Prediction Of Nonlinear Dynamics Research Articles

Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraint

Despite the success of various methods in addressing the issue of spatial reconstruction of dynamical systems with sparse observations, spatio-temporal prediction for sparse fields remains a challenge. Existing Kriging-based frameworks for spatio-temporal sparse field prediction fail to meet the accuracy and inference time required for nonlinear dynamic prediction problems. In this paper, we introduce the Dynamical System Prediction from Sparse Observations using Voronoi Tessellation (DSOVT) framework, an innovative methodology based on Voronoi tessellation which combines convolutional encoder–decoder (CED) and long short-term memory (LSTM) and utilizing Convolutional Long Short-Term Memory (ConvLSTM). By integrating Voronoi tessellations with spatio-temporal deep learning models, DSOVT is adept at predicting dynamical systems with unstructured, sparse, and time-varying observations. CED-LSTM maps Voronoi tessellations into a low-dimensional representation for time series prediction, while ConvLSTM directly uses these tessellations in an end-to-end predictive model. Furthermore, we incorporate physics constraints during the training process for dynamical systems with explicit formulas. Compared to purely data-driven models, our physics-based approach enables the model to learn physical laws within explicitly formulated dynamics, thereby enhancing the robustness and accuracy of rolling forecasts. Numerical experiments on real sea surface data and shallow water systems clearly demonstrate our framework’s accuracy and computational efficiency with sparse and time-varying observations.

Physics-Guided Neural Network Model for Aeroengine Control System Sensor Fault Diagnosis under Dynamic Conditions

Sensor health assessments are of great importance for accurately understanding the health of an aeroengine, supporting maintenance decisions, and ensuring flight safety. This study proposes an intelligent framework based on a physically guided neural network (PGNN) and convolutional neural network (CNN) to diagnose sensor faults under dynamic conditions. The strength of the approach is that it integrates information from physics-based performance models and deep learning models. In addition, it has the structure of prediction–residual–generation-fault classification that effectively decouples the interaction between sensor faults and system state changes. First, a PGNN generates the engine’s non-linear dynamic prediction output because the PGNN has the advantage of being able to handle temporal information from the long short-term memory (LSTM) network. We use a cross-physics–data fusion scheme as the prediction strategy to explore the hidden information of the physical model output and sensor measurement data. A novel loss function that considers physical discipline is also proposed to overcome the performance limitations of traditional data-driven models because of their physically inconsistent representations. Then, the predicted values of the PGNN are compared with the sensor measurements to obtain a residual signal. Finally, a convolutional neural network (CNN) is used to classify faults for residual signals and deliver diagnostic results. Furthermore, the feasibility of the proposed framework is demonstrated on an engine sensor fault dataset. The experimental results show that the proposed method outperforms the pure data-driven approach, with the predicted RMSE being reduced from 1.6731 to 0.9897 and the diagnostic accuracy reaching 95.9048%, thereby confirming its superior performance.

Bistable dynamics analysis using Padé approximation and resultant theory

The bistable structures are widely used for energy harvesting and have also received great attention for vibration isolation recently. The bistable dynamics analysis is a key step for the practical mechanism design, and the Taylor series is usually deployed to approximate the nonlinear irrational structure stiffness. However, the truncation order must be sufficiently high to receive a desirable accuracy since bistable structures can undergo large-amplitude inter-well oscillations. Alternatively, we apply the Padé approximation, which gives a higher accuracy but also a more involved dynamical equation. Combined with the harmonic balance method, a resultant-based analysis framework is accordingly proposed such that we are allowed to handle purely univariate polynomial equations to facilitate calculation. The analysis considers a classic nonlinear isolator structure equipped with three springs and two links without loss of generality, and the theoretical solutions of both the inter- and intra-well frequency responses and the associated jump frequencies are obtained agreeing well with the numerical results. Furthermore, the improved accuracy of the nonlinear dynamic predictions using the Padé approximation and the efficiency of the solving process using the proposed resultant-based algorithms are proved by numerical comparisons. This work presents a distinctive approach to analyzing bistable dynamics with higher accuracy while keeping the computational cost at a desirably low level, which provides a theory for the calculations and analysis of the more advanced and complicated bistable structures.

Causality Analysis and Risk Assessment of Haze Disaster in Beijing

Due to the lack of training data and effective haze disaster prediction model, the research on causality analysis and the risk prediction of haze disaster is mainly qualitative. In order to solve this problem, a nonlinear dynamic prediction model of Beijing haze disaster was built in this study. Based on the macroscopic evaluation of multiple influencing factors of haze disaster in Beijing, a causality model and flow diagrams of the Beijing crude oil consumption system, Beijing coal consumption system, Beijing urban greening system and sulfur dioxide emission system in Hebei and Tianjin were established. The risk prediction of Beijing haze disaster was simulated at different conditions of air pollutant discharge level for the Beijing–Tianjin–Hebei region. Compared with the governance strategies of vehicle emission reduction, petrochemical production emission reduction, coal combustion emission reduction, greening and reducing dust and collaborative governance policy, the Beijing–Tianjin–Hebei cross-regional collaborative governance policy was more effective in controlling the haze disaster of Beijing. In the prediction, from 2011 to 2017, the air quality of Beijing changed from light pollution to good. By 2017, the PM2.5 of Beijing reduced to 75 µg/m3. From 2017 to 2035, the control effect of urban haze disaster for Beijing further strengthened. By 2035, the PM2.5 of Beijing reduced to 35 μg/m3. Finally, the PM2.5 of Beijing continued to reduce from 2035 to 2050. The speed of reduction for PM2.5 in Beijing slowed down. Meanwhile, the achievements of haze control in Beijing were consolidated. By 2050, the risk of haze disaster for Beijing was basically solved. The nonlinear dynamic prediction model in this study provides better promise toward the future control and prediction of global haze disaster under the condition of limited data.

Deep learning based pulse prediction of nonlinear dynamics in fiber optics

The initial state of a nonlinear optical fiber system plays a vital role in the ultrafast pulse evolution dynamic. In this work, a data-driven compressed convolutional neural network, named inverse network, is proposed to predict initial pulse distribution through a series of discrete power profiles at different propagation distances. The inverse network is trained and tested based on two typical nonlinear dynamics: (1) the pulse evolution in a fiber optical parametric amplifier system and (2) soliton pair evolution in high-nonlinear fibers. Great prediction accuracy is reached when the epoch grows to 5000 in both cases, with the normalized root mean square errors below 0.01 on the entire testing set. Meanwhile, the lightweight network is highly effective. In this work, it takes approximately 30 seconds for 5,000 epochs training with a dataset size of 900. The inverse network is further tested and analyzed on the dataset with different signal-to-noise ratios and input sizes. The results show fair stability at the deviation on the testing set. The proposed inverse network demonstrates a promising approach to optimizing the initial pulse of fiber optics systems.

Measurement and prediction of nonlinear dynamics of a gas foil bearing supported rigid rotor system

Gas foil bearings (GFBs) provide reliable supporting force with low drag in high speed microturbomachinery system. The physical parameters of GFBs are important to determine the rotor system performance. Three gas foil journal bearings (GFJBs), with nominal clearances of 30, 40, and 65 μm measured through static load-deflection test, are used in rotordynamic coast down tests. Two groups of tests are designed, 30 μm GFJB in drive end in Test (a), 65 μm GFJB in drive end in Test (b), and share one 40 μm GFJB in both test groups. The bearing dynamic force coefficients calculated using the perturbation method show clear correlation with given nominal clearance magnitudes. Coast down tests from 40 krpm to rest show synchronous motion and evident subsynchronous whip motion in the two test groups. Nonlinear rotordynamic prediction is established with a simplified foil structure stiffness and loss factor model. The predictions demonstrate that the whip motion is largely determined by the foil structure properties. Synchronous motions are also predicted in the two prediction models and show good agreement with the test data. Moreover, the recorded increase in the bearing temperature was correlated with the rotational speeds and operational conditions of GFJBs. Smaller nominal radial clearance results in higher temperature rise. The measurements and predictions obtained indicate that radial clearance and foil structure significantly affect the rotordynamic performance of rotor GFJBs system and provide further insight into the radial clearance of GFBs.

Quantifying self-organization in fusion plasmas

A multifaceted framework for understanding self-organization in fusion plasma dynamics is presented which concurrently manages several important issues related to the nonlinear and multiscale phenomena involved, namely,(1) it chooses the optimal template wavelet for the analysis of temporal or spatio-temporal plasma dynamics, (2) it detects parameter values at which bifurcations occur, (3) it quantifies complexity and self-organization, (4) it enables short-term prediction of nonlinear dynamics, and (5) it extracts coherent structures in turbulence by separating them from the incoherent component. The first two aspects including the detection of changes in the dynamics of a nonlinear system are illustrated by analyzing Stimulated Raman Scattering in a bounded, weakly dissipative plasma. Self-organization in the fusion plasma is quantitatively analyzed based on the numerical simulations of the Gyrokinetic-Vlasov (GKV) model of plasma dynamics. The parameters for the standard and inward shifted magnetic configurations, relevant for the Large Helical Device, were used in order to quantitatively compare self-organization and complexity in the two configurations. Finally, self-organization is analyzed for three different confinement regimes of the MAST device.

Seismic Performance Evaluation of Existing RC Buildings Without Seismic Details. Comparison of Nonlinear Static Methods and IDA

The inelastic response of existing reinforced concrete (RC) buildings without seismic details is investigated, presenting the results from more than 1000 nonlinear analyses. The seismic performance is investigated for two buildings, a typical building form of the 60s and a typical form of the 80s. Both structures are designed according to the old Greek codes. These building forms are typical for that period for many Southern European countries. Buildings of the 60s do not have seismic details, while buildings of the 80s have elementary seismic details. The influence of masonry infill walls is also investigated for the building of the 60s. Static pushover and incremental dynamic analyses (IDA) for a set of 15 strong motion records are carried out for the three buildings, two bare and one infilled. The IDA predictions are compared with the results of pushover analysis and the seismic demand according to Capacity Spectrum Method (CSM) and N2 Method. The results from IDA show large dispersion on the response, available ductility capacity, behaviour factor and failure displacement, depending on the strong motion record. CSM and N2 predictions are enveloped by the nonlinear dynamic predictions, but have significant differences from the mean values. The better behaviour of the building of the 80s compared to buildings of the 60s is validated with both pushover and nonlinear dynamic analyses. Finally, both types of analysis show that fully infilled frames exhibit an improved behaviour compared to bare frames.

System dynamic modelling of industrial growth and landscape ecology in China

With the rapid development of large industrial corridors in China, the landscape ecology of the country is currently being affected. Therefore, in this study, a system dynamic model with multi-dimensional nonlinear dynamic prediction function that considers industrial growth and landscape ecology is developed and verified to allow for more sustainable development. Firstly, relationships between industrial development and landscape ecology in China are examined, and five subsystems are then established: industry, population, urban economy, environment and landscape ecology. The main influencing factors are then examined for each subsystem to establish flow charts connecting those factors. Consequently, by connecting the subsystems, an overall industry growth and landscape ecology model is established. Using actual data and landscape index calculated based on GIS of the Ha-Da-Qi industrial corridor, a typical industrial corridor in China, over the period 2005–2009, the model is validated in terms of historical behaviour, logical structure and future prediction, where for 84.8% of the factors, the error rate of the model is less than 5%, the mean error rate of all factors is 2.96% and the error of the simulation test for the landscape ecology subsystem is less than 2%. Moreover, a model application has been made to consider the changes in landscape indices under four industrial development modes, and the optimal industrial growth plan has been examined for landscape ecological protection through the simulation prediction results over 2015–2020.

Monte Carlo simulation of carbon nanotube nucleation and growth using nonlinear dynamic predictions

The computation time for Monte Carlo (MC) simulation of a nanostructure growth process was shown to be reduced by an order of magnitude compared to conventional atomistic and meso-scale models through the prediction of the structure evolution ahead of every growth step. This approach used to grow of one of the longest (∼194nm) reported carbon nanotubes (CNTs) from atomistic simulations. The key to the approach is the finding from simulation experiments that the CNT synthesis process exhibits nonlinear and recurring near-stationary dynamics.

Dynamic prediction of Chinese development based on the ecological footprint method

Ecological footprint (EF), as a physical indicator to measure the extent of humanity's use of natural resources, is one of the most successful methods used to assess sustainable development. This paper calculated the per capita EF and biocapacity (BC) of China from 1949 to 2008 and the fluctuant cycles of per capita EF and BC, which were decomposed and assessed based on empirical mode decomposition and nonlinear dynamic prediction models. We propose prediction scenarios and the results show that: (1) over the last 60 years, the per capita EF increasingly fluctuated while the per capita BC constantly reduced, and since 1985, China has had an aggregate ecological deficit (ED); (2) the business-as-usual scenario looked at the consequences if average annual change rates of per capita EF and BC are constant, where the per capita ED would be 3.9024 gha in 2030, a very grim situation for China; and (3) if the productivity of natural ecosystems increases by 10%, consumption of natural ecosystems and emission of CO2 and contamination could be reduced by 10% and per capita ED would be 1.5217 gha in 2030, then the potential for sustainable development will be much better than the business-as-usual scenario. Finally, some policy recommendations are presented, such as increased land productivity to meet growing demand, reducing over-consumption of resources to mitigate ecological overload, promoting resource-saving consumption and paying attention to international trade.

Long-term prediction of nonlinear hydrodynamics in bubble columns by using artificial neural networks

An artificial neural network (ANN) model was proposed for the long-term prediction of nonlinear dynamics underlying holdup fluctuations in bubble columns with three different diameters of 200, 400 and 800 mm. Local holdup fluctuations were measured with an optical probe in the bubble columns. The superficial gas velocity was varied in the range of 33–90 mm/s. The time intervals between successive bubbles were extracted from the time series of holdup fluctuations to represent hydrodynamic behaviors in the system and used as training and validation data sets. The effect of data preprocessing as well as the numbers of nodes in input and hidden layers on the ANN training behavior was systematically investigated. The prediction capability of the ANN was evaluated in terms of time-averaged characteristics, power spectra and Lyapunov exponents. It was observed that: the ANN model, which was trained with experimental time series and gas velocity, can be used for the long-term prediction of dynamic characteristics in bubble columns by using random data as the initial input. The results indicate that the trained ANN models have the potential of modeling nonlinear hydrodynamic behaviors in bubble columns.

Global quantitative predictions of complex laser dynamics.

We demonstrate unprecedented agreement between a theoretical two-dimensional bifurcation diagram and the corresponding experimental stability map of an optically injected semiconductor laser over a large range of relevant injection parameter values. The bifurcation diagram encompasses both local and global bifurcations mapping out regions of regular, chaotic, and multistable behavior in considerable detail. This demonstrates the power of dynamical systems modeling for the quantitative prediction of nonlinear dynamics and chaos of semiconductor lasers.