Parameters Of Dynamic System Research Articles

Dynamic response and vibration signature assessment of SDOF steel system using RISAM shaking table

Civil engineering structures face major challenges, particularly earthquakes, which are random phenomena in their intensity and frequency content. The seismic response of structures depends largely on the intensity of an earthquake and especially on its frequency content. Structural Health Monitoring (SHM) is a relevant tool for assessing the dynamic behavior of structures subjected to seismic excitations. This is achieved by using experimental measurements of structural dynamic parameters. The main objective of this study is to identify the vibration signature of a single-degree-of-freedom SDOF steel system. Based on the laws of similarity, a 1:6 reduced-scale model is developed. In this context, dynamic experiments using the shaking table of the RISAM laboratory (Risk Assessment and Management: University of Tlemcen) are carried out to determine the structural dynamic parameters of this steel system. This is achieved through experimental determination of natural frequency and damping of the reduced model. Acceleration and displacement measurements are also established. The experimental estimation of damping is established using the logarithmic decrement method. Several dynamic analyses are carried out based on the finite elements model of the reduced steel system model. The obtained results show that the approach used to determine the dynamic parameters of this reduced model leads to realistic results. On the other hand, a perfect concordance between the numerical and experimental results has been approved.

Dynamic Time Warping as Elementary Effects Metric for Morris-Based Global Sensitivity Analysis of High-Dimension Dynamical Models

This work focused on demonstrating the use of dynamic time warping (DTW) as a metric for the elementary effects computation in Morris-based global sensitivity analysis (GSA) of model parameters in multivariate dynamical systems. One of the challenges of GSA on multivariate time-dependent dynamics is the modeling of parameter perturbation effects propagated to all model outputs while capturing time-dependent patterns. The study establishes and demonstrates the use of DTW as a metric of elementary effects across the time domain and the multivariate output domain, which are all aggregated together via the DTW cost function into a single metric value. Unlike the commonly studied coefficient-based functional approximation and covariance decomposition methods, this new DTW-based Morris GSA algorithm implements curve alignment via dynamic programing for cost computation in every parameter perturbation trajectory, which captures the essence of “elementary effect” in the original Morris formulation. This new algorithm eliminates approximations and assumptions about the model outputs while achieving the objective of capturing perturbations across time and the array of model outputs. The technique was demonstrated using an ordinary differential equation (ODE) system of mixed-order adsorption kinetics, Monod-type microbial kinetics, and the Lorenz attractor for chaotic solutions. DTW as a Morris-based GSA metric enables the modeling of parameter sensitivity effects on the entire array of model output variables evolving in the time domain, resulting in parameter rankings attributed to the entire model dynamics.

A generalized incremental harmonic balance method by combining a data-driven framework for initial value selection of strongly nonlinear dynamic systems

The incremental harmonic balance (IHB) method is a semi-analytical and semi-numerical method that consists of the harmonic balance process and the Newton–Raphson iteration process, which can accurately obtain solutions of strongly nonlinear dynamic systems, and has been successfully applied to many practical problems. However, it is difficult to choose proper initial values for the Newton–Raphson iteration process, especially for strongly nonlinear dynamic systems, which can cause divergence of the IHB method. A novel generalized IHB method by combining a data-driven framework to obtain feasible initial values for strongly nonlinear dynamic systems is proposed in this work. In the proposed data-driven framework, an artificial neural network (ANN) is trained to learn the mapping between small system parameters of a weakly nonlinear dynamic system and corresponding solutions of the IHB method. The amount of data required for training is determined by the number of system parameters, which is usually only a few hundreds to a few thousands, making the training process very expeditious. Once the trained ANN receives other system parameters of a nonlinear dynamic system, it can immediately output a set of feasible initial values for the IHB method, which can make the IHB method quickly converge. Results from extensive testing indicate that the mapping learned by the ANN is effective not only for weakly nonlinear dynamic systems that are characterized by smaller system parameters, but also for strongly nonlinear dynamic systems in most cases that involve larger system parameters. During the testing for strongly nonlinear dynamic systems, successful convergences generate new training data. These data can be leveraged to further fine-tune the ANN to yield an improved ANN, which allows continuous refinement of the ANN and enhances prediction of initial values for strongly nonlinear dynamic systems. With the introduction of this simple yet highly efficient data-driven initial value selection framework, the applicability of the IHB method can be significantly enhanced. Three numerical examples are presented to show the efficiency and advantages of the present methodology.

Stochastic nonlinear model updating in structural dynamics using a novel likelihood function within the Bayesian-MCMC framework

The study presents a novel approach for stochastic nonlinear model updating in structural dynamics, employing a Bayesian framework integrated with Markov Chain Monte Carlo (MCMC) sampling for parameter estimation by using an approximated likelihood function. The proposed methodology is applied to both numerical and experimental cases. The paper commences by introducing Bayesian inference and its constituents: the likelihood function, prior distribution, and posterior distribution. The resonant decay method is employed to extract backbone curves, which capture the non-linear behaviour of the system. A mathematical model based on a single degree of freedom (SDOF) system is formulated, and backbone curves are obtained from time response data. Subsequently, MCMC sampling is employed to estimate the parameters using both numerical and experimental data. The obtained results demonstrate the convergence of the Markov chain, present parameter trace plots, and provide estimates of posterior distributions of updated parameters along with their uncertainties. Experimental validation is performed on a cantilever beam system equipped with permanent magnets and electromagnets. The proposed methodology demonstrates promising results in estimating parameters of stochastic non-linear dynamical systems. Through the use of the proposed likelihood functions using backbone curves, the probability distributions of both linear and non-linear parameters are simultaneously identified. Based on this view, the necessity to segregate stochastic linear and non-linear model updating is eliminated.

Statistical inference with a manifold-constrained RNA velocity model uncovers cell cycle speed modulations

Across biological systems, cells undergo coordinated changes in gene expression, resulting in transcriptome dynamics that unfold within a low-dimensional manifold. While low-dimensional dynamics can be extracted using RNA velocity, these algorithms can be fragile and rely on heuristics lacking statistical control. Moreover, the estimated vector field is not dynamically consistent with the traversed gene expression manifold. To address these challenges, we introduce a Bayesian model of RNA velocity that couples velocity field and manifold estimation in a reformulated, unified framework, identifying the parameters of an explicit dynamical system. Focusing on the cell cycle, we implement VeloCycle to study gene regulation dynamics on one-dimensional periodic manifolds and validate its ability to infer cell cycle periods using live imaging. We also apply VeloCycle to reveal speed differences in regionally defined progenitors and Perturb-seq gene knockdowns. Overall, VeloCycle expands the single-cell RNA sequencing analysis toolkit with a modular and statistically consistent RNA velocity inference framework.

Nonlinear dynamics of continuous steady-state tunable mechanical metamaterials based on planetary gears

Mechanical metamaterials with tunable mechanical properties have received extensive attention. In this work, a continuous steady-state metamaterial with tunable mechanical based on planetary gear cells is designed. Firstly, the excellent tunable properties of metamaterials are studied, which shows the designed metamaterials has a wide range of programmable stiffness and a significantly tunning band gap. The configuration relationship between tunability and structural parameters is analyzed. Then, a rigid-flexible coupling nonlinear dynamic model of planetary gear metamaterials is established and the dynamic characteristics of planetary gear metamaterials in the process of dynamic tunning are explored by numerical simulation. Moreover, the distribution characteristics of the system vibration response with the coupling parameter plane are disclosed, and the influence of the system dynamic parameters on its bifurcation characteristics and stability under coupling excitation is explored. Furthermore, an improved non-iterative cell mapping method is used to analyze the dependence of the vibration response of the system on the initial conditions. This work shows that the planetary gear metamaterials have a wide range of stiffness tunability and significantly variable band gap interval. Under the influences of internal and external excitations, the system exhibits various dynamic characteristics. The dynamic characteristics of flexible construction are mainly affected by structural parameters, and the dynamic characteristics of rigid construction are affected by multiple sets of coupling parameters and initial conditions.

Joint Bayesian estimation of process and measurement noise statistics in nonlinear Kalman filtering

Bayesian filtering aims at sequentially estimating the states and parameters in nonlinear dynamical systems, and finds applications in a variety of engineering fields. Extended and unscented Kalman filter are popular choices for this purpose as they typically achieve a good trade-off between computational complexity and accuracy, while still quantifying posterior uncertainty. However, the accuracy of the identified states and parameters, both in terms of their posterior mean and variance, is heavily influenced by the assumed statistics of both the process and measurement noise terms. Therefore, learning the noise characteristics becomes an essential aspect of Bayesian filtering, but is non-trivial especially in cases where process and measurement noise statistics are jointly non-identifiable. This article proposes a methodology that decomposes measurement and process noise learning in a fully Bayesian setting. For measurement noise estimation, we improve upon a Bayesian method that leverages conjugacy of the inverse-Wishart distribution with respect to the Gaussian likelihood model. For process noise estimation, Bayesian model averaging is coupled with a mutation scheme to compare the performance of competing models while exploring high-probability regions in the space of the unknown process noise variance. The algorithm is first tested on simple numerical models for both state estimation and parameter learning, highlighting the superior accuracy of the proposed measurement noise correction and the benefits of decoupling process and measurement noise learning in non-identifiable settings. Then we demonstrate the usefulness of this algorithm in more challenging problems, namely identification of a multi-degree-of-freedom system under unmeasured excitation, and modeling of the highly nonlinear response of a full-scale bridge pier using experimental data.

3D Chaotic Nonlinear Dynamic Population-Growing Mathematical System Modeling with Multiple Controllers

Modeling, stabilization, and identification processes are significant stages in the process of developing knowledge about chaotic dynamical systems which entail the effective prediction depending on the degree of uncertainty toleration in the forecast, accuracy of the current state to be measured as well as a time scale resting on the dynamics of the system. Control of under-activated dynamical systems has been considered substantially, and it is for periods and is currently developing in various domains such as biology, data analysis, computing systems, and so forth. Dynamic systems of growing population signifies a model describing the way a population evolves over time during which population goes through major life events, split into discrete time periods. The size of the population at a given time period is determined by the rate of growth as well as other related factors. Most progress has been made in model-based control theory, which has drawbacks when the system under consideration is exceedingly complicated, and no model can be constructed. Accordingly, a 3D-discrete and dynamic human population growth system with many controllers is proposed by examining the stability and symmetry of controller system clarifications. The symmetric stability control results are presented by considering a special parametric dynamic system in its coefficients besides suggesting periodic functional coefficients in terms of sin and cos functions. The controllers have the ability to reduce population growth rate unpredictability or enhance system stability under various external conditions. The unique and very effective strategies in relevant domains could provide a deeper understanding of their impact as well as the theoretical or technological innovations thereof. These controllers are capable of reducing population growth rate unpredictability or improving system stability under various external conditions, and applicable strategies in the relevant domains can provide profound comprehension over the impact along with the theoretical as well as technological advancements.

An Exact Theory of Causal Emergence for Linear Stochastic Iteration Systems.

After coarse-graining a complex system, the dynamics of its macro-state may exhibit more pronounced causal effects than those of its micro-state. This phenomenon, known as causal emergence, is quantified by the indicator of effective information. However, two challenges confront this theory: the absence of well-developed frameworks in continuous stochastic dynamical systems and the reliance on coarse-graining methodologies. In this study, we introduce an exact theoretic framework for causal emergence within linear stochastic iteration systems featuring continuous state spaces and Gaussian noise. Building upon this foundation, we derive an analytical expression for effective information across general dynamics and identify optimal linear coarse-graining strategies that maximize the degree of causal emergence when the dimension averaged uncertainty eliminated by coarse-graining has an upper bound. Our investigation reveals that the maximal causal emergence and the optimal coarse-graining methods are primarily determined by the principal eigenvalues and eigenvectors of the dynamic system's parameter matrix, with the latter not being unique. To validate our propositions, we apply our analytical models to three simplified physical systems, comparing the outcomes with numerical simulations, and consistently achieve congruent results.

REACT: Autonomous intrusion response system for intelligent vehicles

Autonomous and connected vehicles are rapidly evolving, integrating numerous technologies and software. This progress, however, has made them appealing targets for cybersecurity attacks. As the risk of cyber threats escalates with this advancement, the focus is shifting from solely preventing these attacks to also mitigating their impact. Current solutions rely on vehicle security operation centers, where attack information is analyzed before deciding on a response strategy. However, this process can be time-consuming and faces scalability challenges, along with other issues stemming from vehicle connectivity. This paper proposes a dynamic intrusion response system integrated within the vehicle. This system enables the vehicle to respond to a variety of incidents almost instantly, thereby reducing the need for interaction with the vehicle security operation center. The system offers a comprehensive list of potential responses, a methodology for response evaluation, and various response selection methods. The proposed solution was implemented on an embedded platform. Two distinct cyberattack use cases served as the basis for evaluating the system. The evaluation highlights the system’s adaptability, its ability to respond swiftly, its minimal memory footprint, and its capacity for dynamic system parameter adjustments. The proposed solution underscores the necessity and feasibility of incorporating dynamic response mechanisms in smart vehicles. This is a crucial factor in ensuring the safety and resilience of future smart mobility.

Least Squares Estimation of Multifactor Uncertain Differential Equations with Applications to the Stock Market

Multifactor uncertain differential equations are powerful tools for studying dynamic systems under multi-source noise. A key challenge in this study is how to accurately estimate unknown parameters based on the framework of uncertainty theory in multi-source noise environments. To address this core problem, this paper innovatively proposes a least-squares estimation method. The essence of this method lies in constructing statistical invariants with a symmetric uncertainty distribution based on observational data and determining specific parameters by minimizing the distance between the population distribution and the empirical distribution of the statistical invariant. Additionally, two numerical examples are provided to help readers better understand the practical operation and effectiveness of this method. In addition, we also provide a case study of JD.com’s stock prices to illustrate the advantages of the method proposed in this paper, which not only provides a new idea and method for addressing the problem of dynamic system parameter estimation but also provides a new perspective and tool for research and application in related fields.

A Novel Path-Following Method for Time-Varying Optimizations with Optimal Parametric Functions

We address a broad category of nonlinear constrained optimization problems. We then reformulate it as a time-varying optimization using continuous-time parametric functions and derive a dynamical system to track the respective optimal solution. We then re-parameterize the dynamical system according to a linear combination of parametric functions. By applying the calculus of variations, we optimize these parametric functions to minimize the optimality distance. Consequently, we develop an iterative dynamic algorithm, termed as OP-TVO, to achieve efficient convergence to the solution. We compare the performance of the proposed algorithm with the prediction correction method (PCM) in terms of optimality and computational complexity. The results demonstrate that OP-TVO effectively competes with PCM for the given class of optimization problems, suggesting a promising alternative to PCM. This work also introduces a novel paradigm for solving parametric dynamic systems.

Bayesian Parameter Estimation of Vibrating Systems via Physics-Based Biases from Neural Networks

Often, Structural Health Monitoring (SHM) campaigns draw damage-identifiers from vibration-based monitoring data. One of the downstream tasks of vibration-based SHM is that of system identification, i.e., inference of a model which is able to describe the system. For vibration-based monitoring, such models often rely on partial-differential equation formulations, where the identification task may be tied to inference of the parameters of such models. The probabilistic nature of SHM incentivises the extraction of stochastic estimates of these parameters, allowing for propagation of uncertainties associated to measurement noise or model imprecision. Common approaches to generating such stochastic estimates require an assumption on the shape and independence of the posterior distributions. To circumvent these assumptions, the Hamiltonian Monte-Carlo (HMC) sampling approach simulates the posterior distribution, allowing for freedom in the posterior. However, this requires intensive computational effort, especially when the governing equations have increased complexities, such as nonlinearities. Physics-informed neural networks (PINNs) utilise physics-based objective functions in the form of known PDEs, exploiting the automatic differentiation of NN architectures. This implies that additional terms in the PDE, such as nonlinearities, or boundary conditions can be accounted for. When the domain of observations encapsulates the collocation domain of the PINN, they can be exploited for parameter identification, by optimising over these parameters in addition to the network weights. However, classic objective functions in the form of mean-squared-norms underperform on noisy data, as a consequence of their deterministic nature. In this work, PINNs are combined with a HMC sampler to estimate the posterior distribution of the parameters of dynamic systems with noisy measurements. Multiple types of dynamic systems are simulated, varying the system complexity in terms of type and strength, and with different levels of noise. The results are assessed against the known values, and the codependent posterior distributions of each system are discussed.

Hybrid passive vibration control of lightweight manipulators

Passive vibration control methods in the literature are known to be highly sensitive to dynamic system parameters and are generally applied one by one. Therefore, their effectiveness in suppressing vibration control is limited. In this work, hybrid passive control (HPC) by integrating the Posicast control (PC) and the motion parameters-based control (MPC) is developed to suppress the during-motion vibrations (DMV) and residual vibrations (RV) of a single-link lightweight manipulator with a payload. PC is designed as a three-step cycle using the first natural frequency and damping ratio of the manipulator. MPC is designed by determining the time parameters of the motion profiles based on the first natural frequency of the manipulator. HPC simulations are performed on MATLAB, creating a Simscape model of the manipulator. Then, the proposed control method is tested in experiments. The prepared hybrid motion inputs actuate the servomotor while the displacements are measured, using a laser sensor at the tip of the manipulator. DMV and RV responses and their RMS values reveal that suppressing the vibration amplitudes efficiently. MPC is mostly effective in eliminating RV, whereas PC is sensitive to DMV as well. HPC combines these methods by eliminating their disadvantages and highlighting their advantages. Moreover, it is also successful in cases where the deceleration time of the trapezoidal input signal is single times half of the natural period, unlike MPC.

An Adaptive Method Based on Local Dynamic Mode Decomposition for Parametric Dynamical Systems

An Adaptive Method Based on Local Dynamic Mode Decomposition for Parametric Dynamical Systems

An information field theory approach to Bayesian state and parameter estimation in dynamical systems

Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable the seamless fusion of different experimental modalities. When the dynamics are discrete and stochastic, one may employ powerful techniques such as Kalman, particle, or variational filters. Practitioners commonly apply these methods to continuous-time, deterministic dynamical systems after discretizing the dynamics and introducing fictitious transition probabilities. However, approaches based on time-discretization suffer from the curse of dimensionality since the number of random variables grows linearly with the number of time-steps. Furthermore, the introduction of fictitious transition probabilities is an unsatisfactory solution because it increases the number of model parameters and may lead to inference bias. To address these drawbacks, the objective of this paper is to develop a scalable Bayesian approach to state and parameter estimation suitable for continuous-time, deterministic dynamical systems. Our methodology builds upon information field theory. Specifically, we parameterize the dynamical system state path using a linear basis. Then, we construct a physics-informed prior probability measure for the coefficients of the linear basis such that functions that satisfy the physics are more likely. This prior allows us to quantify model form errors. We connect the system's response to observations through a probabilistic model of the measurement process. The joint posterior over the system responses and all parameters is given by Bayes' rule. To approximate the intractable posterior, we develop a stochastic variational inference algorithm. In summary, the developed methodology offers a powerful framework for Bayesian estimation in dynamical systems.

Adaptive Iterative Learning Constrained Control for Linear Motor-Driven Gantry Stage with Fault-Tolerant Non-Repetitive Trajectory Tracking

This article introduces an adaptive fault-tolerant control method for non-repetitive trajectory tracking of linear motor-driven gantry platforms under state constraints. It provides a comprehensive solution to real-world issues involving state constraints and actuator failures in gantry platforms, alleviating the challenges associated with precise modeling. Through the integration of iterative learning and backstepping cooperative design, this method achieves system stability without requiring a priori knowledge of system dynamic models or parameters. Leveraging a barrier composite energy function, the proposed controller can effectively regulate the stability of the controlled system, even when operating under state constraints. Instability issues caused by actuator failures are properly addressed, thereby enhancing controller robustness. The design of a trajectory correction function further extends applicability. Experimental validation on a linear motor-driven gantry platform serves as empirical evidence of the effectiveness of the proposed method.

Analysis of Dynamic Systems Through Artificial Neural Networks

Parameter identification techniques for linear and nonlinear dynamic systems currently show a clear orientation toward black box models, with Artificial Neural Networks occupying a prominent place there. This paper presents a procedure for identifying linear dynamic systems parameters in two stages: in the first, a regressive model is fitted from the excitation and response time records, and in the second, its parameters are identified (matrixes of stiffness and damping) and dynamic characteristics (vibration frequencies and modes) based on the previous model. Artificial Neural Networks of the Adaline type and multilayer Perceptions are used for the first stage. The second stage is fully formulated through matrix algebra, which facilitates its systematic implementation and makes it independent of the complexity or dimension of the studied system. The proposed procedure is intended to operate from experimental records, so special attention is paid to the sensitivity of the results to the data interval and noise in the input signals. For the latter, various noise levels were incorporated into the correct responses obtained under ideal conditions, which respond to Gaussian distribution functions with a null mean and specified standard deviation. The proposed procedure justification, the results with the regressive models, and a study of the sensitivity of the results to the variation in the available data quality are presented.

Exploring Simplicity Bias in 1D Dynamical Systems.

Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input-output maps. This phenomenon is known as simplicity bias. By viewing the parameters of dynamical systems as inputs, and the resulting (digitised) trajectories as outputs, we study simplicity bias in the logistic map, Gauss map, sine map, Bernoulli map, and tent map. We find that the logistic map, Gauss map, and sine map all exhibit simplicity bias upon sampling of map initial values and parameter values, but the Bernoulli map and tent map do not. The simplicity bias upper bound on the output pattern probability is used to make a priori predictions regarding the probability of output patterns. In some cases, the predictions are surprisingly accurate, given that almost no details of the underlying dynamical systems are assumed. More generally, we argue that studying probability-complexity relationships may be a useful tool when studying patterns in dynamical systems.

Parameters online identification‐based data‐driven backstepping control of hypersonic vehicles

SummaryThe control problem of the hypersonic vehicles is studied in this article. A new control approach is presented. This approach consists of a data‐driven dynamic model established by multiple neural networks, an online identification method for system parameters, and a basic backstepping controller. The implementation of this approach requires a dynamic model and system parameters including the moment of inertia and aerodynamic parameters of the hypersonic vehicles. The parameter identification problem is regarded as a dynamic optimization process. The loss function is designed by the Lagrange criterion, and its constraints are determined by the physical and the numerical values. In the case of model mutation, the system parameters identified online are used as the nominal values of the output of the neural network in the data‐driven model to adjust the controller through its gradient descent. Simulation comparisons are given to show the effectiveness of the proposed data‐driven approach.