Data-driven Stochastic Model Research Articles

A hierarchical framework for minimising emissions in hybrid gas-renewable energy systems under forecast uncertainty

Developing and deploying renewables in existing energy systems are pivotal in Europe’s transition to net-zero emissions. In this transition, gas turbines (GTs) will be central for balancing purposes. However, a significant hurdle in minimising emissions of GTs operating in combination with intermittent renewables arises from the reliance on unreliable meteorological forecasts. Here, we propose a hierarchical framework for decoupling this operational problem into a balancing and emissions minimisation problem. Balancing is ensured with a high-level stochastic balancing filter (SBF) based on data-driven stochastic grey-box models for the uncertain intermittent renewable. The filter utilises probabilistic forecasting and less conservative chance constraints to compute safe bounds, within which a proposed low-level economic predictive controller further minimises emissions of the GTs during operations. As GTs exhibit semi-continuous operating regions, complementarity constraints are utilised to fully exploit each GT’s allowed operational range. The proposed method is validated in simulation for a gas-balanced hybrid renewable system with batteries, three GTs with varying capacities, and a wind farm. Using real historical operational wind data, our simulation shows that the proposed framework balances the energy demand and minimises emissions with up to 4.35% compared with other conventional control strategies in simulation by minimising the GT emissions directly with complementarity constraints in the low-level controller and indirectly with less conservative chance constraints in the high-level filter. The simulations show that the computational cost of the proposed framework is well within requirements for real-time applications. Thus, the proposed operational framework enables increased renewable share in hybrid energy systems with GTs and renewable energy and subsequently contributes to de-carbonising these types of isolated or grid-connected systems onshore and offshore.

Comparison of data-driven stochastic window operation models for residential buildings

In residential buildings, window opening is typically one of the most significant parameters that affects indoor air temperature and thus the energy required for heating and cooling. While several field measurement campaigns have been undertaken, and datasets have been used to calibrate data-driven stochastic models based on different techniques, a critical comparison between these window operation models, analysing their suitability for building energy simulation, is needed. This study compares seven different modelling approaches including Gaussian distribution function, logistic regression, Markov chain, Markov-logit hybrid, classification tree, artificial neural network and random forest, trained and tested using measurements of 21 living rooms and 10 bedrooms from residential buildings located in Australian subtropical and temperate climates. Two types of modelling approaches were tested: individual, where each window operation was modelled individually, and cohort, where a common model was developed considering all the windows in the dataset. The stochastic nature of window opening was introduced to the models by Monte Carlo methods. True Positive Rate (TPR) and True Negative Rate (TNR), quantified using the Area Under Curve (AUC) method, were used to benchmark the performance of the different models. The classification trees and random forest were identified as more accurate methods (>0.74 median AUC) for cohort modelling, while artificial neural network and Markov-logit hybrid methods were identified as more accurate methods (>0.7 median AUC) for individual window operation modelling in building simulation applications.

Model-data hybrid driven approach for remaining useful life prediction of cutting tool based on improved inverse Gaussian process

In the cutting process, reasonable evaluation of tool remaining useful life (RUL) is essential to ensure machining stability and safety. However, traditional data-driven methods rely on datasets with complete degradation data and prior knowledge, which are usually difficult to obtain in real scenarios. For these problems, this paper proposed a model-data hybrid driven approach for RUL prediction of cutting tool based on improved inverse Gaussian process. The tool wear degradation is considered as a random process, the cutting physical model and the data-driven stochastic process model are fused, so that the prior knowledge from the physical model and the statistical law of measured data are fully utilized to improve the accuracy of tool RUL prediction. The cutting physical model is established, and the prior knowledge of tool wear degradation is obtained based on physical simulation method. A data-driven random effects inverse Gaussian process model is constructed for tool RUL modeling and prediction. According to Bayesian method, the unknown parameters are estimated and updated integrating physical simulated and measured wear data, so as to obtain the probability density function for specific tool RUL, and quantify the prediction uncertainty. Finally, comparative experiments are conducted to validate the performance of the proposed method. The results suggest that the hybrid approach has the best performance in different tool RUL prediction.

Adaptive Design of Solar-Powered Energy Systems Based on Daily Clearness State Evolution

The optimal designing of the hybrid energy system (HES) is a challenging task due to the multiple objectives and various uncertainties. Especially for HES, primarily powered by solar energy, the reference solar radiation data directly impact the result of the optimization design. To incorporate the stochastic characteristics of solar radiation into the sizing process, a data-driven stochastic modeling method for solar radiation is proposed. The method involves two layers of stochastic processes that capture the intraday variation and daily evolution of solar radiation. First, the clearness index (CI) is introduced to describe the radiation intensity at different times. Then, the daily clearness state (DCS) is proposed, based on the statistical indicators of the intraday CI. The Markov model is used to describe the stochastic evolutionary characteristics between different DCSs. The probabilistic distribution of the CI under different DCS is obtained based on the diffusion kernel density estimation (DKDE), which is used for the stochastic generation of the CI at various times of the day. Finally, the radiation profile required for the optimal design is obtained by the stochastic generation of the DCS sequences and the intraday clearness index under corresponding states. A case study of an off-grid solar-powered HES is provided to illustrate this methodology.

Hydroclimatic scenario generation using two-stage stochastic simulation framework

Climate change poses significant challenges for decision-making processes across a range of sectors. From the water resources planning and management perspective, the interest is often in evaluating the performance of a water supply system in a future state considering the potential changes in rainfall and streamflow characteristics. With observed climate change signals, scenario-based projections of rainfall and streamflow simulations are crucial for evaluating the potential impacts of climate change on water resource systems. Given the complexity of the existing approaches, their applications for generating scenario-based projections of streamflow and rainfall are limited. We developed a non-parametric bootstrapping approach, NPScnGen, for future scenario generation of any hydroclimatic variable. The developed approach is flexible and can be used with any physical hydrological or data-driven stochastic model that provides simulations of hydroclimatic variables of interest for the historical climate condition. In NPScnGen, samples of any set of time-series characteristics, such as mean and standard deviation, are generated from a multivariate Gaussian process for the considered scenario, and then bootstrapping is performed to select the closest sample from the historical simulation of that hydroclimatic variable. We have also proposed a modified wavelet-based model, Wavelet-HMM, and used that model to synthetically generate historical climate time-series as a baseline. We present the application of the developed framework consisting of historical climate simulation and future climate projection approaches on rainfall and streamflow datasets for the Tampa Bay region in Florida.Plain Language Summary: Water resources managers require a wide range of hypothetical but potential changes in hydroclimatic variables such as streamflow and rainfall to evaluate the sustenance of water supply systems in future. Existing scenario generation approaches are limited by either the complexity of statistical models or dependency on climate models which have their own limitations. In such a scenario, the developed non-parametric scenario generation framework in this study, NPScnGen, can be very useful. The developed framework can be applied with any sophisticated time-series generation model that can generate synthetic hydroclimatic traces for baseline climate condition, and it is also flexible in generating a wide range of potential climate change scenarios. We show the application of the framework on both streamflow and rainfall datasets.

Data-driven Stochastic Model for Quantifying the Interplay Between Amyloid-beta and Calcium Levels in Alzheimer's Disease.

The abnormal aggregation of extracellular amyloid- in senile plaques resulting in calcium dyshomeostasis is one of the primary symptoms of Alzheimer's disease (AD). Significant research efforts have been devoted in the past to better understand the underlying molecular mechanisms driving deposition and dysregulation. Importantly, synaptic impairments, neuronal loss, and cognitive failure in AD patients are all related to the buildup of intraneuronal accumulation. Moreover, increasing evidence show a feed-forward loop between and levels, i.e. disrupts neuronal levels, which in turn affects the formation of . To better understand this interaction, we report a novel stochastic model where we analyze the positive feedback loop between and using ADNI data. A good therapeutic treatment plan for AD requires precise predictions. Stochastic models offer an appropriate framework for modelling AD since AD studies are observational in nature and involve regular patient visits. The etiology of AD may be described as a multi-state disease process using the approximate Bayesian computation method. So, utilizing ADNI data from 2-year visits for AD patients, we employ this method to investigate the interplay between and levels at various disease development phases. Incorporating the ADNI data in our physics-based Bayesian model, we discovered that a sufficiently large disruption in either metabolism or intracellular homeostasis causes the relative growth rate in both and , which corresponds to the development of AD. The imbalance of ions causes disorders by directly or indirectly affecting a variety of cellular and subcellular processes, and the altered homeostasis may worsen the abnormalities of ion transportation and deposition. This suggests that altering the balance or the balance between and by chelating them may be able to reduce disorders associated with AD and open up new research possibilities for AD therapy.

Visual hazardous models: A hybrid approach to investigate road hazardous events

Road users (drivers, passengers, pedestrians, and Animals) are exposed to hazardous events during their commute. With 23 % of global fatalities among pedestrians, their safety continues to be a principal interest for policymakers worldwide. Owing to limited budgets available, there is a growing emphasis on data-driven stochastic models to decide on policies. However, statistical models have limitations due to crash data having redundant features, inherent heterogeneity, and unobserved characteristics. The random parameter model framework addresses the unobserved heterogeneity, but redundant features and inherent heterogeneity among the data's characteristics still compute the biased estimates. This is further complicated if the data has spatiotemporal attributes. To address this, we developed two visual hazardous (VH) models: (i) addresses the unobserved heterogeneity in the data, and (ii) addresses the dimensionality, inherent heterogeneity among the characteristics and unobserved heterogeneity in the collected data after spatiotemporal pattern identification. The feature selection model reduces the dimensionality, whereas latent class clustering classifies the data into maximum heterogeneity between classes. This integration reduces bias in the estimates. As a use-case, pedestrian crosswalk crashes for a decade (2009–2018) in the Indian state of Tamil Nadu extracted from the Road Accident Database Management System (RADMS) was used to understand model performance. This data comprises the crash location, road, vehicle, driver, pedestrian, and environment details. Results show that visual hazardous model 2 allows for generating crash scenarios with five homogeneous sub-classes and the magnitude with marginal effects of contributing factors impacting it. For example, pedestrians during their crosswalks are likely to sustain 820 times more fatal/grievous injuries than simple injuries on expressways per 1000 crosswalk crashes (posted speed limit: 100 km per hour). Working pedestrian age group (25–64 years), an older pedestrian (>64 years), the pedestrian position on a pedestrian crossing and not in the centre of the road, pedestrian action: walking along the edge of the road, multiple lanes, two lanes, paved shoulder, straight and flat road, motorcycle, bus, truck, medium-duty vehicle, illegal driver (<=17 years), going ahead/ overtaking, high speed, expressways, and rural region were statistically significant (positively) contributing to the fatal/grievous injury pedestrian crashes during their crosswalk. This technique serves as a structure for engineers, researchers, and policymakers to formulate effective countermeasures that enhance road safety.

Data-driven stochastic spectral modeling for coarsening of the two-dimensional Euler equations on the sphere

A resolution-independent data-driven subgrid-scale model in coarsened fluid descriptions is proposed. The method enables the inclusion of high-fidelity data into the coarsened flow model, thereby enabling accurate simulations also with the coarser representation. The small-scale model is introduced at the level of the Fourier coefficients of the coarsened numerical solution. It is designed to reproduce the kinetic energy spectra observed in high-fidelity data of the same system. The approach is based on a control feedback term reminiscent of continuous data assimilation implemented using nudging (Newtonian relaxation). The method relies solely on the availability of high-fidelity data from a statistically steady state. No assumptions are made regarding the adopted discretization method or the selected coarser resolution. The performance of the method is assessed for the two-dimensional Euler equations on the sphere for coarsening factors of 8 and 16 times. Applying the method at these significantly coarser resolutions yields good results for the mean and variance of the Fourier coefficients and leads to improvements in the empirical probability density functions of the attained vorticity values. Stable and accurate large-scale dynamics can be simulated over long integration times and are illustrated by capturing long-time vortex trajectories.

Robust active yaw control for offshore wind farms using stochastic predictive control based on online adaptive scenario generation

Subject to the inherent high uncertainty of wind, the prediction for its speed and direction may be insufficiently accurate, the resulting decision actions of active yaw control (AYC) may degrade the power gain. Therefore, this paper proposes a data-driven stochastic model predictive control (SMPC) using adaptive scenario generation (ASG) for offshore wind farm AYC. First, to build precise scenarios under the nonstationary variation of wind, an adaptive method based on Gaussian mixture model (GMM) clustering is proposed to allow online scenario identification with a compact construction. Specifically, GMM is constructed offline and two online mechanisms are developed for adaptive learning ability. To immunize the power maximization of AYC against prediction error, a data-driven robust optimization strategy is presented to realize SMPC based on generated scenarios. In order to enable real-time operation for large-scale wind farms, a novel parallel marine predator algorithm (PMPA) introduced population improvement strategy is developed to solve the robust problems with a quite lower computational burden. Finally, the simulation based on realistic wind data demonstrates the adaptive learning capacity of the proposed ASG. The result shows that the SMPC can improve the power gain by an average of 2.64% compared to the baseline predictive control.

Prognostics of Lithium-Ion batteries using knowledge-constrained machine learning and Kalman filtering

• Propose a knowledge-constrained machine learning method for batteries prognostics • Propose a data-driven stochastic model for battery degradation • Employ an ANN-based DEKF method to capture the dynamics of lithium-ion batteries • Validate the proposed approach using NASA dataset for battery prognostics Accurately predicting the remaining useful life (RUL) of lithium-ion rechargeable batteries remains challenging as the battery capacity degrades in a stochastic manner given the internal complex electrochemical reactions of the battery and the external operational/environmental conditions. In this work, a knowledge-constrained machine learning framework is developed to learn the stochastic degradation of battery performance over working cycles for health prognostics of Lithium-Ion batteries. An artificial neural network (ANN) model is first trained and synchronized using a Dual Extended Kalman Filter (DEKF) to obtain critical health information of Lithium-Ion batteries. With the obtained health information, a knowledge-constrained machine learning method (KcML) is then developed to predict the stochastic degradation of the battery capacity in operation. Specifically, prior knowledge in battery capacity fade can be formulated as extra constraints to facilitate the development of machine learning models with improved fidelity level for battery capacity predictions. A dataset published by NASA is utilized to demonstrate the effectiveness of the proposed knowledge-constrained machine learning approach.

Real-time Energy Management of Low-carbon Ship Microgrid Based on Data-driven Stochastic Model Predictive Control

Real-time Energy Management of Low-carbon Ship Microgrid Based on Data-driven Stochastic Model Predictive Control

System response of an interlayered deposit with a localized graben deformation in the Northridge earthquake

The Wynne Avenue site in the California San Fernando Valley was analyzed using two-dimensional (2D) nonlinear dynamic analyses (NDAs) with geostatistical subsurface modeling to interpret key mechanisms contributing to a 12-m-wide graben deformation with vertical offsets of 10–20 cm in the 1994 Northridge earthquake. In-situ data from borings and cone penetration tests (CPTs), joined with geological interpretations of the distal alluvial fan deposition, delineate interlayered silty sand lenses within a typically fine-grained soil stratigraphy. The NDAs used the PM4Sand and PM4Silt constitutive models with the FLAC finite difference program. NDAs with uniform properties for distinct soil zones closely reproduced the observed graben. However, stochastic NDAs, modeled with sequential Gaussian simulations (SGS) for conditional random field realizations of critical zones, often obscured the expected graben. The ability of the stochastic NDAs to model the graben was further reduced when SGS was performed collectively over two distinct soil zones. The NDAs provide new insights on the causal mechanisms of liquefaction-induced ground oscillations and lurching, that were not easily deduced from common one-dimensional (1D) liquefaction vulnerability indices (LVIs) and Newmark sliding-block analyses. This case study demonstrates the capabilities of system-level NDAs for modeling localized ground deformation patterns, but also highlights cautionary nuances for their implementation with data-driven stochastic subsurface modeling.

Statistical Learning of Nonlinear Stochastic Differential Equations from Nonstationary Time Series using Variational Clustering

Parameter estimation for non-stationary stochastic differential equations (SDE) with an arbitrary non-linear drift and non-linear diffusion is accomplished in combination with a non-parametric clustering methodology. Such a model-based clustering approach includes a quadratic programming (QP) problem with equality and inequality constraints. We couple the QP problem to a closed-form likelihood function approach based on suitable Hermite-expansions to approximate the parameter values of the SDE model. The classification problem provides a smooth indicator function, which enables us to recover the underlying temporal parameter modulation of the one-dimensional SDE. As shown by the numerical examples, the clustering approach recovers a hidden functional relationship between the SDE model parameters and an additional auxiliary process. The study builds upon this functional relationship to develop closed-form, non-stationary, data-driven stochastic models for multiscale dynamical systems in real-world applications.

A data-driven stochastic model for velocity field and phase distribution in stirred particle-liquid suspensions

A computationally efficient Lagrangian stochastic model driven by short 3D experimental trajectories determined by a technique of positron emission particle tracking, has been developed to study two-phase particle-liquid flow in a mechanically agitated vessel and unravel the complex behaviour of both phases. Using a small set of trajectory driver data, the stochastic model is used in conjunction with a particle-wall collision model to simulate the full velocity field and spatial distribution of particles. The performance of a first and a second order model is evaluated in particle suspensions of various concentrations. Both models are able to predict local phase velocities to a high degree of accuracy. Predictions of spatial particle distribution are reasonable by the first order model but very accurate by the second order model. Furthermore, the latter is able to accurately predict the two-phase velocity field and spatial phase distribution under flow conditions outside the experimental range. • Deterministic multiphase flow models are challenging and computationally costly • A stochastic model accurately predicts 3D two-phase flow field in a stirred vessel • The stochastic model is driven by a small set of Lagrangian input data • The stochastic model is capable of extrapolating flow predictions • The stochastic model is highly computationally efficient

Data-driven stochastic model for train delay analysis and prediction

ABSTRACT A homogeneous Markov chain model is proposed to make delay analysis and prediction for near future train movements in a non-periodic single-track railway timetable setting. The prediction model constitutes two principal processes, namely sectional running and conflict resolution, which are represented by the stochastic recovery and deterioration matrices, respectively. The matrices are developed using a data-driven approach. Given the initial delay of a train at the beginning of the prediction horizon, its delay within the horizon can be estimated by vector and matrix operations, which are performed for individual processes separately or in combination of the processes. A baseline linear model has also been developed for comparison. The numerical tests conducted give consistent and stable predictions for train delays made by the Markov model. This is mainly because of that the Markov model can capture uncertainties deep in the horizon and respond to variations in train movements.

A sparse data-driven stochastic damage model for seismic reliability assessment of reinforced concrete structures

It is important to study the seismic reliability of concrete structures based on real measured data of the material properties. The data of material properties collected in practice is usually sparse in spatial distribution. When assessing the seismic performance of the structures based on data, the statistical inference is usually firstly conducted to evaluate the material properties of the whole structure from the sparse data, and the nonlinear seismic simulation of the structures can be performed. The coupling effect of uncertainty and nonlinearity has not been explained properly. In the present study, the Bayesian compressive sensing – Karhunen Loève expansion (BCS-KL) method is combined with the stochastic damage model (SDM) to build a sparse data-driven stochastic damage model. The model deals with nonlinear seismic stochastic analysis of concrete structures based on sparse data, in which the BCS-KL is applied for uncertainty quantification of the statistical inference and the SDM is used as a physical constitutive model of concrete. The simulation is performed with sophisticated modeling using stochastic finite element method, and the physical synthesis method is applied to assess the seismic reliability of the structure. Finally, a shake table test is conducted to verify the proposed simulation framework.

Data-driven stochastic model for cross-interacting processes with different time scales.

In this work, we propose a new data-driven method for modeling cross-interacting processes with different time scales represented by time series with different sampling steps. It is a generalization of a nonlinear stochastic model of an evolution operator based on neural networks and designed for the case of time series with a constant sampling step. The proposed model has a more complex structure. First, it describes each process by its own stochastic evolution operator with its own time step. Second, it takes into account possible nonlinear connections within each pair of processes in both directions. These connections are parameterized asymmetrically, depending on which process is faster and which process is slower. They make this model essentially different from the set of independent stochastic models constructed individually for each time scale. All evolution operators and connections are trained and optimized using the Bayesian framework, forming a multi-scale stochastic model. We demonstrate the performance of the model on two examples. The first example is a pair of coupled oscillators, with the couplings in both directions which can be turned on and off. Here, we show that inclusion of the connections into the model allows us to correctly reproduce observable effects related to coupling. The second example is a spatially distributed data generated by a global climate model running in the middle 19th century external conditions. In this case, the multi-scale model allows us to reproduce the coupling between the processes which exists in the observed data but is not captured by the model constructed individually for each process.

Data-Driven Stochastic Game With Social Attributes for Peer-to-Peer Energy Sharing

Distributed energy resources create a prosumers era. Peer-to-peer (P2P) energy sharing is an effective way to conduct prosumers-based energy management. Integrating prosumers’ social attributes in energy engineering substantially affects their decisions, which brings challenges to the energy scheduling under the cyber-physical-social environment. In this paper, a data-driven stochastic game model with prosumers’ social attributes is proposed for P2P energy sharing. According to social psychology, the prosumers’ social attributes are expressed as subjective probabilities, which are studied by the spatial-temporal graph convolutional networks. In the network, a double-layer feature graph is built to learn the social attributes based on the social survey data and load metering data. The P2P energy sharing incurred randomness comes from social attributes of interactive prosumers, which is formulated as a stochastic game model. In this game, a subjective utility model is proposed for prosumers, and the energy scheduling is conducted with the designed dynamic interval adjustment method. Numerical analysis reveals the results of the learning network and generalized Nash equilibrium. Through comparing with rational scenarios, the influence of prosumers’ social attributes on P2P energy sharing is concluded.

A flexible data-driven cyclostationary model for the probability density of El Niño-Southern Oscillation.

Model simulations of El Niño-Southern Oscillation (ENSO) are usually evaluated by comparing them to observations using a multitude of metrics. However, this approach cannot provide an objective summary metric of model performance. Here, we propose that such an objective model evaluation should involve comparing the full joint probability density functions (pdf's) of ENSO. For simplicity, ENSO state is defined here as sea surface temperature anomalies over the Niño 3 region and equatorial Pacific thermocline depth anomalies. We argue that all ENSO metrics are a function of the joint pdf, the latter fully specifying the underlying stochastic process. Unfortunately, there is a lack of methods to recover the joint ENSO pdf from climate models or observations. Here, we develop a data-driven stochastic model for ENSO that allows for an analytic solution of the non-Markov non-Gaussian cyclostationary ENSO pdf. We show that the model can explain relevant ENSO features found in the observations and can serve as an ENSO simulator. We demonstrate that the model can reasonably approximate ENSO in most GCMs and is useful at exploring the internal ENSO variability. The general approach is not limited to ENSO and could be applied to other cyclostationary processes.

Data-driven stochastic modeling of coarse-grained dynamics with finite-size effects using Langevin regression

Obtaining coarse-grained models that accurately incorporate finite-size effects is an important open challenge in the study of complex, multi-scale systems. We apply Langevin regression, a recently developed method for finding stochastic differential equation (SDE) descriptions of realistically-sampled time series data, to understand finite-size effects in the Kuramoto model of coupled oscillators. We find that across the entire bifurcation diagram, the dynamics of the Kuramoto order parameter are statistically consistent with an SDE whose drift term has the form predicted by the Ott–Antonsen ansatz in the N→∞ limit. We find that the diffusion term is nearly independent of the bifurcation parameter, and has a magnitude decaying as N−1/2, consistent with the central limit theorem. This shows that the diverging fluctuations of the order parameter near the critical point are driven by a bifurcation in the underlying drift term, rather than increased stochastic forcing.