Stochastic State Research Articles

Estimating temperatures in a district heating network using smart meter data

Smart meters at consumers create opportunities to improve operation of the district heating sector using data-driven methods. Information from these meter measurements carries the potential to increase the energy efficiency of both individual houses and the utility network, for example by identifying buildings with too high return temperature, or by detecting leakage in the network. This paper proposes a method for using meter data to estimate network temperatures. Network temperatures can subsequently be used to estimate the network characteristics, namely the nonlinear relationship between network temperature and the plants’ temperature and flow. A description of the network characteristics is needed for most temperature-optimisation methods to keep the supply temperature as low as possible without violating the system constraints. Traditionally, measurement wells located in the network have been used. These wells are located at critical points in the network where the largest temperature losses occur. Since the lowest temperature often varies over time, multiple critical points are necessary. The method presented in this paper eliminates the need for these physical critical points in the network. It also makes it possible to change the location of the critical points if needed. The network temperature is estimated using a stochastic state–space model of the heat dynamics from the street level distribution pipe over the service pipe and into individual houses. The parameters in the model are estimated using a maximum likelihood approach, and the Kalman Filter is used to evaluate the likelihood function. The estimation process takes advantage of automatic differentiation using the R package Template Model Builder (TMB) to reduce the computational workload. The proposed method is validated by comparing the estimated temperature with the temperature measured from a measurement well.

Control‐oriented estimation of the exchange current density in PEM fuel cells via stochastic filtering

Increasing efficiency and durability of fuel cells can be achieved through advanced model-based optimal control of its operating conditions, and the efficient online estimation of fuel cell parameters and internal states is fundamental for the implementation of such advanced controllers. The exchange current density is a driving parameter of performance for the catalyst layer of proton exchange membrane fuel cells (PEMFC). This study presents a control-oriented, stochastic filtering approach for online, continuous estimation of the exchange current density in low-temperature PEMFCs. The fuel cell is framed as a Markov model where the exchange current density is posed as the stochastic hidden state. The physics-based static equation of the exchange current density is converted into a state transition equation. This transition equation and the equation for cell voltage are used in the stochastic state estimator to approximate the posterior probability distribution of the exchange current density. In order to highlight the usefulness of the approach, the estimated value of the exchange current density is used to approximate the trend of the electrochemical active surface area (ECSA) in the catalyst layer and train a nonlinear auto-regressive model. This data-driven model is used to forecast the evolution in the ECSA associated with long-term degradation. The estimation algorithm is successfully implemented and tested in two different experimental datasets.

Parameter-tuning stochastic resonance as a tool to enhance wavelength modulation spectroscopy using a dense overlapped spot pattern multi-pass cell.

The parameter-tuning stochastic resonance (SR) method can convert part of the noise energy into the signal energy to suppress the noise and amplify the signal, comparing with traditional weak periodic signal detection methods (e.g., time average method, filtering method, and correlation analysis method). In this work, the numerical calculation is conducted to find the optimal resonance parameters for applying the SR method to the wavelength modulation spectroscopy (WMS). Under the stochastic resonance state, the peak value of 2f signal (a constant concentration of CH4∼20 ppm) is effectively amplified to ∼0.0863 V, which is 3.8 times as much as the peak value of 4000-time average signal (∼0.0231 V). Although the standard deviation also increases from ∼0.0015 V(1σ) to ∼0.003 V(1σ), the SNR can be improved by 1.83 times (from ∼25.9 to ∼15.8) correspondingly. A linear spectral response of SR 2f signal peak value to raw 2f signal peak value is obtained. It suggests that the SR method is effective for enhancing photoelectric signal under strong noise background.

A Reconfigurable Modular Vehicle Control Strategy Based on an Improved Artificial Potential Field

The reconfigurable modular vehicle group can transform into different configurations according to different requirements to be competent for various tasks and scenarios and to facilitate the utilization of robots in unstructured scenarios. Efficient and effective reconfiguration strategies and path planning are essential for improving the performance of modular vehicle groups. First, a multi-sensing four-wheel-drive Mecanum vehicle was built, which was equipped with UWB positioning (based on wireless carrier communication technology), communication based on ESP8266 modules, ultrasonic ranging and a magnetic structure. Second, concerning the indoor storage environment, a UWB two-way bilateral ranging and positioning system was designed, and the experimental accuracy for positioning could reach ±0.1 m. Third, a path planning strategy based on the improved artificial potential field method was adopted. According to the target configuration as well as the obstacle avoidance requirements, the motion space was converted into a gravitational field and a repulsive force field, and the vector superposition of the gradients was used for the path planning of each vehicle in turn. Depending on the reconfiguration command and the connection matrix, the magnetic structure would strengthen or disconnect the vehicle group configuration. Finally, the vehicle reconfiguration from the stochastic dispersion state to the target configuration and the transition between different configurations were accomplished using the proposed strategy in both simulations and experiments.

Mechanisms of notch insensitivity in long-fiber discontinuous, prepreg platelet compression molded composites

The present treatise offers an investigation into the operative mechanisms of stress redistribution and notch insensitivity of the prepreg-based, long-fiber discontinuous composites with stochastic fiber orientation state manufactured via a compression molding process. Open-hole tensile behavior is examined to determine the source of notch insensitivity. Both experimental and simulation approaches reveal that local damage mechanisms result in stress redistribution and corresponding reduction in notch sensitivity as measured by the ratio of the notched to un-notched tensile strengths. The analysis showed that open-hole coupon fracture may occur in locations at or away from the hole, depending on the details of the stochastic meso-morphology and the notch size. It was also demonstrated that as the notch diameter is increased, the probability of fracture at the notch is increased. The experimentally observed notch insensitivity of the prepreg platelet composite was reproduced in the numerical simulations.

Online Cognitive Data Sensing and Processing Optimization in Energy-Harvesting Edge Computing Systems

Mobile edge computing (MEC) has recently become a prevailing technique to alleviate the intensive computation burden in Internet of Things (IoT) networks. However, the limited device battery capacity and stringent spectrum resource significantly restrict the data processing performance of MEC-enabled IoT networks. To address the two performance limitations, we consider in this paper an MEC-enabled IoT system with a wireless device (WD) replenishing its battery by means of energy harvesting (EH) and opportunistically accessing the licensed spectrum of an overlaid primary communication link to offload its sensing data to an MEC server (MS) for edge processing. Under time-varying fading channel, random energy arrivals, and stochastic ON-OFF state of the primary link, we aim to design an online algorithm to jointly control the cognitive data sensing rate and processing method (i.e., local and edge processing) without knowing future system information. In particular, we aim to maximize the long-term average sensing rate of the WD subject to quality of service (QoS) requirement of primary link, average power constraint of MS and data queue stability of both MS and WD. We formulate the problem as a multi-stage stochastic optimization and propose an online algorithm named PLySE that applies the perturbed Lyapunov optimization technique to decompose the original problem into per-slot deterministic optimization problems. For each per-slot problem, we derive the closed-form optimal solution of data sensing and processing control to facilitate low-complexity real-time implementation. Interestingly, our analysis finds that the optimal solution exhibits an threshold-based structure related to the current energy state, secondary queueing backlogs and primary link activity. Simulation results collaborate with our analysis and demonstrate more than 46.7% data sensing rate improvement of the proposed PLySE over representative benchmark methods.

Learning to Optimize User Association and Spectrum Allocation With Partial Observation in mmWave-Enabled UAV Networks

To support large-scale unmanned aerial vehicle (UAV) networks with both payload communication (PC) packets and control and non-payload communication (CNPC) packets, millimeter wave (mmWave) communication is convinced to be a promising solution. However, efficient user association and spectrum allocation are still challenging in mmWave-enabled UAV networks considering that the network state is dynamic and the status information of each UAV is incomplete. In this paper, we investigate a joint UAV association and spectrum allocation problem under a hybrid mmWave sharing paradigm, where PC packets are transmitted over both licensed and pooled bands in a shared manner to achieve high throughput and CNPC packets are transmitted over licensed band in an exclusive manner to guarantee high reliability. To this end, we introduce a strategic form game that can characterize network stochastic states and individual partial observations to reformulate the problem, and then propose a counterfactual regret minimization scheme to achieve its correlated equilibrium (CE). Benefited from the updating mechanism on random <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">observation-action</i> pairs, the designed scheme can converge to the corresponding CE solutions for the two types of packets with partial observation. Finally, our simulation results demonstrate the superior performance of the proposed scheme over the baseline schemes.

Stochastic physics-informed neural ordinary differential equations

Stochastic differential equations (SDEs) are used to describe a wide variety of complex stochastic dynamical systems. Learning the hidden physics within SDEs is crucial for unraveling fundamental understanding of these systems' stochastic and nonlinear behavior. We propose a flexible and scalable framework for training artificial neural networks to learn constitutive equations that represent hidden physics within SDEs. The proposed stochastic physics-informed neural ordinary differential equation framework (SPINODE) propagates stochasticity through the known structure of the SDE (i.e., the known physics) to yield a set of deterministic ODEs that describe the time evolution of statistical moments of the stochastic states. SPINODE then uses ODE solvers to predict moment trajectories. SPINODE learns neural network representations of the hidden physics by matching the predicted moments to those estimated from data. Recent advances in automatic differentiation and mini-batch gradient descent with adjoint sensitivity are leveraged to establish the unknown parameters of the neural networks. We demonstrate SPINODE on three benchmark in-silico case studies and analyze the framework's numerical robustness and stability. SPINODE provides a promising new direction for systematically unraveling the hidden physics of multivariate stochastic dynamical systems with multiplicative noise.

Data-Driven Reliability Evaluation of the Integrated Energy System Considering Optimal Service Restoration

The demand for environmental protection and energy utilization transformation has promoted the rapid development of integrated energy systems (IES). Reliability evaluation is a fundamental element in designing IES as it could instruct the planning and operation of IES. This study proposes a novel data-driven reliability improvement and evaluation method considering the three-state reliability model and an optimal service restoration model (OSR). First, a multi-energy flow model is introduced and linearized in order to reduce the computing complexity. Next, a three-state reliability model is developed, considering the transitional process and partial failure mode. Furthermore, an optimal service restoration model is established to determine the best repairment moment for minimizing the load curtailment, and a data-driven reliability evaluation method is developed that integrates OSR and models the stochastic state transition process using the historical measurement data of the smart meters. Finally, the proposed reliability evaluation method is tested on a test IES, and the numerical results validate its effectiveness in evaluating the reliability of IES and improving the overall reliability.

Monitored open fermion dynamics: Exploring the interplay of measurement, decoherence, and free Hamiltonian evolution

The interplay of unitary evolution and local measurements in many-body systems gives rise to a stochastic state evolution and to measurement-induced phase transitions in the pure state entanglement. In realistic settings, however, this dynamics may be spoiled by decoherence, e.g., dephasing, due to coupling to an environment or measurement imperfections. We investigate the impact of dephasing and the inevitable evolution into a non-Gaussian, mixed state, on the dynamics of monitored fermions. We approach it from three complementary perspectives: (i) the exact solution of the conditional master equation for small systems, (ii) quantum trajectory simulations of Gaussian states for large systems, and (iii) a renormalization group analysis of a bosonic replica field theory. For weak dephasing, constant monitoring preserves a weakly mixed state, which displays a robust measurement-induced phase transition between a critical and a pinned phase, as in the decoherence-free case. At strong dephasing, we observe the emergence of a new scale describing an effective temperature, which is accompanied with an increased mixedness of the fermion density matrix. Remarkably, observables such as density-density correlation functions or the subsystem parity still display scale invariant behavior even in this strongly mixed phase. We interpret this as a signature of gapless, classical diffusion, which is stabilized by the balanced interplay of Hamiltonian dynamics, measurements, and decoherence.

Evolutionary game study on the governance and development of online car-hailing based on blockchain technology

Changes in the online car-hailing industry have brought new challenges to government governance. Effectively enhancing governance efficiency has become the focus of academic research. Based on the technical governance perspective, this paper introduces the consortium blockchain to construct an evolutionary game model between the online car-hailing platform and the government under blockchain technology. By solving the replicated dynamic equations and the Jacobian matrix, the influences of the change in initial conditions and decision parameters on the evolutionary stability results are revealed, and numerical experiments are carried out by using the Python programming language. This paper claims that the system presents three evolutionary stable results and a periodic stochastic state when the key parameters are located in different thresholds. The additional cost of the platform’s negative regulation and the government’s punishment intensity have a positive effect on the evolution of the system to the ideal state (active regulation, active governance). Platform technology R&D cost and government innovation input have a negative effect on the evolution of the system to the ideal state. Therefore, using blockchain to increase the additional cost of the platform’s negative regulation, appropriately increasing the government’s punishment intensity, reasonably controlling the government’s innovation input to the platform, and reducing the technology R&D cost of the platform will help the system evolve into an ideal state. This paper provides useful references to implement effective governance and the innovative and healthy development of the online car-hailing industry.

Stochastic graph recurrent neural network

Representation learning over dynamic graphs has attracted much attention because of its wide applications. Recently, sequential probabilistic generative models have achieved impressive results because they can model data distributions. However, modeling the distribution of dynamic graphs is still extremely challenging. Existing methods usually ignore the mutual interference of stochastic states and deterministic states. Besides, the assumption that latent variables follow Gaussian distributions is usually inappropriate. To address these problems, we propose stochastic graph recurrent neural network (SGRNN), a sequential generative model for the representation learning over dynamic graphs. It separates stochastic states and deterministic states in the iterative process. To improve the flexibility of latent variables, we set the prior distribution and posterior distribution as semi-implicit distributions and propose DSI-SGRNN. In addition, to alleviate the KL-vanishing problem in SGRNN, a simple and interpretable structure is proposed based on the lower bound of KL-divergence. The proposed structure introduces a few extra parameters and can be implemented with a few lines of code modification. Extensive experiments on real-world datasets demonstrate the effectiveness of the proposed model.

Optimization of cropping pattern under seasonal fluctuations of surface water using multistage stochastic programming

Abstract Given rapid socio-economic development, increasing food demand and decreasing available resources, the challenge of seasonal fluctuations of surface water has become a major problem in the agricultural sector, causing a change in consumption from surface water to groundwater resources and reduction of farmers' income. Therefore, optimal programming of the cropping pattern is necessary to handle such challenges. To accomplish this aim, a model of irrigation water allocation was developed based on cropping pattern using multistage stochastic programming in accordance with surface water supply fluctuations. In this model, different stochastic states were considered for all irrigation seasons in the irrigation network of the Jiroft plain in Kerman Province, Iran, which faces a severe shortage of surface water resources and the tendency of farmers to overuse groundwater resources. By solving a multistage stochastic model, it can be observed that, by utilizing an appropriate programming of the cropping pattern, more benefits for the farmers could be realized in the conditions of available surface water fluctuations. The results also indicated that if the surface water released into the canals increased in the spring, the share of profitable high water consumption crops in the pattern will increase, which will strengthen farmers' profits and put pressure on groundwater resources. However, this could not be expected to lead to a significant reduction of groundwater resource consumption and a significant increase of cropping intensity. According to the results obtained, surface water resources cannot meet the water needs of the region, even by using optimal cropping patterns, and this has led to overuse of groundwater resources in this area. Finally, such planning can help adoption of desired policies for irrigation water management through the proper release of these resources.

ENDOGENOUS SOCIAL NETWORKS AND INEQUALITY IN AN INTERGENERATIONAL SETTING

AbstractThe article examines the joint evolution of human capital investment and social networking where the network may be endogenous or exogenous. It extends Cabrales et al. (Games and Economic Behavior 72 (2011), 339–60) to dynamic settings to allow for intergenerational transfers of human capital and social networking endowments as joint decisions. Social multipliers characterize the social equilibria. The associated intergenerational transfer elasticities exhibit rich dependence on social effects allowing the intergenerational transfers elasticity to be increasing with inequality in parents' human capitals. The stochastic steady states highlight the cross‐sectional human capital distribution as outcome of shocks to cognitive and social skills coefficients.

Bayesian decision tables for estimation of risk of water management decisions based on uncertain surface water status: a case study of a Polish catchment

BackgroundUncertain results of the status assessment performed as required by the Water Framework Directive can be responsible for misclassification of a water body’s status and may lead either to risk due to undertaking unnecessary remediation actions or risk of penalties for refraining from any action and not reaching environmental goals. Based on Bayesian decision theory, optimal decision tables are shown for two examples of water quality indicators, for a river catchment in central Poland. To overcome the problem of scarcity of publicly available monitoring data, the existing SWAT model for the studied catchment was used to generate nutrient concentration time series for the baseline conditions and under different scenarios. The status classes assessed based on annual mean concentrations of daily values for total phosphorus and total nitrogen were adopted as the ‘true’ status classes of the water bodies based on each indicator. SWAT simulation results enabled calculation of probability distributions of concentrations for the stochastic states of the water body, both for the period before and after the performance of corrective actions.ResultsBayesian decision tables consisted of alternative management decisions including modernization of the existing wastewater treatment plants in the case of phosphorous and also of fallowing agricultural areas in the case of nitrogen. An example of a penalty calculation procedure is presented in the event that the subject of the case before the EU Court of Justice would be failure to achieve the environmental objectives by all water bodies belonging to the selected catchment.ConclusionsDetailed discussion of this analysis indicates the potential benefits in terms of minimization of costs/losses that the proposed methodology may bring to the protection of surface waters.The presented method of risk analysis for making decisions on remedial actions when uncertainty exists about the water status assessment, can be considered as a prototype of a general methodology prepared for implementation in water protection. Unfortunately paying fines instead of taking remediation measures might be optimal for uncertain status of water bodies.

Stability Analysis of DC Distribution System Considering Stochastic State of Electric Vehicle Charging Stations

A DC distribution system integrated with electric vehicle charging stations (EVCSs) is typically constructed to satisfy the large power exchange demand of electric vehicles (EVs). However, the stochastic operating state of the EVCSs results in difficulties in the stability analysis of the DC distribution system. In this study, a linearized model of the DC distribution system connected with multiple EVCSs is established, which considers the charging and the discharging states of the EVCSs. Based on the similarity transformation, this study theoretically verifies the generalized conclusion that a DC distribution system has a higher possibility of instability if the EVCSs are in the charging rather than the discharging state, and that the system stability is the worst if all the EVCSs operate at the maximum charging state. Moreover, a method to quickly evaluate the stability region of the DC distribution system is proposed. It can provide a numerical instability risk estimation of a complex DC distribution system considering all the possible states of the EVCSs. Lastly, the conclusions are validated by two SIMULINK cases, and the application of the numerical instability risk estimation to the DC distribution system is demonstrated.

Arousal elevation drives the development of oscillatory vocal output.

Adult behaviors, such as vocal production, often exhibit temporal regularity. In contrast, their immature forms are more irregular. We ask whether the coupling of motor behaviors with arousal changes gives rise to temporal regularity: Do they drive the transition from variable to regular motor output over the course of development? We used marmoset monkey vocal production to explore this putative influence of arousal on the nonlinear changes in their developing vocal output patterns. Based on a detailed analysis of vocal and arousal dynamics in marmosets, we put forth a general model incorporating arousal and auditory feedback loops for spontaneous vocal production. Using this model, we show that a stable oscillation can emerge as the baseline arousal increases, predicting the transition from stochastic to periodic oscillations observed during marmoset vocal development. We further provide a solution for how this model can explain vocal development as the joint consequence of energetic growth and social feedback. Together, we put forth a plausible mechanism for the development of arousal-mediated adaptive behavior.NEW & NOTEWORTHY The development of motor behaviors, and the influence of energetic and social factors on it, has long been of interest, yet we lack an integrated picture of how these different systems may interact. Through the lens of vocal development in infant marmosets, this study offers a solution for social behavior development by linking motor production with arousal states. Increases in arousal can drive the system out of stochastic states toward oscillatory dynamics ready for communication.

Robust optimal control of compartmental models in epidemiology: Application to the COVID-19 pandemic

In this paper, a spectral approach is used to formulate and solve robust optimal control problems for compartmental epidemic models, allowing the uncertainty propagation through the optimal control model to be represented by a polynomial expansion of its stochastic state variables. More specifically, a statistical moment-based polynomial chaos expansion is employed. The spectral expansion of the stochastic state variables allows the computation of their main statistics to be carried out, resulting in a compact and efficient representation of the variability of the optimal control model with respect to its random parameters. The proposed robust formulation provides the designers of the optimal control strategy of the epidemic model the capability to increase the predictability of the results by simply adding upper bounds on the variability of the state variables. Moreover, this approach yields a way to efficiently estimate the probability distributions of the stochastic state variables and conduct a global sensitivity analysis. To show the practical implementation of the proposed approach, a mathematical model of COVID-19 transmission is considered. The numerical results show that the spectral approach proposed to formulate and solve robust optimal control problems for compartmental epidemic models provides healthcare systems with a valuable tool to mitigate and control the impact of infectious diseases.

Chance constrained stochastic MPC for building climate control under combined parametric and additive uncertainty

This paper presents a chance constrained stochastic model predictive control (SMPC) approach for building climate control under combined parametric and additive uncertainties. The proposed SMPCap approach enables the quantification, and manipulation, of both the mean and covariance of the stochastic system states and inputs. Its enhanced uncertainty anticipation is shown to induce improved thermal comfort in closed-loop simulations compared to the conventional deterministic MPC (DMPC) and the state-of-the-art SMPCa only accounting for additive uncertainties, at the cost of a maximum relative increase in energy use of 21.6% and 4.2%, respectively. By incorporating the SMPCap strategy in an integrated optimal control and design (IOCD) approach, its additional added value for obtaining a more appropriate, yet robust, heat supply system sizing is illustrated. Via simulations, size reductions up to 33.3% are shown to be achievable for a terraced single-family dwelling without increasing thermal discomfort compared to an IOCD approach incorporating DMPC.

Simulation of absorption spectra of molecular aggregates: A hierarchy of stochastic pure state approach.

Simulation of spectroscopic observables for molecular aggregates with strong and structured coupling of electronic excitation to vibrational degrees of freedom is an important but challenging task. The Hierarchy of Pure States (HOPS) provides a formally exact solution based on local, stochastic trajectories. Exploiting the localization of HOPS for the simulation of absorption spectra in large aggregates requires a formulation in terms of normalized trajectories. Here, we provide a normalized dyadic equation where the ket- and bra-states are propagated in different electronic Hilbert spaces. This work opens the door to applying adaptive HOPS methods for the simulation of absorption spectra.