Identification Of Dynamic Systems Research Articles

Aircraft Closed-Loop Dynamic System Identification in the Entire Flight Envelope Range Based on Deep Learning

Aircraft Closed-Loop Dynamic System Identification in the Entire Flight Envelope Range Based on Deep Learning

Reduced-Order Modeling for Dynamic System Identification with Lumped and Distributed Parameters via Receptance Coupling Using Frequency-Based Substructuring (FBS)

Paper presents an effective technique for developing reduced-order models to predict the dynamic responses of systems using the receptance coupling and frequency-based substructuring (RCFBS) method. The proposed approach is particularly suited for reconfigurable dynamic systems across various applications, like cars, robots, mechanical machineries, and aerospace structures. The methodology focuses on determining the overall system receptance matrix by coupling the receptance matrices (FRFs) of individual subsystems in a disassembled configuration. Two case studies, one with distributed parameters and the other with lumped parameters, are used to illustrate the application of this approach. The first case involves coupling three substructures with flexible components under fixed–fixed boundary conditions, while the second case examines the coupling of subsystems characterized by multiple masses, springs, and dampers, with various internal and connection degrees of freedom. The accuracy of the proposed method is validated against a numerical finite element analysis (FEA), direct methods, and a modal analysis. The results demonstrate the reliability of RCFBS in predicting dynamic responses for reconfigurable systems, offering an efficient framework for reduced-order modeling by focusing on critical points of interest without the need to account for detailed modeling with numerous degrees of freedom.

Estimates of the accuracy of identification of a nonlinear dynamic system using step test signals

Machine learning (ML) has become widespread in everyday life. On its basis, programs with artificial intelligence work, on the basis of which many virtual assistants have evolved. ML plays an important role in various spheres of activity of many enterprises. ML helps to automate many processes, simplifying the functioning of the company. Named Entity Recognition (NER) models allow to automatically select and search for information according to certain criteria in mobile data extracted, for example, by the logistic method. Support for NER by Python models makes it possible to flexibly program specific requests that are generated in the forensic examination process. Open source creates a unique opportunity to continuously improve the model by training it on datasets. A powerful NER package is the spaCy framework, which helps to simplify data and extract detailed information from input data, train a model, perform model tuning, and more. spaCy is compatible with 64-bit CPython 3.7+ and runs on Unix/Linux, macOS/OS X and Windows. The latest spaCy releases are available over pip and conda.

Data‐driven control and a prey–predator model for sourcing decisions in the low‐carbon intertwined supply chain

AbstractThis paper addresses the challenges of low‐carbon sourcing in intertwined supply chains by proposing a data‐driven control framework and a prey–predator model for sourcing decisions. The objective is to optimize low‐carbon objectives and reduce environmental impact. Existing static models fail to capture the dynamic nature of supply chain systems and overlook the ripple effects when sourcing decisions propagate throughout the interconnected network. To bridge this gap, our study develops a dynamic model that explicitly captures the bullwhip effect and leverages real‐time and historical data. This model conceptualizes suppliers as prey and manufacturers and consumers as predators, employing an ecological analogy to decipher the intricate interactions and dependencies within the supply chain. Through this approach, we identify strategies to promote sustainable practices and motivate suppliers to adopt low‐carbon measures. We assess two data‐driven algorithms, the nonlinear auto‐regressive exogenous (NARX) network and sparse identification of nonlinear dynamic systems with input variables (SINDYc). The results reveal that SINDYc outperforms prediction accuracy and control, offering significant advantages for rapid decision‐making. The study highlights how shifts in market demands and regulatory pressures critically influence the strategies of chemical firms and fertilizer markets. Moreover, it discusses the economic challenges in transitioning from high carbon footprint suppliers (HCFSs) to low carbon footprint suppliers (LCFSs), exacerbated by a notable cost disparity where HCFSs are approximately 30% cheaper. By advancing beyond conventional static models, this research provides a deeper understanding of the environmental impacts and operational dynamics within supply chains, emphasizing the significant “ripple effect” where decisions at one node profoundly affect others within the chain.

Forward variable selection enables fast and accurate dynamic system identification with Karhunen-Loève decomposed Gaussian processes

A promising approach for scalable Gaussian processes (GPs) is the Karhunen-Loève (KL) decomposition, in which the GP kernel is represented by a set of basis functions which are the eigenfunctions of the kernel operator. Such decomposed kernels have the potential to be very fast, and do not depend on the selection of a reduced set of inducing points. However KL decompositions lead to high dimensionality, and variable selection thus becomes paramount. This paper reports a new method of forward variable selection, enabled by the ordered nature of the basis functions in the KL expansion of the Bayesian Smoothing Spline ANOVA kernel (BSS-ANOVA), coupled with fast Gibbs sampling in a fully Bayesian approach. It quickly and effectively limits the number of terms, yielding a method with competitive accuracies, training and inference times for tabular datasets of low feature set dimensionality. Theoretical computational complexities are O ( N P 2 ) in training and O ( P ) per point in inference, where N is the number of instances and P the number of expansion terms. The inference speed and accuracy makes the method especially useful for dynamic systems identification, by modeling the dynamics in the tangent space as a static problem, then integrating the learned dynamics using a high-order scheme. The methods are demonstrated on two dynamic datasets: a ‘Susceptible, Infected, Recovered’ (SIR) toy problem, along with the experimental ‘Cascaded Tanks’ benchmark dataset. Comparisons on the static prediction of time derivatives are made with a random forest (RF), a residual neural network (ResNet), and the Orthogonal Additive Kernel (OAK) inducing points scalable GP, while for the timeseries prediction comparisons are made with LSTM and GRU recurrent neural networks (RNNs) along with the SINDy package.

Dynamical system identification, model selection, and model uncertainty quantification by Bayesian inference.

This study presents a Bayesian maximum a posteriori (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational justification for the choice of the residual and regularization terms, respectively, from the negative logarithms of the likelihood and prior distributions. In addition to the estimation of model coefficients, the Bayesian interpretation gives access to the full apparatus for Bayesian inference, including the ranking of models, the quantification of model uncertainties, and the estimation of unknown (nuisance) hyperparameters. Two Bayesian algorithms, joint MAP and variational Bayesian approximation, are compared to the least absolute shrinkage and selection operator (LASSO), ridge regression, and the sparse identification of nonlinear dynamics (SINDy) algorithms for sparse regression by application to several dynamical systems with added Gaussian or Laplace noise. For multivariate Gaussian likelihood and prior distributions, the Bayesian formulation gives Gaussian posterior and evidence distributions, in which the numerator terms can be expressed in terms of the Mahalanobis distance or "Gaussian norm" ||y-y^||M-12=(y-y^)⊤M-1(y-y^), where y is a vector variable, y^ is its estimator, and M is the covariance matrix. The posterior Gaussian norm is shown to provide a robust metric for quantitative model selection for the different systems and noise models examined.

Tracking the impact of heavy metals on human health and ecological environments in complex coastal aquifers using improved machine learning optimization.

The rising heavy metal (HM) pollution in coastal aquifers in rapidly urbanizing areas such as Dammam leads to significant risks to public health and environmental sustainability, challenging compliance with Environmental Protection Agency (EPA) guidelines, World Health Organization (WHO) standards, and Sustainable Development Goals (SDGs) related to clean water and life on land. This study developed the predictive-based monitoring of HM concentrations, including cadmium (Cd), chromium (Cr), and mercury (Hg) in the coastal aquifers of Dammam, influenced by industrial, agricultural, and urban activities. For this purpose, dynamic system identification and machine learning (ML) models integrated with three ensemble techniques, namely, simple averaging (SAE), weighted averaging (WAE), and neuro-ensemble (N-ESB), were employed to enhance the accuracy, reliability, and efficiency of environmental monitoring systems. The experimental data were calibrated and validated in addition to k-fold cross-validation to ensure the predictive skills of the models. The methodology integrates extensive data collection across varied land uses in Dammam and accurate model calibration and validation phases to develop highly accurate predictive models. The findings proved that the N-ESB and Hammerstein-Wiener (HW) models surpassed other models in predicting the concentrations of all HM. For Cd, the N-ESB model achieved a root mean square error (RMSE = 0.0010mg/kg). Similarly, Cr demonstrated superior performance (RMSE = 0.0179mg/kg). Further numerical results indicated that the HW algorithm proved the most effective for Hg, with RMSE = 0.0000mg/kg. The quantitative comparison suggested that the N-ESB model's consistently high performance and low error rates make it an optimal choice for real-time, precise monitoring and management of HM pollution in coastal aquifers. The outcomes of this research highlighted the importance of integrating advanced predictive modeling techniques in environmental science, providing significant and practical implications for policymaking and ecological management.

Parameter identification of dynamical systems based on short-term prediction by the generalized cell mapping method with deep learning

Parameter identification of dynamical systems based on short-term prediction by the generalized cell mapping method with deep learning

Deep Embedding Koopman Neural Operator-Based Nonlinear Flight Training Trajectory Prediction Approach

Accurate flight training trajectory prediction is a key task in automatic flight maneuver evaluation and flight operations quality assurance (FOQA), which is crucial for pilot training and aviation safety management. The task is extremely challenging due to the nonlinear chaos of trajectories, the unconstrained airspace maps, and the randomization of driving patterns. In this work, a deep learning model based on data-driven modern koopman operator theory and dynamical system identification is proposed. The model does not require the manual selection of dictionaries and can automatically generate augmentation functions to achieve nonlinear trajectory space mapping. The model combines stacked neural networks to create a scalable depth approximator for approximating the finite-dimensional Koopman operator. In addition, the model uses finite-dimensional operator evolution to achieve end-to-end adaptive prediction. In particular, the model can gain some physical interpretability through operator visualization and generative dictionary functions, which can be used for downstream pattern recognition and anomaly detection tasks. Experiments show that the model performs well, particularly on flight training trajectory datasets.

A few-shot identification method for stochastic dynamical systems based on residual multipeaks adaptive sampling.

Neural networks are popular data-driven modeling tools that come with high data collection costs. This paper proposes a residual-based multipeaks adaptive sampling (RMAS) algorithm, which can reduce the demand for a large number of samples in the identification of stochastic dynamical systems. Compared to classical residual-based sampling algorithms, the RMAS algorithm achieves higher system identification accuracy without relying on any hyperparameters. Subsequently, combining the RMAS algorithm and neural network, a few-shot identification (FSI) method for stochastic dynamical systems is proposed, which is applied to the identification of a vegetation biomass change model and the Rayleigh-Van der Pol impact vibration model. We show that the RMAS algorithm modifies residual-based sampling algorithms and, in particular, reduces the system identification error by 76% with the same sample sizes. Moreover, the surrogate model accurately predicts the first escape probability density function and the P bifurcation behavior in the systems, with the error of less than 1.59×10-2. Finally, the robustness of the FSI method is validated.

Identification of dynamical systems with time-varying disturbances and fractional errors-in-variables. Application example to a drone model

Identification of dynamical systems with time-varying disturbances and fractional errors-in-variables. Application example to a drone model

Critical expert analysis of permanent magnet synchronous motors identification methods and state variable observers

Relevance. In recent years, the oil industry has seen a tendency to transfer low-yield oil wells to intermittent mode. Unregulated electric drive and the open-loop controlled electric drive of electric centrifugal pumping with permanent magnet synchronous motors are typically not suitable for tasks of intermittent operation of wells. Due to objective reasons, there may not be smooth starts and required quality indicators of transient processes, which leads to even more reduction in oil production. The synthesis of a closed-loop electric drive control system of submersible installations is possible only using algorithms for indirect estimation of non-measured mechanical coordinates of the electric drive – state variables identification methods, observers of the rotor angular velocity and the load torque. The installation of sensors of angular velocity and torque on the shaft of the submersible electric motor is associated with technical difficulties, therefore, there is no need for significant modernization of the hardware solutions of the existing electrical equipment system. To date, the theory of identifying non-linear dynamic systems is widely used to derive an indirect estimate of the non-measured state variables of the permanent magnet synchronous motors. The large number of methods presented in scientific sources requires comparative analysis regarding their benefits and disadvantages in order to select the best identification method that meets the requirements of the oil production and takes into account its specificity and features. In this case, identification systems that are focused on minimizing computing power or operating in real time are given priority. Aim. To determine the best in terms of computational complexity and the convenience of practical use method of identifying state variables of permanent magnet synchronous motors operating in submersible oil well pumping units based on comparative analysis of existing methods presented in Russian and foreign sources. Methods. Methods for system analysis and identification of dynamic systems, a method of critical expert analysis. Result and conclusions. The most common methods for identifying and observing the state variables of synchronous motors with permanent magnets have been described in detail, given the general performance of each group of methods, their benefits and disadvantages were reviewed. By comparative critical expert analysis, it was found that for tasks of submersible electric centrifugal pump units electric drive a Luenberger observer, characterized by relatively low computational complexity and ease of setup in engineering practice can be recommended.

A Novel ANN-ARMA Scheme Enhanced by Metaheuristic Algorithms for Dynamical Systems and Time Series Modeling and Identification

A Novel ANN-ARMA Scheme Enhanced by Metaheuristic Algorithms for Dynamical Systems and Time Series Modeling and Identification

Meta-state–space learning: An identification approach for stochastic dynamical systems

Available methods for identification of stochastic dynamical systems from input–output data generally impose restricting structural assumptions on either the noise structure in the data-generating system or the possible state probability distributions. In this paper, we introduce a novel identification method of such systems, which results in a dynamical model that is able to produce the time-varying output distribution accurately without taking restrictive assumptions on the data-generating process. The method is formulated by first deriving a novel and exact representation of a wide class of nonlinear stochastic systems in a so-called meta-state–space form, where the meta-state can be interpreted as a parameter vector of a state probability function space parameterization. As the resulting representation of the meta-state dynamics is deterministic, we can capture the stochastic system based on a deterministic model, which is highly attractive for identification. The meta-state–space representation often involves unknown and heavily nonlinear functions, hence, we propose an artificial neural network (ANN)-based identification method capable of efficiently learning nonlinear meta-state–space models. We demonstrate that the proposed identification method can obtain models with a log-likelihood close to the theoretical limit even for highly nonlinear, highly stochastic systems.

Data-driven reconstruction of chaotic dynamical equations: The Hénon–Heiles type system

In this study, the classical two-dimensional potential VN=12mω2r2+1NrNsin(Nθ), N∈Z+, is considered. At N=1,2, the system is superintegrable and integrable, respectively, whereas for N>2 it exhibits a richer chaotic dynamics. For instance, at N=3 it coincides with the Hénon–Heiles system. The periodic, quasi-periodic and chaotic motions are systematically characterized employing time series, Poincaré sections, symmetry lines and the largest Lyapunov exponent as a function of the energy E and the parameter N. Concrete results for the lowest cases N=3,4 are presented in complete detail. This model is used as a benchmark system to estimate the accuracy of the Sparse Identification of Nonlinear Dynamical Systems (SINDy) method, a data-driven algorithm which reconstructs the underlying governing dynamical equations. We pay special attention at the transition from regular motion to chaos and how this influences the precision of the algorithm. In particular, it is shown that SINDy is a robust and stable tool possessing the ability to generate non-trivial approximate analytical expressions for periodic trajectories as well.

Identification of nonlinear dynamical system based on adaptive radial basis function neural networks

Identification of nonlinear dynamical system based on adaptive radial basis function neural networks

Physics enhanced sparse identification of dynamical systems with discontinuous nonlinearities

Physics enhanced sparse identification of dynamical systems with discontinuous nonlinearities

Dynamic system with correlated noise

Developing mathematical models for dynamic systems presents challenges in selecting state variables, crucial for minimizing computational operations during filter implementation. The paper addresses active identification of dynamic systems amid noise and measurement errors, using the Fisher information matrix. Additionally, it introduces Cholesky decomposition for generating correlated noise, demonstrating its applicability in practical problem-solving.

Identification of Continuous-Time Dynamic Systems With Uncertainties Measured by Fuzzy Sets Subject to Model Structure Errors

Identification of Continuous-Time Dynamic Systems With Uncertainties Measured by Fuzzy Sets Subject to Model Structure Errors

Identification of unknown dynamic system as a way to determine the transient characteristic of the inverse acoustic path

Identification of unknown dynamic system as a way to determine the transient characteristic of the inverse acoustic path