Incorporation of Uncertainties in the Mars Science Laboratory Rover Loads Analysis
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Aerospace structures and spacecraft are a complex assemblage of structural components that are subjected to a variety of complex, cyclic, and transient loading conditions. Significant modeling uncertainties are present in these structures, in addition to the inherent randomness of material properties and loads. To properly account for these uncertainties in evaluating and assessing the reliability of these components and structures, probabilistic structural mechanics (PSM) procedures must be used. Much research has focused on basic theory development and the development of approximate analytic solution methods in random vibrations and structural reliability. Practical application of PSM methods was hampered by their computationally intense nature. Solution of PSM problems requires repeated analyses of structures that are often large, and exhibit nonlinear and/or dynamic response behavior. These methods are all inherently parallel and ideally suited to implementation on parallel processing computers. New hardware architectures and innovative control software and solution methodologies are needed to make solution of large scale PSM problems practical.
The integrated hydrogen energy system incorporates hydrogen energy into the power grid, which has been recognized as a promising option for reaching a 100% renewable electricity supply. It can make a profit because the hydrogen produced can be sold as fuel or used to generate electricity for grid services. In this paper, we develop a planning model for the integrated hydrogen energy system that considers the uncertainty of the load demand, the renewable energy generation, and the market prices. To calculate the hydrogen load, we simulate the refueling operations at a hydrogen fueling station over the course of one day and generate representative load profiles with K-means clustering. Moreover, the long-term profitability of the integrated system under both current and future conditions is validated in 10-year planning results.
The integrated hydrogen energy system incorporates hydrogen energy into the power grid, which has been recognized as a promising option for reaching a 100% renewable electricity supply. It can make a profit because the hydrogen produced can be sold as fuel or used to generate electricity for grid services. In this paper, we develop a planning model for the integrated hydrogen energy system that considers the uncertainty of the load demand, the renewable energy generation, and the market prices. To calculate the hydrogen load, we simulate the refueling operations at a hydrogen fueling station over the course of one day. Moreover, the long-term profitability of the integrated system under both cur-rent and future conditions is compared in the planning results.
Abstract. Floating offshore wind turbine (FOWT) systems are subject to complex environmental loads, with significant potential for damage in extreme storm conditions. Design simulations in these conditions are required to assess the survivability of the device with some level of confidence. Aero-hydro-servo-elastic engineering tools can be used with a reasonable balance of accuracy and computational efficiency. The models require many input parameters to describe the air and water conditions, the system properties, and the load calculations. Each of these parameters has some possible range, due to either statistical uncertainty or variations with time. Variation in the input parameters can have important effects on the uncertainty in the resulting loads, but it is not practical to perform detailed assessments of the impact of this uncertainty for every input parameter. This work demonstrates a method to identify the input parameters that have the most impact on the loads to focus further inspection. The process is done specifically for extreme storm load cases defined in the International Electrotechnical Commission design requirements for floating offshore wind turbines. The analysis was performed using the International Energy Agency Wind 15 MW offshore reference wind turbine atop the University of Maine VolturnUS-S reference platform in two US offshore wind regions, the Gulf of Maine and Humboldt Bay. It was found that the direction of incident waves and current, yaw misalignment, and the length of mooring line sections were among the primary sensitivities.
This work proposes a physics-informed sparse Gaussian process (SGP) for probabilistic stability assessment of large-scale power systems in the presence of uncertain dynamic PVs and loads. The differential and algebraic equations considering uncertainties from dynamic PVs and loads are reformulated to a nonlinear mapping relationship that allows the application of SGP. Thanks to the nonparametric characteristic of Gaussian process, the proposed framework does not require distributions of uncertain inputs and this distinguishes it from existing approaches. As the original Gaussian process is not scalable to large-scale systems with high dimensional uncertain inputs, this paper develops the SGP with a stochastic variational inference technique. It leads to approximately two orders of complex reduction. A data pre-processing step is also introduced to tackle the coexistence of stable and unstable cases by sample clustering and constructing separate SGPs. The probabilistic transient stability index is analyzed to assess system stability under different uncertain dynamics loads and PVs. Comparisons are performed with the sampling-based, the polynomial chaos expansion-based, and traditional Gaussian process-based methods on the modified IEEE 118-bus and Texas 2000-bus systems under various scenarios, including different levels of uncertainties and the existence of nonlinear correlations among dynamic PVs. The impacts of data quality and quantity issues are also investigated. It is shown that the proposed SGP achieves significantly improved computational efficiency while maintaining high accuracy with a limited number of data.
Uncertainty in structural loading during launch is a significant concern in the development of spacecraft and launch vehicles. Small variations in launch vehicle and payload mode shapes and their interaction can result in significant variation in system loads. In many cases involving large aerospace systems it is difficult, not economical, or impossible to perform a system modal test. However, it is still vital to obtain test results that can be compared with analytical predictions to validate models. Instead, the “Building Block Approach” is used in which system components are tested individually. Component models are correlated and updated to agree as best they can with test results. The Space Launch System consists of a number of components that are assembled into a launch vehicle. Finite element models of the components are developed, reduced to Hurty/Craig-Bampton models and assembled to represent different phases of flight. The only opportunity to obtain modal test data from an assembled Space Launch System will be during the Integrated Modal Test. There is always uncertainty in every model, which flows into uncertainty in predicted system results. Uncertainty Quantification is used to determine statistical bounds on prediction accuracy based on model uncertainty. For the Space Launch System, model uncertainty is at the Hurty/Craig-Bampton component level. Uncertainty in the Hurty/Craig-Bampton components is quantified using the hybrid parametric variation approach that combines parametric and nonparametric uncertainty. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. This type of uncertainty cannot be represented by variations infinite element model input parameters and thus cannot be included in a parametric approach. However, model-form uncertainty can be modeled using a nonparametric approach based on random matrix theory. The hybrid parametric variation method requires the selection of dispersion values for the Hurty/Craig-Bampton fixed-interface eigenvalues, and the Hurty/Craig-Bampton stiffness matrices. Component test/analysis frequency error is used to identify the fixed-interface eigenvalue dispersions, while test/analysis cross-orthogonality is used to identify stiffness dispersion values. The hybrid parametric variation uncertainty quantification approach is applied to the Space Launch System Integrated Modal Test configuration. Monte Carlo analysis is performed, and statistics are determined for modal correlation metrics, frequency response from Integrated Modal Test shakers to selected accelerometers, as well as other metrics for determining how well target modes are excited and identified. If the predicted uncertainty envelopes future Integrated Modal Test results, then there will be increased confidence in the utility of the component-based hybrid parametric variation uncertainty quantification approach.
A select overview is provided of ongoing research focusing on the development and verification of integrated structural analysis and optimal design capabilities for advanced aerospace propulsion and power systems. Subjects discussed include the following: (1) Composites - analytical models (composite mechanics), integrated computational methods, and characterization of composite structural response and durability for resin-, metal-, and ceramic-matrix systems; (2) Advanced inelastic analysis - algorithm/numerical methods for more accurate and efficient analysis; (3) Constitutive modeling - theoretical formulation and characterization of thermoviscoplastic material behavior; (4) Computational simulation - engine structures from components to assembly, and up to an entire engine system subjected to simulated test-stand and mission load histories; (5) Probabilistic structural analysis - quantification of the effects of uncertainty in geometry, material, loads, and boundary conditions on structural response for true reliability assessment; and (6) Interdisciplinary optimization - incorporation of mathematical optimization and multidisciplinary analyses to provide streamlined, autonomous optimal design systems.
Load frequency control (LFC) is a key factor to maintain the stable frequency in multi-area power systems. As the modern power systems evolve from centralized to decentralized paradigm, LFC needs to consider the decentralized scheme that considers limited information from the information-exchange graph for the generator control of each interconnected area. This paper aims to solve a data-driven constrained LQR problem with mean-variance risk constraints and output structured feedback, and applies this framework to solve the LFC problem in multi-area power systems. By reformulating the constrained optimization problem into a minimax problem, the stochastic gradient descent max-oracle (SGDmax) algorithm with zero-order policy gradient (ZOPG) is adopted to find the optimal feedback gain from the learning, while guaranteeing the convergence. In addition, to improve the adaptation of the proposed learning method to new or varying models, we construct an emulator grid that approximates the dynamics of a physical grid and performs training based on this model. Once the feedback gain is obtained from the emulator grid, it is applied to the physical grid with a robustness test to check whether the controller from the approximated emulator applies to the actual system. Numerical tests show that the obtained feedback controller can successfully control the frequency of each area, while mitigating the uncertainty from the loads, with reliable robustness that ensures the adaptability of the obtained feedback gain to the actual physical grid.
Ramping products have been introduced or proposed in several U.S. power markets to mitigate the impact of load and renewable uncertainties on market efficiency and reliability. Current methods often rely on historical data to estimate the requirements of ramping products and fail to take into account the effects of the latest weather conditions and their uncertainties, which could lead to overly conservative or insufficient requirements. This study proposes a k-nearest-neighbor-based method to give weather-informed estimates of ramping needs based on short-term probabilistic solar irradiance forecasts. Forecasts from multiple sites are employed in conjunction with principal component analysis to derive numerical classifiers to characterize system-level weather conditions. In addition, we develop a data-driven method to optimize the model parameters in a rolling-forward manner. By using real-world data from the California Independent System Operator, we design two metrics to evaluate method performance: 1) frequency of shortage and 2) oversupply of ramping product. Our proposed method presents advantages in comparison with the baseline and a set of benchmark methods: without compromising system reliability, it reduces system ramping requirements by up to 25%, therefore improving both system reliability and economics.
Solar photovoltaic systems largely integrated within the distribution grid are operated 'behind-the-meter' and power generation cannot be directly monitored by most utilities. The increasing penetration of behind-the-meter solar photovoltaic systems can deter efficient network and market operations due to variability and uncertainty in net load, which is exacerbated by limited visibility and the difficulty in analyzing the hosting capacity. Risk introduced by behind-the-meter solar contributions may hinder reliable and secure grid operations due to biased system monitoring and forecasts. Accurate behind-the-meter estimations, together with capacity and specification forecasts, thus play a key role in balancing supply and demand and this article reviews the pertinent literature, identifying key characteristics and predictive methods for efficient behind-the-meter solar photovoltaic generation. Forecasting is central to methods herein. The fundamental characteristics of behind-the-meter solar forecasting, including which methods are applicable for scenario-driven use cases, are driven by the metrics most useful for system-wide performance evaluation. To this aim, the literature is reviewed with a focus on forecasting applications for aggregate, regional behind-the-meter generation useful to bulk system and utility operations. As distinguished from net load forecasting, subtleties in these coincident tasks are explored before concluding with recommendations for current practice and future implementations.
Wind farm control is an active and growing field of research in which the control actions of individual turbines in a farm are coordinated, accounting for inter-turbine aerodynamic interaction, to improve the overall performance of the wind farm and to reduce costs. The primary objectives of wind farm control include increasing power production, reducing turbine loads, and providing electricity grid support services. Additional objectives include improving reliability or reducing external impacts to the environment and communities. In 2019, a European research project (FarmConners) was started with the main goal of providing an overview of the state-of-the-art in wind farm control, identifying consensus of research findings, data sets, and best practices, providing a summary of the main research challenges, and establishing a roadmap on how to address these challenges. Complementary to the FarmConners project, an IEA Wind Topical Expert Meeting (TEM) and two rounds of surveys among experts were performed. From these events we can clearly identify an interest in more public validation campaigns. Additionally, a deeper understanding of the mechanical loads and the uncertainties concerning the effectiveness of wind farm control are considered two major research gaps.
California has set ambitious decarbonization goals concerning both emissions and the portion of energy generated by renewable resources. However, climate change poses considerable uncertainties. Variation in load is driven both by the level of electrification as well as the impact of climate change on weather. Further, climate change stands to make weather more variable, impacting not just load but generation from renewable resources. In this paper, we approach the issue of the impacts of climate change on decarbonization planning from two perspectives. First, we look at the range of decarbonization pathways through 8 pathways that account for differences in socioeconomic development, global emissions, and warming. Second, we develop a more robust way of ensuring the reliability of energy resources planning than the commonly used planning reserve margin. We show that the proposed method can save between 6 and 14 billion dollars in investment and maintenance costs and outline critical policy implications concerning the reliance of power plants for satisfying planning reliability requirements, including the potential retirement of dozens of peaker power plants.
This study investigates the combined impacts of climate change and agricultural conservation on the magnitude and uncertainty of nutrient loadings in the Maumee River Watershed, the second-largest watershed of the Laurentian Great Lakes. Two scenarios — baseline agricultural management and increased agricultural conservation — were assessed using an ensemble of five Soil and Water Assessment Tools driven by six climate models. The increased conservation scenario included raising conservation adoption rates from a baseline of existing conservation practices to feasible rates in the near future based on farmer surveys. This increased adoption of winter cover crops on 6%–10% to 60% of cultivated cropland; subsurface placement of phosphorus fertilizers on 35%–60% to 68% of cultivated cropland; and buffer strips intercepting runoff from 29%–34% to 50% of cultivated cropland. Increased conservation resulted in statistically significant (p ≤ 0.05) reductions in annual loads of total phosphorus (41%), dissolved reactive phosphorus (18%), and total nitrogen (14%) under the highest emission climate scenario (RCP 8.5). While nutrient loads decreased with increased conservation relative to baseline management for all watershed models, different conclusions on the true effectiveness of conservation under climate change may be drawn if only one watershed model was used.
Hybrid computer solutions for optimal control of time varying systems with parameter uncertainties, exemplifying minimax load relief for large launch vehicles
Application of beryllium to specific full-scale space shuttle structural components and assemblies was studied. Material evaluations were conducted to check the mechanical properties of as-received material to gain design information on characteristics needed for the material in the space shuttle environment, and to obtain data needed for evaluating component and panel tests. Four beryllium structural assemblies were analyzed and designed. Selected components of these assemblies, representing areas of critical loading or design/process uncertainty, were designed and tested, and two panel assemblies were fabricated. Trends in cost and weight factors were determined by progressive estimation at key points of preliminary design, final design, and fabrication to aid in a cost/weight evaluation of the use of beryllium.
In systems where the design inlet and outlet pressures are maintained above the thermodynamic critical pressure, it is often assumed that two phase flows within the system cannot occur. Designers rely on this simple rule of thumb to circumvent problems associated with a highly compressible two phase flow occurring within the supercritical pressure system along with the uncertainties in rotordynamics, load capacity, heat transfer, fluid mechanics, and thermophysical property variations. The simple rule of thumb is adequate in many low power designs but is inadequate for high performance turbomachines and linear systems, where two phase regions can exist even though outlet pressure is greater than critical pressure. Rotordynamic-fluid-mechanic restoring forces depend on momentum differences, and those for a two phase zone can differ significantly from those for a single-phase zone. Using the Reynolds equation the angular velocity, eccentricity, geometry, and ambient conditions are varied to determine the point of two phase flow incipience.
In engineering design practice behavior is usually predicted based on some known nominal design. However, when the design is fabricated it will differ from the nominal design because of manufacturing tolerances. In order to generate nominal designs that will still satisfy behavior constraints in the presence of manufacturing tolerances, engineers resort to the use of safety factors, over and above those introduced to account for other uncertainties (e.g., in load conditions, material properties, analysis modeling). The accurate selection of the values of these manufacturing tolerances safety factors is dependent on the capability of the engineer to determine the sensitivity of the critical constraints to changes in the design variables. This process usually leads to overly conservative designs. The task of choosing safety factors is much more difficult in structural synthesis because: (1) it is not known which constraints will be active at the final design, (2) as the design changes during the synthesis process the sensitivities of the constraints with respect to the design variables also change, and (3) the imposition of the safety factors themselves may change the set of critical constraints. These difficulties can be overcome with the approximation concepts approach to structural synthesis by buffering the approximate constraints with quantities that are related to the design variable tolerances and the accurate sensitivities of the constraints with respect to the design variable. Designs generated by this approach tend to be feasible but not overly conservative.