Quang Hung Pham
email: quang-hung.pham@insa-lyon.fr

Martin Gagnon

Jérôme Antoni

Antoine Tahan

Christine Monette

Rainflow-counting matrix interpolation over different operating conditions for hydroelectric turbine fatigue assessment

Keywords: Hydroelectric turbine, Kriging interpolation, Runner fatigue assessment, Rainflow counting

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Nomenclature

B f t o p h u , , L(.)

Bin value of ARM histogram [probability]

Introduction

Fatigue is one of the damage mechanisms occurring during the operation of a hydroelectric turbine.

Today, runner blades are experiencing increasing dynamic strains due to larger operating range of turbines caused by electrical network usage changes [START_REF] Monette | Cost of enlarged operating zone for an existing Francis runner[END_REF]. These changes mean that the turbine must operate under conditions that deviate significantly from the Best Efficiency Point (BEP), which leads to a higher risk of fatigue crack. [START_REF] Monette | Cost of enlarged operating zone for an existing Francis runner[END_REF] highlighted the reduced fatigue life of turbine runner and the high repair costs generated by this enlarged operating range [START_REF] Monette | Cost of enlarged operating zone for an existing Francis runner[END_REF]. A general overview of conditions and dynamic phenomena that significantly influence runner fatigue is presented by [START_REF] Liu | A review on fatigue damage mechanism in hydro turbines[END_REF], [START_REF] Seidel | Dynamic loads in Francis runners and their impact on fatigue life[END_REF] and [START_REF] Gagnon | Influence of load spectrum assumptions on the expected reliability of hydroelectric turbines: A case study[END_REF] [START_REF] Liu | A review on fatigue damage mechanism in hydro turbines[END_REF][START_REF] Seidel | Dynamic loads in Francis runners and their impact on fatigue life[END_REF][START_REF] Gagnon | Influence of load spectrum assumptions on the expected reliability of hydroelectric turbines: A case study[END_REF]. Steady state operating conditions containing a high stochastic component such as Speed No-Load (SNL) or Deep Part-Load (DPL) or Part load containing vortex rope phenomenon, and transient conditions such as turbine start-up can have major impact on runner fatigue assessment if not properly accounted for.

Fatigue is assessed based on several factors (runner material, stress level, initial crack), and requires a representative strain/stress history. Many approaches are available for improving runner fatigue life estimation. To limit fatigue failure, [START_REF] Gagnon | A probabilistic model for the onset of High Cycle Fatigue (HCF) crack propagation: Application to hydroelectric turbine runner[END_REF] proposed a runner reliability model using the High Cycle Fatigue (HCF) onset as the limit [START_REF] Gagnon | A probabilistic model for the onset of High Cycle Fatigue (HCF) crack propagation: Application to hydroelectric turbine runner[END_REF]. Fatigue damage is linked to the propagation of cracks on the runner, and thus, an investigation of the metallurgical or mechanical behaviour of the material is also needed [START_REF] Trudel | Metallurgical and fatigue assessments of welds in cast welded hydraulic turbine runners[END_REF][START_REF] Thibault | Bridging the gap between metallurgy and fatigue reliability of hydraulic turbine runners[END_REF][START_REF] El Haddad | Prediction of non propagating cracks[END_REF][START_REF] Kitagawa | Applicability of fracture mechanics to very small cracks or the cracks in the early stage[END_REF]. However, fatigue assessment cannot be carried out if the dynamic load information is missing. Computational Fluid Dynamic (CFD) combined with Finite Element Analysis (FEA) can be used to estimate the static and dynamic behaviour of the structure under such as SNL or DPL [START_REF] Nennemann | Challenges in dynamic pressure and stress predictions at no-load operation in hydraulic turbines[END_REF][START_REF] Morissette | Stress predictions in a Francis turbine at no-load operating regime[END_REF][START_REF] Xiao | Dynamic stresses in a Francis turbine runner based on fluid-structure interaction analysis[END_REF]. Nevertheless, numerical prediction is still challenging when turbulence models are not able to properly describe the behaviour of the turbine [START_REF] Presas | Fatigue life estimation of Francis turbines based on experimental strain measurements: Review of the actual data and future trends[END_REF]. Moreover, the validation of numerical simulation depends on the availability of the experimental information.

However, to recover this missing experimental information, other approaches, such as the interpolation and extrapolation of experimental data, can be used [START_REF] Ben Salah | Modélisation de la propagation des incertitudes des mesures sur l'aube d'une turbine hydraulique par Krigeage et simulations stochastiques[END_REF][START_REF] Poirier | Extrapolation of dynamic load behaviour on hydroelectric turbine blades with cyclostationary modelling[END_REF][START_REF] Pham | Interpolation of periodic hidden signal measured at steady-operating conditions on hydroelectric turbine runners[END_REF]. The use of indirect method can also help minimize the measurement requirement, [START_REF] Diagne | Modeling the dynamic behavior of turbine runner blades during transients using indirect measurements[END_REF] utilised the ARMAX (Autoregressive Moving Average with eXogenous input) model to predict the runner dynamic stress using shaft torsion information, which is more readily available [START_REF] Diagne | Modeling the dynamic behavior of turbine runner blades during transients using indirect measurements[END_REF]. For a detailed review of the fatigue life estimation methodologies used for Francis turbines, please refer to Presas et al. (2019) [START_REF] Presas | Fatigue life estimation of Francis turbines based on experimental strain measurements: Review of the actual data and future trends[END_REF]. Our state-of-art summary shows that in situ field strains/stress during or after commissioning provide important and essential information for the study of the hydroelectric turbine runner fatigue.

Finding a solution that can provide missing experimental information and improve knowledge on the dynamic behaviour remains a challenge. Obtaining experimental strains over all the possible states of the hydroelectric turbine operation would be overly costly and time-consuming; hence, experimental measurements are usually limited to a limited set of operating conditions, which leads to difficulties during runner fatigue assessment. The goal of this paper is to propose a methodology to minimize the requirements for experimental strain measurements. There are three difficulties associated with the measurement of strain for fatigue evaluation:

• Limited number of measured locations on runner blades • Limited measurement length

• Limited number of measured operating conditions

The first was studied by Salah where the kriging method was used for the interpolation between different locations of the runner blade [START_REF] Ben Salah | Modélisation de la propagation des incertitudes des mesures sur l'aube d'une turbine hydraulique par Krigeage et simulations stochastiques[END_REF]. For the second, several approaches can be used for temporal extrapolation to obtain long-term fatigue assessments. Poirier et al. (2016) [START_REF] Poirier | Extrapolation of dynamic load behaviour on hydroelectric turbine blades with cyclostationary modelling[END_REF] extrapolated information on the cyclostationary decompositions of the short-term records of strain signals to evaluate runner fatigue cycles over a longer period of usage. Other researchers extrapolated the rainflow matrices directly over longer periods [START_REF] Socie | Modelling expected service usage from short-term loading measurements[END_REF][START_REF] Socie | Modeling variability in service loading spectra[END_REF][START_REF] Johannesson | Extrapolation of load histories and spectra[END_REF][START_REF] Johannesson | Extrapolation of rainflow matrices[END_REF]. However, such strain interpolation between blade locations or a temporal extrapolation can be performed if and only if an estimate of the signal is available (generally in the form of measurements) at a given turbine operating condition. Therefore, the lack of measurements over the complete operating range should be studied as shown in Figure 1.

In a previous work the authors developed an interpolation process for a subcomponent of the strain signal between different turbine operating conditions [START_REF] Pham | Interpolation of periodic hidden signal measured at steady-operating conditions on hydroelectric turbine runners[END_REF]. Only the periodic component of the signal was interpolated while the complete strain signal was overlooked as it is more complex and contains other hidden structures. The direct interpolation of complete strain signal (measurement form) is a complicated problem because of these hidden structures. However, in cases where only fatigue information is needed for further evaluation, the strain signal could be transformed into a cycle counting form (level crossing, peak counting, rainflow matrices, etc.) to simplify the interpolation.

Among cycle counting methods, the rainflow algorithm is commonly used for fatigue assessment of hydroelectric turbines [START_REF] Monette | Cost of enlarged operating zone for an existing Francis runner[END_REF][START_REF] Nennemann | Challenges in dynamic pressure and stress predictions at no-load operation in hydraulic turbines[END_REF][START_REF] Morissette | Stress predictions in a Francis turbine at no-load operating regime[END_REF][START_REF] Poirier | Extrapolation of dynamic load behaviour on hydroelectric turbine blades with cyclostationary modelling[END_REF][START_REF] Pham | Interpolation of periodic hidden signal measured at steady-operating conditions on hydroelectric turbine runners[END_REF]. Therefore, our goal is to interpolate the rainflow counting matrices (instead of the signal itself), which contain information on the fatigue cycles, over the complete range of operating conditions. Notice that there are two important variables that define the operating conditions of turbine: opening vane level and head level. However, in this study, the aim is to focus on the differences of stress level between different opening vane levels for the same head (the data in the case study also comes from the measurements strain at relatively constant head). The head level might be used in the future research if observed data become available for multiple head levels. The kriging method was chosen for this study to interpolate rainflow counting matrices (histogram form), Then, the fatigue cycle reconstruction was generated via stochastic simulations using bivariate Gaussian distributions. This reconstruction step helps recover the long-term information of fatigue, more cycles are generated, more fatigue information is evaluated. The obtained results were compared with the experimental fatigue cycles to evaluate the correctness of the proposed interpolation methodology. In addition, the signal was reconstructed from the simulated cycles by using the inverse method proposed in [START_REF] Socie | Modelling expected service usage from short-term loading measurements[END_REF][START_REF] Socie | Modeling variability in service loading spectra[END_REF] to compare with the measured signal.

The paper is organized as follows: First, the methodology is presented with detailed explanations of the principal methods (rainflow-counting, kriging interpolation, reconstruction simulation). Then, a hydroelectric turbine runner case study is presented followed by interpolation results and a discussion.

Proposed Methodology

Asymmetric Rainflow Counting Matrices

The rainflow algorithm allows the analysis of signal amplitudes (or range) by assigning extreme (max, min) values of closed loading cycles. To evaluate fatigue, only the range/amplitude information of each cycle is often needed. In this study, the strain signal is transformed into an Asymmetric Rainflow Matrix (ARM), which separates the cycles into two types: increasing and decreasing cycles (or standing and hanging cycles in some references) [START_REF] Johannesson | Rainflow analysis of switching Markov loads[END_REF]. These two types of cycles are defined based on the order of occurrence of maximum and minimum values in the signal. To construct the ARM, a rainflow-counting procedure called the Four-Point Counting (FPC) algorithm is used [START_REF] Dreßler | Stochastic reconstruction of loading histories from a rainflow matrix[END_REF].

Considering four consecutive points (three consecutive cycles) in the loading signal, if the cycle range created by the second and the third points is smaller than the range of the two other points, this cycle is reduced and is added to the ARM. An ARM is constructed by two variables: from value (noted as f) corresponding to the amplitude of the first point of the cycle (the first point of the cycle arrives on the axis of time) and to value (noted as t) corresponding to the amplitude of the final point of the cycle (Figure 2). In our study, the created ARM is represented under histogram density form where each bin contains the number of cycles or the probability of occurrence of cycles. The ARM is a composition of max-min cycles (above the matrix diagonal) and min-max cycles (below the matrix diagonal). Furthermore, the choice of the asymmetric rainflow matrix allows a distinction to be made between increasing and decreasing cycles during the signal reconstruction. To properly apply the FPC, the turning points, which represent the peak and the valley of the signal, are extracted before the ARM is constructed. This extraction deletes variations that are neither peaks nor valleys (these small variations in the rainflow approach are considered to have minor impact on the fatigue assessment).

Kriging Interpolation Method

Before presenting the interpolation method, the context must be clarified. The interpolation input is a set of ARM histograms, which are spread across the different turbine operating conditions. The histogram bins are fixed for all the histograms. The goal is to estimate new ARM histograms at any given operating conditions (see Figure 3).

The relation between the bins of each ARM matrix is an important bit of information that cannot be ignored in the interpolation phase. Hence, the kriging interpolation method is a suitable method to preserve the spatial covariance within the ARM histogram. However, there is also a covariance to preserve between each operating condition. Thus, a multivariate kriging method, inspired by Spatio-Temporal Kriging (STK), where the temporal and spatial coordinates are treated separately, is applied, and developed for this study. Readers can consult the general definition of the kriging principle in [START_REF] Deutsch | Geostatistical software library and user's guide[END_REF][START_REF] Goovaerts | Geostatistics for natural resources evaluation[END_REF][START_REF] Montero | Spatial and spatio-temporal geostatistical modeling and kriging[END_REF][START_REF] Pebesma | Spatio-temporal interpolation using gstat[END_REF].

, ! " = $ $ , ! " , ! % &' ∈) * (1)
where is a given bin position in the ARM histogram (p depends on a 'from value' + and a 'to value' , : + , , , ! " is a given operating condition of the turbine, * , ! " is the interpolated value of bin at the condition ! " , , ! is the known bin value at location , ! , , ! " is the regression weight to optimize during the interpolation process (details below), is the number of experimental turbine conditions, is a set of neighbourhood positions of (including ) . It must be noted that the spatial covariance map is obtained from the whole histograms of all the experimental turbine conditions, while Eq. 1 searches for the input in the neighbourhood of the target bin. This reduces the calculation time and avoids the interpolation smoothing effect.

Kriging allows the unbiased estimation of values at given locations by determining the weights which minimize the error variance , ! " between the real value B and the interpolated value * at the same location, , ! " = ./01 , ! " - * , ! " 3. The condition for non-bias relating to the regression weights is ∑ ∑ , ! " % &' ∈) * = 1; it ensures a constant local mean value in every location. Therefore, to impose this non bias constraint, the minimization system is updated by adding a Lagrange parameter : 6 , = ./01 , ! " - * , ! " 3 788888888988888888:

; < = * , > + 2 A $ $ , ! " % &' ∈) * -1B (2)
where 6 , is the Lagrange function. Making use of Eq.1, the minimization of Eq.2 leads to the system that allows to obtain the and :

C ∑ ∑ , ! " % &' D E F G D , | I F J | ∈) * -= K D * F G D , | > F J | L , M ∈ , N = 1, … , ∑ ∑ , ! " % &' ∈) * = 1 (3)
where

1 ‖ Q F R ‖ , | S F T | 3 = 0.5 × ./0Y Z , ! [ - , ! \ ] (4)
is the semivariogram, which depends on the increments and , Z and are two positions of the bin in the histogram, ! [ and ! \ are two turbine operating conditions such that: = ‖ Z -‖ and

= |! [ -! \ |.
Based on Eq. 4, the semivariogram is defined as the half variance between two values separated by the increments and . This semivariogram can be considered as a simpler representative of the covariance map that does not require information on the mean value of B (that is often unknown in practice [START_REF] Montero | Spatial and spatio-temporal geostatistical modeling and kriging[END_REF]). To obtain the semivariogram at any possible increment ( , ), some numerical models can be used to fit to the semivariogram using analysis estimations (e.g., Least

Squares method) [27][30]. However, to choose the best numerical model, one needs to create a semivariogram from the experimental data. In practice, the quantity of data is not enough to provide values exactly separated by = ‖ Z -‖ and = |! [ -! \ |, as in Eq. 4. Consequently, to create the Experimental Semivariogram (ES), Eq. 5 is used. This equation allows an estimation of the semivariogram value associated with a set of (h, u) values, where and are midpoints of imposed spatial increment intervals:

, = 1 2 , $ Y Z , ! [ - , ! \ ] Z,[, ,\ ∈^ _,` (5)
where , is the experimental semivariogram, , is a set of paired points separated such that

‖ Z -‖ ∈ Y -a , + a ] and |! [ -! \ | ∈ Y -a , + a ] with dh > 0, du > 0, , is cardinal of , .
The next step is to fit the ES with a numerical model that will make a continuity throughout the increments for the semivariogram. Classes of semivariogram models are presented in [START_REF] Montero | Spatial and spatio-temporal geostatistical modeling and kriging[END_REF][START_REF] Pebesma | Spatio-temporal interpolation using gstat[END_REF]. For example, the sum-metric model (Figure 4), which turns out as one of the best fitting models in our study, is expressed as: [START_REF] Deutsch | Geostatistical software library and user's guide[END_REF]. The schema in Figure 5 summarizes the kriging interpolation approach used in our case study. In this study, since the interpolation input comes from the experimental strains measured by gauges, we impose the strain gauge uncertainty as a limited level of variability, which limits the variability of generated point outside each bin. For example, if the relative error of the strain gauge is ±y%, the imposed limited level for the variability will be y%. It must be noted that the experimental uncertainties are not the focused problem of this study. The test of variability is then launched for several variability parameters. For each ARM, Monte Carlo simulation is generated from the bivariate normal distribution with the mean [0,0] and the covariance c . If the percentage of the sample values outside the bin dimension is approximately equals to the limited level y% (Figure 6), this variability parameter is chosen for the ARM histogram smoothing process. The reader can also optimize the variability parameter by using or adding other uncertainty types (e.g., error of kriging interpolation) if needed for other study. In addition, other approaches, such as the Kernel Density Estimation (KDE), can also be useful for smoothing the histogram [START_REF] Socie | Modelling expected service usage from short-term loading measurements[END_REF][START_REF] Socie | Modeling variability in service loading spectra[END_REF]. Finally, the cycles are randomly generated from the set of BGDs by respecting the probability of occurrence of cycles in each bin (the sum of all the probability values in the histogram is equal to 1).This generation process allows an observation of a set of simulations, which is useful for the industry when evaluating the fatigue. The risk of fatigue will be predicted with a set of possibilities instead of a unique prediction.

, = + + 1b + . 3 (

Figure 6. Percentage of the sample values outside the bin dimension is approximately equal to y%

In addition, an inverse method is used to reconstruct the strain signal from the simulated samples

Case Study

The data used in this case study were obtained from experimental measurements conducted using strain gauges, which were installed on the runner blade of a Francis hydroelectric turbine of a power plant in Quebec (Canada). The measured locations on the blade are close to critical locations where the highest stress levels are found. For the purpose of this paper, the experimental uncertainties (ambiance error, human error, error of installation, etc.) are ignored. The interpolation is performed between different steady-operating conditions of the turbine. Transient operating conditions, such as start-ups or stops, are not considered in this research because their specific dynamic behaviours do not correlate with steady-operating conditions. A steady-operating condition is approximately defined as a regime of the turbine under which the guide vane opening, power and turbine head can be considered as quasi constant. For the interpolation, steady states are separated by different opening levels of the turbine guide vane (noted as %OV) (Figure 8). The guide vanes control the flow rate into the runner.

Due to the high quantity of cycles in each strain signal, the ARMs are presented under the histogram density form with a prior fixed bin number where each bin contains the probability of occurrence of cycles (Figure 8). The choice of input/output bin number is an important parameter. A higher number of bins significantly increases the calculation time, while a smaller one leads to imprecise results because of the large interval of values covered by each bin.

Fitting a model to the experimental semivariogram is an important step of the interpolation process. We highly recommend using the cross-validation technique for this step [START_REF] Montero | Spatial and spatio-temporal geostatistical modeling and kriging[END_REF]. This technique removes some point values in the input set and then predicts these values from the remaining points using fitted semivariogram models. This procedure is repeated several times for each semivariogram model to observe the interpolation performance of this model. Moreover, other error estimations such as Root Mean Square Error (RMSE) or Mean Absolute Error (MAE) are additionally used to obtain the best semivariogram model. In our case study, based on a good cross-validation performance (Figure 9) and on the small error estimation values (see MAE and RMSE in Table 1), the chosen semivariogram model was sum-metric model ( see Eq. 6 and Table 1). For each univariate model, was modeled by sum of an exponential model and a Gaussian model, and 1b + .

3 was respectively modeled by a Gaussian and an exponential model (Table 1).

i j k j l " Z = mnoo - . p1 -q F r._ Z f s + tZ`uu Z = mnoo - . p1 -q F r.` = Z f = s + (7)
where mnoo corresponds to the average variance where the experimental semivariogram stabilizes, range presents the distance from which no more correlations exist between the data, and is a small value added to the sill parameter to represent a very short-range variability in the dataset (Nugget effect) [14][27].

Figure 9. Cross validation performance of sum-metric model (its parameters are presented in Table 1)

The neighbourhood set (Eq. 1) is chosen using the cross-validation technique. Several sets with different numbers of neighbourhood positions are tested and the optimized set is chosen based on the smallest RMSE and based on the similarity between theoretical and estimated line (see APPENDIX).

Notice that the set of neighbourhoods is applied only for the histogram position " ", but not for operating conditions "!". Thus, the points in a neighbourhood set correspond to the closest points from the target points in ARMs. In this case study, the set of 9 nearest positions is chosen for the neighbourhood set in Eq. 1 (see APPENDIX).

Table 1 shows the optimized parameters used for this case study. To verify the quality of the interpolated result, a validation is made using known experimental operating conditions (not included in the set of interpolation inputs).

Parameters

Results and Discussions

The interpolated results (corresponding to each step illustrated in The interpolated ARM shows the same number of distribution modes (dashed line in Figure 10) as in the experimental ones; this means that this interpolation did not generate large overestimation in positions the null bins. Nonetheless, some differences are observed at the frontier positions of each mode in the interpolation result (Figure 10 , 11). Graphically, the reconstructed signal (Figure 12) is not similar to the experimental one like we have foreseen, however its amplitudes have the same level as the experimental one. To verify the quality of interpolation process, we have compared the rainflow strain spectrums (strain range as a function of cumulative number of fatigue cycles) between 500 simulations (sampled from the set of BGDs) and the experimental values at some operating conditions (Figure 13).

For fatigue assessment, the expected goal in this study is to capture the amplitude/range level of fatigue cycle (especially high range cycles which cause more damage). At 55 %OV and 65 %OV, the experimental rainflow (the blue line in Figure 13) is mostly within of the set of simulations while there seems to be some overestimations at the high ranges at 80 %OV. This difference might be explained by that there are more operating conditions close to the 55 %OV, 65 %OV in the interpolation input set (see Table 1).

An unusual variability is observed at 30 %OV. The interpolation result depends on the nature of known data. The more complicated the combination of phenomena hidden in the signal, the less confident we might be in the interpolation result. Therefore, at some partial load conditions of turbine, this unusual variability of the interpolated result occurs when an operating condition with a complicated dynamic behavior is presented next to the interpolation target condition. Some of those conditions contain specific fluctuation coming from the vortex in the draft tube [START_REF] Seidel | Dynamic loads in Francis runners and their impact on fatigue life[END_REF], which appears and disappears over limited set of measured operating conditions rendering the interpolation difficult. This problem provides new challenge for further research, in which we would like to recover such fluctuation information. For the runner maintenance strategy, even if the reconstructed signal is not similar to the experimental one (Figure 12), the interpolated strain ranges might be more representative of data variability and uncertainty than reusing experimental measurements from nearby operating conditions.

Also, the proposed interpolation can be a solution to reduce the measurement requirements for runner fatigue assessment.

Conclusions

In this article, an interpolation process using kriging has been presented to estimate the strain range at any steady state operating condition based on rainflow cycle counting for hydroelectric turbine runner fatigue assessment. A set of bivariate Gaussian distributions were used to smooth the histogram, allowing quicker simulations of the loading cycles. It must be noted that the proposed interpolation process is sensitive to the parameters used (i.e., the semivariogram model, etc.), using the error optimizing methods (such as cross-validation, Mean Absolute Error, etc.) are therefore highly recommended. The results of the case study show that even when the reconstructed signal is not similar to the experimental one, our proposed interpolation might be useful to estimate the dynamic strain level using only the load cycles information of strain signal.

The advantage of the proposed method is that it creates a stochastic process accounting for uncertainty hence contributing to fatigue risk assessment by generating loading cycles representative of observed behaviours. Moreover, it can help to optimize the requirements for experimental measurements.

In the result of this case study, the complicated phenomena hidden in strain signal caused the unusual variability at some partial load conditions. For further research, preserving other information of strain signal (not only the strain range information) during the interpolation phase will be interested to improve the quality of missing data recovery at unmeasured operating conditions.

About 4410 words (excluding abstract, figure captions and references). Figure 10, 13 must be printed in color

Figure 1 .

 1 Figure 1. Measurement limits and interpolation/extrapolation solutions for the fatigue assessment of hydroelectric turbine runner

Figure 2 .

 2 Figure 2. Four Point Counting algorithm applied for strain signal.

Figure 3 .

 3 Figure 3. Interpolation objective: new ARM histogram (at a given turbine operating condition) is interpolated from all experimental ARM histogramsIn our case, the position of bins in the ARM histogram and the operating condition are considered as coordinates. The estimator used in this study can be written as:

Figure 4 .

 4 Figure 4. Experimental semivariogram and example of semivariogram model (Sum-metric). Semivariogram values in this figure are normalized.

Figure 5 .

 5 Figure 5. Schema of the Kriging process in this paper applied for the studied variables 2.3 Simulation Reconstruction To generate strain cycles from an interpolated ARM histogram, it must be converted to a continuous distribution. A smoothing process for the interpolated histogram is proposed by considering that the cycles inside each bin follow a Bivariate Gaussian Distribution (BGD). The BGD mean corresponds to the coordinates of the center point of the bin and the proposed covariance matrix is c , where = d.e×[ \ Zf Z gZ Z[ h Z Z

[ 19 -

 19 [START_REF] Socie | Modeling variability in service loading spectra[END_REF]. The signal reconstruction consists of two steps: First, the largest cycles (the furthest points from the ARM diagonal), either a Decreasing Cycle (DC) or an Increasing Cycle (IC), are used to create an initial reconstructed signal (also called the remaining residue in Figure2). Second, all the other cycles are randomly inserted into the remaining residue descending order (from the furthest to the closet point from the diagonal) by respecting the rule proposed by Socie et al.[START_REF] Socie | Modelling expected service usage from short-term loading measurements[END_REF][START_REF] Socie | Modeling variability in service loading spectra[END_REF]. The smaller IC is added to the position of the larger DC (peak and valley values of the smaller cycle fall within the range of the larger cycle) and vice versa. Each cycle added to the remaining residue is removed in the ARM until there are no cycles left. It is not expected that the reconstructed signal will be similar to the experimental one because only the rainflow information is considered for the interpolation; nevertheless, the signal should represent a time history that generates equivalent fatigue damage. The flowchart in Figure7illustrates the interpolation scheme used in this study.

Figure 7 .

 7 Figure 7. Flowchart displays the interpolation scheme

Figure 8 .

 8 Figure 8. ARMs over different operating conditions for this case study and example of ARM histogram (the white bin corresponds to the null value)

Figure 7 )

 7 and their comparison with experimental ones at 55% OV are presented in the Figures 10-12. All the results are normalized to respect the confidential information.

Figure 10 .Figure 11 .Figure 12 .

 101112 Figure 10. Comparison between experimental and Interpolated ARM histogram at 55% OV

Figure 13 .

 13 Figure 13. Rainflow strain spectrum between experimental values and simulations

Figure 14 .

 14 Figure 14. Cross-validation performances for several neighbourhood sets

Table 1 .

 1 Parameters of the proposed interpolation process adapted for the case study dataset

		Semivariogram model parameters (fitted to normalized ES-see Figure 4)
	Input/Output	Optimized sum-metric model (RMSE = 0.0993, MAE= 0.0747)
	histogram bins number:	Eq. 6:	, = Model type +	+ Sill	1b + . range	3

Acknowledgments

The author would like to thank the Hydro-Québec Research Institute (IREQ), Andritz Hydro Canada LTD, INSA de Lyon (France), École de Technologie Supérieure de Montréal (Quebec, Canada) and the Mitacs Acceleration program for their support and financial contribution.

Appendix: The cross-validation performances for several neighbourhood sets

The cross-validation technique was performed for several neighbourhood sets (with the same semivariogram model). The optimized neighbourhood set for the interpolation is chosen based on the smallest RSME and based on the similarity between theoretical (black) and estimated line (red) in the cross-validation. In observing Figure 14, if one chooses a small set (the case of 5 points) or a big set (the cases of 35 or 49 points), the variation and the RMSE values are larger. In this case study, the set of 9 neighbourhood points is chosen (row 1 and column 2 in Figure 14).


MD Thierry Secheresse
email: thierry.secheresse@ch-metropole-savoie.fr

PhD Laurent Lima
email: laurent.lima@univ-grenoble-alpes.fr

PhD Pascal Pansu
email: pascal.pansu@univ-grenoble-alpes.fr

FOCUSING ON EXPLICIT DEBRIEFING FOR NOVICE LEARNERS IN HEALTHCARE SIMULATIONS: A RANDOMIZED PROSPECTIVE STUDY

Keywords: Simulation, Debriefing, Explicit learning, Healthcare training

Conclusion

Although the results revealed a beneficial effect of simulation training on self-efficacy, the explicit debriefing technique was shown to produce greater knowledge improvement than the implicit debriefing method in novice learners. Consequently, debriefing technique should be adapted to the objectives of the training and learners.

Highlights

• Explicit debriefing is more effective than implicit debriefing for novice learners

• Explicit debriefing involves active trainer management of the debriefing

• Presenting new information is an explicit manner is more effective for novice learners

Introduction

Debriefing is essential in simulation-based training, but it is not clear what exactly constitutes a successful debriefing session. Research in educational sciences shows that a structured, explicit and trainer-directed approach is systematically more effective than an implicit, reflective approach with minimal guidance, particularly for novice or intermediate learners.

The aim of this study is to compare explicit strongly trainer-guided debriefing with implicit and weakly guided debriefing in nursing training.

Method

Single-centre randomized prospective study comparing effectiveness of explicit and implicit debriefing techniques. We focused on the description and the analysis phases of the debriefing. Our main aim was to assess the effectiveness of debriefing in terms of knowledge improvement. We also assessed its effectiveness for self-efficacy and self-confidence.

Results

136 nursing students participated in 46 simulation sessions. Knowledge, self-efficacy and self-confidence increased in all conditions. The results also showed that debriefing with explicit analysis improved learning significantly when compared to the control session.

Simulation is essential in training for healthcare professionals. Therefore, it is important to identify the mechanisms applied at each step of a simulation session in order to ensure its effectiveness [START_REF] Abelsson | Nurse students learning acute care by simulation -Focus on observation and debriefing[END_REF]. The debriefing is the last step of a simulation session. It is recognised as the core of the learning process [START_REF] Dieckmann | The art and science of debriefing in simulation: ideal and practice[END_REF][START_REF] Krogh | Thinking on your feet"-a qualitative study of debriefing practice[END_REF][START_REF] Lavoie | Development of a post-simulation debriefing intervention to prepare nurses and nursing students to carefor deteriorating patients[END_REF]. However, debriefing remains a complex and poorly understood process that is often a source of difficulty for both trainers and learners [START_REF] Nestel | A national training program for simulation educators and technicians: evaluation strategy and outcomes[END_REF][START_REF] Sawyer | More than one way to debrief. A critical review of healthcare simulation debriefing methods[END_REF]. Several reviews and meta-analyses have tried to identify effective debriefing techniques and have concluded that there is no perfect debriefing technique [START_REF] Cheng | Debriefing for technology-enhanced simulation : a systematic review and meta analysis[END_REF][START_REF] Dufrene | Successful debriefing -Best methods to achieve positive learning outcomes: A literature review[END_REF][START_REF] Garden | Debriefing after simulationbased non-technical skill training in healthcare : a systematic review of effective practice[END_REF][START_REF] Hall | Best practice recommendations for debriefing in simulation-based education for Australian undergraduate nursing students : an integrative review[END_REF][START_REF] Levett-Jones | A systematic review of the effectiveness of simulation débriefing in health Professional education[END_REF][START_REF] Tannenbaum | Do team and individual debriefs enhance performance ? A Meta-analysis[END_REF]. To date the reflective technique has been considered as best practice [START_REF] Dreifuerst | The essentials of debriefing in simulation learning: a concept analysis[END_REF][START_REF] Husebø | Reflective practice and its role in simulation[END_REF][START_REF] Rudolph | Debriefing as formative assessment: Closing performance gaps in medical education[END_REF]. The underlying idea is to raise learner awareness of the gaps between their performance and the objective fixed by the trainer. Learners are therefore considered as being able to make an accurate assessment of their own performance and correct their errors when necessary [START_REF] Mann | Reflexion and reflective practice in health professions education: a systematic review[END_REF]. The Debriefing Assessment for Simulation in Healthcare (DASH, [START_REF] Simon | Debriefing Assessment for Simulation in Healthcare -Rater Version[END_REF] was designed to guide learner assessment by developing debriefing skills and by encouraging learners to explore and analyse their performance, their thought processes, their emotional states, so that they can perform better in real-life situations. (Ararfeh et al., 2011).

The reflectiveness induced during the debriefing also would promote the acquisition of new factual and procedural knowledge [START_REF] Eppich | Promoting Excellence and Reflective Learning in simulation (PEARLS). Development and rationale for a blended approach to health care simulation debriefing[END_REF].

Recently, new explicit debriefing techniques have come into use. For example, the Rapid Cycle Deliberate Practice incorporates explicit debriefing stages during the simulated situation. These new techniques have proven to be particularly effective for novice learners and teams of mixed healthcare professionals [START_REF] Cory | Rapid cycle deliberate practice versus reflective debriefing for pediatric septic shock training[END_REF][START_REF] Lemke | Improved team performance during pediatric resuscitations after rapid cycle deliberate practice compared with traditional debriefing: A pilot study[END_REF][START_REF] Magee | Improvement of immediate performance in neonatal resuscitation through rapid cycle deliberate practice training[END_REF]. This is in line with the conclusions in educational sciences literature, which clearly prove the benefits of explicit and structured learning strategies [START_REF] Rosenshine | Synthesis of research on explicit teaching[END_REF]. [START_REF] Hattie | Visible Learning: a synthesis of 800+ meta analyse on achievement[END_REF][START_REF] Hattie | Visible Learning for teachers[END_REF]) also showed that this explicit technique is more beneficial than the implicit technique for novice learners. For more experienced learners, explicit techniques are as efficient as implicit ones (Kirshner et al., 2006).

The aim of this study is to compare the effectiveness of four simulation sessions for student nurses: one using an explicit debriefing technique, one using an implicit debriefing technique, one using implicit description and explicit analysis, and one without any debriefing. We measured the improvement in knowledge, and self-efficacy, which is a predictive factor of future behaviour. Self-efficacy is defined as an individual's belief in his or her ability to carry out a required behaviour to produce a desired result [START_REF] Bandura | Self-efficacy. The exercise of control[END_REF]. The confidence that an individual has in his or her ability to accomplish a specific task conditions his or her commitment and how he or she will perform in the future.

Material and methods

This study complies with the principles of the Declaration of Helsinki. It is defined as noninterventional research as mentioned in the French Public Health code. It obtained approval from the Savoie School of Nursing management committee.

Participants

One hundred thirty-six French students in the second year of a Bachelor's degree in nursing took part in the study. There were one hundred and twenty-three women and thirteen men.

The average age of participants was 24.9 years (SD = 6.3). All the students were volunteers for this study and participants and trainers signed consent forms. There was no impact on the students' grades.

How the simulation session was conducted

The simulation-training programme

The study took place in the context of a full-scale simulation programme in a simulation centre. Each session lasted two hours. Three student nurses were present at every session, except one where two student nurses were present. Each session began with a "setting intro", which included a simulator-environment briefing. The simulator used was a SimMan 3G (Laerdal, Stavanger, Norway). There were two simulations per session, each followed by a debriefing.

The first simulation, which lasted ten minutes, concerned the post-operative management of a 70-year-old patient who had undergone a total hip replacement. The scenario started with the patient's return to his room after the surgery. He was equipped with a peripheral venous catheter with perfusion of 250 ml of NaCl 0.9%, a blood-soaked bandage on the left hip with 2 drains filled respectively with 250 ml and 300 ml of blood, with active bleeding. The initial parameters included a heart rate (HR) of 100 bpm, a respiratory rate (RR) of 20, blood pressure (BP) at 100/80 mmHg and peripheral oxygen saturation (SpO2) of 96%. After 5 minutes, the patient complained of dizziness and the haemodynamic situation deteriorated with an HR at 120 and a BP of 80/60. After the scenario, the participants went to three different rooms and were individually debriefed by three separate trainers. The debriefings, which lasted 20 minutes, were carried out individually to isolate the effects directly associated with the specific debriefing techniques. The second simulation was then completed with the same participants. This scenario concerned a 50-year-old patient hospitalised after abdominal trauma. He was equipped with a peripheral venous catheter with perfusion of 250 ml of NaCl 0.9%. After 5 minutes, the patient complained of dizziness and the hemodynamic situation deteriorated due to an internal bleeding on a spleen lesion. The changes in the patient's condition were the same as in the previous scenario. A group debriefing followed this second simulation.

Experimental debriefing techniques

Debriefing took place in four stages: reactions, description, analysis and summary. The differences between the types of debriefing were only on the description and analysis phases.

Three debriefing techniques were tested: (1) explicit description and analysis, (2) implicit description and analysis, (3) implicit description and explicit analysis. A fourth condition without debriefing was added (control session).

Debriefing with explicit description and analysis (EDA)

Explicit description was done by the trainer, which used direct questions about how the scenario played out. The questions were written on a whiteboard. The trainer guided the participant in an explicit manner by giving assertive feedback.

Explicit analysis was a structured interview with considerable trainer guidance, stating objectives, providing explicit presentation of the procedure and giving frequent summaries.

The content was presented in an explicit manner, with knowledge input concerning the signs of circulatory distress. The procedure for managing a patient in circulatory distress was explicitly presented by the trainer. Before the knowledge input, the trainer asked to the participant about the appropriate course of action when a patient is in circulatory distress.

These questions made it possible to explore the participant's prior knowledge. When the participant was unable to answer, the trainer provided the answers. The trainer's feedback focused on the results observed during patient management and the processes that led to this choice of patient management. The trainer made frequent summaries to check the participant's understanding and regularly asked how they could use what they had learned in a real-life clinical situation.

Debriefing with implicit description and analysis (IDA)

Implicit description: the participant described in the events that occurred during the scenario.

The trainer did not interrupt the participant at the stage. When the participant finished speaking, the trainer added specific reminders but did not input additional information.

Implicit analysis was a structured interview with a low level of trainer guidance. This was to encourage the participant's to reflect upon their actions. The trainer did not provide any additional knowledge, but tried to elicit knowledge of the signs of circulatory distress and patient management procedures in this situation. When the participant did not respond, the trainer did not volunteer the knowledge. Instead, the trainer asked more general questions about the signs and management of circulatory distress and asked the participants to make a summary. The trainer did not provide summaries during this analysis phase.

Debriefing with implicit description and explicit analysis (ID-EA)

In this condition, the debriefing was associated with an implicit description phase and an explicit analysis phase.

Control session (CS)

There was no debriefing in the control session. After the scenario, the participants immediately went to three different rooms. They were told to wait for 20 minutes. No particular task was given to the participants during this time.

Data collection

Three different data sets were collected: factual knowledge, self-confidence and self-efficacy.

Knowledge

Knowledge was assessed by a paper questionnaire about paramedical management of circulatory distress according to the nursing curriculum. The questionnaires were pre-tested with another group of student nurses (n = 12). An emergency physician and three nursing schools teachers developed it together. This questionnaire was composed of ten open questions: three focused on clinical evaluation of circulatory function, three on the signs of circulatory distress, two on recognising circulatory distress in a specific context (postoperative, trauma patient monitoring), and two focused on circulatory distress management.

Each question covered several aspects of nursing knowledge. The answers were scored 1 (satisfactory), 0.5 (partially satisfactory) or 0 (unsatisfactory). The final score was the total of the scores for each answer. These questions were given before the simulation session (pretest) and after it (post-test), but the item order was modified.

Self-efficacy and Self-confidence

Self-efficacy (SE) and self-confidence (SC) were measured using a 22-item questionnaire [START_REF] Bandura | Guide for constructing self-efficacy scales[END_REF]. The questionnaires were pre-tested with another group of student nurses (n = 12). Heighteen items measured SE (Cronbach α = .84), and 4 items measured SC (Cronbach α = .76). Twelves items were positive (e.g. "I fell capable to check pulse of a patient with circulatory distress") and ten items were negative (e.g. "I found it hard to measure the patient's heart rate"). The participants were asked to assess their perception of being able to complete each task on a scale of 0 (not at all) to 5 (absolutely). These items were given before the simulation session (pre-test) and after it (post-test), but the item order was modified.

Procedure

Figure 1: Study procedure The participants were placed into one of the three experimental debriefing conditions by computer-generated randomisation. Some were placed into the control session without debriefing. After the introduction and the simulator-environment briefing, the participants completed the knowledge and the SE-SC questionnaires (pre-test measures). The first simulation was then carried out. Immediately after the simulation, an individual debriefing took place using the different experimental techniques, or no debriefing. Then, all the participants took part in the second scenario and their knowledge and SE-SC were measured (post-test measures). Finally, a common debriefing session took place in order to give the same information at all participants.

Results

Forty-six simulation sessions were carried out during the study with 32 student nurses in the EDA group, 36 in the IDA group, 35 in the ID-EA group, and 33 in the CS group. Before the intervention, no knowledge, self-efficacy, or self-confidence differences were observed between the groups (knowledge: F (3, 132) = 0.819, p = .486; SE: F (3, 129) = .819, p = .486; SC: F (3, 131) = 2,169, p = .095).

Knowledge score

The knowledge score increased between pre-test and post-test for all four groups (Table 1).

The mean pre-test knowledge score was 11.47 (SD = 4.54, Skewness = .141, Kurtosis = -.399), whereas the mean post-test knowledge score was 19.55 (SD = 5.60, Skewness = .152, Kurtosis =. 137). The findings showed that while pre-test knowledge explained 17.7% of post-test variance, introducing the "condition" variable explained 14% of additional variance. Pre-test SC and pre-test SE did not influence post-test knowledge. The results also showed that debriefing with explicit analysis (EDA, ID-EA) improved learning significantly when compared to the control session. The progress observed in the IDA group was not significantly different from the progress in the control session.

Self-efficacy

Concerning self-efficacy, the results showed that the higher the pre-test score was, the higher the post-test score was for every group (Table 3). The results showed that pre-test SE explained 27.6% of variance in post-test SE. Introducing the "debriefing" variable explained 24.2% of additional variance. At identical initial SE, carrying out any type of debriefing led to a significant increase in SE compared to the control session (Table 4).

Self-confidence

Self-confidence increased between pre-test and post-test for all the debriefing techniques and for participants in the control session (table 5).

Table 5. Self-confidence mean scores (standard deviation) according to the debriefing technique used in the simulation session The findings showed that post-test SC was strongly related to pre-test SC (table 6). Initial knowledge and initial SE did not influence the post-test SC score. In step 2, although we observed a significant effect of IDA, ∆R2 was not significant when debriefing techniques were added in the model.

Discussion

The aim of this study was to test the effectiveness of different debriefing techniques after a simulation session, compared with an absence of debriefing. Two of our results merit closer attention.

First of all, our results showed a beneficial effect of simulation training on self-efficacy [START_REF] Bandura | Self-efficacy mechanism in human agency[END_REF]. This is important because the relationship between self-efficacy and performance has been proven among learners of all ages. Although this relationship is moderate (.38 to .50), self-efficacy is considered to be a predictive behavioural factor: the higher a person's self-efficacy is, the more likely it is that the person will apply or use his/her learning/knowledge in a real-life situation. Our results show that simulation-based training, with or without debriefing, reinforces self-efficacy, and self-efficacy levels improve more rapidly when the simulation is followed by a debriefing. This is not surprising since the newly acquired knowledge gained during the simulation session experience (successes and failures), along with vicarious experience, contribute directly to a person's self-efficacy. The debriefing is an additional source of self-efficacy reinforcement due to the verbal persuasion of feedback given to the person (encouragement, opinions of significant others, etc.). Pajares andZeldin (1999, 2000) arrived at same conclusion in their study of self-efficacy in mathematics among women in scientific careers. They showed that verbal persuasion techniques such as feedback and encouragements, as well as vicarious experiences, contributed directly to the reinforcement of self-efficacy. Our results also revealed that the variance due to the debriefing type (24.2) is as large as the variance caused by the initial self-efficacy score (27.6). This is a clear indication of the importance of debriefing in SE development. At a similar initial SE level, carrying out any debriefing technique led to a significant increase in SE compared to the control session, which had no debriefing. As regards self-confidence, the picture is somewhat different because the introduction of the debriefing type variable does not significantly improve the model. This may be due to the fact that self-confidence is a process that develops more slowly over repeated experiences. Second, our results showed that the explicit debriefing technique is more effective for knowledge acquisition than the implicit reflective debriefing technique. This is in line with educational science research, which has emphasized the structured, explicit nature of precise, targeted feedback in apprenticeship training as a means to promote effective teaching. For example, [START_REF] Hattie | Visible Learning: a synthesis of 800+ meta analyse on achievement[END_REF][START_REF] Hattie | Visible Learning for teachers[END_REF] notably studied publications on effective teaching, corresponding to the analysis of 1,200 metaanalyses, more than 65,000 studies on almost 250 million learners, from elementary to higher education. The results of Hattie's study (2012) revealed that explicit instructor-led teaching methods have greater efficacy (size effect d = .61) than implicit methods focusing on the learner (size effect d = .19). Direct teaching with a size effect of d = .59 appears to be one of the most effective factors. For novice learners, presenting information in an explicit manner is more effective than eliciting the information by means of a reflective process, thus justifying the use of explicit teaching methodologies, particularly in initial training. This explicit instructor-led teaching approach consists in an explicit presentation of the lesson objectives and content, frequent checking of learner understanding, and controlled practice [START_REF] Rosenshine | Principles of instruction. Research-based strategies that all teachers should know[END_REF]. On the whole, our results for knowledge acquisition are similar. They show that the variance due to the debriefing type ( 14) is as large as the variance caused by the initial knowledge score (17.4). This is a clear indication of the importance of debriefing in knowledge development [START_REF] Shinnick | Debriefing: The most important component in simulation[END_REF]. They also reveal that for a comparable initial knowledge level, the two explicit debriefing techniques (EDA, ID-EA) improved learning significantly when compared to the control session. This is not the case for implicit debriefing. [START_REF] Kihlgren | Investigating novice doctors' reflections in debriefings after simulation scenarios[END_REF] observed similarities in their investigations into reflection in debriefings by assessing participants' reflection levels using a framework of reflection levels developed by [START_REF] Fleck | Rating reflection on experience: A case study of teachers' and tutors' reflection around images[END_REF]. The participants' reflection levels were low in the cohort of novice doctors. Thus, although a reflective approach to debriefing is recommended, the real level of learner reflectivity in the debriefing seems to be rather low [START_REF] Husebø | The Relationship between facilitators's questions and the level of reflexion in post simulation debriefing[END_REF]. In addition, recent works in healthcare simulation have confirmed the importance of a structured approach [START_REF] Kim | Focused and Corrective Feedback Versus Structured and Supported Debriefing in a Simulation-Based Cardiac Arrest Team Training: A Pilot Randomized Controlled Study[END_REF]. Presenting information in an active manner, using a demonstration model during the debriefing, was effective in developing clinical judgment and, to a lesser degree, self-confidence in student nurses [START_REF] Weaver | The effect of a model demonstration during debriefing on student's clinical judgment, self-confidence and satisfaction during a simulated learning experience[END_REF]. Using an explicit teaching model in simulations, such as the rapid cycle deliberate practice, has been shown to be as effective, or even more effective, than traditional reflective debriefing methods [START_REF] Cory | Rapid cycle deliberate practice versus reflective debriefing for pediatric septic shock training[END_REF][START_REF] Lemke | Improved team performance during pediatric resuscitations after rapid cycle deliberate practice compared with traditional debriefing: A pilot study[END_REF][START_REF] Magee | Improvement of immediate performance in neonatal resuscitation through rapid cycle deliberate practice training[END_REF]. While explicit debriefing seems to be especially effective for student nurses, recent findings showed that for highly experienced healthcare professionals both explicit and implicit debriefing techniques can be used in an equivalent manner [START_REF] Secheresse | Focusing on an explicit debriefing in healthcare simulation[END_REF].

Limitations

This study has some weaknesses, which limit the scope of its conclusions. First, we assessed knowledge acquisition following a short simulation session. Therefore, it is difficult to predict if this knowledge will be retained over time, and this needs to be studied in the future.

Secondly, the results focus on knowledge, and while self-efficacy may be used as a predictive behavioural factor, it will also be necessary in future research to assess the impact of the debriefing type on behaviour and the transfer of learning to real clinical practice.

Conclusion

To conclude, the choice of the debriefing technique is an essential component in the in simulation-based training process as it directly influences the effectiveness of the training (Cheng & al., 2016). From an applied perspective, our results also suggest that the debriefing technique used should be adapted to the objectives of the training and learners, especially their level of expertise [START_REF] Cheng | Conceptual Framework for the Development of Debriefing Skills. A Journey of Discovery, Growth, and Maturity[END_REF]. Today, the best way forward at this point would therefore be to consider that a changing debriefing style may be more appropriate, moving from a more explicit to a more implicit technique depending on the progress made by the learner.

  The simulation objectives were to: o recognise life-threatening signs o perform nursing care for a patient in circulatory distress o give relevant information to the physician.Based on the participants' answers, three outcomes were possible: (1) satisfactory patient management: improved clinical condition and hemodynamics (2) sub-optimal patient management: unchanged clinical condition and hemodynamics, (3) unsatisfactory patient management: worsened clinical condition and hemodynamics.

Table 1 .

 1 Mean knowledge scores (standard deviation) according to the debriefing technique used in the simulation session

	Debriefing techniques		Knowledge score
		Pre-test	Post-test	t	p
	EDA	11.25 (4.79)	21.94 (5.65)	-10.974	< .001
	IDA	12.28 (4.33)	19,06 (4.63)	-8.082	< .001
	ID-EA	11.66 (4.19)	21.09 (4.99)	-9.547	< .001
	No debriefing (CS)	10.60 (4.79)	16.15 (5.56)	-7.443	< .001
	A multivariate analysis was done to determine how a specific type of debriefing and how the
	pre-test SC and SE influenced the post-test knowledge score (table 2).
	Table 2. Post-test knowledge scores controlling for the participants' pre-test knowledge, self-
	efficacy and self-confidence scores
			Postest knowledge score
	Model	Unstandardised	Standardised	t	p

Table 3 .

 3 Self-efficacy mean scores (standard deviation) according to the debriefing technique used in the simulation session.

	Debriefing techniques		Self-efficacy score
		Pre-test	Post-test	t	p
	EDA	43.87 (8.12)	61.23 (7.48)	-11.197	< .001
	IDA	39.61 (9.15)	57.30 (8.56)	-14.445	< .001
	ID-EA	41.39 (12.12) 57.84 (7.71)	-14.445	< .001
	No debriefing (CS)	41.12 (9.14)	47.73 (9.56)	-4.730	< .001

Table 4 .

 4 Post-test self-efficacy scores controlling for the participants' pre-test knowledge,

		self-efficacy and self-confidence scores
			Postest self efficacy score
		Unstandardised	Standardised
	Model	coefficient B (SE)	coefficient β	t	p
	Step1
	Constant	34.232 (3.188)		10.738	< .001
	Pre-test knowledge score				ns
	Pre-test SC score	.			ns
	Pre-test SE score	.524 (.075)	.525	6.984	< .001
	Step 2
	Constant	26.960 (2.840)		9.492	< .001
	Pre-test knowledge score				ns
	Pre-test SC score				ns
	Pre-test SE score	.505 (.063)	.507	8.055	< .001
	EDA	12.120 (1.736)	.528	6.983	< .001
	IDA	10.341 (1.653)	.479	6.257	< .001
	ID-EA	9.977 (.712)	.440	5.826	< .001
	R2 = .276 for step1; ∆R2 = .242 for step 2 (p < .001)

Table 6 .

 6 Self-confidence post-test scores controlling for the participants' pre-test knowledge,

		self-efficacy and self-confidence scores
			Postest self-confidence score
		Unstandardised	Standardised
	Model	coefficient B (SE)	coefficient β	t	p
	Step1
	Constant	6.69 (.644)		10.44	< .001
	Pre-test knowledge score				ns
	Pre-test SC score	.622 (.064)	.644	9.72	< .001
	Pre-test SE score				ns
	Step 2
	Constant	5.75 (.756)		7.601	< .001
	Pre-test knowledge score				ns
	Pre-test SC score	.636 (.065)	.66	9.803	< .001
	Pre-test SE score				ns
	EDA	.810 (.595)	.11	.363	.175
	IDA	1.273 (.583)	.18	2.183	.031
	ID-EA	10.080 (.585)	.149	1.845	.067
	R2 = .415 for step 1; ∆R2 = .024 for step 2 (p = .144)

Acknowledgements

The authors wants to acknowledge nursing students and instructors of the "Institut de Formation en Soins Infirmiers de Savoie" for their participation in this study

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Fundings

This research did not receive any grants from funding agencies.

Declaration of interest: none