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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

An Impedance-Based Complexity Metric for Unmanned Aircraft System Traffic Scenario Classification

This paper introduces an impedance-based metric to capture the complexity of a given unmanned aircraft system traffic scenario. The metric accounts for both the number of aircraft and the traffic flow pattern. The work presented here extends an earlier approach that introduced another scenario complexity metric based on the number of potential conflicts weighted by the conflict resolution cost associated. Complexity measurements for randomly-generated scenarios were produced through high-fidelity fast-time simulations and treated as baseline. Then the impedance based metric was evaluated, for the same scenarios, without the need for an actual flight simulation and a conflict resolution method. The results show that the impedance-based metric has a strong correlation to the baseline data and performs marginally better than the weighted conflict-based complexity metric introduced in the earlier work. The metric computation generates impedance maps which are useful for identifying high complexity regions in a scenario, where flight plan changes might be necessitated. This metric can therefore be used, in conjunction with other complexity metrics, to inform adequate traffic management strategies and classify a traffic scenario as acceptable, unacceptable or acceptable with changes made to flight plans that pass through the high complexity regions. The metric can also be used as a guidance metric for strategic conflict management methods.

Complexity↗
NASA NTRSDate not supplied

The System Complexity Metric (SCM) Predicts System Costs and Failure Rates

A complex system has many parts and interactions and so is difficult to understand. Systems with higher complexity generally have higher costs and failure rates. A System Complexity Metric (SCM) is defined to be the sum of the number of nodes, N, in the system block diagram plus the number of one-way interactions, I, between the nodes. SCM = N + I. SCMs are easily determined by direct inspection of high level block diagrams of life support systems. System cost was found to be directly proportional to SCM. The system MTBF (Mean Time Before Failure) is the inverse of the system failure rate. MTBF = 1/f. The system MTBF was found to be proportional to SCM^(-2.2) for estimated preflight MTBFs. As is typical for systems that are not extensively tested and redesigned to eliminate unexpected failure modes, the life support flight failure rates were about ten times higher than the preflight estimates and the MTBFs one-tenth the preflight estimates. The system MTBF was found to be proportional to SCM^(-2.6) for observed flight MTBFs.

System compleity↗
NASA NTRS1994

The development and application of composite complexity models and a relative complexity metric in a software maintenance environment

A great deal of effort is now being devoted to the study, analysis, prediction, and minimization of software maintenance expected cost, long before software is delivered to users or customers. It has been estimated that, on the average, the effort spent on software maintenance is as costly as the effort spent on all other software costs. Software design methods should be the starting point to aid in alleviating the problems of software maintenance complexity and high costs. Two aspects of maintenance deserve attention: (1) protocols for locating and rectifying defects, and for ensuring that noe new defects are introduced in the development phase of the software process; and (2) protocols for modification, enhancement, and upgrading. This article focuses primarily on the second aspect, the development of protocols to help increase the quality and reduce the costs associated with modifications, enhancements, and upgrades of existing software. This study developed parsimonious models and a relative complexity metric for complexity measurement of software that were used to rank the modules in the system relative to one another. Some success was achieved in using the models and the relative metric to identify maintenance-prone modules.

Hops, J. M.↗
NASA NTRSDate not supplied

Applying the System Complexity Metric (SCM)

A fundamental cause of difficulty in larger engineering projects is their inherent complexity. An impression of complexity occurs if a system is simply difficult to understand, so that there is no obvious mental model that correctly predicts its behavior. Higher complexity is usually associated with higher cost and higher failure rate. Complexity is indicated by a system having more and diverse components, multiple interactions and feedback loops, transients and dynamic behavior, and often the emergence of unanticipated failure modes. Identifying and removing these signs of complexity should reduce complexity and improve performance. Here we limit complexity measurement to the number of components and their interactions. A System Complexity Metric (SCM) is defined as equal to the sum of the number of parts in a system, N, plus the sum of the one-way interconnections between them, I. SCM = N + I. The SCM is easily determined by direct inspection of system block diagrams. Previous work found that life support system cost was directly proportional to SCM and that failure rate increased faster than SCM squared. SCM can be used to compare systems or to guide their redesign to reduce cost and failure rate. Carbon dioxide removal systems will be analyzed using SCM, cost, and failure rate.

Harry W Jones↗
NASA NTRSDate not supplied

Using the System Complexity Metric (SCM) to Compare CO2 Removal Systems

A fundamental cause of difficulty in large engineering projects is their inherent complexity. An impression of complexity occurs if a system is simply difficult to understand, where there is no obvious mental model that correctly predicts its behavior. Higher system complexity is usually associated with higher cost and higher failure rate. Complexity is perceived if a system has many diverse components, multiple interactions and feedback loops, transients and dynamic behavior, and unanticipated failure modes. Identifying and removing these signs of complexity should improve performance and reduce the cost and failure rate. Complexity can be directly measured by the number of components and their interactions. The System Complexity Metric (SCM) is defined as the sum of the number of parts in a system, N, plus the number of the one-way interconnections between them, I. SCM = N + I. The SCM is easily determined by direct inspection of the system block diagram. SCM can be used to compare systems and to guide their redesign to reduce cost and failure rate. Carbon dioxide removal systems are analyzed using SCM, cost, and failure rate. As in previous work, cost is directly proportional to SCM and that failure rate increases as a power of SCM for large differences in SCM. The SCM ranking of carbon dioxide removal systems is the same as their ranking in detailed analysis and practice.

Harry W. Jones↗
NASA NTRSDate not supplied

Using the System Complexity Metric (SCM) to Compare CO2 Reduction Systems

A fundamental cause of difficulty in large engineering projects is their inherent complexity. An impression of complexity occurs if a system is simply difficult to understand, where there is no obvious mental model that correctly predicts its behavior. Higher system complexity is usually associated with higher cost and higher failure rate. Complexity is perceived if a system has many diverse components, multiple interactions and feedback loops, transients and dynamic behavior, and unanticipated failure modes. Identifying and removing these signs of complexity should improve performance and reduce the cost and failure rate. Complexity can be directly measured by the number of components and their interactions. The System Complexity Metric (SCM) is defined as the sum of the number of parts in a system, N, plus the number of the one-way interconnections between them, I. SCM = N + I. The SCM is easily determined by direct inspection of the system block diagram. SCM can be used to compare systems and to guide their redesign to reduce cost and failure rate. Carbon dioxide reduction systems are analyzed using SCM, cost, and failure rate. As in previous work, cost is directly proportional to SCM and that failure rate increases as a power of SCM for large differences in SCM. The SCM ranking of carbon dioxide reduction systems is the same as their ranking in detailed analysis and practice.

Harry W. Jones↗
NASA NTRS2009

A Complexity Metric for Automated Separation

A metric is proposed to characterize airspace complexity with respect to an automated separation assurance function. The Maneuver Option metric is a function of the number of conflict-free trajectory change options the automated separation assurance function is able to identify for each aircraft in the airspace at a given time. By aggregating the metric for all aircraft in a region of airspace, a measure of the instantaneous complexity of the airspace is produced. A six-hour simulation of Fort Worth Center air traffic was conducted to assess the metric. Results showed aircraft were twice as likely to be constrained in the vertical dimension than the horizontal one. By application of this metric, situations found to be most complex were those where level overflights and descending arrivals passed through or merged into an arrival stream. The metric identified high complexity regions that correlate well with current air traffic control operations. The Maneuver Option metric did not correlate with traffic count alone, a result consistent with complexity metrics for human-controlled airspace.

Aweiss, Arwa↗
NASA NTRS2018

Uncertainty in Heart Rate Complexity Metrics Caused by R-Peak Perturbations

Heart rate complexity (HRC) is a proven metric for gaining insight into human stress and physiological deterioration. To calculate HRC, the detection of the exact instance of when the heart beats, the R-peak, is necessary. Electrocardiogram (ECG) signals can often be corrupted by environmental noise (e.g., from electromagnetic interference, movement artifacts), which can potentially alter the HRC measurement, producing erroneous inputs which feed into decision support models. Current literature has only investigated how HRC is affected by noise when R-peak detection errors occur (false positives and false negatives). However, the numerical methods used to calculate HRC are also sensitive to the specific location of the fiducial point of the R-peak. This raises many questions regarding how this fiducial point is altered by noise, the resulting impact on the measured HRC, and how we can account for noisy HRC measures as inputs into our decision models. This work uses Monte Carlo simulations to systematically add white and pink noise at different permutations of signal-to-noise ratios (SNRs), time segments, sampling rates, and HRC measurements to characterize the influence of noise on the HRC measure by altering the fiducial point of the R-peak. Using the generated information from these simulations provides improved decision processes for system design which address key concerns such as permutation entropy being a more precise, reliable, less biased, and more sensitive measurement for HRC than sample and approximate entropy.

Napoli, Nicholas J.↗
NASA NTRSDate not supplied

The System Complexity Metric (SCM) Explains Systems Design and is Correlated with Cost and Failure Rate

The human short term memory span and working capacity is limited to three to five items, especially if they are organized complex “chunks” of information. The impression of complexity occurs when a system is simply difficult to understand, where there is no apparent pattern to predict its behavior. Hierarchical systems design can reduce perceived complexity and increase the amount of information that can be managed. The SCM was developed to measure complexity and help compare proposed overall system architectures before detailed design information is available. The SCM is defined as the sum of the number of major nodes, N, in the system block diagram plus the number of one-way interactions, I, between the nodes. SCM = N + I. SCM’s are easily determined by direct inspection of high-level block diagrams of life support systems. Axiomatic design develops a hierarchy of subsystem requirements and designs together in a top-down, back-and-forth process. A coupling matrix is used to control the relationships between the subsystem functions and design concepts. Axiomatic design can improve system design by decoupling requirements and designs. Axiomatic design was applied to the planning of a closed life support system, similar to that used on the International Space Station. A materially open as opposed to a closed system design was created by removing the interconnections required to close the system. The open system had the same number of designed subsystems as the closed system, but it had many fewer interconnections and its SCM was lower by about half. The costs were estimated and the MTBF (Mean Time Before Failure) tabulated for open and closed space life support systems. The estimated costs were linearly proportional to SCM for the wide variations of SCM in life support, but small differences may not be significant. The flight and preflight MTBF’s both declined exponentially with increasing MTBF, faster than MTBF-2, even though the preflight estimated MTBF’s were about ten times higher than the flight MTBF’s.

System Complexity Metric (SCM)↗
NASA NTRS1991

A Dynamic Testing Complexity Metric

This paper introduces a dynamic metric that is based on the estimated ability of a program to withstand the effects of injected "semantic mutants" during execution by computing the same function as if the semantic mutants had not been injected. Semantic mutants include: (1) syntactic mutants injected into an executing program and (2) randomly selected values injected into an executing program's internal states. The metric is a function of a program, the method used for injecting these two types of mutants, and the program's input distribution; this metric is found through dynamic executions of the program. A program's ability to withstand the effects of injected semantic mutants by computing the same function when executed is then used as a tool for predicting the difficulty that will be incurred during random testing to reveal the existence of faults, i.e., the metric suggests the likelihood that a program will expose the existence of faults during random testing assuming faults were to exist. If the metric is applied to a module rather than to a program, the metric can be used to guide the allocation of testing resources among a program's modules. In this manner the metric acts as a white-box testing tool for determining where to concentrate testing resources. Index Terms: Revealing ability, random testing, input distribution, program, fault, failure.

Voas, Jeffrey↗
NASA NTRS1997

Systems Engineering Metrics: Organizational Complexity and Product Quality Modeling

Innovative organizational complexity and product quality models applicable to performance metrics for NASA-MSFC's Systems Analysis and Integration Laboratory (SAIL) missions and objectives are presented. An intensive research effort focuses on the synergistic combination of stochastic process modeling, nodal and spatial decomposition techniques, organizational and computational complexity, systems science and metrics, chaos, and proprietary statistical tools for accelerated risk assessment. This is followed by the development of a preliminary model, which is uniquely applicable and robust for quantitative purposes. Exercise of the preliminary model using a generic system hierarchy and the AXAF-I architectural hierarchy is provided. The Kendall test for positive dependence provides an initial verification and validation of the model. Finally, the research and development of the innovation is revisited, prior to peer review. This research and development effort results in near-term, measurable SAIL organizational and product quality methodologies, enhanced organizational risk assessment and evolutionary modeling results, and 91 improved statistical quantification of SAIL productivity interests.

Mog, Robert A.↗
NASA NTRS2019

A Validation Study of the Performance Prediction Methodology of the Early Warning Metrics

Complex projects frequently experience delays and develop backlogs of their project control milestones during the acquisition and development lifecycles. In response, the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC) formed an independent group of Subject Matter Experts (SMEs) to monitor the execution performance of GSFC Flight projects and instruments that are under development. The SME team’s objective is to generate data driven performance-based indicators that quantify the degree to which projects are meeting their respective schedule and budget commitments. One of these performance-based indicators, the Early Warning Metrics, provides performance forecasts and insight to project performance relative to historical successful projects. Herein this paper describes the purpose and utility of the Early Warning Metrics. Additionally, the initial prediction method used in the creation of the metrics is described along with its validity and the validity of comparable prediction methods.

Holloman, Sherrica↗
NASA NTRS2019

Scenario Complexity for Unmanned Aircraft System Traffic

This work introduces an approach to estimate the complexity of a low-altitude air traffic scenario involving multiple UASs using mathematical programming. Given a set of multi-point UAS flight trajectories, vehicle dynamics, and a conflict resolution algorithm, an abstract model is developed such that it can be solved quickly using a mathematical programming optimization software without running high-fidelity simulations that can be computationally expensive and may not suit real-time apA quick and accurate assessment of complexity for a given traffic scenario can help plan and schedule flights to alleviate traffic bottleneck and mitigate operation risks, especially for unmanned aerial system traffic management where high traffic density or complexity is expected. This work introduces a traffic scenario complexity metric that was constructed based on the number of potential conflicts weighted by the conflict resolution cost associated. The cost associated with a conflict is calculated based on the corresponding conflict resolution maneuvers. To obtain the conflict resolution maneuvers, a MILP-based optimization was formulated with the vehicle model and conflict management parameters incorporated. To evaluate the complexity metrics, an approach of using measurements from high-fidelity simulations was proposed. The scenario complexity measurements for 920 random-generated scenarios were obtained through high-fidelity simulations and treated as the ground truth. Two statistics methods: Pearson and Alternative Conditional Expectations were applied for analysis. The results showed that the number of flights has low correlation with the scenario complexity according to the correlation coefficients calculated by both methods. The Alternative Conditional Expectations method shows that the proposed scenario complexity metric has better correlation with the ground truth than the number of potential conflicts.plications. In the abstract model, each vehicle is represented by a time-varied vector associated with position, speed, and heading information. The total extra distance that aircraft need to divert from their original routes to avoid collisions is computed and used to setup a quadratic programming formula. The metrics including the number of conflicts and extra distances travelled by all vehicles are then utilized to estimate the complexity of a given UAS flight scenario. Results and verification against high-fidelity simulations will be provided in the final draft.

traffic complexity↗
NASA NTRS1999

Systems Engineering Design Via Experimental Operation Research: Complex Organizational Metric for Programmatic Risk Environments (COMPRE)

Unique and innovative graph theory, neural network, organizational modeling, and genetic algorithms are applied to the design and evolution of programmatic and organizational architectures. Graph theory representations of programs and organizations increase modeling capabilities and flexibility, while illuminating preferable programmatic/organizational design features. Treating programs and organizations as neural networks results in better system synthesis, and more robust data modeling. Organizational modeling using covariance structures enhances the determination of organizational risk factors. Genetic algorithms improve programmatic evolution characteristics, while shedding light on rulebase requirements for achieving specified technological readiness levels, given budget and schedule resources. This program of research improves the robustness and verifiability of systems synthesis tools, including the Complex Organizational Metric for Programmatic Risk Environments (COMPRE).

Mog, Robert A.↗
NASA NTRS2009

Trajectory-Oriented Approach to Managing Traffic Complexity: Trajectory Flexibility Metrics and Algorithms and Preliminary Complexity Impact Assessment

This document describes exploratory research on a distributed, trajectory oriented approach for traffic complexity management. The approach is to manage traffic complexity based on preserving trajectory flexibility and minimizing constraints. In particular, the document presents metrics for trajectory flexibility; a method for estimating these metrics based on discrete time and degree of freedom assumptions; a planning algorithm using these metrics to preserve flexibility; and preliminary experiments testing the impact of preserving trajectory flexibility on traffic complexity. The document also describes an early demonstration capability of the trajectory flexibility preservation function in the NASA Autonomous Operations Planner (AOP) platform.

Idris, Husni↗
NASA NTRS1989

Initial Ada components evaluation

The SAIC has the responsibility for independent test and validation of the SSE. They have been using a mathematical functions library package implemented in Ada to test the SSE IV and V process. The library package consists of elementary mathematical functions and is both machine and accuracy independent. The SSE Ada components evaluation includes code complexity metrics based on Halstead's software science metrics and McCabe's measure of cyclomatic complexity. Halstead's metrics are based on the number of operators and operands on a logical unit of code and are compiled from the number of distinct operators, distinct operands, and total number of occurrences of operators and operands. These metrics give an indication of the physical size of a program in terms of operators and operands and are used diagnostically to point to potential problems. McCabe's Cyclomatic Complexity Metrics (CCM) are compiled from flow charts transformed to equivalent directed graphs. The CCM is a measure of the total number of linearly independent paths through the code's control structure. These metrics were computed for the Ada mathematical functions library using Software Automated Verification and Validation (SAVVAS), the SSE IV and V tool. A table with selected results was shown, indicating that most of these routines are of good quality. Thresholds for the Halstead measures indicate poor quality if the length metric exceeds 260 or difficulty is greater than 190. The McCabe CCM indicated a high quality of software products.

Moebes, Travis↗