Norbert Ulbrich

Strain-Gage Balance Calibration Analysis Using Automatically Selected Math Models

A technique is presented that determines a set of candidate math models in order to analyze strain–gage balance calibration data using global regression. At first, a permitted and a required math model are defined in order to bound possible candidate math models. In the second step, starting with the permitted math model, families of possible candidate math models are created by generating all possible math term combinations for a fixed number of terms. Then, after the global regression has been applied to the calibration data using each family member, the next candidate math model is found by comparing the standard deviation of the response residual. This process is repeated for each gage using the updated candidate math model until only the required math model remains. A three component balance calibration data set is used to illustrate the determination of candidate math models. In addition, results from a six component balance calibration are discussed in order to show the application of the proposed method to realistic balance calibration data.

Application Of A New Calibration Analysis Process To The MK-III-C Balance

A new process was developed at Ames Research Center for the analysis of internal strain–gage balance calibration data. The process uses an automatic math model selection algorithm that determines two possible math models for the calibration analysis. The first math model consists of the largest number of terms that the calibration data supports. The second math model uses only the most significant terms of each gage. Check load residuals are compared in order to decide which math model should be used for the final calibration analysis. The application of the new process to the Ames MK–III–C balance is discussed. In addition, a new calibration data screening technique is presented that uses a dimensionless difference between loads and responses for the identification of possible bad calibration points. Experience showed that this dimensionless difference may also be used to study interactions between gages.

Regression Model Term Selection for the Analysis of Strain-Gage Balance Calibration Data

The paper discusses the selection of regression model terms for the analysis of wind tunnel strain-gage balance calibration data. Different function class combinations are presented that may be used to analyze calibration data using either a non-iterative or an iterative method. The role of the intercept term in a regression model of calibration data is reviewed. In addition, useful algorithms and metrics originating from linear algebra and statistics are recommended that will help an analyst (i) to identify and avoid both linear and near-linear dependencies between regression model terms and (ii) to make sure that the selected regression model of the calibration data uses only statistically significant terms. Three different tests are suggested that may be used to objectively assess the predictive capability of the final regression model of the calibration data. These tests use both the original data points and regression model independent confirmation points. Finally, data from a simplified manual calibration of the Ames MK40 balance is used to illustrate the application of some of the metrics and tests to a realistic calibration data set.

Analysis of Floor Balance Calibration Data Using Automatically Generated Math Models

A new analysis process was applied to the Ames MC–400 floor balance calibration data set. The new process uses an automatic math term selection algorithm in order to determine two possible math models for the analysis. The first math model is called the permitted math model. It consists of the largest number of terms that the calibration load schedule supports. The second math model is called the recommended math model. It uses only the most significant terms of each gage. Calibration load residuals for both math models were compared. Residuals show very small differences. In addition, check load residuals of load combinations were compared that were not a part of the original calibration load schedule. Again, residuals for both math models are small. They are equal or below an upper bound of the estimated check load error. In conclusion, investigations showed that calibration load and check load residuals of the recommended math model are as good as corresponding residuals of the permitted math model even though the recommended math model uses less than half the number of math terms of the permitted math model. Therefore, the recommended math model may be a better choice for balance calibration analysis as simplicity helps guard against overfitting calibration data.

Development of a User Interface for a Regression Analysis Software Tool

An easy–to–use user interface was implemented in a highly automated regression analysis tool. The user interface was developed from the start to run on computers that use the Windows, Macintosh, Linux, or UNIX operating system. Many user interface features were specifically designed such that a novice or inexperienced user can apply the regression analysis tool with confidence. Therefore, the user interface’s design minimizes interactive input from the user. In addition, reasonable default combinations are assigned to those analysis settings that influence the outcome of the regression analysis. These default combinations will lead to a successful regression analysis result for most experimental data sets. The user interface comes in two versions. The text user interface version is used for the ongoing development of the regression analysis tool. The official release of the regression analysis tool, on the other hand, has a graphical user interface that is more efficient to use. This graphical user interface displays all input file names, output file names, and analysis settings for a specific software application mode on a single screen which makes it easier to generate reliable analysis results and to perform input parameter studies. An object–oriented approach was used for the development of the graphical user interface. This choice keeps future software maintenance costs to a reasonable limit. Examples of both the text user interface and graphical user interface are discussed in order to illustrate the user interface’s overall design approach.

Analysis of Balance Calibration Machine Data Using Automatically Generated Math Models

A new process was developed at Ames Research Center that automatically generates a permitted and a recommended math model for the analysis of strain–gage balance calibration data. The accuracy of these math models was investigated using two calibration data sets that were provided by the German– Dutch Wind Tunnels. These calibration data sets were obtained in a balance calibration machine. The first calibration data set was generated using the traditional OFAT method. The second data set was obtained using the MDOE approach. A single data reduction matrix was computed for the OFAT data set using the permitted math model. Two data reduction matrices were calculated for the MDOE data set using the permitted and the recommended math model. Measured and fitted loads at check points were compared in order to assess the accuracy of the three data reduction matrices. This comparison showed that the data reduction matrix of the recommended math model, i.e., of the math model that uses only the most significant terms of each gage, is as accurate as the data reduction matrix of the much larger permitted math model. In addition, it was demonstrated that, for the given balance calibration task, the two data reduction matrices of the MDOE data set are as accurate as the data reduction matrix of the much larger OFAT data set.

A New Load Residual Threshold Definition for the Evaluation of Wind Tunnel Strain-Gage Balance Data

A new definition of a threshold for the detection of load residual outliers of wind tunnel strain-gage balance data was developed. The new threshold is defined as the product between the inverse of the absolute value of the primary gage sensitivity and an empirical limit of the electrical outputs of a strain{gage. The empirical limit of the outputs is either 2.5 microV/V for balance calibration or check load residuals. A reduced limit of 0.5 microV/V is recommended for the evaluation of differences between repeat load points because, by design, the calculation of these differences removes errors in the residuals that are associated with the regression analysis of the data itself. The definition of the new threshold and different methods for the determination of the primary gage sensitivity are discussed. In addition, calibration data of a six-component force balance and a five-component semi-span balance are used to illustrate the application of the proposed new threshold definition to different types of strain{gage balances. During the discussion of the force balance example it is also explained how the estimated maximum expected output of a balance gage can be used to better understand results of the application of the new threshold definition.

Calibration and Data Analysis of the MC-130 Air Balance

Design, calibration, calibration analysis, and intended use of the MC–130 air balance are discussed. The MC–130 balance is an 8.0 inch diameter force balance that has two separate internal air flow systems and one external bellows system. The manual calibration of the balance consisted of a total of 1854 data points with both unpressurized and pressurized air flowing through the balance. A subset of 1160 data points was chosen for the calibration data analysis. The regression analysis of the subset was performed using two fundamentally different analysis approaches. First, the data analysis was performed using a recently developed extension of the Iterative Method. This approach fits gage outputs as a function of both applied balance loads and bellows pressures while still allowing the application of the iteration scheme that is used with the Iterative Method. Then, for comparison, the axial force was also analyzed using the Non–Iterative Method. This alternate approach directly fits loads as a function of measured gage outputs and bellows pressures and does not require a load iteration. The regression models used by both the extended Iterative and Non–Iterative Method were constructed such that they met a set of widely accepted statistical quality requirements. These requirements lead to reliable regression models and prevent overfitting of data because they ensure that no hidden near–linear dependencies between regression model terms exist and that only statistically significant terms are included. Finally, a comparison of the axial force residuals was performed. Overall, axial force estimates obtained from both methods show excellent agreement as the differences of the standard deviation of the axial force residuals are on the order of 0.001 % of the axial force capacity.

Load Envelope Analysis of Strain-Gage Balance Data

A load envelope analysis process was developed for strain–gage balance data. The process compares wind tunnel test loads with balance calibration loads in order to identify calibration load envelope outliers. The process uses electrical responses from all calibration points, electrical responses from wind tunnel test points, and the data reduction matrix of the balance as input. Then, after calculating calibration and wind tunnel test loads from the responses, plots of all possible gage load combinations are used to display the calibration load envelope and to highlight possible load envelope outliers. Two criteria are applied to identify load envelope outliers. The first criterion compares individual loads of a data point with the corresponding calibration load range. The second criterion compares load combinations of a data point with load combinations that were applied during the balance calibration. A six–component balance example is used to illustrate benefits of the new load envelope analysis process.

A Universal Threshold for the Assessment of Load and Output Residuals of Strain-Gage Balance Data

A new universal residual threshold for the detection of load and gage output residual outliers of wind tunnel strain{gage balance data was developed. The threshold works with both the Iterative and Non{Iterative Methods that are used in the aerospace testing community to analyze and process balance data. It also supports all known load and gage output formats that are traditionally used to describe balance data. The thresholds definition is based on an empirical electrical constant. First, the constant is used to construct a threshold for the assessment of gage output residuals. Then, the related threshold for the assessment of load residuals is obtained by multiplying the empirical electrical constant with the sum of the absolute values of all first partial derivatives of a given load component. The empirical constant equals 2.5 microV/V for the assessment of balance calibration or check load data residuals. A value of 0.5 microV/V is recommended for the evaluation of repeat point residuals because, by design, the calculation of these residuals removes errors that are associated with the regression analysis of the data itself. Data from a calibration of a six-component force balance is used to illustrate the application of the new threshold definitions to real{world balance calibration data.