Time Step Intervals Research Articles

Bridge pier under coupled earthquake and wave - Current actions: Numerical model establishing, optimization and structural response analysis

Bridges located in earthquake-prone areas may be subjected to earthquake, wave and current actions simultaneously. Current investigations on bridge piers under these complex loading conditions were generally performed through underwater shaking table (UST) tests, which required advanced test setups and great expenses. With the aim of eliminating these limits and developing a comprehensive understanding of the performance of deep-water bridge piers under coupled earthquake and wave-current actions, the present study carried out systematic numerical investigations. Wave generation and propagation were first simulated, for which thorough sensitivity analysis was conducted to obtain the optimal parameters, including mesh size, time step intervals, damping zone length and damping coefficients. Numerical models which are able to simulate nonlinear wave-current interactions were then established and validated. Following this, structural responses of bridge piers under wave, wave-current and coupled earthquake and wave-current actions were numerically simulated and validated by test results. Finally, parametric analysis was conducted on a pile of a practical deep-water bridge in China using the validated model with consideration of various water depth levels, diverse wave heights, different current velocities, varied earthquakes and different peak ground accelerations to reveal the influence of different excitation parameters on structural responses.

Multi-Architecture Multi-Expert Diffusion Models

In this paper, we address the performance degradation of efficient diffusion models by introducing Multi-architecturE Multi-Expert diffusion models (MEME). We identify the need for tailored operations at different time-steps in diffusion processes and leverage this insight to create compact yet high-performing models. MEME assigns distinct architectures to different time-step intervals, balancing convolution and self-attention operations based on observed frequency characteristics. We also introduce a soft interval assignment strategy for comprehensive training. Empirically, MEME operates 3.3 times faster than baselines while improving image generation quality (FID scores) by 0.62 (FFHQ) and 0.37 (CelebA). Though we validate the effectiveness of assigning more optimal architecture per time-step, where efficient models outperform the larger models, we argue that MEME opens a new design choice for diffusion models that can be easily applied in other scenarios, such as large multi-expert models.

Mitigating vulnerability of a multimodal public transit system for sustainable megacities: a real-time operational control method

The multimodal public transit system (MPTS) has been recognized as a primary mobility support system for sustainable megacities. However, it is often vulnerable to various service disruptions, and the most severe circumstance is the interdependent cascading failures interacting among urban rail transit, bus transit, and road transit networks. The vulnerability of an MPTS against this severe failure, associated with extreme performances, limits the building of future resilient megacities. In this paper, a real-time operational control method based on the system emergency capability (SEC) is developed to block the dynamic unfolding paths of this severe failure considering network topology characteristics and dynamic evolution characteristics. This method is immediately available for real-time emergency control, while previous studies on qualitative optimization strategies cannot. Remarkably, a three-stage association design process is conducted to explore the most efficient SEC loading strategy, involved with multiple intertwined influential factors, including the target loading stations, loading time-step intervals, and loading interval length and loading strength. Finally, a case simulation is undertaken to indicate the adaptability of the proposed method. This work can provide critical insights into real-world emergency resource allocation and an underlying simulator with search direction knowledge for future intelligent algorithm-based optimal control.

Unsteady Heat Flux Measurement and Predictions Using Long Short-Term Memory Networks

Energy consumption modeling has evolved along with building technology. Modeling techniques can be largely classified into white box, gray box, and black box. In this study, the thermal behavior characteristics of building components were identified through time-series data analysis using LSTM neural networks. Sensors were installed inside and outside the test room to measure physical quantities. As a result of calculating the overall heat transfer coefficient according to the international standard ISO 9869-1, the U value of the multi-window with antireflection coating was 1.84 W/(m2∙K). To understand the thermal behavior of multiple windows, we constructed a neural network using an LSTM architecture and used the measured data-set to predict and evaluate the heat flux through deep learning. From the measurement data, a wavelet transform was used to extract features and to find appropriate control time-step intervals. Performance was evaluated according to multistep measurement intervals using the error metric method. The multistep time interval for control monitoring is preferably no more than 240 s. In addition, multivariate analysis with several input variables was performed. In particular, the thermal behavior of building components can be analyzed through heat flux and temperature measurements in the transient state of physical properties of pre-installed building components, which were difficult to access with conventional steady-state measurement methods.

Unique Observational Constraints on the Seasonal and Longitudinal Variability of the Earth’s Planetary Albedo and Cloud Distribution Inferred From EPIC Measurements

Thorough comparison to observations is key to developing a credible climate model forecasting capability. Deep Space Climate Observatory (DSCOVR) measurements of Earth’s reflected solar and emitted thermal radiation provide a unique observational perspective that permits a more reliable model/data comparison than is possible with the otherwise available satellite data. The uniqueness is in the DSCOVR satellite’s viewing geometry, which enables continuous viewing of the Earth’s sunlit hemisphere from its Lissajous orbit around the Lagrangian L1 point. The key instrument is the Earth Polychromatic Imaging Camera (EPIC), which views the Earth’s sunlit hemisphere with 1024-by-1024-pixel imagery in 10 narrow spectral bands from 317 to 780 nm, acquiring up to 22 high spatial resolution images per day. The additional feature is that the frequency of EPIC image acquisition is nearly identical to that of the climate GCM data generation scheme where climate data for the entire globe are ‘instantaneously’ calculated at 1-h radiation time-step intervals. Implementation of the SHS (Sunlit Hemisphere Sampling) EPIC-view geometry for the in-line GCM output data sampling establishes a precise self-consistency in the space-time data sampling between EPIC observational and GCM output data generation and sampling. The remaining problem is that the GCM generated data are radiative fluxes, while the EPIC measurements are backscatter-dependent radiances. Radiance to flux conversion is a complex problem with no simple way to convert GCM radiative fluxes into spectral radiances. The more expedient approach is to convert the EPIC spectral radiances into broadband radiances by MODIS/CERES-based regression relationships and then into solar radiative fluxes using the CERES angular distribution models. Averaging over the sunlit hemisphere suppresses the meteorological weather noise, but preserves the intra-seasonal larger scale variability. Longitudinal slicing by the Earth’s rotation permits a self-consistent model/data comparison of the longitudinal model/data differences in the variability of the reflected solar radiation. Ancillary EPIC Composite data provide additional cloud property information for climate model diagnostics. Comparison of EPIC-derived seasonal and longitudinal variability of the Earth’s planetary albedo with the GISS ModelE2 results shows systematic overestimate of cloud reflectivity over the Pacific Ocean with corresponding underestimates over continental land areas.

Study on Brain Plasticity of Music Training Based on Network Technology

Spectral wave models have experienced constant development and vast improvements over the past decades. They are constantly being extended and refined in order to cover the complex wave transformation processes that take place in the coastal zone. Nevertheless, wave transmission due to overtopping has not been treated similarly yet. In this paper, a methodology to include wave generation due to overtopping in spectral wave models is presented. Incorporation of overtopping aims at better simulating the wave disturbance in the lee side of a system of offshore breakwaters and the induced hydrodynamic processes. So far, the waves generated due to wave overtopping were being neglected. The methodology consists of executing sequential simulations at small time step intervals and whenever wave overtopping occurs in a breakwater, waves are generated and transmitted in the lee side of the structure. This is achieved by modifying the boundary condition at the lee of a coastal structure to account for wave generation due to overtopping. Additionally, the transmitted spectrum source function was modified, to capture the observed transfer of energy in the higher frequencies of the spectrum due to the aforementioned overtopping process. The above methodology was implemented in the open source wave model TOMAWAC and verification with experimental measurements was carried out yielding satisfactory results. Inclusion of wave transmission due to overtopping in spectral wave models is considered to be a valuable asset, especially for the simulation of inshore hydrodynamic processes.

Galilean invariance of shallow cumulus convection large-eddy simulations

In large-eddy simulations (LES) a computational-domain translation velocity can be used to improve performance by allowing longer time-step intervals. The continuous equations are Galilean invariant. However, standard finite-difference-based discretizations are not discretely invariant with the error being proportional to the product of the local translation velocity and the truncation error. Even though such numerical errors are expected to be small, it is shown that in LES of buoyant convection the turbulent large-scale flow organization can modulate and amplify the error. Galilean invariance of global flow statistics is observed in well-resolved direct numerical simulations (DNS). In LES of single-phase convection under an inversion, flow statistics are nearly Galilean invariant and do not depend on the order of accuracy of the finite difference approximation. In contrast, in LES of cloudy convection, flow statistics show strong dependence on the frame of reference and the order of approximation. The error with respect to the frame of reference becomes negligible as the order of accuracy is increased from second to sixth in the present LES. Schemes with low resolving power can produce large dispersion errors in the surface-fixed frame that can be amplified by large-scale flow anisotropies, such as strong updrafts rising in a non-turbulent free troposphere in cumulus-cloud layers. Interestingly, in the present large-eddy simulations, a second-order discretization in the proper Galilean frame can yield comparable accuracy as a high-order scheme in the surface-fixed frame.

Assessing trends and predicting the cover management factor in a tropical island state using Enhanced Vegetation Index

Soil erosion is a complex process involving multiple factors that contribute to the amount of soil loss. The amount of vegetation cover is one of the main factors used to estimate soil loss and is an important risk factor in informing land use management and soil conservation policies. Cover/crop management (C-factor) is a dynamic soil loss factor and analysing C-factor trends in the context of both space and time, to build a multi-dimensional data structure, increased the value of the trend analysis. The objectives of the study were to (1) utilise EVI dependent static and dynamic predictive equations to compute the C-factor, and (2) to investigate the spatio-temporal changes of the C-factor and hotspots in a tropical small island developing state (SIDS) from 2010 to 2019. ArcGIS Model Builder was utilised to automate the computation of the C-factor using Moderate Resolution Imaging Spectroradiometer (MODIS) Enhanced Vegetation Index (EVI) data and compute the ordinary least square regression. Spatio-temporal analysis was performed using the novel emerging hot spot analysis in ArcGIS to identify statistically significant hot and cold spot trends of cover management to locate new, intensifying, persistent, or sporadic hot spot patterns at different time-step intervals. The regression output for the C-factor and EVI values indicated a strong r2, explaining on average 90% of the models. There was no statistically significant (P value > 0.05) increase in C-factor trend over a 10 year period (2010–2019, P-value = 0.92), a 5 year period (2015–2019; P-value = 0.59), or a 3 year period (2017–2019; P-Value = 0.31). Our results showed that intensifying hot spots (27%) were concentrated along the north–south corridor of the study area, highlighting areas with a statistically significant increase of the C-factor, thus a reduction in vegetation cover over the study period. Integrating spatio-temporal data and spatial technology provided vital cover management estimates for soil practitioners and farmers to guide conservation strategies.

Simulating wave transmission in the lee of a breakwater in spectral models due to overtopping

Spectral wave models have experienced constant development and vast improvements over the past decades. They are constantly being extended and refined in order to cover the complex wave transformation processes that take place in the coastal zone. Nevertheless, wave transmission due to overtopping has not been treated similarly yet. In this paper, a methodology to include wave generation due to overtopping in spectral wave models is presented. Incorporation of overtopping aims at better simulating the wave disturbance in the lee side of a system of offshore breakwaters and the induced hydrodynamic processes. So far, the waves generated due to wave overtopping were being neglected. The methodology consists of executing sequential simulations at small time step intervals and whenever wave overtopping occurs in a breakwater, waves are generated and transmitted in the lee side of the structure. This is achieved by modifying the boundary condition at the lee of a coastal structure to account for wave generation due to overtopping. Additionally, the transmitted spectrum source function was modified, to capture the observed transfer of energy in the higher frequencies of the spectrum due to the aforementioned overtopping process. The above methodology was implemented in the open source wave model TOMAWAC and verification with experimental measurements was carried out yielding satisfactory results. Inclusion of wave transmission due to overtopping in spectral wave models is considered to be a valuable asset, especially for the simulation of inshore hydrodynamic processes.

Investigating Optimal Time Step Intervals of Imaging for Data Quality through a Novel Fully-Automated Cell Tracking Approach.

Computer-based fully-automated cell tracking is becoming increasingly important in cell biology, since it provides unrivalled capacity and efficiency for the analysis of large datasets. However, automatic cell tracking’s lack of superior pattern recognition and error-handling capability compared to its human manual tracking counterpart inspired decades-long research. Enormous efforts have been made in developing advanced cell tracking packages and software algorithms. Typical research in this field focuses on dealing with existing data and finding a best solution. Here, we investigate a novel approach where the quality of data acquisition could help improve the accuracy of cell tracking algorithms and vice-versa. Generally speaking, when tracking cell movement, the more frequent the images are taken, the more accurate cells are tracked and, yet, issues such as damage to cells due to light intensity, overheating in equipment, as well as the size of the data prevent a constant data streaming. Hence, a trade-off between the frequency at which data images are collected and the accuracy of the cell tracking algorithms needs to be studied. In this paper, we look at the effects of different choices of the time step interval (i.e., the frequency of data acquisition) within the microscope to our existing cell tracking algorithms. We generate several experimental data sets where the true outcomes are known (i.e., the direction of cell migration) by either using an effective chemoattractant or employing no-chemoattractant. We specify a relatively short time step interval (i.e., 30 s) between pictures that are taken at the data generational stage, so that, later on, we may choose some portion of the images to produce datasets with different time step intervals, such as 1 min, 2 min, and so on. We evaluate the accuracy of our cell tracking algorithms to illustrate the effects of these different time step intervals. We establish that there exist certain relationships between the tracking accuracy and the time step interval associated with experimental microscope data acquisition. We perform fully-automatic adaptive cell tracking on multiple datasets, to identify optimal time step intervals for data acquisition, while at the same time demonstrating the performance of the computer cell tracking algorithms.

Development and Validation of a Predictive Model for Hemodynamic Responses to Resuscitation during Uncontrolled Hemorrhage.

We investigated whether a statistical model could predict mean arterial pressure (MAP) during uncontrolled hemorrhage; such a model could be used for automated decision support, to help clinicians decide when to provide intravascular volume to achieve MAP goals. This was a secondary analysis of adult swine subjects during uncontrolled splenic bleeding. By protocol, after developing severe hypotension (MAP < 60 mmHg), subjects were resuscitated with either saline (NS) or fresh frozen plasma (FFP), determined randomly. Vital signs were documented at quasi-regular time-step intervals, until either subject death or 300 min. Subjects were randomly separated 50%/50% into training/validation sets, and regression models were developed to predict MAP for each subsequent (i.e., future) time-step. Median time-steps for serially recorded vital signs were +15 min. 5 subjects survived the protocol; 17 died after a median time of 87 min (IQR 78 - 134). The final model consisted of: current MAP; heart rate (HR); prior NS; imminent NS; and imminent FFP. The 95% limits-of-agreement between true subsequent MAP vs. predicted subsequent MAP were +10/-11 mmHg for the 79 time-steps in the training set; and +14/-13 for the 64 time-steps in the validation set. A total of 10 sudden death events (i.e., rapid, fatal MAP decrease within one single time-step) were excluded from analysis. In conclusion, for uncontrolled hemorrhage in a swine model, it was possible to estimate the next documented MAP value on the basis of the subject's current documented MAP; HR; prior NS; and the volume of resuscitation about to be administered. However, the model was unable to predict "sudden death" events. The applicability to populations with wider heterogeneity of hemorrhage patterns and with comorbidities requires further investigation.

Precipitation phase uncertainty in cold region conceptual models resulting from meteorological forcing time-step intervals

Abstract Precipitation phase determination is a known source of uncertainty in surface-based hydrological, ecological, safety, and climate models. This is primarily due to the surface precipitation phase being a result of cloud and atmospheric properties not measured at surface meteorological or hydrological stations. Adding to the uncertainty, many conceptual hydrological models use a 24-h average air temperature to determine the precipitation phase. However, meteorological changes to atmospheric properties that control the precipitation phase often substantially change at sub-daily timescales. Model uncertainty (precipitation phase error) using air temperature (AT), dew-point temperature (DP), and wet-bulb temperature (WB) thresholds were compared using averaged and time of observation readings at 1-, 3-, 6-, 12-, and 24-h periods. Precipitation phase uncertainty grew 35–65% from the use of 1–24 h data. Within a sub-dataset of observations occurring between AT −6 and 6 °C representing 57% of annual precipitation, misclassified precipitation was 7.9% 1 h and 11.8% 24 h. Of note, there was also little difference between 1 and 3 h uncertainty, typical time steps for surface meteorological observations.

A moment limiter for the discontinuous Galerkin method on unstructured tetrahedral meshes

We propose a moment limiter for the second order discontinuous Galerkin method on unstructured meshes of tetrahedra. We provide a systematic way for reconstructing and limiting the solution moments from the cell averages. Our analysis, which is based on the linear advection equation, reveals a restriction on the time step and local intervals in which each moment must belong such that a local maximum principle is satisfied. The time step restriction is based on a new measure of cell size that is approximately twice as large as the radius of the inscribed sphere that is typically used. Finally, we discuss limiting across reflecting boundaries for the Euler equations. The efficacy of our limiting algorithm is demonstrated with a number of test problems.

An improved particle shifting technique for incompressible smoothed particle hydrodynamics methods

SummaryThe smoothed particle hydrodynamics (SPH) method is one of the powerful Lagrangian tools for modeling free surface flows. However, it suffers from particle disorder, which leads to interpolation and numerical errors. To overcome this problem, several techniques have been introduced until now, among which the particle shifting technique (PST) based on Fick's law is an efficient one. The current form of this method needs tuning parameters to fulfill numerical stability criteria. In this study, to eliminate calibration factors, a new shifting coefficient is derived theoretically based on particle positions before and after shifting, regardless of other parameters such as velocity, pressure, time step intervals, etc. The only required input is particle positions, and the main concern is conserving particle densities in their updated positions. In addition to the proposed PST, a new distribution index (DI) is introduced for measuring the spatial uniformity of particles. Furthering the research, some novel treatments are also studied to improve particle movements near free surface boundary. The proposed idea is only assessed for ISPH method in this study, and its performance in other SPH schemes needs more investigations. Following this innovative method, it is validated by modeling different cases including dam break flow, paddle movement, and elliptical water drop. In all cases, particle arrangements have been improved by means of the modified shifting method. In that sense, good agreements between simulation results with experimental data, analytical solutions, and other numerical methods approve the ability of the developed method in simulating free surface flows.

A weakly compressible scheme with a diffuse-interface method for low Mach number two-phase flows

A weakly compressible scheme for gas–liquid two-phase flows with low Mach number is proposed for a fully-explicit time integration. The scheme is based on the fractional-step method with the Euler equation solver and time integration for viscous, surface tension and gravity terms. For the efficient solution of the Euler equation, we introduce the directional-splitting method and the method of characteristics which is applicable to semi-Lagrangian methods. A reduction of the speed of sound is also taken into consideration to enlarge the time step intervals. The primitive flow variables are time-integrated on the node-center configuration. To capture the gas–liquid interface, the conservative phase-field equation is solved by using the multi-moment method. It is computed as a conservative form for the volume-averaged value defined at the cell center, in which the flow velocities are given on the node. We discard the exact momentum conservation, however the total mass of gas and liquid is conserved by introducing a phase-field variable. Several benchmark problems are examined and the results of the explicit scheme are in good agreement with the experimental and computational references.

An Accurate 3-D CFS-PML Based Crank–Nicolson FDTD Method and Its Applications in Low-Frequency Subsurface Sensing

An unsplit-field and accurate Crank–Nicolson cycle-sweep-uniform finite-difference time-domain (CNCSU-FDTD) method based on the complex-frequency-shifted perfectly matched layer (CFS-PML) is proposed. It is applied to 3-D low-frequency subsurface electromagnetic sensing problems. The presented CNCSU-FDTD takes advantage of both CFS-PML and unconditionally stable CN method so that it can attenuate evanescent waves, eliminate late-time reflections, and overcome the stability limits of the FDTD method. The time step intervals in CNCSU-FDTD can be 1000 times larger than that in the regular FDTD for the low-frequency sensing centered at 25 Hz while remaining accurate. Several 3-D numerical examples in the airborne transient electromagnetics system have been demonstrated to validate the proposed method. The CFS-PML-based CNCSU-FDTD method not only attains good accuracy but also saves several dozen times of CPU time as compared with the regular FDTD method.

Numerical treatment for the point reactor kinetics equations using theta method, eigenvalues and eigenvectors

The point reactor kinetics model is a stiff system of linear/nonlinear ordinary differential equations. In fact, the numerical solutions of this stiff model need a smaller time step intervals within various computational schemes. The aim of this work is an accurate numerical solution without need to the smaller time step intervals. Theta method is the most popular, simplest and widely used method for solving the first order ordinary differential equations. In light of this fact, theta method is treated for solving the matrix form of this model via the eigenvalues and corresponding eigenvectors of the coefficient matrix. In this work, the matrix form of the stiff point kinetics equations with multi-group of delayed neutrons is introduced. The treatment theta method is applied to solve the stiff point kinetics equations with six groups of delayed neutrons. The performance of the treatment theta method is evaluated in several case studies involving step, ramp, sinusoidal and pulse reactivities. The results of the treatment theta method are more accurate than the theta method comparing with the conventional methods.

A numerical solution to the point kinetic equations using Taylor–Lie series combined with a scaling and squaring technique

A system of differential equations is derived to model the dynamics of neutron density and the delayed neutron precursors within a point kinetics equation modeling framework for a nuclear reactor. The point kinetic equations are mathematically characterized as stiff, occasionally nonlinear, ordinary differential equations, posing significant challenges when numerical solutions are sought, and traditionally resulting in the need for smaller time step intervals within various computational schemes. In light of the above realization, the present paper proposes a new discretization/simulation method that is: (i) conceptually inspired by system-theoretic notions used in the analysis of sampled-date system dynamics (discrete-time system dynamics) under potentially irreducible large sampling periods/time steps, and (ii) technically based on Taylor–Lie series and the zero-order hold (ZOH). Within the proposed time discretization framework, the sampled-data representation of the original point kinetic system of equations is derived for an arbitrary size of the time-step used. Furthermore, within the context of the proposed approach, the integration of a scaling-and-squaring technique is pursued for the attainment of further performance enhancement of the proposed simulation technique. The performance of the proposed approach is evaluated in several case studies involving step and ramp-like reactivity profiles as well as multiple input examples that simultaneously account for variations in reactivity and neutron source function profiles. In particular, it is demonstrated, that by applying the proposed method, the inherent stiffness problem associated with the simulation challenges of the point kinetic equations can be adequately addressed within a wide range of reactor operating conditions, including large sampling periods dictated by physical and/or technical limitations associated with the current state of sensor and digital reactor control system technology.

Time discretization of the point kinetic equations using matrix exponential method and First-Order Hold

A system of nonlinear differential equations is derived to model the dynamics of neutron density and the delayed neutron precursors within a point kinetics equation modeling framework for a nuclear reactor. The point kinetic equations are mathematically characterized as stiff, occasionally nonlinear, ordinary differential equations, posing significant challenges when numerical solutions are sought and traditionally resulting in the need for smaller time step intervals within various computational schemes. In light of the above realization, the present paper proposes a new discretization method inspired by system-theoretic notions and technically based on a combination of the matrix exponential method (MEM) and the First-Order Hold (FOH) assumption. Under the proposed time discretization structure, the sampled-data representation of the nonlinear point kinetic system of equations is derived. The performance of the proposed time discretization procedure is evaluated using several case studies with sinusoidal reactivity profiles and multiple input examples (reactivity and neutron source function). It is shown, that by applying the proposed method under a First-Order Hold for the neutron density and the precursor concentrations at each time step interval, the stiffness problem associated with the point kinetic equations can be adequately addressed and resolved. Finally, as evidenced by the aforementioned detailed simulation studies, the proposed method retains its validity and accuracy for a wide range of reactor operating conditions, including large sampling periods dictated by physical and/or technical limitations associated with the current state of sensor and digital reactor control system technology.

Time-bridge estimators of integrated variance

We present a set of log-price integrated variance estimators, equal to the sum of open-high-low-close bridge estimators of spot variances within n subsequent time-step intervals. The main characteristics of some of the introduced estimators is to take into account the information on the occurrence times of the high and low values. The use of the high’s and low’s of the bridge associated with the original process makes the estimators significantly more efficient that the standard realized variance estimators and its generalizations. Adding the information on the occurrence times of the high and low values improves further the efficiency of the estimators, much above those of the wellknown realized variance estimator and those derived from the sum of Garman and Klass spot variance estimators. The exact analytical results are derived for the case where the underlying log-price process is an Ito stochastic process. Our results suggests more efficient ways to record financial prices at intermediate frequencies. Didier Sornette Department of Management, Technology and Economics (D-MTEC, KPL F38.2) ETH Zurich Kreuzplatz 5 CH-8032 Zurich Switzerland