Nonlinear Transformation Method Research Articles

Co-optimization of virtual power plants and distribution grids: Emphasizing flexible resource aggregation and battery capacity degradation

Coordination between virtual power plants and active distribution networks is crucial as these plants increasingly aggregate distributed resources within the power system. This study introduces a bilevel optimization framework to coordinate the scheduling of multiple virtual power plants and an active distribution network using pricing strategies for energy and reserves. The upper-level optimization minimizes total operating costs by incorporating bidding plans of the active distribution network in various markets, its interactions with multiple virtual power plants, and operational costs. The lower-level optimization maximizes revenue for each virtual power plant, considering both battery capacity degradation costs and operational costs of various resources. To facilitate solutions, this research developed a nonlinear transformation method for modeling capacity degradation. Based on the dispatching strategy from the virtual power plant, this study uses the squared difference between energy consumption of equipment for controllable loads and the strategy as the optimization target to derive control strategies for two equipment types. Results show that the framework effectively integrates dispatch and control strategies without oversimplifying the system model, proving its applicability in various scenarios with diverse resource compositions.

Design and application of a radar target simulator

Abstract To fulfill the need for debugging boundary scenes in radar data processing development, this paper proposes a simulator design method for the editing and simulation of diverse combat scenes as required. The simulator was developed based on the VPX platform, including external control equipment, resource scheduling, beam control, target simulation, and data processing. The motion model is based on linear and circular models, the clutter model algorithm is the zero memory nonlinear transformation method based on K distributions, and the noise model is designed as Gaussian white noise, characterized by a probability distribution in the Gaussian distribution and a constant power spectrum. The generated plots are condensed, and their quality is calculated, for which the rate of plot rejection can reach more than 50% by controlling the feature elements. Finally, the simulated target trajectory is visually verified through Matlab.

THREE-DIMENSIONAL MODEL OF EQUIVALENT ROLL GAP OF CVC MILL UNDER CONDITIONS OF ROLL CROSSING AND NO LOAD

Traditional roll technologies focus solely on the contour of the roll gap at the outlet under ideal conditions. However, upon roll crossing, the three-dimensional distribution of the deformation zone becomes asymmetrical, leading to an adverse impact on the rolling pressure in the deformation zone. To study the screw-down load deviation of plate mills, it is necessary to accurately calculate the equivalent three-dimensional roll gap in the deformation zone under roll-crossing conditions. In this paper a model for calculating the equivalent three-dimensional roll gap under the conditions of roll crossing and no load was established based on the method of the coordinate nonlinear transformation of the spatial rectangular coordinate system. Based on this model, the influences of roll-crossing angles and translation parameters on the symmetry of the equivalent three-dimensional roll gap were analyzed. The distribution of the three-dimensional equivalent roll gap was calculated with different roll lengths, roll radii, and the roll gap’s nominal thickness. The intuitive contour map reveals that under the same condition of crossing angle and translation parameters, the larger the roll length and roll radii and the smaller the roll gap’s nominal thickness are, the greater the influence of the roll crossing on the asymmetrical distribution of roll gap is. It put forward a quantitative calculation method for evaluating the symmetrical distribution of the roll gap, and the calculation results can provide the equivalent roll profile for the roll-deformation model.

Command-Filter-Based Region-Tracking Control for Autonomous Underwater Vehicles with Measurement Noise

This paper investigates the AUV region-tracking control problem with measurement noise and transient and steady-state constraints. To achieve the fluctuation of AUV tracking error within an expected region while satisfying the transient and steady-state performance constraints, this paper proposes an improved nonlinear tracking error transformation method. This method converts the tracking error into a new virtual error variable through nonlinear conversion, thus transforming the above performance requirements for the tracking error into boundedness requirements for the new virtual error variable. In addition, aiming at the problem of measurement noise causing strong fluctuation of the control signal, this paper proposes a finite-time AUV control method based on a two-stage command filter. This method utilizes a finite-time sliding mode differentiator to filter the virtual control signal during the derivation of the control law using the backstepping technique. In light of the signal loss incurred by two-stage filtering and its potential impact on system stability, a finite-time compensator is designed to compensate the signal loss and achieve finite-time stability of the closed-loop system. Finally, simulations conducted using ODIN AUV demonstrate that the proposed method exhibits smooth control signal and low energy consumption characteristics. Furthermore, the tracking error meets the requirements for both transient and steady-state performance, as well as regional tracking.

A Nonlinear Grid Transformation Method for Extrapolating and Predicting the Convective Echo of Weather Radar

A nonlinear grid transformation (NGT) method is proposed for weather radar convective echo extrapolation prediction. The change in continuous echo images is regarded as a nonlinear transformation process of the grid. This process can be reproduced by defining and solving a 2 × 6 transformation matrix, and this approach can be applied to image prediction. In ideal experiments with numerical and path changes of the target, NGT produces a prediction result closer to the target than does a conventional optical flow (OF) method. In the presence of convection lines in real cases, NGT is superior to OF: the critical success index (CSI) for 40 dBZ of the echo prediction at 60 min is approximately 0.2 higher. This is due to the better estimation of the movement of the whole cloud system in the NGT results since it reflects the continuous change in the historical images. For the case with a mesoscale convective complex, the NGT results are better than the OF results, and a deep learning result is cited from a previous study for the same case for 20 and 30 dBZ. However, the result is the opposite for 40 dBZ, where the deep learning method may produce an overestimation of the stronger echo.

Investigation of planar translational and rotational stationary non-Gaussian random vibration test

Multi-shaker random vibration control with coordinate transformation technique is an advanced mechanical environment test method that translational and rotational vibrations of structure can be controlled simultaneously. This work presents theoretical and experimental investigations of multi-shaker planar translational and rotational non-Gaussian random vibration tests. First, the coordinate transformation technique is used to obtain the translational and rotational vibration responses of the test structure. Then the control procedure is formulated theoretically with matrix presentation in which a new nonlinear transformation method for generating non-Gaussian random signals is proposed. The correlation between translational and rotational vibrations is explored briefly from the perspective of common square control and transformation control. The influence of elastic characteristics of the test structure on the response spectral densities is investigated and a level definition method for translational and rotational vibrations is proposed. Finally, a planar translational and rotational non-Gaussian random vibration test is carried out to verify the validity of the proposed methods.

KIND: A Novel Image-Mutual-Information-Based Decision Fusion Method for Saturation Attack Detection in SD-IoT

Software-defined networking for IoT (SD-IoT), as an emerging architecture, is suffering from numerous security issues. Saturation attacks against the SDN switches and controllers are major security concerns in SD-IoT. When using the Dempster–Shafer evidence theory (DSE) to detect various saturation attacks, the simple mutual information calculation may cause information loss problem, leading to the decrease of detection accuracy. Therefore, how to avoid information loss problem to improve the detection performance is a key issue. Aiming to solve the above-mentioned issues, we propose KIND, a novel image mutual information-based decision fusion method for saturation attack detection in SD-IoT. The main idea of KIND is that it converts the probability matrix of binary classifiers to images and detects the saturation attacks by fusing these images. More specifically, when executing the evidence fusion, each evidence is converted to an image by a nonlinear transformation method. Each image is converted from the related probability-supported matrix. Then, the evidence can be fixed by comparing structural similarities among different images. After that, all evidence can be utilized to obtain the final detection results using the conducted combination rule. The evaluation results demonstrate that KIND can achieve high detection performance, which outperforms other state-of-the-art methods, in terms of TPR, TNR, FPR, FNR, accuracy, precision, recall, F-score, confusion matrix, ROC curves, PR curves, Chi-square test, correlation coefficient, and the quantitative strategy test. In conclusion, KIND can detect saturation attacks with high precision while causing acceptable storage overload.

Failure diagnosis system using a new nonlinear mapping augmentation approach for deep learning algorithm

This paper develops a new nonlinear transformation-based augmentation method for Convolutional Neural Network (CNN) approach with vibration signals of simple, small scale and elementary reference models for the classification or prediction of vibration signals of perplex healthy or damaged systems using a smart diagnosis system. The accuracy of deep learning algorithm being highly dependent on the quantity of qualified data, the acquiring of a large set of formatted data for the training and verification of a deep learning algorithm is essential. Unfortunately, many scientific and engineering application domains do not allow access to a Big Data accurately bearing domain knowledge and the artificial intelligent (AI) based classification methods suffer from the lack of data and often end up with poor prediction. To overcome this issue, data augmentation approaches have been utilized. In many applications, however, the obtaining of data reflecting physical phenomena is even not possible. To overcome this issue, this research suggests a new nonlinear transformation-based augmentation approach mapping from the data obtained from lab-scale healthy models to the data of complex real healthy models whose data in the damaged status are hard to be obtained. The nonlinear transformation method defined between the data of lab-scale healthy models and the data of complex real healthy model is then applied to predict the data of complex real damaged models for an accurate classification. To validate the concept of the nonlinear transformation augmentation, several vibration examples including an example showing the mode switching are considered. To extract discriminating features from the vibration-based spectrograms using a deep learning algorithm, the nonlinear transformation-based augmentation and the classification between healthy and damaged structures are presented.

Direct Flux Vector Control of Synchronous Motor Drives: Accurate Decoupled Control With Online Adaptive Maximum Torque Per Ampere and Maximum Torque Per Volts Evaluation

Direct flux vector control has an unique advantage in facilitating flux-weakening operation due to the choice of controlled variables: stator flux linkage magnitude and torque producing current. However, the dynamics in stator flux oriented reference frame is heavily affected by the nonlinear cross-coupling between the two axes. This article presents a nonlinear transformation method to decouple the axes for a uniform bandwidth at all operating points. Respect to the literature, the proposed transformation takes magnetic saturation into account without approximation. Furthermore, the auxiliary-flux and auxiliary-current vectors are introduced to design a new adaptive evaluation of maximum torque per ampere and maximum torque per volt control laws, enabling to track the optimal control laws without the need for preprocessed lookup tables. The proposed scheme is experimentally validated on a 1.1 kW synchronous reluctance machine test bench.

Low Light Image Enhancement Based on Multi-Scale Network Fusion

At present, researchers have made great progress in the research of object detection, however, these studies mainly focus on the object detection of images under normal lighting, ignoring the target detection under low light. And images in the fields of automatic driving at night and surveillance are usually obtained in low-light environments. These images have problems such as poor brightness, low contrast, and obvious noise, which lead to a large amount of information loss in the image. And the performance of object detection in low light is reduced. In this paper, we propose a low-light image enhancement method based on multi-scale network fusion to solve the problems of images in low-light environments. Aiming at the problem that the effective information of low-light images is relatively small, we propose a preprocessing method for image nonlinear transformation and fusion, which improves the amount of available information in the light image. Then, in order to obtain a better enhancement effect, a multi-scale feature fusion method is proposed, which fuses features from different resolution levels in the network. The details of low-light areas in the image are improved, and the problem of feature loss caused by too deep network layers is solved. The experimental results show that our proposed method can achieve better enhancement effects on different datasets compared with the current mainstream methods. The average recall value of the object detection with our method is improved by 38.25%, which shows that our proposed method is effective and can promote the development of autonomous driving, monitoring, and other fields.

INVARIANT RELATIVISTIC THEORY OF IDEAL GAS

The purpose of this study is to develop an original theory of a relativistic ideal gas and to prove the validity of the postulate of the special theory of relativity for the characteristic (i.e., arithmetic mean, root-mean-square) velocities of particles of a relativistic ideal gas even in the massless limit. In this work, the following original methods are used for the first time in the theory of a relativistic ideal gas: the method of nonlinear transformation to prove of the distribution function to find the distribution function of the velocities of particles of a relativistic ideal gas; the equation of state of a relativistic ideal gas was first obtained by averaging the relativistic - invariant components of the energy - momentum tensor of a system of noninteracting particles, i.e. ideal gas by the distribution function of the velocities of their particles. The uniqueness and definiteness of the distribution function of the velocities of the particles of a relativistic ideal gas are proved on the basis of the well-known relativistic invariance of the distribution function. For the first time, expressions were obtained for the arithmetic mean and mean square velocities of particles of a relativistic ideal gas. For the first time, a fundamental conclusion is made about the validity of the postulates of the special theory of relativity for the characteristic velocities of particles of a relativistic ideal gas. An equation of state for a relativistic ideal gas is obtained, which relates its pressure, average energy density and temperature.

Fracture mechanics analysis of two-dimensional cracked thin structures (from micro- to nano-scales) by an efficient boundary element analysis

In this paper, the boundary element method (BEM) based on the elasticity theory is developed for fracture analysis of cracked thin structures with the relative thickness-to-length ratio in the micro- or nano-scales. A special crack-tip element technique is employed for the direct and accurate calculation of stress intensity factors (SIFs). The nearly singular integrals, which are crucial in applying the BEM for thin-structural problems, are calculated accurately by using a nonlinear coordinate transformation method. The present BEM procedure requires no remeshing procedure regardless of the thickness of thin structure. Promising SIFs results with only a small number of boundary elements can be achieved with the relative thickness of the thin film is as small as 10−9, which is sufficient for modeling most of the thin bodies as used in, for example, smart materials and micro/nano-electro-mechanical systems.

Fracture analysis of ultra-thin coating/substrate structures with interface cracks

This paper presents a fracture analysis of ultra-thin coating/substrate structures with interface cracks. For this purpose, an advanced boundary element method (BEM) is adopted. To correctly describe the oscillatory displacement and stress fields near the interfacial crack-tip, a new set of novel special crack-tip elements are implemented. The complex interfacial stress intensity factors (SIFs) can be directly and accurately computed at the collocation points extremely close to the crack-tip by using the proposed computational strategy based on the novel special crack-tip elements. Furthermore, the troublesome nearly-singular boundary integrals, which are crucial in the application of the BEM for both crack-like and ultra-thin structural problems, are calculated accurately by using a nonlinear coordinate transformation method. It is shown that the advanced BEM based on the novel special crack-tip elements and appropriate technique for evaluating nearly-singular boundary integrals provides an accurate and robust numerical tool for interfacial crack analysis of ultra-thin coating structures. Accurate and reliable BEM results with only a small number of boundary elements can be obtained for a relative coating-to-substrate thickness as small as 10-9, which is important for modeling ultra-thin coating structures as used in smart materials and micro/nano-electro-mechanical systems (MEMS/NEMS). Several representative numerical examples will be presented and discussed to reveal the effects of the key geometrical and material parameters, the crack configuration and the loading conditions on the interfacial fracture parameters such as energy release rate and complex SIFs

State estimator design for genetic regulatory networks with leakage and discrete heterogeneous delays: A nonlinear model transformation approach

We address the state estimation problem for a class of genetic regulatory networks (GRNs) with leakage and discrete heterogeneous delays in this paper. In order to simplify the complexity of designing the state estimator for nonlinear delayed model of GRNs, a state estimate algorithm based on a model transformation method is presented, which goal is to get the entire system state. First, in light of the Lagrange’s mean-value theorem, the nonlinear model transformation method is applied to describe the nonlinear error system as a linear time-varying model. Second, by constructing the Lyapunov–Krasovskii functional dependent on the composite function variables of state estimate errors, a new technique lemma is provided and applied to the stability analysis. Third, the sufficient condition of state estimator design is obtained in term linear matrix inequalities, under which, the certification of the uniform asymptotic stability for state estimate error system is derived. Finally, a simulation example illustrates the rationality and effectiveness of the proposed theoretical results.

Adaptive Neural Output Feedback Control for MSVs With Predefined Performance

In this paper, we investigate the problem of trajectory tracking control for marine surface vehicles (MSVs), which are subject to dynamic uncertainties, external disturbances and unmeasurable velocities. To recover the unmeasurable velocities, a novel adaptive neural network-based (NN-based) state observer is constructed. To guarantee the transient and steady-state tracking performance of the system, a novel nonlinear transformation method is proposed by employing a tracking error transformation together with a newly constructed performance function, which is characterized by a user-defined settling time and tracking control accuracy. With the aid of the state observer and the nonlinear transformation method in combination with the adaptive NN technique and vector-backstepping design tool, an adaptive neural output-feedback trajectory tracking control scheme with predefined performance is developed. With regard to the developed control scheme, uncertainties can be reconstructed only by utilizing the position and heading of the MSVs. Independent designs of the state observer and the controller can be achieved, and the position tracking error can be guaranteed to fall into a predefined residual set in the user-defined time frame and remain in the above set. A rigorous stability analysis validates that all signals in the closed-loop trajectory tracking control system for MSVs are uniformly ultimately bounded. Simulation results verify the effectiveness of the developed adaptive neural output-feedback trajectory tracking control scheme.

Electroelastic analysis of two‐dimensional ultrathin layered piezoelectric films by an advanced boundary element method

AbstractThe aim of the present study is to present an effect boundary element method (BEM) for electroelastic analysis of ultrathin piezoelectric films/coatings. The troublesome nearly singular integrals, which are crucial in applying the BEM for thin‐structural problems, are calculated accurately by using a nonlinear coordinate transformation method. The advanced BEM presented requires no remeshing procedure regardless of the thickness of the thin structure. Promising BEM results with only a small number of boundary elements can be achieved with the relative thickness of the thin piezoelectric film is as small as 10−8, which is sufficient for modeling many ultrathin piezoelectric films as used in smart materials and micro‐electro‐mechanical systems. The present BEM procedure with thin‐body capabilities is also extended to general multidomain problems and used to model ultrathin coating/substrate piezoelectric structures. The influence of relative layer‐to‐substrate thickness and the bimaterial mismatch parameters are carefully investigated. Excellent agreement between numerical and theoretical solutions has been demonstrated.

High-Order Approximation of Heteroclinic Bifurcations in Truncated 2D-Normal Forms for the Generic Cases of Hopf-Zero and Nonresonant Double Hopf Singularities

Based on the nonlinear time transformation method, in this paper we propose a recursive algorithm for arbitrary order approximation of heteroclinic orbits. This approach works fine for a wide class of systems that are perturbations of non-Hamiltonian integrable planar vector fields. Specifically, our method can provide an approximation up to any desired order, both for the locus where the heteroclinic bifurcation occurs in the parameter space and for the orbit in the phase space. We also give proofs that guarantee the existence and uniqueness of the solution. As illustrations, we apply it to the generic Hopf-zero and nonresonant double Hopf singularities which give rise to an intricate bifurcation scenario in the cases where a heteroclinic cycle appears in the corresponding unfolding of normal forms. The obtained high-order approximations are expressed in terms of symbolic nonzero normal form coefficients which improve the existing first-order approximations in the literature. They are also in excellent agreement with numerical continuations. Note that the derived formulas can be practically important in many control engineering applications in which certain constants of the problem may not be known in advance.

Continuous convolution and nonlinear transformation for multi-shaker non-Gaussian random vibration control

This study proposes a continuous convolution method combined with memoryless nonlinear transformation for multi-input multi-output stationary non-Gaussian random vibration tests. The challenge of the multi-shaker non-Gaussian random vibration test lies in the coupling problems that are manifested in the inherent physical system and in the existence of cross-spectral densities. In the presented method, the independent stationary Gaussian random signals pass through a designed finite impulse response filter with a convolution manipulation first, and then the resulting signals are transformed to the non-Gaussian random signals by the memoryless nonlinear transformation method. The desired drive signals are obtained by the input–output relationship in the frequency domain. The finite impulse response filter is constructed by the frequency sampling technique in which the amplitude characteristics of the filter are determined by the predefined reference power spectral densities. A new monotonic nonlinear transformation function with an approximate kurtosis solution is provided. It only contains one parameter for kurtosis control both in sub-Gaussian and super-Gaussian cases. The memoryless nonlinear transformation is used to maintain the cross-spectral densities, although some distortions are introduced to the power spectra during the transformation process. The inverse system method is used to overcome the coupling problem caused by the inherent physical system. A simulation example and a triaxial vibration test are carried out, and the results indicate the validity and feasibility of the proposed method.

High-Order Analysis of Canard Explosion in the Brusselator Equations

The aim of this paper is to obtain a high-order approximation of the canard explosion in the Brusselator equations. This classical chemical system has been extensively studied but, until now, only first-order approximation to the canard explosion has been provided. Here, with the help of the nonlinear time transformation method, we are able to obtain an approximation to any desired order. Our results strongly agree with those obtained by numerical continuation.

High-order study of the canard explosion in an aircraft ground dynamics model

A planar system has been proposed in the paper Rankin et al. (Nonlinear Dyn 66:681–688, 2011) to understand the canard explosion detected in a 6D aircraft ground dynamics model. A specific feature of this minimal 2D system is a critical manifold with a single fold and an asymptote. In this paper, we provide a high-order analytical prediction (in fact, up to any wanted order) of the canard explosion in this system. Using a nonlinear time transformation method, we are able to approximate not only the critical parameter value, but also the critical manifold in the phase space. The comparison of our theoretical results with the corresponding numerical continuations shows a very good agreement.