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Evaluation of Wing Load Calibration and Sensing Methods Using Conventional Strain Gages and a Fiber Optic Sensing System Installed on a Straight Tapered Wing

State-of-the-art instrumentation techniques have provided an opportunity to obtain greater insight into structural wing loads during flight. An investigation was undertaken to research new wing instrumentation and load sensing techniques for measuring accurate in-flight spanwise load distributions on wing structures. A straight tapered wing was instrumented with both conventional foil strain gages at five spanwise wing stations and fiber optic strain sensors at every half inch along the entire wing span. Thirty-nine unique load cases were applied to the wing lower surface using hydraulic actuators to obtain various shear, bending moment, and torque load distributions on the wing. This paper will highlight three load calibration approaches. Conventional linear regression calibration methods were applied to foil strain gages providing a single wing station vertical shear, bending moment, and torque load. Linear regression methods were applied to a fiber optic sensing system to provide bending moment and torque spanwise load distributions. A load sensing scheme using strain derived wing shape information derived from a single load case provided vertical shear and bending moment spanwise load distribution information. Aspects of the three different approaches will be compared and contrasted to inform the reader of the benefits or disadvantages of each. Instrument installation, sensor characteristics, test execution aspects, and recommended calibration techniques will be discussed.

structural mechanics

Deriving Broadband Radiances from Geostationary Satellite Visible Radiance Channels for Use in the CERES SYN1deg Product

The NASA CERES project was designed to monitor the Earth’s radiation budget, both at the regional and global scale. The CERES SSF1deg single satellite product provides TOA flux observations from Aqua, Terra, NPP, and NOAA-20. The SYN1deg product incorporates observations from Terra, Aqua, and geostationary (GEO) satellites. The GEO observations are included in the SYN1deg product to infer the regional diurnal cycle between CERES observations. GEO satellites throughout the CERES record have different narrowband spectral response functions and do not directly observe radiances over the broadband spectra of CERES instruments. Hence the emphasis of this study is improving the process of deriving broadband radiances from the myriad GEO visible channel observations. We present a new method for converting the narrowband radiances observed from GEO operational satellites. This study relies on radiative transfer model hyper-spectral radiances for many cloud and surface conditions under all angular conditions observed by GEO sensors. First, the hyper-spectral radiances from a radiative transfer model must be convolved with the spectral response function of the visible imager for each GEO sensor in the CERES record. For each angular bin and surface type, the clear-sky and multiple optical depth and phase cloudy-sky narrowband and broadband reflectance pairs are linearly regressed. This study found that, no matter how the scene conditions are stratified, for example the all-sky, clear-sky, ice or water clouds, they all provide similar linear regressions. This includes ocean glint conditions, where the clear-sky reflectance exceeds cloudy conditions and yet the relationship was found to be linear in the given angular bin. This infers that no GEO retrieved cloud information is necessary in the narrowband to broadband conversion process, which relies only on visible channel reflectance. Over land, most of the GEO visible channels do not observe the NIR vegetation reflectance. We intend to use land adjustment factors developed using the TOA reflectance difference between the real-time MODIS .86um and the .64um channel. We validate this approach by using coincident observational data between CERES and MODIS aboard Aqua and Terra as well as GEO and CERES observations .

CERES

Comparison Study of Machine Learning Techniques to Predict Flight Energy Consumption for Advanced Air Mobility

This paper addresses the need to predict the flight energy consumption of aerial vehicles in the presence of wind using machine learning techniques. The presented work is critical to achieving sustainable and efficient operations for Advanced Air Mobility (AAM) and to evaluating the readiness of the ground-supporting energy infrastructure, e.g., electric grid and AAM portals. The flight energy consumption is described using the "energy per meter" (EPM) metric. We present a comparison study of influential machine learning techniques in predicting EPM using real-world flight test data. We presented new results of using the Decision Tree, Random Forest, and linear regression techniques, along with our previous results using the Recurrent Neural Network and Feed Forward Neural Network techniques. The comparison results show that the Linear Regression method outperforms other methods on the basis of the Mean Squared Error and error variance.

Machine Learning

The Added Value of SMAP Soil Moisture in Crop Yield Forecasting Over Argentina

Argentina is one of the major producers and exporter of soybeans, corn, and wheat to the world market; therefore, the accurate and timely forecasting of those crops yield is crucial to national crop management and global food security. Previous studies have mainly focused on developing forecasting models for a specific crop type and location using a single source of data (e.g., vegetation indices), thus providing little insight into the forecasting models' performance on different crop types and regions. Besides, these models are based on traditional statistical regression algorithms, while more advanced machine learning approaches have not been explored. This study investigated the estimation of crop yields of three major crops (corn, soybean, and winter wheat) using Multiple Linear Regression (MLR) and Support Vector Machine (SVM), over major growing provinces in Argentina. Our models were trained and evaluated on data from 2015 to 2020, where three remote sensing products (Normalized difference vegetation index (NDVI), SMAP soil moisture, and MODIS evapotranspiration) were used as predictors. Our results indicated that accurate crop yield forecasts using the developed regression models could be made one to two months before harvest. The MLR and SVM model performance varied among different crop types, where soybean and corn exhibited better predictability compare to the wheat. In most cases, the SVM outperformed the multiple linear regression model due to its ability to capture the nonlinear and complex features of the crop-production process. The forecasted model that combines data from multiple sources outperformed single-source satellite data. The highest accuracy was obtained when the three data sources were all considered in the model development. Results also indicated that the inclusion of SMAP soil moisture improved crop yield forecasting in most provinces, and the most significant improvements occurred in the drier region.

Nazmus Shams Sazib

On vertical profile of ozone at Syowa

The difference in the vertical ozone profile at Syowa between 1966-1981 and 1982-1988 is shown. The month-height cross section of the slope of the linear regressions between ozone partial pressure and 100-mb temperature is also shown. The vertically integrated values of the slopes are in close agreement with the slopes calculated by linear regression of Dobson total ozone on 100-mb temperature in the period of 1982-1988.

Chubachi, Shigeru

Validation of MODIS Aerosol Optical Depth Retrievals over a Tropical Urban Site, Pune, India

In the present paper, MODIS (Terra and Aqua; level 2, collection 5) derived aerosoloptical depths (AODs) are compared with the ground-based measurements obtained from AERONET (level 2.0) and Microtops - II sun-photometer over a tropical urban station, Pune (18 deg 32'N; 73 deg 49'E, 559 m amsl). This is the first ever systematic validation of the MODIS aerosol products over Pune. Analysis of the data indicates that the Terra and Aqua MODIS AOD retrievals at 550 nm have good correlations with the AERONET and Microtops - II sun-photometer AOD measurements. During winter the linear regression correlation coefficients for MODIS products against AERONET measurements are 0.79 for Terra and 0.62 for Aqua; however for premonsoon, the corresponding coefficients are 0.78 and 0.74. Similarly, the linear regression correlation coefficients for Microtops measurements against MODIS products are 0.72 and 0.93 for Terra and Aqua data respectively during winter and are 0.78 and 0.75 during pre-monsoon. On yearly basis in 2008-2009, correlation coefficients for MODIS products against AERONET measurements are 0.80 and 0.78 for Terra and Aqua respectively while the corresponding coefficients are 0.70 and 0.73 during 2009-2010. The regressed intercepts with MODIS vs. AERONET are 0.09 for Terra and 0.05 for Aqua during winter whereas their values are 0.04 and 0.07 during pre-monsoon. However, MODIS AODs are found to underestimate during winter and overestimate during pre-monsoon with respect to AERONET and Microtops measurements having slopes 0.63 (Terra) and 0.74 (Aqua) during winter and 0.97 (Terra) and 0.94 (Aqua) during pre-monsoon. Wavelength dependency of Single Scattering Albedo (SSA) shows presence of absorbing and scattering aerosol particles. For winter, SSA decreases with wavelength with the values 0.86 +/- 0.03 at 440 nm and 0.82 +/- 0.04 at 1020nm. In pre-monsoon, it increases with wavelength (SSA is 0.87 +/- 0.02 at 440nm; and 0.88 +/-0.04 at 1020 nm).

More, Sanjay

Algorithm Development and Validation of CDOM Properties for Estuarine and Continental Shelf Waters Along the Northeastern U.S. Coast

An extensive set of field measurements have been collected throughout the continental margin of the northeastern U.S. from 2004 to 2011 to develop and validate ocean color satellite algorithms for the retrieval of the absorption coefficient of chromophoric dissolved organic matter (aCDOM) and CDOM spectral slopes for the 275:295 nm and 300:600 nm spectral range (S275:295 and S300:600). Remote sensing reflectance (Rrs) measurements computed from in-water radiometry profiles along with aCDOM() data are applied to develop several types of algorithms for the SeaWiFS and MODIS-Aqua ocean color satellite sensors, which involve least squares linear regression of aCDOM() with (1) Rrs band ratios, (2) quasi-analytical algorithm-based (QAA based) products of total absorption coefficients, (3) multiple Rrs bands within a multiple linear regression (MLR) analysis, and (4) diffuse attenuation coefficient (Kd). The relative error (mean absolute percent difference; MAPD) for the MLR retrievals of aCDOM(275), aCDOM(355), aCDOM(380), aCDOM(412) and aCDOM(443) for our study region range from 20.4-23.9 for MODIS-Aqua and 27.3-30 for SeaWiFS. Because of the narrower range of CDOM spectral slope values, the MAPD for the MLR S275:295 and QAA-based S300:600 algorithms are much lower ranging from 9.9 and 8.3 for SeaWiFS, respectively, and 8.7 and 6.3 for MODIS, respectively. Seasonal and spatial MODIS-Aqua and SeaWiFS distributions of aCDOM, S275:295 and S300:600 processed with these algorithms are consistent with field measurements and the processes that impact CDOM levels along the continental shelf of the northeastern U.S. Several satellite data processing factors correlate with higher uncertainty in satellite retrievals of aCDOM, S275:295 and S300:600 within the coastal ocean, including solar zenith angle, sensor viewing angle, and atmospheric products applied for atmospheric corrections. Algorithms that include ultraviolet Rrs bands provide a better fit to field measurements than algorithms without the ultraviolet Rrs bands. This suggests that satellite sensors with ultraviolet capability could provide better retrievals of CDOM. Because of the strong correlations between CDOM parameters and DOM constituents in the coastal ocean, satellite observations of CDOM parameters can be applied to study the distributions, sources and sinks of DOM, which are relevant for understanding the carbon cycle, modeling the Earth system, and to discern how the Earth is changing.

CDOM Properties

Can Functional Cardiac Age be Predicted from ECG in a Normal Healthy Population

In a normal healthy population, we desired to determine the most age-dependent conventional and advanced ECG parameters. We hypothesized that changes in several ECG parameters might correlate with age and together reliably characterize the functional age of the heart. Methods: An initial study population of 313 apparently healthy subjects was ultimately reduced to 148 subjects (74 men, 84 women, in the range from 10 to 75 years of age) after exclusion criteria. In all subjects, ECG recordings (resting 5-minute 12-lead high frequency ECG) were evaluated via custom software programs to calculate up to 85 different conventional and advanced ECG parameters including beat-to-beat QT and RR variability, waveform complexity, and signal-averaged, high-frequency and spatial/spatiotemporal ECG parameters. The prediction of functional age was evaluated by multiple linear regression analysis using the best 5 univariate predictors. Results: Ignoring what were ultimately small differences between males and females, the functional age was found to be predicted (R2= 0.69, P < 0.001) from a linear combination of 5 independent variables: QRS elevation in the frontal plane (p<0.001), a new repolarization parameter QTcorr (p<0.001), mean high frequency QRS amplitude (p=0.009), the variability parameter % VLF of RRV (p=0.021) and the P-wave width (p=0.10). Here, QTcorr represents the correlation between the calculated QT and the measured QT signal. Conclusions: In apparently healthy subjects with normal conventional ECGs, functional cardiac age can be estimated by multiple linear regression analysis of mostly advanced ECG results. Because some parameters in the regression formula, such as QTcorr, high frequency QRS amplitude and P-wave width also change with disease in the same direction as with increased age, increased functional age of the heart may reflect subtle age-related pathologies in cardiac electrical function that are usually hidden on conventional ECG.

Schlegel, Todd

Improved Rainfall Data in the Philippines through Concurrent Use of GPM IMERG and Ground-Based Measurements

The availability of accurate and reliable rainfall data that are applicable to various phenomenological, climatological, and modeling studies is important, especially in the Philippines, which is considered to be highly vulnerable to natural hazards and a changing climate. The presented strategy involved constructing a dataset consisting of synoptic data, automatic rain gauge (ARG) measurements, and satellite data that are co-registered, consistent, and formatted in the same manner. Although sparse in number, the synoptic stations provide the most accurate rainfall information and were used as the baseline for creating the dataset. The ARGs that are within a distance of 1 km to the synoptic stations were used to determine the correction factors needed to make the synoptic and ARG data consistent. Subsequently, the corrected ARGs were used to make the satellite IMERG data consistent with both ARG and synoptic data. In case of the latter, only IMERG pixels with at least 10 ARGs within the relatively large footprint of the satellite sensor were used in estimating the required correction parameters derived from a combination of a power transform and linear regression correction techniques. The final results show good agreement of synoptic and corrected ARG data with correlation coefficients of 0.94 and 0.97 for the 10 day and monthly data, respectively, and improvement in the linear regression slope from 0.67 to 0.90 for 10 day data, and 0.70 to 0.94 for monthly data. In addition, the corrected ARG data agree well with the corrected IMERG data, with correlation coefficients of 0.88 and 0.93 for the 10 day and monthly data, respectively, and an improvement in slope from 0.66 to 0.87 for 10 day data, and 0.74 to 0.99 for monthly data. The merit of using a combined dataset is illustrated through comparative analyses of the IMERG data and spatially interpolated synoptic and ARG data. The results show general agreements in spatial patterns of rainfall across the datasets, especially in areas where in situ measurements are recorded. The observed discrepancy when ground data is limited emphasizes the need for satellite IMERG data to obtain the true spatial patterns of rainfall distribution.

rainfall

Multi-Axis Identifiability Using Single-Surface Parameter Estimation Maneuvers on the X-48B Blended Wing Body

The problem of parameter estimation on hybrid-wing-body type aircraft is complicated by the fact that many design candidates for such aircraft involve a large number of aero- dynamic control effectors that act in coplanar motion. This fact adds to the complexity already present in the parameter estimation problem for any aircraft with a closed-loop control system. Decorrelation of system inputs must be performed in order to ascertain individual surface derivatives with any sort of mathematical confidence. Non-standard control surface configurations, such as clamshell surfaces and drag-rudder modes, further complicate the modeling task. In this paper, asymmetric, single-surface maneuvers are used to excite multiple axes of aircraft motion simultaneously. Time history reconstructions of the moment coefficients computed by the solved regression models are then compared to each other in order to assess relative model accuracy. The reduced flight-test time required for inner surface parameter estimation using multi-axis methods was found to come at the cost of slightly reduced accuracy and statistical confidence for linear regression methods. Since the multi-axis maneuvers captured parameter estimates similar to both longitudinal and lateral-directional maneuvers combined, the number of test points required for the inner, aileron-like surfaces could in theory have been reduced by 50%. While trends were similar, however, individual parameters as estimated by a multi-axis model were typically different by an average absolute difference of roughly 15-20%, with decreased statistical significance, than those estimated by a single-axis model. The multi-axis model exhibited an increase in overall fit error of roughly 1-5% for the linear regression estimates with respect to the single-axis model, when applied to flight data designed for each, respectively.

Ratnayake, Nalin A.

Quantitative Validation of the Integrated Medical Model (IMM) for ISS Missions

Lifetime Surveillance of Astronaut Health (LSAH) provided observed medical event data on 33 ISS and 111 STS person-missions for use in further improving and validating the Integrated Medical Model (IMM). Using only the crew characteristics from these observed missions, the newest development version, IMM v4.0, will simulate these missions to predict medical events and outcomes. Comparing IMM predictions to the actual observed medical event counts will provide external validation and identify areas of possible improvement. In an effort to improve the power of detecting differences in this validation study, the total over each program ISS and STS will serve as the main quantitative comparison objective, specifically the following parameters: total medical events (TME), probability of loss of crew life (LOCL), and probability of evacuation (EVAC). Scatter plots of observed versus median predicted TMEs (with error bars reflecting the simulation intervals) will graphically display comparisons while linear regression will serve as the statistical test of agreement. Two scatter plots will be analyzed 1) where each point reflects a mission and 2) where each point reflects a condition-specific total number of occurrences. The coefficient of determination (R2) resulting from a linear regression with no intercept bias (intercept fixed at zero) will serve as an overall metric of agreement between IMM and the real world system (RWS). In an effort to identify as many possible discrepancies as possible for further inspection, the -level for all statistical tests comparing IMM predictions to observed data will be set to 0.1. This less stringent criterion, along with the multiple testing being conducted, should detect all perceived differences including many false positive signals resulting from random variation. The results of these analyses will reveal areas of the model requiring adjustment to improve overall IMM output, which will thereby provide better decision support for mission critical applications.

validation

Taxi-Out Time Prediction for Departures at Charlotte Airport Using Machine Learning Techniques

Predicting the taxi-out times of departures accurately is important for improving airport efficiency and takeoff time predictability. In this paper, we attempt to apply machine learning techniques to actual traffic data at Charlotte Douglas International Airport for taxi-out time prediction. To find the key factors affecting aircraft taxi times, surface surveillance data is first analyzed. From this data analysis, several variables, including terminal concourse, spot, runway, departure fix and weight class, are selected for taxi time prediction. Then, various machine learning methods such as linear regression, support vector machines, k-nearest neighbors, random forest, and neural networks model are applied to actual flight data. Different traffic flow and weather conditions at Charlotte airport are also taken into account for more accurate prediction. The taxi-out time prediction results show that linear regression and random forest techniques can provide the most accurate prediction in terms of root-mean-square errors. We also discuss the operational complexity and uncertainties that make it difficult to predict the taxi times accurately.

Safe and efficient surface operations

High resolution magnetic resonance imaging of the calcaneus: age-related changes in trabecular structure and comparison with dual X-ray absorptiometry measurements

A high-resolution magnetic resonance imaging (MRI) protocol, together with specialized image processing techniques, was applied to the quantitative measurement of age-related changes in calcaneal trabecular structure. The reproducibility of the technique was assessed and the annual rates of change for several trabecular structure parameters were measured. The MR-derived trabecular parameters were compared with calcaneal bone mineral density (BMD), measured by dual X-ray absorptiometry (DXA) in the same subjects. Sagittal MR images were acquired at 1.5 T in 23 healthy women (mean age: 49.3 +/- 16.6 [SD]), using a three-dimensional gradient echo sequence. Image analysis procedures included internal gray-scale calibration, bone and marrow segmentation, and run-length methods. Three trabecular structure parameters, apparent bone volume (ABV/TV), intercept thickness (I.Th), and intercept separation (I.Sp) were calculated from the MR images. The short- and long-term precision errors (mean %CV) of these measured parameters were in the ranges 1-2% and 3-6%, respectively. Linear regression of the trabecular structure parameters vs. age showed significant correlation: ABV/TV (r2 = 33.7%, P < 0.0037), I.Th (r2 = 26.6%, P < 0.0118), I.Sp (r2 = 28.9%, P < 0.0081). These trends with age were also expressed as annual rates of change: ABV/TV (-0.52%/year), I.Th (-0.33%/year), and I.Sp (0.59%/year). Linear regression analysis also showed significant correlation between the MR-derived trabecular structure parameters and calcaneal BMD values. Although a larger group of subjects is needed to better define the age-related changes in trabecular structure parameters and their relation to BMD, these preliminary results demonstrate that high-resolution MRI may potentially be useful for the quantitative assessment of trabecular structure.

NASA Discipline Number 26-10

Altered central nervous system processing of baroreceptor input following hindlimb unloading in rats

The effect of cardiovascular deconditioning on central nervous system processing of baroreceptor afferent activity was evaluated following 14 days of hindlimb unloading (HU). Inactin-anesthetized rats were instrumented with catheters, renal sympathetic nerve electrodes, and aortic depressor nerve electrodes for measurement of mean arterial pressure, heart rate, renal sympathetic nerve activity (RSNA), and aortic depressor nerve activity (ADNA). Baroreceptor and baroreflex functions were assessed during infusion of phenylephrine and sodium nitroprusside. Central processing of baroreceptor afferent input was evaluated by linear regression relating RSNA to ADNA. The maximum baroreflex-elicited increase in RSNA was significantly reduced in HU rats (122 +/- 3.8 vs. 144 +/- 4.9% of baseline RSNA), whereas ADNA was not altered. The slope (-0.18 +/- 0.04 vs. -0.40 +/- 0.04) and y-intercept (121 +/- 3.2 vs. 146 +/- 4.3) of the linear regression relating increases in efferent RSNA to decreases in afferent ADNA during hypotension were significantly reduced in HU rats. There were no differences during increases in arterial pressure. Results demonstrate that the attenuation in baroreflex-mediated increases in RSNA following HU is due to changes in central processing of baroreceptor afferent information rather than aortic baroreceptor function.

NASA Discipline Cardiopulmonary

Developing Empirical Lightning Cessation Forecast Guidance for the Cape Canaveral Air Force Station and Kennedy Space Center

This research addresses the 45th Weather Squadron's (45WS) need for improved guidance regarding lightning cessation at Cape Canaveral Air Force Station and Kennedy Space Center (KSC). KSC's Lightning Detection and Ranging (LDAR) network was the primary observational tool to investigate both cloud-to-ground and intracloud lightning. Five statistical and empirical schemes were created from LDAR, sounding, and radar parameters derived from 116 storms. Four of the five schemes were unsuitable for operational use since lightning advisories would be canceled prematurely, leading to safety risks to personnel. These include a correlation and regression tree analysis, three variants of multiple linear regression, event time trending, and the time delay between the greatest height of the maximum dBZ value to the last flash. These schemes failed to adequately forecast the maximum interval, the greatest time between any two flashes in the storm. The majority of storms had a maximum interval less than 10 min, which biased the schemes toward small values. Success was achieved with the percentile method (PM) by separating the maximum interval into percentiles for the 100 dependent storms.

LDAR (LIGHTNING DETECTION AND RANGING)

Cascade Optimization for Aircraft Engines With Regression and Neural Network Analysis - Approximators

The NASA Engine Performance Program (NEPP) can configure and analyze almost any type of gas turbine engine that can be generated through the interconnection of a set of standard physical components. In addition, the code can optimize engine performance by changing adjustable variables under a set of constraints. However, for engine cycle problems at certain operating points, the NEPP code can encounter difficulties: nonconvergence in the currently implemented Powell's optimization algorithm and deficiencies in the Newton-Raphson solver during engine balancing. A project was undertaken to correct these deficiencies. Nonconvergence was avoided through a cascade optimization strategy, and deficiencies associated with engine balancing were eliminated through neural network and linear regression methods. An approximation-interspersed cascade strategy was used to optimize the engine's operation over its flight envelope. Replacement of Powell's algorithm by the cascade strategy improved the optimization segment of the NEPP code. The performance of the linear regression and neural network methods as alternative engine analyzers was found to be satisfactory. This report considers two examples-a supersonic mixed-flow turbofan engine and a subsonic waverotor-topped engine-to illustrate the results, and it discusses insights gained from the improved version of the NEPP code.

Patnaik, Surya N.

Soil moisture estimation using GOES-VISSR infrared data - A case study with a simple statistical method

Five days of clear sky observations of Kansas and Nebraska are used to examine the statistical relationship between soil moisture and infrared surface temperature observations taken from a geosynchronous satellite. Linear regression is used to relate soil moisture to surface temperature and other variables that represent wind speed, vegetation cover, and low-level temperature advection. Results show good agreement between estimated and observed soil moisture features on each of the 5 days. The average coefficient of determination for five pseudoindependent tests in which the test day is held out of the regression is 0.71. It is shown that a depletion coefficient of 0.92, when used to compute antecedent precipitation index (API), produces the best correlation between API and soil moisture as inferred from GOES thermal infrared data. By averaging daily predicted values over the 5-day rain-free case study period, 92 percent of the variance of the morning surface temperature change is explained by a simple multiple linear regression with all independent variables, or, alternatively, 85 percent of the observed variance in API is explained. It is concluded that this approach can distinguish at least four classes of soil wetness, but the necessity for measurement of surface advection may limit its usefulness in remote areas.

Wetzel, Peter J.

Open-source Numerical Modeling of Solidification Cracking Susceptibility: Application to Refractory Alloy Systems

Introduction. Alloys such as aluminum, nickel-base, and austenitic stainless steels are susceptible to solidification cracking during welding and 3D printing. Compositional optimization is one method used to effectively mitigate solidification cracking of those alloy systems. With the surge in hypersonic and in-space propulsion activities, refractory metals (Nb, Mo, Ta, W, and Re) and their alloy derivatives are increasing in importance due to their extreme high melting point and retention of high-temperature strength; however, their chemistry was most typically optimized to promote ductility during mechanical operations such as drawing and forming. Welding of such alloys has been a challenge due to a number of issues including solidification cracking, atmospheric contamination (O, C, and N), as well as a shift in ductile-to-brittle transition to higher temperature following grain growth induced by welding. Compositional optimization of refractory alloys for solidification cracking resistance in particular is desirable as their usage increases with the advent of advanced manufacturing methods such as 3D printing. This work evaluates the effect of compositional variation in refractory metal systems on the solidification cracking susceptibility with the goals of optimizing existing alloys and joining process techniques, and formulating new alloys with increased solidification cracking resistance. Experimental Procedures. A python code was developed in a Jupyter notebook environment (Michael and Sowards, 2023) to facilitate the calculation of crack susceptibility index proposed by Kou (2015). Composition is entered as a single point, or as a 1-D or 2-D array. The notebook calls pycalphad (Otis and Liu, 2017 and Bocklund et al, 2020) to calculate the evolution of fraction solid as a function of temperature (under either Scheil or equilibrium assumptions) and then evaluates steepness of the fraction solid curve near the terminal stage of solidification to predict solidification cracking resistance. Open source thermodynamic databases available at online repositories are used (van de Walle). The process is setup in an automated fashion to generate plots that show variation in solidification cracking susceptibility according to composition on 1-D line plots or 2-D contour plots. The Jupyter notebook and crack susceptibility algorithm was also integrated with a widely used commercial CALPHAD code for validation and alloy exploration. Results and Discussion. The crack susceptibility model was first validated against a series of refractory alloy compositions evaluated in past work which utilized a specialized Varestraint test built inside a vacuum chamber environment (Lessman and Gold, 1971). The alloys tested in the Varestraint apparatus included T-111 (Ta-8W-2Hf), ASTAR-811C (Ta-8W-1Re-0.7Hf-0.025C), FS-85 (Nb-27Ta-10W-1Zr), T-222 (Ta-9.6W-2.4Hf-0.01C), Ta-10W, B-66 (Nb-5Mo-5V-1Zr), and SCb-291 (Nb-10W-10Ta). The initial test of the model showed a strong correlation with empirical Varestraint data, i.e., a Spearman rank correlation between model predictions and hot cracking measurements was observed to be greater than 0.8. Following the validation, a set of refractory metal binary mixtures was investigated to evaluate sensitivity of Nb, Mo, W, and Ta to C, N, and O content. A series of plots were produced that suggest ppmw ranges of C, N, and O where solidification cracking increases significantly and reaches a maximum. Also comparative ranking of each primary refractory metal to each interstitial was produced. For example C produces greater cracking response in Mo whereas O produces greater cracking response in Ta and Nb. Such compositional values have utility in setting limits on pickup of these interstitial elements during welding and printing rather than using a one-size-fits-all approach. Furthermore, the results have use in determining additive powder recycling requirements, which is especially pertinent for refractory metal powders due to their high cost compared to conventional alloys. Another application created thousands of hypothetical alloys within the nominal specified composition range of two widely used refractory alloys C103 (Nb-10Hf-1Ti) and TZM (Mo-0.5Ti-0.1Zr). The cracking index was calculated for the alloys and results were fed into machine learning regression techniques including Multiple Linear Regression, Ridge Regression, and Lasso Regression to determine relative potency each alloying element had on computed solidification cracking index. A series of linear equations were produced that relate composition of C103 and TZM to solidification cracking index. The crack susceptibility of C103 for example is described by an equation of the form: cracking index ~ O + 0.667*C + 0.635*N + 0.00037*Ta – 0.0008*Hf (in wt.%) From that equation, it is clear that O has strong propensity to induce solidification cracking. Interestingly, Hf is shown to reduce calculated cracking response. Finally, realizing the potential of this method to discover new refractory alloy formulations across the period table that have low solidification cracking sensitivity, the code was applied to new untested alloy systems including W-Zr-C, W-Ta-C, and others. Conclusions. In summary, an open source numerical method has been developed using Python code to calculate Kou’s crack susceptibility index. The method was applied to refractory metals which are inherently difficult to study from a weldability testing standpoint since inert shielding gas is not sufficient and welding is typically done in vacuum, especially in light of findings presented here where oxygen has profound influence on solidification cracking. This work revealed the effect of compositional variations on a series of refractory metals and showed the framework defined here will be useful in 1) the development of new alloys that have improved weldability and 3D printability, 2) placing compositional limits on existing alloys, and 3) ensuring adequate controls of manufacturing processes such as 3D printing where powder reuse is critical. Keywords. pycalphad; Python; refractory metals; solidification cracking. References. B. Bocklund et. al. (2020) http://doi.org/10.5281/zenodo.3630657. S. Kou. (2015) https://doi.org/10.1016/j.actamat.2015.01.034. G.G. Lessmann and R.E. Gold. Welding Journal, issue 1, pp. 1-s – 8-s (1971). F.N. Michael and J.W. Sowards. NASA/TM-20230002218 (2023). R. Otis and Z.-K. Liu. (2017) http://doi.org/10.5334/jors.140. A. Van de Wallle et. al. (2018) https://doi.org/10.1016/j.calphad.2018.04.003.

pycalphad