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Particle image velocimetry analysis with simultaneous uncertainty quantification using Bayesian neural networks
Particle image velocimetry (PIV) is an effective tool in experimental fluid mechanics for extracting flow fields from images. Recently, convolutional neural networks (CNNs) have been used to perform PIV analysis with accuracy on par with classical methods. Here we extend the use of CNNs to analyze PIV data while providing simultaneous uncertainty quantification on the inferred flow field. The method we apply in this paper is a Bayesian convolutional neural network (BCNN) which learns distributions of the CNN weights through variational Bayes. In order to demonstrate the utility of BCNNs for the PIV task, we compare the performance of three distinct BCNN models with simple architectures. The first network estimates flow velocity from image interrogation regions only. Our second model learns to infer velocity from both the image interrogation regions and interrogation region cross-correlation maps. Finally, our best performing network infers velocities from interrogation region cross-correlation maps only. We find that BCNNs using interrogation region cross-correlation maps as inputs perform better than those using interrogation windows only as inputs and discuss reasons why this may be the case. Additionally, we test the best performing BCNN on a full synthetic test image pair and a real image pair from the 1st International PIV Challenge. We show that ~98% of true particle displacements from the full synthetic image pair can be captured within the BCNN's 95% confidence intervals, and that the BCNN's performance on the real image pair is quantitatively similar to that of algorithms tested in the 1st International PIV Challenge. Finally, we show that BCNNs can be generalized to be used with multi-pass PIV algorithms with a moderate loss in accuracy, which may be overcome by future work on finetuning and training schemes. So to our knowledge, this is the first use of Bayesian neural networks to perform PIV.
GradientGraph
Under this SBIR Phase II, Reservoir Labs has developed G2 Analytics, a new technology that allows network operators to analyze bottleneck and flow performance with high precision. G2 delivers a new analytical approach and framework to resolve a variety of key problems found in modern communication networks, including: traffic engineering, routing, flow scheduling, network design, capacity planning, resiliency analysis, network slicing, or service level agreement (SLA) management, among others. G2 leverages the bottleneck structure of congestion-controlled communication networks, a recent mathematical discovery by the Reservoir team [RL19b, RL20a, RL20b, RL21a]. Bottleneck structures reveal how perturbations on flows and links propagate through the network, providing an analytical framework to measure (qualitatively and quantitatively) the ripple effects induced as they traverse the network. Leveraging the mathematics of bottleneck structures, Reservoir Labs is developing the G2 technology to provide network operators with a framework to design, optimize and troubleshoot network performance. This delivery includes the G2 software stack.
Assignment of Freight Traffic in a Large-scale Intermodal Network under Uncertainty
This paper presents a methodology for freight traffic assignment in a large-scale road-rail intermodal network under uncertainty. Network uncertainties caused by natural disasters have dramatically increased in recent years. Several of these disasters (e.g., Hurricane Sandy, Mississippi River Flooding, and Hurricane Harvey) severely disrupted the U.S. freight transportation network, and consequently, the supply chain. To account for these network uncertainties, a stochastic freight traffic assignment model is formulated. An algorithmic framework, involving the sample average approximation and gradient projection algorithm, is proposed to solve this challenging problem. The developed methodology is tested on the U.S. intermodal network with freight flow data from the Freight Analysis Framework. The experiments consider three types of natural disasters that have different risks and impacts on transportation networks: earthquakes, hurricanes, and floods. It is found that for all disaster scenarios, freight ton-miles are higher compared to the base case without uncertainty. The increase in freight ton-miles is the highest under the flooding scenario; this is because there are more states in the flood-risk areas, and they are scattered throughout the U.S.
Netostat: analyzing dynamic flow patterns in high-speed networks
Understanding flow traffic patterns in networks, such as the Internet or service provider networks, is crucial to improving their design and building them robustly. However, as networks grow and become more complex, it is increasingly cumbersome and challenging to study how the many flow patterns, sizes and the continually changing source-destination pairs in the network evolve with time. Here, we present Netostat, a visualization-based network analysis tool that uses visual representation and a mathematics framework to study and capture flow patterns, using graph theoretical methods such as clustering, similarity and difference measures. Netostat generates an interactive graph of all traffic patterns in the network, to isolate key elements that can provide insights for traffic engineering. We present results for U.S. and European research networks, ESnet and GEANT, demonstrating network state changes, to identify major flow trends, potential points of failure, and bottlenecks.
Improving Trustworthiness of Data-Driven Power Grid Contingency Analysis With Bayesian Residual Graph Neural Networks
The evolving energy landscape requires novel tools to efficiently perform contingency analysis and reliability assessment of power grids, potentially in real-time. The high computational cost of traditional power flow solvers limits their applicability in practice. Machine learning (ML) surrogates such as deep neural networks (NNs) accelerate power flow solvers computations, enabling high-order contingency analysis and real-time decision-making by learning highly nonlinear functions and integrating grid topology via graph architectures. However, (graph) NNs lack predictive power away from training data and do not provide predictive confidence estimates. Here, we present a Bayesian residual graph NN that integrates knowledge from low-fidelity data via residual training and embeds granular quantification of uncertainties, improving trustworthiness critical for high-consequence decision-making. Applying Bayesian concepts to NNs is challenging due to the high-dimensionality of both the parameter space, complicating derivation of a meaningful prior, and the output space in large grid systems, requiring enhanced techniques to assess the predicted high-dimensional uncertainties. Our contributions include: (1) Deriving a prior for fully connected and graph NNs that leverages low-fidelity data to guide mean predictions and appropriately control prior predictive uncertainty. (2) Integrating this prior within an ensembling with anchoring scheme for efficient approximate posterior inference. (3) Deriving enhanced metrics to assess accuracy of both the mean and uncertainty predictions in high dimensions, appropriately accounting for correlations propagated through graph layers. The resulting Bayesian residual graph NN is tested on a contingency analysis task for 14-bus and 118-bus grids.
Understanding Discrete Fracture Networks Through Spectral Graph Theory
Discrete Fracture Network models (DFNs) are used to simulate fluid flow and particle transport through fracture networks in low permeability rock. Understanding these processes are essential in many subsurface applications, such as environmental restoration of contaminated fractured media, CO 2 sequestration, detection of low-level nuclear tests, and hydrocarbon extraction. Compared with other models, DFNs allow for incorporation of a wider range of network characteristics but have substantially greater computation cost. These networks can be represented with graphs, allowing the use of graph theory tools to study the networks. I used Python to simulate flow and transport on a range of DFNs and analyzed these networks using methods from network analysis and spectral graph theory. My purpose was to find ways to gain insight about flow and transport on DFNs using these graph representations, bypassing the computationally intensive meshing typically required. My work is still in progress, but I have discovered several interesting trends and patterns that I believe could be useful towards my goal. If I am able to bring these results to fruition, they will aid subsurface geologists in extracting flow and transport information about fracture networks more efficiently.
Optimal Energy Scheduling and Sensitivity Analysis for Integrated Power-Water-Heat Systems
The conventionally independent power, water, and heating networks are becoming more tightly connected, which motivates their joint optimal energy scheduling to improve the overall efficiency of an integrated energy system. However, such a joint optimization is known as a challenging problem with complex network constraints and couplings of electric, hydraulic, and thermal models that are nonlinear and nonconvex. We formulate an optimal power-water-heat flow (OPWHF) problem and develop a computationally efficient heuristic to solve it. The proposed heuristic decomposes OPWHF into subproblems, which are iteratively solved via convex relaxation and convex-concave procedure. Simulation results validate that the proposed framework can improve operational flexibility and social welfare of the integrated system, wherein the water and heating networks respond as virtual energy storage to time-varying energy prices and solar photovoltaic generation. Moreover, we perform sensitivity analysis to compare two modes of heating network control: by flow rate and by temperature. Our results reveal that the latter is more effective for heating networks with a wider space of pipeline parameters.
HPNAIDM: The High-Performance Network Anomaly/Intrusion Detection and Mitigation System
Identifying traffic anomalies and attacks rapidly and accurately is critical for large network operators. With the rapid growth of network bandwidth, such as the next generation DOE UltraScience Network, and fast emergence of new attacks/virus/worms, existing network intrusion detection systems (IDS) are insufficient because they: • Are mostly host-based and not scalable to high-performance networks; • Are mostly signature-based and unable to adaptively recognize flow-level unknown attacks; • Cannot differentiate malicious events from the unintentional anomalies. To address these challenges, we proposed and developed a new paradigm called high-performance network anomaly/intrustion detection and mitigation (HPNAIDM) system. The new paradigm is significantly different from existing IDSes with the following features (research thrusts). • Online traffic recording and analysis on high-speed networks; • Online adaptive flow-level anomaly/intrusion detection and mitigation; • Integrated approach for false positive reduction. Our research prototype and evaluation demonstrate that the HPNAIDM system is highly effective and economically feasible. Beyond satisfying the pre-set goals, we even exceed that significantly (see more details in the next section). Overall, our project harvested 23 publications (2 book chapters, 6 journal papers and 15 peer-reviewed conference/workshop papers). Besides, we built a website for technique dissemination, which hosts two system prototype release to the research community. We also filed a patent application and developed strong international and domestic collaborations which span both academia and industry.
Autonomous plug and play electric vehicle charging scenarios including reactive power provision: a probabilistic load flow analysis
Electric vehicle (EV) charging can have various impacts on low‐voltage distribution systems, along with increasing the uncertainty of network load levels. One method for capturing the statistical uncertainty is probabilistic load flow (PLF). A primary concern of such an approach is determining the correlation between the input variables. Since data are limited, a 1 min resolution bottom‐up time‐variant load model, capturing the changing voltage dependencies of the load, is used for modelling household electrical demand to provide pseudo‐meter data for the three‐phase PLF analysis of a residential distribution network. The correlation between the household and EV charging loads are implicitly taken into account by modelling the EV plug‐in and departure times with the corresponding occupancy model. Two autonomous plug‐and‐play charging scenarios are compared with a standard charging arrangement at both unity and 0.95 capacitive power factors. Four different PLF input correlation scenarios, varying from fully correlated to fully independent, are considered. The proposed charging scenarios and reactive power provision reduce the likelihood of system voltage violations introduced by EVs. The PLF results are verified against those from the initial time‐series analysis providing valuable insight into the uncertainty introduced by EVs and the correlation between household and EV loads.
Role of physics in physics-informed machine learning
Physical systems are characterized by inherent symmetries, one of which is encapsulated in the units of their parameters and system states. These symmetries enable a lossless order-reduction, e.g., via dimensional analysis based on the Buckingham theorem. Despite the latter's benefits, machine learning (ML) strategies for the discovery of constitutive laws seldom subject experimental and/or numerical data to dimensional analysis. We demonstrate the potential of dimensional analysis to significantly enhance the interpretability and generalizability of ML-discovered secondary laws. Our numerical experiments with creeping fluid flow past solid ellipsoids show how dimensional analysis enable both deep neural networks and sparse regression reproduce old results, e.g., Stokes law for a sphere, and generate new ones, e.g., an expression for an ellipsoid misaligned with the flow direction. Furthermore, our results suggest the need to incorporate other physics-based symmetries and invariances into ML-based techniques for equation discovery.
Discrete Mathematical Approaches to Graph-Based Traffic Analysis
Modern cyber defense and anlaytics requires general, formal models of cyber systems. Multi-scale network models are prime candidates for such formalisms, using discrete mathematical methods based in hierarchically-structured directed multigraphs which also include rich sets of labels. An exemplar of an application of such an approach is traffic analysis, that is, observing and analyzing connections between clients, servers, hosts, and actors within IP networks, over time, to identify characteristic or suspicious patterns. Towards that end, NetFlow (or more generically, IPFLOW) data are available from routers and servers which summarize coherent groups of IP packets flowing through the network. In this paper, we consider traffic analysis of Netflow using both basic graph statistics and two new mathematical measures involving labeled degree distributions and time interval overlap measures. We do all of this over the VAST test data set of 96M synthetic Netflow graph edges, against which we can identify characteristic patterns of simulated ground-truth network attacks.
NetFlow Dynamics
NetFlow Dynamics is a web-accessible analysis environment for simulating dynamic flows of materials on model networks. Performing a simulation requires both the NetFlow Dynamics application and a network model which is a description of the structure of the nodes and edges of a network including the flow capacity of each edge and the storage capacity of each node, and the sources and sinks of the material flowing on the network. NetFlow Dynamics consists of databases for storing network models, algorithms to calculate flows on networks, and a GIS-based graphical interface for performing simulations and viewing simulation results. Simulated flows are dynamic in the sense that flows on each edge of the network and inventories at each node change with time and can be out of equilibrium with boundary conditions. Any number of network models could be simulated using Net Flow Dynamics. To date, the models simulated have been models of petroleum infrastructure. The main model has been the National Transportation Fuels Model (NTFM), a network of U.S. oil fields, transmission pipelines, rail lines, refineries, tank farms, and distribution terminals. NetFlow Dynamics supports two different flow algorithms, the Gradient Flow algorithm and the Inventory Control algorithm, that were developed specifically for the NetFlow Dynamics application. The intent is to add additional algorithms in the future as needed. The ability to select from multiple algorithms is desirable because a single algorithm never covers all analysis needs. The current algorithms use a demand-driven capacity-constrained formulation which means that the algorithms strive to use all available capacity and stored inventory to meet desired flows to sinks, subject to the capacity constraints of each network component. The current flow algorithms are best suited for problems in which a material flows on a capacity-constrained network representing a supply chain in which the material supplied can be stored at each node of the network. In the petroleum models, the flowing materials are crude oil and refined products that can be stored at tank farms, refineries, or terminals (i.e. the nodes of the network). Examples of other network models that could be simulated are currency flowing in a financial network, agricultural products moving to market, or natural gas flowing on a pipeline network.
Novel artificial neural network model for instantaneous power losses and operational efficiency mapping of MW-scale vanadium redox flow battery for improved technoeconomic analysis
A novel data-driven, machine-learning-based method for modeling the instantaneous power losses of a distribution-sited 2 MW/8MWh vanadium redox flow battery (VRFB), a grid-scale electrochemical storage technology, is introduced and compared against benchmark empirical modeling approaches, including symmetric and asymmetric models, as well as a recent convex hull modeling approach. The novel loss modeling method introduces several advantages over the benchmark models and over simplistic efficiency estimates, the most significant of which is that the model can accurately reflect the stepwise and non-linear parasitic losses associated with the duty cycles of mechanical auxiliary systems like pump motor drives and blower fans. Residuals of the models are compared; the proposed data driven model features significantly improved accuracy over the benchmark models. The model's coefficient of determination is also improved relative to that of the benchmark models. Furthermore, a novel method for visualization of operational efficiency of the grid-scale storage technology is introduced. To demonstrate the benefits of the novel data-driven method for modeling the VRFB, the benchmark models and the proposed models are embedded into an Open DSS distribution network model to study two applications of the grid-scale electrical storage system: load leveling for grid support and energy arbitrage. This article demonstrates that the accuracy of the instantaneous power loss model significantly impacts the understanding of the state of charge of the VRFB. In turn, the accuracy of the efficiency modeling of the VRFB impacts the understanding of the potential economic value and technical benefits to the distribution network operators. In conclusion, the presented power loss modeling approach is, therefore, highly relevant for utility-stakeholders, battery asset owners, system engineers, system designers, and financial planners interested in evaluating or optimizing the operation of grid-scale VRFBs.
A Network Management System for Handling Scientific Data Flows
Large scientific data transfers often occur at high rates causing increased burstiness in Internet traffic. To limit the adverse effects of these high-rate large-sized flows, which are referred to as $\alpha $ flows, on delay-sensitive audio/video flows, a network management system called Alpha Flow Traffic Engineering System (AFTES) is proposed for intra-domain traffic engineering. An offline approach is used in which AFTES analyzes NetFlow records collected by routers, extracts source–destination address prefixes of $\alpha $ flows, and uses these prefixes to configure firewall filters at ingress routers of a provider’s network to redirect future $\alpha $ flows to traffic-engineered paths and isolated queues. The effectiveness of this scheme was evaluated through an analysis of 7 months of NetFlow data obtained from an ESnet router. For this data set, 91 % of bytes generated by $\alpha $ flows during high-rate intervals would have been directed had AFTES been deployed. The negative aspect of using address prefixes in firewall filters, i.e., the redirection of $\beta $ flows to $\alpha $-flow paths/queues, was also quantified.
A Sparse Tableau Formulation for Node-Breaker Representations in Security-Constrained Optimal Power Flow
Realistic representations of contingencies in AC optimal power flow (ACOPF) often challenge traditional bus-branch network models. Derived from nodal analysis, such approaches represent network constraints in terms of the familiar bus admittance matrix, Ybus. A fixed Ybus is unable to represent common circuit breaker actions such as bus splitting. Work-arounds for Ybus-based analysis typically rely on topology processing, switching between different Ybus matrices depending on breaker settings. In this paper, we propose a very general node-breaker approach, employing multi-port element models and using a sparse tableau formulation (STF) for network constraints. Instead of treating breaker action as altering network topology, and hence changing the structure of Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL) equations, this approach represents a breaker’s position as impacting only constraints associated with a single component, thereby maintaining fixed structure in the KVL and KCL constraints. While larger numbers of variables are required, STF proves sparser than Ybus formulations. Numerical case studies herein demonstrate that STF provides computational efficiency comparable to a Ybus-based ACOPF at the scale of several hundred buses, and lower computational cost in an example of over one thousand buses.
Three‐phase probabilistic load flow in radial and meshed distribution networks
With the introduction of higher levels of renewables and demand response programs, traditional deterministic power system tools fall short of expectations. Probabilistic load flow (PLF) takes into account the inconsistency or the unknown loads, and generation in the fundamental load flow analysis. This study proposes a PLF solution for both balanced and unbalanced, radial and weakly meshed networks without explicitly using the Y ‐bus matrix. It allows for discrete probability density functions as input variables without having to assume a predefined distribution. The nodal voltages and the power flows can be calculated independently from one another. The proposed method is applied to the IEEE 123 Node Test Feeder and the IEEE 13 Node Test Feeder in both its original radial configuration and a modified mesh configuration, including a load replaced with a wind turbine. The results are validated by comparison of the proposed method's solutions to those obtained using cumulants and Monte Carlo simulation. The proposed PLF method provides an accurate and practical way for finding the solution to stochastic problems occurring in power distribution systems allowing for real‐system data to be analysed.
AI4MG-networked-microgrid-models
SF-26-123 24-hour scaled power-flow analysis of a modified IEEE 123-bus distribution feeder using OpenDSS. The simulation runs 24 snapshot power-flow cases (one per hour) with independent hourly scaling profiles for base loads, added loads, generators, and battery storage, and writes per-hour CSV/Excel reports plus a 24-panel voltage-profile plot.