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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A randomized sketching trust-region secant method for low-memory dynamic optimization

The numerical solution of dynamic optimization problems is often limited by the memory required to store the state trajectory, which is used to evaluate the objective function and its derivatives. Recently, [R. Muthukumar et al., SIAM Journal on Optimization 31(2), pp. 1242–1275 (2021)] introduced a trust-region method for dynamic optimization that employs randomized sketching to compress the state trajectory, resulting in inexact derivative computations. By adaptively learning the sketch rank, the trust-region algorithm achieves rigorous convergence guarantees. Here, we extend this approach to use secant Hessian approximations. Due to the randomness introduced by the sketch, the traditional secant update formulae can produce poor Hessian approximations. In particular, the difference of two gradients, computed from two different sketches, may be inconsistent. To overcome this, we employ a sketched approximation of the Hessian application, in lieu of computing the gradient difference. We numerically demonstrate the improved stability of this approach on an example from PDE-constrained optimization.

dynamic optimization↗
DOE OSTI2019

Optimization of CCT Equations Using Calculated Grain Boundary Soluble Compositions for the Simulation of Austenite Decomposition of Steels

New CCT equations have been developed and optimized to simulate the start temperatures of the austenite decomposition process in low-alloyed steels using experimental CCT data published in the literature. Exceptionally, this optimization does not apply the nominal compositions of the steels, but the corresponding soluble compositions of the grain boundaries calculated using IDS software, depending on the reported austenitization treatments of the steels. These compositions, rather than the nominal ones, are expected to control the start of the austenite decomposition, which usually initiates at the grain boundaries. The new optimization treatment takes into account the solute microsegregation and the possible precipitate formation. Using IDS software, the new equations were validated with new experimental CCT data. Agreement was good not only for the austenite decomposition start temperatures, but also for the final phase fractions, indicating fairly reasonable predictions of phase transformation kinetics by the IDS. In addition, IDS simulations were compared with the experimental CCT data of five high-carbon steels, applying both the new equations based on grain boundary soluble compositions as well as the equations based on the nominal compositions. With the same experimental CCT data used in optimization, better agreement was obtained with the new equations, indicating the importance of determining the soluble compositions at the grain boundaries where the austenite decomposition process is likely to begin.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Melt Pool and Heat Treatment Optimization for the Fabrication of High-Strength and High-Toughness Additively Manufactured 4340 Steel

Additively manufactured (AM) components offer superior design flexibility compared to their conventionally manufactured counterparts, and optimizing processing parameters is key to achieving high-quality depositions with desirable and predictable mechanical properties. This study was focused on 4340 steel fabricated using laser powder bed fusion (LPBF), and 42 laser power and scan speed combinations have been systematically investigated to determine an optimized melt pool geometry that would ensure fully-dense parts. The AM material was compared with a wrought 4340 equivalent and studied in two customized heat treated conditions, optimized for strength and toughness, respectively. The microstructures of the as-fabricated and heat treated AM and wrought materials were characterized to assess differences introduced by the layer-by-layer fabrication process and subsequent heat treatment. Tensile properties of both materials were also evaluated and demonstrate that the AM materials offer equal or superior properties compared to the wrought equivalents. Differences in fracture surface morphologies indicate the distinct failure mechanisms associated with the materials’ characteristic microstructures, and the role of inclusions in the failures was studied to elucidate these differences. Complementary to the experimental investigations, the dataset was leveraged to make recommendations for future design of experiments to optimize AM build parameters in other material systems. A statistical Monte Carlo analysis was used to predict the interpolation error produced using reduced datasets and to enable informed processing parameters selection. These findings are discussed to make recommendations for the use of AM materials for high-integrity structural applications.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Optimization of Feasibility Stage for Hydrogen/Deuterium Exchange Mass Spectrometry

The practice of HDX-MS remains somewhat difficult, not only for newcomers but also for veterans, despite its increasing popularity. While a typical HDX-MS project starts with a feasibility stage where the experimental conditions are optimized and the peptide map is generated prior to the HDX study stage, the literature usually reports only the HDX study stage. In this protocol, we describe a few considerations for the initial feasibility stage, more specifically, how to optimize quench conditions, how to tackle the carryover issue, and how to apply the pepsin specificity rule. Two sets of quench conditions are described depending on the presence of disulfide bonds to facilitate the quench condition optimization process. Four protocols are outlined to minimize carryover during the feasibility stage: (1) addition of a detergent to the quench buffer, (2) injection of a detergent or chaotrope to the protease column after each sample injection, (3) back-flushing of the trap column and the analytical column with a new plumbing configuration, and (4) use of PEEK (or PEEK coated) frits instead of stainless steel frits for the columns. The application of the pepsin specificity rule after peptide map generation and not before peptide map generation is suggested. The rule can be used not only to remove falsely identified peptides, but also to check the sample purity. A well-optimized HDX-MS feasibility stage makes subsequent HDX study stage smoother and the resulting HDX data more reliable. .

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2019

Design Characteristics to Eliminate the Need for Parameter Optimization in Nanoflow ESI-MS

The sampling efficiency in electrospray ionization-mass spectrometry (ESI-MS) can be improved by decreasing the liquid flow rate to the nanoflow regime, where it is possible to draw a large fraction of the ESI plume into the mass spectrometer. This mode of operation is typically more difficult than ESI-MS at higher flow rates because it requires careful optimization of a number of parameters to achieve optimal sampling efficiency. In this work, we screened the relative impact on signal intensity and spray stability of factors that included sprayer position, spray electrode protrusion, sprayer tip shape, spray angle relative to the MS inlet, nebulizer gas flow rate, ESI potential, and means for generating the electric field to initiate electrospray. Based on the screening results, we explore the possibility of providing fixed optimal values for many of the key source parameters to eliminate much of the tuning that is required for conventional nanoflow sources. This approach has potential to greatly simplify nanoflow ESI-MS, while providing optimized sensitivity, stability, and robustness, with decreased variability between analyses. .

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimension. In this paper, we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control. We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians. Additionally, we present an efficient, grid-free numerical solver based on our representation formulas, which is shown to scale linearly with the state dimension, and thus, to overcome the curse of dimensionality. Using existing optimization methods and the min-plus technique, we extend our numerical solvers to address more general classes of convex and nonconvex initial costs. We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit (CPU) and a field-programmable gate array (FPGA). In several cases, our FPGA implementation obtains over a 10 times speedup compared to the CPU, which demonstrates the promising performance boosts FPGAs can achieve. Furthermore, our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Physics-Informed Neural Networks for PDE-Constrained Optimization and Control

The goal of optimal control is to determine a sequence of inputs for maximizing or minimizing a given performance criterion subject to the dynamics and constraints of the system under observation. This work introduces Control Physics-Informed Neural Networks (PINNs), which simultaneously learn both the system states and the optimal control signal in a single-stage framework that leverages the system’s underlying physical laws. While prior approaches often follow a two-stage process-modeling, the system first and then devising its control—the presented novel framework embeds the necessary optimality conditions directly into the network architecture and loss function. We demonstrate the effectiveness of the novel methodology by solving various open-loop optimal control problems governed by analytical, one-dimensional, and two-dimensional partial differential equations (PDEs).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Chapter Nine - Automated Optimal Control in Energy Systems: The Reinforcement Learning Approach

With the development of smart grid technologies an increasing number of new devices and participants have joined modern energy systems and are inevitably making them more complicated and interdependent than ever. Optimally controlling such a complex energy system and maintaining its operation in a high-efficient, secure, and resilient manner are challenging tasks to the system operators. Fortunately, the revolution in deep learning and artificial intelligence (AI), both from hardware and algorithms perspectives, has provided new ideas and solutions to many previously intractable problems. As a result, this advance in computer science also sparked great research interests in utilizing AI in solving engineering problems related to the modern energy systems. Among many AI techniques, deep reinforcement learning (DRL) has demonstrated great potential for solving sequential optimization problems, which are very common in the engineering domains. Its ability to handle nonlinearity and stochasticity in controlled systems has out-competed many traditional optimal control algorithms. Therefore in this chapter, we focus on the state-of-the-art of DRL concepts and related algorithms, compare their pros and cons with traditional optimal control approaches and discuss the typical workflow for leveraging RL in solving complex problems in modern energy systems.

artificial intelligence↗
DOE OSTI2022

Multi-objective materials bayesian optimization with active learning of design constraints: Design of ductile refractory multi-principal-element alloys

We report Bayesian Optimization (BO) has emerged as a powerful framework to efficiently explore and exploit materials design spaces. To date, most BO approaches to materials design have focused on the materials discovery problem as if it were a single expensive-to-query ‘black box’ in which the target is to optimize a single objective (i.e., material property or performance metric). Also, such approaches tend to be constraint agnostic. Here, we present a novel multi-information BO framework capable of actively learning materials design as a multiple objectives and constraints problem. We demonstrate this framework by optimally exploring a Refractory Multi-Principal-Element Alloy (MPEA) space, here specifically, the system Mo-Nb-Ti-V-W. The MPEAs are explored to optimize two density-functional theory (DFT) derived ductility indicators (Pugh’s Ratio and Cauchy pressure) while learning design constraints relevant to the manufacturing of high-temperature gas-turbine components. Alloys in the BO Pareto-front are analyzed using DFT to gain an insight into fundamental atomic and electronic underpinning for their superior performance, as evaluated within this framework.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A propagation-based fault detection and discrimination method and the optimization of sensor deployment

Industrial processes can be affected by faults having a serious impact on operation when not promptly detected and diagnosed. Here in this paper, a propagation-based fault detection and discrimination(PFDD) method is proposed to develop a strategy for fault diagnosis while in the design phase of a system. The PFDD method constructs the system model using the Integrated System Fault Analysis(ISFA) technique. Based on the system model, the propagation of hardware and software faults are simulated qualitatively. Given the results of the simulation, the process by which a fault propagates can be characterized using the qualitative features of system variables including the deviation of the system variables from their expected values, the variation of the system variables over time, and the order in which each variable is influenced during the propagation of the fault. The strategy by which a fault can be detected and discriminated is defined using those features. The PFDD method supports the detection and discrimination of faults in both steady states and transient states. Based on the PFDD method, the optimization of sensor deployment in a system is discussed. A brute force algorithm is developed to examine the system’s capability at diagnosing faults and the cost of sensor deployment for all possible configurations of sensors. The optimal sensor deployment strategy can be derived accordingly. However, the brute force method is only applicable to small-scale systems due to its high computational cost. A genetic algorithm is used to optimize sensor deployment in large-scale systems. The PFDD and sensor deployment optimization methods are applied to the Experimental Breeder Reactor II (EBR-II) for verification.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

Bidirectional low temperature district energy systems with agent-based control: Performance comparison and operation optimization

Bidirectional low temperature networks are a novel concept that promises more efficient heating and cooling of buildings. Early research shows theoretical benefits in terms of exergy efficiency over other technologies. Pilot projects indicate that the concept delivers good performance if heating and cooling demands are diverse. However, the operation of these networks is not yet optimized and there is no quantification of the benefits over other technologies in various scenarios. Moreover, there is a lack of understanding of how to integrate and control multiple distributed heat and cold sources in such networks. Thus, this paper develops a control concept based on a temperature set point optimization and agent-based control which allows the modular integration of an arbitrary number of sources and consumers. Afterwards, the concept is applied to two scenarios representing neighborhoods in San Francisco and Cologne with different heating and cooling demands and boundary conditions. The performance of the system is then compared to other state-of-the-art heating and cooling solutions using dynamic simulations with Modelica. The results show that bidirectional low temperature networks without optimization produce 26% less emissions in the San Francisco scenario and 63% in the Cologne scenario in comparison to the other heating and cooling solutions. Savings of energy costs are 46% and 27%, and reductions of primary energy consumption 52% and 72%, respectively. The presented operation optimization leads to electricity use reductions of 13% and 41% when compared to networks with free-floating temperature control and the results indicate further potential for improvement. The study demonstrates the advantage of low temperature networks in different situations and introduces a control concept that is extendable for real implementation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2018

Cascade energy optimization for waste heat recovery in distributed energy systems

The efficiency of distributed energy systems can be significantly increased through waste heat recovery from industry or power generation. The technologies used for this process are typically dependent on the quality and temperature grades of waste heat. To maximize the efficiency of cascade heat utilization, it is important to optimize the choice of waste heat recovery technologies and their operation. Here, a detailed mixed integer linear programming optimization model is proposed for waste heat recovery in a district-scale microgrid. The model can distinguish waste heat quality for planning and operation optimization of distributed energy systems. Heat utilization technologies are formulated in this developed model and categorized in different temperature grades. The developed model is validated using four typical cases under different settings of system operation and business models. It is found that the optimization model, by distinguishing waste heat temperature, can increase energy cost savings by around 5%, compared to models that do not consider waste heat temperature grades. Additionally, the results indicate that the developed model can provide more realistic configuration and technologies dispatch.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Dynamic optimization and economic evaluation of flexible heat integration in a hybrid concentrated solar power plant

Hybridization of concentrated solar power (CSP) plants provides flexibility in operation that can drastically improve the solar-to-electric (STE) efficiency and levelized cost of electricity (LCOE) relative to standalone CSP plants. Flexible heat integration (FHI) is a novel concept where the collection and integration of CSP within a power plant is modified relative to the amount of solar energy available. FHI improves the thermal efficiency of a hybrid solar tower steam Rankine cycle power plant but leads to increased pumping needs due to continuously elevated molten salt flow rates through the collection system, which can negatively impact STE efficiency. The present work is carried out to maximize the STE efficiency of a hybrid CSP plant utilizing FHI by employing a dynamic optimization framework where a genetic algorithm optimizes the operation of the plant over a given solar irradiance profile. The study concerns a plant hypothetically located in Salt Lake City, Utah. Here, the optimization results confirm the accuracy of a predictive heuristic where the preferred operation of the plant can be estimated relative to local peaks in the incident power generated by the heliostat collection field. The optimized FHI operation demonstrates a yearly STE efficiency of 13.8%, whereas the equivalent base-level hybrid and solar-only plants exhibit solar efficiencies of 13.4% and 11.2%, respectively. Economic analysis shows that FHI reduces yearly natural gas costs, leading to a $\$0.5$/MWh reduction in LCOE relative to the base-level hybrid configuration. Overall, the results show that hybrid FHI schemes exhibit economic benefits along with observed thermodynamic improvements.

14 SOLAR ENERGY↗
DOE OSTI2021

A novel machine learning-based optimization algorithm (ActivO) for accelerating simulation-driven engine design

A novel design optimization approach (ActivO) that employs an ensemble of machine learning algorithms is presented. The proposed approach is a surrogate-based scheme, where the predictions of a weak leaner and a strong learner are utilized within an active learning loop. The weak learner is used to identify promising regions within the design space to explore, while the strong learner is used to determine the exact location of the optimum within promising regions. For each design iteration, exploration is done by randomly selecting evaluation points within regions where the weak learner-predicted fitness is high. The global optimum obtained by using the strong learner as a surrogate is also evaluated to enable rapid convergence once the most promising region has been identified. First, the performance of ActivO was compared against five other optimizers on a cosine mixture function with 25 local optima and one global optimum. In the second problem, the objective was to minimize indicated specific fuel consumption of a compression-ignition internal combustion (IC) engine while adhering to desired constraints associated with in-cylinder pressure and emissions. In this work, the efficacy of the proposed approach is compared to that of a genetic algorithm, which is widely used within the internal combustion engine community for engine optimization, showing that ActivO reduces the number of function evaluations needed to reach the global optimum, and thereby time-to-design by 80%. Furthermore, the optimization of engine design parameters leads to savings of around 1.9% in energy consumption, while maintaining operability and acceptable pollutant emissions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Optimizing design and dispatch of a renewable energy system

Renewable energy technologies are becoming increasingly important due to their cost-competitiveness, and because of enhanced climate concerns. We demonstrate the capabilities of an integer-programming optimization model that minimizes capital (investment) and operational costs, and utility charges, while adhering to system sizing constraints, demand requirements, and interoperability characteristics of the systems chosen. Furthermore, the model recommends an optimally sized mix of renewable energy, conventional generation, and energy storage technologies, while simultaneously optimizing the corresponding dispatch strategy. Our case studies explore several venues, i.e., a small campus and a local hospital, with complex utility rate tariffs, multi-technology integration opportunities, and incentives for renewable power production. Using an optimization model, versus applying rules of thumb, can produce millions of dollars in savings over a 25-year time horizon and result in thousands of kilowatts of installed renewable energy.

25 ENERGY STORAGE↗
DOE OSTI2022

Optimizing the physical design and layout of a resilient wind, solar, and storage hybrid power plant

We report as wind and solar technologies improve and their costs decrease, the share of power produced by these sources will increase. As the market penetration increases, these power sources will need to provide grid services, such as dispatchability, in addition to providing energy. One way to reduce variability, provide higher quality power to the grid, and address local grid stability issues is through colocating wind and solar power plants. In addition to operating reliably during normal operating conditions, in scenarios with high penetrations of renewable generation, it is important that these hybrid plants can withstand production disruptions and continue to supply power despite prolonged resource reduction, extreme weather events, or other disruptions. In this paper, we present a methodology to optimize a wind-solar-battery hybrid power plant down to the component level that is resilient against production disruptions and that can continually produce some minimum required power. We introduce the models and assumptions we used to simulate a hybrid power plant as well as the design variable parameterization and specific methods we used to optimize the plant. We demonstrate the performance of our method by comparing a plant optimized for different objectives, generation outage durations, minimum power requirements, and power purchase agreements. Although the plant design is sensitive to model parameters and various other assumptions, our results demonstrate some of the optimal designs that occur in different scenarios and what one should expect when designing a hybrid wind-solar-storage power plant.

14 SOLAR ENERGY↗
DOE OSTI2019

Mass optimization of a supercritical CO 2 Brayton cycle with a direct cooled nuclear reactor for space surface power

A long life, reliable, and compact surface power system will be necessary to achieve future goals in space exploration. This application uniquely requires the system to be optimized with respect to mass because system mass directly drives the space launch cost associated with transporting the system to its desired location. In this study, a supercritical CO 2 Brayton cycle coupled to a direct-cooled nuclear reactor was designed and optimized for mass. Robust models were developed for each Brayton cycle component in order to model the cycle performance. The three most massive components of this cycle are the radiator-based heat rejection system (subsequently referred to as the “radiator”), recuperator, and reactor. Mass correlations for the recuperator and radiator were established through interactions with component experts from industry and national labs. A reactor model was developed to predict the minimum mass reactor that satisfies neutronic and thermal limitations for given cycle conditions. The system optimization explores tradeoffs between the reactor, recuperator, and radiator sizes in order to identify the least massive system that will satisfy the power (40 kWe) and life (10 yr) requirements. To explore the effects of turbine inlet temperature on system mass, three types of microtube and shell recuperator technologies were considered: baseline stainless steel (which is consistent with the industry partner’s current designs), stainless steel with non-heritage tube sizes (which requires further development of manufacturing techniques), and Inconel (which is not a current/legacy design). Both stainless steel designs have a temperature limit of 823 K, which limits the turbine inlet temperature to 900 K. The baseline stainless steel design results in a combined mass of 738 kg. The stainless steel design allowing for non-heritage tube sizes reduces the combined mass to 674 kg (a 9% improvement). The Inconel design leads to an optimal turbine inlet temperature of 1120 K and reduces the combined mass to 391 kg (a 47% improvement). Furthermore, the interesting conclusion from this study include: (1) radiator mass dominates the total mass, and this drives the cycle to relatively high heat rejection temperatures resulting in a compressor inlet state point that is not close to the vapor dome; thus, the typical advantages of an sCO 2 system are not realized, and a working fluid with a higher critical temperature may be more suitable, and (2) neutronic limitations cause the reactor size to be relatively unaffected by the power level.

42 ENGINEERING↗
DOE OSTI2024

Implementation and validation of optimal start control strategy for air conditioners and heat pumps

Commercial buildings are responsible for approximately 20 % of the total energy consumption and greenhouse gas emissions in the United States. Over 85 % of these buildings lack building automation systems, and many are small (<50,000 square feet), underserved, and use rooftop units (RTUs) for heating, ventilation, and air-conditioning needs. Because these buildings lack proper energy management systems, several operational deficiencies lead to excess energy consumption. Studies have shown that managing the RTUs’ heating and cooling set points, schedules, setbacks, and optimal start can result in a 20 % to 25 % reduction in electricity consumption in small commercial buildings. These buildings typically use fixed schedules to start the RTUs 60 to 120 min before occupancy begins, which results in excess energy consumption. This paper presents research that demonstrates and evaluates the performance of four optimal start methods, which utilize data-based modeling as a key element in facilitating adaptive control in response to time-varying inputs while requiring minimal sensor inputs. The evaluation found energy savings in two commercial buildings equipped with RTUs by periodically alternating four different optimal start models during the cooling and heating season. The resulting energy savings are positive for all models and range from 2 to 5 kWh/day/unit. The units on the east side of the building showed higher savings, while interior units showed greater variability in savings due to the differences in capacities and room sizes. Savings were considerably greater during the heating season compared to the cooling season. The performance of all four models on Mondays was poor; models suggested a shorter optimal start time, which resulted in relatively larger errors. Finally, the future work will look at using a different model for the days after weekends and holidays.

42 ENGINEERING↗