Previous Time Step Research Articles

Transient Weighted Moving-Average Model of Photovoltaic Module Back-Surface Temperature

Accurate modeling of photovoltaic (PV) performance requires the precise calculation of module temperature. Currently, most temperature models rely on steady-state assumptions that do not account for the transient climatic conditions and thermal mass of the module. On the other hand, complex physics-based transient models are computationally expensive and difficult to parameterize. In order to address this, a new approach to transient thermal modeling was developed, in which the steady-state predictions from previous timesteps are weighted and averaged to accurately predict the module temperature at finer time scales. This model is informed by 3-D finite-element analyses, which are used to calculate the effect of wind speed and module unit mass on module temperature. The model, in application, serves as an added filter over existing steady-state models that smooths out erroneous values that are a result of intermittency in solar resource. Validation of this moving-average model has shown that it can improve the overall PV energy performance model accuracy by as much as 0.58% over steady-state models based on mean absolute error improvements and can significantly reduce the variability between the model predictions and measured temperature times series data.

The cell transmission model with free-flow speeds varying over time or space

In the cell transmission model (CTM), time is discretised into time-steps and links discretised into cells. In the original CTM, and usually thereafter, the cell lengths are chosen so that, at free-flow speeds (ffs), traffic travels exactly one cell per time-step (1 cpts), so that the ffs, denoted α, is exactly α = 1 cpts and, to avoid computational complications, the length of each cell is normally held constant over time. But the actual observed ffs's in a cell will often differ by time of day or traffic type or traffic lane, or due to speed limits that vary over time or space, or due to stochastic effects. By construction, the maximum ffs in each cell is 1 cpts (α = 1), hence when the ffs is varying within a cell, it will often be less than 1 (α < 1).We show that when traffic in a cell has a ffs α < 1 cpts then the flows and occupancies obtained from the standard CTM can be very inaccurate. For example, consider a cell of length 1 that is in a free flow state with free-flow speed α < 1 and no further flow into the cell. Then all traffic in the cell will have exited by time 1/α and the cell will then be empty. In contrast, for the same scenario, the CTM lets a fraction α < 1 of the remaining traffic in the cell exit in each time step, so that the cell outflow and occupancy decline geometrically toward zero, so that the cell never fully empties.The problem is serious since in traffic networks there may be large numbers, or a large proportion, or a majority, of cells and links that are in a free-flow state for all or part of the time span being modelled. To overcome the above problem, we propose that the CTM not be applied to cells that are in a free-flow state with ffs α < 1 cpts. Instead, for those cells and links, we let traffic move forward at its ffs rather than as computed from the CTM. This is easily accomplished since, in the CTM the computations roll forward one time step at a time and, in each time step, the cell occupancy is updated from the previous time step, hence is known and the known occupancy immediately indicates whether the cell will be in a free-flow state.

Categorization Problem on Controllability of Boolean Control Networks

A Boolean control network (BCN) is a discrete-time dynamical system whose variables take values from a binary set {0,1}. At each time step, each variable of the BCN updates its value simultaneously according to a Boolean function which takes the state and control of the previous time step as its input. Given an ordered pair of states of a BCN, we define the set of reachable time steps as the set of positive integer k's where there exists a control sequence such that the BCN can be steered from one state to the other in exactly k time steps; and the set of unreachable time steps as the set of k's where there does not exist any control sequence such that the BCN can be steered from one state to the other in exactly k time steps. We consider in this article the so-called categorization problem of a BCN, i.e., we develop a method, via algebraic graph theoretic approach, to determine whether the set of reachable time steps and the set of unreachable time steps, associated with the given pair of states, are finite or infinite. Our results can be applied to classify all ordered pairs of states into four categories, depending on whether the set of reachable (unreachable) time steps is finite or not.

Interface Flux Recovery coupling method for the ocean–atmosphere system

Component coupling is a crucial part of climate models, such as DOE’s E3SM (Caldwell et al., 2019). A common coupling strategy in climate models is for their components to exchange flux data from the previous time-step. This approach effectively performs a single step of an iterative solution method for the monolithic coupled system, which may lead to instabilities and loss of accuracy. In this paper we formulate an Interface-Flux-Recovery (IFR) coupling method which improves upon the conventional coupling techniques in climate models. IFR starts from a monolithic formulation of the coupled discrete problem and then uses a Schur complement to obtain an accurate approximation of the flux across the interface between the model components. This decouples the individual components and allows one to solve them independently by using schemes that are optimized for each component. To demonstrate the feasibility of the method, we apply IFR to a simplified ocean–atmosphere model for heat-exchange coupled through the so-called bulk condition, common in ocean–atmosphere systems. We then solve this model on matching and non-matching grids to estimate numerically the convergence rates of the IFR coupling scheme.

World Refrigeration Day 2020

An air-conditioning system equipped with a latent thermal energy storage is analyzed thermodynamically and economically. A new solution method is introduced and used to solve the phase change problem. In addition, based on the 2-D modified enthalpy method, a numerical solution is carried out. The numerical results are validated using the existing experimental ones. The results obtained from the proposed method are compared with those of the numerical ones for some effective parameters. A maximum difference of 2.7% is obtained between them. By applying the proposed method, the effects of parameters such as the inlet and outlet air temperatures on the operating parameters including the coefficient of performance, exergy efficiency, total product unit cost, total investment cost, phase change material (PCM) slabs’ thickness, and length are investigated. The thermodynamic and economic performances of the overall system are compared for three types of PCMs with identical melting point temperatures, namely; RT27, S27 and PureTemp27. It is shown that the total product unit cost decreases as the air temperature difference in passing through the air-conditioning system increases. This occurs in spite of the increment of investment cost because of the thermal efficiency enhancement. In the proposed method, the desired output can be obtained at any time and location with no need to previous time steps and other discretized points. This improves the optimization process for the system. The results show that, compared to the other PCM types, the PureTemp27 brings about better thermodynamic and thermoeconomic performances for the system.

HPC compact quasi-Newton algorithm for interface problems

In this work we present a robust interface coupling algorithm called Compact Interface quasi-Newton (CIQN). It is designed for computationally intensive applications using an MPI multi-code partitioned scheme. The algorithm allows to reuse information from previous time steps, feature that has been previously proposed to accelerate convergence. Through algebraic manipulation, an efficient usage of the computational resources is achieved by: avoiding construction of dense matrices and reduce every multiplication to a matrix–vector product and reusing the computationally expensive loops. This leads to a compact version of the original quasi-Newton algorithm. Altogether with an efficient communication, in this paper we show an efficient scalability up to 4800 cores. Three examples with qualitatively different dynamics are shown to prove that the algorithm can efficiently deal with added mass instability and two-field coupled problems. We also show how reusing histories and filtering does not necessarily makes a more robust scheme and, finally, we prove the necessity of this HPC version of the algorithm. The novelty of this article lies in the HPC focused implementation of the algorithm, detailing how to fuse and combine the composing blocks to obtain an scalable MPI implementation. Such an implementation is mandatory in large scale cases, for which the contact surface cannot be stored in a single computational node, or the number of contact nodes is not negligible compared with the size of the domain.

Co-regularized nonnegative matrix factorization for evolving community detection in dynamic networks

Community detection in static networks solely emphasizes the clustering accuracy, while evolving community detection in dynamic networks simultaneously takes into account both the clustering accuracy and clustering drift. The available evolutionary clustering algorithms are criticized for failing to fully characterize dynamics of networks and to accurately balance the clustering accuracy and clustering drift. To solve these problems, we propose a co-regularized evolutionary nonnegative matrix factorization for evolving communities in dynamic networks (Cr-ENMF). Specifically, both the network and communities at the previous time step are utilized to characterize the clustering drift, which are incorporated into the objective function of Cr-ENMF by regularization. We show that the well-known temporal smoothness framework for evolutionary clustering is a special case of the proposed framework, and prove the equivalence between Cr-ENMF and evolutionary clustering. Thereafter, an iterative strategy is presented to optimize the objective function. The experimental results over both artificial and real world dynamic networks illustrate that Cr-ENMF outperforms state-of-the-art approaches.

Self-Attention ConvLSTM for Spatiotemporal Prediction

Spatiotemporal prediction is challenging due to the complex dynamic motion and appearance changes. Existing work concentrates on embedding additional cells into the standard ConvLSTM to memorize spatial appearances during the prediction. These models always rely on the convolution layers to capture the spatial dependence, which are local and inefficient. However, long-range spatial dependencies are significant for spatial applications. To extract spatial features with both global and local dependencies, we introduce the self-attention mechanism into ConvLSTM. Specifically, a novel self-attention memory (SAM) is proposed to memorize features with long-range dependencies in terms of spatial and temporal domains. Based on the self-attention, SAM can produce features by aggregating features across all positions of both the input itself and memory features with pair-wise similarity scores. Moreover, the additional memory is updated by a gating mechanism on aggregated features and an established highway with the memory of the previous time step. Therefore, through SAM, we can extract features with long-range spatiotemporal dependencies. Furthermore, we embed the SAM into a standard ConvLSTM to construct a self-attention ConvLSTM (SA-ConvLSTM) for the spatiotemporal prediction. In experiments, we apply the SA-ConvLSTM to perform frame prediction on the MovingMNIST and KTH datasets and traffic flow prediction on the TexiBJ dataset. Our SA-ConvLSTM achieves state-of-the-art results on both datasets with fewer parameters and higher time efficiency than previous state-of-the-art method.

Spread of Information With Confirmation Bias in Cyber-Social Networks

This paper provides a model to investigate information spreading over cyber-social network of agents communicating with each other. The cyber-social network considered here comprises individuals and news agencies. Each individual holds a belief represented by a scalar. Individuals receive information from news agencies that are closer to their belief, confirmation bias is explicitly incorporated into the model. The proposed dynamics of cyber-social networks is adopted from DeGroot-Friedkin model, where the individual's opinion update mechanism is a convex combination of his innate opinion, his neighbors' opinions at the previous time step (obtained from the social network), and the opinions passed along by news agencies from cyber layer which he follows. The characteristics of the interdependent social and cyber networks are radically different here: the social network relies on trust and hence static while the news agencies are highly dynamic since they are weighted as a function of the distance between an individual state and the state of news agency to account for confirmation bias. The conditions for convergence of the aforementioned dynamics to a unique equilibrium are characterized. The estimation and exact computation of the steady-state values under non-linear and linear state-dependent weight functions are provided. Finally, the impact of polarization in the opinions of news agencies on the public opinion evolution is numerically analyzed in the context of the well-known Krackhardt's advice network.

A domain decomposition method for the time-dependent Navier-Stokes-Darcy model with Beavers-Joseph interface condition and defective boundary condition

In this article a domain decomposition method is proposed to solve a time-dependent Navier-Stokes-Darcy model with Beavers-Joseph interface condition and defective boundary condition. Robin boundary conditions between the Navier-Stokes domain and Darcy domain are constructed by directly re-organizing the terms in the three interface conditions, including the Beavers-Joseph condition. In order to avoid the traditional iteration for the domain decomposition method at each time step, the interface information, which is needed for the Robin type transmission conditions at the current time step, is directly predicted based on the numerical solution of the previous time steps. Backward Euler scheme is first utilized for the temporal discretization while finite elements are used for the spatial discretization. The convergences of this domain decomposition method are rigorously analyzed for the time-dependent Navier-Stokes-Darcy model with Beavers-Joseph interface condition. The major difficulties in the analysis arise from nonlinear terms and Beavers-Joseph interface condition, including a series of technical treatments and the final special norm used in the discrete Gronwall's inequality for the analysis of full discretization. Based on the above preparation, we further develop a Lagrange multiplier method under the framework of the domain decomposition method to overcome the difficulty of non-unique solutions arising from the defective boundary condition. One interesting finding of this paper is that the Lagrange multipliers are time dependent functions instead of constants. In order to improve the accuracy order for the temporal discretization, a three-step backward differentiation scheme is used to replace the backward Euler scheme. Compared with the first scheme, the second one allows us to use the relative larger time step to reduce the computational cost while keeping the same accuracy. Numerical examples are provided to illustrate the features of the proposed method.

An Improved Fast Finite Element Time-Domain Method Based on Compressive Sensing for Cavity Problems

To avoid directly solving linear equations for major time marching in the finite element time-domain (FETD) method, the compressive sensing (CS) theory is introduced to construct an explicit iterative scheme instead of an implicit form. In this method, Whitney elements and a leapfrog model are applied to time-dependent Maxwell curl equations for space and time discretization. After a small number of iterations, steps for linear equations in the initial time, the electric field intensity and magnetic flux density are updated just by the linear combination of results of previous time steps. Furthermore, a restart mechanism is built to control the computational complexity and accuracy over a long simulation time. The effectiveness of the new algorithm is verified by analyzing 3-D resonant cavities.

Sparse Bayesian Multi-Task Learning of Time-Varying Massive MIMO Channels With Dynamic Filtering

Sparsity of channel in the next generation of wireless communication for massive multiple-input-multiple-output (MIMO) systems can be exploited to reduce the overhead in the training. The multi-task (MT)-sparse Bayesian learning (SBL) is applied for learning time-varying sparse channels in the uplink for multi-user massive MIMO orthogonal frequency division multiplexing systems. In particular, the dynamic information of the sparse channel is used to initialize the hyperparameters in the MT-SBL procedure for the next time step. Then, the expectation maximization based updates are applied to estimate the underlying parameters for different subcarriers. Through the simulation studies, it is observed that using the dynamic information from the previous time step considerably reduces the complexity and the required time for the convergence of MT-SBL algorithm with negligible sacrifice of the estimation accuracy. Finally, the power leakage is reduced due to considering angular refinement in the proposed algorithm.

An Implicit Coupled 1D/2D Model for Unsteady Subcritical Flow in Channel Networks and Embayment

In this study, 1D and 2D shallow-water models were coupled to simulate unsteady flow in channel networks and embayment. The 1D model solved the 1D shallow-water equations (St. Venant) using the Preissmann box method and targeted long narrow reaches of the river networks, while the 2D model targeted broad channels and embayment and solved the 2D shallow-water equations using a semi-implicit scheme applied to an unstructured grid of triangular cells. The 1D and 2D models were solved simultaneously by building a matrix for the free surface elevation at every 1D junction and 2D cell center. Velocities were then computed explicitly based on the results at the previous time step and the updated water level. The originality of the scheme arose from a novel coupling method. The results showed that the coupled 1D/2D model produced identical results as the full 2D model in classical to benchmark problems with considerable savings in computational effort. Application of the model to the Pearl River Estuary in southern China showed that complex patterns of tidal wave propagation could be efficiently modeled.

Iterative acceleration methods with second-order time accuracy for nonlinear diffusion equations

For a two-layer finite difference scheme with second-order time accuracy of nonlinear diffusion equations, we present three iterative solving algorithms, including Picard, Picard-Newton and derivative-free Picard-Newton iterations. The main purpose of this paper is to solve the two-layer scheme efficiently and accurately, and give strict theoretical proofs of the convergence and efficiency of the three iterative methods. For the three iterative methods, two strategies are adopted to offer iterative initial evaluations, one is to use the value at the previous time step with first-order accuracy, the other is an extrapolation with second-order accuracy. With an induction reasoning technique, we prove that the solutions of the three iterative methods all converge to the exact solution of the diffusion problem with second-order accuracy both in space and time after two nonlinear iteration steps, even if the first-order initial value is used. It is also proved that the solutions of Picard iteration converge linearly to the solution of the discrete scheme, while Picard-Newton and derivative-free Picard-Newton iterative solutions converge with a quadratic speed. Moreover, no difference occurs in convergent speed with the two different initial values. Finally, some numerical tests are presented to verify our theoretical results, which show that compared with Picard iteration, Picard-Newton and derivative-free Picard-Newton iterations are more efficient for solving nonlinear problems.

Probabilistic framework to evaluate the resilience of engineering systems using Bayesian and dynamic Bayesian networks

Resilience indicators are a convenient tool to assess the resilience of engineering systems. They are often used in preliminary designs or in the assessment of complex systems. This paper introduces a novel approach to assess the time-dependent resilience of engineering systems using resilience indicators. A Bayesian network (BN) approach is employed to handle the relationships among the indicators. BN is known for its capability of handling causal dependencies between different variables in probabilistic terms. However, the use of BN is limited to static systems that are in a state of equilibrium. Being at equilibrium is often not the case because most engineering systems are dynamic in nature as their performance fluctuates with time, especially after disturbing events (e.g. natural disasters). Therefore, the temporal dimension is tackled in this work using the Dynamic Bayesian Network (DBN). DBN extends the classical BN by adding the time dimension. It permits the interaction among variables at different time steps. It can be used to track the evolution of a system's performance given an evidence recorded at a previous time step. This allows predicting the resilience state of a system given its initial condition. A mathematical probabilistic framework based on the DBN is developed to model the resilience of dynamic engineering systems. Two illustrative examples are presented in the paper to demonstrate the applicability of the introduced framework. One example evaluates the resilience of Brazil. The other one evaluates the resilience of a transportation system.

An improved implicit method with dissipation control capability: The simple generalized composite time integration algorithm

In this paper, a simple and accurate implicit composite time integration scheme is newly developed for more efficient transient analyses of structural problems. The new scheme does not require the acceleration vector of the previous time step, and the initial acceleration vector is not needed, either. As a result, the factorization of the mass matrix is unnecessary, while factorizations of the effective coefficient matrix are still needed. Besides, the new method is designed to possess controllable algorithmic dissipation. Despite the absence of the acceleration vector of the previous time step, the numerical performance of the new method is equivalent to those of the existing methods. The excitation of an elastic bar problem and the simple nonlinear pendulum problem are numerically analyzed for the test of the new scheme. In the numerical experiments, the effects of consistent and lumped mass matrices are also discussed.

Temporal rainfall disaggregation using a micro-canonical cascade model: possibilities to improve the autocorrelation

Abstract. In urban hydrology rainfall time series of high resolution in time are crucial. Such time series with sufficient length can be generated through the disaggregation of daily data with a micro-canonical cascade model. A well-known problem of time series generated in this way is the inadequate representation of the autocorrelation. In this paper two cascade model modifications are analysed regarding their ability to improve the autocorrelation in disaggregated time series with 5 min resolution. Both modifications are based on a state-of-the-art reference cascade model (method A). In the first modification, a position dependency is introduced in the first disaggregation step (method B). In the second modification the position of a wet time step is redefined in addition by taking into account the disaggregated finer time steps of the previous time step instead of the previous time step itself (method C). Both modifications led to an improvement of the autocorrelation, especially the position redefinition (e.g. for lag-1 autocorrelation, relative errors of −3 % (method B) and 1 % (method C) instead of −4 % for method A). To ensure the conservation of a minimum rainfall amount in the wet time steps, the mimicry of a measurement device is simulated after the disaggregation process. Simulated annealing as a post-processing strategy was tested as an alternative as well as an addition to the modifications in methods B and C. For the resampling, a special focus was given to the conservation of the extreme rainfall values. Therefore, a universal extreme event definition was introduced to define extreme events a priori without knowing their occurrence in time or magnitude. The resampling algorithm is capable of improving the autocorrelation, independent of the previously applied cascade model variant (e.g. for lag-1 autocorrelation the relative error of −4 % for method A is reduced to 0.9 %). Also, the improvement of the autocorrelation by the resampling was higher than by the choice of the cascade model modification. The best overall representation of the autocorrelation was achieved by method C in combination with the resampling algorithm. The study was carried out for 24 rain gauges in Lower Saxony, Germany.

Comparison of Long Short Term Memory Networks and the Hydrological Model in Runoff Simulation

Runoff modeling is one of the key challenges in the field of hydrology. Various approaches exist, ranging from physically based over conceptual to fully data driven models. In this paper, we propose a data driven approach using the state-of-the-art Long-Short-Term-Memory (LSTM) network. The proposed model was applied in the Poyang Lake Basin (PYLB) and its performance was compared with an Artificial Neural Network (ANN) and the Soil &amp; Water Assessment Tool (SWAT). We first tested the impacts of the number of previous time step (window size) in simulation accuracy. Results showed that a window in improper large size will dramatically deteriorate the model performance. In terms of PYLB, a window size of 15 days might be appropriate for both accuracy and computational efficiency. We then trained the model with 2 different input datasets, namely, dataset with precipitation only and dataset with all available meteorological variables. Results demonstrate that although LSTM with precipitation data as the only input can achieve desirable results (where the NSE ranged from 0.60 to 0.92 for the test period), the performance can be improved simply by feeding the model with more meteorological variables (where NSE ranged from 0.74 to 0.94 for the test period). Moreover, the comparison results with the ANN and the SWAT showed that the ANN can get comparable performance with the SWAT in most cases whereas the performance of LSTM is much better. The results of this study underline the potential of the LSTM for runoff modeling especially for areas where detailed topographical data are not available.

A local character based method for solving linear systems of radiation diffusion problems

The radiation diffusion problem is a kind of time-dependent nonlinear equations. For solving the radiation diffusion equations, many linear systems are obtained in the nonlinear iterations at each time step. The cost of linear equations dominates the numerical simulation of radiation diffusion applications, such as inertial confinement fusion, etc. Usually, iterative methods are used to solve the linear systems in a real application. Moreover, the solution of the previous nonlinear iteration or the solution of the previous time step is typically used as the initial guess for solving the current linear equations. Because of the strong local character in ICF, with the advancing of nonlinear iteration and time step, the solution of the linear system changes dramatically in some local domain, and changes mildly or even has no change in the rest domain.In this paper, a local character-based method is proposed to solve the linear systems of radiation diffusion problems. The proposed method consists of three steps: firstly, a local domain (algebraic domain) is constructed; secondly, the subsystem on the local domain is solved; and lastly, the whole system will be solved. Two methods are given to construct the local domain. One is based on the spatial gradient, and the other is based on the residual. Numerical tests for a two-dimensional heat conduction model problem, and two real application models, the multi-group radiation diffusion equations and the three temperature energy equations, are conducted. The test results show that the solution time for solving the linear system can be reduced dramatically by using the local character-based method.

A Multilayer Nonlinear Elimination Preconditioned Inexact Newton Method for Steady-State Incompressible Flow Problems in Three Dimensions

We develop a multilayer nonlinear elimination preconditioned inexact Newton method for a nonlinear algebraic system of equations, and a target application is the three-dimensional steady-state incompressible Navier--Stokes equations at high Reynolds numbers. Nonlinear steady-state problems are often more difficult to solve than time-dependent problems because the Jacobian matrix is less diagonally dominant, and a good initial guess from the previous time step is not available. For such problems, Newton-like methods may suffer from slow convergence or stagnation even with globalization techniques such as line search. In this paper, we introduce a cascadic multilayer nonlinear elimination approach based on feedback from intermediate solutions to improve the convergence of Newton iteration. Numerical experiments show that the proposed algorithm is superior to the classical inexact Newton method and other single layer nonlinear elimination approaches in terms of the robustness and efficiency. Using the proposed nonlinear preconditioner with a highly parallel domain decomposition framework, we demonstrate that steady solutions of the Navier--Stokes equations with Reynolds numbers as large as 7,500 can be obtained for the lid-driven cavity flow problem in three dimensions without the use of any continuation methods.