State Vector Research Articles

Using Hybrid LSTM Neural Networks to Detect Anomalies in the Fiber Tube Manufacturing Process

The production process of tubes for fiber optic cables is a complex process, where proper execution is crucial to the quality of the final product. This process has a complex state vector whose structure and coordinates dynamically change during the tube extrusion process. Small fluctuations in process parameters, such as temperature, extrusion pressure, production speed, and optical fiber tension, affect the optical attenuation of the final product. Such defects necessitate the withdrawal of the product. Due to the high number of process coordinates and the technological inability to automatically label those segments of the production process that cause anomalies in the final product, the authors used data clustering methods to create a training set that enabled the use of neural tools for anomaly detection. The system proposed in the main part of the paper includes a hybrid Long short-term memory (LSTM) network model, which is fed with data streams recorded on the tube extrusion production line. The input module, which performs preprocessing of input data, conducts multiresolution analysis of recorded process parameters, and recommends the process state’s belonging to a set of classes describing individual production anomalies to appropriate LSTM network modules. The learning process of the three–channel network allowed effective recognition of five classes of the monitored tube production process. The fit level of the proposed network model reached R2 values of ≥0.85.

Precision Quaternion Estimation with Partially Norm-Constrained Unscented Kalman Filtering

Abstract Accurate orientation estimation is a key challenge in dynamics and control, particularly for rigid body motion. Quaternions are commonly used to represent rotations due to their computational efficiency, but they must always maintain a unit norm to function correctly. If this constraint is not enforced properly, it can lead to significant errors in orientation estimation. This paper proposes an unscented Kalman filter that ensures the quaternion parameters, a subvector within the state vector, adhere to the unit norm constraint. The proposed method provides a closed-form solution without dividing the state vector into constrained and unconstrained vectors. In simulation studies under high noise conditions, the filter demonstrates significantly improved performance compared to standard unscented and pseudo-unscented Kalman filters, enhancing accuracy during both transient and steady-state phases. These results highlight the importance of enforcing quaternion constraints to reduce mean square error and improve convergence.

ANÁLISE MATEMÁTICA E SIMULAÇÃO DO SISTEMA DE AMORTECIMENTO VEICULAR COM MATLAB

Abstract: In modern control theory, the concept of state variables plays a crucial role in the modeling and analysis of dynamic systems. These variables provide a comprehensive description of the system’s future behavior over time. The organization into a state vector enables a compact and complete representation of the system’s internal state. The state-space function describes the temporal evolution of these variables in response to system inputs, offering an efficient mathematical approach for the design and analysis of control systems. Applications range from industrial process control to autonomous vehicle control and robotics. By understanding and applying these concepts, control engineers develop effective solutions for challenges in complex systems, ensuring performance, stability, and efficiency in dynamic environments. Keywords: state variables; dynamic systems; state-space; control; stability.

Polariton spectra under the collective coupling regime. I. Efficient simulation of linear spectra and quantum dynamics.

We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holstein-Tavis-Cummings (HTC) model Hamiltonian. The first one takes advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of acting polariton Hamiltonian onto a state vector to the linear order of the number of states, instead of the quadratic order. The second one is applying the well-known Chebyshev series expansion approach for quantum dynamics propagation and to simulate the polariton dynamics in the HTC system; this approach allows us to use a much larger time step for propagation and only requires a few recursive operations of the polariton Hamiltonian acting on state vectors. These two theoretical approaches are general and can be applied to any trajectory-based non-adiabatic quantum dynamics methods. We apply these two techniques with our previously developed Lindblad-partially linearized density matrix approach to simulate the linear absorption spectra of the HTC model system, with both inhomogeneous site energy disorders and dipolar orientational disorders. Our numerical results agree well with the previous analytic and numerical work.

Symplectic contact analysis of a finite-sized horizontally graded magneto-electro-elastic plane

Material characterization using high-throughput testing (HTT) techniques has shown great promise in expediting the advancement of high-performance materials. A key step in HTT is the adoption of functionally graded specimens, whose material inhomogeneity, however, imposes a great challenge for analytically evaluating its responsive behaviour under external loads. This work establishes the first symplectic framework for contact analysis of a finite-sized magneto-electro-elastic plane with an exponential material gradient along the horizontal direction. The governing equations are first represented in matrix form in a state space, with the full state vector defined and the operator matrix derived. The operator matrix is found to be distinct from the Hamiltonian operator matrix in the case of a homogeneous medium. With all the eigen-solutions obtained, the Hamiltonian mixed energy variational principle is then introduced to derive the coefficients in the symplectic expansion. The developed analytical solution not only exhibits asymmetry properties but also converges rapidly. The analytical results are validated through comparison with the finite element simulations. The analytical platform established here would work as an effective theoretical basis for the subsequent development of quantitative HTT techniques.

REACHABLE SET OF SOME DISCRETE SYSTEM WITH UNCERTAIN LIU DISTURBANCES

In this paper, we consider a problem of finding of the attainability set for a linear system with determinate and stochastic Liu's uncertainties. In the capacity of Liu's disturbances are used ordinary uniformly distributed and independent among themselves uncertain values defined on some uncertain space. This fact means that the state vector of the system and the entire problem become infinite dimensional one. As the determinate disturbances are taken in attention feedback controls and unknown initial states. Besides, the restriction in the form of the sum of uncertain expectations is set. The initial estimation problem is reduced to the determinate multistage problem for matrices and with the fixed restriction on the right end of trajectory. This reduction demands some information about Liu's theory. We give necessary and sufficient conditions for finiteness of target functional in the obtained determinate problem. A numerical example for two-dimensional and two-stage system is given.

Adaptive Software Component for Predicting Energy Consumption of an Electric Vehicle on a Planned Route

This paper presents the development of an adaptive software component for forecasting the energy consumption of electric vehicles along planned routes. It includes a conceptual framework, architectural design, and modular software composition, introducing mathematical models for managing energy consumption with a model-based design approach for precise predictions and optimization. The importance of data sources such as route information, vehicle condition, and driver behavior is emphasized to create a comprehensive state vector for energy optimization. Following ISO 26262 and A-SPICE 3.1 standards, the implementation uses a model-based approach with Simulink and aligns with the V-Model for rigorous validation. The methodology details segmenting routes and optimizing energy consumption for each segment, considering driving style and environmental conditions. The gradient search method adjusts energy consumption to minimize usage while maximizing comfort and ensuring route completion. This research lays the groundwork for future advancements in predictive energy management systems for electric vehicles, with potential real-world applications. Future work will focus on refining predictive models, exploring machine learning for improved accuracy, and integrating real-time data from connected vehicle technologies for dynamic optimization.

Joint Fault Diagnosis of IGBT and Current Sensor in LLC Resonant Converter Module Based on Reduced Order Interval Sliding Mode Observer.

LLC resonant converters have emerged as essential components in DC charging station modules, thanks to their outstanding performance attributes such as high power density, efficiency, and compact size. The stability of these converters is crucial for vehicle endurance and passenger experience, making reliability a top priority. However, malfunctions in the switching transistor or current sensor can hinder the converter's ability to maintain a resonant state and stable output voltage, leading to a notable reduction in system efficiency and output capability. This article proposes a fault diagnosis strategy for LLC resonant converters utilizing a reduced-order interval sliding mode observer. Initially, an augmented generalized system for the LLC resonant converter is developed to convert current sensor faults into generalized state vectors. Next, the application of matrix transformations plays a critical role in decoupling open-circuit faults from the inverter system's state and current sensor faults. To achieve accurate estimation of phase currents and detection of current sensor faults, a reduced-order interval sliding mode observer has been designed. Building upon the estimation results generated by this observer, a diagnostic algorithm featuring adaptive thresholds has been introduced. This innovative algorithm effectively differentiates between current sensor faults and open switch faults, enhancing fault detection accuracy. Furthermore, it is capable of localizing faulty power switches and estimating various types of current sensor faults, thereby providing valuable insights for maintenance and repair. The robustness and effectiveness of the proposed fault diagnosis algorithm have been validated through experimental results and comparisons with existing methods, confirming its practical applicability in real-world inverter systems.

Detection of Energetic Low Dimensional Subspaces in Spatio-Temporal Space in Turbulent Pipe Flow

AbstractLow dimensional subspaces are extracted out of highly complex turbulent pipe flow at $$Re_{\tau }=181$$ R e τ = 181 using a Characteristic Dynamic Mode Decomposition (CDMD). Having lower degrees of freedom, the subspaces provide a more clear basis to detect events which meet our understanding of large-scale coherent structures. To this end, a temporal sequence of state vectors from direct numerical simulations are rotated in space-time such that persistent dynamical modes on a hyper-surface are found travelling along its normal in space-time, which serves as the new time-like coordinate. The main flow features are captured with a minimal number of modes on a moving frame of reference whose velocity matches that of the most energetic scale. Reconstruction of the candidate modes in physical space gives the low rank model of the flow. The structures living in this subspace have long lifetimes, posses wide range of length-scales and travel at group velocities close to that of the moving frame of reference. The modes within this subspace are highly aligned, but are separated from the remaining modes by larger angles. We are able to capture the essential features of the flow like the spectral energy distribution and Reynolds stresses with a subspace consisting of about 10 modes. The remaining modes are collected in two further subspaces, which distinguish themselves by their axial length scale and degree of isotropy.

Algebraic Language for the Efficient Representation and Optimization of Quantum Circuits

Abstract The use of graphical language in quantum computing for the representation of algorithms, although intuitive, is not very useful for different tasks such as the description of quantum circuits in text environments, the calculation of quantum states or the optimization of quantum circuits. While classical circuits can be represented either by circuit graphs or by Boolean expressions, quantum circuits have until now predominantly been illustrated as circuit graphs because no formal language for quantum circuits that allows algebraic manipulations has so far been accepted. This work proposes a means to represent quantum circuits in a convenient and concise manner, similar to the way Boolean expressions are used in classical circuits. The proposed notation allows the consistent and parameterized description of quantum algorithms, as well as the easy handling of the elements that compose it to achieve powerful optimizations in the number of gates of the circuits. To visualize it, a software implementation of an algebraic quantum circuit framework has been made, which allows describing quantum circuits, as well as their respective state vectors, using the proposed algebraic language.

Potyvirus-Based Vectors for Heterologous Gene Expression in Plants.

Over the past two decades, plant viral vectors have emerged as a powerful tool for the production of recombinant proteins in plants. Among the different plant viruses engineered to carry foreign genes of interest in their genomes, potyviruses have gained attention due to their polyprotein expression strategy and broad host range. To date, at least eleven different species belonging to the genus Potyvirus have been used for heterologous gene expression in both their natural and experimental hosts. This review article provides an overview of the current state of potyvirus-based plant viral vectors, discussing the advantages and limitations of these systems. We also discuss the future challenges and potential applications of potyvirus-based expression vectors, including the production of vaccines, nanoparticles, therapeutics, and metabolic engineering. Overall, we highlight the potential of potyvirus-based vectors as a versatile tool for recombinant protein production in plants.

BACKSTEPPING STABILIZATION OF NONLINEAR DYNAMICAL SYSTEMS UNDER STATE CONSTRAINTS

The problem of stabilizing the zero value of the state vector of constrained nonlinear dynamical systems written in a special form is solved. The proposed control design accounts for magnitude constraints on the values of state variables and is based on the integrator backstepping approach using logarithmic Lyapunov barrier functions. The obtained stabilizing feedbacks, in contrast to similar known results, are based on the use of linear virtual stabilizing functions that do not grow unbounded as state variables approach the boundary values. As an example, we consider a state constraints aware solution to the control problem of positioning an autonomous underwater vehicle at a given point in space.

ON THE STABILITY BY THE NONLINEAR NON-STATIONARY HYBRID APPROXIMATION

The paper investigates the effect of non-stationary perturbations on the stability of nonlinear nonautonomous systems with switching and impulsive effects. Sufficient conditions have been obtained to guarantee the asymptotic stability of a given equilibrium position of the initial system, and restrictions have been established under which the asymptotic stability is preserved under perturbations acting on the system. Note that the non-stationarities present both in the system itself and in perturbations can be described by unbounded functions with respect to time, as well as functions arbitrarily close to zero. It is assumed that the basic system is homogeneous in terms of the state vector. To find the required results, the second Lyapunov method is used in combination with the theory of differential inequalities.

Conversion of Arbitrary Three-Dimensional Polarization States to Regular States via Spin Cancellation

The present work is motivated by the necessity of handling and controlling three-dimensional polarization states, whose appropriate preparation has increasing interest in areas like nanotechnologies, quantum computing and near-field phenomena. By virtue of the so-called characteristic decomposition, any polarization state of light can be represented as an incoherent superposition of a pure state, a fully unpolarized state and a discriminating state. The discriminating component has nonzero spin in general, in which case the state is said to be nonregular. A simple procedure to transform an arbitrary nonregular state to a regular one through its incoherent composition with a pure state is described, resulting in a state that lacks a discriminating component. In addition, a method to suppress the spin vector of any given polarization state through its incoherent combination with a circularly polarized pure state is presented. Both approaches allow for the configuration of polarization states with simple features.

Design a chaotic circuit using tunable and power efficient memristor emulator circuit for image encryption

Abstract In a non-linear dynamic system, chaos is a deterministic phenomenon that arises when the state vector trajectories become highly sensitive to the initial conditions, given certain criteria and periodic. The memristor, being the fourth essential component of a two-terminal device, has the potential to overcome the barrier for secure communication against eavesdroppers and manufacturing of duplicate chaotic transrecivers by the untrusted foundaries.It can close a gap among secure manufacturing and reliable communication because its resistance can be programmed by the designer not by the foundary. This property makes the communication system more efficient, reliable secure, and provides more security. In this study, the memristor and analog design of a chaotic transreviver is designed. The memristor model is designed using a Current mirror operational transconductance amplifier (OTA) and an analog multiplier with sinusoidal input having amplitude (V_m) and input frequency (f). Variations in input frequency, and amplitude have an impact on conductance and resistance state and the OTA parameter g_m Also affects the V-I response. The research focuses on memristor tunability with a variation of the hysteresis curve using factors such as temperature, amplitude, load resistance, frequency, and incremental and decremental behavior and secure communication using a Chaotic circuit using memristor. The maximum operational frequency that exhibits a pintch hystresis curve is 100 kilohertz, and a power dissipation of 3.1 µW with noise 56nV/Hz^(1/2). The results also show the chaotic system are sensitive with their secret key or starting conditions of integrator which is uses for the encryption approach.

Ensemble Kalman filter with precision localization

AbstractWe propose a novel localization strategy for the ensemble Kalman filter procedure based on sparse precision matrices, which we denote precision localization. We assume the latent state vector to come from a Gaussian Markov random field and use the iterative proportional scaling algorithm to estimate the associated sparse precision matrix. Precision localization is compared against a standard covariance localization technique in two simulation studies; one with a Gauss-linear model and one based on the Lorenz 96 model. We evaluate the results by their prediction accuracy and to what degree the generated ensembles give a realistic representation of the exact filtering distributions. In the Gauss-linear example we also compare our results with the Kalman filter solution. Here we see that both precision and covariance localization produce reasonably good results in terms of prediction accuracy, but that precision localization provides the best representation of the correlation structure in the filtering distribution. For the Lorenz model we cannot compare with the Kalman filter solution, but precision localization seems to provide the most accurate predictions and the most realistic uncertainty representation.

Predictive Complexity of Quantum Subsystems.

We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory but is intrinsically quantum. Predictive states of a subsystem are formed by equivalence classes of state vectors in the exterior Hilbert space that effectively predict the same future behavior of that subsystem for some time. As an illustrative example, we present calculations in the dynamics of an isotropic Heisenberg model spin chain and show that, in comparison to the entanglement entropy, the predictive complexity better signifies dynamically important events, such as magnon collisions. It can also serve as a local order parameter that can distinguish long and short range entanglement.

A robust distributed interaction multiple model filter for jump Markov systems with heavy-tailed measurement noise

When heavy-tailed measurement noises (HTMNs) are introduced by outliers, the estimation accuracy of traditional distributed interaction multiple model (IMM) algorithms will be severely reduced in some target tracking scenarios. To solve the problem, a new distributed robust filter algorithm using cubature information filtering and weighted average consensus approach in the framework of IMM filtering is proposed. Firstly, the HTMNs are modeled as Student’s t-distributions, and as conjugate prior distributions for the degree of freedom parameters and the scale matrices, the Gamma distributions and the inverse-Wishart distributions have been chosen. Secondly, the system state vectors, noise corresponding parameters, and model probabilities are inferred utilizing the variational Bayesian method. What’s more, in order to increase the stability of sensor networks and improve the estimation accuracy of the proposed filtering algorithm, the weighted average consensus approach is used to update information pairs and model probabilities. Finally, a target tracking simulation experiment is used to verify that the proposed algorithm has higher estimation accuracy and robustness than existing advanced filtering algorithms in dealing with HTMN.

Nonlinear Optimal and Multi-Loop Flatness-Basedcontrol of Omnidirectional 3-Wheel Mobile Robots

In this article, the control problem for omnidirectional 3-wheel autonomous mobile robots is solved with the use of (i) a nonlinear optimal control method (ii) a flatness-based control approach which is implemented in successive loops. To apply method (i) that is nonlinear optimal control, the dynamic model of the omnidirectional 3-wheel autonomous mobile robots undergoes approximate linearization at each sampling instant with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrix. The linearization point is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. To compute the feedback gains of the optimal controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the nonlinear optimal control method are proven through Lyapunov analysis. To implement control method (ii), that is flatness-based control in successive loops, the state-space model of the omnidirectional 3-wheel autonomous mobile robot is separated into chained subsystems, which are connected in cascading loops. Each one of these subsystems can be viewed independently as a differentially flat system and control about it can be performed with inversion of its dynamics as in the case of input-output linearized flat systems. The state variables of the preceding (i-th) subsystem become virtual control inputs for the subsequent (i+1-th) subsystem. In turn, exogenous control inputs are applied to the last subsystem. The whole control method is implemented in successive loops and its global stability properties are also proven through Lyapunov stability analysis. The proposed method achieves trajectory tracking and autonomous navigation for the omnidirectional 3-wheel autonomous mobile robots without the need of diffeomorphisms and complicated state-space model transformations.

A Physics-Informed Auto-Learning Framework for Developing Stochastic Conceptual Models for ENSO Diversity

Abstract Understanding El Niño–Southern Oscillation (ENSO) dynamics has tremendously improved over the past few decades. The ENSO diversity in spatial pattern, peak intensity, and temporal evolution is, however, still poorly represented in conceptual ENSO models. In this paper, a physics-informed auto-learning framework is applied to derive ENSO stochastic conceptual models with varying degrees of freedom. The framework is computationally efficient and easy to apply. Once the state vector of the target model is set, causal inference is exploited to build the right-hand side of the equations based on a mathematical function library. Fundamentally different from standard nonlinear regression, the auto-learning framework provides a parsimonious model by retaining only terms that improve the dynamical consistency with observations. It can also identify crucial latent variables and provide physical explanations. This methodology successfully reconstructs the equations of a realistic six-dimensional reference ENSO model based on the recharge oscillator theory from its data. A hierarchy of lower-dimensional models is derived, and their representation of ENSO (including its diversity) is systematically assessed. The minimum model that represents ENSO diversity is four-dimensional, with three interannual variables describing the western Pacific thermocline depth, the eastern and central Pacific sea surface temperatures (SSTs), and one intraseasonal variable for westerly wind events. Without the intraseasonal variable, the resulting three-dimensional model underestimates extreme events and is too regular. A limited number of weak nonlinearities in the model are essential in reproducing the observed extreme El Niño events and the observed nonlinear relationship between eastern and western Pacific SSTs. Significance Statement This study develops a physics-informed auto-learning approach to improve the modeling and understanding of El Niño–Southern Oscillation (ENSO), a major climate phenomenon influencing global weather and climate. The auto-learning framework explores the causality between key processes to systematically produce stochastic conceptual models with different climate factors that simulate the diversity of observed ENSO events. The key finding is that the minimal model for characterizing the ENSO diversity (with the least number of climate factors) is a four-variable model capturing thermocline depth, sea surface temperatures, and wind bursts that can reproduce intensity and spatial pattern variation. This advancement provides an interpretable tool to identify the minimum sufficient processes governing ENSO behavior for improved predictability.