Nonlinear Model Tracking in Application to Failed Nondestructive Evaluations

2011 ◽  
Author(s):  
Timothy A. Doughty ◽  
Natalie S. Higgins ◽  
Nicholas G. Etzel
Keyword(s):  
Natural Frequency ◽  
Nonlinear Model ◽  
Equation Model ◽  
False Alarms ◽  
Parameter Estimates ◽  
Nonlinear Phenomena ◽  
Time Data ◽  
Monitoring Method ◽  
Cantilevered Beam ◽  
Nondestructive Evaluations

The nondestructive health monitoring method of Nonlinear Model Tracking (NMT) is introduced and tested under various conditions. The study involves the fatigue and failure of a slender cantilevered beam subject to harmonic nonstationary base excitation around the beam’s second natural frequency. A nonlinear differential equation model for the system is assumed and parameters for the model are estimated using Continuous Time System Identification populated with healthy system stimulus and response data. Updated with real time data sets from the system in operation, the method tracks changes in parameter estimates. The NMT method indicates with repeatability the onset of plasticity, crack initiation and growth well in advance of system failure. Additionally, the NMT method is shown to not give false alarms when system behavior varies in a way that is associated with nonlinear phenomena. Linear methods based on tracking the system’s natural frequency are shown to misidentify the onset of failure for fully healthy systems.

Impact of Blue Force Tracking on Combat Identification Judgments

2012 ◽  
Vol 55 (1) ◽  
pp. 75-89 ◽  
Author(s):  
David J. Bryant ◽  
David G. Smith
Keyword(s):  
Decision Support ◽  
Situation Awareness ◽  
Performance Standards ◽  
Positional Information ◽  
False Alarms ◽  
Time Data ◽  
Position Information ◽  
Person Perspective ◽  
Force Tracking ◽  
Gaming Environment

Objective: We examined the effectiveness of blue force tracking (BFT) decision support for dismounted infantry soldiers. Background: Technologies to support combat identification (CID) are rapidly evolving and may be deployable to dismounted soldiers in the future. BFT systems are designed to mitigate the risk of fratricide by supplying positional information regarding friendly units to enhance situation awareness. Method: Participants played the role of a dismounted infantry soldier in a first-person perspective gaming environment and made engagement decisions for a series of simulated targets, half of which were enemies and half of which were friends. Results: Participants performed better overall when they were able to use a BFT system than when they performed the task without assistance. When a 10-s latency was added to the updating of position information in the BFT, participants made significantly more false alarms (engaged a friendly target) regardless of whether they knew about the latency. Conclusion: The results indicate the promise of a personal BFT device to reduce the likelihood of fratricide by dismounted infantry soldiers. The results, however, also indicate that the effectiveness of such a device can be dramatically reduced when it does not provide real-time data. Application: Potential applications of this research include development of performance standards for BFT devices and assessment of decision support for dismounted soldiers.

scholarly journals PREDICTING THE PROBABILITY OF PERSISTENCE OF HIV INFECTION WITH THE STANDARD MODEL

2011 ◽  
Vol 19 (04) ◽  
pp. 747-762 ◽  
Author(s):  
HENRY C. TUCKWELL ◽  
PATRICK D. SHIPMAN
Keyword(s):  
Hiv Infection ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Equation Model ◽  
Parameter Estimates ◽  
Host Immune System ◽  
Stable Node ◽  
Asymptotically Stable ◽  
Discordant Couple ◽  
First Case

It is not well understood why the transmission of HIV may have a small probability of occurrence despite frequent high risk exposures or ongoing contact between members of a discordant couple. We explore the possible contributions made by distributions of system parameters beginning with the standard three-component differential equation model for the growth of a HIV virion population in an infected host in the absence of drug therapy. The overall dynamical behavior of the model is determined by the set of values of six parameters, some of which describe host immune system properties and others which describe virus properties. There may be one or two critical points whose natures play a key role in determining the outcome of infection and in particular whether the HIV population will persist or become extinct. There are two cases which may arise. In the first case, there is only one critical point P1at biological values and this is an asymptotically stable node. The system ends up with zero virions and so the host becomes HIV-free. In the second case, there are two critical points P1and P2at biological values. Here P1is an unstable saddle point and P2is an asymptotically stable spiral point with a non-zero virion level. In this case the HIV population persists unless parameters change. We let the parameter values take random values from distributions based on empirical data, but suitably truncated, and determine the probabilities of occurrence of the various combinations of critical points. From these simulations the probability that an HIV infection will persist, across a population, is estimated. It is found that with conservatively estimated distributions of parameters, within the framework of the standard 3-component model, the chances that a within-host HIV population will become extinct is between 0.6% and 6.9%. With less conservative parameter estimates, the probability is estimated to be as high as 24%. The many complicating factors related to the transmission and possible spontaneous elimination of the virus and the need for experimental data to clarify whether transient infections may occur are discussed. More realistic yet complicated higher dimensional models are likely to yield smaller probabilities of extinction.

Dynamic models for the contact analysis of a tensioned beam with a moving oscillator

2013 ◽  
Vol 228 (4) ◽  
pp. 676-689
Author(s):  
Kyuho Lee ◽  
Jintai Chung
Keyword(s):  
Natural Frequency ◽  
Nonlinear Model ◽  
Frequency Ratio ◽  
Dynamic Models ◽  
Equations Of Motion ◽  
Contact Analysis ◽  
Contact Forces ◽  
Accurate Analysis ◽  
Moving Oscillator ◽  
Velocity Decrease

Several dynamic models are proposed for the contact analysis of a tensioned beam with a moving oscillator. Depending on whether the strain and stress used to derive the equations of motion are nonlinear, four models are established to analyze the beam deflections and the contact force between the beam and moving oscillator. We find that the differences in the contact forces and deflections computed with the models become large as the beam tension and moving velocity decrease and the natural frequency ratio of the oscillator to the beam increases. The nonlinear model derived with nonlinear strain and stress is desirable for an accurate analysis.

scholarly journals Real-Time Data Assimilation for Operational Ensemble Streamflow Forecasting

2006 ◽  
Vol 7 (3) ◽  
pp. 548-565 ◽  
Author(s):  
Jasper A. Vrugt ◽  
Hoshin V. Gupta ◽  
BreanndánÓ Nualláin ◽  
Willem Bouten
Keyword(s):  
Data Assimilation ◽  
Simultaneous Optimization ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Optimization Approach ◽  
Streamflow Forecasting ◽  
Time Data ◽  
Forecast Performance ◽  
Performance Improvements ◽  
Using Data

Abstract Operational flood forecasting requires that accurate estimates of the uncertainty associated with model-generated streamflow forecasts be provided along with the probable flow levels. This paper demonstrates a stochastic ensemble implementation of the Sacramento model used routinely by the National Weather Service for deterministic streamflow forecasting. The approach, the simultaneous optimization and data assimilation method (SODA), uses an ensemble Kalman filter (EnKF) for recursive state estimation allowing for treatment of streamflow data error, model structural error, and parameter uncertainty, while enabling implementation of the Sacramento model without major modification to its current structural form. Model parameters are estimated in batch using the shuffled complex evolution metropolis stochastic-ensemble optimization approach (SCEM-UA). The SODA approach was implemented using parallel computing to handle the increased computational requirements. Studies using data from the Leaf River, Mississippi, indicate that forecast performance improvements on the order of 30% to 50% can be realized even with a suboptimal implementation of the filter. Further, the SODA parameter estimates appear to be less biased, which may increase the prospects for finding useful regionalization relationships.

scholarly journals An Artificially Intelligent System for the Automated Issuance of Tornado Warnings in Simulated Convective Storms

2020 ◽  
Vol 35 (5) ◽  
pp. 1939-1965
Author(s):  
Dylan Steinkruger ◽  
Paul Markowski ◽  
George Young
Keyword(s):  
Machine Learning ◽  
Lead Time ◽  
Intelligent System ◽  
Grid Point ◽  
False Alarms ◽  
Time Data ◽  
Convective Storms ◽  
Tornado Warnings ◽  
Optimization Function ◽  
Tornado Warning

AbstractThe utility of employing artificial intelligence (AI) to issue tornado warnings is explored using an ensemble of 128 idealized simulations. Over 700 tornadoes develop within the ensemble of simulations, varying in duration, length, and associated storm mode. Machine-learning models are trained to forecast the temporal and spatial probabilities of tornado formation for a specific lead time. The machine-learning probabilities are used to produce tornado warning decisions for each grid point and lead time. An optimization function is defined, such that warning thresholds are modified to optimize the performance of the AI system on a specified metric (e.g., increased lead time, minimized false alarms, etc.). Using genetic algorithms, multiple AI systems are developed with different optimization functions. The different AI systems yield unique warning output depending on the desired attributes of the optimization function. The effects of the different optimization functions on warning performance are explored. Overall, performance is encouraging and suggests that automated tornado warning guidance is worth exploring with real-time data.

scholarly journals Analyzing ordinal data with metric models: What could possibly go wrong?

2017 ◽  
Author(s):  
Torrin Liddell ◽  
John K. Kruschke
Keyword(s):  
Ordinal Data ◽  
Ordered Probit ◽  
False Alarms ◽  
Parameter Estimates ◽  
Type I ◽  
Type I Errors ◽  
Psychological Science ◽  
Probit Models ◽  
Ordered Probit Models ◽  
Type Ii Errors

We surveyed all articles in the Journal of Personality and Social Psychology (JPSP), Psychological Science (PS), and the Journal of Experimental Psychology: General (JEP:G) that mentioned the term "Likert," and found that 100% of the articles that analyzed ordinal data did so using a metric model. We present novel evidence that analyzing ordinal data as if they were metric can systematically lead to errors. We demonstrate false alarms (i.e., detecting an effect where none exists, Type~I errors) and failures to detect effects (i.e., loss of power, Type II errors). We demonstrate systematic inversions of effects, for which treating ordinal data as metric indicates the opposite ordering of means than the true ordering of means. We show the same problems --- false alarms, misses, and inversions --- for interactions in factorial designs and for trend analyses in regression. We demonstrate that averaging across multiple ordinal measurements does not solve or even ameliorate these problems. We provide simple graphical explanations of why these mistakes occur. Moreover, we point out that there is no sure-fire way to detect these problems by treating the ordinal values as metric, and instead we advocate use of ordered-probit models (or similar) because they will better describe the data. Finally, although frequentist approaches to some ordered-probit models are available, we use Bayesian methods because of their flexibility in specifying models and their richness and accuracy in providing parameter estimates.

Using Market-Level Data to Understand Promotion Effects in a Nonlinear Model

1997 ◽  
Vol 34 (3) ◽  
pp. 322-334 ◽  
Author(s):  
Markus Christen ◽  
Sachin Gupta ◽  
John C. Porter ◽  
Richard Staelin ◽  
Dick R. Wittink
Keyword(s):  
Nonlinear Model ◽  
Simulated Data ◽  
Parameter Estimates ◽  
Econometric Modeling ◽  
Scanner Data ◽  
Aggregation Method ◽  
Marketing Manager ◽  
New Approach ◽  
Level Data

The authors show analytically, empirically, and numerically through simulation that the estimated effects from linearly aggregated market-level data differ substantially from comparable effects that are obtained from store-level data. The magnitude of this difference renders market-level data largely unsuitable for econometric modeling, unless the marketing manager compensates for the bias that results from the incompatible aggregation. The authors introduce a new approach, a relatively simple debiasing procedure derived from simulated data. They show that this debiasing approach results in substantially improved parameter estimates. They illustrate the value of the procedure by applying it to scanner data for powdered detergents and comparing the debiased parameter estimates to results obtained from store-level data and an alternative aggregation method that maintains homogeneity for selected promotional activities.

Investigation of the nonlinear phenomena of a Langevin ultrasonic transducer caused by high applied voltage

2021 ◽  
pp. 095440622110093 ◽  
Author(s):  
Shibo Zhang ◽  
Yang Li ◽  
Sisi Li ◽  
Yongbo Wu ◽  
Jiang Zeng
Keyword(s):  
Nonlinear Model ◽  
Longitudinal Vibration ◽  
Ultrasonic Transducer ◽  
Linear Functions ◽  
Vibration Velocity ◽  
System Response ◽  
Nonlinear Phenomena ◽  
Amplitude Curve ◽  
Nonlinear Phenomenon ◽  
Physical Point

In the field of power ultrasound, Langevin ultrasonic transducers (LUTs) usually operate at a large displacements output power by applying high voltages. However, empirically, a LUT exhibits nonlinearities such as amplitude jumping and peak hysteresis for high voltages in actual operations. The nonlinearities would reduce the efficiency and output accuracy of an LUT. In this research, the burst-mode method was used to measure the longitudinal vibration velocity of the LUT, which gradually decreased with time after the excitation voltage was turned off. The equivalent mechanical losses and equivalent spring constants were determined using the velocity attenuation rate and resonant frequency and they were found to be the linear functions of velocity, helping to develop a novel nonlinear model. This model contained two quadratic nonlinear terms based on the linear model. Furthermore, the developed nonlinear model was analyzed using the Lagrangian method as well as the multiscale method, which confirmed that the model was effective in describing the nonlinear behavior. It was also found that the frequency-amplitude curve bent when the nonlinear term was taken into account, which resembled the nonlinear phenomenon tested experimentally. From a physical point of view, this bending was meaningful because it led to the formation of multi-valued response regions with jumping phenomena. Additionally, according to the obtained results, the maximum value of the system response was independent of the degree of nonlinearity of the system.

scholarly journals Forecasting auroras from regional and global magnetic field measurements

2016 ◽  
Author(s):  
K. Kauristie ◽  
M. Myllys ◽  
N. Partamies ◽  
A. Viljanen ◽  
P. Peitso ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Geomagnetic Storms ◽  
Time Derivative ◽  
Field Measurements ◽  
False Alarms ◽  
Research Station ◽  
Time Data ◽  
Number Of False Alarms ◽  
Northern Fennoscandia ◽  
Probability Estimates

Abstract. We present a concept for a Regional Auroral Forecast service (RAF), which uses near-real-time data from the IMAGE network of ground-based magnetometers operated in Northern Fennoscandia. Performance of RAF is demonstrated in a case study with auroral recordings from the Sodankylä research station. RAF is based on archived National Oceanic and Atmospheric Administration (NOAA) space weather alerts and regional magnetic field recordings (years 2002–2012). The archives are used to create a set of conditional probabilities, which tell the service user when the probability to see auroras exceeds the average conditions in Fennoscandia during the coming 0–12 hours. Favourable conditions for auroral displays are associated with ground magnetic field time derivative values (dB/dt) exceeding certain latitude dependent threshold values. Our statistical analyses reveal that the probabilities to record dB/dt exceeding the thresholds stay below 50% after NOAA alerts on X-ray bursts or on energetic particle flux enhancements. Therefore, those alerts are not very useful for auroral forecasts, if we want to keep the number of false alarms low. However, NOAA alerts on global geomagnetic storms (characterized with Kp values >4) enable probability estimates of >50% with lead times of 3–12 hours. RAF forecasts thus rely heavily on the well-known fact that bright auroras appear during geomagnetic storms. The additional new piece of information which RAF brings to the previous picture is the knowledge on typical storm durations at different latitudes. For example, the service users south of the Artic Circle will learn that after a NOAA ALTK06 issuance in night, auroral spotting should be done within 12 hours after the alert, while at higher latitudes conditions can remain favourable during the next night.

scholarly journals Estimating DSGE model parameters in a small open economy: Do real-time data matter?

2015 ◽  
Vol 15 (1) ◽  
pp. 89-114 ◽  
Author(s):  
Jan Capek
Keyword(s):  
Real Time ◽  
Euro Area ◽  
Open Economy ◽  
Response Analysis ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Gdp Growth ◽  
Time Data ◽  
Data Revisions ◽  
Real Time Data

Abstract This paper investigates the differences between parameters estimated using real-time and those estimated with revised data. The models used are New Keynesian DSGE models of the Czech, Polish, Hungarian, Swiss, and Swedish small open economies in interaction with the euro area. The paper also offers an analysis of data revisions of GDP growth and inflation and trend revisions of interest rates. Data revisions are found to be unbiased and not autocorrelated in all countries. Inflation is usually measured more accurately in real-time than GDP growth, but this is not the case in the euro area. The results of the core analysis suggest that there are significant differences between parameter estimates using real-time data and those estimated using revised data. The model parameters that are most prone to significant differences between real-time and revised estimations are habit in consumption and persistence of domestic supply, of demand, and of world-wide technology shocks. The impulse response analysis suggests that the model behavior based on real-time and revised data is different.

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