a nonlinear approximation of the grid functions in time, which depends on the fraction of the volume occupied by the fluids in the pores, and is easy to implement.

Design of Manipulator Control System of Forest Picking Robot Based on Fractional Order PID Sliding Mode Control

This paper studies the control system design of forest picking robot manipulator based on fractional PID sliding mode control. In this paper, the structure characteristics, learning algorithm and application of fractional order PID sliding mode control in manipulator control are analyzed. In this paper, the nonlinear approximation property of fractional order PID sliding mode control is theoretically verified. This paper analyzes the basic structure of picking manipulator system in detail. At the same time, the Lagrange Euler method is used to deduce the dynamic equation of the two degree of freedom series manipulator, and the inertia characteristics, Coriolis force and centripetal force characteristics, heavy torque characteristics are analyzed. The nonlinear system model of manipulator based on S-function is established in MATLAB, and the dynamic model is transformed into the form of second-order differential equation to facilitate the introduction of the designed algorithm.

Nonlinear approximation of wildfire front temperature on MODIS data for sub-pixel analysis of burning

An improved approach to evaluate thermal anomalies characteristics using the pixel-based analysis of the MODIS imagery was proposed. The approach allows us to improve the accuracy in estimating characteristics of active combustion zones comparing to the standard Dozier method. We used the imagery of active wildfires in Siberian forests from the MODIS radiometer acquired in the spectral ranges of 3.930–3.990 and 10.780–11.280 mm (bands 21 and 31, respectively). Nonlinear exponential function was used to describe the approximation of the temperature of combustion zones. Available data of field and numerical experiments were used for validating of the approximation accuracy. Nonlinear approximation of wildfire front temperature allows to determine the portion of the active pixel of the MODIS image with the given temperature excess comparing to the temperature of background cover. This improves the accuracy in extracting of active burning zones as well as in classifying the heat release rate at the sub-pixel level of analysis.

Development of a simulation model of energy-saving system based on CCGT-110 and ABСM for energy and thermodynamic analysis

Objectives. Simulation modeling is increasingly being used for the study of complex economic, technical, biological, etc. systems. Such systems are characterized by multifactorial relationships of their functioning, nonlinear dependencies between system elements and stochasticity of their parameters, etc. The purpose of this work is to develop a simulation model based on the C# programming language for the energy-saving CCGT-110 and ABCM system based on the results of manual analysis according to the data of a full-scale experiment.Method. Methods of linear and nonlinear approximation, methods of energy and thermodynamic analysis, as well as methods of mathematical simulation modeling are used to develop the simulation model.Result.The result of this work is the developed software SAESS 3.0, which allows you to analyze the operation of the CCGT-110 and ABCM systems together and separately in a wide range of parameters and in real time. Conclusion.To assess the adequacy of the developed program, a comparative analysis of software and manual calculation was carried out. Deviations do not exceed an average of 3 %, which confirms the reliability of the simulation model.

The renewal equation in nonlinear approximation

The family of Markov processes are considered in the article. We study the multidimensional renewal equation in nonlinear approximation. The purpose of the work is to find the limit of renewal function.

Fuzzy adaptive fault diagnosis and compensation for variable structure hypersonic vehicle with multiple faults

Based on the type-II fuzzy logic, this paper proposes a robust adaptive fault diagnosis and fault-tolerant control (FTC) scheme for multisensor faults in the variable structure hypersonic vehicles with parameter uncertainties. Type-II fuzzy method approximates the original models while eliminating the parameter uncertainties. Hence the sensor faults are detected and isolated by the multiple output residuals and thresholds considering nonlinear approximation errors and disturbance. Based on the fuzzy adaptive augmented observer, the faults and disturbance are all estimated accurately by an improved proportional-differential part. Then a variable structure FTC scheme repairs the faults by the estimation, the fast-varying disturbance is considered in FTC scheme and is compensated by the control parameters designed based on its derivative function, thereby enhancing the output robust tracking accuracy of the variable structure hypersonic vehicles. The Lyapunov theory proves the system robust stability, semi-physical simulation verifies the validity of the proposed method and the superiority compared with the traditional method.

Design of Picking Robot Manipulator Control System Based on Fuzzy Compensation RBF Neural Network

Industrial manipulator occupies a very important position in industrial production. The tracking control of its control system and joint trajectory has always been a research hotspot. But the manipulator is a multi input multi output system, which has the characteristics of nonlinearity and strong coupling. Radial basis function (RBF) neural network has high nonlinear mapping ability. In this paper, the structure characteristics, learning algorithm and application of RBF neural network in manipulator control are analyzed. In this paper, the nonlinear approximation property of RBF neural network is theoretically verified. This paper analyzes the basic structure of picking manipulator system in detail. At the same time, the Lagrange Euler method is used to deduce the dynamic equation of the two degree of freedom series manipulator, and the inertia characteristics, Coriolis force and centripetal force characteristics, heavy torque characteristics are analyzed. The nonlinear system model of manipulator based on S-function is established in MATLAB, and the dynamic model is transformed into the form of second-order differential equation to facilitate the introduction of the designed algorithm.