Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Convex optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Parallel hybrid quantum-classical machine learning for kernelized time-series classification

Supervised time-series classification garners widespread interest because of its applicability throughout a broad application domain including finance, astronomy, biosensors, and many others. Here, in this work, we tackle this problem with hybrid quantum-classical machine learning, deducing pairwise temporal relationships between time-series instances using a timeseries Hamiltonian kernel (TSHK). A TSHK is constructed with a sum of inner products generated by quantum states evolved using a parameterized time evolution operator. This sum is then optimally weighted using techniques derived from multiple kernel learning. Because we treat the kernel weighting step as a differentiable convex optimization problem, our method can be regarded as an end-to-end learnable hybrid quantum-classical-convex neural network, or QCC-net, whose output is a data set-generalized kernel function suitable for use in any kernelized machine learning technique such as the support vector machine (SVM). Using our TSHK as input to a SVM, we classify univariate and multivariate time-series using quantum circuit simulators and demonstrate the efficient parallel deployment of the algorithm to 127-qubit superconducting quantum processors using quantum multi-programming.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Novel Modular, Reconfigurable Battery Energy Storage System: Design, Control, and Experimentation

This paper presents a novel modular, reconfigurable battery energy storage system. The proposed design is characterized by a tight integration of reconfigurable power switches and DC/DC converters. This characteristic enables isolation of faulty cells from the system and allows fine power control for individual cells toward optimal system-level performance. An optimal power management approach is developed to extensively exploit the merits of the proposed design. Based on receding-horizon convex optimization, this approach aims to minimize the total power losses in charging/discharging while allocating the power in line with each cell’s condition to achieve state of-charge (SoC) and temperature balancing. By appropriate design, the approach manages to regulate the power of a cell across its full SoC range and guarantee the feasibility of the optimization problem. Here, we perform extensive simulations and further develop a lab-scale prototype to validate the proposed system design and power management approach.

25 ENERGY STORAGE↗
DOE OSTI2021

A Network-Aware Distributed Energy Resource Aggregation Framework for Flexible, Cost-Optimal, and Resilient Operation

To efficiently use the ubiquitous behind-the-meter distributed energy resources (DERs) in distribution systems for providing grid services, this paper presents a hierarchical control framework for DER optimal aggregation and control. We first develop a convex optimization model to evaluate the DER flexibility, and then use a convex model-predictive-control based approach to dispatch those DERs. The hierarchical control framework consists of a utility controller, community aggregators and multiple home energy management systems. The flexibility of the DERs is evaluated by each controller in the hierarchy such that the resultant flexibility is feasible given its operational domain. Based on the determined flexibility, the hierarchical controllers then compute optimal setpoints for the DERs to help the distribution system regulate node voltages and provide other distribution grid services. Numerical simulations performed on a model of a real distribution feeder in Colorado, using actual DER data in a residential community demonstrate that the proposed approach can effectively alleviate voltage issues and support resilient operation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

A Scalable Meter Placement Method for Distribution System State Estimation

This paper studies the optimal meter placement problem for distribution system state estimation given limited measurement resources. We formulate the problem as a mixed integer semi-definite programming that minimizes the worst case estimation errors over a set of operating points. To solve the problem, we first relax the problem as a convex optimization problem. Motivated by the lack of scalability of existing solvers, we next leverage the special structure of the cost function and propose an algorithm based on barrier method that solves the problem with significantly better numerical performance. The proposed method has been validated on the IEEE 13-bus, IEEE 123-bus, and IEEE 8,500-bus feeders.

barrier method↗
DOE OSTI2026

Dual Representations and H ∞ -Optimal Control of Partial Differential Equations

We consider H ∞ -optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While linear matrix inequalities are commonly used for optimal control of Ordinary Differential Equations (ODEs), the absence of a universal state-space representation and suitable dual form prevents such methods from being applied to optimal control of PDEs. Specifically, for ODEs, the controller synthesis problem is defined in state-space, and duality is used to resolve the bilinearity of that synthesis problem. Recently, the PIE representation was proposed as a universal state-space representation for linear PDE systems. In this paper, we show that any PDE system represented by a PIE admits a dual PIE with identical stability and I/O properties. This result allows us to reformulate the stabilizing and optimal state-feedback control problems as convex optimization over the cone of positive Partial Integral (PI) operators. Operator inversion formulae then allow us to construct feedback gains for the original PDE system. The results are verified through application to several canonical problems in optimal control of PDEs and indicate the resulting bounds on H ∞ norm are not conservative.

42 ENGINEERING↗
DOE OSTI2023

A Novel Multi-Agent Deep Reinforcement Learning-enabled Distributed Power Allocation Scheme for mmWave Cellular Networks

We consider the power allocation problem over shared spectrum for millimeter-Wave (mmWave) cellular downlink. Existing approaches usually find sub-optimal solutions by solving a non-convex optimization which leads to scalability issues due to centralized control. Therefore, distributed and adaptive approaches are desirable. Recently, model-free Deep Reinforcement Learning (DRL) has achieved success in such wireless resource management tasks. By modeling the radio environment as a Markov Decision Process (MDP) with the base stations (BSs) being the agents, power allocation can be automated at the agent level with comparable throughput performance to conventional centralized schemes. The multi-agent setting presents new challenges as the radio environment is impacted by the joint actions of the agents and is no longer stationary from any individual agent’s perspective. Existing literature bypasses this non-stationarity violation by ignoring it which may cause performance degradation. To tackle this issue, we propose a distributed continuous power allocation scheme based on a modified version of multi-agent Deep Deterministic Policy Gradient (MADDPG) that is tailored for the distributed multiple-agent setting. The proposed scheme employs a centralized-training distributed-execution framework where Q-functions are trained over subsets of BSs while each BS determines its transmit power based only on its own local observation. It admits constant per-BS communication and computation complexity and is thus scalable to large networks. Numerical evaluation shows that the proposed scheme adapts well to a wide range of interference conditions and can achieve comparable or better performance than several state-of-the-art non-learning approaches.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2024

Automatic Loss Factor Modeling and Attribution on Unlabeled PV Energy Data

We present a novel approach for modeling the loss factors of photovoltaic power generation systems (PV systems). This method is a white-box machine learning model built on convex optimization that is fast, interpretable, and auditable. It takes as an input the measured daily energy produced by the system, over a multi-year period, and returns a multiplicative decomposition model of the daily energy signal and full attribution of the total energy loss to each feature. The methods section of this paper has two major components: (1) the description of the signal decomposition (SD) model, expressed in the SD framework, and (2) the attribution of total energy losses via Shapley values. We validate the method on synthetic and open-source data sets and compare to similar methods from the literature.

artificial intelligence↗
DOE OSTI2021

Sensor System and Observer Algorithm Co-Design For Modern Internal Combustion Engine Air Management Based on H2 Optimization

This paper outlines a novel sensor selection and observer design algorithm for linear time-invariant systems with both process and measurement noise based on H 2 optimization to optimize the tradeoff between the observer error and the number of required sensors. The optimization problem is relaxed to a sequence of convex optimization problems that minimize the cost function consisting of the H 2 norm of the observer error and the weighted l 1 norm of the observer gain. An LMI formulation allows for efficient solution via semi-definite programing. The approach is applied here, for the first time, to a turbo-charged spark-ignited engine using exhaust gas circulation to determine the optimal sensor sets for real-time intake manifold burnt gas mass fraction estimation. Simulation with the candidate estimator embedded in a high fidelity engine GT-Power model demonstrates that the optimal sensor sets selected using this algorithm have the best H 2 estimation performance. Sensor redundancy is also analyzed based on the algorithm results. This algorithm is applicable for any type of modern internal combustion engines to reduce system design time and experimental efforts typically required for selecting optimal sensor sets.

Zhang, Xu↗
DOE OSTI2021

Ensemble Learning Based Convex Approximation of Three-Phase Power Flow

Though the convex optimization has been widely used in power systems, it still cannot guarantee to yield a tight (accurate) solution to some problems. To mitigate this issue, this paper proposes an ensemble learning based convex approximation for alternating current (AC) power flow equations that differs from the existing convex relaxations. The proposed approach is based on three-phase quadratic power flow equations in rectangular coordinates. To develop this data-driven convex approximation of power flows, the polynomial regression (PR) is first deployed as a basic learner to fit convex relationships between the independent and dependent variables. Then, ensemble learning algorithms such as gradient boosting (GB) and bagging are introduced to combine learners to boost model performance. Based on the learned convex approximation of power flow, optimal power flow (OPF) is formulated as a convex quadratic programming problem. The simulation results on IEEE standard cases of both balanced and unbalanced systems show that, in the context of solving OPF, the proposed data-driven convex approximation outperforms the conventional semi-definite programming (SDP) relaxation in both accuracy and computational efficiency, especially in the cases that the conventional SDP relaxation fails

Convex approximation↗
DOE OSTI2025

Optimizing on-ramp merging for connected and automated vehicles: A hierarchical approach using deep reinforcement learning and optimal control

On-ramp merging for Connected and Automated Vehicles (CAVs) presents significant challenges in dynamic traffic environments. Traditional methods and recent learning-based approaches often fail to simultaneously address decision-making complexity and execution precision under fluctuating conditions. This study introduces a novel hierarchical framework that combines: (1) a high-level Deep Reinforcement Learning (DRL) module that coordinates merging sequences through Virtual Traffic Signals (VTS) with Yield/Green phases and (2) a low-level optimal controller generating collision-free speed trajectories via pseudospectral convex optimization. A convolutional autoencoder compresses high-dimensional traffic states to enhance responsiveness. Extensive simulations demonstrate a 12.5% improvement in mainline throughput a 28% reduction in emergency braking events, and 31.66% lower fuel consumption compared to baseline methods. Furthermore, the framework’s effectiveness in coordinating CAV merges highlights its potential for real-world deployment. Future work will extend validation to multi-lane scenarios with mixed traffic and large-scale multiple merging points.

Connected and automated vehicles↗
DOE OSTI2021

Sequence of polyhedral relaxations for nonlinear univariate functions

Here, given a nonlinear, univariate, bounded, and differentiable function f(x), this article develops a sequence of Mixed Integer Linear Programming (MILP) and Linear Programming (LP) relaxations that converge to the graph of f(x) and its convex hull, respectively. Theoretical convergence of the sequence of relaxations to the graph of the function and its convex hull is established. For nonlinear non-convex optimization problems, the relaxations presented in this article can be used to construct tight MILP and LP relaxations. These MILP and the LP relaxations can also be used with MILP-based and spatial branch-and-bound based global optimization algorithms, respectively.

42 ENGINEERING↗
DOE OSTI2023

Measure This, Not That: Pareto Optimal Trade-Offs between Model-Based Information Content and Measurements Cost

The slides present a novel convex optimization formulation to compute the best set of measurements for multi-response dynamical systems with asynchronous time steps that maximize the Fisher information content subject to budget constraints. The trace (A-optimality) or determinant (D-optimality) of the Fisher Information Matrix (FIM) quantifies the information content. The framework supports arbitrary (positive semi-definite) variance and covariances between every pair of responses and their time steps.

Wang, Jialu↗
DOE OSTI2022

Two-Stage Reinforcement Learning Policy Search for Grid-Interactive Building Control

This paper develops an intelligent grid-interactive building controller, which optimizes building operation during both normal hours and demand response (DR) events. To avoid costly on-demand computation and to adapt to non-linear building models, the controller utilizes reinforcement learning (RL) and makes real-time decisions based on a near-optimal control policy. Learning such a policy typically amounts to solving a hard non-convex optimization problem. We propose to address this problem with a novel global-local policy search method. In the first stage, an RL algorithm based on zero-order gradient estimation is leveraged to search for the optimal policy globally, due to its scalability and the potential to escape some poor performing local optima. The obtained policy is then fine-tuned locally to bring the first-stage solution closer to that of the original unsmoothed problem. Experiments on a simulated five-zone commercial building demonstrate the advantages of the proposed method over existing learning approaches. They also show that the learned control policy outperforms a pragmatic linear model predictive controller (MPC) and approaches the performance of an oracle MPC in testing scenarios. Using a state-of-the-art advanced computing system, we demonstrate that the controller can be learned and deployed within hours of training.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

ACOPF Transmission Switching Using Open-Source MINLP Solvers

The optimal transmission switching (OTS) problem with AC physics represents a mixed integer non-linear non-convex optimization problem which can provide benefits to transmission level power system operations. In this paper we benchmark a set of open-source mixed integer non-linear programming (MINLP) solvers on the OTS problem with AC physics using the pglib set of power system test cases. Results characterizing the performance of the different solvers are reported and discussed.

ACOPF↗
DOE OSTI2021

Iterative Linearization for Phasor-Defined Optimal Power Dispatch

Optimal power flow (OPF) problems, which dispatch power targets to controllable generating units across a network, must generally account for non-convex constraints on power flow. Furthermore, adapting those problems so as to make them solvable with convex optimization techniques is an area of much academic and operational interest. In this paper, we present a method for solving OPF as a quadratic program by iteratively refining and re-initializing a linearized model of power flow based on the outputs of an associated nonlinear solver. The linear model on which we demonstrate this method is an adapted version of an approximation designed for use with unbalanced distribution networks. As an important benefit, the model allows for the explicit inclusion of nodal voltage phasor values in both the OPF problem's objective and its constraints, which opens the door to the idea of phasor-based control (PBC) design. We show in simulations on the IEEE 13-node test feeder that our method quickly converges to a set of phasor targets that are sufficiently precise for use in operations at the distribution level.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

A hybrid robust-stochastic optimization approach for day-ahead scheduling of cascaded hydroelectric system in restructured electricity market

Uncertainties arising from complicated natural and market environments pose great challenges for the efficient operation of cascaded hydroelectric systems. To overcome these challenges, this paper studies the day-ahead scheduling of cascaded hydroelectric systems in a restructured electricity market with the presence of uncertainties in electricity price and natural water inflow. To properly model the uncertainty, we consider the unique characteristics of these two types of uncertainties and capture them via the uncertainty set and stochastic scenarios, respectively. Further, a hybrid robust-stochastic optimization model is developed to simultaneously hedge against these two types of uncertainties, which is formulated as a large-scale non-convex optimization problem with mixed integer recourse. After introducing linearization of nonlinear terms, a tailored hybrid decomposition scheme combining Lagrangian relaxation and Dantzig-Wolfe decomposition is adopted to achieve efficient computation of the proposed model. Two real-world cases are conducted to demonstrate the capability and characteristics of the proposed model and algorithms.

13 HYDRO ENERGY↗
DOE OSTI2022

Uncertainty-Informed Operation Coordination in a Water-Energy Nexus

The widespread deployment of smart heterogeneous technologies and the growing complexity in our modern society calls for effective coordination of the interdependent lifeline networks. In particular, operation coordination of electric power and water infrastructures is urgently needed as the water system is one of the most energy-intensive networks, an interruption in which may quickly evolve into a dramatic societal concern. This paper develops a novel analytic for uncertainty-aware day-ahead operation optimization of the interconnected power and water systems (PaWS). Joint probabilistic constraint (JPC) programming is employed to capture the uncertainties in wind resources and water demand forecasts. The proposed integrated stochastic model is presented as a non-linear non-convex optimization problem, where the non-linear hydraulic constraints in the water network are linearized using piece-wise linearization technique, and the non-convexity is efficiently tackled with a solution methodology to convert the proposed model with JPCs to a tractable mixed-integer linear programming (MILP) formulation that can be quickly solved to optimality. Here, the suggested framework is applied to a 15-node commercial-scale water network jointly operated with a power transmission system using a modified IEEE 57-bus test system. The numerical results demonstrate the of the proposed stochastic framework, resulting in cost reduction (13% on average when compared to the traditional setting) and energy saving of the integrated model under different realizations of uncertain renewable energy sources (RESs) and water demand scenarios. Additionally, the scalability of the proposed model is tested on a modified IEEE 118-bus test system connected to five water networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

ZEUS: An Efficient GPU Optimization Method Integrating PSO, BFGS, and Automatic Differentiation

We introduce a novel, efficient computational method, ZEUS, for numerical optimization, and provide an open-source implementation. It has four key ingredients: (1) particle swarm optimization (PSO), (2) the use of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method, (3) automatic differentiation (AD), and (4) GPUs. Our approach addresses the computational challenges inherent in high-dimensional, non-convex optimization problems. In the first phase of the algorithm, we get a potentially good set of starting points using PSO. Thereafter, we run BFGS independently in parallel from these starting points. BFGS is one of the best-performing algorithms for numerical optimization. However, it requires the gradient of the function being optimized. ZEUS integrates automatic differentiation into BFGS thus avoiding the need for the user to calculate derivatives explicitly. The use of GPUs allows ZEUS to speed up the calculations substantially. We carry out systematic studies to explore the trade-offs between the number of PSO iterations taken, starting points, and BFGS iteration depth. We show that a handful of iterations of PSO can improve global convergence when combined with BFGS. We also present performance studies using common test functions. The source code can be found at https://github.com/fnal-numerics/global-optimizer-gpu.

Soos, Dominik [Old Dominion U.]↗