Soufyane Benaboud
email: soufyane.benaboud@unilim.fr

Mokhfi Takarli
email: mokhfi.takarli@unilim.fr

Bertrand Pouteau
email: bertrand.pouteau@eurovia.com

Fatima Allou
email: fatima.allou@unilim.fr

Frédéric Dubois
email: frederic.dubois@unilim.fr

Pierre Hornych
email: pierre.hornych@univ-eiffel.fr

Mai Lan Nguyen
email: mai-lan.nguyen@univ-eiffel.fr

A New Analysis of Fatigue Test for Bituminous Mixtures using Fourier Series Fitting and Acoustic Emission Measurements

Keywords: Bending fatigue test, Fatigue failure criterion, Fatigue life, Damage and failure behavior, Acoustic Emission (AE), Curve-fitting, Continuous Fourier series

This paper presents a new method for analysing of experimental data stemming from the Two-Point Bending (2PB) fatigue test conducted on French standardized trapezoidal specimens, in accordance with NF EN 12697-24. These tests were performed on an asphalt mix specimen sawn from an in-service road pavement, adopting a loading frequency of 25 Hz and a target temperature of 10°C. The Acoustic Emission (AE) technique was implemented to monitor the damage and failure processes during fatigue. The fatigue life, defined as the critical number of loading cycles inducing specimen failure, is investigated herein according to several methods, including normalized criterion, models proposed in the literature, experimental fitting and Acoustic Emission activity analysis. First, the mechanical behaviour is fitted, in terms of strain, force, stiffness modulus and phase angle obtained from the fatigue test, in accordance with four functions, namely: a polynomial function, a continuous Fourier series, a sum of sine functions, and a Gaussian function. In a second step, a new damage criterion is proposed and validated with AE results based on a Fourier series decomposition. Lastly, a phenomenological analysis is carried out in order to understand the damage and failure process stages.

Introduction

This study is a part of the French ANR project entitled MOVEDVDC "Modeling of aging and damage for pavement lifetime assessment", whereby the research consortium aims to propose new approaches to both assess residual performance of bituminous road materials and better construe the mechanism of aging and damage in old asphalt mixes.

Asphalt mixes are subjected to range of loading conditions (mechanical, thermal and chemical) which lead to pavement deterioration in addition to determining their service life. Fatigue damage is one of the major forms of distress in asphalt pavements; occurs under a repeated traffic loading and causes a loss of stiffness relative to the initial state. Various phenomena can appear during fatigue tests, including: damage initiation and propagation, and a coalescence of macrocracks inducing the specimen failure. This damage and failure process, which depends not only on the asphalt mix composition of the asphalt mix and paving conditions but also on its loading history, is therefore quite complex to characterize by conventional fatigue tests. A number of methods have been performed in the past to characterize the fatigue of bituminous mixes using both homogenous and non-homogeneous tests [START_REF] Di Benedetto | Stiffness testing for bituminous mixtures[END_REF], [START_REF] Medani | Estimation of fatigue characteristics of asphaltic mixes using simple tests[END_REF]. Many researchers have investigated the fatigue of asphalt mixes [START_REF] Baaj | Effect of Binder Characteristics on Fatigue of Asphalt Pavement Using an Intrinsic Damage Approach[END_REF] [START_REF] Tayebali | Fatigue Response of Asphalt-Aggregate Mixtures[END_REF]. The literature review reveals that the fatigue failure of asphalt mixes subjected to cyclic loading is currently analysed using criteria based on: energy approaches [START_REF] Ghuzlan | Fatigue damage analysis in asphalt concrete mixtures using the dissipated energy approach[END_REF], [START_REF] Modarres | Comparison between the fatigue response of hot and warm mix asphalts based on the dissipated energy approach[END_REF], the modulus decrease during testing [START_REF] Tapsoba | Analysis of Fatigue Test for Bituminous Mixtures[END_REF], phase angle evolution, and an analysis of specimen homogeneity [START_REF] Baaj | Comportement à la fatigue des matériaux granulaires traités aux liants hydrocarbonés SCIENCES APPLIQUEES[END_REF].

In civil engineering research, depending on the studied failure modes, several test methods and analytical tools have been developed, in particular Acoustic Emission (AE). AE is a passive Non-Destructive Testing (NDT) method that relies on the transient elastic waves generated by the rapid release of strain energy in a material. A number of micro and macro processes contribute to both the deformation and deterioration of a material under loading, resulting in a series of acoustic events. The events produced by the given material thus contain information regarding global deformation. This technique is widely used in civil engineering to monitor damage in materials such as rocks [START_REF] Takarli | Damage in granite under heating/cooling cycles and water freeze thaw condition[END_REF], concrete [START_REF] Lacidogna | Acoustic Emission and Modal Frequency Variation in Concrete Specimens under Four-Point Bending[END_REF] or wood [START_REF] Lamy | Acoustic emission technique for fracture analysis in wood materials[END_REF]. Despite widespread use of the AE technique to characterize and monitor damage evolution of construction materials (often with a brittle behavior at low temperatures), few studies have focused on use of this technique to characterize asphalt concrete behavior. A substantial amount of literature is available on acoustic emission studies on bitumen and asphalt materials featuring: low temperature cracking (embrittlement temperature and thermal fatigue) [START_REF] Behnia | Characterization of embrittlement temperature of asphalt materials through implementation of acoustic emission technique[END_REF], [START_REF] Sinha | Acoustic emissions in asphalt subjected to thermal cycling at low temperature -NRC Publications Archive -Canada[END_REF], and static and dynamic loadings (fracture process and fatigue behavior) [START_REF] Chang | Application of Acoustic Emission to Study the Cohesive And Adhesive Strength of Asphalt[END_REF] [START_REF] Li | Investigation of Low Temperature Cracking in Asphalt Mixtures by Acoustic Emission[END_REF]. Fatigue behavior has been much less investigated by means of AE techniques.

Uniaxial tensile fatigue tests were conducted by Seo and Kim [START_REF] Seo | Using Acoustic Emission to monitor fatigue damage and healing in Asphalt Concrete[END_REF] and showed the influence of rest periods between loading cycles on the mechanical behavior of AC. Both the cumulative AE energy and cumulative AE counts increase when the fatigue test includes rest periods between loading cycles. This finding is due to both internal friction in existing defects and the complex restacking that raises AC resistance to fatigue damage; it indicates that rest periods improve fatigue life due to the healing phenomenon [START_REF] Castro | Fatigue and Healing of Asphalt Mixtures: Discriminate Analysis of Fatigue Curves[END_REF]. Moreover, the Kaiser effect is commonly related to damage state in the material. However, fatigue tests without rest periods have not systematically exposed this effect. Results also revealed that the level of cumulative AE energy can be used as a viable AE parameter to detect fatigue damage and identify the Fracture Process Zone (FPZ) as well as healing phenomena in AC. Diakhaté et al. [START_REF] Diakhaté | Acoustic Techniques for Fatigue Cracking Mechanisms Characterization in Hot Mix Asphalt (HMA)[END_REF] reported an experimental study which the AE technique was used to characterize AC behavior under a double shear cyclic loading. The results showed that a critical threshold can be identified at a 49% drop in the initial value of specimen stiffness; this value corresponds to a significant increase in acoustic energy levels and number of located events. Moreover, this critical threshold also matches the conventional failure criterion for asphalt concrete mixes (i.e. a 50% decrease in the initial specimen stiffness modulus). Furthermore, by studying cumulative events, several stages could be defined in fatigue testing, corresponding to various mechanisms such as micro or macrocracking.

Recently, shear-torque tests were introduced for the first time to assess the fatigue behavior of asphalt pavement interlayers by using the AE technique to evaluate the damage process leading to failure. This AE analysis included the cumulative number of AE events and their localization [START_REF] Ragni | Use of acoustic techniques to analyse interlayer shear-torque fatigue test in asphalt mixtures[END_REF]. In comparing the results of both mechanical and AE analyses, the available data suggest that despite an AE activity (formation of cracks) mainly occurs during the final test stage. The abrupt rise in AE events starts when the corresponding decrease in the norm of the complex modulus equal 70-75%. The authors concluded that the classical failure criterion ( 50 f N ) for predicting asphalt pavement fatigue life, as typically proposed in the literature, does not seem to correspond to the critical damage condition of double layered specimens and therefore should be revised.

Investigating the fatigue phenomenon is a critical field of research for enhancing the durability of pavement structures. In spite of the advances made in understanding the fatigue of Asphalt Concrete (AC), some outstanding questions remain, such as a proper evaluation and characterization of : wave velocity dispersions, and the attenuation factor for combined effects (viscosity, heterogeneity and damage) [START_REF] Larcher | Towards a viscoelastic mechanical characterization of asphalt materials by ultrasonic measurements[END_REF].

The work presented herein constitutes the first experimental attempt to apply AE in order to investigate the damage evolution in AC under a bending load. In addition, a new approach is proposed to analyse the mechanical data stemming from fatigue tests (strain, force, complex modulus, phase angle) by the use of curve-fitting with Fourier series.

Materials and experimental set-up 2.1 Material characteristics

The tested asphalt material was extracted from the subbase layer of an in-service highway pavement built in June 2002. The material formulation is provided in Table 1, in accordance with the grading curve plotted in Figure 1.

Two-point bending fatigue test

The two-point bending fatigue test performed in this study adheres to the method described in Standard EN 12697-24:2018 (see appendix A). This test method aims to characterize the resistance to bituminous mixture fatigue.

A set of 18 specimens is subjected to elementary fatigue tests; each test allows determining the number of cycles f N at which the specimen reaches the failure criterion, when subjected to a cyclic sinusoidal loading at a given strain level with a determined frequency and temperature. The specimens shaped like an isosceles trapezoid, with a constant thickness (see Figure 2), whose The principle behind this unit test is illustrated in Figure 3. Specimen (3) is glued to a metal base

(2) to ensure a fixed specimen base. A metal cap (1), glued to the top of the specimen, allows applying a displacement along the x-axis. A displacement with a sinusoidal variation [START_REF] Tayebali | Fatigue Response of Asphalt-Aggregate Mixtures[END_REF], according to a time (6)-displacement (5) diagram, is imposed at the top of the specimen (1) and generates bending in the specimen. The strain amplitude is maximal at 1/3 the height of the specimen (4), with damage therefore starting in the vicinity of this point [START_REF] Ghuzlan | Fatigue damage analysis in asphalt concrete mixtures using the dissipated energy approach[END_REF]. The strain at point (4) can be calculated from the specimen geometry and displacement; it also displays a sinusoidal variation [START_REF] Modarres | Comparison between the fatigue response of hot and warm mix asphalts based on the dissipated energy approach[END_REF]. All tests presented in this study were performed at a strain amplitude of 175 µm/m, a frequency of 25 Hz and a temperature of 10°C. During all tests, the load and displacement applied at the top of the specimen were monitored. These measurements and the specimen characteristics (geometry, mass) were then used to determine the stresses and strains applied at point [START_REF] Ghuzlan | Fatigue damage analysis in asphalt concrete mixtures using the dissipated energy approach[END_REF]. From these stresses and strains, the apparent modulus of the specimen could be calculated at each cycle, and the evolution of the normalized apparent modulus of the specimen [START_REF] Baaj | Comportement à la fatigue des matériaux granulaires traités aux liants hydrocarbonés SCIENCES APPLIQUEES[END_REF] with the number of cycles [START_REF] Takarli | Damage in granite under heating/cooling cycles and water freeze thaw condition[END_REF] was plotted [START_REF] Lacidogna | Acoustic Emission and Modal Frequency Variation in Concrete Specimens under Four-Point Bending[END_REF]. The normalized apparent modulus is defined as the ratio of the current apparent modulus to the initial apparent modulus (determined as the mean modulus between cycles 100 and 500).

Acoustic Emission instrumentation

During the fatigue test, acoustic emissions were recorded using a Euro Physical Acoustics (EPA) system. Eight piezoelectric transducers (miniature Nano30), with a frequency response range of 125-750 kHz and two resonant frequencies (140 and 300 kHz), were installed on the four lateral sides of the sample, as shown in Figure 5. The sensors are labelled from 1 to 8, according to the connected acquisition channel. The transducers were attached to the sample using silicon grease to enhance coupling and minimize acoustic signal attenuation at the transducer-sample interface.

AE signal amplification was provided by four (IL40S) preamplifiers with a gain factor set to 40 dB in order to reduce noise. The AE signals were sampled at a rate of 20 MHz, and a threshold was set at about 40 dB to remove background noise throughout the test. A single AE event is therefore defined as an AE signal that exceeds the threshold level; it can be detected by several sensors. The acquisition parameters and wave propagation velocity were calibrated using the Pencil Lead Breaking (PLB) protocol.

Mechanical fatigue curve

The fatigue test was performed on five samples. The mechanical data sampling acquisition frequency was 0.5 Hz (which represents 1 point every 50 cycles at a 25Hz loading frequency). As shown in Figure 6, the modulus decrease curve presents three characteristic phases [START_REF] Moreno-Navarro | A review of fatigue damage in bituminous mixtures: Understanding the phenomenon from a new perspective[END_REF], [START_REF] Di Benedetto | Fatigue of bituminous mixtures[END_REF]. Observed first is a rapid decrease in the complex modulus, due to thixotropy and self-heating effects that can coexist with damage [START_REF] Di Benedetto | Nonlinearity, Heating, Fatigue and Thixotropy during Cyclic Loading of Asphalt Mixtures[END_REF]. During the second phase, the modulus decrease exhibits a linear trend; this phase is explained by fatigue damage initiation. The last phase leads to a rapid Figure 6 indicates that even with very small variations in the initial modulus |E*|0 (less than 1%), the fatigue curves display differences in both shape and number of cycles leading to failure. This outcome is likely due to the different levels and distributions of the preexisting damage.

To analyze these fatigue curves, let s consider the first derivative form, as defined in Equation 1, calculated for each successive data point. The objective here is to find a better way to represent the evolution observed during fatigue tests for a damaged AC:

( ) ( ) dx x N N x N dN N (1)
Where N denotes the cycle number and N the range of the cycle number according to a discrete derivative process that . For four values of N , the evolution in loss rate for the complex modulus is presented in Figure 7 for 50, 100, 200 and 400 cycles, respectively. ). This technique therefore serves to delimit the stage when the slope

* | | d E
dN is constant, which corresponds to the fatigue damage phase (or Phase II). The transition between Phase II and III is also more visible for the lowest sampling frequency ( 400 N

), and appears at around 40,000 cycles.

Fitting of experimental data

Fitting functions

As demonstrated in the last section, extracting useful information from fatigue test results is challenging. For this reason, various functions were tested to fit the fatigue results, for purpose of reducing noise and smoothing data for subsequent processing. The functions tested included: polynomials [START_REF] Biligiri | DEVELOPMENT OF COMPUTATIONAL METHODS TO ESTIMATE PHASE ANGLE OF ASPHALT MIXTURES[END_REF], Fourier series [START_REF]A simple algorithm for fitting measured data to Fourier series models[END_REF], [28], and Gaussian and sine functions. They were first fitted

n i i i p x p x (2)
where i p represents the polynomial function coefficients and n the considered polynomial order.

Continuous Fourier series:

0 1 1 ( ) cos( ) sin( ) n n i i i i f x a a i x b i x (3)
where 0 a , i a , i b are the Fourier series coefficients, is the pulsation, and n the Fourier series order.

Sum of sine functions:

n i i i i s x c d x e 1 ( ) sin( )
where i c , i d and i e are the fitting parameters of sine, and n the number of terms considered.

Gaussian function:

2 1 ( ) exp (( ) / ) n i i i i g x k x l m (5)
where i k , i l and i m denote the fitting coefficients for the Gaussian function, and n the number of terms considered.

These functions were used to fit range of experimental data, such as force f , strain , complex modulus * | | E and phase angle .

Estimation of noise filtering characteristics

The difference between the experimental and fitted data is expressed point-by-point by the residual function f R i , defined for point i as follows:

exp exp erimental fitted i i f erimental i X X R i X (6)
To allow for a global comparison between the various fitting functions, a relative average residual error (µRf) is proposed (Equation 7):

exp exp 1 1 erimental fitted n i i Rf erimental i i X X n X (7)
In this equations, exp erimental X denotes the experimental data under consideration, fitted X the fitted values, and n the signal length.

Figure 8 compares the relative residual errors of the various fitting functions of order 8. This figure shows that the largest errors are obtained for the phase angle ( ), which can be explained by the significant noise amplitude visible in Figure 9. On the whole, the Fourier series leads to the best fit of the various parameters and the most realistic shape of the experimental curves (Figure 9); it will be used to process the fatigue measurements. This section will present a parametric analysis of the Fourier series fitting method performance.

Error! Reference source not found.(a) shows the residual error of the fit of the complex modulus fatigue curve as a function of series order. Increasing the series order reduces the residual error, particularly during the last stage of the fatigue test. Similar results are observed for the strain, force and phase angle curves (Error! Reference source not found.(b)).The processing program used is limited to the eight order, but errors are already quite at this order. An asymptotic value could be attained for higher orders. to determine the fatigue life based on energy approaches, namely Black space, phase angle evolution and damage analysis [START_REF] Boussabnia | Comparison of Fatigue Law Parameters obtained from Two-Point Bending and Tension-Compression Tests[END_REF]. The fatigue criteria evaluated in this work are as follows:

1) Nf30% and Nf50% are the number of cycles corresponding to a complex modulus loss of 30 % and 50% [START_REF]Bituminous mixtures-Test methodsfatigue[END_REF], respectively. As shown in Figure 12, the Nf50% criterion is reached during the failure phase (Phase III). At this stage of the fatigue process, the modulus value decreases very rapidly until the sample fails; this phenomenon is caused by microcracks coalescence, leading to macrocrack emergence and propagation in the sample [START_REF] Boussabnia | Comparison of Fatigue Law Parameters obtained from Two-Point Bending and Tension-Compression Tests[END_REF]. For this reason, the Nf50% criterion is not really appropriate for quantifying the fatigue life of damaged AC. The Nf30% criterion, positioned at the end of the second phase and governed by fatigue phenomena, seems to be more relevant. 2) The Dissipated Energy (DE) criterion represents the viscous energy lost by the AC in each cycle. This energy dissipation induces specimen heating and causes a modulus decrease [START_REF] Riahi | Quantification of selfheating and its effects under cyclic tests on a bituminous binder[END_REF]; it is defined as follows: sin( )

i i i i w (8)
The proposed f N DE criterion corresponds to the number of cycles at which the increase in dissipated energy related to the heating phenomenon reaches its maximum (Figure 13). The observed decrease in dissipated energy after this peak suggests the existence of additional processes affecting the energy equilibrium. This criterion coincides with the transition between Phases I and II of the fatigue process, thus corresponding to the damage initiation. 3) The Dissipated Energy Ratio (DER), introduced by Hopman et al., [START_REF] Hopman | A renewed interpretation method for fatigue measurements verif[END_REF], has been proposed with a modified expression adapted to controlled-strain tests in Equation 9.

0 0 0 0 [ sin( )] sin( ) i i i i i i w i DER w (9)
where 0 w and i w are respectively the energy dissipated in the first cycle and at the i th cycle. , and represent respectively the strain, stress amplitude and phase angle. i denotes the number of load cycles.

When plotting DER versus load cycles, a peak can be clearly observed and easily identified. As a result, the fatigue life is defined as the number of load cycles corresponding to the peak value where cracks are assumed to initiate (Figure 14). As observed for the Nf50% criterion, this method is inappropriate for quantifying the fatigue life of a damaged AC. 4) The Cumulative Dissipated Energy Ratio (CDER) index, calculated according to Equation 10[33], [START_REF] Rowe | Improved Techniques To Evaluate The Fatigue Resistance Of Asphaltic mixtures[END_REF], is defined by:

1 n i i n n w CDER w (10)
The fatigue life determined with this method corresponds to the intersection between two linear regression lines on the CDER versus load cycles curve (Figure 15). It should be noted that this criterion is highly dependent on the points selected for the regression procedure, particularly for the second line. Once again, the fatigue life determined with the CDER criterion is positioned in the third phase of the fatigue process. The last part of the curves in Figure 16 exhibits a transition zone, where variation rate starts to increase more rapidly. To identify this threshold, a new criterion (Cumulative Variation Ratio, or is proposed and expressed by Equation 11. The CVR values are plotted in Figure 17

Analysis of Acoustic Emission (AE) activity

A large amount of literature is available on AE studies of construction materials under a variety of loading conditions. Several approaches have been adapted to analyze the various aspects of microcracking and fracture processes, for example: (1) recording of events and expressing them in the form of event rate or cumulative events; (2) determination of source locations and study of individual events mechanisms; (3) study of amplitude distributions; and (4) the investigation of the frequency characteristics associated with emission events. However, the most widely used and simplest approach to quantifying AE activity remains counting each signal that exceeds a set threshold. The process of detecting and measuring an AE signal on a channel is referred to as

The number of AE-hits is then plotted as a function of time or load, either cumulatively (Cumulative AE-hits) or in the form of a count rate histogram (or scatter plot of AE-hits).

Figure 18 displays evolution in cumulative AE-hits, for each sensor, versus the number of load cycles. The shape of AE activity curves is similar; however, sensors located at the bottom of the sample do output greater numbers of AE-hits, thus indicating that the AE-sources generated by the fatigue loading lie closer to these sensors. This result is logical since like in 2PB tests, failure usually occurs at 1/3 of the specimen height, where the bending moment is maximum [START_REF] Harvey | Four Point Bending[END_REF], [START_REF] Maggiore | Evaluation of Stiffness and Fatigue Using 2 Point Bending and Indirect Tensile Fatigue Tests[END_REF]. AE-signal amplitudes depend on the distance between sensors and source event, as attenuation increases with propagation length. Localization of AE-sources requires additional signal processing since it is necessary account for the various wave propagation modes and effects of damage on velocities; future work will focus on this topic. The evolution in non-cumulative AE activity (Figure 19) allows identifying three main phases in the damage and failure process:

1) AE-Phase I: AE-activity is detected at the beginning of the test and is probably related to preexisting damage in the sample. The AE-source may be due to either friction between crack surfaces or reactivation of propagation of suitably-oriented cracks. The number of AE-hits then decreases gradually until reaching a minimum, at approx. 20,000 cycles.

Heating, which occurs during the first fatigue phase [START_REF] De La Roche | Evaluation thermographie infrarouge[END_REF], causes viscous wave attenuation and reduce AE-system capacity to detect and record acoustic activity.

2) AE-Phase II: After reaching a minimum, AE activity slowly increases with the number of load cycles, due to the microcracks induced stress. This phase corresponds to the beginning of crack initiation and the stable crack growth stage. 3) AE-Phase III: During third phase, the number of AE-hits starts to display irregular variations, with successive increases and decreases. This behavior implies the presence of obstacles to crack propagation, such as inter or intragranular fracture processes. This phase corresponds to crack coalescence and unstable crack growth; however, more analysis is required to define an objective criterion characterizing the beginning of this phase. In order to identify the onset of the third stage, the Akaike Information Criterion (AIC) [START_REF] Kurz | Strategies for reliable automatic onset time picking of acoustic emissions and of ultrasound signals in concrete[END_REF], [START_REF] Zhang | Automatic P-Wave Arrival Detection and Picking with Multiscale Wavelet Analysis for Single-Component Recordings[END_REF] is applied to the Non-Cumulative Hits Variation Rate (VR), i.e.:

( 1) Hits i and ( ) Hits i respectively refer to the numbers of hits at the 1 i and i load cycles.

The AIC is based on the assumption that a time series (discrete signals) can be divided into locally stationary segments (each modelled as an autoregressive process). The point at which the AIC is minimized (Figure 20) represents the optimal separation between the two time series (noise and signal). The AIC function minimum corresponds herein to the onset of the third phase characterized by irregular and more significant AE activity variation in the material (Figure 19).

The AIC function can be computed using Equation13.

[ ] .log var [1,..., ] ( ).log var [ 1,..., ]

AIC k k x k N k x k N (13)
where [ ]

x k is the signal value at index k , N the length of the signal and var the variance.

Conclusion and Outlook

In this study, we have experimentally investigated the fatigue process of an aged asphalt concrete by combining fitting of the mechanical data with analysis of the AE generated during the test.

Below are the major conclusions drawn from this work: (1) The recorded (force f and strain or displacement) and calculated ( and * | | E ) mechanical data contain a very low noise level, which nevertheless remains sufficient to modify analysis of the fatigue process. The fitting using Fourier series allows filtering this noise and yields the lowest residual error.

(2) Analyzing the first derivative of the fatigue curve highlights the existence of a Global Minimum of the First Derivative (GMFD) and variation rate (VR). The most significant change in VR can be observed as a peak of the Cumulative Variation Ratio (CVR).

(3) The acoustic measurements show a significant difference in AE-hits between top and bottom sensor groups. Furthermore, the sensor located nearest to the fracture initiation zone outputs the highest number of AE-hits throughout the test. In future work, AE analyses will be continued by considering wave form parameters such as: amplitude, rise time, duration, energy, and

The location of the AE-sources will also be considered. Regarding the damage and failure criteria stemming from the fitting process, the same approach will be applied to specimens with and without initial damage, and across different types of fatigue tests (Two-Point Bending, Four Point Bending, Tension-Compression and shear tests).

Figure 1

 1 Figure 1 Grading curve of the aggregates in the studied asphalt mix

  dimensions are: B = 56 ± 1 mm, b = 25 ± 1 mm, e = 25 ± 1 mm and h = 250 ± 1 mm. In this study, the specimens have been sawn to the required dimensions from slabs removed from the road layers.

Figure 2

 2 Figure 2 Specimen geometry (extract from Standard EN 12697-24, see Appendix A)

Figure 3

 3 Figure 3 Principal behind the unit fatigue test

Figure 4

 4 Figure 4 illustrates the sensor layout. Load is applied by an actuator (5) moving along the x-axis,

Figure 4

 4 Figure 4 Layout of the fatigue test sensors

Figure 5

 5 Figure 5 Sample geometry and AE sensor locations

Figure 6

 6 Figure 6 Experimental fatigue curves (decrease in complex modulus)

  due to the formation and propagation of macrocracks resulting in the sample collapse.

Figure 7

 7 Figure 7 First derivative of the complex modulus vs number of cycles with a 1 measurement for a) 50 N b) 100 N , c) 200 N , d) 400 N

  -F-107 to the experimental data to reproduce the overall shape of the fatigue curves and then used to analyze the slope on the first derivative of the fatigue curves.

Figure 8 Figure 9

 89 Figure 8 Comparison of the average relative residual errors obtained with the various fitting functions

Figure 10 aFigure 11 3 . 3 .

 101133 Figure 10 a) Variation in residual error Rf vs number of load cycles for the modulus; b) relative average residual error µRf for various Fourier series orders

Figure 12

 12 Figure 12 Complex modulus evolution vs the number of cycles and indication of the two considered criteria (Nf30% and Nf30%)

Figure 14

 14 Figure 14 DER criterion and modulus loss curves

Figure 15 Figure 16

 1516 Figure 15 Curves showing the CDER and modulus loss versus number of cycles

Figure 17

 17 Figure 17 Representation of the CVR criterion applied to strain, force, |E*| and phase angle

Figure 18

 18 Figure 18 Evolution in cumulative AE hits for the eight sensors

Figure 19 a

 19 Figure 19 a) Evolution in non-cumulative AE hits for all sensors; b) AE phases sequencing for bottom sensors

Figure 20 6 . 1 ) 2 )

 20612 Figure 20 Third phase (EA_III) identification with the AIC criterion, for the average number of hits from all eight sensors

Figure 21

 21 Figure 21 Curves showing the evolution in non-cumulative hits, first derivative of |E*| and modulus decrease

Figure 22 .Figure 23

 2223 Figure 22.a Comparison of fatigue life determined with the considered criteria

( 4 )

 4 According to the analysis of AE-activity, the fatigue process can be divided into three phases: AE-Phase I (activation of preexisting damage); AE-Phase II (initiation and propagation of fatigue damage); and AE-Phase III (crack coalescence and failure initiation).

( 5 )

 5 The thresholds, in terms of number of load cycles, characterizing the transition between AE-phases agree with the new failure criteria based on mechanical data fitting. For a strain-controlled test, the fGMFDf N and fDER N criteria agree well with the fatigue damage and failure thresholds, respectively. The fGMFD N criterion, corresponds approximately to the middle of the second phase of the fatigue process. However, the 50 f N criterion does appear to overestimate the fatigue life.

Table 1

 1 Formulation of the studied asphalt mix

	Component	Content (%)
	Sand 0/4	42
	Gravel 4/6	10
	Gravel 6/10	10
	Gravel 10/14	36
	Added filler	2
	Binder content (35/50 penetration)	4.6 ppc*
	*percent by weight of aggregates

Acknowledgement

This work was carried out as part of the ANR-MOVEDVDC project supported by the National Research Agency (ANR-17-CE22-0014).


Marcin Lefik
email: marcin.lefik@p.lodz.pl

Krzysztof Komeza
email: krzysztof.komeza@p.lodz.pl

Ewa Napieralska-Juszczak
email: ewa.napieralskajuszczak@univ-artois.fr

Daniel Roger
email: daniel.roger@univ-artois.fr

Senior Member, IEEE Piotr Napieralski
email: piotr.napieralski@p.lodz.pl

Senior Member, IEEE Ewa Napieralska Juszczak

IEEE Senior Member

Comparison of the Reluctance Laminated and Solid Rotor Synchronous Machine operating at High Temperatures

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I. INTRODUCTION

The HT (High temperatures) electric machines are designed for special purposes. They are used in environments where the ambient temperature is much higher than typical ones. Of course, this also causes an increase the temperature inside the motor housing. For example, the Reluctance Synchronous Machine (RSM) designed for working in the vicinity of the aircraft turbines, where the ambient temperature is about 200°C, will work with an internal temperature estimated to 450-500°C at the hottest point. In order to work continuously at such internal temperatures it is necessary to use inorganic Electrical Insulation Systems (EIS) and to adapt the machine design to this inorganic technology [START_REF] Iosif | An insulation solution for coils of high temperature motors (500°C)[END_REF][START_REF] Liu | Thermal stability and performance data for SmCo 2:17 high-temperature magnets on ppm focusing structures[END_REF][START_REF] Cozonac | Materials characterization and geometry of a high temperature induction machine[END_REF][START_REF] Iosif | Assessment and improvements of inorganic insulation for high temperature low voltage motors[END_REF]. With this topology, two main options are possible: a synchronous permanent magnet machine, or a reluctance synchronous machines which produces torque from variations of the reluctance of the magnetic circuit [START_REF] Pyrhoonen | Design of Rotating Machines[END_REF][START_REF] Belhadi | Switched reluctance motor with magnetic slot wedges for automotive traction application[END_REF][START_REF] Lipo | Synchronous reluctance machines-A viable alternative for a.c. drives?[END_REF]. The HT° motor, made with rigid inorganic coils, requires a specific design of the stator with rectangular teeth and opened slots. Thus, the design calculations of those electromechanical transducers require specific electromagnetic and thermal analyses, which allow calculating additionally the thermal effects of power losses. The paper describes the electromagnetic and thermal analysis of HT° Synchronous Reluctance Machine (SRM) operating at high ambient temperatures using 3D field calculations. The machine is run at the rated speed of 4800 rpm. To analyse this phenomenon the 3D coupled thermal-fluid (CFD) model is used. Due to the specific design of the stator associated with the technology of making and setting coils and the large number of poles, the choice of rotor design was quite limited. Simple design with salient pole rotor was chosen. In order to increase the torque, in the poles longitudinal cuts and a circular hole at the base of the pole, acting as a flux barrier, were additionally made. Next figure shows main parts of reluctance motor. The rotor can be made as a solid or as a laminated. Solid construction is mechanically more robust allowing higher rotation speed, moreover induced currents can generate torque during starting. Unfortunately stator construction, even with used stator slot wedges, generate higher flux harmonics which produced high losses in rotor at synchronous speed. Induced in solid rotor poles currents weakened the effect of reluctance changes. Next figure show comparison of torque versus load angle for both: laminated and solid design. As can be seen from Fig. 2 solid rotor motor produced torque almost seven time smaller than laminated rotor motor. Therefore when efficiency for laminated construction can obtained 58.9% then solid construction only 9.92%.

II. ELECTROMAGNETIC FIELD SIMULATION

In order to obtain heat sources for the thermal model, calculations of the electromagnetic field were made using the Opera program. As commonly known the 3D time-stepping FEM is very time-consuming [START_REF] Ionel | Finite element surrogate model for electric machines with revolving field-Application to IPM motors[END_REF][START_REF] Bianchi | Relationship Between Rotor Losses and Size of Permanent-Magnet Machines[END_REF][START_REF] Ponomarev | Influence of Travelling Current Linkage Harmonics on Inductance Variation Torque Ripple and Sensorless Capability of Tooth-Coil Permanent-Magnet Synchronous Machines[END_REF] and thus the use of 2D analysis is preferred [START_REF] El-Refaie | Fractional-Slot Concentrated-Windings Synchronous Permanent Magnet Machines: Opportunities and Challenges[END_REF][START_REF] Komeza | Analysis of the impast of the design of HT machines on the cogging torque and losses In permanent magnet[END_REF][START_REF] El-Refaie | Optimal flux weakening in surface PM machines using fractional-slot concentrated windings[END_REF][START_REF] Tang | Analysis of Iron Loss in Interior PM Machines With Distributed Windings Under Deep Field Weakening[END_REF]. The time-stepping analysis was performed over approximately 20 cycles until the steady state was reached. First 2D and after 3D simulation was realize. For the purpose of the 3D simulation a quarter of the machine has been considered to benefit from the magnetic symmetry. The time stepping analysis was performed assuming constant speed of rotation of the rotor. The 3D mesh contains 4.264778 million elements in total. In the conductive areas, the elements size was chosen to be less than one-third of the penetration depth. Moreover, the distribution of the density of the mesh is greater than to correctly reproduce the effect of rotation of the rotor relative to the stator. To reduce the computation times the simulations were performed on a virtual machine with eight cores.

Figures 2 and3 shows the comparison of torque for laminated and solid rotor (made from steel C10) calculated by 2D and 3D models. While for laminated rotor 2D and 3D results were almost the same for solid rotor they differ significantly. Even for synchronous speed, higher harmonics cause significant losses in the conductive material of the rotor (despite the elevated temperature the conductivity is 2.24 MS/m). Next figure shows rotor losses versus time for one period. The total losses in the rotor are practically independent of the load angle and amount to 1030 W for the maximum torque.

III. SUMARY

In this study, we analysed the influence of the design of the rotor (solid or laminated) on efficiency and temperature of the motor active parts. The presented results show clearly that laminated construction is much better from a point of view of efficiency and temperature. However solid construction can be interesting for high speed machines due to their mechanical robustness.

Fig. 1 .

 1 Fig.1. Reluctance motor

Fig. 2 .

 2 Fig.2. Comparison of torque for laminated and solid rotor design

Fig. 3 .Fig. 4 .Fig. 5 .

 345 Fig.3. Comparison of torque for laminated rotor design calculated by 2D and 3D models


Mathieu Acher
email: mathieu.acher@irisa.fr

A Demonstration of End-User Code Customization Using Generative AI

Keywords: Software and its engineering → Software product lines, Context specific languages, • Computing methodologies → Machine learning approaches variability, end-user programming, software product lines, generator, generative AI, LLM, code synthesis, customization

Producing a variant of code is highly challenging, particularly for individuals unfamiliar with programming. This demonstration introduces a novel use of generative AI to aid end-users in customizing code. We first describe how generative AI can be used to customize code through prompts and instructions, and further demonstrate its potential in building end-user tools for configuring code. We showcase how to transform an undocumented, technical, low-level TikZ into a user-friendly, configurable, Web-based customization tool written in Python, HTML, CSS, and JavaScript and itself configurable. We discuss how generative AI can support this transformation process and traditional variability engineering tasks, such as identification and implementation of features, synthesis of a template code generator, and development of end-user configurators. We believe it is a first step towards democratizing variability programming, opening a path for end-users to adapt code to their needs.

INTRODUCTION

Customizing code is highly challenging, particularly for individuals unfamiliar with programming. The customization of code involves modifying or extending an existing piece of software code to create a new, different variant that has, e.g., different features or functionalities. The process involves different activities. There is first the need to understand existing code. A code can be more or less documented, written by someone else, or simply challenging to comprehend. There is also the need to master different programming languages, technologies, frameworks, or libraries, each with a specific syntax. A person familiar with one language may struggle to read, let alone modify, code written in a different language. Furthermore, each modification can potentially affect other parts of the code. In general, there is a gap between the intention and the technical realization. Programming per se is already a difficult task and variability further increases this complexity since multiple features, code variations, and an exponential number of possible variants should be implemented [START_REF] Apel | Feature-Oriented Software Product Lines: Concepts and Implementation[END_REF][START_REF] Gabriela K Michelon | The life cycle of features in highlyconfigurable software systems evolving in space and time[END_REF].

In this demonstration paper, we defend the idea that generative AI and large language models (LLMs) can be leveraged to support end-users in the customization of code. We first show how generative AI can be used to customize code through prompts and instructions. In a sense, LLMs act as a new variability tool capable of transforming a high-level specification (prompt) into variable code or features. We then demonstrate LLMs' potential in building end-user tools for configuring code. Such dedicated tools for endusers do not operate over technical code and provide simplified interfaces for customization.

Throughout the demonstration, we aim to show how to transform an undocumented, technical, low-level TikZ code into a userfriendly, configurable version via a Web-based customization tool. This transformation process involves identifying and implementing explicit features, leading to a template code generator accessible to the end-user. Moreover, the Web application, written in Python, HTML, CSS, and JavaScript, is itself customizable, thanks to enduser interactions with generative AI to control the layout, the image border or size. We believe it is a first step towards democratizing variability programming, opening a path for end-users to adapt code to their needs.

Related work

LLMs such as BERT [START_REF] Devlin | BERT: Pre-training of deep bidirectional transformers for language understanding[END_REF], GPT-2 [START_REF] Radford | Language models are unsupervised multitask learners[END_REF], GPT-3 [START_REF] Brown | Language models are few-shot learners[END_REF], GPT-4 [33], PaLM [START_REF] Chowdhery | Palm: Scaling language modeling with pathways[END_REF], to name a few, are scaling to support a variety of tasks such as text generation, question-answering, arithmetic on numbers, etc. [START_REF] Du | GLaM: Efficient Scaling of Language Models with Mixture-of-Experts[END_REF][START_REF] Geva | Injecting Numerical Reasoning Skills into Language Models[END_REF][START_REF] Jiang | How Can We Know What Language Models Know[END_REF][START_REF] Rush | A Neural Attention Model for Abstractive Sentence Summarization[END_REF][START_REF] Srivastava | Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models[END_REF]. In software engineering [START_REF] Fan | Large Language Models for Software Engineering: Survey and Open Problems[END_REF][START_REF] Hou | Large language models for software engineering: A systematic literature review[END_REF], code assistants have been proposed like Alphacode, CodeParrot or Codex [START_REF] Chen | Evaluating Large Language Models Trained on Code[END_REF][START_REF] Wolf | Natural Language Processing with Transformers[END_REF] and are now deployed at scale, such as GitHub Copilot [START_REF]GitHub Copilot • Your AI pair programmer[END_REF].

The application of machine learning in Software Product Line (SPL) and variability engineering encompass various use cases [3, 17, 20, 22, 30-32, 37, 38, 40-43, 45]. These use cases include performance prediction, optimization, specialization, debugging, detection of configuration-related errors, etc. In the current study, we focus on the potential of generative artificial intelligence and LLMs that rely on transformers' technology, an advanced deep learning architecture initially developed for Natural Language Processing (NLP) applications. The adoption of NLP in SPL engineering has drawn several interests, predominantly for domain analysis and requirements engineering [START_REF] Carbonnel | L'analyse formelle de concepts: un cadre structurel pour l'étude de la variabilité de familles de logiciels[END_REF][START_REF] Ferrari | Mining commonalities and variabilities from natural language documents[END_REF][START_REF] Itzik | SOVA -A Tool for Semantic and Ontological Variability Analysis[END_REF][START_REF] Munoz | Category Theory Framework for Variability Models with Non-functional Requirements[END_REF][START_REF] Murashkin | Visualization and exploration of optimal variants in product line engineering[END_REF][START_REF] Reinhartz-Berger | Comparing functionality of software systems: An ontological approach[END_REF]. The usage of LLMs into variability has recently started to catch attention. Acher and Martinez [START_REF] Acher | Generative AI for Reengineering Variants into Software Product Lines: An Experience Report[END_REF] explored how SPL can be synthesized out of variants. Galindo et al. [START_REF] José | Large Language Models to generate meaningful feature model instances[END_REF] evaluated the ability of LLMs to synthesize valid instances of feature models. Acher et al. [START_REF] Acher | On Programming Variability with Large Language Model-based Assistant[END_REF] introduced the use of LLMs to assist developers in implementing variability in different programming languages and mechanisms. In this demonstration paper, (1) we specifically target end-users' scenarios; [START_REF] Acher | Generative AI for Reengineering Variants into Software Product Lines: An Experience Report[END_REF] we span different kinds of artifacts (not only TikZ) and replicate on different codes, engineering different generators and configurators; [START_REF] Pereira | Learning Software Configuration Spaces: A Systematic Literature Review[END_REF] we give more details about the process (feature location, template synthesis, etc.).

End-user software engineering [START_REF] Ko | The State of the Art in End-User Software Engineering[END_REF][START_REF] Mackay | Patterns of Sharing Customizable Software[END_REF], a branch of software engineering, focuses on empowering individuals who are not professional programmers to design, implement, and maintain software applications. This paper specifically considers how end-users can implement variability with the assistance of generative AI. While traditional works in end-user programming have typically focused on providing dedicated tools and notations, this research proposes two novel directions: first, relying on LLMs to construct these specialized tools, and second, considering LLMs themselves as a tool and an interface for end-users. Additionally, our approach is tailored to assist users in dealing with "unfamiliar" software-intensive artifacts, aiming to enable or simplify their customization.

Audience

We believe a demonstration of generative AI technology can be of interest for the variability community, especially when specifically targeting end-users and variability. We are targeting two kinds of users: (1) end-users that want to synthesize variants of a piece of (unfamiliar) code, automatically generate and configure variants with dedicated tools; (2) developers that want to build generators, configurators, or SPLs. Both can benefit from generative AI for some variability tasks (feature location, template synthesis, variation implementation, automated derivation of variants). The approach is also applicable to different kinds of technical artefacts and code: TikZ, HTML, CSS, JavaScript, SVG, SCAD, etc.

We share sessions (prompts used, sequences of interactions, etc.) and resulting codes: https://github.com/acherm/progvary-withgpt/ The repository contains additional examples that go beyond the end-to-end demonstration we plan to conduct. During the demonstration, the sessions will be presented, reviewed and discussed. We believe our prompts can be reused and revisited on top of different LLMs and generative AI technologies.

FROM UNFAMILIAR, NON-CUSTOMIZABLE CODE TO END-USER CUSTOMIZATION WITH LLM

We are tasked with the challenge of personalizing a squid image, developed in TikZ, a commonly utilized package within L A T E X for creating illustrations. A visual of the squid is rendered in the bottom right of Figure 2. Due to the lack of space, we refer to Listing 1 that gives a rough idea of the TikZ code. It should be noted that the original TikZ code is not subject to variation and here to produce a unique squid. The 40 lines of code are arguably hard to understand: there is no comment for describing the different parts of the squid while TikZ code combines different low-level primitives like fill, ellipse, etc. The code was found in a public forum [START_REF]Stackexchange thread about TikZ[END_REF], created by a TikZ expert, without many explanations.

Hence, the challenge is as follows: transforming the unfamiliar, non-variable code into something configurable by end-users.

Customizing code with LLM

We now detail how LLMs assisted us in customizing the TikZ code. We have used 1 ChatGPT-4 [33], using the Web chat interface of OpenAI. Using "prompts" (referred to as (User) green boxes 1 Recordings of the sessions and interactions will be made available for sharing.

), which are natural language instructions that can incorporate existing code, LLMs automatically generates programs and potential explanations (see (LLM) red boxes hereafter). We start asking about the TikZ code.

(User) What's this TikZ code is doing?

(LLM) This TikZ code defines a custom drawing or picture called "squid" using the ".pic" syntax. The code specifies the coordinates, shapes, and colors of various elements to create the image of a squid. The code consists of several parts: This block of code defines the symmetrical parts of the squid , such as the body and tentacles . It uses a custom reflect command that is not part of the standard TikZ package ( you will need the corresponding macro definition for this to work ) . The split option specifies the colors for the left and right halves of the squid . ...

\ begin { scope }[ x =3 cm /
A line-by-line technical explanation of the TikZ code is not that helpful, especially for end-users. The level of details is too low, and the explanations are not really actionable, especially for relating code elements to visual aspects.

Instead, we can directly ask what kinds of customizations we want.

(User) can you vary the eye of the squid with the blue color? tell me what to varies in the TikZ code (LLM) To change the color of the squid's eye to blue, you'll need to modify the fill commands that define the eye. The lines that define the eye are: The answer is correct. The visual and high-level description ("eyes") has been mapped to a precise line of code. The proposed variation is syntactically correct and only focuses on code parts that need to be customized. End-users can locate and implement other features related to the number of spots, the tentacles, etc. A series of prompts can be fed to an LLM that then returns the piece of code to modify and the suggested modification corresponding to a feature.

Building customizable tools with LLM

So far, end-users can customize parts of the code with LLM. However, there are some limitations:

• end-users have to manually integrate the code and follow technical instructions; • end-users can apply individual customizations but not their combinations; • interactions of LLMs can change from time to time, even with the same prompt. LLMs are by construction non-determinist, and so are corresponding suggestions of customization.

An answer to these limitations is to engineer customization tools and build an actual configurable system composed of different features. It has several benefits: (1) the integration of customized transformations can be automated; (2) features can be combined to synthesize variants; (3) the engineering of tools maturates the customization knowledge and makes it reliable. Our idea is to build customization tools with LLM.

(User) would it be possible to vary the original code using a templating engine in Python in such a way it is possible to have either eye of the squid with the blue color or the original eye (as in the original TikZ code)? ... can you parameterize the spots with a random color? if not random mode, then it's the default color Listing 2 provides an excerpt of the Python generator in charge of deriving variants out of template instantiations of Listing 1. Listing 2: Generated Python generator Once individual features have been implemented, there is then the need to combine all variations together. As TikZ has no obvious built-in mechanisms to support variation, we can implement a template-based code generator with LLM. Listing 1 shows an excerpt of the template. It should be noted that the prompt comes after the series of prompts for locating and implementing features (9 features were identified at the time of the session).

Further customization

The Python generator can then be used to synthesize a gallery of diverse squids (e.g., with random colors and scales). The generator can also be controlled through a Web application (see Figure 2). The client side offers to users the control to configure different features of a squid, while the server side internally calls the template-based generator and renders the images in SVG. During the demonstration, we will describe (1) the use of the Web configurator; (2) the effort needed to engineer it. Moreover, end-users can also customize other aspects of the Website. In the top, right-hand side of Figure 2, there is a configuration panel that controls different features: (1) layout: vertical, horizontal, or hybrid, having an effect on how the image is located w.r.t. the squid configurator panel; (2) whether there is a border on top of the image. This configuration perspective operates over the HTML and CSS. It has been typically obtained through high-level interactions describing some refinements of the Website.

In the bottom, right-hand side of Figure 2, there is another configuration panel that can customize the image (1) its relative position and the ability to move from left to right the squid; (2) its size;

(3) its padding; (4) the ability to flip or mirror the image; (5) its rotation. This configuration aspect of the squid internally operates over an SVG artefact. For each variation point, high-level instructions have been formulated to specify the intent. The variations have then been implemented by the LLM through the synthesis of JavaScript functions that manipulate the SVG. Finally, at the center of Figure 2 and below the SVG image, the variant of the TikZ code is depicted. More technical users can benefit from this code, and the idea is that end-users never interact with it. Overall, all these features and variations, including the underlying Python, HTML, CSS, and JavaScript have been synthesized through interactions with generative AI.

To summarize, Figure 2 demonstrates the final result of end-user customization of TikZ code, but also with Python, HTML, CSS, and JavaScript. We also show that the approach is applicable to other technical artefacts like SVG.

THE RISE AND FALL OF LLMS

LLMs can support end-users or developers in the following variability activities, with pros and cons. Code understanding. Gaining a thorough comprehension of a technical artifact is important before customization to ensure any edits will have the expected effect. Unfortunately, the explanations, though correct, are often too low-level and may not resonate with the intended audience (e.g., users not familiar with TikZ). Feature location. Instead of directly editing the code, users formulate prompts and LLMs can map high-level descriptions into lines of code. The promise is to raise the level of abstraction and gives to end-users the means to express their intent onto a technical artefact. The counterpart is that LLMs can be inaccurate and provide a wrong mapping, with unexpected results. In our experience, several interactions might be needed to guide or correct the LLM. A challenge, and a possible barrier for end-users, is that some interactions require a technical expertise (e.g., to report on compilation errors). Feature and variation implementation. LLMs can synthesize variants of a piece of code, aiding end-users who do not have to write code themselves. For developers, this generative approach not only boosts productivity, but is also advantageous for those unfamiliar with a particular technological domain. A risk is that the generated code can be of bad quality, leading to compilation errors or wrong implementation of a feature, and calling to debug and further interact. Another challenge arises from feature interactions: as the code base expands with added features, managing and understanding the complex interplay between them can become increasingly difficult, especially for end-users that are not supposed to deal with this kind of technical complexity. Combination of features and automated derivation. LLMs can synthesize template-based generators or configurators (including user interfaces) that provide the means to combine different features. This task falls beyond the skill set of end-users, whereas the boilerplate code can significantly enhance developers' experience. A counterpart is that LLMs might improperly handle the underlying logics, such as commonalities and dependencies between features. In our end-user scenarios, we did not use LLMs for specifying constraints across features, though some works have emerged to synthesize feature models [START_REF] José | Large Language Models to generate meaningful feature model instances[END_REF]. Code integration, back and forth. Incorporating LLM outcomes require a back-and-forth with the code base. It is an obstacle for fully automating the involvement of end-users. This iterative process often requires continuous switching and adjustments, adding layers of complexity and potential frustration for developers. The emergence of AI-based code environments can mitigate this issue. We envision specialized development environments, geared towards end-users, and capable of parsing, integrating, and executing the suggested modifications. Prompts. Specifying effective, tailored prompts for each intermediate task, ranging from code understanding to variation implementation, is essential. A research direction is to thoroughly evaluate LLMs for their robustness and sensitivity to prompts in realizing variability tasks. Existing studies suggests that prompt variations can have an impact on the quality of the generated code [START_REF] Döderlein | Copilot and Codex: Hot Temperature, Cold Prompts, or Black Magic?[END_REF][START_REF] Fan | Large Language Models for Software Engineering: Survey and Open Problems[END_REF][START_REF] Hou | Large language models for software engineering: A systematic literature review[END_REF][START_REF] Mastropaolo | On the robustness of code generation techniques: An empirical study on github copilot[END_REF]. Our goal is to maintain the possibility of informal, high-level formulations, embracing the spirit of end-user programming. However, it might well be the case that more structure and detail are needed to make an LLM effective. We envision having a systematic prompting strategy that could integrate the informal directives of end-users while offering a structured framework for more technical people.

CONCLUSION

In this demonstration, we plan to showcase how LLMs can be leveraged to support end-users in the customization of code and technical artefacts. We aim to describe how to transform an undocumented, technical, low-level TikZ into a user-friendly, configurable, Web-based customization tool written in Python, HTML, CSS, and JavaScript and itself customizable. Other demonstrations over SVG and OpenSCAD artefacts are also planned. Spanning topics from code understanding to implementing features and offering end-user configurators, the presentations will provide an opportunity to review the benefits and drawbacks of generative AI for supporting variability tasks.

  480 , y =3 cm /480]: This line begins a scope environment and scales the x and y coordinates to create a proportional drawing . ... \ reflect [ split ={ DeepOrange500 and DeepOrange700 }]{...}:

  16) circle [radius=32]; \fill [BlueGrey900] (64, 16) circle [radius=12]; To change the eye color to blue, you can replace the colors ... \fill [blue] (64, 16) circle [radius=32]; \fill [blue!60!white] (64, 16) circle [radius=12]; ...

Figure 1 :

 1 Figure 1: Three variants of a squid: original configuration, manual configuration, random configuration

  from jinja2 import Environment , FileSystemLoader import random def random_color () : color_options = [ ' Blue500 ' , ' Yellow50 ' , ' Lime900 ' , ' DeepOrange900 '] return random . choice ( color_options ) ... # Define the random_mode flag ( True for random colors , False for the default color ) random_mode = True # Define the spots o_spots = [ ... ] # Render the template with the chosen eye colors / spots crazy_tentacles = False # True original_tentacles = False # True prominent_mouth = True agressive_shading = True # Render the template with chosen values with open ( ' squid_output . tex ', 'w ') as output_file : output_file . write ( template . render ( eye_colors , spots = extra_spots , crazy_tentacles = crazy_tentacles , prominent_mouth = prominent_mouth , agressive_shading = agressive_shading , original_tentacles = original_tentacles ) )

Figure 2 :

 2 Figure 2: End-user customization of (1) TikZ code (squid) (2) HTML/CSS (Website layout) (3) SVG (post-process over the resulting image). The Python template-based generator produces a variant of the TikZ code, which is displayed, but end-users do not interact with it.

Acknowledgements. We thank reviewers for their valuable suggestions for future work.