Golam Sarwar

Roksana Boreli

Emmanuel Lochin

Performance of VoIP with DCCP for satellite links

We present experimental results for the performance of selected voice codecs using the Datagram Congestion Control Protocol (DCCP) with TCP-Friendly Rate Control (TFRC) congestion control mechanism over a satellite link. We evaluate the performance of both constant and variable data rate speech codecs (G.729, G.711 and Speex) for a number of simultaneous calls, using the ITU E-model and identify problem areas and potential for improvement. Our experiments are done on a commercial satellite service using a data stream generated by a VoIP application, configured with selected voice codecs and using the DCCP/CCID4 Linux implementation. We analyse the sources of packet losses which are a main contributor to reduced voice quality when using CCID4 and additionally analyse the effect of jitter which is one of the crucial parameters contributing to VoIP quality and has, to the best of our knowledge, not been considered previously in the published DCCP performance results. We propose modifications to the CCID4 algorithm and demonstrate how these improve the VoIP performance, without the need for additional link information other than what is already monitored by CCID4 (which is the case for Quick Start). We also demonstrate the fairness of the proposed modifications to other flows. We identify the additional benefit of DCCP when used in VoIP admission control mechanisms and draw conclusions about the advantages and disadvantages of the proposed DCCP/ CCID4 congestion control mechanism for use with VoIP applications.

I. INTRODUCTION

Voice over IP (VoIP) has become a well established technology with a large number of operators offering services and an ever growing number of end users. A large proportion of VoIP services use the public Internet, rather than a globally reserved bandwidth. This presents a problem both for the VoIP quality and the congestion of public Internet, as VoIP most commonly uses the UDP protocol which has no congestion control and has no concept of fairness to other flows which share the same networks.

To bridge the gap between UDP and TCP, which is a reliable transport protocol and is not suitable for real time traffic, a new transport protocol for multimedia applications, Datagram Congestion Control Protocol (DCCP), has been proposed by IETF [START_REF] Kohler | Datagram Congestion Control Protocol (DCCP), IETF[END_REF]. The main driver for having congestion control in an unreliable transport protocol was fairness to TCP traffic, which constitutes majority of the traffic on any Internet link. DCCP includes multiple congestion control algorithms identified by the Congestion Control ID (CCID), so that the application not needing reliable transport can select the appropriate congestion control method. CCID3 [START_REF] Floyd | Profile for Datagram Congestion Control Protocol (DCCP) Congestion Control ID 3: TCP-Friendly Rate Control (TFRC), IETF[END_REF] and its small packet variant CCID4 [START_REF] Floyd | Profile for Datagram Congestion Control Protocol (DCCP) Congestion Control ID 4: the Small-Packet Variant of TFRC Congestion Control, IETFWork[END_REF] rely on the TCP-Friendly Rate Control (TFRC) algorithm which is suitable for traffic with smooth changes in sending rates, such as telephony or video streaming. The TFRC is based on the TCP throughput equation [START_REF] Handley | TCP Friendly Rate Control (TFRC): Protocol Specification, IETF[END_REF] and is therefore shown to be reasonably fair when competing with TCP flows. CCID3 is more suitable for streaming applications while CCID4 has been designed for applications with small packets and is primarily applicable to VoIP.

In geographically large countries with sparse population outside of the main centres like Australia, US or Canada and also in countries with a quickly growing infrastructure like India, there has been a number of new satellite network deployments in recent times [START_REF] Floyd | Profile for Datagram Congestion Control Protocol (DCCP) Congestion Control ID 4: the Small-Packet Variant of TFRC Congestion Control, IETFWork[END_REF]- [START_REF]IPSTAR[END_REF]. These networks have an increasing amount of multimedia and real time traffic and need to be considered in developing and evaluating new protocols like DCCP.

In this paper, we present results of an experimental evaluation of the performance of selected voice codecs which use DCCP/CCID4 with TFRC congestion control over the IPSTAR satellite network [START_REF]IPSTAR[END_REF] which is operational in Australia and a large number of other countries in Asia. To the best of our knowledge, this study is the first one presenting results from live satellite network performance measurements of a real VoIP data stream using DCCP. We measure the losses and the variation in the received voice packet delay as perceived by the VoIP application and evaluate the VoIP quality under different conditions of network load using the ITU E-model [START_REF]The E-Model, a computational model for use in transmission planning[END_REF]. We also evaluate fairness to competing TCP traffic sharing the same network. To mitigate the packet loss resulting from DCCP/CCID4 congestion control, we propose a modification to the CCID4 algorithm, which, compared to an alternative proposal QuickStart [START_REF]Use of Quickstart for Improving the Performance of TFRC-SP Over Satellite Networks[END_REF], does not require any additional information in regards to the link rate from the receiver. We demonstrate that the modification results in a significantly improved VoIP quality compared to the original CCID4, while still preserving the farness advantage to other flows that CCID4 has over UDP.

The rest of the paper is structured as follows. Section II provides an overview of the related work and a description of the DCCP congestion control mechanism used for VoIP. Section III presents the experimental setup for live satellite tests. The following sections present experimental results, analysis of the results and our proposed modifications to the CCID4 protocol. In Section VI we present evaluation of the VoIP quality for different protocols. Section VII presents conclusions and a discussion of future work.

II. TFRC AND CONGESTION CONTROL FOR VOIP

This section presents an overview of the TFRC congestion control mechanism and a summary of related work. DCCP/CCID3 [START_REF] Floyd | Profile for Datagram Congestion Control Protocol (DCCP) Congestion Control ID 3: TCP-Friendly Rate Control (TFRC), IETF[END_REF] and DCCP/CCID4 [START_REF] Floyd | Profile for Datagram Congestion Control Protocol (DCCP) Congestion Control ID 4: the Small-Packet Variant of TFRC Congestion Control, IETFWork[END_REF] use TFRC [START_REF] Handley | TCP Friendly Rate Control (TFRC): Protocol Specification, IETF[END_REF] congestion control. In the TFRC congestion control mechanism, based on the monitored network conditions, the appropriate sending rate is computed by a combination of mechanisms in the sender and the receiver. Sender regulates the transmitted rate based on the received feedback messages which include the measured received rate, delay and an approximation of the packet loss rate. TFRC congestion control includes, similar to TCP congestion control, a slow start phase and a congestion avoidance phase. In slow start, before the sender has received any receiver feedback, the senders transmit rate X is set to one packet per second [START_REF] Floyd | Profile for Datagram Congestion Control Protocol (DCCP) Congestion Control ID 3: TCP-Friendly Rate Control (TFRC), IETF[END_REF].

This is also the minimum rate maintained by the CCID3/CCID4 sender at any time [START_REF] Floyd | Profile for Datagram Congestion Control Protocol (DCCP) Congestion Control ID 3: TCP-Friendly Rate Control (TFRC), IETF[END_REF]. After the receiver feedback is available, the senders initial rate is calculated as equation 1

X = min(4 • s, max(2 • s, 4380)) RT T (1)
Where:

• RT T is the estimated round trip time in seconds • s the packet mean size in bytes.

During the reminder of the slow start phase, the sender rate is approximately doubled with every received feedback, as per equation 2

X = max(2 • X, 2 • X recv ) (2)
Where X rec is the received reported rate in bytes/second. When the receiver reports the first error, TFRC enters the congestion avoidance phase, which uses equation 3 approximating the transmitted rate to what would be an equivalent rate of TCP under the same network conditions.

X = s • f (p, RT T ) (3)
Where,

f (p, RT T ) = 1 (RT T • p•2 3 + RT O • p•27 8 • p • (1 + 32 • p 2 )) (4
) Where,

• p is the loss event rate, between 0 and 1.0, to represent the number of loss events as a fraction of the number of packets transmitted; • RT O is the TCP retransmission timeout value in seconds. CCID4 [START_REF] Floyd | Profile for Datagram Congestion Control Protocol (DCCP) Congestion Control ID 4: the Small-Packet Variant of TFRC Congestion Control, IETFWork[END_REF] differs from CCID3 only in the congestion avoidance phase. To calculate the sending rate, in place of the packet size s in formula [START_REF]IPSTAR[END_REF], CCID4 uses a fixed packet size of 1460 bytes modified by a header correction factor, resulting in the following equation 5

X = 1460 • f (p, RT T ) • s s + oh (5)
Where,

• oh is the size of protocol overhead in Bytes. This change to the rate control ensures that the formula based rate is fair to both TCP and DCCP traffic: the rate is equivalent to the rate of TCP which would most commonly have larger packet sizes than DCCP traffic which consists of small VoIP packets; the calculated rate is reduced appropriately by the header correction factor, as the header size is significant compared to the size of the VoIP application payload.

In previous work, the performance of VoIP with DCCP/CCID4 protocol over satellite links has been studied in [START_REF] Sathiaseelan | Performance of VoIP using DCCP over a DVB-RCS Satellite Network[END_REF], [START_REF]Use of Quickstart for Improving the Performance of TFRC-SP Over Satellite Networks[END_REF], using ns-2 [START_REF]DCCP site[END_REF] simulation. The authors propose the use of Quick Start [START_REF]Methods for subjective determination of transmission quality[END_REF] and Fast Restart [START_REF]The E-Model, a computational model for use in transmission planning[END_REF] mechanisms and show that these methods provide only a partial improvement to the DCCP performance over a long delay network. In this paper, our intention was to analyse DCCP/CCID4 performance in a more dynamic environment than what has been considered in previous work and to provide additional insight into how DCCP handles real VoIP traffic.

In our previous work, we have proposed a dynamic computation of the number of sent DCCP/CCID3 feedback messages as a function of the end-to-end connection delay [START_REF] Sarwar | Jourjon Experimental performance of DCCP over live satellite and long range wireless links[END_REF]. This modification greatly improves the rate computation of DCCP/CCID3 over long delay links by increasing the responsiveness of TFRC. The latter is achieved by a more accurate and timely estimation of network parameters. In this previous work, we aimed at achieving a data rate comparable to TCP when sending or receiving a high rate data stream using CCID3. In this paper, we push further the idea of dynamic adjustments based on observed network conditions by investigating the parameters which will affect the perceived quality of VoIP carried by CCID4 over satellite links.

In the following section we present details of our experimental setup used to evaluate the VoIP performance with DCCP/CCID.

III. EXPERIMENTAL SETUP

Our experimental setup at the NICTA Laboratory in Sydney, Australia is presented in Figure 1. We use the IPSTAR satellite service, with the satellite modem connected to the remote site (client side) and through the IPSTAR satellite gateway to our gateway through the public Internet. For DCCP/CCID4, we use the experimental version of Linux kernel implementation (Aberdeen), which we have modified to include our proposed changes as described in Section V.

The VoIP application used is Asterisk Private Branch Exchange (PBX) [START_REF]Asterisk PBX[END_REF], with voice codecs commonly used in IP telephony. We use G.711 [START_REF]Pulse code modulation of voice frequencies[END_REF], Speex [START_REF]Speex codec[END_REF], with and without discontinuous transmission (DTX) and G.729 [START_REF]Coding of speech at 8 kbit/s using conjugatestructure algebraic-code-excited linear prediction (CS-ACELP)[END_REF]. The following table I lists details of the voice codecs used.

To have a fair comparison of quality with different codecs and different transport protocols, we use a pre-recoded sample of speech which is one side of a 10 min conversation. The analogue wave file is played into the VoIP PBX, encoded with Previous experimental results [START_REF] Sarwar | Jourjon Experimental performance of DCCP over live satellite and long range wireless links[END_REF] characterised the IPSTAR satellite network, which we consider a good representative of the growing number of IP based satellite services. IPSTAR uses shared access over radio channels and consequently can have both congestion and errors on the link. The network RTT and loss characterised during our long term experiments show, for small packet sizes, an average RTT of around 1000msec and a packet error rate (PER) of 0.1%, consistent with published results which indicate an operating bit error rate (BER) of 10-7 [START_REF] Thesling | Two Way Internet over IPSTAR Using Advanced Error Correctiona and Dynamic Links[END_REF]. Other satellite networks of interest would have similar or lower PER for packets of the same size, e.g. DVB-RCS [START_REF]Interaction channel for satellite distribution systems[END_REF] which has a specified BER of lower than 10-9.

The following section presents a summary of tests on IPSTAR performed for the DCCP/CCID4 and UDP protocol, the latter being currently most commonly used for VoIP applications.

IV. TEST RESULTS AND PERFORMANCE ANALYSIS

We have performed a number of experiments over the IPSTAR satellite network, for different voice codecs and under different load conditions. All experiments are of 10min duration. On IPSTAR, groups of experiments were performed at the same time to avoid differences in IPSTAR service load conditions impacting the test results.

We measure the packet loss rate and jitter values at the DCCP receiver, which we will use to calculate the VoIP quality in Section VI. We also monitor the various parameters which contribute to the DCCP/CCID4 sender rate, including RTT, loss event rate p and receiver reported rate, to assist with analysis of the results. A summary of the results from 10 IPSTAR experiments, performed for the selected number of simultaneous calls, is presented in the following table II.

It can be observed that the packet loss with CCID4 has significantly higher values than UDP. Jitter values observed in the experiments are shown in the following table III Our observations show that the main source of jitter is the network rather than the DCCP congestion control algorithm, i.e. the average and maximum jitter values do not noticeably differ between DCCP and UDP experiments.

The following section analyses the performance of DCCP in more detail and proposes an improvement to the algorithm.

A. Performance Analysis

To assist with analysis of the error rate results, we consider the potential sources of packet loss as perceived by the VoIP application. Packet loss rate at the input of the voice decoder can be broken down into the following contributing sources: 1) packet loss between the application and the transport protocol, resulting from the inability of the transport protocol rate control to provide adequate sending rate to the application; 2) packet loss on the link, which can be due to errors and/or congestion (closely related to the DCCP error event rate p);

3) the loss resulting from jitter, as the voice codec will consider all packets which arrive with incorrect timing as lost.

It is important to note that the packet loss between the application and the transport protocol will only be applicable to DCCP, as UDP does not have a specific sender rate and it just forwards application packets to the link.

For all experiments, in addition to capturing the transmitted and received data stream, we monitor the packets lost between the application and the DCCP sender and the DCCP reported losses. For the results summarised in Table II, only the experiments with G.711 had DCCP reported losses on the link and all other losses were between the application and DCCP sender. Therefore, it can be concluded that the majority of losses are caused by the inability of DCCP/CCID4 protocol to provide a high enough sending rate to the VoIP application. Additionally, as there are no reported losses, CCID4 is operating in slow start phase and never reaches the (expected and desired) congestion avoidance phase where the formula ensures TCP fairness.

The following section presents our proposals to modify the DCCP/CCID4 protocol in a way which will enable better handling of the VoIP application traffic while bearing in mid the requirements for fairness to competing TCP flows.

V. IMPROVING DCCP/CCID4 FOR LONG DELAY LINKS

By observing how the sender rate in calculated in CCID3/CCID4 phases described in Section II, it is intuitively clear that the VoIP packet losses will occur whenever there is transition from no speech to speech. Based on these observations and the experimental results presented in the previous sections, we propose to modify the CCID4 rate control in the two different ways.

In the first proposal, CCID4-N, we apply the existing CCID4 concept of replacing the measured packet size s by the equivalent packet size (of 1460 Bytes modified by the header correction factor) to the slow start phase.

Consequently, in slow start, the senders starting rate will remain one packet per second, but with the packet size modified according to our proposal. After the receiver feedback is available, the initial rate will be calculated by the following formula, which will replace formula 1 in rate calculations:

X = 4380 RT T • s s + oh (6)
The proposed modification will increase the starting rate and the initial rate, which will result in less packet loss in the initial stage of VoIP transmission and in transitions between silence and speech.

We also apply the CCID3 modification proposed in [START_REF] Sarwar | Jourjon Experimental performance of DCCP over live satellite and long range wireless links[END_REF], so that N feedback messages per RTT are used by the receiver in place of the default one feedback per RTT, when RTT is longer than a nominal value of e.g. 100msec. This increases the speed of rate growth in slow start phase by applying formula 5 with increased frequency and, during the congestion control phase, provides more accurate values for changes of the RTT parameter used in formula 2 by more frequent measurements.

Our second proposal, CCID4-SCA, provides further optimisation for long delay links. We enhance the CCID4-N proposal by using a nominal value of RTT, e.g. 100msec in formula 6, so the initial rate is provided by the following equation, which will replace formula 1 in DCCP rate calculations:

X = 4380 • s • s + oh (7)
The proposed modification will further increase the initial rate for links with a delay longer than 100msec, which should result in further reduction of packet loss in VoIP transmission in long delay links. As we only insert a fixed low RTT in calculating the initial rate, if the VoIP rate is too high for the potentially congested link, the standard CCID4 mechanism will detect and report errors and take DCCP into congestion control phase, which is where we want to operate in as this phase ensures long term fairness to other traffic sharing the link.

A. Performance Evaluation

The following table presents the summary of the packet error rate results from 10 IPSTAR experiments using the proposed modified CCID4 protocols, CCID4-N and CCID4-SCA. For comparison purposes we also include the CCID4 results from Table II.

It can be observed that the packet error rate is significantly reduced by our proposed CCID4 modifications. Our proposal CCID4-N enables lower rate codecs and/or a lower number of multiplexed calls to perform with minimal loss rates. For higher number of calls producing data rates above the link rate, or in congested situations, our proposals will provide congestion control in the same way as CCID4.

In the following section we evaluate the VoIP quality for the different voice codecs, using the transport protocols and network load scenarios from our experiments.

VI. EVALUATION OF VOIP QUALITY

Mean Opinion Score (MOS) is an ITU defined quality metrics for voice [START_REF]Methods for subjective determination of transmission quality[END_REF]. As MOS is a subjective measurement which cannot be easily applied to a variety of changing network conditions, ITU has also defined an objective evaluation methodology, the E-Model [START_REF]The E-Model, a computational model for use in transmission planning[END_REF], which enables evaluation of the voice quality based on measured network parameters. The E-Models quality metrics is the R factor which can be used to calculate the MOS values as per [START_REF]The E-Model, a computational model for use in transmission planning[END_REF].

We calculate the values of the R factor and MOS values using the overall packet loss rate as perceived by the voice codec at the receiving VoIP application, and measured delay. The results are shown for DCCP/CCID4, CCID4-N, CCID4-SCA and UDP, which represents the baseline performance of voice codecs over the IPSTAR satellite network. To calculate the packet loss rate resulting from jitter in the received VoIP stream, we choose a buffer size of 400 msec, as a compromise between adding delay and loosing an increasing number of packets at the voice decoder. The jitter buffer size can be varied to further compensate for high jitter values, however that will not have an impact on the difference between the performance of DCCP and UDP as measured jitter values do not differ between those protocols.

Speex is not an ITU codec and does not have the defined parameter values necessary for calculating the R factor. For the purpose of estimating the performance of Speex, we roughly approximate the quality and error resilience of a Speex codec to the corresponding parameters for the G.729 codec. We consider this approximation sufficiently accurate for the purpose of this evaluation, as the reported MOS score for the Speex codec used in our experiments is 4.1 [START_REF]Speex codec[END_REF], comparable to the MOS value of 4.18 for the G.729 codec, resulting from the E-Model and MOS calculations under the same network conditions.

Figure 2 shows the R factor for selected codecs and numbers of calls on the IPSTAR satellite network for all the transport protocols considered. The value of advantage factor used in all R factor calculations is 30. and it also has more errors with CCID4 as the higher rate change in the early part of the conversation results in more losses.

Our proposals improves the MOS values ... Overall, there will be a cost to using a transport protocol which has rate control and ensures fairness to other competing flows and we believe the changes proposed in this paper minimise this cost.

In the following section, we will evaluate the fairness of the proposed DCCP/CCID4 modifications to competing TCP flows.

VII. FAIRNESS TO OTHER FLOWS

To evaluate fairness of multiple flows, we use Jains fairness index [START_REF] Jain | The Art of Computer Systems Performance Analysis: Techniques for Experimental Design, Measurement, Simulation, and Modeling[END_REF].

As VoIP traffic is limited by the application, farness can only be considered for VoIP streams which result from a number of parallel (multiplexed) calls which would require unfair capacity when sharing the link with other flows. We compare fairness to TCP of a VoIP data stream resulting from 12 parallel G.711 calls (with a data rate higher than half the nominal link rate on the IPSTAR equivalent link). We also show the fairness to TCP of a flow with rate equivalent to the nominal link rate on the IPSTAR link To illustrate the advantage of using DCCP, we also present the fairness results for UDP. The results of the fairness test are presented in the following table VI.

It can be observed that both DCCP and DCCP-N are equally fair to a TCP flow and that UDP, as expected, takes all the bandwidth it requires regardless of other flows.

The following section presents our conclusions and ideas for future work.

VIII. CONCLUSIONS AND FUTURE WORK

We have evaluated the performance of DCCP/CCID4 on a live satellite link and proposed improvements which result in no loss of fairness to TCP traffic compared to the original CCID4, with both being fair. We have demonstrated the advantage of using DCCP over UDP when the network is shared with other TCP traffic flows as is the case in the vast majority of scenarios where VoIP is present, by evaluating a number of cases which include different voice codecs and different number of multiplexed simultaneous VoIP calls.

The main issue identified with using CCID4 for VoIP. Firstly, in majority of the cases, due to low VoIP application rate, CCID4 only operates in the slow start phase and does not use the congestion avoidance mechanism. Secondly, in periods of transition from silence to speech, depending on the rate required by the VoIP application, in most cases CCID4 cannot support the required application rate and this results in significant packet loss, particularly on long delay links.

Our proposed modifications significantly reduce the packet loss between the application and DCCP sender in a long delay environment. They could also provide similar benefits in networks which have a lower delay, in enabling a faster slow start, higher minimum rate and a more accurate parameter measurement resulting in a more responsive rate adjustment which better matches the varying network conditions. Both proposals require minimal changes to CCID4 specification and no interworking with other network components.

We would also like to point out another advantage which DCCP can provide over UDP for VoIP, in addition to fairness. DCCP awareness of transport layer losses can be used for call admission control in VoIP applications. As the number of calls increases and reaches the level where packets are lost, the DCCP measured loss rate can be used to block further calls being allowed by the VoIP application.

  21] and captured by Wireshark[25]. Our stream replicator application reads the UDP/IP payload and reproduces the timing and packet sizes of the VoIP packets. This data stream is transmitted using DCCP and captured at the receiving end for analysis of packet loss and jitter. To produce examples of multiple conversations multiplexed into one data stream, we randomly start the pre-recorded conversation and apply the IAX2 multiplexing (trunking) option.

Figure 1 .

 1 Figure 1. Experimental setup for live tests

Figure 2 .

 2 Figure 2. R factor for IPSTAR experiments, G.711, one and 12 calls, G.729, Speex, 1 and 5 calls, UDP, CCID4 and CCID4-N

We plan to extend the evaluation of DCCP to long range wireless links like WiMax and consider further improvements to CCID4 and CCID3 algorithms.

IX. ACKNOWLEDGEMENT

This research work has been supported by funding from National ICT Australia (NICTA). Authors would also like to thank IPSTAR Australia for their continuing support.


Yassine El Khessaimi

Youssef El Hafiane

Claire Peyratout

Karim Tamine

Samir Adly

Moulay Barkatou

Agnès Smith

Yassine El Khessaimi
email: yassine.el-khessaimi@unilim.fr

Youssef El

Yassine El

Towards accelerating the development of calcined clay cements: data-driven prediction of compressive strength exploiting machine learning algorithms

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The development of calcined clay cement has been receiving a particular attention from industrials and scientific researchers as an option for decreasing the CO 2 emissions coming from production of Portland cement (PC). The goal is to develop novel cements, in which the percentage of clinker is reduced as much as possible, or completely eliminated, while having materials consolidated with hopefully equivalent performances to Portland cements in terms of mechanical properties and durability. These cements consist of a mixture of clinker with gypsum, calcined clay and limestone [START_REF] Antoni | Cement substitution by a combination of metakaolin and limestone[END_REF][START_REF] Fernandez | The origin of the pozzolanic activity of calcined clay minerals: A comparison between kaolinite, illite and montmorillonite[END_REF][START_REF] Avet | Investigation of the calcined kaolinite content on the hydration of Limestone Calcined Clay Cement (LC3)[END_REF]. The major interest of these new binders lies in the substitution of clinker by calcined clay [START_REF] Rojo-López | Quaternary blends of portland cement, metakaolin, biomass ash and granite powder for production of self-compacting concrete[END_REF]. The clays are calcined between 600 and 900 °C, while the manufacture of Portland clinker requires heat treatment at about 1450 °C [START_REF] Avet | Investigation of the calcined kaolinite content on the hydration of Limestone Calcined Clay Cement (LC3)[END_REF][START_REF] Avet | Investigation of CASH composition, morphology and density in Limestone Calcined Clay Cement (LC3)[END_REF].

As a result, energy consumption and CO 2 emissions are reduced by [START_REF] Tinoco | Soil-cement mixtures reinforced with fibers: a data-driven approach for mechanical properties prediction[END_REF] to 40% [START_REF] Sharma | Limestone calcined clay cement and concrete: A state-of-the-art review[END_REF][START_REF] Zhang | Engineered Cementitious Composites (ECC) with limestone calcined clay cement (LC3)[END_REF].

It is highly difficult to model mechanical properties of calcined clay cements using empirical models, because of the complex and dynamic behavior of cement hydration, adding to that, the not complete comprehension of pozzolanic reactivity [START_REF] Cyr | Efficiency of mineral admixtures in mortars: Quantification of the physical and chemical effects of fine admixtures in relation with compressive strength[END_REF]. But, machine learning (ML) algorithms demonstrate high prediction performance for Portland cement. It should be the case for calcined clay, since ML need data as feeding input without deep theoretical considerations [START_REF] Van Damme | Concrete material science: Past, present, and future innovations[END_REF][START_REF] Luzu | Packing density of limestone calcined clay binder[END_REF].

In the last decades, data-driven methods such as ML and artificial intelligence were the solution to predict many materials properties knowing their composition and their synthesis parameters. ML approach consists of feeding an algorithm with input data to carry out models allowing the optimization of materials properties. ML was applied in many studies dedicated to predict properties of cementitious materials. This research topic can be considered as an emerging area of research. According to published documents indexed in Scopus concerning the two key words "machine learning" & "cement" [11], it can be noted that the number of articles published has increased significantly starting from 2018, to reach 123 published documents in 2021 (Figure 1). Then, to date, the peer-reviewed journal in which the largest number of papers are published is 'Construction & Building Materials' with a dozen of articles only in 2022 (Figure 2). Finally, at the international scale, China, followed by the United States and India are the largest providers of scientific articles in the field of exploiting ML to study cementitious materials (Figure 3). European countries also show significant activity.

The application of ML approach requires good comprehension of the problem and expert choice of data size and models. Several authors applied ML to predict properties of Portland cement or alkali-activated materials [START_REF] Tutmez | A data-driven study for evaluating fineness of cement by various predictors[END_REF][START_REF] Cruz | A neural network approach for predicting microstructure development in cement[END_REF][START_REF] Chen | An approach for predicting the compressive strength of cement-based materials exposed to sulfate attack[END_REF][START_REF] Kumar | Cement strength prediction using cloud-based machine learning techniques[END_REF][START_REF] Huang | Data-driven machine learning approach for exploring and assessing mechanical properties of carbon nanotube-reinforced cement composites[END_REF][START_REF] Mohanty | Estimating the strength of stabilized dispersive soil with cement clinker and fly ash[END_REF][START_REF] Verma | Kernel-based models for prediction of cement compressive strength[END_REF][START_REF] Jueyendah | Predicting the mechanical properties of cement mortar using the support vector machine approach[END_REF]. They handled different databases and parameters. These parameters are summarized in Appendix A. The size of the database is the first parameter to be considered. This size varies from tens to thousands of samples. In these studies, the most used ML algorithms were support vector regressor (SVR), random forest (RF), XGboost and artificial neural network (ANN). For example, to predict the plastic viscosity of cement, Sathyan et al. [START_REF] Sathyan | Modelling the Shear Flow Behaviour of Cement Paste Using Machine Learning-XGBoost[END_REF] used the XGboost algorithm applied to a dataset containing 252 experimental formulations of blended PC. The input parameters were cement amount, superplasticizer amount, and temperature. The ML predictions were very close to the observed results. The hydration heat of cement materials was as well the subject of ML application. Cook et al. [START_REF] Cook | Machine learning for high-fidelity prediction of cement hydration kinetics in blended systems[END_REF] used the random forest algorithm for predicting heat of hydration based on 10 input parameters. The database consisted of 7800 calorimetric measurements.

The results showed high accuracy obtained by the RF algorithm expressed by a determination coefficient of 0.93.

From the data given in Appendix A, it is worth noting that input parameters cover a broad spectrum: (i) chemical and mineralogical composition; (ii) physical properties of cement (specific surface area, microstructure and grain size); (iii) rheology of cement paste; and (iv) hardening conditions. Target parameters to judge the performance of consolidated materials are essentially: (i) composition of the hydrated cement; (ii) microstructure; (iii) compressive strength. The parameter which has been the object of prediction by ML algorithms in most of articles is the compressive strength (Appendix A), which is a justified fact. For structural purposes, the compressive strength of cement material is usually the parameter to be evaluated in the first rang before rheology and durability [START_REF] Nguyen | Influence of calcined clay reactivity on the mechanical properties and chloride diffusion resistance of limestone calcined clay cement (LC3) concrete[END_REF][START_REF] Rodriguez | Influence of calcined clay/limestone, sulfate and clinker proportions on cement performance[END_REF].

The rapid development of calcined clay cements will help to achieve as quickly as possible carbon neutrality in the cement sector. The main interest of this work is to contribute to this development through the application of novel prediction paradigm. To meet this task, the present paper aims to apply ML approach, especially supervised regression algorithms, to predict compressive strength of calcined clay cements. Then, to investigate how raw materials composition, calcination conditions of clays and hardening environment, influence the compressive strength.

Method

Experimental database

The size and the quality of the dataset are significant for the accuracy of the ML model [START_REF] Zhang | A strategy to apply machine learning to small datasets in materials science[END_REF].

An experimental database of 323 mix design (10692 data values), containing partial replacement of Portland cement with calcined clay and limestone, was compiled from previous studies that were reported in the literature [START_REF] Antoni | Cement substitution by a combination of metakaolin and limestone[END_REF][START_REF] Fernandez | The origin of the pozzolanic activity of calcined clay minerals: A comparison between kaolinite, illite and montmorillonite[END_REF][START_REF] Akindahunsi | The Influence of some calcined clays from Nigeria as clinker substitute in cementitious systems[END_REF][START_REF] Lin | Experimental studies on hydration-strengthdurability of limestone-cement-calcined Hwangtoh clay ternary composite[END_REF][START_REF] Dixit | Performance of mortar incorporating calcined marine clays with varying kaolinite content[END_REF][START_REF] Krishnan | Hydration kinetics and mechanisms of carbonates from stone wastes in ternary blends with calcined clay[END_REF][START_REF] Mishra | Influence of temperature on hydration and microstructure properties of limestone-calcined clay blended cement[END_REF][START_REF] Dhandapani | Assessment of pore structure evolution in the limestone calcined clay cementitious system and its implications for performance[END_REF][START_REF] Avet | Development of a new rapid, relevant and reliable (R3) test method to evaluate the pozzolanic reactivity of calcined kaolinitic clays[END_REF][START_REF] Msinjili | Comparison of calcined illitic clays (brick clays) and low-grade kaolinitic clays as supplementary cementitious materials[END_REF][START_REF] Alujas | Pozzolanic reactivity of low grade kaolinitic clays: Influence of calcination temperature and impact of calcination products on OPC hydration[END_REF][START_REF] Lorentz | Feasibility Study for Calcined Clay Use in the Southeast USA[END_REF][START_REF] Machner | Portland metakaolin cement containing dolomite or limestone-Similarities and differences in phase assemblage and compressive strength[END_REF]. Data splitting is a usually used method for model validation, where the dataset is split into two separate parts: the first for training, and the second for testing and validation [START_REF] Larsen | On optimal data split for generalization estimation and model selection[END_REF]. The data was randomly partitioned into training, testing and validation sets: 80% of the data was used for training and testing (258 samples) and the remaining 20% was used for validation (65 samples). This data splitting ratio (80/20) is the most adopted according to previous works in literature (Appendix A) [START_REF] Tutmez | A data-driven study for evaluating fineness of cement by various predictors[END_REF][START_REF] Cruz | A neural network approach for predicting microstructure development in cement[END_REF][START_REF] Chen | An approach for predicting the compressive strength of cement-based materials exposed to sulfate attack[END_REF][START_REF] Kumar | Cement strength prediction using cloud-based machine learning techniques[END_REF][START_REF] Huang | Data-driven machine learning approach for exploring and assessing mechanical properties of carbon nanotube-reinforced cement composites[END_REF][START_REF] Mohanty | Estimating the strength of stabilized dispersive soil with cement clinker and fly ash[END_REF][START_REF] Verma | Kernel-based models for prediction of cement compressive strength[END_REF][START_REF] Jueyendah | Predicting the mechanical properties of cement mortar using the support vector machine approach[END_REF].

The collected database is destined to link the chemical composition of raw materials, calcination conditions of the clay and hardening conditions, with the resulting compressive strength of the mortar. The corresponding data presented in literature are mostly unstructured. For example, the compressive strength values are presented in the form of histogram graphs, so the extraction of these values was carried out manually. Henceforth, during structuring the database different selection criteria were respected. This selection approach was involved by Zhang et al. [START_REF] Zhang | Chemistry-informed machine learning prediction of compressive strength for alkali-activated materials[END_REF] for other type of cement materials: Given the considerable number of oxides in each component of the calcined clay cement, the dataset has a large dimension, which affects the accuracy and robustness of the ML models.


Hence, the chemical compositions of calcined clay, limestone and Portland cement are substituted with their reactivity ratios [START_REF] Taylor | Cement chemistry[END_REF]. Chemical analysis of clinker, limestone and clays are commonly expressed in terms of weight percentages of oxides, but it is often useful to employ quantities derived from these percentages [START_REF] Zhang | Chemistry-informed machine learning prediction of compressive strength for alkali-activated materials[END_REF][START_REF] Taylor | Cement chemistry[END_REF][START_REF] Xie | A unified approach for mix design of concrete containing supplementary cementitious materials based on reactivity moduli[END_REF]. In the equations that follow, chemical formulae also denote weight percentages. The following parameters are widely used:

(1)

(2) (3) (4)
It is worth noting that RR (reactivity ratio) and HR (hydraulic ratio) are generally applied to evaluate hydraulic binding properties, while AR (alumina ratio) and SR (silica ratio) are applied to evaluate pozzolanic properties [START_REF] Zhang | Chemistry-informed machine learning prediction of compressive strength for alkali-activated materials[END_REF].

The reactivity ratio of each cement mix was defined through the weighted average as follows:

(5) (6) (7) [START_REF] Cyr | Efficiency of mineral admixtures in mortars: Quantification of the physical and chemical effects of fine admixtures in relation with compressive strength[END_REF] where is the weight percentage of each constituent in the calcined clay cement. The constituents are calcined clay, limestone and Portland cement.

Description of the data features

From the collected data [1,2,47-57], 14 input features are considered. The inputs contain the weight percentage of clay, OPC, and limestone, chemical composition of each constituent expressed in terms of reactivity ratios, calcination conditions of the clay, and hardening conditions. For the output, there is one targeted feature which is the compressive strength of the low carbon cement. Table 1 shows units and statistical parameters of the features. The analysis shows that there is no outlier or aberrant values. Thereby the data can be used as it is for the next steps of machine learning application.

Machine learning models

 Linear Regression (LR)

Linear regression is a regression model in which the target value is expected to be a linear combination of the features noted to [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF][START_REF] Ray | A quick review of machine learning algorithms[END_REF]. In mathematical notation, is the predicted value (equation ( 9)):

The vector is the model coefficients and as intercept value of the model.

Ordinary Least Squares method aims to fit a linear model with coefficients to minimize the residual sum of squares between the observed targets in the dataset, and the targets predicted by the linear approximation. Mathematically it solves a problem of the form given by equation ( 10): [START_REF] Luzu | Packing density of limestone calcined clay binder[END_REF] It is worth noting that the coefficient estimated for Ordinary Least Squares method relies on the independence of the features.

 Linear Regression with the Ridge Regularization (LR-RR)

Ridge regression addresses some of the problems of Ordinary Least Squares method by imposing a penalty on the size of the coefficients [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF][START_REF] Saunders | Ridge regression learning algorithm in dual variables[END_REF]. The ridge coefficients minimize a penalized residual sum of squares given by equation ( 11):

(11)

The complexity parameter controls the amount of shrinkage. The higher the value of , the larger is the amount of shrinkage.

 Support Vector Regressor (SVR)

The aim of SVR is to seek the hyperplane which will separate at best, then to try to estimate the target values . It amounts to determine and , such as [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF][START_REF] Smola | A tutorial on support vector regression[END_REF]: [START_REF] Sathyan | Modelling the Shear Flow Behaviour of Cement Paste Using Machine Learning-XGBoost[END_REF] where is a small positive value. Then is determined to minimize: [START_REF] Wu | Forecasting the deterioration of cement-based mixtures under sulfuric acid attack using support vector regression based on Bayesian optimization[END_REF] under the constraints [START_REF] Qi | Improving pressure drops estimation of fresh cemented paste backfill slurry using a hybrid machine learning method[END_REF] The constraints imply that all observations must be defined in a margin of . This hypothesis may lead the user to use large values, and consequently prevent the solution to adjust the scatter points. To overcome this, a spring variable is introduced to allow certain observations to be outside the margin. The problem to be solved then comes to finding ( ) that minimizes:

Here again the parameter will have to be calibrated and the kernel method is used.

Under the constraints (16)

The solution vector is written as a linear combination of support vectors:

The supporting vectors are the observations verifying  Decision Trees for Regression (DTR)

Decision Trees for Regression (DTR) are a supervised learning method used for regression [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF][START_REF] Apté | Data mining with decision trees and decision rules[END_REF]. The goal is to create a model that predicts the value of a target variable by learning simple decision rules inferred from the data features. The algorithm used to train a decision tree is called CART, for Classification And Regression Tree. It is an algorithm for partitioning space through a gluttonous, recursive and divisive approach [START_REF] Cutler | Random forests[END_REF][START_REF] Breiman | Bagging predictors[END_REF]. At each node of a decision tree built by CART corresponds a splitting variable according to which the data will be partitioned [START_REF] Song | Decision tree methods: applications for classification and prediction[END_REF]. This separator variable defines two regions, corresponding to the children of the node in question [START_REF] Azencott | Machine learning and genomics: precision medicine versus patient privacy[END_REF][START_REF] Azencott | Statistical machine learning and data mining for chemoinformatics and drug discovery[END_REF].

In the case where the separation variable is a real variable, it is then accompanied by a splitting point ( ) which is the value of the attribute against which the decision will be made.

The two regions are then: ;

At each iteration of the CART algorithm, all possible values of and, if applicable, all possible values of are used to determine that minimizes a predefined criterion.

This criterion is usually the mean square error. So, the variable and the splitting point were chosen as:

were (respectively ) is the label value associated with the region

(respectively ) at this stage, which is the average of the labels in this region.

 Random Forest (RF)

The "random forest" algorithm performs a parallel learning on multiple decision trees built randomly and driven on different subsets of data. The ideal number of trees can go up to several hundred or more [START_REF] Cutler | Random forests[END_REF][START_REF] Breiman | Random forests[END_REF]. Practically, each tree in the random forest is trained on a random part of data according to the principle of bagging, with a random part of features according to the principle of «random projections». Predictions are then averaged when the data are quantitative, as it is the case for regression [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF][START_REF] Smith | A comparison of random forest regression and multiple linear regression for prediction in neuroscience[END_REF].

Let us assume that samples are randomly collected from (the training set) with a probability of selection for each sample. These samples are called bootstrap sample

, where is an independently distributed vector. Assume that bootstrap samples ( , are chosen using the bagging algorithm and that regression trees are trained on the subsets The outputs are:

. The final output is the average value of the q outputs. The illustration of this concept is shown in Figure 4.

 eXtreme gradient boosting (XGboost)

XGboost algorithm consists on growing sequentially decision trees; each tree is grown using information from previously grown trees to progress its performance [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF][START_REF] Chen | Xgboost: A scalable tree boosting system[END_REF].

In the case of XGboost, the learning objective consists of two parts: the loss function and the regularization term. Mathematically, XGboost's learning objective may be defined as follows:

(20)

Here, is the loss function, which is the Mean Squared Error (MSE) for regression, and is the regularization function, which is a penalty term to prevent over-fitting.

The loss function, defined as the MSE for regression, can be written in summation notation, as follows:

(21)
Here, is the target value for the i th row and is the value predicted by the machine learning model for the i th row.

Let be the vector space of leaves. Then, , the function mapping the tree root to the leaves, can be recast in terms of , as follows:

(22)
Here, is the function assigning data points to leaves and T is the number of leaves.

XGboost settles on the following as the regularization function, where and are penalty constants to reduce overfitting:

 Multi-layered perceptron (MLP)

Artificial neural networks are basically systems inspired by the functioning of biological neurons [START_REF] Hopfield | Artificial neural networks[END_REF]. The most famous of these is the multi-layered perceptron (MLP), an artificial system capable of learning by the experience. It was introduced in 1957 by Franck Rosenblatt, it has only been used since 1982 after its improvement [START_REF] Rosenblatt | The perceptron: a probabilistic model for information storage and organization in the brain[END_REF][START_REF] Barto | Neuronlike adaptive elements that can solve difficult learning control problems[END_REF]. Thanks to the computational power of the 2000s, the perceptron is used in a set of neurons organized in layers (Figure 5). From one layer to another, the input signal propagates to the output, activating or not as the neurons progress.

The output formula of a hidden neuron will therefore always be of the form [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF][START_REF] Murtagh | Multilayer perceptrons for classification and regression[END_REF]: [START_REF] Lapeyre | Machine learning enables prompt prediction of hydration kinetics of multicomponent cementitious systems[END_REF] where are the weights of the system. In practice, they are randomly initialized when the neural network is created, and refers to the bias.

The contribution of an input neuron will be that the contribution of an output neuron will be

The activation function decides whether a neuron should be activated or not. Thereafter some activation functions applied for the MLP algorithm:

-Sigmoid/Logistic function (

-Tanh function

-Rectified Linear Unit (RELU) function ( 27)

Hyperparameter tuning and K-fold cross-validation

Hyperparameters are tunable parameters that allow the control of the model training process.

Hyperparameter tuning is the method of finding the hyperparameter configuration that produces the best performance of the ML algorithm. In the present work, Bayesian optimization method was used to tune hyperparameters [START_REF] Swersky | Multi-task bayesian optimization[END_REF]. The search intervals for hyperparameters tuning used in the present work are given in Table 2.

Bayesian optimization needs a prior knowledge to guess the hyperparameter [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF]. It is based on a probabilistic model matching hyperparameters with a probability function of a score on the objective function. These probability functions are defined below:

This function is also called "surrogate" of the objective function. To check whether the developed machine learning model is efficient enough to predict the outcome of a test data set, performance evaluation of the applied machine learning model was carried out using the K-fold cross-validation. This technique is basically a method of resampling the dataset in order to evaluate ML trained algorithm and to prevent overfitting and underfitting [START_REF] Refaeilzadeh | Cross-validation[END_REF]. In this technique, the parameter K is the number of different subsets into which the given data set should be divided. Additionally, K-1 subsets are used to train the model and the left-out subsets are used as the testing set. An illustration is given in Figure 6.

Model performance evaluation

The predictive performance of the applied machine learning algorithms can be evaluated using three different indicators [START_REF] Botchkarev | Performance metrics (error measures) in machine learning regression, forecasting and prognostics: Properties and typology[END_REF], which are defined as:

-Coefficient of determination (R 2 ) (29)
-Root Mean Squared Error (RMSE)

-Mean Absolute Error (MAE) [START_REF] Wang | Multivariable nonlinear predictive control of a clinker sintering system at different working states by combining artificial neural network and autoregressive exogenous[END_REF] where and are the Predicted and Tested compressive strength values, respectively; is the mean value of all the tested values; n is the total number of samples in the dataset.

The metric R 2 shows the extent of the linear correlation between the predicted and tested values. The closer R 2 is to 1, the better is the performance of the model. RMSE provides information on the deviation between the predicted values and the tested values. MAE indicates the prediction error. Among the three performance indicators, R 2 is mainly used as the representative quantity to discuss the performance of the trained models in this study.

Experimental scenarios

Different experimental scenarios were designed to simulate real cases. The goal is to predict compressive strength of different mixes of low carbon cements using the best performed ML algorithm. These scenarios have been organized in such a way to evaluate quantitatively the effect of inputs on the compressive strength. The evaluated input parameters were: (i) weight fraction of each constituent of the calcined clay cement, (ii) chemical composition of the clay, (iii) calcination conditions of the clay, (iv) and hardening conditions. It leads to the design of four scenarios. Each one contains variable inputs to be evaluated and fixed inputs. Table 3 represents this designation.

Results and discussion

Linear correlation between variables and feature importance analysis

The statistical correlations between the input features and the target are shown in Table 4.

The analysis results show that the features named age_D (hardening age) and OPC% (weight percentage of OPC) have the strongest positive correlation with the compressive strength as expected, with correlation coefficients equal to 0.50 and 0.24, respectively. This suggests that the compressive strength can possibly increase as the hardening age and weight percentage of OPC increase. The input feature named CL% (weight percentage of calcined clay) has a negative correlation of -0.21 with the compressive strength, indicating that the increase of CL% has likely a negative effect on the compressive strength. Besides, there is some weak correlation between the other features with the compressive strength.

Even if statistical correlations are useful for initial data analysis, they do not show the nonlinear dependencies between the different features and the compressive strength which is extremely important for prediction studies and that's why ML algorithms were adopted.

Feature importance analysis denotes to techniques that allocate a score to input features based on how useful they are at predicting a target variable [START_REF] Altmann | Permutation importance: a corrected feature importance measure[END_REF]. For the case of linear regression algorithms, the feature importance score is merely the coefficients of the model.

These coefficients can be used directly as a basic type of feature importance score. Based on the linear regression with Ridge regularization algorithm, the features importance is calculated and shown in Figure 7-a. The results show that RM reactivity ratio and W/B are the most important features to predict the compressive strength, whereas the hardening age (age_D) was shown as the feature with the least importance (Figure 7-a). These results do not fit with our common knowledge on cementitious materials, nor with correlation results (Table 4). It is well known that hardening age is the most impacting parameter on the development of compressive strength. This unpredictable result shown in Figure 7-a, can be explained by the difference in the standard deviation of the features (Table 1). For example, the standard deviation value of the hardening age is 41.3 MPa and that of the reactivity is 0.5, indicating a large difference between the two values, which induce errors during feature importance analysis. To correct this mismatch, all the features were rescaled using the following formula: [START_REF] Guo | Predicting mechanical properties of highperformance fiber-reinforced cementitious composites by integrating micromechanics and machine learning[END_REF] where is the rescaled variable, is the original variable, is the average, and is the standard deviation.

The normalization assumes that the input variables have the same scale, and the results of feature importance calculation can then well be interpreted. The feature importance analysis after rescaling is given in

Predictive performance of the ML algorithms

The hyperparameters of the seven selected ML algorithms are optimized using the Bayesian optimization method coupled with K-fold cross-validation. Since the iteration number is an interesting hyperparameter for MLP to optimize the calculation cost, Figure 8 shows the convergence of the prediction error using the MLP algorithm. As the iteration number increases from 1 to 5, the loss function of compressive strength decreases from 870 to 98.

As the iteration number further increases from 5 to 100, the loss function decreases from 98 to 0. Such tendency shows that 100 is a reasonable number of iterations to achieve convergence for the MLP loss function. Overfitting problems usually occur when very complex models are used with a lack of generalization for simple problems. To detect a model that overfit, it offers very good performance on training data, but does not succeed when it is actually in production, as it was the case for DTR and MLP (Figure 9). Higher R Since there is an absence of works dealing with the prediction of compressive strength of calcined clay cements, it can be difficult to compare the prediction performance results of our work with previous studies from literature. However, if the comparison is exclusively made with previous works dealing with alkali-activated materials or Portland cements, it can be worth nothing that our results agree with almost previous studies. For the prediction of compressive strength of alkali-activated cementitious materials, Zhang et al. [START_REF] Zhang | Chemistry-informed machine learning prediction of compressive strength for alkali-activated materials[END_REF] revealed that the XGboost algorithm (676 samples) performed better than SVR and DTR, with an R 2 training = 0.98 and R 2 testing = 0.94. Gomaa et al. [START_REF] Gomaa | Machine learning to predict properties of fresh and hardened alkali-activated concrete[END_REF] found that RF algorithm (202 samples) performed well for the prediction of compressive strength in the case of alkali-activated concretes. This means that although a large set of data samples might produce a better generalization of the model, the prediction accuracy can be different. In fact, the selection of adequate hyperparameter optimization method can be a crucial parameter in improving the accuracy of the algorithm. Besides, boosting algorithms confirms their high prediction accuracy for the prediction of compressive strength of OPC-MK cement mortars. Asteris et al. [START_REF] Asteris | Prediction of cement-based mortars compressive strength using machine learning techniques[END_REF] found that AdaBoost algorithm (424 samples) shows R 2 training = 0.99 and R 2 testing = 0.94, performing better than SVR, DTR and RF.

Among the seven algorithms selected in our case, XGboost algorithm presents the best prediction performance during training and testing, and thus it is selected for further prediction of compressive strength in different experimental scenarios. 11-c). This result is in good agreement with many previous studies [START_REF] Akindahunsi | The Influence of some calcined clays from Nigeria as clinker substitute in cementitious systems[END_REF][START_REF] Lin | Experimental studies on hydration-strengthdurability of limestone-cement-calcined Hwangtoh clay ternary composite[END_REF][START_REF] Msinjili | Comparison of calcined illitic clays (brick clays) and low-grade kaolinitic clays as supplementary cementitious materials[END_REF] because the major part of compressive strength development is coming from the hydration of the clinker cementitious phases, namely alite, belite, alumino-ferrite and tricalcium aluminate [START_REF] Briki | Understanding of the factors slowing down metakaolin reaction in limestone calcined clay cement (LC3) at late ages[END_REF]. It is worth noting that in the region of composition corresponding to 55-75 wt.% of OPC, 20-35 wt.% of calcined clay, and 0-15 wt.% of limestone (Figure 11), we can assign a significant increase of compressive strength. It reaches a value of 59 MPa at 28 d for 65 wt.% of OPC, 30 wt.% of calcined clay and 5 wt.% of limestone. This region of composition corresponds to the LC3 cement composition as expected. The increase of compressive strength can be explained by the presence of calcined kaolin, which through a synergetic reaction with limestone enables a denser microstructure, and consequently a higher compressive strength [START_REF] Avet | Investigation of CASH composition, morphology and density in Limestone Calcined Clay Cement (LC3)[END_REF][START_REF] Avet | Development of a new rapid, relevant and reliable (R3) test method to evaluate the pozzolanic reactivity of calcined kaolinitic clays[END_REF][START_REF] Briki | Understanding of the factors slowing down metakaolin reaction in limestone calcined clay cement (LC3) at late ages[END_REF][START_REF] Scrivener | Impacting factors and properties of limestone calcined clay cements (LC3)[END_REF]. During hydration of LC3, additional reactions occur compared with OPC. Metakaolin, the product of kaolinite calcination, reacts as a pozzolanic material, consuming Portlandite and forming mainly calcium aluminum silicate hydrate (C-A-S-H). Limestone also reacts with the calcium aluminate coming from clinker to form carboaluminate hydrates. The formation of these additional fine hydrate phases leads to a denser microstructure showing higher compressive strength [START_REF] Scrivener | Impacting factors and properties of limestone calcined clay cements (LC3)[END_REF].

In addition, in either hardening age at 3, 7 or 28 d, there is a drop of compressive strength when weight fraction of limestone ranges between 20 and 30 %, and that of calcined clay is between 20 and 40%. In comparison with experimental values of compressive strength reported in literature, the predicted compressive strength values of the present work have the same order of magnitude. For example, Antoni et al. [START_REF] Antoni | Cement substitution by a combination of metakaolin and limestone[END_REF] tested a mix containing 40 wt.% Metakaolin, 40 wt.% OPC and 20 wt.% limestone, and they found a compressive strength of 46 MPa at 28 days. Our predicted values for this mix is 47 2.5 MPa at 28 days, which confirms the prediction performance of the XGboost algorithm.

 Effect of calcination conditions of clay (scenario 2)

Given the other input features fixed, the effect of calcination conditions of clay on the compressive strength at 3, 7 and 28 d are given in Figure 12. In the calcination temperature range between 600 and 920 °C, the compressive strength shows a slight downward trend at 3 and 7 d. At 28 d, however, a drop of values is observed for a calcination temperature between 680 and 825 °C (Figure 12-c). This drop of values can be neglected considering the mean absolute error of 2.5 MPa. Above 920 °C, the compressive strength deceases drastically by 5 to 7 MPa at all hardening ages, and visually observing. This decrease corresponds to the changeover of bar color from green to blue at the three hardening ages (Figure 12). According to Rashad et al. [START_REF] Rashad | Metakaolin as cementitious material: History, scours, production and composition-A comprehensive overview[END_REF], the best calcination temperature of kaolin in order to obtain amorphous metakaolin is likely in the range of 600 to 850 °C for heating period of 2-5 h. Extending calcination temperature above 920 °C of the metakaolin does not noticeably improve its pozzolanicity [START_REF] Salvador | Pozzolanic properties of flash-calcined kaolinite: a comparative study with soak-calcined products[END_REF]. High calcination temperature can lead to the formation of non-reactive phases, namely mullite, resulting from structural rearrangement and recrystallization of the amorphous phases [START_REF] Kakali | Thermal treatment of kaolin: the effect of mineralogy on the pozzolanic activity[END_REF]. Based on solid-state NMR Studies, the reactivity of metakaolinite is at a maximum at 750-800 °C when the population of hexacoordinate Al is at a minimum and tetra-and pentacoordinate populations at a maximum [START_REF] Rocha | Solid-state NMR studies of the structure and reactivity of metakaolinite[END_REF]. Concerning the calcination duration, there is no significant effect on compressive strength at 3 and 7 d. Whereas at 28 d, the effect becomes almost more important. For example, at 800 °C (Figure 12-c), the compressive strength decreases continuously from 58 to 50 MPa when the duration goes from 3 to 0.5 h.

 Effect of chemical composition of calcined clay (scenario 3)

To evaluate the influence of chemical composition of clay on the compressive strength, Figure 13 depicts predictive compressive strength according to cement reactivity ratios. To avoid message ambiguity, only results at 28d are presented. It is noted that in this simulated experiment, the variation in reactivity ratios values is induced exclusively by variation in the clay chemistry, as the chemical composition of OPC and limestone were fixed (Table 5). At which can result in swelling and cracks [START_REF] Danner | The effect of calcite in the raw clay on the pozzolanic activity of calcined illite and smectite[END_REF]. However, substituting MK by 10-20% of calcined marl (containing 40 wt.% CaO) can be effective, because calcium hydroxide which is formed during hydration of this CaO reacts with dehydroxylated clay minerals through pozzolanic reaction to form more binding hydrates [START_REF] Rakhimov | Properties of Portland cement pastes enriched with addition of calcined marl[END_REF][START_REF] Cardinaud | Calcined clay-Limestone cements: Hydration processes with high and lowgrade kaolinite clays[END_REF]. This later case corresponds to HM between 1.6 and 1.7 (Figure 14-a andc).

Briki et al. [START_REF] Briki | Understanding of the factors slowing down metakaolin reaction in limestone calcined clay cement (LC3) at late ages[END_REF] observe a slowdown of metakaolin reaction degree when it is replaced with silica fume, which can possibly explain the decrease of compressive strength by increasing SM moduli. On another hand, the enhancement of compressive strength by increasing AM to the concrete mixture leads to an excess of free water when the mortar hardens. This free water will create a higher porosity, leading to a reduction in compressive strength. Briki et al. [START_REF] Briki | Understanding of the factors slowing down metakaolin reaction in limestone calcined clay cement (LC3) at late ages[END_REF] found that the reaction of metakaolin in calcined clay slows down after 28 days with the water to binder ratio of 0.6. Similar effect is observed for hardening temperature, in the range of 14-30 °C (Figure 14), there is no significant variation in compressive strength.

Conclusion and perspectives

This study presented the application of machine learning models on the prediction of compressive strength of calcined clay cement. For this purpose, seven algorithms of supervised machine learning were exploited to predict the compressive strength. The models were trained and tested with an experimental database of 323 mix design.

The results show that rescaling of input features is indispensable for a good interpretability of the feature importance analysis. Among the evaluated models, XGboost model was identified as the most accurate for the prediction. K-fold cross validation and Bayesian optimization method were combined to find the optimal hyperparameters of the developed XGboost model. Further, these novel machine learning results reveal that once the model is correctly trained, prediction of compressive strengh of calcined clay cement with different mixture design is possible, with mean absolute error of 2.5 MPa.

The deployment of the XGboost model shows that alumina to silica ratio (alumina ratio) of clays is the most impacting input feature on compressive strength of calcined clay cements.

Then, interesting composition domains of raw materials were identified for further optimization of calcined clay cements. Prediction of compressive strengh exploiting machine learning approach show a downtrend of strength above 920 °C, which confirms experimental results published in literature.

The original work within this paper denotes the successful feasibility of machine learning approach to predict the compressive strength of calcined clay cement which represents an interesting initial milestone for design of potential compositions. Additionally, our future studies will deal with the prediction of rheology and durability properties exploiting machine learning which constitutes a potential opportunity to improve the design optimization of this low carbon cement.



  Only articles published in journals indexed in Scopus database have been retained for data collection.  A detailed chemical composition of binders must have been clearly presented.  The mix proportion of each component of the low carbon cement must have been provided. Calcination conditions and powder fineness of the involved clay must have been provided.  A detailed description of hydration and hardening conditions must have been presented. Compressive strength of the mortar must have been established according to a normalized protocol (for example: EN 197 or ASTM C109). Mortars were prepared using a sand to cement ratio equal to 3:1.

  It is much easier to optimize than the objective function. Below are the stages for applying Bayesian optimization for hyperparameter tuning: 1-Construct a substitution probability model of the objective function; 2-Determine the hyperparameters of the surrogate model; 3-Apply these hyperparameters to the original objective function; 4-Evaluate the surrogate model using new results; 5-Repeat stages 2,3 and 4 up to a defined iterations number.

Figure 7 -

 7 b. From the figure, it can be observed that hardening age (age_D) is the most important variable affecting compressive strength. This is in alignment with the practical knowledge related to cementitious materials. The second important identified feature are alumina ratio (AM), reactivity ratio (RM) and calcination duration of the clay (time_calcin(h)). The weight fraction of OPC (%OPC) is ranked as the third important input variable. From this figure, it can be observed that the hardening relative humidity (RH_cure), water to binder ratio (W/B), calcination temperature (T_calcin) and hardening temperature (T_cure) are the least important variables. Lastly, hydraulic ratio (HM), silica ratio (SM), weight fraction of calcined clay (CL%) and weight fraction of limestone (CC%) have a negative importance on the prediction of compressive strength. These results offer new perceptions on the parameters affecting the compressive strength of calcined clay cements and open the door to further studies to better understand the governing mechanisms.

Figure 9

 9 Figure9shows the error metrics of the seven selected ML algorithms including their tuned hyperparameters. The linear regression (LR, LR-RR) and SVR models show lower R 2 with

Figure 10

 10 Figure 10 presents a comparison of predicted compressive strength and measured values

3. 3 .

 3 Figure11shows the effect of weight fraction of each constituent of the calcined clay cement

7 ( 5 (

 75 28 d, the higher compressive strength values (48 to 49.7 MPa) are attained for HM = 1.6-1.Figure13-a and c), SM = 1.8-2 (Figure13-a), RM = 2.9-3.1 (Figure13-b) and AM = 4-4.Figure13-b and c). By considering an analysis on overall values of compressive strength including low values, it can be obviously noted that predicted compressive strength at 28 d decreases by increasing SM and HM (Figure13-a and c), and it shows an upward trend by increasing AM (Figure13-b and c), without any flagrant trend for RM variation (Figure13-b).The depletion of compressive strength by increasing HM ratio, can be explained by the negative effect of CaO on the development of compressive strength. In fact, calcareous clay is often regarded as not suitable for blended cements, explained by the decomposition of CaCO 3 to CaO after calcination. During service, CaO may react with water forming Ca(OH) 2



  Figures 14 presents the effect of hardening conditions on the predicted compressive strength at (a) 3, (b) 7 and (c) 28 d. In the range of W/B between 0.4 and 0.6, the graphs indicate that

  2 values with lower RMSE and MAE values for training and testing were found for the RF and XGboost models. In particular,

	XGboost can be distinguished as the best performing model with high determination
	coefficients: R 2 training = 0.99 and R 2 testing = 0.95. XGboost shows a very close link between
	predicted and actual values with RMSE training = 2.21 MPa and RMSE testing = 11.4 MPa. And it
	exhibits a high accuracy with MAE training = 1.1 MPa and MAE testing = 2.5 MPa.

Table 5 :

 5 Chemical composition of the cement constituents used for the calculation of reactivity ratios given in Table3.

		CaO	SiO 2	Al 2 O 3 Fe 2 O 3	MgO	Na 2 O	K 2 O	CO 2	Other
										element
										s
	Kaolin	0.03 56.79 35.63	2	0.34	0.2	3.49	0	1.52
	OPC	65.2	21.27	4.57	3.25	1.62	0.08	0.76	0	3.24
		1
	Limestone	54.9	0.33	0.24	0.04	0.88	0	0.04	43.46	0.03
		8

Acknowledgement

This work is supported by institutional grants from the National Research Agency under the Investments for the future program with the reference ANR 10 LABX 0074 01 Sigma LIM.

Appendix A.

Data available in the literature concerning the application of ML for cements. The meanings of the abbreviations are given below this table*.