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This report attempts to unify in a single document the results of a series of studies on fighter aircraft agility funded by the NASA Ames Research Center, Dryden Flight Research Facility and conducted at the University of Kansas Flight Research Laboratory during the period January 1989 through December 1993. New metrics proposed by pilots and the research community to assess fighter aircraft agility are collected and analyzed. The report develops a framework for understanding the context into which the various proposed fighter agility metrics fit in terms of application and testing. Since new metrics continue to be proposed, this report does not claim to contain every proposed fighter agility metric. Flight test procedures, test constraints, and related criteria are developed. Instrumentation required to quantify agility via flight test is considered, as is the sensitivity of the candidate metrics to deviations from nominal pilot command inputs, which is studied in detail. Instead of supplying specific, detailed conclusions about the relevance or utility of one candidate metric versus another, the authors have attempted to provide sufficient data and analyses for readers to formulate their own conclusions. Readers are therefore ultimately responsible for judging exactly which metrics are 'best' for their particular needs. Additionally, it is not the intent of the authors to suggest combat tactics or other actual operational uses of the results and data in this report. This has been left up to the user community. Twenty of the candidate agility metrics were selected for evaluation with high fidelity, nonlinear, non real-time flight simulation computer programs of the F-5A Freedom Fighter, F-16A Fighting Falcon, F-18A Hornet, and X-29A. The information and data presented on the 20 candidate metrics which were evaluated will assist interested readers in conducting their own extensive investigations. The report provides a definition and analysis of each metric; details of how to test and measure the metric, including any special data reduction requirements; typical values for the metric obtained using one or more aircraft types; and a sensitivity analysis if applicable. The report is organized as follows. The first chapter in the report presents a historical review of air combat trends which demonstrate the need for agility metrics in assessing the combat performance of fighter aircraft in a modern, all-aspect missile environment. The second chapter presents a framework for classifying each candidate metric according to time scale (transient, functional, instantaneous), further subdivided by axis (pitch, lateral, axial). The report is then broadly divided into two parts, with the transient agility metrics (pitch lateral, axial) covered in chapters three, four, and five, and the functional agility metrics covered in chapter six. Conclusions, recommendations, and an extensive reference list and biography are also included. Five appendices contain a comprehensive list of the definitions of all the candidate metrics; a description of the aircraft models and flight simulation programs used for testing the metrics; several relations and concepts which are fundamental to the study of lateral agility; an in-depth analysis of the axial agility metrics; and a derivation of the relations for the instantaneous agility and their approximations.
The accuracy and precision of digital image correlation (DIC) is a function of three primary ingredients: image acquisition, image analysis, and the subject of the image. Development of the first two (i.e. image acquisition techniques and image correlation algorithms) has led to widespread use of DIC; however, fewer developments have been focused on the third ingredient. Typically, subjects of DIC images are mechanical specimens with either a natural surface pattern or a pattern applied to the surface. Research in the area of DIC patterns has primarily been aimed at identifying which surface patterns are best suited for DIC, by comparing patterns to each other. Because the easiest and most widespread methods of applying patterns have a high degree of randomness associated with them (e.g., airbrush, spray paint, particle decoration, etc.), less effort has been spent on exact construction of ideal patterns. With the development of patterning techniques such as microstamping and lithography, patterns can be applied to a specimen pixel by pixel from a patterned image. In these cases, especially because the patterns are reused many times, an optimal pattern is sought such that error introduced into DIC from the pattern is minimized. DIC consists of tracking the motion of an array of nodes from a reference image to a deformed image. Every pixel in the images has an associated intensity (grayscale) value, with discretization depending on the bit depth of the image. Because individual pixel matching by intensity value yields a non-unique scale-dependent problem, subsets around each node are used for identification. A correlation criteria is used to find the best match of a particular subset of a reference image within a deformed image. The reader is referred to references for enumerations of typical correlation criteria. As illustrated by Schreier and Sutton and Lu and Cary systematic errors can be introduced by representing the underlying deformation with under-matched shape functions. An important implication, as discussed by Sutton et al., is that in the presence of highly localized deformations (e.g., crack fronts), error can be reduced by minimizing the subset size. In other words, smaller subsets allow the more accurate resolution of localized deformations. Contrarily, the choice of optimal subset size has been widely studied and a general consensus is that larger subsets with more information content are less prone to random error. Thus, an optimal subset size balances the systematic error from under matched deformations with random error from measurement noise. The alternative approach pursued in the current work is to choose a small subset size and optimize the information content within (i.e., optimizing an applied DIC pattern), rather than finding an optimal subset size. In the literature, many pattern quality metrics have been proposed, e.g., sum of square intensity gradient (SSSIG), mean subset fluctuation, gray level co-occurrence, autocorrelation-based metrics, and speckle-based metrics. The majority of these metrics were developed to quantify the quality of common pseudo-random patterns after they have been applied, and were not created with the intent of pattern generation. As such, it is found that none of the metrics examined in this study are fit to be the objective function of a pattern generation optimization. In some cases, such as with speckle-based metrics, application to pixel by pixel patterns is ill-conditioned and requires somewhat arbitrary extensions. In other cases, such as with the SSSIG, it is shown that trivial solutions exist for the optimum of the metric which are ill-suited for DIC (such as a checkerboard pattern). In the current work, a multi-metric optimization method is proposed whereby quality is viewed as a combination of individual quality metrics. Specifically, SSSIG and two auto-correlation metrics are used which have generally competitive objectives. Thus, each metric could be viewed as a constraint imposed upon the others, thereby precluding the achievement of their trivial solutions. In this way, optimization produces a pattern which balances the benefits of multiple quality metrics. The resulting pattern, along with randomly generated patterns, is subjected to numerical deformations and analyzed with DIC software. The optimal pattern is shown to outperform randomly generated patterns.
This study is a direct result of an on-going project to model the reliability of a large real-time control avionics system. In previous modeling efforts with this system, hardware reliability models were applied in modeling the reliability behavior of this system. In an attempt to enhance the performance of the adapted reliability models, certain software attributes were introduced in these models to control for differences between programs and also sequential executions of the same program. As the basic nature of the software attributes that affect software reliability become better understood in the modeling process, this information begins to have important implications on the software development process. A significant problem arises when raw attribute measures are to be used in statistical models as predictors, for example, of measures of software quality. This is because many of the metrics are highly correlated. Consider the two attributes: lines of code, LOC, and number of program statements, Stmts. In this case, it is quite obvious that a program with a high value of LOC probably will also have a relatively high value of Stmts. In the case of low level languages, such as assembly language programs, there might be a one-to-one relationship between the statement count and the lines of code. When there is a complete absence of linear relationship among the metrics, they are said to be orthogonal or uncorrelated. Usually the lack of orthogonality is not serious enough to affect a statistical analysis. However, for the purposes of some statistical analysis such as multiple regression, the software metrics are so strongly interrelated that the regression results may be ambiguous and possibly even misleading. Typically, it is difficult to estimate the unique effects of individual software metrics in the regression equation. The estimated values of the coefficients are very sensitive to slight changes in the data and to the addition or deletion of variables in the regression equation. Since most of the existing metrics have common elements and are linear combinations of these common elements, it seems reasonable to investigate the structure of the underlying common factors or components that make up the raw metrics. The technique we have chosen to use to explore this structure is a procedure called principal components analysis. Principal components analysis is a decomposition technique that may be used to detect and analyze collinearity in software metrics. When confronted with a large number of metrics measuring a single construct, it may be desirable to represent the set by some smaller number of variables that convey all, or most, of the information in the original set. Principal components are linear transformations of a set of random variables that summarize the information contained in the variables. The transformations are chosen so that the first component accounts for the maximal amount of variation of the measures of any possible linear transform; the second component accounts for the maximal amount of residual variation; and so on. The principal components are constructed so that they represent transformed scores on dimensions that are orthogonal. Through the use of principal components analysis, it is possible to have a set of highly related software attributes mapped into a small number of uncorrelated attribute domains. This definitively solves the problem of multi-collinearity in subsequent regression analysis. There are many software metrics in the literature, but principal component analysis reveals that there are few distinct sources of variation, i.e. dimensions, in this set of metrics. It would appear perfectly reasonable to characterize the measurable attributes of a program with a simple function of a small number of orthogonal metrics each of which represents a distinct software attribute domain.
The Advanced Life Support (ALS) Metric is the predominant tool for predicting the cost of ALS systems. Metric goals for the ALS Program are daunting, requiring a threefold increase in the ALS Metric by 2010. Confounding the problem, the rate new ALS technologies reach the maturity required for consideration in the ALS Metric and the rate at which new configurations are developed is slow, limiting the search space and potentially giving the perspective of a ALS technology, the ALS Metric may remain elusive. This paper is a sequel to a paper published in the proceedings of the 2003 ICES conference entitled, "Managing to the metric: an approach to optimizing life support costs." The conclusions of that paper state that the largest contributors to the ALS Metric should be targeted by ALS researchers and management for maximum metric reductions. Certainly, these areas potentially offer large potential benefits to future ALS missions; however, the ALS Metric is not the only decision-making tool available to the community. To facilitate decision-making within the ALS community a combination of metrics should be utilized, such as the Equivalent System Mass (ESM)-based ALS metric, but also those available through techniques such as life cycle costing and faithful consideration of the sensitivity of the assumed models and data. Often a lack of data is cited as the reason why these techniques are not considered for utilization. An existing database development effort within the ALS community, known as OPIS, may provide the opportunity to collect the necessary information to enable the proposed systems analyses. A review of these additional analysis techniques is provided, focusing on the data necessary to enable these. The discussion is concluded by proposing how the data may be utilized by analysts in the future.
A flow-through balance is provided which includes a non-metric portion and a metric portion which form a fluid-conducting passage in fluid communication with an internal bore in the sting. The non-metric and metric portions of the balance are integrally connected together by a plurality of flexure beams such that the non-metric portion, the metric portion and the flexure beams form a one-piece construction which eliminates mechanical hysteresis between the non-metric and the metric portion. The system includes structures for preventing the effects of temperature, pressure and pressurized fluid from producing asymmetric loads on the flexure beams. A temperature sensor and a pressure sensor are located within the fluid-conducting passage of the balance. The system includes a longitudinal bellows member connected at two ends to one of the non-metric portion and the metric portion and at an intermediate portion thereof to the other of (1) and (2). A plurality of strain gages are mounted on the flexure beams to measure strain forces on the flexure beams. The flexure beams are disposed so as to enable symmetric forces on the flexure beams to cancel out so that only asymmetric forces are measured as deviations by the strain gages.
Recent changes in the climate system have led to growing concern, especially in communities which are highly vulnerable to resource shortages and weather extremes. There is an urgent need for better climate information to develop solutions and strategies for adapting to a changing climate. Climate models provide excellent tools for studying the current state of climate and making future projections. However, these models are subject to biases created by structural uncertainties. Performance metrics-or the systematic determination of model biases-succinctly quantify aspects of climate model behavior. Efforts to standardize climate model experiments and collect simulation data-such as the Coupled Model Intercomparison Project (CMIP)-provide the means to directly compare and assess model performance. Performance metrics have been used to show that some models reproduce present-day climate better than others. Simulation data from multiple models are often used to add value to projections by creating a consensus projection from the model ensemble, in which each model is given an equal weight. It has been shown that the ensemble mean generally outperforms any single model. It is possible to use unequal weights to produce ensemble means, in which models are weighted based on performance (called "intelligent" ensembles). Can performance metrics be used to improve climate projections? Previous work introduced a framework for comparing the utility of model performance metrics, showing that the best metrics are related to the variance of top-of-atmosphere outgoing longwave radiation. These metrics improve present-day climate simulations of Earth's energy budget using the "intelligent" ensemble method. The current project identifies several approaches for testing whether performance metrics can be applied to future simulations to create "intelligent" ensemble-mean climate projections. It is shown that certain performance metrics test key climate processes in the models, and that these metrics can be used to evaluate model quality in both current and future climate states. This information will be used to produce new consensus projections and provide communities with improved climate projections for urgent decision-making.
Recent changes in the climate system have led to growing concern, especially in communities which are highly vulnerable to resource shortages and weather extremes. There is an urgent need for better climate information to develop solutions and strategies for adapting to a changing climate. Climate models provide excellent tools for studying the current state of climate and making future projections. However, these models are subject to biases created by structural uncertainties. Performance metrics-or the systematic determination of model biases-succinctly quantify aspects of climate model behavior. Efforts to standardize climate model experiments and collect simulation data-such as the Coupled Model Intercomparison Project (CMIP)-provide the means to directly compare and assess model performance. Performance metrics have been used to show that some models reproduce present-day climate better than others. Simulation data from multiple models are often used to add value to projections by creating a consensus projection from the model ensemble, in which each model is given an equal weight. It has been shown that the ensemble mean generally outperforms any single model. It is possible to use unequal weights to produce ensemble means, in which models are weighted based on performance (called "intelligent" ensembles). Can performance metrics be used to improve climate projections? Previous work introduced a framework for comparing the utility of model performance metrics, showing that the best metrics are related to the variance of top-of-atmosphere outgoing longwave radiation. These metrics improve present-day climate simulations of Earth's energy budget using the "intelligent" ensemble method. The current project identifies several approaches for testing whether performance metrics can be applied to future simulations to create "intelligent" ensemble-mean climate projections. It is shown that certain performance metrics test key climate processes in the models, and that these metrics can be used to evaluate model quality in both current and future climate states. This information will be used to produce new consensus projections and provide communities with improved climate projections for urgent decision-making.
The Advanced Life Support (ALS) has used a single number, Equivalent System Mass (ESM), for both reporting progress and technology selection. ESM is the launch mass required to provide a space system. ESM indicates launch cost. ESM alone is inadequate for technology selection, which should include other metrics such as Technology Readiness Level (TRL) and Life Cycle Cost (LCC) and also consider perfom.arxe 2nd risk. ESM has proven difficult to implement as a reporting metric, partly because it includes non-mass technology selection factors. Since it will not be used exclusively for technology selection, a new reporting metric can be made easier to compute and explain. Systems design trades-off performance, cost, and risk, but a risk weighted cost/benefit metric would be too complex to report. Since life support has fixed requirements, different systems usually have roughly equal performance. Risk is important since failure can harm the crew, but it is difficult to treat simply. Cost is not easy to estimate, but preliminary space system cost estimates are usually based on mass, which is better estimated than cost. Amass-based cost estimate, similar to ESM, would be a good single reporting metric. The paper defines and compares four mass-based cost estimates, Equivalent Mass (EM), Equivalent System Mass (ESM), Life Cycle Mass (LCM), and System Mass (SM). EM is traditional in life support and includes mass, volume, power, cooling and logistics. ESM is the specifically defined ALS metric, which adds crew time and possibly other cost factors to EM. LCM is a new metric, a mass-based estimate of LCC measured in mass units. SM includes only the factors of EM that are originally measured in mass, the hardware and logistics mass. All four mass-based metrics usually give similar comparisons. SM is by far the simplest to compute and easiest to explain.
The objective of this paper is to develop further a framework for computationally modeling microstructurally small fatigue crack growth in AA 7075-T651 [1]. The focus is on the nucleation event, when a crack extends from within a second-phase particle into a surrounding grain, since this has been observed to be an initiating mechanism for fatigue crack growth in this alloy. It is hypothesized that nucleation can be predicted by computing a non-local nucleation metric near the crack front. The hypothesis is tested by employing a combination of experimentation and nite element modeling in which various slip-based and energy-based nucleation metrics are tested for validity, where each metric is derived from a continuum crystal plasticity formulation. To investigate each metric, a non-local procedure is developed for the calculation of nucleation metrics in the neighborhood of a crack front. Initially, an idealized baseline model consisting of a single grain containing a semi-ellipsoidal surface particle is studied to investigate the dependence of each nucleation metric on lattice orientation, number of load cycles, and non-local regularization method. This is followed by a comparison of experimental observations and computational results for microstructural models constructed by replicating the observed microstructural geometry near second-phase particles in fatigue specimens. It is found that orientation strongly influences the direction of slip localization and, as a result, in uences the nucleation mechanism. Also, the baseline models, replication models, and past experimental observation consistently suggest that a set of particular grain orientations is most likely to nucleate fatigue cracks. It is found that a continuum crystal plasticity model and a non-local nucleation metric can be used to predict the nucleation event in AA 7075-T651. However, nucleation metric threshold values that correspond to various nucleation governing mechanisms must be calibrated.
The national airspace has evolved over many years to accommodate increased traffic demand [1] while simultaneously maintaining one of the safest forms of transportation [2], [3]. One of the reasons for this success is the ability of the system and the operators to adapt and accommodate to situations that routinely disrupt optimal operations. These situations may include: adverse weather, delays, early arrivals, equipment outages, and other factors that are outside the operators ability to control. These factors can lead to states where automation is unable to properly handle these issues and therefore air traffic controllers and pilots have to intervene, ultimately increasing communication between operators resulting in higher workload. As controller workload increases to handle sub-optimal operating conditions this can be viewed as an increase in complexity. The reasoning for this is because humans are now required to make tactical decisions in response to external factors, resulting in a departure from the strategic plan where operations would be more efficiently managed. Human operators control airspace complexity under rigid regulations that are constantly changing. The airspace is divided into sectors and the number of aircraft assigned to each controller is limited for safe handling. There has been past work that devised airspace complexity metrics in commercial aviation and related these metrics to controller workload (e.g., [4],[5]). The upper bounds on the system load are pre-determined. Such bounds on complexity make for a safe system, but the system cannot scale and adapt to autonomous, dense, and heterogeneous traffic, including the many types of Unmanned Aerial Vehicles (UAVs) envisioned to be added to the operations. We hypothesize that, as traffic density and heterogeneity grow, and other key metrics change, there will be phase transitions at which the way traffic should be managed changes significantly [6]. We offer a method for in-time detection of contributing factors that lead to phase transitions, characterized by increased complexity. To the best of our knowledge, there is no tool similar to our proposed effort that identifies such contributing factors or precursor patterns. To define the scope we are proposing to measure complexity from the viewpoint of the Terminal Radar Approach Control Facilities (TRACON) controller’s perspective. In particular we are analyzing arrivals into KSFO. With safety as the top concern for airspace operators, it is important to recognize that as density and heterogeneity grow, the focus of the system will change. Times of the day when the airspace has low density and heterogeneity, the flights will follow more efficient paths where the aircraft move on established routes that are more or less directly to the destination. However, when density and heterogeneity increases, the system will begin changing focus to avoiding conflicts and collisions and route the flights in a more flexible way. Higher flexibility requires more communication and coordination between controllers and pilots which the current automation is unable to handle. This paper proposes a novel approach that monitors airspace complexity at multiple scales, uses a Machine Learning-based tool that predicts when operations will transition to a regime of greater complexity, and identifies actions that can reduce the complexity while still maintaining efficient and safe operations. We demonstrate our proposed approach using data from multiple complementary sources. This includes, but is not limited to: historical aircraft surveillance data from NASA’s Sherlock Data Warehouse [7], METAR weather data, and airport configuration data from Aviation System Performance Metrics (ASPM). The surveillance data flight paths are sampled at a variable sample rate — increasing as the aircraft approaches the airport. This is due to how Sherlock manages flight track stitching between different radar facilities which have different sampling rates. The weather and performance data are logged at defined intervals throughout the day at a courser refresh rate. In addition to the logged data and metrics, we leverage pre-defined Standard Terminal Arrival Routes (STARs) procedures to characterize the path of each flight. Each flight files for one of these routes in the flight plan well before entering the terminal airspace, and approximately follows the route until it leaves the STAR, typically on the final fix of a runway transition. However, most flights do not always fly the full STAR procedure to completion [8], but the majority do adhere to the fixes within the common route of the procedure. Our approach leverages fixes in the common route of each of the STARs to build a reference path to the airport. This allows us to characterize the flight paths in what we are defining as the “maneuvering area” (the airspace between the STAR and before the flight is lined up on the runway’s final approach) to determine how off nominal the flights are to calculate its complexity score. Determining airspace complexity is a concept that does not have a concrete answer. In designing this metric, we consider what increases the workload for the air traffic controllers. Consequently more specialized vectoring maneuvers results in higher workload. Accordingly, we start with a theory: each flight has a direct path it takes from the STAR’s common route to the final approach’s outer marker fix for the flight’s landing runway. It is important to note that the direct path is only used as a reference. If the majority of the flights have a large consistent offset as compared to other routes it does not necessarily mean that those flights have higher complexity. We are merely building a distribution based on this direct path for that particular STAR and runway pair to determine the normal mode of operations for that route. Flights that are in the upper tail of these distributions will result in higher complexity scores and flights that fly in the median will represent the normal mode of operations and therefore will have lower complexity scores. Since flights following each STAR route take different paths to the airport, we have a different distribution for each STAR route and therefore can model these distributions to compute a complexity score from their respective normalized distributions. To evaluate the effectiveness of our proposed airspace complexity metric we will compare against an established approach based on trajectory clustering [9]. This unsupervised learning technique consists of the following steps: (1) identify the general maneuvering areas (waypoints) by performing $\kappa$-means or DBSCAN clustering on locations where aircraft frequently turn based on the surveillance radar track data, (2) map flight trajectories onto sequences of waypoints, and (3) cluster the sequences based on their common subsequences. From a high-level perspective, this baseline model learns nominal operations in the airspace through the sequence of waypoints that are representative of where aircraft change direction and defines deviations from the nominal operations as “complex.” Therefore, more deviations from the nominal operations correspond to higher complexity values. For our validation, we re-implemented this technique and tune model hyper-parameters to correctly detect waypoints for the arrival traffic into the San Francisco bay area. We will compute the complexity measure over a one-year period using our proposed technique as well as the baseline. Our validation will be based on each technique’s ability to detect a set of undesirable outcomes (e.g., go-arounds, holding patterns, average time in the airspace, etc.). Since our current complexity metric is derived from the offset from the direct reference path, it’s important to understand what causes these offsets. In many of the flights with high offset distance, flights performing holding patterns and S turns can be observed. These maneuvering tactics are utilized to add distance between the aircraft and the destination runway to prevent multiple flights from having conflicting arrival times. In order to predict a rise in complexity (or the precursor to complexity), it’s necessary to be able to identify these potential conflicts (which in turn, result in higher offsets). To do this, we define a “representative flight” for each STAR route and runway pair. This flight is approximately the path the flight would take if there was a clear path with no other flights in the airspace — including the time remaining to the airport. We first identify the flights for a given STAR runway pair using the offset to the reference path distributions that fall between the 44-55 percentiles. This yields the flights that conform to the most normal mode of operation. Each of these flights is partitioned based on the percent complete from the entry point into the maneuvering areas from 0\% – 100\% complete. Then for each percent “bin”, we take the median value of the flight’s latitude/longitude coordinates, airspeed, and (non causal) time remaining to the airport to construct a lookup table for each percent complete bin on a given route. As a flight enters the maneuvering area, we can find the estimated arrival time of a flight to the airport by finding the closest point to the representative path’s percent complete bin (relative to the flight’s current position at any snapshot in the airspace) and therefore retrieve the corresponding remaining time left on the “representative path”. We assume that the flight will follow the representative path to completion when deriving these estimates. We can then compare these estimated arrival times against other flights for the same snapshot in time to identify potential conflicts. If more flights are estimated to arrive within a tolerance window than there are runways available, then we have a potential conflict. We can use this derived measure along with other factors expected to add disruption to the operation such as weather and runway configuration changes as an input to machine learning tools to detect precursors that increases in our complexity measure. This novel method will assist in uncovering insights into the contributing factors that lead to increased complexity that may allow for in-time responses to avoid reaching a high complexity state in the airspace.
JPL has operated the Deep Space Network (DSN) on behalf of NASA since the 1960's. Over the last two decades, the DSN budget has generally declined in real-year dollars while the aging assets required more attention, and the missions became more complex. As a result, the DSN budget has been increasingly consumed by Operations and Maintenance (O&M), significantly reducing the funding wedge available for technology investment and for enhancing the DSN capability and capacity. Responding to this budget squeeze, the DSN launched an effort to improve the cost-efficiency of the O&M. In this paper we: elaborate on the methodology adopted to understand "where the time and money are used"-surprisingly, most of the data required for metrics development was readily available in existing databases-we have used commercial Business Intelligence (BI) tools to mine the databases and automatically extract the metrics (including trends) and distribute them weekly to interested parties; describe the DSN-specific effort to convert the intuitive understanding of "where the time is spent" into meaningful and actionable metrics that quantify use of resources, highlight candidate areas of improvement, and establish trends; and discuss the use of the BI-derived metrics-one of the most fascinating processes was the dramatic improvement in some areas of operations when the metrics were shared with the operators-the visibility of the metrics, and a self-induced competition, caused almost immediate improvement in some areas. While the near-term use of the metrics is to quantify the processes and track the improvement, these techniques will be just as useful in monitoring the process, e.g. as an input to a lean-six-sigma process.
Loudness is the quality of human perception that is most related to acoustic intensity and energy, however there is no agreed-upon way of integrating loudness over time for the prediction of noise-induced annoyance. Most noise metrics used today for aircraft certification and regulation employ the “Equal-Energy Hypothesis” (EEH) and sum the acoustical energy of one or more noise events over time to create a single metric value that represents the entire exposure. Using the EEH creates a natural tradeoff between the peak energy and the duration of a single noise event, the “hypothesis” being that this tradeoff optimally predicts annoyance in a wide variety of situations. This work proposes a strategy for integrating a loudness-like time series which is flexible in two ways: First, it includes a parameter b ∈ [0,1]. When b = 0, the metric will return the peak of the time series. At b = .5, the metric will behave in accordance with the EEH. At b = 1, the metric will penalize the duration of the sound more than the EEH would. Second, transformations are given so that the strategy can be computed from, or generate quantities in units analogous to, decibels (or phon), physical units (acoustic pressure/power), or perceptually-scaled units (sone). This approach is demonstrated on a dataset of annoyance responses to single events of UAV and road vehicle noise that is fit with an augmented linear regression. Analyses based on this integration of A-weighted level and the output of the “Zwicker” loudness model yield similar results: that subjects may have been slightly more sensitive to the durations of the events than the EEH would suppose, but that the EEH cannot be disproven using these data. The time-integrated metrics outperform both time-averaged and centile-based metrics.
Loudness is the quality of human perception that is most related to acoustic intensity and energy, however there is no agreed-upon way of integrating loudness over time for the prediction of noise-induced annoyance. Most noise metrics used today for aircraft certification and regulation employ the “Equal-Energy Hypothesis” (EEH) and sum the acoustical energy of one or more noise events over time to create a single metric value that represents the entire exposure. Using the EEH creates a natural tradeoff between the peak energy and the duration of a single noise event, the “hypothesis” being that this tradeoff optimally predicts annoyance in a wide variety of situations. This work proposes a strategy for integrating a loudness-like time series which is flexible in two ways: First, it includes a parameter b ∈ [0,1]. When b = 0, the metric will return the peak of the time series. At b = .5, the metric will behave in accordance with the EEH. At b = 1, the metric will penalize the duration of the sound more than the EEH would. Second, transformations are given so that the strategy can be computed from, or generate quantities in units analogous to, decibels (or phon), physical units (acoustic pressure/power), or perceptually-scaled units (sone). This approach is demonstrated on a dataset of annoyance responses to single events of UAV and road vehicle noise that is fit with an augmented linear regression. Analyses based on this integration of A-weighted level and the output of the “Zwicker” loudness model yield similar results: that subjects may have been slightly more sensitive to the durations of the events than the EEH would suppose, but that the EEH cannot be disproven using these data. The time-integrated metrics outperform both time-averaged and centile-based metrics.