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NASA NTRS1999

Feature extraction of event-related potentials using wavelets: an application to human performance monitoring

This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWT was compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many free parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWT network or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. The efficiency of the DWT is discussed in terms of its decorrelation and energy compaction properties. In addition, the DWT models provided evidence that a pattern of low-frequency activity (1 to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance. Copyright 1999 Academic Press.

Evoked Potentials↗

NASA NTRS1986

A survey of the state of the art and focused research in range systems, task 2

Many communication, control, and information processing subsystems are modeled by linear systems incorporating tapped delay lines (TDL). Such optimized subsystems result in full precision multiplications in the TDL. In order to reduce complexity and cost in a microprocessor implementation, these multiplications can be replaced by single-shift instructions which are equivalent to powers of two multiplications. Since, in general, the obvious operation of rounding the infinite precision TDL coefficients to the nearest powers of two usually yield quite poor system performance, the optimum powers of two coefficient solution was considered. Detailed explanations on the use of branch-and-bound algorithms for finding the optimum powers of two solutions are given. Specific demonstration of this methodology to the design of a linear data equalizer and its implementation in assembly language on a 8080 microprocessor with a 12 bit A/D converter are reported. This simple microprocessor implementation with optimized TDL coefficients achieves a system performance comparable to the optimum linear equalization with full precision multiplications for an input data rate of 300 baud. The philosophy demonstrated in this implementation is dully applicable to many other microprocessor controlled information processing systems.

Yao, K.↗

NASA NTRS1991

High-efficiency heteroepitaxial InP solar cells

High-efficiency, thin-film InP solar cells grown heteroepitaxially on GaAs and Si single-crystal bulk substrates are being developed as a means of eliminating the problems associated with using single-crystal InP substrates. A novel device structure employing a compositionally graded Ga(x)In(1-x)As layer between the bulk substrate and the InP cell layers is used to reduce the dislocation density and improve the minority carrier properties in the InP. The structures are grown in a continuous sequence of steps using computer-controlled atmospheric pressure metalorganic vapor phase epitaxy (APMOVPE). Dislocation densities as low as 3 x 10(exp 7) sq cm and minority carrier lifetimes as high as 3.3 ns are achieved in the InP layers with this method using both GaAs or Si substrates. Structures prepared in this fashion are also completely free of microcracks. These results represent a substantial improvement in InP layer quality when compared to heteroepitaxial InP prepared using conventional techniques such as thermally cycled growth and post-growth annealing. The present work is is concerned with the fabrication and characterization of high-efficiency, thin-film InP solar cells. Both one-sun and concentrator cells were prepared for device structures grown on GaAs substrates. One-cell cells have efficiencies as high as 13.7 percent at 25 C. However, results for the concentrator cells are emphasized. The concentrator cell performance is characterized as a function of the air mass zero (AM0) solar concentration ratio and operating temperature. From these data, the temperature coefficients of the cell performance parameters are derived as a function of the concentration ratio. Under concentration, the cells exhibit a dramatic increase in efficiency and an improved temperature coefficient of efficiency. At 25 C, a peak conversion efficiency of 18.9 percent is reported. At 80 C, the peak AM0 efficiency is 15.7 percent at 75.6 suns. These are the highest efficiencies yet reported for InP heteroepitaxial cells. Approaches for further improving the cell performance are discussed.

Wanlass, M. W.↗

NASA NTRS1988

Investigation of oscillating cascade aerodynamics by an experimental influence coefficient technique

Fundamental experiments are performed in the NASA Lewis Transonic Oscillating Cascade Facility to investigate the torsion mode unsteady aerodynamics of a biconvex airfoil cascade at realistic values of the reduced frequency for all interblade phase angles at a specified mean flow condition. In particular, an unsteady aerodynamic influence coefficient technique is developed and utilized in which only one airfoil in the cascade is oscillated at a time and the resulting airfoil surface unsteady pressure distribution measured on one dynamically instrumented airfoil. The unsteady aerodynamics of an equivalent cascade with all airfoils oscillating at a specified interblade phase angle are then determined through a vector summation of these data. These influence coefficient determined oscillation cascade data are correlated with data obtained in this cascade with all airfoils oscillating at several interblade phase angle values. The influence coefficients are then utilized to determine the unsteady aerodynamics of the cascade for all interblade phase angles, with these unique data subsequently correlated with predictions from a linearized unsteady cascade model.

Buffum, Daniel H.↗

NASA NTRS1988

Investigation of oscillating cascade aerodynamics by an experimental influence coefficient technique

Fundamental experiments are performed in the NASA Lewis Transonic Oscillating Cascade Facility to investigate the torsion mode unsteady aerodynamics of a biconvex airfoil cascade at realistic values of the reduced frequency for all interblade phase angles at a specified mean flow condition. In particular, an unsteady aerodynamic influence coefficient technique is developed and utilized in which only one airfoil in the cascade is oscillated at a time and the resulting airfoil surface unsteady pressure distribution measured on one dynamically instrumented airfoil. The unsteady aerodynamics of an equivalent cascade with all airfoils oscillating at a specified interblade phase angle are then determined through a vector summation of these data. These influence coefficient determined oscillating cascade data are correlated with data obtained in this cascade with all airfoils oscillating at several interblade phase angle values. The influence coefficients are then utilized to determine the unsteady aerodynamics of the cascade for all interblade phase angles, with these unique data subsequently correlated with predictions from a linearized unsteady cascade model.

Buffum, Daniel H.↗

NASA NTRS2005

F119 Nozzle Flaps Tested at Lewis' CE-22 Facility

The next generation of aircraft fighters requires higher engine performance and enhanced stealth characteristics for air superiority. A Lockheed-Martin/Boeing aircraft with a Pratt & Whitney F119 engine was selected by the Air Force for the next advanced tactical fighter (ATF). As part of this program, the NASA Lewis Research Center entered into a cooperative test program with Pratt & Whitney along with the Air Force to study the performance for various advanced nozzle concepts for the F119 engine. The area of interest was to measure the internal performance (both thrust and flow coefficients) of nozzle flaps redesigned for low observability with minimal performance loss. The experimental program was successfully completed May 1995 in Lewis' CE-22 facility. The models were tested over a wide range of geometric variations and nozzle pressure ratios. Results confirmed that the redesigned nozzle flaps had an insignificant effect on the thrust performance and that the resulting flow patterns should not be a problem in the cooling flow design. The results also agreed well with Pratt & Whitney's computational fluid dynamics analysis. The data obtained from this test were added to the current data base to help validate other performance prediction methodology.

Source record↗

NASA NTRS2000

Effect of Film-Hole Shape on Turbine Blade Film Cooling Performance

The detailed heat transfer coefficient and film cooling effectiveness distributions as well as tile detailed coolant jet temperature profiles on the suction side of a gas turbine blade A,ere measured using a transient liquid crystal image method and a traversing cold wire and a traversing thermocouple probe, respectively. The blade has only one row of film holes near the gill hole portion on the suction side of the blade. The hole geometries studied include standard cylindrical holes and holes with diffuser shaped exit portion (i.e. fanshaped holes and laidback fanshaped holes). Tests were performed on a five-blade linear cascade in a low-speed wind tunnel. The mainstream Reynolds number based on cascade exit velocity was 5.3 x 10(exp 5). Upstream unsteady wakes were simulated using a spoke-wheel type wake generator. The wake Strouhal number was kept at 0 or 0.1. Coolant blowing ratio was varied from 0.4 to 1.2. Results show that both expanded holes have significantly improved thermal protection over the surface downstream of the ejection location, particularly at high blowing ratios. However, the expanded hole injections induce earlier boundary layer transition to turbulence and enhance heat transfer coefficients at the latter part of the blade suction surface. In general, the unsteady wake tends to reduce film cooling effectiveness.

Han, J. C.↗

NASA NTRS2014

Estimation of Crop Gross Primary Production (GPP): I. Impact of MODIS Observation Footprint and Impact of Vegetation BRDF Characteristics

Accurate estimation of gross primary production (GPP) is essential for carbon cycle and climate change studies. Three AmeriFlux crop sites of maize and soybean were selected for this study. Two of the sites were irrigated and the other one was rainfed. The normalized difference vegetation index (NDVI), the enhanced vegetation index (EVI), the green band chlorophyll index (CIgreen), and the green band wide dynamic range vegetation index (WDRVIgreen) were computed from the moderate resolution imaging spectroradiometer (MODIS) surface reflectance data. We examined the impacts of the MODIS observation footprint and the vegetation bidirectional reflectance distribution function (BRDF) on crop daily GPP estimation with the four spectral vegetation indices (VIs - NDVI, EVI, WDRVIgreen and CIgreen) where GPP was predicted with two linear models, with and without offset: GPP = a × VI × PAR and GPP = a × VI × PAR + b. Model performance was evaluated with coefficient of determination (R2), root mean square error (RMSE), and coefficient of variation (CV). The MODIS data were filtered into four categories and four experiments were conducted to assess the impacts. The first experiment included all observations. The second experiment only included observations with view zenith angle (VZA) ≤ 35◦ to constrain growth of the footprint size,which achieved a better grid cell match with the agricultural fields. The third experiment included only forward scatter observations with VZA ≤ 35◦. The fourth experiment included only backscatter observations with VZA ≤ 35◦. Overall, the EVI yielded the most consistently strong relationships to daily GPP under all examined conditions. The model GPP = a × VI × PAR + b had better performance than the model GPP = a × VI × PAR, and the offset was significant for most cases. Better performance was obtained for the irrigated field than its counterpart rainfed field. Comparison of experiment 2 vs. experiment 1 was used to examine the observation footprint impact whereas comparison of experiment 4 vs. experiment 3 was used to examine the BRDF impact. Changes in R2, RMSE,CV and changes in model coefficients "a" and "b" (experiment 2 vs. experiment 1; and experiment 4 vs. experiment 3) were indicators of the impacts. The second experiment produced better performance than the first experiment, increasing R2 (↑0.13) and reducing RMSE (↓0.68 g C m−2 d−1) and CV (↓9%). For each VI, the slope of GPP = a × VI × PAR in the second experiment for each crop type changed little while the slope and intercept of GPP = a × VI × PAR + b varied field by field. The CIgreen was least affected by the MODIS observation footprint in estimating crop daily GPP (R2, ↑0.08; RMSE, ↓0.42 g C m−2 d−1; and CV, ↓7%). Footprint most affected the NDVI (R2, ↑0.15; CV, ↓10%) and the EVI (RMSE, ↓0.84 g C m−2 d−1). The vegetation BRDF impact also caused variation of model performance and change of model coefficients. Significantly different slopes were obtained for forward vs. backscatter observations, especially for the CIgreen and the NDVI. Both the footprint impact and the BRDF impact varied with crop types, irrigation options, model options and VI options.

Chlorophyll↗

NASA NTRS2012

Aircraft Anomaly Detection Using Performance Models Trained on Fleet Data

This paper describes an application of data mining technology called Distributed Fleet Monitoring (DFM) to Flight Operational Quality Assurance (FOQA) data collected from a fleet of commercial aircraft. DFM transforms the data into aircraft performance models, flight-to-flight trends, and individual flight anomalies by fitting a multi-level regression model to the data. The model represents aircraft flight performance and takes into account fixed effects: flight-to-flight and vehicle-to-vehicle variability. The regression parameters include aerodynamic coefficients and other aircraft performance parameters that are usually identified by aircraft manufacturers in flight tests. Using DFM, the multi-terabyte FOQA data set with half-million flights was processed in a few hours. The anomalies found include wrong values of competed variables, (e.g., aircraft weight), sensor failures and baises, failures, biases, and trends in flight actuators. These anomalies were missed by the existing airline monitoring of FOQA data exceedances.

Gorinevsky, Dimitry↗

NASA NTRS2003

A Wind Tunnel Study of Icing Effects on a Business Jet Airfoil

Aerodynamic wind tunnel tests were conducted to study the effects of various ice accretions on the aerodynamic performance of a 36-inch chord, two-dimensional business jet airfoil. Eight different ice shape configurations were tested. Four were castings made from molds of ice shapes accreted in an icing wind tunnel. Two were made using computationally smoothed tracings of two of the ice shapes accreted in the icing tunnel. These smoothed profiles were then extended in the spanwise direction to form a two-dimensional ice shape. The final two configurations were formed by applying grit to the smoothed ice shapes. The ice shapes resulted in as much as 48% reduction in maximum lift coefficient from that of the clean airfoil. Large increases in drag and changes in pitching moment were also observed. The castings and their corresponding smoothed counterparts yielded similar results. Little change in performance was observed with the addition of grit to the smoothed ice shapes. Changes in the Reynolds number (from 3 x 10(exp 6) to 10.5 x 10(exp 6) and Mach number (from 0.12 to 0.28) did not significantly affect the iced-airfoil performance coefficients.

Addy, Harold E., Jr.↗

NASA NTRS1991

Optical analysis of thermal induced structural distortions

The techniques used for the analysis of thermally induced structural distortions of optical components such as scanning mirrors and telescope optics are outlined. Particular attention is given to the methodology used in the thermal and structural analysis of the GOES scan mirror, the optical analysis using Zernike coefficients, and the optical system performance evaluation. It is pointed out that the use of Zernike coefficients allows an accurate, effective, and simple linkage between thermal/mechanical effects and the optical design.

Weinswig, Shepard↗

NASA NTRS1998

Bulk-Flow Analysis of Hybrid Thrust Bearings for Advanced Cryogenic Turbopumps

A bulk-flow analysis and computer program for prediction of the static load performance and dynamic force coefficients of angled injection, orifice-compensated hydrostatic/hydrodynamic thrust bearings have been completed. The product of the research is an efficient computational tool for the design of high-speed thrust bearings for cryogenic fluid turbopumps. The study addresses the needs of a growing technology that requires of reliable fluid film bearings to provide the maximum operating life with optimum controllable rotordynamic characteristics at the lowest cost. The motion of a cryogenic fluid on the thin film lands of a thrust bearing is governed by a set of bulk-flow mass and momentum conservation and energy transport equations. Mass flow conservation and a simple model for momentum transport within the hydrostatic bearing recesses are also accounted for. The bulk-flow model includes flow turbulence with fluid inertia advection, Coriolis and centrifugal acceleration effects on the bearing recesses and film lands. The cryogenic fluid properties are obtained from realistic thermophysical equations of state. Turbulent bulk-flow shear parameters are based on Hirs' model with Moody's friction factor equations allowing a simple simulation for machined bearing surface roughness. A perturbation analysis leads to zeroth-order nonlinear equations governing the fluid flow for the thrust bearing operating at a static equilibrium position, and first-order linear equations describing the perturbed fluid flow for small amplitude shaft motions in the axial direction. Numerical solution to the zeroth-order flow field equations renders the bearing flow rate, thrust load, drag torque and power dissipation. Solution to the first-order equations determines the axial stiffness, damping and inertia force coefficients. The computational method uses well established algorithms and generic subprograms available from prior developments. The Fortran9O computer program hydrothrust runs on a Windows 95/NT personal computer. The program, help files and examples are licensed by Texas A&M University Technology License Office. The study of the static and dynamic performance of two hydrostatic/hydrodynamic bearings demonstrates the importance of centrifugal and advection fluid inertia effects for operation at high rotational speeds. The first example considers a conceptual hydrostatic thrust bearing for an advanced liquid hydrogen turbopump operating at 170,000 rpm. The large axial stiffness and damping coefficients of the bearing should provide accurate control and axial positioning of the turbopump and also allow for unshrouded impellers, therefore increasing the overall pump efficiency. The second bearing uses a refrigerant R134a, and its application in oil-free air conditioning compressors is of great technological importance and commercial value. The computed predictions reveal that the LH2 bearing load capacity and flow rate increase with the recess pressure (i.e. increasing orifice diameters). The bearing axial stiffness has a maximum for a recess pressure rati of approx. 0.55. while the axial damping coefficient decreases as the recess pressure ratio increases. The computer results from three flow models are compared. These models are a) inertialess, b) fluid inertia at recess edges only, and c) full fluid inertia at both recess edges and film lands. The full inertia model shows the lowest flow rates, axial load capacity and stiffness coefficient but on the other hand renders the largest damping coefficients and inertia coefficients. The most important findings are related to the reduction of the outflow through the inner radius and the appearance of subambient pressures. The performance of the refrigerant hybrid thrust bearing is evaluated at two operating speeds and pressure drops. The computed results are presented in dimensionless form to evidence consistent trends in the bearing performance characteristics. As the applied axial load increases, the bearing film thickness and flow rate decrease while the recess pressure increases. The axial stiffness coefficient shows a maximum for a certain intermediate load while the damping coefficient steadily increases. The computed results evidence the paramount of centrifugal fluid inertia at low recess pressures (i.e. low loads), and where there is actually an inflow through the bearing inner diameter, accompanied by subambient pressures just downstream of the bearing recess edge. These results are solely due to centrifugal fluid inertia and advection transport effects. Recommendations include the extension of the computer program to handle flexure pivot tilting pad hybrid bearings and the ability to calculate moment coefficients for shaft angular misalignments.

SanAndres, Luis↗

NASA NTRS1984

Rotordynamic Instability Problems in High-Performance Turbomachinery

Rotordynamics and predictions on the stability of characteristics of high performance turbomachinery were discussed. Resolutions of problems on experimental validation of the forces that influence rotordynamics were emphasized. The programs to predict or measure forces and force coefficients in high-performance turbomachinery are illustrated. Data to design new machines with enhanced stability characteristics or upgrading existing machines are presented.

Source record↗

NASA NTRS2021

Performance of JAXA’s SGLI standard ocean color products for oceanic to coastal waters: chlorophyll a concentration and light absorption coefficients of colored dissolved organic matter

We present the performance of JAXA’s SGLI standard algorithms for estimating chlorophyll a (chl a) concentration and the light absorption coefcients of colored dissolved organic matter (CDOM) using recently compiled high-quality data obtained from oceanic to coastal waters. Prior to the evaluation of the algorithms, we frst compare two forward models (Gordon et al. in J Geophys Res 93(D9):10909-10924, 1988: G88 and Park and Ruddick in Appl Opt 44(7):1236–1249, 2005: PR05) using a wide range of inherent optical properties (IOPs) to (1) examine if the water refectance is appropriately reproduced and (2) correct measured refectance in terms of its bidirectionality. Based on a good reproducibility of water refectance using the PR05, the optimized IOPs are further used for explaining errors in estimates of chl a concentration and CDOM absorption when using the SGLI, the GSM (Maritorena et al. in Appl Opt 41:2705–2714, 2002), and the QAA (Lee et al. in Appl Opt 41:5755, 2002) inversion algorithms. Results show that the mean error for estimating chl a concentration using the SGLI algorithm is 110% for our dataset. Although this error is lower than that of the GSM and the QAA algorithms, a signifcant underestimate at chl a higher than 2.0 mg m−3 is observed, which is further shown by independent match-up analyses. Another SGLI CDOM product includes the mean error of 50% and shows deviation at high CDOM range (>1.0 per m). A similar trend is observed for the GSM but not for the QAA when a global relationship of CDOM to colored detrital matter is applied. The sources of errors are discussed for potentially improving the retrievals

Second-generation GLobal Imager (SGLI)↗

NASA NTRS1987

Thermal finite-element analysis of space shuttle main engine turbine blade

Finite-element, transient heat transfer analyses were performed for the first-stage blades of the space shuttle main engine (SSME) high-pressure fuel turbopump. The analyses were based on test engine data provided by Rocketdyne. Heat transfer coefficients were predicted by performing a boundary-layer analysis at steady-state conditions with the STAN5 boundary-layer code. Two different peak-temperature overshoots were evaluated for the startup transient. Cutoff transient conditions were also analyzed. A reduced gas temperature profile based on actual thermocouple data was also considered. Transient heat transfer analyses were conducted with the MARC finite-element computer code.

Abdul-Aziz, Ali↗

NASA NTRS1972

Influence of contraction section shape and inlet flow direction on supersonic nozzle flow and performance.

Wall static pressure measurements and performance parameters are presented for axisymmetric supersonic nozzles with relatively steep convergent sections and comparatively small radius-of-curvature throats. The nozzle walls were essentially adiabatic. These results are compared with those obtained in other nozzles tested previously to appraise the influence of contraction shape on performance. Both the flow coefficient and the thrust were less than the corresponding values for one-dimensional, isentropic, plane flow for both the axial and radial inflow nozzles considered, but the specific impulse, the most important performance parameter, was found to be relatively unchanged. The thrust decrement for the axial inflow nozzles was established primarily by the shape of the contraction section, and could be estimated reasonably well from a conical sink flow consideration. The radial inflow nozzle has a potential advantage from a cooling point of view if used in a rocket engine.

Back, L. H.↗

NASA NTRS2011

A Piezoelectric PZT Ceramic Mulitlayer Stack for Energy Harvesting Under Dynamic Forces

Piezoelectric energy harvesting transducers (PEHTs) are commonly used in motion/vibration energy scavenging devices. To date, most researchers have focused on energy harvesting at narrow bandwidths around the mechanical resonance frequency, and most piezoelectric harvesting devices reported in the literature have very low effective piezoelectric coefficient (d(sub eff)) (< 10(exp 4) pC/N). For instance, more than 80% of PEHT related papers are on transverse "31" mode cantilever beam type PEHTs (CBPEHTs) having piezoelectric coefficients of about 100 pC/N. The level of harvested electrical power for CBPEHTs is on the order of microW even at resonance mode. In order to harvest more electrical energy across broader bandwidth, high effective piezoelectric coefficient structures are needed. In this study, we investigate a "33" longitudinal mode, piezoelectric PZT ceramic multilayer stack (PZT-Stack) with high effective piezoelectric coefficient for high-performance PEHTs. The PZT-Stack is composed of 300 layers of 0.1 mm thick PZT plates, with overall dimensions of 32.4 mm X 7.0 mm X 7.0 mm. Experiments were carried out with dynamic forces in a broad bandwidth ranging from 0.5 Hz to 25 kHz. The measured results show that the effective piezoelectric coefficient of the PZT-stack is about 1 X 10(exp 5) pC/N at off-resonance frequencies and 1.39 X 10(exp 6) pC/N at resonance, which is order of magnitude larger than that of traditional PEHTs. The effective piezoelectric coefficients (d(sub eff)) do not change significantly with applied dynamic forces having root mean square (RMS) values ranging from 1 N to 40 N. In resonance mode, 231 mW of electrical power was harvested at 2479 Hz with a dynamic force of 11.6 N(sub rms), and 7.6 mW of electrical power was generated at a frequency of 2114 Hz with 1 N(sub rms) dynamic force. In off-resonance mode, an electrical power of 18.7 mW was obtained at 680 Hz with a 40 N(sub rms) dynamic force. A theoretical model of energy harvesting for the PZT-Stack is established. The modeled results matched well with experimental measurements. This study demonstrated that high effective piezoelectric coefficient structures enable PEHTs to harvest more electrical energy from mechanical vibrations or motions, suggesting an effective design for high-performance low-footprint PEHTs with potential applications in military, aerospace, and portable electronics. In addition, this study provides a route for using piezoelectric multilayer stacks for active or semi-active adaptive control to damp, harvest or transform unwanted dynamic vibrations into useful electrical energy.

Xu, Tian-Bing↗

NASA NTRS1994

An investigation of angular stiffness and damping coefficients of an axial spline coupling in high-speed rotating machinery

This paper provided an opportunity to quantify the angular stiffness and equivalent viscous damping coefficients of an axial spline coupling used in high-speed turbomachinery. A unique test methodology and data reduction procedures were developed. The bending moments and angular deflections transmitted across an axial spline coupling were measured while a nonrotating shaft was excited by an external shaker. A rotor dynamics computer program was used to simulate the test conditions and to correlate the angular stiffness and damping coefficients. In addition, sensitivity analyses were performed to show that the accuracy of the dynamic coefficients do not rely on the accuracy of the data reduction procedures.

Ku, C.-P. Roger↗