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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2015

Developing Probabilistic Safety Performance Margins for Unknown and Underappreciated Risks

Probabilistic safety requirements currently formulated or proposed for space systems, nuclear reactor systems, nuclear weapon systems, and other types of systems that have a low-probability potential for high-consequence accidents depend on showing that the probability of such accidents is below a specified safety threshold or goal. Verification of compliance depends heavily upon synthetic modeling techniques such as PRA. To determine whether or not a system meets its probabilistic requirements, it is necessary to consider whether there are significant risks that are not fully considered in the PRA either because they are not known at the time or because their importance is not fully understood. The ultimate objective is to establish a reasonable margin to account for the difference between known risks and actual risks in attempting to validate compliance with a probabilistic safety threshold or goal. In this paper, we examine data accumulated over the past 60 years from the space program, from nuclear reactor experience, from aircraft systems, and from human reliability experience to formulate guidelines for estimating probabilistic margins to account for risks that are initially unknown or underappreciated. The formulation includes a review of the safety literature to identify the principal causes of such risks.

Safety Performance Margin↗
NASA NTRS2019

Blind Validation Study of Parametric Cost Estimation Tool SEER-H for NASA Space Missions

One of the primary parametric cost modeling tools used by NASA and the aerospace industry to estimate the development and production cost of future spacecraft hardware is SEER-H by Galorath. To date, no independent validation of this tool for cost estimation of space missions has been reported in the literature. In the present validation study, cost estimators used SEER-H to estimate the cost of twelve different past NASA science missions. The estimators were prevented from knowing the actual cost of the missions in an effort to minimize cognitive biases. The point estimates of SEER-H had an average error of 23%, median error of -0.3%, and a standard deviation of 43%. Nine of the twelve mission's actual costs fell within the 80% confidence interval of SEER's probabilistic estimates. Several factors independent of SEER that may have affected the accuracy of the results have been identified and are discussed; these include: uncertainty in the technical data used for the estimates, the methods used to estimate uncertainty in spacecraft component mass and numbers of prototypes, and the experience of the estimators.

SEER-H↗
DOE OSTI2026

Assessing Photovoltaic Capacity Factor Variability Using Long-Term Satellite Derived Solar Resource Data Under Brazilian Climate

Accurate estimation of photovoltaic (PV) energy yield and its variability is essential for reducing financial risk and supporting reliable system planning for rapidly expanding PV markets. In Brazil, high solar adoption and increasing levels of distributed energy resources are beginning to introduce operational challenges such as curtailment and evolving grid requirements. Understanding how natural variability in solar resource propagates into PV system performance is therefore increasingly important for both project design and grid integration. Modern PV yield assessments commonly rely on multi-year meteorological datasets and probabilistic exceedance metrics (e.g., P50/P90) to quantify energy yield uncertainty for project financing. However, the implications of long-term solar resource variability for PV system design choices and high-adoption grid conditions remain less well characterized for rapidly expanding markets such as Brazil. In particular, understanding how weather-driven variability propagates into PV production distributions and capacity factor expectations is important for evaluating curtailment exposure, deployment strategies, and storage requirements in regions experiencing rapid growth of distributed and utility-scale PV. Seasonal and interannual variability in atmospheric conditions can produce substantial fluctuations in monthly PV energy production, which propagate into uncertainty in annual energy yield and capacity factor expectations. Characterizing this variability using long-term meteorological datasets allows probabilistic estimation of PV system performance and provides improved insight into the range of expected PV energy outcomes. This study explores the use of long-term satellite-derived meteorological data from the National Solar Radiation Database (NSRDB) to evaluate the variability of photovoltaic system performance across multiple locations in Brazil. Using a 27-year dataset (1998-2024), PV system simulations are performed to characterize the distribution of annual and seasonal capacity factors and energy yield outcomes, while propagating key sources of meteorological variability and model uncertainty through the PV modeling chain. The analysis also investigates the sensitivity of PV performance outcomes to key system design assumptions within the PV modeling chain, including tracking configuration and system sizing parameters. The resulting probabilistic performance characterization provides insight into how weather-driven variability influences PV production expectations and capacity factor distributions. These results provide a foundation for evaluating how weather-driven variability interacts with high PV adoption and potential storage or curtailment mitigation strategies.

14 SOLAR ENERGY↗
NASA NTRSDate not supplied

Blind Validation Study of PRICE TruePlanning and SEER-H

Two of the primary parametric costing tools used to estimate the development and production cost of future spacecraft hardware are PRICE TruePlanning by PRICE Systems, and System Estimation and Evaluation of Resources-Hardware (SEER-H) by Galorath. These are standard tools used by NASA and industry to estimate the cost of new aerospace hardware. This study is an independent verification of the accuracy of these tools and was originally published in 2018. The purpose of this presentation is to circulate the findings of that study among the NASA cost community. Both PRICE Systems and Galorath have completed internal validation studies of their parametric cost estimating tools; however, they only provided the results of the studies and did not detail the exact methods used to perform the validation. In the present study, cost estimators used PRICE TruePlanning and SEER-H to estimate the cost of twelve different past NASA science missions. The estimators were prevented from knowing the actual cost of the missions in an effort to minimize cognitive biases. In the present study, SEER-H had an average error of 23%, median error of -0.3%, with a standard deviation of 43%. PRICE had an average error of 52%, median error of 50%, and standard deviation of 45%. Nine of the twelve mission's actual costs fell within the 80% confidence interval of SEER's probabilistic estimates; however, none of the missions fell within PRICE’s confidence intervals. There were several factors independent of PRICE and SEER-H which may have affected the accuracy of the results in the present study including: uncertainty in the technical data used for the estimates, the methods used to estimate uncertainty in spacecraft component mass and numbers of prototypes, and the experience of the estimators.

SEER↗
NASA NTRS2011

Bridging Empirical and Physical Approaches for Landslide Monitoring and Early Warning

Rainfall-triggered landslides typically occur and are evaluated at local scales, using slope-stability models to calculate coincident changes in driving and resisting forces at the hillslope level in order to anticipate slope failures. Over larger areas, detailed high resolution landslide modeling is often infeasible due to difficulties in quantifying the complex interaction between rainfall infiltration and surface materials as well as the dearth of available in situ soil and rainfall estimates and accurate landslide validation data. This presentation will discuss how satellite precipitation and surface information can be applied within a landslide hazard assessment framework to improve landslide monitoring and early warning by considering two disparate approaches to landslide hazard assessment: an empirical landslide forecasting algorithm and a physical slope-stability model. The goal of this research is to advance near real-time landslide hazard assessment and early warning at larger spatial scales. This is done by employing high resolution surface and precipitation information within a probabilistic framework to provide more physically-based grounding to empirical landslide triggering thresholds. The empirical landslide forecasting tool, running in near real-time at http://trmm.nasa.gov, considers potential landslide activity at the global scale and relies on Tropical Rainfall Measuring Mission (TRMM) precipitation data and surface products to provide a near real-time picture of where landslides may be triggered. The physical approach considers how rainfall infiltration on a hillslope affects the in situ hydro-mechanical processes that may lead to slope failure. Evaluation of these empirical and physical approaches are performed within the Land Information System (LIS), a high performance land surface model processing and data assimilation system developed within the Hydrological Sciences Branch at NASA's Goddard Space Flight Center. LIS provides the capabilities to quantify uncertainty from model inputs and calculate probabilistic estimates for slope failures. Results indicate that remote sensing data can provide many of the spatiotemporal requirements for accurate landslide monitoring and early warning; however, higher resolution precipitation inputs will help to better identify small-scale precipitation forcings that contribute to significant landslide triggering. Future missions, such as the Global Precipitation Measurement (GPM) mission will provide more frequent and extensive estimates of precipitation at the global scale, which will serve as key inputs to significantly advance the accuracy of landslide hazard assessment, particularly over larger spatial scales.

Kirschbaum, Dalia↗
NASA NTRS2021

Probabilistic Machine Learning Estimation of Ocean Mixed Layer Depth from Dense Satellite and Sparse In-Situ Observations

The ocean mixed layer plays an important role in the coupling between the upper ocean and atmosphere across a wide range of time scales. Estimation of the variability of the ocean mixed layer is therefore important for atmosphere-ocean prediction and analysis. The increasing coverage of in situ Argo profile data allows for an increasingly accurate analysis of the mixed layer depth (MLD) variability associated with deviations from the seasonal climatology. However, sampling rates are not sufficient to fully resolve subseasonal (<90 day) MLD variability. Yet, many multivariate observations-based analyses include implicit modeled subseasonal MLD variability. One analysis method is optimal interpolation of in situ data, but the interior analysis can be improved by leveraging surface data with regression or variational approaches. Here, we demonstrate how machine learning methods and satellite sea surface temperature, salinity, and height facilitate MLD estimation in a pilot study of two regions: the mid-latitude southern Indian and the eastern equatorial Pacific Oceans. We construct multiple machine learning architectures to produce weekly 1/2° gridded MLD anomaly fields (relative to a monthly climatology) with uncertainty estimates. We test multiple traditional and probabilistic machine learning techniques to compare both accuracy and probabilistic calibration. We validate our methodology by applying it to ocean model simulations. We find that incorporating sea surface data through a machine learning model improves the performance of spatiotemporal MLD variability estimation compared to optimal interpolation of Argo observations alone. These preliminary results are a promising first step for the application of machine learning to MLD prediction.

Machine Learning↗
DOE OSTI2024

Artificial-intelligence-driven shot reduction in quantum measurement

Variational Quantum Eigensolver (VQE) provides a powerful solution for approximating molecular ground state energies by combining quantum circuits and classical computers. However, estimating probabilistic outcomes on quantum hardware requires repeated measurements (shots), incurring significant costs as accuracy increases. Optimizing shot allocation is thus critical for improving the efficiency of VQE. Current strategies rely heavily on hand-crafted heuristics requiring extensive expert knowledge. This paper proposes a reinforcement learning (RL)-based approach that automatically learns shot assignment policies to minimize total measurement shots while achieving convergence to the minimum of the energy expectation in VQE. The RL agent assigns measurement shots across VQE optimization iterations based on the progress of the optimization. This approach reduces VQE's dependence on static heuristics and human expertise. When the RL-enabled VQE is applied to a small molecule, a shot reduction policy is learned. The policy demonstrates transferability across systems and compatibility with other wavefunction Ansätze. In addition to these specific findings, this work highlights the potential of RL for automatically discovering efficient and scalable quantum optimization strategies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Stochastic Model Predictive Control With Gaussian Wind Direction Preview for Wake Steering

This article addresses the problem of wake steering control for wind farms that explicitly consider the tradeoff between farm-level power generation and yaw duty cycle under variable and uncertain wind conditions. A novel stochastic model predictive control (MPC) algorithm is presented, which utilizes a stochastic model of the freestream wind field components in a receding horizon framework to compute optimal yaw set points that maximize the expected value of the farm power while constraining the yaw actuation. Different configurations of the algorithm are evaluated using a steady-state wind farm simulator. The proposed stochastic MPC algorithm can plan control actions over a future prediction horizon based on probabilistic estimates of the incoming wind magnitude and direction.

17 WIND ENERGY↗
DOE OSTI2020

A Bayesian Approach for Statistical–Physical Bulk Parameterization of Rain Microphysics. Part II: Idealized Markov Chain Monte Carlo Experiments

Observationally informed development of a new framework for bulk rain microphysics, the Bayesian Observationally Constrained Statistical–Physical Scheme (BOSS; described in Part I of this study), is demonstrated. This scheme’s development is motivated by large uncertainties in cloud and weather simulations associated with approximations and assumptions in existing microphysics schemes. Here, a proof-of-concept study is introduced using a Markov chain Monte Carlo sampling algorithm with BOSS to probabilistically estimate microphysical process rates and parameters directly from a set of synthetically generated rain observations. The framework utilized is an idealized steady-state one-dimensional column rainshaft model with specified column-top rain properties and a fixed thermodynamical profile. Different configurations of BOSS—flexibility being a key feature of this approach—are constrained via synthetic observations generated from a traditional three-moment bulk microphysics scheme. The ability to retrieve correct parameter values when the true parameter values are known is illustrated. For cases when there is no set of true parameter values, the accuracy of configurations of BOSS that have different levels of complexity is compared. It is found that addition of the sixth moment as a prognostic variable improves prediction of the third moment (proportional to bulk rain mass) and rain rate. In contrast, increasing process rate formulation complexity by adding more power terms has little benefit—a result that is explained using further-idealized experiments. BOSS rainshaft simulations are shown to well estimate the true process rates from constraint by bulk rain observations, with the further benefit of rigorously quantified uncertainty of these estimates.

58 GEOSCIENCES↗
DOE OSTI2020

Combining Emergent Constraints for Climate Sensitivity

A method is proposed for combining information from several emergent constraints into a probabilistic estimate for a climate sensitivity proxy Y such as equilibrium climate sensitivity (ECS). The method is based on fitting a multivariate Gaussian PDF for Y and the emergent constraints using an ensemble of global climate models (GCMs); it can be viewed as a form of multiple linear regression of Y on the constraints. The method accounts for uncertainties in sampling this multidimensional PDF with a small number of models, for observational uncertainties in the constraints, and for overconfidence about the correlation of the constraints with the climate sensitivity. Its general form (Method C) accounts for correlations between the constraints. Method C becomes less robust when some constraints are too strongly related to each other; this can be mitigated using regularization approaches such as ridge regression. An illuminating special case, Method U, neglects any correlations between constraints except through their mutual relationship to the climate proxy; it is more robust to small GCM sample size and is appealingly interpretable. These methods are applied to ECS and the climate feedback parameter using a previously published set of 11 possible emergent constraints derived from climate models in the Coupled Model Intercomparison Project (CMIP). The ±2σ posterior range of ECS for Method C with no overconfidence adjustment is 4.3 ± 0.7 K. For Method U with a large overconfidence adjustment, it is 4.0 ± 1.3 K. This study adds confidence to past findings that most constraints predict higher climate sensitivity than the CMIP mean.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Multi-Mechanism Flood Hazard Assessment: Example Use Case Studies

Multi-mechanism flood (MMF) events are caused by the combined effects of more than one flooding mechanism. Although floods can result from the occurrence of individual flood mechanisms, they can (and often do) result from multiple flooding mechanisms. MMF events may be more severe than single mechanism events, or they may differ in characteristics. To facilitate comprehensive risk-informed decision-making to protect against and mitigate the effects of flood events, understanding the hazard contributions from MMFs is important. Nevertheless, conventional probabilistic flood hazard assessment approaches typically focus on individual flood hazard mechanisms. This report is part of a research project funded by the US Nuclear Regulatory Commission (NRC) intended to assist NRC in developing the technical basis for guidance on developing probabilistic estimates of flood hazards for combinations of flood mechanisms. Specifically, the purpose of this report is to document two case studies to illustrate approaches for quantifying MMF hazards for inland and coastal flooding scenarios.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

IACMI Project 4.2: Thermoplastic Composite Development for Wind Turbine Blades

(Section 5.1) Composites made from Arkema’s Elium® thermoplastic resin and Johns Manville fiberglass were researched during this project for applications in wind blade manufacturing. A techno-economic model was developed to model this wind blade manufacturing process using these materials in place of traditional composites made with thermoset resin. This model was based on manufacturing a 61.5-meter wind blade, which showed a 4.7% reduction in wind blade cost as compared traditional thermoset materials. These cost savings were not from the thermoplastic material costing less than traditional thermoset materials, but rather from decreased capital costs, faster cycle times and reduced energy requirements and labor costs. (Section 5.2) An infusion and curing model was developed for thermoplastic composite wind blades using PAM-RTM. The primary goal was to demonstrate the infusion simulation for the Elium® resin system on a 13-meter wind blade. Additionally, the exotherm temperature was predicted and compared to measurements, which showed model results within 10% of actual measurements. (Section 5.3) Composite laminate panels and composite sandwich panels with a balsa core were produced; specimens were cut and characterized. Similar composite specimens were made with Elium® thermoplastic resin and Hexion thermoset epoxy (RIMR135/RIMH1366) to enable comparisons between these resin systems. The static test methods included: tensile, compression, in-plane shear, interlaminar shear, flexural, sandwich core shear flexure, and single cantilever beam tests for sandwich beams. Fatigue testing at room temperature was completed to composite laminate panels at a stress ratio of R=0.1 and R=10. In addition, fatigue testing to laminate panels was completed at -30°C, and at room temperature after conditioning specimens at 70°C and 90% relative humidity. Overall, mechanical test results from Elium® composites are similar to epoxy composites. (Section 5.4) Elium composite panels were produced with intentional defects such as voids and nonwetting of fibers to begin to understand performance sensitivity to defects. A thermal digital image correlation (TDIC) method provides high spatial resolution strain field at elevated temperatures and can be used to identify defective regions within composite panels. Flexural modulus differences of 21% were seen between defect and non-defect panels. Other Elium® composite panels were forced to be defective by boiling the resin after infusion, which created voids throughout the composite laminate. X-ray computed tomography scanning was used to view the internal structure of the defect panels. Defect panels had a significant reduction in fatigue life as compared to baseline panels produced without intentional defects. (Section 5.5) Lap shear specimens were fabricated to compare the lap shear strength of an off-the-shelf adhesive (Plexus MA590) and two new adhesives developed by Arkema (Bostik SAF30 90 and Bostik SAF30 120). ISO standard 4587:2003 was used to standardize the testing method and sample fabrication. Lap shear specimens were made at 1mm, 3mm, and 10mm thicknesses. The Bostik adhesive lap shear test results were similar to Plexus for all thicknesses. (Section 5.6) Fiber-reinforced polymer (FRP) composites are typically used in high-performance applications (e.g., aerospace), and their expansion into high-volume industries (e.g. consumer automotive and wind turbine blade manufacturer or similar) is hindered by their cost and a lack of efficient manufacturing techniques. Monitoring the curing process of these composites during manufacturing can improve the efficiency of the process, and therefore reduce the manufacturing cost. Cure monitoring techniques were developed that use probabilistic estimation methods and surface temperature measurements made using infrared cameras. These techniques enable real-time monitoring of the infusion process to locate manufacturing flaws, and they can, potentially, estimate residual stresses in the part. Their commercialization will help facilitate expansion of FRP composites in high-volume industries. (Section 5.7) A 13-meter composite wind blade was produced with Elium® resin and Johns Manville fiberglass; this blade was made with VARTM processing similar to how megawatt-scale wind blades are currently manufactured, but no post-mold heating was used for this thermoplastic composite blade. The wind blade underwent full-scale validation for static loading (4-different load orientations) and flapwise fatigue loading to simulate 20-years of operational loads. The thermoplastic composite wind blade withstood the loading without any noted issues and performed similar to results from a previous full-scale validation to an equivalent epoxy composite wind blade produced with the same blade molds. (Section 5.8) A study was conducted to determine the feasibility of recycling composite wind turbine blade components fabricated with glass fiber reinforced Elium® thermoplastic resin. Dissolution, which is a process unique to thermoplastic matrices, allows recovery of both the polymer matrix and full-length glass fibers, while maintaining their stiffness and strength throughout the recovery process. The economics of recycling is favorable if 50% of the glass fiber is recovered and resold for a process of $\$$ 0.28/kg, and 90% of the resin is recovered and resold at a price of $\$$ 2.50/kg.(Section 10) Recommendations are outlined for commercializing thermoplastic resin for composite wind blade production, in addition to recommended areas for future research.

17 WIND ENERGY↗
DOE OSTI2024

SOSAT: Geohazard Risk Assessment in Carbon Sequestration Operations

Like all operations in which fluids are injected into the subsurface, geologic carbon storage (GCS) presents inherit risks that must be assessed and mitigated to successfully deploy such technology in the field. For example, alterations to pore pressure and the stress state due to fluid injection may trigger certain geohazards, such as potential fault activation and induced seismicity or unintentional hydraulic fracturing. Here we present capabilities for assessing these potential risks using the State of Stress Analysis Tool (SOSAT): a Python library and web-based application capable of probabilistically estimating the subsurface state of stress informed by various field observations. Using posterior distributions of principal stress components, SOSAT can assess the risk of fault activation within the injection formation for either a critically oriented fault or a fault with a user-prescribed orientation. Additionally, SOSAT can estimate the probability of unintentional hydraulic fracturing of the intact reservoir rock. Here, we demonstrate these SOSAT capabilities using a hypothetical GCS site. This type of risk assessment can assist with the effective deployment of GCS technology in the field by informing safe design and management practices.

Haagenson, Ryan J.↗
NASA NTRS1991

Probabilistic/Fracture-Mechanics Model For Service Life

Computer program makes probabilistic estimates of lifetime of engine and components thereof. Developed to fill need for more accurate life-assessment technique that avoids errors in estimated lives and provides for statistical assessment of levels of risk created by engineering decisions in designing system. Implements mathematical model combining techniques of statistics, fatigue, fracture mechanics, nondestructive analysis, life-cycle cost analysis, and management of engine parts. Used to investigate effects of such engine-component life-controlling parameters as return-to-service intervals, stresses, capabilities for nondestructive evaluation, and qualities of materials.

Watkins, T., Jr.↗
NASA NTRS2012

Design and Application of the Exploration Maintainability Analysis Tool

Conducting human exploration missions beyond Low Earth Orbit (LEO) will present unique challenges in the areas of supportability and maintainability. The durations of proposed missions can be relatively long and re-supply of logistics, including maintenance and repair items, will be limited or non-existent. In addition, mass and volume constraints in the transportation system will limit the total amount of logistics that can be flown along with the crew. These constraints will require that new strategies be developed with regards to how spacecraft systems are designed and maintained. NASA is currently developing Design Reference Missions (DRMs) as an initial step in defining future human missions. These DRMs establish destinations and concepts of operation for future missions, and begin to define technology and capability requirements. Because of the unique supportability challenges, historical supportability data and models are not directly applicable for establishing requirements for beyond LEO missions. However, supportability requirements could have a major impact on the development of the DRMs. The mass, volume, and crew resources required to support the mission could all be first order drivers in the design of missions, elements, and operations. Therefore, there is a need for enhanced analysis capabilities to more accurately establish mass, volume, and time requirements for supporting beyond LEO missions. Additionally, as new technologies and operations are proposed to reduce these requirements, it is necessary to have accurate tools to evaluate the efficacy of those approaches. In order to improve the analysis of supportability requirements for beyond LEO missions, the Space Missions Analysis Branch at the NASA Langley Research Center is developing the Exploration Maintainability Analysis Tool (EMAT). This tool is a probabilistic simulator that evaluates the need for repair and maintenance activities during space missions and the logistics and crew requirements to support those activities. Using a Monte Carlo approach, the tool simulates potential failures in defined systems, based on established component reliabilities, and then evaluates the capability of the crew to repair those failures given a defined store of spares and maintenance items. Statistical analysis of Monte Carlo runs provides probabilistic estimates of overall mission safety and reliability. This paper will describe the operation of the EMAT, including historical data sources used to populate the model, simulation processes, and outputs. Analysis results are provided for a candidate exploration system, including baseline estimates of required sparing mass and volume. Sensitivity analysis regarding the effectiveness of proposed strategies to reduce mass and volume requirements and improve mission reliability is included in these results.

Stromgren, Chel↗
NASA NTRS2020

A Digital Twin Feasibility Study (Part II):Non-Deterministic Predictions of Fatigue Life Using In-Situ Diagnostics and Prognostics

The Digital Twin (DT) concept has the potential to revolutionize the way systems and their components are designed, managed, maintained, and operated across a vast number of fields from engineering to healthcare. The focus of this work is the implementation of DT for the health management of fatigue critical structures. This paper is the second part of a two-part series. The first of the series demonstrated the use of multi-scale, initiation-to-failure crack growth modeling to form non-deterministic predictions of fatigue life. In this second part, a general method for reducing uncertainty in fatigue life predictions is presented that couples in-situ diagnostics and prognostics in a probabilistic framework. Monte Carlo methods and high-fidelity finite element models are used to (i) generate probabilistic estimates of crack state throughout the life of the same geometrically complex test specimen and (ii) predict fatigue life with decreasing uncertainty as more of these diagnoses are obtained. The ability to predict accurately and in the presence of uncertainty is demonstrated, suggesting that the proposed DT method is feasible for fatigue life prognosis and should be pursued further with a focus on increasing application realism.

Patrick E Leser↗
NASA NTRS1991

Development of a probabilistic analysis methodology for structural reliability estimation

The novel probabilistic analysis method for assessment of structural reliability presented, which combines fast-convolution with an efficient structural reliability analysis, can after identifying the most important point of a limit state proceed to establish a quadratic-performance function. It then transforms the quadratic function into a linear one, and applies fast convolution. The method is applicable to problems requiring computer-intensive structural analysis. Five illustrative examples of the method's application are given.

Torng, T. Y.↗