July 5, 2018

Accurate prediction of static and dynamic loads for helicopters

Industry: Aerospace | Product: pSeven Core | Company: Airbus Helicopters


One of the activities of the Airbus Helicopters flight test department is to measure loads for different components (through load sensors, or gauges) and flight configurations (described by the Flight Configuration Parameters, FCP). This data is used to establish the inspections and retirement time for each principal structural element of the helicopter and to list the parts which need to be re-designed to enhance the flight envelope. Before the in-flight measurements (required for certification) are done, analyses are carried out through models based on physics (combining aerodynamic and mechanical laws) to estimate the missing loads, which is a costly procedure.

h225 heliocpter

The objective is to automatically build accurate and robust approximation models from the existing load database for the automatic prediction of the missing helicopter static and dynamic loads as a function of FCP. Predictions will guarantee a drastic reduction in the time and workforce needed for such analysis.


  • The loads' database used to build the approximation models with the highest predictive power for the selected type of helicopter is huge:
    • 66 loads (Main Rotor shaft bending, Main Rotor pitch rod load, etc.) with 2 available outputs (maximum signed static and dynamic loads),
    • many flight configurations regrouped into 32 maneuver families: 66 x 2 x 32 = 4224 cases in total, from which 3956 cases are left after the screening and filtering for zero/too small sample size.
  • The number of points for each case is disparate and needs to be taken into account for the model selection to guarantee accuracy and robustness:
    • 1.7% of the cases have 0 points
    • 4.6% of the cases have 1 point
    • 38% of the cases have fewer points than parameters
    • 32% of the cases have a small number of points
    • 23.7% of the cases have an appropriate number of points
  • Selection of the best model for each case should automatically be made.
  • The possibility to add or update new helicopters, load types, maneuvers and other parameters is to be provided.
  • The final user should be warned when the prediction may be unreliable or constant.


pSeven Core GT Approx module with its wide range of approximation techniques and its automatic selection of the appropriate approximation technique was applied to build 3 types of approximation models (automatically selected depending on the training sample size):

  • Response surface models
  • Gaussian processes
  • High-Dimensional Approximation

Also, constant models were used for cases with very small sample size.

The built-in pSeven Core Internal Validation functionality was applied to select the best model for each case. Thanks to this functionality, the cross-validation fit error check can be done in case the training sample size is limited in order to check the ability of the model to predict outputs in new input points. Cross-validation is a conventional approach to estimate model predictive power: one object (data point) is removed from the sample, the model is built with all the other objects and the fit quality is checked on the removed object. The procedure is repeated for all the objects in the sample, thus giving the average model prediction accuracy on the training sample.

The requirements for the models were to be accurate and robust, and in case it’s not possible to achieve (for example, due to small sample size) constant models were selected, and a report that no trustworthy results are available is generated, avoiding misleading predictions.


For all static and dynamic loads, predictions were compared to Airbus Helicopters measurements for each maneuver family. The comparison is done for both all flight configurations and filtered ones when only the good approximations are considered. Three types of approximation models (depending on training data) are considered: models providing a high-accuracy, models with a low-accuracy due to an inherent scatter in the data and constant models.

Predictions showed a good accuracy when the data on which the model was based was good enough.


Prediction/measurement comparison (all flight configurations)

When considering all flights configurations, for dynamic loads, respectively 71% and 86% of predictions have a precision better than ±10% and ±20 %. Points marked in red in the above figure are constant approximation models, decreasing the accuracy of prediction.


Prediction/measurement comparison (filtered flight configurations, ~ 50% of all flight configurations for this load)

But when considering only the filtered flight configurations, and still for dynamic loads, respectively 89% and 98% of the predictions have an accuracy better than ±10% and ±20%.

The customer finds this approach very promising. About 50% of missing loads may be calculated by using approximation models with sufficient accuracy (< ±20 %), drastically reducing the time and workforce needed for such analysis.

Based on the publication "Surrogate Models for Helicopter Loads Problems" by Alan Struzik (Airbus Helicopters), Evgeny Burnaev, Pavel Prikhodko (DATADVANCE) 


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