Nonlinear State Research Articles

Analyzing and identifying predictable time range for stress prediction based on chaos theory and deep learning

ProposeStress is a common problem globally. Prediction of stress in advance could help people take effective measures to manage stress before bad consequences occur. Considering the chaotic features of human psychological states, in this study, we integrate deep learning and chaos theory to address the stress prediction problem.MethodsBased on chaos theory, we embed one’s seemingly disordered stress sequence into a high dimensional phase space so as to reveal the underlying dynamics and patterns of the stress system, and meanwhile are able to identify the stress predictable time range. We then conduct deep learning with a two-layer (dimension and temporal) attention mechanism to simulate the nonlinear state of the embedded stress sequence for stress prediction.ResultsWe validate the effectiveness of the proposed method on the public available Tesserae dataset. The experimental results show that the proposed method outperforms the pure deep learning method and Chaos method in both 2-label and 3-label stress prediction.ConclusionIntegrating deep learning and chaos theory for stress prediction is effective, and can improve the prediction accuracy over 2% and 8% more than those of the deep learning and the Chaos method respectively. Implications and further possible improvements are also discussed at the end of the paper.

Numerical investigation of fluid flowing through rough fractures subject to shear

Comprehending fluid flow in rock masses is essential for modern underground engineering, including chemical energy extraction, nuclear pollutant remediation, and hydrocarbon utilization, complicated by shear-induced and surface roughness effects in fractures. This study employed numerical simulations to investigate the fluid flow behavior in fractures with different surface roughness under shear, where the shear direction is perpendicular to the flow direction. The nonlinear flow of the fluid is observed to have a strong correlation with the confining pressure (Pz), roughness (JRC), and shear displacement (u). The generation of eddy currents is frequently linked to the presence of flow channel intricacies and the velocity of flow at a microscopic scale. The Forchheimer equation could describe the process of nonlinear phenomena accentuation very well. The fracture under Pz caused a reduction in hydraulic transmissivity (T) due to compression. Furthermore, the T changes dramatically as the shear process progresses. Based on the analysis of the Forchheimer coefficient (β) and critical Reynolds number (Rec) parameters used to determine the response of nonlinear flow, it appears that an increase in Pz facilitates the transition of the fluid into a nonlinear flow state. Conversely, shearing has the opposite effect and reduces the tendency toward nonlinear flow.

Learning-Based Faulty State Estimation Using SOH-Coupled Model Under Internal Thermal Faults in Lithium-Ion Batteries

Estimating the state of charge (SOC), state of health (SOH), and core temperature under internal faults will significantly improve the battery management system’s (BMS’s) autonomy and accuracy in range prediction. This paper presents a neural network (NN) based state estimation scheme that can estimate the SOC, core temperature, and SOH under internal faults in lithium-ion batteries (LIBs). First, we propose a model-based internal fault detection scheme by employing a SOH-coupled electro-thermal-aging model (ETA) of the LIB. Then, a nonlinear observer is used to estimate the proposed SOH-coupled model’s healthy states for a residual generation. The fault diagnosis scheme compares the output voltage and surface temperature residuals against the designed adaptive threshold to detect thermal faults. The adaptive threshold effectively alleviates the false positives due to degradation and model uncertainties of the battery under no-fault conditions. Upon fault detection, we employ an additional NN-based observer in the second step to learn the faulty dynamics. A novel NN weight tuning algorithm is proposed using the measured voltage, surface temperature, and estimated healthy states. The convergence of the nonlinear and NN-based observer state estimation errors is proven using the Lyapunov theory. Finally, numerical simulation results are presented.

Bayesian approximation for parameterized KALMAN filter for investigation and simulation of unknown noise variance trajectory following in state space models with different noise distributions

Bayesian approach can be used for parameter identification and extraction in state space models and its ability for analyzing sequence of data in dynamical system is proved in different literatures. In this paper, Bayesian approach for approximation of variances in measurement noise with KALMAN filter is applied for estimation of the dynamical state and measurement data in discrete dynamical system. Detection of uncertainty and estimation of those can be done simultaneously with adaptive KALMAN filter. This algorithm at each step time estimates noise variance and state of system with KALMAN filter. Then, approximation is formed at each step separately and at each step sufficient statistics of the state and noise variances are computed with a fixed-point iteration of a KALMAN filter. For showing influence of variance in measurement data on algorithm different simulations is applied. First, effect of variance and its distribution on detection performance is simulated in KALMAN filter without Bayesian formulation. Then simulation is applied to KALMAN filter with ability of variance tracking of measurement data.in these simulations, influence of distribution of measurement data in each step is estimated and true variance of data is obtained by algorithm and is compared in different scenarios. Afterwards, one typical modeling of nonlinear state space model with inducing noise measurement is simulated by this approach. Finally, the performance and the important limitations of this algorithm in these simulations are explained.

An algorithm to transform discrete-time state equations into the extended observer form

The problem of transforming a single-input single-output nonlinear discrete-time state equations into the extended observer form is studied in this paper. Unlike previous solutions which compute the injection terms from the input–output equations, in this paper the computations utilize directly the given state equations. An algorithm is given to find step-by-step the necessary transformation by computing backward-shifts of functions computed in previous step. It is shown that the integrability conditions presented in the algorithm are necessary and sufficient for solvability of the problem. Various examples have been studied to demonstrate the usefulness of the algorithm.

Dynamics analysis of a nonlinear controlled predator–prey model with complex Poincaré map

In this paper, we propose a class of predator–prey models with nonlinear state-dependent feedback control in the saturated state. The nonlinear state impulse control leads to a diversity of pulse and phase sets such that the Poincaré map built on the corresponding phase sets behaves like the single-peak function and multi-peak function with multiple discontinuities. We start our study by analyzing the exact pulse and phase sets of models under various cases generated by the dependent parameter space of nonlinear state feedback control, then construct the Poincaré map that is followed by investigating their monotonicity, continuity, concavity, and immobility properties. We also explore the existence, uniqueness, and sufficient conditions for the global stability of the order-1 periodic solutions of the systems. Numerical simulations are carried out to illustrate and reveal the biological significance of our theoretical findings.

Developing a dynamic quality prediction model for limited samples target grade based on transfer learning

In response to the dynamic demands of the market, this study addresses the challenge of frequent operational adjustments in a production line to accommodate diverse product grades. The resulting scarcity of data in the new operating conditions (target grade) impedes the development of reliable soft-sensor prediction models. A two-step learning method, termed S2-LGMNSSM-TS-T, is proposed. This method employs a semi-supervised latent Gaussian mixture nonlinear state space model (S2-LGMNSSM-TS) trained on both target and source data, providing a dynamic, one-step-ahead predictive soft sensor. To overcome data scarcity in the target grade, insights from the source are utilized. With a Gaussian mixture prior distribution, S2-LGMNSSM-TS identifies dynamic behaviors in both target and source grades. The enhanced S2-LGMNSSM-TS-T configuration focuses on target-grade predictions, leveraging source knowledge and mitigating data scarcity issues. A numerical example and an industrial case study demonstrate the model's effectiveness in improving target-grade predictions through source knowledge utilization.

Spatial Nonlinear Conversion of Structured Light for Machine Learning Based Ultra‐Accurate Information Networks

AbstractStructured light can be encoded to carry information for free‐space optical communications with an extended degree of freedom to increase the capacity, however, the accuracy issue along with capacity increase is one of the biggest challenges that prevent practical applications. To achieve high accuracy with high capacity by a simple method, they propose the spatial nonlinear conversion of structured light into a communication network, especially, realizing an ultra‐high‐accuracy point‐to‐multipoint (PtoMP) information transmission link. A series of coherently superposed spatial modes and their spatial nonlinear conversion states are used as information carriers to replace the prior orbital angular momentum beams and greatly expand channel capacity within quite low spatial mode order. Through the spatial nonlinear conversion of simple dual‐mode superposition and a very basic neural network for machine learning‐based recognition, as high as 99.5% accuracy for more than 500 modes is obtained. By a combination of diffuse reflection screens and multiple CCDs, the large observation angle PtoMP information transmission is also proved to be feasible. This work paves the way for practical large‐scale multi‐party information networks using structured light.

False Data Injection Attack with Max-Min Optimization in Smart Grid

With the proliferation of information and communication technology (ICT), the smart grid is critically vulnerable to cyber-attacks such as false data injection (FDI), denial-of-service, and data spoofing. The cyber-attackers defunctionalize critical operations of the smart grid by compromising the ICT. The decisions for the critical operation of the smart grid are processed with a state estimator, and ICT makes the state estimator vulnerable to FDI attacks. Hence, vulnerability analysis of the state estimator needs to be investigated for potential FDI attacks to protect it from future cyber-attacks. This work proposes the FDI attack vector construction without the knowledge of bad data detection (BDD) threshold on linear and non-linear state estimators using max-min optimization considering the partial network information. The optimization problem is formulated from the attacker's perspective to target the manipulation of measurements in the attack zone so as to increase the generation cost. The equivalent power injection model is developed for the attack zone to construct the deceptive attacks using DC and AC power flow models. The effectiveness of the proposed framework has been tested on 5 bus PJM network, modified IEEE 30 bus, IEEE 57 bus, and IEEE 118 bus system. The proposed framework is compared with existing state-of-art methods (viz., linear attack policy, non-linear attack policy, load redistribution attack, and line flow attack) to assess its efficacy. It is observed that the developed FDI attack vector successfully bypasses the bad data detectors such as the chi-square test, largest normalized residue, and l2 detector that is normally used by the system operator. Moreover, the study compares and discusses the impact of FDI attacks on the estimated state variables obtained with state estimators and, thereby, the generation cost calculated with the DC & AC optimal power flow tool.

A novel fractional nonlinear state estimation algorithm in non-Gaussian noise environment

This paper presents research on state estimation for nonlinear fractional-order systems in non-Gaussian noise. Traditional estimation methods based on the minimum mean square error criterion perform poorly for fractional-order systems in non-Gaussian noise Using the Bayesian filtering framework and information theoretic learning, a novel fractional central difference Kalman filter based on the maximum correntropy criterion is firstly proposed and named MC-FCDKF. The proposed MC-FCDKF contains prior state update step, regression model construction and posterior state update step. The regular Taylor series expansion is replaced by the Stirling interpolation technique. The conventional measurement prediction and the associated calculation of covariances are also eliminated, enhancing practicality and real-time performance. Finally, the performance of the proposed algorithm is compared with several other algorithms through lithium battery state-of-charge estimation to verify the effectiveness and benefits under non-Gaussian noise perturbation.

A two-dimensional numerical study of ion-acoustic turbulence

We investigate the linear and nonlinear evolution of the current-driven ion-acoustic instability in a collisionless plasma via two-dimensional (2-D) Vlasov–Poisson numerical simulations. We initialise the system in a stable state and gradually drive it towards instability with an imposed, weak external electric field, thus avoiding physically unrealisable super-critical initial conditions. A comprehensive analysis of the nonlinear evolution of ion-acoustic turbulence (IAT) is presented, including the detailed characteristics of the evolution of the particles’ distribution functions, (2-D) wave spectrum and the resulting anomalous resistivity. Our findings reveal the dominance of 2-D quasi-linear effects around saturation, with nonlinear effects, such as particle trapping and nonlinear frequency shifts, becoming pronounced during the later stages of the system's nonlinear evolution. Remarkably, the Kadomtsev–Petviashvili (KP) spectrum is observed immediately after the saturation of the instability. Another crucial and noteworthy result is that no steady saturated nonlinear state is ever reached: strong ion heating suppresses the instability, which implies that the anomalous resistivity associated with IAT is transient and short-lived, challenging earlier theoretical results. Towards the conclusion of the simulation, electron-acoustic waves are triggered by the formation of a double layer and strong modifications to the particle distribution induced by IAT.

3D Heat Conduction Solver for Complex Geometries

Abstract: The essential pre-requisites for any solver to tackle real life 3D problems are to handle complex geometries and quick turnaround time. In this direction an Unstructured Finite Volume (FVM) based multi-threaded heat conduction solver has been developed to address both the issues respectively. The solver is object oriented and written in Java language. Unstructured Finite Volume method has been utilized for the space discretization and a four stage Runge-Kutta scheme is used for time integration. This solution methodology is highly parallelizable and extensively used in CFD codes. The present solver can handle non-linear steady state and transient 3D thermal problems with Dirichlet, Neumann and surface radiation boundary conditions. The solver has been validated against bench mark problems. In the present work a 3D complex geometry is discretised into 2.5 lakh hexahedrons has been taken as a test case to demonstrate the efficiency of the solver with multi-threading in dual processor machines. The results obtained are presented.

Construction and Method Study of the State of Charge Model for Lithium-Ion Packs in Electric Vehicles Using Ternary Lithium Packs as an Example

Accurate and real-time estimation of pack system-level chips is essential for the performance and reliability of future electric vehicles. Firstly, this study constructed a model of a nickel manganese cobalt cell on the ground of the electrochemical process of the packs. Then, it used methods on the grounds of the unscented Kalman filter and unscented Kalman particle filter for system-level chip estimation and algorithm construction. Both algorithms are on the ground of Kalman filters and can handle nonlinear and uncertain system states. In comparative testing, it can be seen that the unscented Kalman filter algorithm can accurately evaluate the system-level chip of the nickel manganese cobalt cell under intermittent discharge conditions. The system-level chip was 0.53 at 1000 s and was reduced to 0.45 at 1500 s. These results demonstrate that the evaluation of the ternary lithium battery pack’s performance is time-dependent and indicate the accuracy of the algorithm used during this time period. These data should be considered in the broader context of the study for a comprehensive understanding of their meaning. In the later stage, the estimation error of the recursive least-squares unscented Kalman particle filter method for system-level chips began to significantly increase, gradually exceeding 1%, with a corresponding root-mean-square error of 0.002171. This indicates that the recursive least-squares optimization algorithm, the unscented Kalman particle filter algorithm, diminished its root mean square error by 27.59%. The unscented Kalman filter and unscented Kalman particle filter are effective in estimating the system-level chip of nickel manganese cobalt cells. However, UPF performs more robustly in handling complex situations, such as pack aging and temperature changes. This study provides a new perspective and method that has a high reference value for pack management systems. This helps to achieve more effective energy management and improve pack life, thereby enhancing the reliability and practicality of electric vehicles.

NN‐mCRE: A modified constitutive relation error framework for unsupervised learning of nonlinear state laws with physics‐augmented neural networks

AbstractThis article proposes a new approach to train physics‐augmented neural networks with observable data to represent mechanical constitutive laws. To train the neural network and learn thermodynamics potentials, the proposed method does not rely on strain‐stress or strain‐free energy pairs but needs only partial strain or displacement measurements inside the structure. The neural network is trained thanks to an unsupervised procedure in which the modified constitutive relation error (mCRE) is minimized. The mCRE functional provides a bias‐aware data assimilation framework with a rich physical sense as the constitutive relation error (CRE) part can be interpreted as a modeling error continuously defined over the structure, and can be used as a prediction quality in the inference phase. This article also extends previous works on the mCRE by introducing a new minimization procedure in the case of nonlinear state laws. As typical structural health monitoring applications may require that the neural networks should be trained online, an important focus is thus made on automatic and adaptive tuning of sensitive hyperparameters (learning rate, weighting between losses, number of epochs and initialization). It is shown that when the training database is rich enough with respect to the loading cases, the proposed method achieves remarkable performance regarding the quality of the learned model, noise robustness, and low sensitivity to user‐defined hyperparameters. The method is evaluated on two test cases: a non‐quadratic potential in the small strain regime with synthetic optic fiber measurements, and a Mooney–Rivlin model in the hyperelastic case with synthetic digital image correlation observations.

A deep learning technique to control the non-linear dynamics of a gravitational-wave interferometer

Abstract In this work we developed a deep learning technique that successfully solves a non-linear dynamic control problem. Instead of directly tackling the control problem, we combined methods in probabilistic neural networks and a Kalman-filter-inspired model to build a non-linear state estimator for the system. We then used the estimated states to implement a trivial controller for the now fully observable system. We applied this technique to a crucial non-linear control problem that arises in the operation of the Laser Interferometer Gravitational-Wave Observatory (LIGO) system, an interferometric gravitational-wave observatory. We demonstrated in simulation that our approach can learn from data to estimate the state of the system, allowing a successful control of the interferometer’s mirror. We also developed a computationally efficient model that can run in real time at high sampling rate on a single modern CPU core, one of the key requirements for the implementation of our solution in the LIGO digital control system. We believe these techniques could be used to help tackle similar non-linear control problems in other applications.

New energy power demand prediction and optimal scheduling based on artificial intelligence in smart grid

Abstract With the development of smart grid, the demand for new energy power increases. Improving the accuracy of new energy power demand forecast is an important basis for the orderly operation of power system. This article presents a new energy power demand forecasting method based on DESSA-NESN algorithm. First, differential evolution algorithm (DE) and sparrow search algorithm (SSA) are combined, and operations such as mutation, crossing and screening are introduced into the population updating process of SSA. The internal state function of the savings pool of the standard echo state network (ESN) is replaced by the hyperbolic tangent function to obtain the nonlinear echo state network (NESN). Then, the parameters of deep echo state network (DESN) are optimized using DESSA algorithm. The DESSA-DESN prediction model is established. Finally, the mean absolute percentage error (MAPE) and root mean square error (RMSE) of DESSA-NESN were 15.84 and 0.12%, respectively, and the prediction effect was better than other comparison models.

Free-electron interaction with nonlinear optical states in microresonators.

The short de Broglie wavelength and strong interaction empower free electrons to probe structures and excitations in materials and biomolecules. Recently, electron-photon interactions have enabled new optical manipulation schemes for electron beams. In this work, we demonstrate the interaction of electrons with nonlinear optical states inside a photonic chip-based microresonator. Optical parametric processes give rise to spatiotemporal pattern formation corresponding to coherent or incoherent optical frequency combs. We couple such "microcombs" to electron beams, demonstrate their fingerprints in the electron spectra, and achieve ultrafast temporal gating of the electron beam. Our work demonstrates the ability to access solitons inside an electron microscope and extends the use of microcombs to spatiotemporal control of electrons for imaging and spectroscopy.

The Non-Singular Terminal Sliding Mode Control of Underactuated Unmanned Surface Vessels Using Biologically Inspired Neural Network

Underactuated Unmanned Surface Vessels (USVs) are widely used in civil and military fields due to their small size and high flexibility, and trajectory tracking control is a critical research area for underactuated USVs. This paper proposes a trajectory tracking control strategy using the Biologically Inspired Neural Network (BINN) for USVs to improve tracking speed and accuracy. A virtual control law is designed to obtain the required virtual velocity for trajectory tracking control, in which the velocity error is calibrated to ensure that the position error converges to zero. To observe and compensate for unknown and complex environmental disturbances such as wind, waves, and currents, a nonlinear extended state observer (NESO) is designed. Then, a controller based on Non-singular Terminal Sliding Mode (NTSM) is designed to resolve the problems of singular value and controller chattering and to improve the controller response speed. A BINN is introduced to simplify the process of differentiation, reduce the input values of the initial state, and solve the problem of thruster input saturation. Finally, the Lyapunov stability theory is utilized to analyze the stability of the proposed algorithm. The simulation results show that the proposed algorithm has a higher trajectory tracking accuracy and speed than traditional methods.

A Bayesian Kalman filter algorithm for quantifying estimation uncertainty of track irregularity on bridges with randomness in system parameters

Vehicle on-board monitoring methods use responses of running vehicles to identify track irregularity in real time. But the parameters of both the bridges and the vehicles in such processes may have a non-negligible degree of uncertainty or randomness that will inevitably lead to uncertainty in the track irregularity identification. Quantifying such uncertainty is a great challenge as the vehicle-bridge system (VBS) to be treated with is time-dependent and random. This paper proposes an on-board track irregularity identification algorithm that realizes an inverse random dynamic analysis of the VBS to quantify estimation uncertainty by using a Bayesian Kalman filter technology. The proposed algorithm utilizes sigma point sets to simulate the random parameters and the noises, and is therefore capable of implementing high-fidelity probability density propagation in the nonlinear state transfer and observation functions describing the VBS. The proposed algorithm is validated by numerical examples with various running states and parameter uncertainty levels.

Nonlinear Performance of Steel Tube Tower in Ultra-High Voltage Transmission Lines under Wind Loads

As complex, statically indeterminate structures, transmission towers are subject to complex forces and are usually simplified into truss structures that only consider the effects of axial force. When the load and deformation of a tower are small, it is reasonable to carry out analysis according to the linear elasticity theory. However, the height of an ultra-high voltage (UHV) transmission tower is significantly large, meaning that the calculation result according to the current elastic analysis method often has a large deviation from the actual stress of the structure. With the influence of the bending moment at the end of the member, a numerical model is established considering the influence of geometric nonlinearity and material nonlinearity in this paper. The stress distribution characteristics and development law of UHV transmission towers in linear and nonlinear stress states are analyzed and studied. The real tower test and elastoplastic ultimate bearing capacity analysis show that the elastoplastic analysis is closer to the actual tower. The UHV steel pipe tower designed according to the linear elasticity and small deformation theory has a large safety margin under the design load, resulting in a significant waste of materials. Under the action of heavy load, the tower exhibits strong nonlinearity, and the influence of geometric and material nonlinear factors should be fully considered when designing the structural components in UHV transmission towers.