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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Tuning and Verification of an Internal Flooding Model for Dynamic PRA

In probabilistic risk assessment (PRA), the likelihoods and consequences of basic events are combined to determine possible system level outcomes and the likelihood of each outcome given an initial event. Both the consequences and likelihoods of basic events may be informed by the use of mathematical models or experimental data regarding the phenomena of interest. In either case, the impact of uncertainties on the results need to be evaluated. If a model is used to predict the evolution of an initiating event, uncertainty quantification can be computationally challenging for complex phenomena with many epistemic (e.g., model) uncertainties. In this work, a reduced order model is introduced for the flooding analysis of a multi-room building at a nuclear power plant under uncertainties which can require long run times using high fidelity computer models. The reduced order model focuses on macro-level transfer of water between rooms and tracks the water level within each room. In order to verify the model's fidelity, its results for the phenomena involved in a scenario of interest are compared to those of a computational fluid dynamics (CFD) code, which are taken to represent reality. This work does not focus on the overall fidelity of the flooding model, as the goal of the project for which it was developed is to develop a methodology rather than to analyze a particular case. The focus instead is on the tunability and verifiability of the reduced order model for relevant physical measures. In analyzing a particular case, the model may be required to incorporate more realistic description of phenomena; however, the procedure described in this work may be used to verify its performance as well. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Rich-Text based PSA Model Transformation and Verification in RiskA

Nuclear Energy is one of the most possible alternative to fossil energy in large-scale. Nuclear safety is the lifeline of nuclear energy development, and has been an important part of national security, especially after the accident of Fukushima. On the basis of computer codes, reliability engineering and Probabilistic Risk Assessment (PSA) is effective methods to improve the safety of nuclear power plants. After many years of development, the methodologies, applications and relevant soft programs have been quite sufficient in the area of nuclear safety. However, it is still difficult for the current PSA technologies and software to meet the needs of dealing with the problems of quantitatively public risk assessment in the digital society. Especially, there are so many software that adopted different modeling and analyzing methods, which brings difficulties to the comparison, evaluation or verification for different software and models. By using its own academic advantages, the advanced nuclear energy research team, i.e., FDS Team has invested a few hundreds person-years of independent research and development of a reliability and probabilistic safety assessment software system RiskA. The system consists of three main functions: device reliability optimization management, probabilistic safety assessment and instantaneous risk monitoring, and the comprehensive public risk assessment in digital society. RiskA establishes an integrated risk evaluation system for the device reliability, nuclear power plant (NPP) risk monitoring and public risk assessment. Currently, RiskA has successfully been applied in more than 600 organizations and institutes from a variety of fields in 39 countries, involving nuclear, aerospace, defense and so on. For example, RiskA has been used in the safety analysis of International Thermonuclear Experimental Reactor (ITER), FDS series fusion reactor, and the Strategic Priority Research Program of Chinese Academy of Sciences 'the Future Advanced Nuclear Fission Energy - Accelerator Driven Sub-critical (ADS) transmutation system'. Also, RiskA has been used in public risk communication and risk assessment. Among them, Third Qinshan nuclear power plant Risk Monitor (TQRM), which is the China's first domestic nuclear safety analysis software used in the actual online operation, has been highly apprised by renowned experts in the field. Meanwhile, it has been identified as the first domestic nuclear power plant risk monitoring system with completely independent intellectual property rights, and has reached the international advanced level. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Identification of Significant NPP Cyber-Attack Scenarios based on Risk Information

For the last decades, analog instrumentation and control (I and C) systems have been replaced with digital systems in nuclear power plants (NPPs). While there are various advantages of the digital technology for the plant safety, new threats have been introduced such as cyber security. In fact, there have been cyber-attacks on nuclear facilities adopting digital systems. The cyber-attack on the Iran nuclear facility is a typical example which shows the possibility of a cyber-attack on safety critical infrastructures with intra-network. Cyber security has been introduced as one of the significant issues for NPP safety and recently its importance has been more highlighted, but the research in this field is not mature yet. Moreover, there is not much information about cyber security of NPPs. In this work, as a fundamental research for risk evaluation of cyber-attacks, a method to identify significant cyber-attack scenarios on NPPs was proposed based on the probabilistic risk assessment (PRA) method which is widely used for evaluating the safety of NPPs. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

A Simplified Multi-Path Event Tree for the Integral, Inherently-Safe Light Water Reactor (I{sup 2}S-LWR)

The Integral, Inherently-Safe Light Water Reactor (I{sup 2}S-LWR) concept aims to raise the bar for nuclear power plant safety while maintaining the economic advantages of large, gigawatt-scale plants.1 To obtain this goal, the project safety team seeks to eliminate initiating events where possible, maximize passivity of safety systems, and optimize a balance of redundancy, diversity, and simplicity of safety systems.2 Achievement of these objectives, particularly the last set, requires detailed, quantitative risk information from the earliest stages of development. Therefore, despite limited design information, we have constructed a preliminary probabilistic risk assessment (PRA) for I{sup 2}S-LWR. Safety implementation for I{sup 2}S-LWR, then, requires an iterative process involving system design, thermal-hydraulic (T/H) and neutronic deterministic analyses, and risk-informing PRA studies. Due to this parallelism, it is vital those team members without PRA expertise quickly and correctly understand preliminary PRA results. To this end, we have developed a method to condense the entire PRA into a single, multi-path event tree (MPET). (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Development of a Severe Accident Analysis Engine Using Approximate Reasoning

In hypothetical severe accident scenarios, nuclear power plant safety is challenged by core degradation and release of fission products. To aid the plant operator and technical support center staff, research has been performed to develop understanding of severe accident phenomenology, assessing their risk and devise measures to mitigate accident consequences (Sehgal, 2011). Nuclear power plant accidents involve highly complex physical and chemical interactions, a large number of safety related systems, and emergency operating procedures (EOP) and severe accident management guidelines (SAMG). Large number of factors with uncertainty and stress can overwhelm the operators. The overall objective of the present research is to develop a methodology and tools that an operator can use to predict severe accident progression and make effective decisions to arrest and manage the accident under large uncertainties. Towards this goal, this study examines a novel approach that brings to bear a combined use of techniques in artificial intelligence (Russel and Norvig, 2010), including Bayesian Network (BN), Answer Set Programming (ASP) and Fuzzy Inference (FI) to achieve faster-than-real-time, yet sufficiently accurate analysis of severe accident progression. Bayesian network (BN) is a type of probabilistic graphical models that can be used to represent knowledge and conditional dependencies about an uncertain realm. It is useful for capturing the causal relationships in a complex system. It also allows prediction via Bayesian inference (Kelly and Smith, 2012). It is composed of nodes and edges, which express random variables and probabilistic relationships between the nodes, respectively. This relationship, given by conditional probability is calculated using stochastic methods. The BN is used in several systems for analysis and management of accident risk; e.g. (Knochenhauer and Frid, 2010). In those systems, the nodes or so-called 'effective factors' are presumably known within the network by system descriptions in SAMGs. There are two steps to configure the BN, namely (i) identifying compositions within the network and (ii) defining conditional dependency between nodes. The first step is performed following the spirit of ASP (Baral, 2003) using Prolog (Wielemaker, 2005). Knowledge representation is used to build databases required for processing by ASP. Knowledge representation is defined as the expression of knowledge in a way that is understandable to both human and computers. Originally knowledge indicates data, information and facts. To focus, knowledge should be formed to achieve a goal. In a severe accident, key physics and safety related components status are defined according to a failure mode. The conditional dependencies between nodes are generated by approximate reasoning using Fuzzy inference (Zadeh, 1995). Fuzzy logic is a multiple-valued logic to treat ambiguous features such as linguistic description. It indicates possibility, which is distinguished from probability. Fuzzy set consists of linguistic variables according to the fixed rule. In other words, even uncertain states could be expressed as not binary logic, but as many-value logic by rule-based technology. Fuzzy control system is comprised of Fuzzy inference engine that is performed based on the 'If-Then Rule'. The 'If-Then Rule' is of the following form. If Y1 is B11 and Y2 is B12 then Z is C1. If Y1 is B21 and Y2 is B22 then Z is C2. Y1 and Y2 are inputs, which indicate conditional variables. Z indicates decision-making and both B and C are linguistic variables. With this rule-based technique, the approximate reasoning can be realized by Fuzzy inference. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

PWR Station Blackout and External Events Analysis for LWRS/RISMC Project

In the framework of the US-DOE Light Water Reactor Sustainability/ Risk-Informed Safety Margin Characterization (LWRS/RISMC) project, methods, data and tools are being developed with the ultimate scope of improving the safety and operation of the current US nuclear fleet. A set of Industrial Applications (IA) concerning the most relevant safety issues is defined for applying and testing the developed tool kits. The ultimate scope of IA no. 2 is a realistic simulation of natural external hazards that impose threat to a Nuclear Power Plant (NPP). This scope requires the development of a methodology and of a qualified set of tools able to perform advanced risk-informed safety analysis. In particular the methodology should be able to combine results from seismic, flooding and thermal-hydraulic (TH) deterministic calculations with dynamic Probabilistic Risk Assessment (PRA). A so-called Risk Informed Margin Management (RIMM) approach is being used to represent meaningful (i.e., realistic facility representation and simulation) event scenarios and consequences by linking probabilistic simulations to external events physics. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Systems Safety Evaluation Based on System Thinking

Every engineer knows well and always considers about 'The local optimization makes the entire worst', and therefore well balanced design is required. Even the total safety has been assured by the safety design based on defense in depth concept, operational problem would occur by the chain of the fallacy of the defense in depth, then safety culture degradation, and finely organizational accident eventually happened. Probabilistic approach is required to the problem. We should answer to the question 'Safety Goal: How safe is safe enough?' for public acceptance. To respond to the operational problem and safety goal question, PRA, Probabilistic Risk Analysis is required. Further, Risk Communication should include comparison and selection among technical systems by risk and benefit analysis. Therefore, systems safety consideration is important based on systems thinking with considering following characteristics: - Goal-oriented- Optimization, Alternative proposals; - Global perspective- Bird's Eye; - Hierarchy- Isomorphism; - Life Cycle: Plan-Design-Construction-Use-Disposal; - Learning and Evolution. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

Assembling Multiple Models Within the RAVEN Framework

RAVEN (Risk Analysis Virtual Environment) is an INL-developed software tool that can be used to identify and increase the safety margin in complex systems. As a generic software framework, RAVEN is designed to perform parametric and probabilistic analysis based on the response of complex system codes. RAVEN is capable of investigating the system response as well as the input space using Monte Carlo, Grid, or Latin Hyper Cube sampling schemes, but its strength is focused toward system feature discovery, such as limit surfaces, separating regions of the input space leading to system failure, using dynamic supervised learning techniques. RAVEN is currently able to construct multi-targets Reduced Order Models (ROMs), which are aimed to represent the response of a system (in a fixed configuration) for multiple Figures of Merits (FOMs) and time-dependent ROMs. These capabilities represent the initial steps for a larger implementation about the interaction of multiple models. In fact, in several cases, multiple models need to interface with each other since the initial conditions of one are dependent on the outcomes of another. To better understand the problem that here is solved, it is useful to consider a simple example: The following problem is considered: a weather forecast simulation code 'a' is used to compute the external (i.e. ambient) temperature in a certain location. A second model 'b' is inquired to compute the average temperature in a room having as boundary condition, among several others, the external ambient temperature. The response of the model 'b' depends on the outcome of the model 'a'. The reported example is only aimed to illustrate the reason why the creation of a framework to make interact different models is a key development for the advancement of RAVEN as a comprehensive calculation flow driver. Before reporting how the ensemble-models have been implemented, it is necessary to briefly describe the representative Model 'entities' that are available in RAVEN.

42 ENGINEERING↗
DOE OSTI2017

Sensitivity Analysis of Successful Evacuee Proportion in Hypothetical Seismic Nuclear Emergency Situation

A magnitude 5.8 earthquake, which is the strongest earthquake ever detected in Korea, occurred in Gyeongju on 12 September, 2016. People were worried about not only the impact to their safety and quality of life as directly affected from the earthquake, but also the secondary impact from such a nuclear power plant (NPP) accident incurred by the earthquake. Public awareness is changing such that the risk of earthquakes is no longer a story of other countries. Even if the current situation in Korea is not regarded, it is important to assess the seismic hazard to an NPP and prepare for preventing the effects related with the earthquake impact. Developing a seismic evacuation model is necessary in a part of a level 3 probabilistic safety assessment (PSA) because it is one of the most affecting factors of public radiation exposure and health effects in an emergency phase. In a previous study, a sensitivity analysis of the evacuation speed in a hypothetical NPP accident by an earthquake has been carried out, and population doses resulting from various seismic evacuation scenarios associated with evacuation speed have been compared. In addition to the previous study, the proportion of evacuees who evacuate successfully with adequate speed has been considered and a sensitivity analysis has been performed in this study.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

Operator Action Time Evaluation of Emergency Water Injection Strategy for Extreme SGTR Accidents

In terms of severe accidents caused by earthquakes or tsunamis that are beyond expectation, a special safety inspection for operating plants, following the Fukushima accident, has been conducted by the government of Korea to verify that nation's nuclear power plants have been adequately designed to respond to extreme accidents. The inspection results show that Korean nuclear power plants in operation have no imminent risk for an expected maximum potential earthquake or coastal flooding based on the up-to-date investigation. However, there is a need to implement long- and short-term safety improvements in order to secure the level of safety for natural beyond-design-basis events. One of the measures to increase the mitigation capability during extreme accidents is installing the injection flow paths to provide emergency cooling water of extemal sources using fire engines to the steam generators (SGs) or reactor cooling system (RCS). An emergency cooling water system consists of a fixed pipe connected from the RCS or SGs to the outside of the containment. A standby valve is installed on the pipe. Following the occurrence of an extreme accident, movable equipment (for example, a fire truck hose) can be connected to the pipe hole at the opening of the isolation valve. The emergency cooling water injection strategy was not taken into account for the steam generator tube rupture (SGTR) accident management strategy of the OPR-1000. Therefore, it is necessary to develop some guidelines or strategies to cope with an extreme SGTR scenarios using the newly installed injection flow paths and fire engines. As long as the fission products released from the core during severe accidents are kept inside the containment, there may be several ways to reduce the radionuclide release into the environment, for example, by using plant safety features. The containment bypass sequences, however, allow the fission products to be released into the environment or directly to the auxiliary building. The SGTR accidents, which are one of the containment bypass sequences, have shown during various probabilistic safety assessments (PSAs) to be contributors to plant risk, mainly because of their potential for causing a release outside containment. This paper is intended to be an investigation of the characteristics of accident progressions and assessments for the mitigative effectiveness of the external cooling water injection strategies during extreme SGTR accidents in a typical OPR-1000 plant. Analyses were performed using a MAAP computer code version 5.03. The MAAP code is a system-level computer code capable of conducting integral analyses of potential severe accident progressions in nuclear power plants, whose main purpose is to support a level 2 PSA or severe accident management strategy developments.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Quantification of storage required for preserving frequency security in wind‐integrated systems

Abstract The penetration of wind power generation into the power grid has been accelerated in recent times due to the aggressive emission targets set by governments and other regulatory authorities. Although wind power has the advantage of being environment‐friendly, wind as a resource is intermittent in nature. In addition, wind power contributes little inertia to the system as most wind turbines are connected to the grid via power electronic converters. These negative aspects of wind power pose serious challenges to the frequency security of power systems as penetration increases. In this work, an approach is proposed where an energy storage system (ESS) is used to mitigate frequency security issues of wind‐integrated systems. ESSs are well equipped to supply virtual inertia to the grid due to their fast‐acting nature, thus replenishing some of the energy storage capability of displaced inertial generation. In this work, a probabilistic approach is proposed to estimate the amount of inertia required by a system to ensure frequency security. Reduction in total system inertia due to the displacement of conventional synchronous generation by wind power generation is considered in this approach, while also taking into account the loss of inertia due to forced outages of conventional units. Monte Carlo simulation is employed for implementing the probabilistic estimation of system inertia. An ESS is then sized appropriately, using the system swing equation, to compensate for the lost inertia. The uncertainty associated with wind energy is modeled into the framework using an autoregressive moving average technique. Effects of increasing the system peak load and changing the wind profile on the expected system inertia are studied to illustrate various factors that might affect system frequency security. The proposed method is validated using the IEEE 39‐bus test system.

17 WIND ENERGY↗
DOE OSTI2017

Radar Detectability Studies of Slow and Small Zodiacal Dust Cloud Particles. III. The Role of Sodium and the Head Echo Size on the Probability of Detection

We present a path forward on a long-standing issue concerning the flux of small and slow meteoroids, which are believed to be the dominant portion of the incoming meteoric mass flux into the Earth’s atmosphere. Such a flux, which is predicted by dynamical dust models of the Zodiacal Cloud, is not evident in ground-based radar observations. For decades this was attributed to the fact that the radars used for meteor observations lack the sensitivity to detect this population, due to the small amount of ionization produced by slow-velocity meteors. Such a hypothesis has been challenged by the introduction of meteor head echo (HE) observations with High Power and Large Aperture radars, in particular the Arecibo 430 MHz radar. Janches et al. developed a probabilistic approach to estimate the detectability of meteors by these radars and initially showed that, with the current knowledge of ablation and ionization, such particles should dominate the detected rates by one to two orders of magnitude compared to the actual observations. In this paper, we include results in our model from recently published laboratory measurements, which showed that (1) the ablation of Na is less intense covering a wider altitude range; and (2) the ionization probability, β{sub ip}, for Na atoms in the air is up to two orders of magnitude smaller for low speeds than originally believed. By applying these results and using a somewhat smaller size of the HE radar target we offer a solution that reconciles these observations with model predictions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Estimating the Likelihood of GHG Concentration Scenarios From Probabilistic Integrated Assessment Model Simulations

The climate scenarios that form the basis for current climate risk assessments have no assigned probabilities, and this impedes the analysis of future climate risks. This paper proposes an approach to estimate the probability of carbon dioxide (CO 2 ) concentration scenarios used in key climate change modeling experiments. It computes the CO 2 emissions compatible with the concentrations prescribed by Coupled Model Intercomparison Project Phase 5 (CMIP5) and CMIP6 experiments. The distribution of these compatible cumulative emissions is interpreted as the likelihood of future emissions given a concentration pathway. Using Bayesian analysis, the probability of each pathway can be estimated from a probabilistic sample of future emissions. The approach is demonstrated with five probabilistic CO 2 emission simulation ensembles from four Integrated Assessment Models (IAM), leading to independent estimates of the likelihood of the CO 2 concentration of Representative Concentration Pathways (RCP) and Shared Socioeconomic Pathways (SSP). Results suggest that SSP5-8.5 is unlikely for the second half of the 21st century, but offer no clear consensus on which of the remaining scenarios is most likely. Estimates of likelihoods of CO 2 concentrations associated with RCP and SSP scenarios are affected by sampling errors, differences in emission sources simulated by the IAMs, and a lack of a common experimental framework for IAM simulations. These shortcomings, along with a small IAM ensemble size, limit the applicability of the results presented here. Novel joint IAM and the Earth System Model experiments are needed to deliver actionable probabilistic climate risk assessments.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Probabilistic Data Association for Orbital-Element Estimation Using Multistage Expectation–Maximization

Tracking space objects is important for managing space traffic and predicting collisions, but is difficult in part due to data association and orbit model uncertainty. Expectation–maximization (EM) is a commonly used tracking method that has not been widely considered for tracking space objects. The technique consists of iteratively computing data association probabilities with a set of current element estimates, and updating estimates of the elements by solving a nonlinear weighted least-squares regression problem where the weights are the data association probabilities. In this paper, we demonstrate the use of EM for probabilistic data association and orbital-element estimation by applying the technique to simulated data from two angles-only tracking scenarios. In both scenarios, EM provides correct data associations and accurate maximum likelihood estimates of orbital elements. One scenario considers tracking a single object in clutter and quantifies the improvement of the orbital-element estimates and data associations as the detection probability increases. However, standard application of EM requires knowing the number of objects or may fail when a large number of objects are present. To address these issues, this paper employs a multistage version of EM that is applicable when there are a large and possibly unknown number of objects.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

QRF4P-NRT: Probabilistic Post-Processing of Near-Real-Time Satellite Precipitation Estimates Using Quantile Regression Forests

Accurate and reliable near-real-time satellite precipitation estimation is of great importance for operational large-scale flood forecasting and drought monitoring. The state-of-the-art precipitation post-processing model is based on a deterministic approach to construct relationships between satellites estimates and ground observations. We propose a probabilistic postprocessor, the Probabilistic Post-Processing of Near-Real-Time Satellite Precipitation Estimates using Quantile Regression Forests (QRF4P-NRT), based on quantile modeling, yielding both deterministic and probabilistic predictions. The experimental design incorporates different solutions of near-real-time predictors to further improve the model performance. Using the Integrated Multi-satellitE Retrievals Early Run for Global Precipitation Measurement Mission (IMERG-E) product as an example, we illustrate that the proposed method significantly improves the overall quality of the raw IMERG-E and is also superior to the bias-corrected product (IMERG Final Run, IMERG-F) at daily scale in a complex mountain basin. Evaluations of the corrected IMERG-E, raw IMERG-E, and IMERG-F using ground observation show that the corrected IMERG-E improves correlation coefficients (0.7), mean error (-0.14 mm/day) and root mean square error (3.3 mm/day) relative to the raw IMERG-E (0.31, -0.72 and 5.5 mm/day) and IMERG-F (0.34, -0.09 and 6.0 mm/day). The error decomposition further confirms that the QRF4P-NRT improves on the various deficiencies of the raw IMERG-E product. The ensemble assessment also demonstrates that the quantile outputs provide reliable prediction spread and sharp prediction intervals. The promising results indicate the great potential of the proposed method for probabilistic post-processing for near-real-time satellite precipitation estimates, and for further applications such as hydrological ensemble forecasting.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Safety envelope for load tolerance of structural element design based on multi-stage testing

Structural elements, such as stiffened panels and lap joints, are basic components of aircraft structures. For aircraft structural design, designers select predesigned elements satisfying the design load requirement based on their load-carrying capabilities. Therefore, estimation of safety envelope of structural elements for load tolerances would be a good investment for design purpose. In this article, a method of estimating safety envelope is presented using probabilistic classification, which can estimate a specific level of failure probability under both aleatory and epistemic uncertainties. An important contribution of this article is that the calculation uncertainty is reflected in building a safety envelope using Gaussian process, and the effect of element test data on reducing the calculation uncertainty is incorporated by updating the Gaussian process model with the element test data. It is shown that even one element test can significantly reduce the calculation uncertainty due to lacking knowledge of actual physics, so that conservativeness in a safety envelope is significantly reduced. The proposed approach was demonstrated with a cantilever beam example, which represents a structural element. The example shows that calculation uncertainty provides about 93% conservativeness against the uncertainty due to a few element tests. As a result, it is shown that even a single element test can increase the load tolerance modeled with the safety envelope by 20%.

42 ENGINEERING↗
NASA NTRS1976

Probabilistic and deterministic aspects of linear estimation in geodesy

Recent advances in observational techniques related to geodetic work (VLBI, laser ranging) make it imperative that more consideration should be given to modeling problems. Uncertainties in the effect of atmospheric refraction, polar motion and precession-nutation parameters, cannot be dispensed with in the context of centimeter level geodesy. Even physical processes that have generally been previously altogether neglected (station motions) must now be taken into consideration. The problem of modeling functions of time or space, or at least their values at observation points (epochs) is explored. When the nature of the function to be modeled is unknown. The need to include a limited number of terms and to a priori decide upon a specific form may result in a representation which fails to sufficiently approximate the unknown function. An alternative approach of increasing application is the modeling of unknown functions as stochastic processes.

Dermanis, A.↗