Coarse-grained Time Research Articles

A memetic NSGA-II for the multi-objective flexible job shop scheduling problem with real-time energy tariffs

AbstractRising costs for energy are increasingly becoming a vital factor for the production planning of manufacturing companies. Manufacturers face the challenge to react to dynamic energy prices and design energy cost efficient schedules in their production planning. In the literature, the energy cost-aware Flexible Job Shop Scheduling Problem addresses minimization of both makespan and energy costs. Recent studies provide multi-objective approaches to model the trade-off of minimizing makespan and energy costs. However, the literature is limited to coarse-grained time periods and does not consider dynamic tariffs where costs change at short intervals, so that production schedules may fall short on energy costs. We aim to close this research gap by considering frequently changing real-time energy tariffs. We propose a multi-objective memetic algorithm based on the non-dominated sorting genetic algorithm (NSGA-II) with both makespan and energy cost minimization as the objectives. We evaluate our approach by conducting computational experiments using prominent FJSP-benchmark instances from the literature, which we supplement with empiric dynamic energy prices. We show results on method performance and compare the memetic NSGA-II with the results of an exact state-of-the-art solver. To investigate the trade-off between a short makespan and low energy costs, we present solutions on the approximated Pareto front and discuss our results.

Fine-grained Network Traffic Prediction from Coarse Data

ICT systems provide detailed information on computer network traffic. However, due to storage limitations, some of the information on past traffic is often only retained in an aggregated form. In this paper we show that Linear Gaussian State Space Models yield simple yet effective methods to make predictions based on time series at different aggregation levels. The models link coarse-grained and fine-grained time series to a single model that is able to provide fine-grained predictions. Our numerical experiments show up to 3.7 times improvement in expected mean absolute forecast error when forecasts are made using, instead of ignoring, additional coarse-grained observations. The forecasts are obtained in a Bayesian formulation of the model, which allows for provisioning of a traffic prediction service with highly informative priors obtained from coarse-grained historical data.

Tales of Tails

Typical human-scaled considerations of thermodynamic states depend primarily on the core of associated speed or other relevant distributions, because the wings of those distributions are so improbable that they cannot contribute significantly to averages. However, for long timescale regimes (slow time), previous papers have shown otherwise. Fluctuating local equilibrium systems have been proven to have distributions with non-Gaussian tails demanding more careful treatment. That has not been needed in traditional statistical mechanics. The resulting non-Gaussian distributions do not admit notions such as temperature; that is, a global temperature is not defined even if local regimes have meaningful temperatures. A fluctuating local thermodynamic equilibrium implies that any local detector is exposed to sequences of local states which collectively induce the non-Gaussian forms. This paper shows why tail behavior is observationally challenging, how the convolutions that produce non-Gaussian behavior are directly linked to time-coarse graining, how a fluctuating local equilibrium system does not need to have a collective temperature, and how truncating the tails in the convolution probability density function (PDF) produces even more non-Gaussian behaviors.

Temporal Extraction of Complex Medicine by Combining Probabilistic Soft Logic and Textual Feature Feedback

In medical texts, temporal information describes events and changes in status, such as medical visits and discharges. According to the semantic features, it is classified into simple time and complex time. The current research on time recognition usually focuses on coarse-grained simple time recognition while ignoring fine-grained complex time. To address this problem, based on the semantic concept of complex time in Clinical Time Ontology, we define seven basic features and eleven extraction rules and propose a complex medical time-extraction method. It combines probabilistic soft logic and textual feature feedback. The framework consists of two parts: (a) text feature recognition based on probabilistic soft logic, which is based on probabilistic soft logic for negative feedback adjustment; (b) complex medical time entity recognition based on text feature feedback, which is based on the text feature recognition model in (a) for positive feedback adjustment. Finally, the effectiveness of our approach is verified in text feature recognition and complex temporal entity recognition experimentally. In the text feature recognition task, our method shows the best F1 improvement of 18.09% on the Irregular Instant Collection type corresponding to utterance l17. In the complex medical temporal entity recognition task, the F1 metric improves the most significantly, by 10.42%, on the Irregular Instant Collection type.

Coarse-Grained Effective Hamiltonian via the Magnus Expansion for a Three-Level System.

Quantum state processing is one of the main tools of quantum technologies. While real systems are complicated and/or may be driven by non-ideal control, they may nevertheless exhibit simple dynamics approximately confined to a low-energy Hilbert subspace. Adiabatic elimination is the simplest approximation scheme allowing us to derive in certain cases an effective Hamiltonian operating in a low-dimensional Hilbert subspace. However, these approximations may present ambiguities and difficulties, hindering a systematic improvement of their accuracy in larger and larger systems. Here, we use the Magnus expansion as a systematic tool to derive ambiguity-free effective Hamiltonians. We show that the validity of the approximations ultimately leverages only on a proper coarse-graining in time of the exact dynamics. We validate the accuracy of the obtained effective Hamiltonians with suitably tailored fidelities of quantum operations.

Extended Detrended Fluctuation Analysis of Coarse-Grained Time Series

A coarse-graining procedure, which involves averaging time series in non-overlapping windows followed by processing of the obtained multiple data sets, is the initial step in the multiscale entropy computation method. In this paper, we discuss how this procedure can be applied with other methods of time series analysis. Based on extended detrended fluctuation analysis (EDFA), we compare signal processing results for data sets with and without coarse-graining. Using the simulated data provided by the interacting nephrons model, we show how this procedure increases, up to 48%, the distinctions between local scaling exponents quantifying synchronous and asynchronous chaotic oscillations. Based on the experimental data of electrocorticograms (ECoG) of mice, an improvement in differences in local scaling exponents up to 41% and Student's t-values up to 34% was revealed.

Coarse graining in time with the functional renormalization group: Relaxation in Brownian motion.

We apply the functional renormalization group (fRG) to study relaxation in a stochastic process governed by an overdamped Langevin equationwith one degree of freedom, exploiting the connection with supersymmetric quantum mechanics in imaginary time. After reviewing the functional integral formulation of the system and its underlying symmetries, including the resulting Ward-Takahashi identities for arbitrary initial conditions, we compute the effective action Γ from the fRG, approximated in terms of the leading and subleading terms in the gradient expansion: the local potential approximation and wave-function renormalization, respectively. This is achieved by coarse graining the thermal fluctuations in time resulting in, e.g., an effective potential incorporating fluctuations at all timescales. We then use the resulting effective equationsof motion to describe the decay of the covariance and the relaxation of the average position and variance toward their equilibrium values at different temperatures. We use as examples a simple polynomial potential, an unequal Lennard-Jones type potential, and a more complex potential with multiple trapping wells and barriers. We find that these are all handled well, with the accuracy of the approximations improving as the relaxation's spectral representation shifts to lower eigenvalues, in line with expectations about the validity of the gradient expansion. The spectral representation's range also correlates with temperature, leading to the conclusion that the gradient expansion works better for higher temperatures than lower ones. This paper demonstrates the ability of the fRG to expedite the computation of statistical objects in otherwise long-timescale simulations, acting as a first step to more complicated systems.

Finite-time thermodynamics of fluctuations in microscopic heat engines

Fluctuations of thermodynamic quantities become non-negligible and play an important role when the system size is small. We develop finite-time thermodynamics of fluctuations in microscopic heat engines whose environmental temperature and mechanical parameter are driven periodically in time. Within the slow-driving regime, this formalism universally holds in a coarse-grained time scale whose resolution is much longer than the correlation time of the fluctuations, and is shown to be consistent with the relation analogous to the fluctuation-dissipation relation. Employing a geometric argument, a scenario to simultaneously minimize both the average and fluctuation of the dissipation in the Carnot cycle is identified. For this simultaneous optimization, the existence of a zero eigenvalue of the singular metric for the scale invariant equilibrium state is found to be essential. Furthermore, we demonstrate that our optimized protocol can improve the dissipation and its fluctuation over the current experiment.

Fault Diagnosis of Rolling Bearings Using Dual-Tree Complex Wavelet Packet Transform and Time-Shifted Multiscale Range Entropy

Most existing fault diagnosis methods for rolling bearings are single-stage; these methods can only judge the fault type but cannot detect the existence of a fault. Moreover, the uncertainty in pattern recognition may lead to misclassification of healthy bearings as faulty ones. This paper proposes a multistage fault detection scheme for rolling bearings. In the first stage, the sensitivity of the range entropy to bearing failure is used to define a threshold, based on which the health status of the bearing is judged. If the unknown bearing is judged to be faulty, the next stage is implemented. In the second stage, a fault feature extraction method based on dual-tree complex wavelet packet transform (DTCWPT), time-shifted multiscale range entropy (TSMRE), and t-distributed stochastic neighbor embedding (t-SNE) is proposed, and a random forest (RF) discriminator is used for fault classification. To achieve the desired performance of fault classification, a new coarsening approach for complexity measurement called TSMRE is developed on the basis of the range entropy (RE). First, the RE value of each time-shifted coarse-grained time series is calculated, and the TSMRE is obtained by averaging the entropy values. The TSMRE improves the coarse-graining processing of the MRE and enhances the stability and reliability of the algorithm. In addition, it can obtain more information from short time series using the time-shifted coarse-grained technology. Therefore, it is less dependent on the length of the original time series. Two sets of rolling bearing data are used for this experiment. The fault recognition rate of each category of samples is 100%. Therefore, the proposed multistage fault diagnosis method can pre-screen healthy bearings and accurately identify the failure types of faulty bearings.

Multi-Time-Scale Optimal Scheduling in Active Distribution Network with Voltage Stability Constraints

The uncertainty associated with loads and renewable-energy sources affects active distribution networks in terms of the operation and voltage stability on different time scales. To address this problem, a multi-time-scale voltage stability constrained optimal scheduling framework is proposed, which includes a day-ahead model with a coarse-grained time resolution and an intra-day model with a fine-grained time resolution. The day-ahead economic-scheduling model maps out a scheme to operate different types of devices with the aim of minimizing the network losses. Following the scheme, the intra-day corrective-adjustment model based on model predictive control is proposed to regulate the flexible devices, such as the energy storage systems and the photovoltaic converters. In particular, the proposed optimal scheduling framework embeds a voltage stability constraint which is constructed by using a novel index, defined based on the Distflow model Jacobian. As the index at each bus is a linear function of the locally measurable power flow variables, the proposed constraint does not introduce additional computational burdens. Simulation results demonstrate the necessity and effectiveness of the proposed multi-time-scale voltage stability constrained optimal scheduling model. The results also show that the variation trend of the proposed index is consistent with that of the commonly used voltage stability index.

Stability and bifurcations in Wilson-Cowan systems with distributed delays, and an application to basal ganglia interactions

The traditional Wilson-Cowan model of excitatory and inhibitory meanfield interactions in neuronal populations considers a weak Gamma distribution of time delays when processing inputs, and is obtained via a time-coarse graining technique that averages the population response. Previous analyses of the stability of the Wilson-Cowan model focused on more simplified cases, where the delays were either not present, constant or were of a specific type. Since these simplifications may significantly alter the behavior of the model, we focus on understanding the behavior of the system before time-course graining, and for a wider range of delay distributions.For these generalized delay equations, we perform stability and bifurcation analyses with respect to parameters that capture both the coupling profile, and the time delay. The investigation is done through the examination of the system’s associated characteristic equation. Under mild assumptions, we give complete mathematical proofs of our theoretical results, for the model with general delay distributions and prove the transversality condition for the possible Hopf bifurcations, in a generalized context. The stability region in this parameter space is described theoretically for several types of delay kernels, and numerical simulations are presented to substantiate the theoretical results.We found that the stability regions and bifurcations differ significantly between different types of delay distributions: weak Gamma distributions promote stable firing rates, while strong Gamma distributions are associated with regular oscillations, and Dirac distributions appear to facilitate more complex aperiodic patterns. This supports the unexplored possibility of different delay distributions being used as the substrate for different functional behaviors, and emphasizes the importance of a careful choice of the delay kernel in the mathematical model.We illustrate these theoretical principles in an application to a basal ganglia circuit, in which β-band oscillations have been associated with Parkinson’s Disease.

Multi-time scale energy management framework for smart PV systems mixing fast and slow dynamics

We propose a multi-time scale energy management framework for a smart photovoltaic (PV) system that can calculate optimized schedules for battery operation, power purchases, and appliance usage. A smart PV system is a local energy community that includes several buildings and households equipped with PV panels and batteries. However, due to the unpredictability and fast variation of PV generation, maintaining energy balance and reducing electricity costs in the system is challenging. Our proposed framework employs a model predictive control approach with a physics-based PV forecasting model and an accurately parameterized battery model. We also introduce a multi-time scale structure composed of two-time scales: a longer coarse-grained time scale for daily horizon with 15-minutes resolution and a shorter fine-grained time scale for 15-minutes horizon with 1-second resolution. In contrast to the current single-time scale approaches, this alternative structure enables the management of a necessary mix of fast and slow system dynamics with reasonable computational times while maintaining high accuracy. Simulation results show that the proposed framework reduces electricity costs up 48.1% compared with baseline methods. The necessity of a multi-time scale and the impact on accurate system modeling in terms of PV forecasting and batteries are also demonstrated.

Determining the dependence of the power supply to the ocean on the length and time scales of the dynamics between the meso-scale and the synoptic scale, from satellite data

The input of mechanical power to the ocean due to the surface wind stress, in regions which correspond to different regimes of ocean dynamics, is considered using data from satellites observations. Its dependence on the coarse-graining range of the atmospheric and oceanic velocity in space from 0.5 to 10∘ and time from 6 h to 40 days is determined. In the area of the Gulf Stream and the Kuroshio extensions, the dependence of the power input on space-time coarse-graining varies over tenfold for the coarse-graining considered. It decreases over twofold for the Gulf Stream extension and threefold for the Kuroshio extension, when the coarse-graining length scale passes from a few degrees to 0.5∘ at a temporal coarse-graining scale of a few days. It increases over threefold in the Gulf Stream and the Kuroshio extensions when the coarse-graining passes from several days to 6 h at a spatial coarse-graining of a few degrees. The power input is found to increase monotonically with shorter coarse-graining in time. Its variation with coarse-graining in space has no definite sign. Results show that including the dynamics at scales below a few degrees reduces considerably the power input by air-sea interaction in regions of strongly nonlinear ocean currents. When the ocean velocities are not considered in the shear calculation, the power input is considerably (up to threefold) increased. The dependence of the power input on coarse-graining in space and time is close to being multiplicatively separable in all regions and for most of the coarse-graining domain considered.

Generalized Composite Multiscale Diversity Entropy and Its Application for Fault Diagnosis of Rolling Bearing in Automotive Production Line

This paper considers the entropy based feature extraction method for the fault diagnosis of rolling bearings in automobile production line, where the fault information is difficult to identify due to the strong nonlinear and non-stationary characteristics of the fault vibration signals. In our work, a novel entropy based method called generalized composite multiscale diversity entropy (GCMDiEn) is developed. This method can effectively track the inside pattern changes of the time series by the description of cosine similarity between adjacent orbits. Unlike most of the existing entropy based results which concentrate on the static orderliness, we analyze the dynamic complexity characteristics of the arbitrary time series. Moreover, compared with the multiscale diversity entropy, GCMDiEn calculates all coarse-grained time series entropy value with the same scale and extends the first-order moment to second-order moment to mitigate the shortcomings of the short time series instability and losing part of the frequency region information. This paper proposed a new rolling bearing fault diagnosis framework which combined the GCMDiEn with the empirical wavelet transform (EWT), Laplacian score (LS), and particle swarm optimization-based support vector machine (PSO-SVM). Finally, the simulation results show the superiority of the GCMDiEn method over the multiscale diversity entropy method. The proposed framework has a higher fault recognition rate (99.38%) than the existing methods.

Composite Multiscale Cross-Sample Entropy Analysis for Long-Term Structural Health Monitoring of Residential Buildings.

This study proposesd a novel, entropy-based structural health monitoring (SHM) system for measuring microvibration signals generated by actual buildings. A structural health diagnosis interface was established for demonstration purposes. To enhance the reliability and accuracy of entropy evaluation at various scales, composite multiscale cross-sample entropy (CMSCE) was adopted to increase the number of coarse-grained time series. The degree of similarity and asynchrony between ambient vibration signals measured on adjacent floors was used as an in-dicator for structural health assessment. A residential building that has been monitored since 1994 was selected for long-term monitoring. The accumulated database, including both the earthquake and ambient vibrations in each seismic event, provided the possibility to evaluate the practicability of the CMSCE-based method. Entropy curves obtained for each of the years, as well as the stable trend of the corresponding damage index (DI) graphs, demonstrated the relia-bility of the proposed SHM system. Moreover, two large earthquake events that occurred near the monitoring site were analyzed. The results revealed that the entropy values may have been slightly increased after the earthquakes. Positive DI values were obtained for higher floors, which could provide an early warning of structural instability. The proposed SHM system is highly stable and practical.

Non-Clausius heat transfer: The method of the nonstationary Langevin equation.

Compared to other formulations of the second law of thermodynamics, the Clausius statement that heat does not spontaneously flow from cold to hot concerns a system in nonequilibrium states, and in that respect is more ambitious but also more ambiguous. We discuss two scenarios when the Clausius statement in its plain form does not hold. First, for ergodic systems, the energy transfer may be consistent with the statement on a coarse-grained timescale, but be anomalously directed during time intervals shorter than the thermalization time. In particular, when an initially colder system is brought in contact to a hotter bath, the internal energy of the former increases with time in a long run but not monotonically. Second, the heat transfer may not respect the Clausius statement on any timescale in nonergodic systems due to the formation of localized vibrational modes. We illustrate the two scenarios with a familiar model of an isotope atom attached to a semi-infinite harmonic atomic chain. Technically, the discussion is based on a Langevin equation for the isotope, using the initial condition when the isotope and chain are initially prepared in uncorrelated canonical states under the constraint that the boundary atom between the isotope and chain is initially fixed and later released. In such setting, the noise in the Langevin equation is nonstationary, and the fluctuation-dissipation relation has a nonstandard form.

Reconciling Time Slice Conflicts of Virtual Machines With Dual Time Slice for Clouds

The proliferation of system virtualization poses a new challenge for the coarse-grained time sharing techniques for consolidation, since operating systems are running on virtual CPUs. The current system stack was designed under the assumption that operating systems can seize CPU resources at any moment. However, for the guest operating system on a virtual machine (VM), such assumption cannot be guaranteed, since virtual CPUs of VMs share a limited number of physical cores. Due to the time-sharing of physical cores, the execution of a virtual CPU is not contiguous, with a gap between the virtual and real time spaces. Such a virtual time discontinuity problem leads to significant inefficiency for lock and interrupt handling, which rely on the immediate availability of CPUs whenever the operating system requires computation. To reduce scheduling latencies of virtual CPUs, shortening time slices can be a straightforward strategy, but it may lead to the increased overhead of context switching costs across virtual machines for some workloads. It is challenging to determine a single time slice to satisfy all the VMs. In this article, we propose to have dual time slice to resolve the time slice conflict problem occurred in different types of virtual machines.

Diagnosis of hepatocellular carcinoma based on a terahertz signal and VMD-CWSE.

A novel strategy on combining variational mode decomposition (VMD) and composite weighted-scale sample entropy (CWSE) modified from composite multiscale entropy (CMSE) is proposed to screen hepatocellular carcinoma (HCC) by measuring the terahertz (THz) pulse signals of ten normal and ten HCC serums. Eight measured HCC specimens are negative in serum biomarker alpha fetoprotein (AFP) determination. In CWSE, the time series with weighted-scales are generated from the weighted average processing in the coarse-grained time series corresponding to each scale of the CMSE algorithm. VMD served as a preprocessing method was introduced into decomposing THz signal to obtain the mode functions of specific bandwidth for identification. Final results reveal that more obtainable entropy values of CWSE for recognition in comparison to those of CMSE on the basis of the rule of statistically significant difference and effect size and also manifest the stronger discriminability than the traditional THz parameters. This study provides a new potential auxiliary tool for diagnosis HCC and develops the methodology on the discrimination for similar THz signals.

The interplay between local and non-local master equations: exact and approximated dynamics

Master equations are a useful tool to describe the evolution of open quantum systems. In order to characterize the mathematical features and the physical origin of the dynamics, it is often useful to consider different kinds of master equations for the same system. Here, we derive an exact connection between the time-local and the integro-differential descriptions, focusing on the class of commutative dynamics. The use of the damping-basis formalism allows us to devise a general procedure to go from one master equation to the other and vice versa, by working with functions of time and their Laplace transforms only. We further analyze the Lindbladian form of the time-local and the integro-differential master equations, where we account for the appearance of different sets of Lindbladian operators. In addition, we investigate a Redfield-like approximation, that transforms the exact integro-differential equation into a time-local one by means of a coarse graining in time. Besides relating the structure of the resulting master equation to those associated with the exact dynamics, we study the effects of the approximation on Markovianity. In particular, we show that, against expectation, the coarse graining in time can possibly introduce memory effects, leading to a violation of a divisibility property of the dynamics.

Evolution Equations for Quantum Semi-Markov Dynamics.

Using a newly introduced connection between the local and non-local description of open quantum system dynamics, we investigate the relationship between these two characterisations in the case of quantum semi-Markov processes. This class of quantum evolutions, which is a direct generalisation of the corresponding classical concept, guarantees mathematically well-defined master equations, while accounting for a wide range of phenomena, possibly in the non-Markovian regime. In particular, we analyse the emergence of a dephasing term when moving from one type of master equation to the other, by means of several examples. We also investigate the corresponding Redfield-like approximated dynamics, which are obtained after a coarse graining in time. Relying on general properties of the associated classical random process, we conclude that such an approximation always leads to a Markovian evolution for the considered class of dynamics.