Consecutive Time Steps Research Articles

Long-time gap crowd prediction using time series deep learning models with two-dimensional single attribute inputs

Crowd prediction is a crucial aspect of modern life with innumerable applications. By predicting future human occupancy in advance, crowd prediction can support the decision-making processes of facility stakeholders, e.g., the campus operator can schedule facility maintenance during the period of lowest pedestrian flow to eliminate any disturbance. Conventional crowd prediction utilizes statistical models and rule-based data mining techniques, which are tedious in data processing and error-prone. Hence, this study formulates crowd prediction into a time-series analysis based on deep learning. Despite its wide adaptability in various research fields, deep learning-based time series analysis is seldom adopted in crowd prediction. There are two major limitations in previous studies: firstly, the prediction accuracy notably degrades with increased prediction length, and secondly only the temporal pattern along a single time dimension is exploited, i.e., the consecutive time steps in the most recent input data. Therefore, a Long-Time Gap Two-Dimensional method, entitled LT2D-method, is proposed to increase the crowd prediction length of with high accuracy. The LT2D-method is composed of two parts, (1) long-time gap prediction, which extends the prediction length to 240 time steps (1 day) with high accuracy, and (2) 2D inputs method, which exploits the prior knowledge from different time dimensions to further improve the prediction accuracy of long-time gap prediction. The proposed LT2D-method can be generally adapted to deep learning models, such as LSTM, BiLSTM, and GRU, to improve the prediction accuracy. By incorporating the proposed LT2D-method into different baseline models, the accuracy is generally improved by around 22%, demonstrating the robustness and generalizability of our method.

Sequential convex programming approach for real-time guidance during the powered descent phase of mars landing missions

• The main contribution of this study is the development of a new sequential-convex-programming-based technique that can periodically update the real-time guidance solution in consideration of the minimum-fuel Mars powered descent guidance problem with free final time. • To illustrate the validity of the proposed strategy for on-board real-time applications, an on-board test was conducted using the GR740, which is the processor of choice for the next-generation on-board computers of the European Space Agency (ESA) and Korea Aerospace Research Institute (KARI). • To assess the performance of the strategy, numerical simulations were conducted under various conditions. • Furthermore, the results of Monte Carlo simulations revealed that the proposed strategy is adequately robust against environmental and systematic disturbances. An on-board guidance generation approach for Mars pinpoint landing has been developed based on sequential convex programming. To optimize the flight time in the formulation, a discretized form of the landing problem was constructed under the conditions of linearized states, controls, and time increment between consecutive time steps. To implement this strategy in real time, on-board demonstrations were conducted with the GR740, which is the next-generation on-board processor of choice for the European Space Agency. The total number of time steps was determined based on the results of these demonstrations. The numerically simulated results also indicate that the solution obtained via the proposed strategy is close to the optimized GPOPS-II solution under the condition of no disturbance. Even under disturbances such as navigation errors, initial prediction errors, and perturbation forces, the proposed strategy ensures that the spacecraft reaches its target position with near-optimal fuel consumption.

Three-dimensional imaging of swirled spray injection in a generic aero engine burner under realistic operating conditions

Tomographic shadowgraph imaging is applied to reconstruct the instantaneous three-dimensional spray field immediately downstream of a generic aero engine fuel injector. Within the swirl passage of the injector model, a single kerosene jet undergoes air-blast atomization in a cross-flow configuration at Weber numbers of text {We}=360-770, air pressures of p_a=4-7,text{ bar } and air temperatures of T_a=440-570,text{ K }. High-speed, high magnification shadowgraphy is used to visualize the initial fuel atomization stages within the fuel injector before the spray enters the spray chamber. The 4-camera tomographic measurement setup is described in detail and includes a depth-of-field analysis with respect to droplet size based on Mie simulations and calibration data of the point-spread function. For a volume size of 16times 13times 10,text{ mm}^3 , the smallest resolvable droplet diameter is estimated to be d=10,mu text{ m } within the focal plane and increases to d approx 20,mu text{ m } toward the edges of the volume. Droplet velocities above the resolution limit were retrieved by 3-d cross-correlation of two volumetric reconstructions recorded at two consecutive time-steps. This is accompanied by an error analysis on the random error dependency on the camera viewing geometry. The results indicate increasing motion and fluctuations of the spray tail with increasing temperature and Weber number. Validation against PDA data further downstream of the burner plate revealed consistency for size classes d=10,mu text{ m } and d=15,mu text{ m }. Deviations from PDA occur in regions with strong velocity gradients due to different spatial resolutions, the presence of reconstruction ambiguities (ghost particles), uncertainties inherent to the two-frame cross-correlation of spray volumes and the finite LED pulse duration.Graphical

Reconstructing Unsteady Flow Data From Representative Streamlines via Diffusion and Deep-Learning-Based Denoising.

We propose VFR-UFD, a new deep learning framework that performs vector field reconstruction (VFR) for unsteady flow data (UFD). Given integral flow lines (i.e., streamlines), we first generate low-quality UFD via diffusion. VFR-UFD then leverages a convolutional neural network to reconstruct spatiotemporally coherent, high-quality UFD. The core of VFR-UFD lies in recurrent residual blocks that iteratively refine and denoise the input vector fields at different scales, both locally and globally. We take consecutive time steps as input to capture temporal coherence and apply streamline-based optimization to preserve spatial coherence. To show the effectiveness of VFR-UFD, we experiment with several vector field data sets to report quantitative and qualitative results and compare VFR-UFD with two VFR methods and one compression algorithm.

Multi-objective optimization algorithm based on characteristics fusion of dynamic social networks for community discovery

The network structure exhibits a variety of changes over time. Fusing this structure and the development of communities in dynamic networks plays an important role in analyzing the evolution and development of the entire network. How to ensure the division of the community structure in social network big data, as well as ensure the continuity of the community between the current time and previous time period, are issues that need to be explored. This problem can be solved by fusing the three characteristics of temporal variability, stability, and continuity in dynamic social network communities, and by adopting the multi-objective optimization method to detect community structures in dynamic networks. The probability fusion method is added to the initial step of the algorithm to generate suitable network partitions and ensure fast convergence and high accuracy. Two neighboring fusion strategies are proposed that are suitable for communities: the neighbor diversity strategy and the neighbor crowd strategy. These two strategies make different changes to the candidate network partitions. A continuity metric for dynamic community evolution is formulated to compare the similarity of the dynamic network communities of two consecutive time steps. Experiments on synthetic datasets and actual datasets prove that the proposed method in this paper provides better performance than existing methods.

Typical periods or typical time steps? A multi-model analysis to determine the optimal temporal aggregation for energy system models

Energy system models are challenged by the need for high temporal and spatial resolutions in order to appropriately depict the increasing share of intermittent renewable energy sources, storage technologies, and the growing interconnectivity across energy sectors.This study compares different temporal aggregation strategies, which reduce the number of considered time steps, to maintain computational viability of these models. The work focuses on the representation of time series by a subset of single time steps (i.e., typical time steps), or by groups of consecutive time steps (i.e., typical periods), which are commonly applied in the literature using clustering. We test these techniques for two different energy system models and benchmark the optimization results based on aggregation to those of the fully resolved models. Further, centroids and medoids are used to represent the clustered datasets and it is investigated whether the optimal aggregation method can be determined based on clustering indicators only.The results reveal that typical time steps consistently outperform typical periods with respect to clustering indicators, but do not lead to more accurate optimization results when applied to a model that takes numerous storage technologies into account. Although both aggregation techniques are capable of coupling the aggregated time steps, typical periods offer more options to depict storage operations, whereas typical time steps are more effective for models that neglect time-linking constraints. Further, this observation is independent from the choice of centroids or medoids to represent the clustered time series.In summary, the adequate choice of aggregation methods strongly depends on the mathematical structure of the considered energy system optimization model, and a priori decisions of a sufficient temporal aggregation are only possible with good knowledge of the mathematical structure of the underlying optimization problem.

Forecasting Variation Trends of Stocks via Multiscale Feature Fusion and Long Short-Term Memory Learning

Forecasting stock price trends accurately appears a huge challenge because the environment of stock markets is extremely stochastic and complicated. This challenge persistently motivates us to seek reliable pathways to guide stock trading. While the Long Short-Term Memory (LSTM) network has the dedicated gate structure quite suitable for the prediction based on contextual features, we propose a novel LSTM-based model. Also, we devise a multiscale convolutional feature fusion mechanism for the model to extensively exploit the contextual relationships hidden in consecutive time steps. The significance of our designed scheme is twofold. (1) Benefiting from the gate structure designed for both long- and short-term memories, our model can use the given stock history data more adaptively than traditional models, which greatly guarantees the prediction performance in financial time series (FTS) scenarios and thus profits the prediction of stock trends. (2) The multiscale convolutional feature fusion mechanism can diversify the feature representation and more extensively capture the FTS feature essence than traditional models, which fairly facilitates the generalizability. Empirical studies conducted on three classic stock history data sets, i.e., S&P 500, DJIA, and VIX, demonstrated the effectiveness and stability superiority of the suggested method against a few state-of-the-art models using multiple validity indices. For example, our method achieved the highest average directional accuracy (around 0.71) on the three employed stock data sets.

Shake-The-Box particle tracking with variable time-steps in flows with high velocity range (VT-STB)

We present a novel evaluation mode for Lagrangian Particle Tracking methods in general, applied to the Shake-The-Box method specifically. The aim is to attain high levels of accuracy and a removal of false (‘ghost’) tracks in flow situations, where significant amounts of particles show small relative movement with respect to each other in consecutive time-steps. An iterative approach using variable time separations is employed, which starts by tracking particles at high timeseparations, followed by an iterative reduction of time separation, while feeding the particle tracked within the previous iterations. The process allows for applying tracking parameters fine-tuned to the different flow regimes tracked within each iteration. Experimental validation was performed using a dataset on impinging jet flow, created in collaboration with the School of Mechanical Engineering of Pusan National University. Evaluation of this flow with high velocity range shows distinct advantages in reduction of ghost tracks and in tracking accuracy.

Sentinel-1 Backscatter Analysis and Radiative Transfer Modeling of Dense Winter Wheat Time Series

This study evaluates a temporally dense VV-polarized Sentinel-1 C-band backscatter time series (revisit time of 1.5 days) for wheat fields near Munich (Germany). A dense time series consisting of images from different orbits (varying acquisition) is analyzed, and Radiative Transfer (RT)-based model combinations are adapted and evaluated with the use of radar backscatter. The model shortcomings are related to scattering mechanism changes throughout the growth period with the use of polarimetric decomposition. Furthermore, changes in the RT modeled backscatter results with spatial aggregation from the pixel to field scales are quantified and related to the sensitivity of the RT models, and their soil moisture output are quantified and related to changes in backscatter. Therefore, various (sub)sets of the dense Sentinel-1 time series are analyzed to relate and quantify the impact of the abovementioned points on the modeling results. The results indicate that the incidence angle is the main driver for backscatter differences between consecutive acquisitions with various recording scenarios. The influence of changing azimuth angles was found to be negligible. Further analyses of polarimetric entropy and scattering alpha angle using a dual polarimetric eigen-based decomposition show that scattering mechanisms change over time. The patterns analyzed in the entropy-alpha space indicate that scattering mechanism changes are mainly driven by the incidence angle and not by the azimuth angle. Besides the analysis of differences within the Sentinel-1 data, we analyze the capability of RT model approaches to capture the observed Sentinel-1 backscatter changes due to various acquisition geometries. For this, the surface models “Oh92” or “IEM_B” (Baghdadi’s version of the Integral Equation Method) are coupled with the canopy model “SSRT” (Single Scattering Radiative Transfer). To resolve the shortcomings of the RT model setup in handling varying incidence angles and therefore the backscatter changes observed between consecutive time steps of a dense winter wheat time series, an empirical calibration parameter (coef) influencing the transmissivity (T) is introduced. The results show that shortcomings of simplified RT model architectures caused by handling time series consisting of images with varied incidence angles can be at least partially compensated by including a calibration coefficient to parameterize the modeled transmissivity for the varying incidence angle scenarios individually.

A θ-finite difference scheme based on cubic B-spline quasi-interpolation for the time fractional Cattaneo equation with Caputo–Fabrizio operator

In this paper, a θ-finite difference scheme based on cubic B-spline quasi-interpolation has been derived for the solution of time fractional Cattaneo equation. The fractional derivative of the mentioned equation has been described in the Caputo–Fabrizio sense. Time fractional derivative is approximated by a scheme of order . The spatial second derivative in two consecutive time steps has been approximated using the second derivative of the cubic B-spline quasi-interpolation. For this scheme, the Fourier analysis method is used to discuss the stability and convergence. It has also been shown that the method is the convergence of order . Finally, five numerical examples have been illustrated to verify the efficiency and high accuracy of the proposed scheme.

Sliding window temporal graph coloring

Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static graphs, which often stand in contrast to practice where data is inherently dynamic. A temporal graph has an edge set that changes over time. We present a natural temporal extension of the classical graph coloring problem. Given a temporal graph and integers k and Δ, we ask for a coloring sequence with at most k colors for each vertex such that in every time window of Δ consecutive time steps, in which an edge is present, this edge is properly colored at least once. We thoroughly investigate the computational complexity of this temporal coloring problem. More specifically, we prove strong computational hardness results, complemented by efficient exact and approximation algorithms.

Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods

We present a posteriori error estimates for inconsistent and non-hierarchical Galerkin methods for linear parabolic problems, allowing them to be used in conjunction with very general mesh modification for the first time. We treat schemes which are non-hierarchical in the sense that the spatial Galerkin spaces between time-steps may be completely unrelated from one another. The practical interest of this setting is demonstrated by applying our results to finite element methods on moving meshes and using the estimators to drive an adaptive algorithm based on a virtual element method on a mesh of arbitrary polygons. The a posteriori error estimates, for the error measured in the [Formula: see text] and [Formula: see text] norms, are derived using the elliptic reconstruction technique in an abstract framework designed to precisely encapsulate our notion of inconsistency and non-hierarchicality and requiring no particular compatibility between the computational meshes used on consecutive time-steps, thereby significantly relaxing this basic assumption underlying previous estimates.

Causal Mechanism Transfer Network for Time Series Domain Adaptation in Mechanical Systems

Data-driven models are becoming essential parts in modern mechanical systems, commonly used to capture the behavior of various equipment and varying environmental characteristics. Despite the advantages of these data-driven models on excellent adaptivity to high dynamics and aging equipment, they are usually hungry for massive labels, mostly contributed by human engineers at a high cost. Fortunately, domain adaptation enhances the model generalization by utilizing the labeled source data and the unlabeled target data. However, the mainstream domain adaptation methods cannot achieve ideal performance on time series data, since they assume that the conditional distributions are equal. This assumption works well in the static data but is inapplicable for the time series data. Even the first-order Markov dependence assumption requires the dependence between any two consecutive time steps. In this article, we assume that the causal mechanism is invariant and present our Causal Mechanism Transfer Network (CMTN) for time series domain adaptation. By capturing causal mechanisms of time series data, CMTN allows the data-driven models to exploit existing data and labels from similar systems, such that the resulting model on a new system is highly reliable even with limited data. We report our empirical results and lessons learned from two real-world case studies, on chiller plant energy optimization and boiler fault detection, which outperform the existing state-of-the-art method.

A time-varying parameter estimation approach using split-sample calibration based on dynamic programming

Abstract. Although the parameters of hydrological models are usually regarded as constant, temporal variations can occur in a changing environment. Thus, effectively estimating time-varying parameters becomes a significant challenge. Two methods, including split-sample calibration (SSC) and data assimilation, have been used to estimate time-varying parameters. However, SSC is unable to consider the parameter temporal continuity, while data assimilation assumes parameters vary at every time step. This study proposed a new method that combines (1) the basic concept of split-sample calibration, whereby parameters are assumed to be stable for one sub-period, and (2) the parameter continuity assumption; i.e. the differences between parameters in consecutive time steps are small. Dynamic programming is then used to determine the optimal parameter trajectory by considering two objective functions: maximization of simulation accuracy and maximization of parameter continuity. The efficiency of the proposed method is evaluated by two synthetic experiments, one with a simple 2-parameter monthly model and the second using a more complex 15-parameter daily model. The results show that the proposed method is superior to SSC alone and outperforms the ensemble Kalman filter if the proper sub-period length is used. An application to the Wuding River basin indicates that the soil water capacity parameter varies before and after 1972, which can be interpreted according to land use and land cover changes. A further application to the Xun River basin shows that parameters are generally stationary on an annual scale but exhibit significant changes over seasonal scales. These results demonstrate that the proposed method is an effective tool for identifying time-varying parameters in a changing environment.

Tracking Turbulent Coherent Structures by Means of Neural Networks

The behaviours of individual flow structures have become a relevant matter of study in turbulent flows as the computational power to allow their study feasible has become available. Especially, high instantaneous Reynolds Stress events have been found to dominate the behaviour of the logarithmic layer. In this work, we present a viability study where two machine learning solutions are proposed to reduce the computational cost of tracking such structures in large domains. The first one is a Multi-Layer Perceptron. The second one uses Long Short-Term Memory (LSTM). Both of the methods are developed with the objective of taking the the structures’ geometrical features as inputs from which to predict the structures’ geometrical features in future time steps. Some of the tested Multi-Layer Perceptron architectures proved to perform better and achieve higher accuracy than the LSTM architectures tested, providing lower errors on the predictions and achieving higher accuracy in relating the structures in the consecutive time steps.

Identifying and tracking bubbles and drops in simulations: A toolbox for obtaining sizes, lineages, and breakup and coalescence statistics

Knowledge of bubble and drop size distributions in two-phase flows is important for characterizing a wide range of phenomena, including combustor ignition, sonar communication, and cloud formation. The physical mechanisms driving the background flow also drive the time evolution of these distributions. Accurate and robust identification and tracking algorithms for the dispersed phase are necessary to reliably measure this evolution and thereby quantify the underlying mechanisms in interface-resolving flow simulations. The identification of individual bubbles and drops traditionally relies on an algorithm used to identify connected regions. This traditional algorithm can be sensitive to the presence of spurious structures. A cost-effective refinement is proposed to maximize volume accuracy while minimizing the identification of spurious bubbles and drops. An accurate identification scheme is crucial for distinguishing bubble and drop pairs with large size ratios. The identified bubbles and drops need to be tracked in time to obtain breakup and coalescence statistics that characterize the evolution of the size distribution, including breakup and coalescence frequencies, and the probability distributions of parent and child bubble and drop sizes. An algorithm based on mass conservation is proposed to construct bubble and drop lineages using simulation snapshots that are not necessarily from consecutive time steps. These lineages are then used to detect breakup and coalescence events, and obtain the desired statistics. Accurate identification of large-size-ratio bubble and drop pairs enables accurate detection of breakup and coalescence events over a large size range. Accurate detection of successive breakup and coalescence events requires that the snapshot interval be an order of magnitude smaller than the characteristic breakup and coalescence times to capture these successive events while minimizing the identification of repeated confounding events. Together, these algorithms serve as a toolbox for detailed analysis of two-phase simulations, and enable insights into the mechanisms behind bubble and drop formation and evolution in flows of practical importance.

Anomaly detection of structural health monitoring data using the maximum likelihood estimation-based Bayesian dynamic linear model

Enormous data are continuously collected by the structural health monitoring system of civil infrastructures. The structural health monitoring data inevitably involve anomalies caused by sensors, transmission errors, or abnormal structural behaviors. It is important to identify the anomalies and find their origin (e.g. sensor fault or structural damage) to make correct interventions. Moreover, online anomaly identification of the structural health monitoring data is critical for timely structural condition assessment and decision-making. This study proposes an online approach for detecting anomalies of the structural health monitoring data based on the Bayesian dynamic linear model. In particular, Bayesian dynamic linear model, consisting of various components, is implemented to characterize the feature of real-time measurements. Expectation maximization algorithm and Kalman smoother are combined to estimate the Bayesian dynamic linear model parameters and generate log-likelihood functions. The subspace identification method is introduced to overcome the initialization issue of the expectation maximization algorithm. The log-likelihood difference of consecutive time steps is then used to determine thresholds without introducing extra anomaly detectors. The proposed Bayesian dynamic linear model-based approach is first illustrated by the simulation data and then applied to the structural health monitoring data collected from two long-span bridges. The results indicate that the proposed method exhibits good accuracy and high computational efficiency and also allows for reconstructing the strain measurements to replace anomalies.

Extended Horizon ECMS Control of PHEVs With 2D Electricity Price Adaptation Policy

This article proposes new improvements to the ECMS-based control of plug-in hybrid electric vehicles (PHEVs) using macro-level trip forecast information. First, the dynamic programming (DP) optimization is applied to a power-split PHEV model to obtain the optimal powertrain trajectories for benchmarking the energy economy of the proposed controllers. An instantaneous energy cost minimization process is then formulated to compute the optimal mix of fuel and electricity, subject to the state and input constraints. To improve the speed and accuracy of the energy management system, the Nelder-Mead simplex search algorithm is used for the instantaneous optimizations. To account for the battery capacity limitation, an adaptive electricity pricing policy is introduced to control battery discharge rate based on the remaining trip distance, average speed, and elevation forecasts. The parameters of the proposed policy are optimized for a group of 5 urban and highway drive cycles to obtain a robust controller which can serve a wide spectrum of driving patterns. To further improve the energy economy, an extended-horizon optimization algorithm is proposed to account for control input transitions between consecutive time steps. Finally, a revised speed forecast formula is implemented during the low-SOC intervals to lift battery SOC ahead of high-demand periods. The combination of the proposed schemes enables reaching over 99% average optimality compared to a finely discretized DP optimization for the adopted drive cycles, and above 98% optimality for a test PHEV drive cycle.

Crack Propagation Velocity Determination by High-speed Camera Image Sequence Processing.

The determination of crack propagation velocities can provide valuable information for a better understanding of damage processes of concrete. The spatio-temporal analysis of crack patterns developing at a speed of several hundred meters per second is a rather challenging task. In the paper, a photogrammetric procedure for the determination of crack propagation velocities in concrete specimens using high-speed camera image sequences is presented. A cascaded image sequence processing which starts with the computation of displacement vector fields for a dense pattern of points on the specimen’s surface between consecutive time steps of the image sequence chain has been developed. These surface points are triangulated into a mesh, and as representations of cracks, discontinuities in the displacement vector fields are found by a deformation analysis applied to all triangles of the mesh. Connected components of the deformed triangles are computed using region-growing techniques. Then, the crack tips are determined using the principal component analysis. The tips are tracked in the image sequence and the velocities between the time stamps of the images are derived. A major advantage of this method as compared to the established techniques is in the fact that it allows spatio-temporally resolved, full-field measurements rather than point-wise measurements. Furthermore, information on the crack width can be obtained simultaneously. To validate the experimentation, the authors processed image sequences of tests on four compact-tension specimens performed on a split-Hopkinson tension bar. The images were taken by a high-speed camera at a frame rate of 160,000 images per second. By applying the developed image sequence processing procedure to these datasets, crack propagation velocities of about 800 m/s were determined with a precision in the order of 50 m/s.

Numerical simulation for a time-fractional coupled nonlinear Schrödinger equations

In this paper, we attempt to find an approximate solution of time-fractional coupled nonlinear Schrödinger equations (TFCNLS) through one of the meshless approach based on radial basis functions (RBFs) collocation. The time-fractional derivative is described in terms of the Caputo derivative. Discretizing the time-fractional derivative of the mentioned equation, we first use a scheme of order , and then the average value of the function in a consecutive time step is used for other terms. Also, we use the RBFs collocation method to approximate the spatial derivative. On the other hand, the stability analysis of the suggested scheme is investigated in a similar way to the classic von Neumann technique for TFCNLS equations. This present paper is to indicate that the meshfree methods are appropriate and reliable to obtain a numerical solution of fractional partial differential equations. This efficiency and accuracy of the present method are verified by solving two examples. We obtain the numerical results from solving this problem on the rectangular domain. All obtained numerical experiments are presented in tables and figures. Finally, it can be said that the main advantage of the mentioned scheme is that the algorithm is very simple and easy to apply.