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conventional control-theoretic models for fault detection rely on an accurate model of the system being monitored: frequently in practice no such model exists for complex non-linear systems.
Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.
During the design phases of large and complex systems such as NASA's Space Station Freedom (SSF), there are few, if any physical prototypes built. This is often due to their expense and the realization that the design is likely to change. This poses a problem for training, maintainability, and operations groups who are tasked to lay the foundation of plans for using these systems. The Virtual Reality and Visualization Laboratory at the Boeing Advanced Computing Group's Huntsville facility is supporting the use of high fidelity, detailed design models that are generated during the initial design phases, for use in training, maintainability and operations exercises. This capability was used in its non-immersive form to great effect at the SSF Critical Design Review (CDR) during February, 1993. Allowing the user to move about within a CAD design supports many efforts, including training and scenario study. We will demonstrate via a video of the Maintainability SSF CDR how this type of approach can be used and why it is so effective in conveying large amounts of information quickly and concisely. We will also demonstrate why high fidelity models are so important for this type of training system and how it's immersive aspects may be exploited as well.
Markov and semi-Markov processes are increasingly being used in the modeling of complex reconfigurable systems (fault tolerant computers). The estimation of the reliability (or some measure of performance) of the system reduces to solving the process for its state probabilities. Such a model may exhibit numerous states and complicated transition distributions, contributing to an expensive and numerically delicate solution procedure. Thus, when a system exhibits a decomposition property, either structurally (autonomous subsystems), or behaviorally (component failure versus reconfiguration), it is desirable to exploit this decomposition in the reliability calculation. In interesting cases there can be failure states which arise from non-failure states of the subsystems. Equations are presented which allow the computation of failure probabilities of the total (combined) model without requiring a complete solution of the combined model. This material is presented within the context of closed-form functional representation of probabilities as utilized in the Symbolic Hierarchical Automated Reliability and Performance Evaluator (SHARPE) tool. The techniques adopted enable one to compute such probability functions for a much wider class of systems at a reduced computational cost. Several examples show how the method is used, especially in enhancing the versatility of the SHARPE tool.
This workshop aims to identify key research directions for transforming biology using artificial intelligence (AI), machine learning (ML) and computational methods to facilitate the discovery of new behaviors, mechanisms, and designs of biological processes relevant to DOE missions, underpinning a broader U.S. bioeconomy. By developing novel AI/ML technologies to analyze and interpret complex biological data, researchers can organize and simulate biological processes at various scales as well as advance predictive understanding and manipulation of biological systems. This integration of computation, experimentation, and next-generation experimental technologies can lead to discoveries in new biological behaviors and mechanisms relevant to DOE missions. The focus is on how advanced computational and mathematical methods can impact this mission by exploring digital twins, foundation models, automated laboratory experiments, modeling of complex living systems, and data-driven approaches for the biodesign of plants and microbial systems. While data management is important, it is not the primary focus of this workshop, which will assess the current state, trends, and AI/ML challenges at the interface between biology and computational science to identify opportunities for high-impact research at their intersection. The goal is to define research needs and opportunities that align with biological sciences, computational sciences, and applied mathematics research.
The Cellular-Potts model is a powerful and ubiquitous framework for developing computational models for simulating complex multicellular biological systems. Cellular-Potts models (CPMs) are often computationally expensive due to the explicit modeling of interactions among large numbers of individual model agents and diffusive fields described by partial differential equations (PDEs). In this work, we develop a convolutional neural network (CNN) surrogate model using a U-Net architecture that accounts for periodic boundary conditions. We use this model to accelerate the evaluation of a mechanistic CPM previously used to investigate in vitro vasculogenesis. The surrogate model was trained to predict 100 computational steps ahead (Monte-Carlo steps, MCS), accelerating simulation evaluations by a factor of 562 times compared to single-core CPM code execution on CPU. Over short timescales of up to 3 recursive evaluations, or 300 MCS, our model captures the emergent behaviors demonstrated by the original Cellular-Potts model such as vessel sprouting, extension and anastomosis, and contraction of vascular lacunae. This approach demonstrates the potential for deep learning to serve as a step toward efficient surrogate models for CPM simulations, enabling faster evaluation of computationally expensive CPM simulations of biological processes.
A simple model of interacting complex systems of species is tested to assess the binding behavior of monomeric nucleic acid and protein components during evolution. Nine representative amino acids are immobilized by the formation of an amide linkage on a prepared chromatographic support. Selective binding of ribonucleoside 5-phosphates in these amino acids is achieved under standardized conditions, and a site-binding model is derived to characterize the binding. It is shown that the binding behavior of the reactants during nucleic acid-protein interactions depends on the nature of the base and the amino acid. The results of the study are assessed as useful for the interpretation of more complex nucleic acid-protein systems and of their role in the evolution of the cell.
To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Latest achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision making. In principle, data driven approaches can replace expensive experimental test-setups as well as reduce the number of simulations needed to explore, e.g., the parametric space of a multi-parameter model. Nonetheless, the limitations of pure data-driven methods came to light rather quickly, at least for some industries. In many industrial applications, data acquisition is costly, and the volume of data that can be collected does not satisfy the requirements for an effective model training and cross-validation. Therefore, some recent works in the area of machine learning is focusing on blending physics with data-driven algorithms, thus mitigating the drawbacks of the two approaches and emphasizing respective advantages. Partial physical knowledge of the problem can aid the learning process by “guiding” the algorithm towards efficient solutions that satisfy the physics driving the system behavior. The result is a hybrid modeling approach combining physical knowledge as well data driven methods to develop a unified hybrid approach. A hybrid framework for fusing information from physics-based performance models along with deep learning algorithms for prognostics of complex safety critical systems is presented. In this framework, physics-based performance models infer unobservable model parameters related to the system's components health solving a calibration problem in the deep learning approach.
This is a previously approved and published presentation. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Present achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision-making. In principle, data-driven approaches can replace expensive experimental test-setups as well as reduce the number of simulations needed to explore, e.g., the parametric space of a multi-parameter model. Nonetheless, the limitations of pure data-driven methods came to light rather quickly, at least for some industries. In many industrial applications, data acquisition is costly, and the volume of data that can be collected does not satisfy the requirements for effective model training and cross-validation. Therefore, some recent works in the area of machine learning is focusing on blending physics with data-driven algorithms, thus mitigating the drawbacks of the two approaches and emphasizing respective advantages. Partial physical knowledge of the problem can aid the learning process by “guiding” the algorithm towards efficient solutions that satisfy the physics driving the system behavior. The result is a hybrid modeling approach combining physical knowledge as well data-driven methods to develop a unified hybrid approach. A hybrid framework for fusing information from physics-based performance models along with deep learning algorithms for prognostics of complex safety-critical systems is presented. In this framework, physics-based performance models infer unobservable model parameters related to the system's components health solving a calibration problem in the deep learning approach.
A new Lightning Protection System (LPS) was designed and built at Launch Complex 39B (LC39B), at the Kennedy Space Center (KSC), Florida, which consists of a catenary wire system (at a height of about 181 meters above ground level) supported by three insulators installed atop three towers in a triangular configuration. A total of nine downconductors (each about 250 meters long, on average) are connected to the catenary wire system. Each of the nine downconductors is connected to a 7.62-meter radius circular counterpoise conductor with six equally spaced 6-meter long vertical grounding rods. Grounding requirements at LC39B call for all underground and above ground metallic piping, enclosures, raceways, and cable trays, within 7.62 meters of the counterpoise, to be bounded to the counterpoise, which results in a complex interconnected grounding system, given the many metallic piping, raceways, and cable trays that run in multiple direction around LC39B. The complexity of this grounding system makes the fall of potential method, which uses multiple metallic rods or stakes, unsuitable for measuring the grounding impedances of the downconductors. To calculate the downconductors grounding impedance, an Earth Ground Clamp (a stakeless grounding resistance measuring device) and a LPS Alternative Transient Program (ATP) model are used. The Earth Ground Clamp is used to measure the loop impedance plus the grounding impedance of each downconductor and the ATP model is used to calculate the loop impedance of each downconductor circuit. The grounding impedance of the downconductors is then calculated by subtracting the ATP calculated loop impedances from the Earth Ground Clamp measurements.
We propose a method for the application of single event upset (SEU) data towards the analysis of complex systems using transformed reliability models (from the time domain to the particle fluence domain) and space environment data.
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An efficient diagnosis engine - a combination of mathematical models and algorithms - has been developed for identifying faulty components in a possibly complex engineering system. This model-based diagnosis engine embodies a twofold approach to reducing, relative to prior model-based diagnosis engines, the amount of computation needed to perform a thorough, accurate diagnosis. The first part of the approach involves a reconstruction of the general diagnostic engine to reduce the complexity of the mathematical-model calculations and of the software needed to perform them. The second part of the approach involves algorithms for computing a minimal diagnosis (the term "minimal diagnosis" is defined below). A somewhat lengthy background discussion is prerequisite to a meaningful summary of the innovative aspects of the present efficient model-based diagnosis engine. In model-based diagnosis, the function of each component and the relationships among all the components of the engineering system to be diagnosed are represented as a logical system denoted the system description (SD). Hence, the expected normal behavior of the engineering system is the set of logical consequences of the SD. Faulty components lead to inconsistencies between the observed behaviors of the system and the SD (see figure). Diagnosis - the task of finding faulty components - is reduced to finding those components, the abnormalities of which could explain all the inconsistencies. The solution of the diagnosis problem should be a minimal diagnosis, which is a minimal set of faulty components. A minimal diagnosis stands in contradistinction to the trivial solution, in which all components are deemed to be faulty, and which, therefore, always explains all inconsistencies.
A system is safety-critical if its failure can endanger human life or cause significant damage to property or the environment. State-of-the-art computer systems on commercial aircraft are highly complex, software-intensive, functionally integrated, and network-centric systems of systems. Ensuring that such systems are safe and comply with existing safety regulations is costly and time-consuming as the level of rigor in the development process, especially the validation and verification activities, is determined by considerations of system complexity and safety criticality. A significant degree of care and deep insight into the operational principles of these systems is required to ensure adequate coverage of all design implications relevant to system safety. Model-based development methodologies, methods, tools, and techniques facilitate collaboration and enable the use of common design artifacts among groups dealing with different aspects of the development of a system. This paper examines the application of model-based development to complex and safety-critical aircraft computer systems. Benefits and detriments are identified and an overall assessment of the approach is given.
Program goals at the Center for Modeling of Turbulence and Transition (CMOTT), NASA Lewis Research Center, are (1) to develop reliable turbulence (including bypass transition) and combustion models for complex flows in propulsion systems and (2) to integrate developed models into deliverable CFD tools for propulsion systems in collaboration with industry. This viewgraph presentation covers the following topics: development of turbulence and combustion models; collaboration with industry and technology transfer; isotropic eddy viscosity models; algebraic Reynolds stress models; scalar turbulence models; second order closure models; multiple scale k-epsilon models; and PDF modeling of turbulent reacting flows.
We propose a method for the application of single event upset (SEU) data towards the analysis of complex systems using transformed reliability models (from the time domain to the particle fluence domain) and space environment data.
The design, implementation, and empirical evaluation of task-analytic models and intelligent aids for operators in the control of complex dynamic systems, specifically aerospace systems, are studied. Three related activities are included: (1) the models of operator decision making in complex and predominantly automated space systems were used and developed; (2) the Operator Function Model (OFM) was used to represent operator activities; and (3) Operator Function Model Expert System (OFMspert), a stand-alone knowledge-based system was developed, that interacts with a human operator in a manner similar to a human assistant in the control of aerospace systems. OFMspert is an architecture for an operator's assistant that uses the OFM as its system and operator knowledge base and a blackboard paradigm of problem solving to dynamically generate expectations about upcoming operator activities and interpreting actual operator actions. An experiment validated the OFMspert's intent inferencing capability and showed that it inferred the intentions of operators in ways comparable to both a human expert and operators themselves. OFMspert was also augmented with control capabilities. An interface allowed the operator to interact with OFMspert, delegating as much or as little control responsibility as the operator chose. With its design based on the OFM, OFMspert's control capabilities were available at multiple levels of abstraction and allowed the operator a great deal of discretion over the amount and level of delegated control. An experiment showed that overall system performance was comparable for teams consisting of two human operators versus a human operator and OFMspert team.
The dynamic evolution of precipitates and second phases dictates the strength and stability of most engineering alloys. By design, or as a consequence of thermo-mechanical aging, engineering metals and alloys often form precipitates of second phases when subjecting to diverse thermal and mechanical loads. Precipitation is governed by several factors, including the alloy’s composition, processing/operating temperature, and stresses — either as a result of external loads or from residual stresses. However, state-of-the-art models for precipitate nucleation (i.e., classical nucleation theory) typically lacks consistent method to capture the effects of externally applied and/or internal stresses on nucleation; thereby severely limiting the applicability of these models to complex materials systems and to representative loading scenarios. Here, in this work, we extend upon classical nucleation theory to account for the effect of stresses on precipitation kinetics and thermodynamics. This is achieved via the use of an Eshelbian micromechanics framework keeping track of (i) the stress build up resulting from second phase formation as a function of mechanical load and, (ii) the effects of dislocations on precipitate formation. This new model is applied to σ precipitate in Fe–Cr binary alloys and M 23 C 6 precipitate in 316H stainless steel (SS). Simulations demonstrate the important role of both the remotely applied loads and dislocation pile ups on precipitate nucleation.