State Space Of System Research Articles

A hybrid rotordynamic modeling method for a rotor system with flexible foundation and nonlinear support force: Numerical and experimental investigation

The dynamic characteristics of a flexible foundation would greatly affect the dynamic behavior of the rotor system. In this paper, a hybrid dynamic model method in time domain combines the finite element (FE) method and the subspace-based identification method to model a rotor system with the consideration of a flexible foundation and nonlinear support forces. The state-space model of flexible foundation is identified by the subspace state-space system identification algorithm with measured frequency response functions (FRFs). To solve the calculation problem of the hybrid dynamic model in time domain, a general algorithm named the hybrid model fusion solution (HMFS) method is proposed, which combines the linear and nonlinear nodes separation method used in the FE model and the trapezoidal rule used in the state-space model, improving the calculation efficiency of solving transient response with nonlinear forces. Simulations for the hybrid dynamic model under constant speed and speed-up cases were carried out, resulting that the dynamic characteristics of the entire system can be represented when the nonlinear factors of rolling bearings and gravity were also taken into consideration. Additionally, owe to the consideration of tested dynamic behaviors of flexible base, experimental results in the laboratory test rig are well agreed with the numerical ones under two different test configurations. The investigation provides a complete modeling and highly efficient solution framework for the rotor system with a flexible foundation and nonlinear rolling bearings, with the abilities of further consideration of more nonlinear components such as squeeze film dampers and rubbing forces.

Quantum Time

A short introduction, with extended interpretations, to the Projection Evolution approach is presented. In this model time is like the other space positions represented by an operator in the state space of a physical system. As a pedagogigal example the Minkowski spacetime is considered. Finally, a short analysis of the time reversal symmetry is presented.

Hierarchy of Quadratic Lyapunov Functions for Linear Time-Varying and Related Systems

A method for constructing homogeneous polynomial Lyapunov functions is presented for linear time-varying or switched-linear systems and the class of nonlinear systems that can be represented as such. The method uses a simple recursion based on the Kronecker product to generate a hierarchy of related dynamical systems, whose first element is the system under study and the second element is the well-known Lyapunov differential equation. It is then proven that a quadratic Lyapunov function for the system at one level in the hierarchy, which can be found via semidefinite programming, is a homogeneous polynomial Lyapunov function for the system at the base level in the hierarchy. Searching for Lyapunov functions of the foregoing kind is equivalent to searching for homogeneous polynomial Lyapunov functions via the formulation of sum-of-squares programs. The quadratic perspective presented in this paper enables the easy development of procedures to compute bounds on pointwise-in-time system metrics, such as peak norms, system stability margins, and many other performance measures. The applications of the theory to analyzing an aircraft model, on the one hand, and an experimental aerospace vehicle, on the other hand, are presented. The theory can be comprehended with a first course on state-space control systems and an elementary knowledge of convex programming.

State estimation in labeled time Petri net systems using observed modified state class graph

In this paper, we present an improved method for the state estimation of a labeled time Petri net (LTPN) system with unobservable transitions. Precisely, we provide a computationally efficient graph, called an observed modified state class graph (OMSCG), that represents a partial state space of an LTPN system based on the logic label sequence of an observed time-label sequence (TLS), motivated by the modified state class graph reported in the literature. Taking advantage of the OMSCG, we can effectively estimate all the transition sequences that are logically consistent with a TLS. By employing the transitions-related timing constraints of the OMSCG, we then present an approach to determine the set of transition sequences that are timing consistent with a timed observation (i.e., a TLS observed at a time instant) by solving linear programming problems. Finally, we provide an algorithm to implement the state estimation of an LTPN system under a timed observation.

Using statistical linearization to optimize a class of semi-active on-off control in a general state space system

This paper uses statistical linearization to analyze a state space system controlled by a class of semi-active on-off control. The control input is proportional to a feedback state, while the coefficient of proportionality is switched based on the sign of the product of feedback state and a control state. The explicit simultaneous equations are derived to obtain the system's statistics. The usefulness of the approach is demonstrated through 4 examples. In the example of vibration isolation system, the analytical best performance of skyhook control is found. In the example of mass damper system, the analytical best performance of groundhook control is presented. In the example of quarter-car suspension system, the skyhook-groundhook control is optimized. At last, in the example of 4-mass system, the clipped-linear-quadratic-regulator control is demonstrated.

Mass and Force Lumping: An Essential Enhancement to the Intrinsic Beam Finite Element Discretization

This paper introduces the novel application of the mass and force lumping technique to enhance the finite element discretization of the fully intrinsic beam formulation. In our aeroelastic system model, 2-D unsteady aerodynamics were incorporated alongside simple calculations for thrust and gravity. Through the central difference discretization method, the discretized system was thoroughly examined, shedding light on the advantages of the mass and force lumping approach. With the use of a first-order lumping method, we successfully reconstructed the inertia matrices, external forces, and moments. The resulting equations are more systematically structured, facilitating the extraction of a regular state-space linear system using the direct index reduction method post-linearization. Numerical results further confirm that the proposed techniques can effectively capture the nonlinear dynamics of aeroelastic systems, enabling equation reconstruction and leading to significant benefits in system order reduction and flight dynamical analysis.

Time distance-based computation of the DBM over-approximation of preemptive real-time systems

The verification of preemptive real-time systems is a crucial aspect in ensuring their correctness and reliability to meet strict time constraints. Generally, the analysis of the behaviors of such systems requires the computation of the reachability graphs encoding their state space. However, the construction of the latter is computationally expensive and resource-consuming as it involves, for each graph node, managing and solving polyhedral constraints whose complexity is exponential.In this paper, we explore a novel approach that builds an over-approximation of the state space of preemptive real-time systems. Our graph construction extends the expression of a node to the time-distance system that encodes the quantitative properties of past-fired subsequences. This makes it possible to restore relevant time information that is used to compute in a polynomial time a tighter difference bound matrix over-approximation of the polyhedral constraints. We show that the obtained graph is more appropriate to restore the quantitative properties of the model. The simulation results show that our graphs are almost of the same size as the exact graphs, while improving by far the times needed for their computation.

Using graphics processing units for the efficient dynamic simulation of wind farms

Dynamic simulations are crucial for proper power system operation. However, these can be computationally expensive. This article introduces an efficient CUDA kernel for GPU acceleration, that achieves parallelization without the need to solve many different power systems at once. The proposal unifies generator and grid execution within a single CUDA kernel, ensuring accurate dynamic simulations of wind farms. A custom solution from scratch was developed, that integrates the power system network solver with connected devices. Wind turbines are modeled as state-space linear systems, while the grid is parallelized through subunit partitioning and small submatrix inverses to reduce computational costs. The resulting kernel extracts parallelism in grids with limited inherent parallelism, outperforming previous methods such as column-level parallelism. Simulations on an NVIDIA GeForce RTX 3090 show a 26.39x speedup with respect to the C++ version, and the cooperative groups' synchronization primitives provide optimal performance while simulating up to 2464 wind turbines.

Global Temperature Projections from a Statistical Energy Balance Model Using Multiple Sources of Historical Data

Abstract This paper estimates a two-component energy balance model as a linear state-space system (EBM-SS model) using historical data. It is a joint model for the temperature in the mixed layer, the temperature in the deep ocean layer, and radiative forcing. The EBM-SS model allows for the modeling of nonstationarity in forcing and the incorporation of multiple data sources for the unobserved processes. We estimate the EBM-SS model using historical datasets at the global level for the period 1955–2020 by maximum likelihood. We show in the empirical estimation and in simulations that using multiple data sources for the unobserved processes reduces parameter estimation uncertainty. When fitting the EBM-SS model to six observational global mean surface temperature (GMST) anomaly series, the GMST projections under representative concentration pathway scenarios are comparable to those from Coupled Model Intercomparison Project models. The results show that a simple statistical climate model estimated on the historical period can produce GMST projections compatible with output from large-scale Earth system models. Significance Statement We develop a statistical model to understand Earth’s energy balance and how it impacts temperature across the planet’s surface and deep oceans. Unlike previous approaches, ours is fully statistical. This means that we use maximum likelihood to calculate the estimates and evaluate the level of uncertainty in the model’s parameters. By applying the model to historical data from 1955 to 2020, we are able to make predictions about the average global surface temperature that are consistent with those from the Coupled Model Intercomparison Project. Our findings support current predictions about global temperatures using a straightforward statistical climate model, grounded in historical data.

Causal inference from cross-sectional earth system data with geographical convergent cross mapping

Causal inference in complex systems has been largely promoted by the proposal of some advanced temporal causation models. However, temporal models have serious limitations when time series data are not available or present insignificant variations, which causes a common challenge for earth system science. Meanwhile, there are few spatial causation models for fully exploring the rich spatial cross-sectional data in Earth systems. The generalized embedding theorem proves that observations can be combined together to construct the state space of the dynamic system, and if two variables are from the same dynamic system, they are causally linked. Inspired by this, here we show a Geographical Convergent Cross Mapping (GCCM) model for spatial causal inference with spatial cross-sectional data-based cross-mapping prediction in reconstructed state space. Three typical cases, where clearly existing causations cannot be measured through temporal models, demonstrate that GCCM could detect weak-moderate causations when the correlation is not significant. When the coupling between two variables is significant and strong, GCCM is advantageous in identifying the primary causation direction and better revealing the bidirectional asymmetric causation, overcoming the mirroring effect.

Nonlinear optimal control for permanent magnet synchronous spherical motors

Nonlinear optimal control for permanent magnet synchronous spherical motors

Duality of averaging of quantum states over arbitrary symmetry groups revealing Schur–Weyl duality

It is a well-established fact in quantum information theory, that uniform averaging over the collective action of a unitary group on a multipartite quantum state projects the state to a form equivalent to a permutation operator of the subsystems. Hence states equivalent to permutation operators are untouched by collective unitary noise. A trivial observation shows that uniform averaging over permutation operators projects the state into a form with block-diagonal structure equivalent to the one of the collective action of the unitary group. We introduce a name for this property: duality of averaging. The mathematical reason behind this duality is the fact that the collective action of the unitary group on the tensor product state space of a multipartite quantum system and the action of the permutation operations are mutual commutants when treated as matrix algebras. Such pairs of matrix algebras are known as dual reductive pairs. In this work we show, that in the case of finite dimensional quantum systems such duality of averaging holds for any pairs of symmetry groups being dual reductive pairs, regardless of whether they are compact or not, as long as the averaging operation is defined via iterated integral over the Cartan decomposition of the group action. Although our result is very general, we focus much attention on the concrete example of a dual reductive pair consisting of collective action of special linear matrices and permutation operations, which physically corresponds to averaging multipartite quantum states over non-unitary SLOCC-type (Stochastic Local Operations and Classical Communication) operations. In this context we show, that noiseless subsystems known from collective unitary averaging persist in the case of SLOCC averaging in a conditional way: upon postselection to specific invariant subspaces.

Experimental modal analysis of a single-link flexible robotic manipulator with curved geometry using applied system identification methods

In this paper, the principal time-domain system identification methods are studied and used to carry out the experimental modal analysis of a single-link flexible manipulator with curved geometry in a comparative fashion. The identification process carried out in this study is aimed at deriving first-order state-space dynamical models and second-order configuration-space dynamical models of the single-link flexible manipulator by using an array of fundamental system identification procedures, which includes the ARX (AutoRegressive eXogenous method), SSEST (State-Space ESTimation method), N4SID (Numerical Algorithm for Subspace State-Space System Identification), ERA/OKID (Eigensystem Realization Algorithm combined with the Observer/Kalman Filter Identification method), and TFEST (Transfer Function ESTimation method) methods. The main goal of this paper is, therefore, to perform a comparative study between the most fundamental system identification procedures applied to the numerical and experimental analysis of the structural vibrations of a flexible manipulator having a curved geometric shape. First, this paper poses the theoretical foundations for the development of the numerical study and the experimental testing to be performed for the case study. Subsequently, the flexible manipulator analyzed in this work is modeled with various levels of complexity, which range from a simple lumped parameter model to a linear finite element model developed by integrating the interconnections between the SOLIDWORKS and ANSYS software. By doing so, the computational procedures applied to the time-domain experimental measurements of the dynamic behavior of the flexible manipulator allow for reconstructing first-order and second-order mechanical models of the structural system of interest in the MATLAB simulation environment. The numerical results and the experimental tests reported in this investigation demonstrate the effectiveness of all the time-domain system identification approaches considered in the paper.

: A Semantics-Guided Safety Enhancement Framework for AI-Enabled Cyber-Physical Systems

Cyber-Physical Systems (CPSs) have been widely adopted in various industry domains to support many important tasks that impact our daily lives, such as automotive vehicles, robotics manufacturing, and energy systems. As Artificial Intelligence (AI) has demonstrated its promising abilities in diverse tasks like decision-making, prediction, and optimization, a growing number of CPSs adopt AI components in the loop to further extend their efficiency and performance. However, these modern AI-enabled CPSs have to tackle pivotal problems that the AI-enabled control systems might need to compensate the balance across <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multiple operation requirements</i> and avoid possible defections in advance to safeguard human lives and properties. Modular redundancy and ensemble method are two widely adopted solutions in the traditional CPSs and AI communities to enhance the functionality and flexibility of a system. Nevertheless, there is a lack of deep understanding of the effectiveness of such ensemble design on AI-CPSs across diverse industrial applications. Considering the complexity of AI-CPSs, existing ensemble methods fall short of handling such huge state space and sophisticated system dynamics. Furthermore, an ideal control solution should consider the multiple system specifications in real-time and avoid erroneous behaviors beforehand. Such that, a new specification-oriented ensemble control system is of urgent need for AI-CPSs. In this paper, we propose <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathtt {SIEGE}$</tex-math></inline-formula> , a semantics-guided ensemble control framework to initiate an early exploratory study of ensemble methods on AI-CPSs and aim to construct an efficient, robust, and reliable control solution for multi-tasks AI-CPSs. We first utilize a semantic-based abstraction to decompose the large state space, capture the ongoing system status and predict future conditions in terms of the satisfaction of specifications. We propose a series of new semantics-aware ensemble strategies and an end-to-end Deep Reinforcement Learning (DRL) hierarchical ensemble method to improve the flexibility and reliability of the control systems. Our large-scale, comprehensive evaluations over five subject CPSs show that 1) the semantics abstraction can efficiently narrow the large state space and predict the semantics of incoming states, 2) our semantics-guided methods outperform state-of-the-art individual controllers and traditional ensemble methods, and 3) the DRL hierarchical ensemble approach shows promising capabilities to deliver a more robust, efficient, and safety-assured control system. To enable further research along this direction to build better AI-enabled CPS, we made all of the code and experimental results data publicly available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://sites.google.com/view/ai-cps-siege/home</uri> .

Generalization and optimization of switching controller to control free vibration of a multi-linear state space system

This paper studies the optimized quadratic integral of a generalized multi-linear state space system under free vibration. The general formulation of the optimization problem is presented and can be solved by the standard numerical procedure. For demonstration, two examples are examined thoroughly and analytically. First, the minimized integral of mechanical energy for a single-dof semi-active damping or stiffness controlled system are shown analytically and compared with the best active and passive ones. The Pontryagin Maximum Principle is used to prove the true optimality of the presented semi-active damping control. The Linear Quadratic Regulator on/off or continuous clipping controller is shown to be truly optimized in the first example. In the second example, the maximized dissipation energy of the single-dof on-off damping system is studied and verified by a sensorless experiment.

Development of a gray box system identification model to estimate the parameters affecting traffic accidents

Abstract In this study, the gray box method has been used to model traffic accidents for the first time. This work examines the problem of estimating and identifying a single-input single-output state-space system. In this way, the state-space model was used, which has both a black box section (experimental data) and the parameters have been estimated by acquiring prior knowledge (white box). First, the state-space of the desired system is formed, and the algorithm for estimating the parameters and their convergence and the state vector estimation algorithm are written. In comparison, the system changes from nonlinear to linear. The parameters and prior knowledge are entered from the system. Finally, by implementing the presented method on the data related to the factors affecting accidents in Qazvin (Iran), the accuracy of the presented materials is investigated. The error output shows that initially, the error increased slightly, but then it shows a downward trend, and with the increase in the data, the error tends to zero (0.658). The results also show good fit and optimal accuracy of the model in less processing time.

A solution to the global identification problem in DSGE models

We develop an analytical framework to study global identification in structural models with forward-looking expectations. Our identification condition combines the similarity transformation linking the observationally equivalent state space systems with the constraints imposed on them by the model parameters. The key step of solving the identification problem then reduces to finding all roots of a system of polynomial equations. We show how it can be done using the concept of a Gröbner basis and recently developed algorithms to compute it analytically. In contrast to frameworks relying on numerical search, our approach can prove whether a model is identified or not at a given parameter point, explicitly delivering the complete set of observationally equivalent parameter vectors. We present the solution to the global identification problem for several popular dynamic stochastic general equilibrium (DSGE) models.

Variational Identification of Linearly Parameterized Nonlinear State-Space Systems

A variational Bayesian (VB) approach to the identification of linearly parameterized nonlinear state-space models (LP-NSSMs) is developed in this article. Conjugate priors over the unknown parameters are introduced, and the posterior distributions are approximated under the VB framework. In order to estimate the hidden states of the LP-NSSMs with random parameters, the augmented LP-NSSMs are established such that nonlinear smoothing methods can be applied. An extension to comprehensively tackling data anomalies, such as outliers and missing observations, is also considered to further improve the robustness of the presented method. Finally, a numerical example and the practical benchmarks are adopted to validate the efficacy of the proposed algorithm.

A state-space model-based temperature control system for laser remanufacturing molten pool

ABSTRACT Laser remanufacturing is a key technology for remanufacturing, which has been widely used in aerospace, metallurgy, energy and other fields. However, the problem of shape control has been the bottleneck that restricts the scale and industrial application. In the laser remanufacturing process, the molten pool temperature is the critical to determine the shape and performance stability of remanufactured parts. Based on this, the paper proposes a real-time online control method for laser remanufacturing molten pool temperature based on state space model, which solves the problem of difficult to establish control mechanism model and multiple variable constraints. Develop a real-time online control system for molten pool temperature of laser remanufacturing process based on state space model and incremental integral separation PID control, which uses a single sampling point as temperature feedback, solving the problem of lag generated by traditional feedback cycle, realizing real-time online control of molten pool temperature of laser remanufacturing process. Finally, the experimental results show that the developed molten pool temperature control system can effectively eliminate the sudden and gradual temperature change in the deposition process and significantly improve the thermal accumulation phenomenon in the deposition process, thus improving the forming quality and performance stability of remanufactured parts.

Trend and seasonality features extraction with pre-trained CNN and recurrence plot

GoogLeNet is a pre-trained Convolutional Neural Network (CNN) that allows transfer learning and has achieved high recognition rates in image classification tasks. A Recurrence Plot (RP) is an imaging method that depicts the recurrence of the state space system using coloured points and lines in 2D images. This work contributes to facilitating time series feature extraction by proposing a method that applies the GoogLeNet to time series images obtained with RP. The developed method is tested using simulated time series and selected time series from the M3 competition dataset. The results shows that the transfer learning approach allowed the extraction of business time series features by means of a GoogLeNet fine-tuned using 100 simulated time series. The combination of GoogLeNet and RPs outperforms the alternative and easier combination of GoogLeNet and plots of the time series and support the convenience of the RP transformation step. This application of deep learning techniques to business time series imaging offers opportunity for further developments.