H Geoffroy

D Nguyen Minh

H Maitournam

J Bergues

C Putot

EVALUATION OF DRILLING PARAME TERS OF A PDC BI T

A drilling model for PDC bit is presented herein within steady bit advance hypoth esis, with taking into account influence of wear and its evolution. First, friction mechanism on cutter wear flats, is studied by experimental and numerical ap proach. It is shown to correspond to a relationship between the normal applied pressure to the cutter wear flat, and its subsequent dip angle a into the rock sur face. It is shown that frictional wear is directly influenced by bit profile. Typical results are exhibited for elliptic profiles and compared with literature.

1

Introduction

Polycrystalline Diamond Compact (PDC) bits were introduced in petroleum industry in the early 1970's. A PDC bit is composed of a multiplicity of individual cutters mounted on the surface of the bit body (Figure 1). The high rate of penetration ( RO P) of these bits is due to shearing action of cutters instead of crushing, producing faster penetration rates with less weight on bit (WOB) than roller cone bits. A sharp PDC bit will typically drill two to three times faster than the best tricone in soft formations, but such performance will gradually decrease with increasing wear.

In normal drilling conditions, e.g. under moderate temperature condition not exceeding 350°C, abrasion is the main cause of wear, resulting in growth of a wear flat on the cutter base (Glowka2). Friction on wear flat can dissipate up to 50 % of the total energy for drilling. For this reason, a better understanding of bit performance has to consider the worn tool. Although many studies have dealt with this subject in literature, the frictional mechanism generated by wear on cutters has still been overlooked.

This study is devoted to model the frictional mechanism on a single worn cutter in relation with rheology of the rock, in order to integrate it in a global drilling model. Illustrative examples are given for some bit geometries.

aNow in LGM-ENTPE, 69518 Vaulx-en-Velin, France

PDC bit

Po/ycrystalline diamond compact Eo of the order of the rock compressive strength in atmospheric conditions. We have :

(2) Ac is the cross-sectional area swept the cutter in its movement. ( is given by ( = tan(O + 1/J). 8 is the back rake angle and 1/.J the interface friction angle.

Things are not so clear for the frictional mechanism. Kunf, sets the mean normal pressure on wear flat to point load strength, Sellamii to the normal cutting stresses, and Detournay to the uniaxial compressive strength.

Alternatively, on the basis of experimental observations, Nguyen Minh 6, proposes a mechanism related to elastoplastic deformations. The author per formed drag tests on a flat based cutter on a model material standing for a plastic rock (sand mixed with paraffin). The cutter penetrates into the hor izontal rock surface with a dip angle o:, increasing with the normal applied load unless the surface bearing capacity of the sample is exceeded. This be haviour would fully represent the friction mechanism on the wear flat, but needs to be verified, namely by experimental confirmation on actual rocks and by numerical validation. This is the first objective this study, which aims at finding out, for a given elastoplastic rock behaviour, a relationship between o: and the applied forces on the wear flat. For a flat nose bit, with cutter wear flats parallel to bottom face, angle o: represents the dip angle of the helical trajectory of each cutter (Figure 3).

With a typical penetration rate ranging from 15 m/h to 60 m/h, and average 120 rev /mn rotary speed, penetration per revolution o range from 2 to 8 mm. So, for a 216 mm diameter bit, we have typically 3.10-3 <tan o: < 6.10-2

Experimental analysis

In order focus on parameter a, tests were performed with constant normal applied load (Figure 4). With regard to the small a angle involved, it would not be possible to run classical tests with constant depth of cut. A circular sample is rotated by an electric motor, allowing measurement of an average penetration slope of the cutter on a great distance, e.g. on several rounds. The cutter is mounted on a ram fixed on a rigid frame. The ram can be placed at different radii in order to simulate different cutter positions on the bit. Forces applied on the cutter are recorded by a three dimensional piezoelectric force gage, and depth of penetration by LV DT. The rock tested is-a chalk from Liege (Belgium). Its complex behaviour exhibits important plastic deformations due to the gradual breakage of t h e porous structure, bot h under h ydrostatic and deviatoric loadings. This rock was selected because of its good homogeneity and small grain size, and its low strength.

Two different tests were performed with iron cutter models, one with a sharp circular cylinder with back rake angle 20° and 13 mm diameter, to identify cutting mechanism, the other with a flat based parallelepiped 10 mm long, 3 mm large and 6 mm thick with 0° rake angle () to enhance friction mechanism. (Geoffroy 7). Depth of cut (d) versus displacement of the cutter ... 5). The sharp cutter stabilizes rapidly to a definite depth, whereas the flat based par allelepiped penetrates gradually into the rock with a mean dip angle a, which has to be related to the mean applied normal stress.

Numerical analysis of the fr ictional mechanism

Formulation Within the hypothesis of two independent mechanisms of the worn tool -cut ting and friction -the frictional contact between the cutter wear flat and the rock can be idealised by a plane strain problem, with a constant velocity mov ing rigid slider inclined by angle a on the surface of a half plane (Figure 6). The steady motion of the slider is simulated, using a specifi c steady algo rithm in plane strain finite element code. This algorithm allows, in a reference moving with the cutter, to treat the stationary problem on a fixed geometry (Maitournam 9).

Two models were used to describe elastoplastic rock mass behaviour.

A Von Mises law, as a perfect elastoplastic model, is intended to confirm the a vs Fl relationship revealed by tests, and to verify whether the "frictional mechanism" may be related to a deformation of elastoplastic type, and to show how transition to the limit point load occurs. A Cam-Clay model precises the plastic volumetric strains inside the rock medium, taking into account strain hardening and softening, pressure depen dency, dilatancy and pore collapse of chalk.

Indeed, an approximate solution of the frictional problem is obtained in two steps. First, the smooth slider is considered, 2a and p(x) are calculated for a prescribed a angle (10-3 �a� 5.10-2 rd). Then, for the frictional case (J.l = 0.5), pressure distribution p(x) already obtained in the former calculation and a shear stress distribution r(x) = J.lp(x) are prescribed on the contact length 2a, so that a mean a angle can be evaluated.

Numerical simulation data

Let P be the mean normal pressure on the slider contact area.

With Von Mises model, P initially increases with a until 2 . 10-2 rad, then reaches a stationary value, which appears to be close to the theoretical bearing capacity of a flat punch (Figure 8). In the same way, as a increases, the distribution of normal pressure p(x) under the punch tends towards a uniform distribution when limit point load is approached (Figure 7). But, with Cam-Clay model, P increases continuously, due to strain hard ening, and an ultimate bearing capacity does not appear in this case. For a given mean applied normal stress P, a: is larger if friction increases.

Plastic volumetric strains under the slider have been represented for Cam-Clay law in the smooth slider case (Figure 9). Contractant zones appear beneath the punch (pale zone, water drop shape) . Behind the punch, near the surface, a thin contractant zone appears too, overlying a more important dilatant region in the rockmass (dark zone) . However, with frictional contact, all the domain turns to be contractant.

Conclusion

We have shown that friction mechanism on cutter wear flat can be understood as an elastoplastic driven mechanism which expresses as a relationship P = f(o:) between the mean applied normal pressure P on the wear flat surface, and its subsequent dip angle a:. This angle will be locally determined by the movement of the wear flat relative to rock surface. To sum up, simplified forms can be proposed, which take into account an eventual existence of a limit load o-o:

f( o:) = o-o(l-exp ( -o:fo:o)) if a limit point load exists (3)
.... . L Jl= 0,5 a= 0,04 rad

A drill bit model

It is now possible to propose a drill bit model with taking into account wear effect and wear evolution, provided a relevant wear law be choosen. The ge ometry of the bit has first to be precised .

1 geometry of the bit

Let us define the bit profile (curve z(y)), as the locus of all the PDC centres when projected on a same fixed meridian plane (y, z), moving along with the bit on direction z {Figure 10). This profile is supposed to be a smooth curve z(y). A cutter on the bit is then defined by a point on the bit profile and its angular position (). The bit is supposed to proceed steadily, with constant rotation and advance rate.

As no viscous effects or cutting evacuation problem is considered herein, the movement of the bit can be simply described by its depth of penetration o l . It is usually admitted that wear flat develops parallel to the wall of the rock e.g. practically tangent to the axisymmetric volume defined by the bit profile, which is supported by experimental evidence (Warren, 11 ) .

Volumetric wear law is usually proposed in the general form (Glowka, 10 ) :

dVw C * Fn . h dz = Am Wlt 0 � m � 1 w ( 5
)
Where Vw is the volume of PDC cutter removed by wear, l the linear displace ment of the cutter on the rock surface, Fn the total normal force applied to the cutter, Aw the wear fl at area, and C* a wear coefficient.

Instead of this global law, since it is possible to separate the forces on the cutter, it seems reasonable to postulate a more rational law in terms of thickness � lost by wear on the cutter wear flat and shear stress F/ / Aw applied on it, as follows:

d� dl

1 F1 t CAw JJF/.. CAw ( 6
)
This law is equivalent to (5) when setting m = 0, and noticing that dVw

ii is the unit external normal to bit profile and f is the unit tangent to the helicodal trajectory of a cutter passing through the bit profile.

expressing distance increment dl in terms of the rotational frequency N gives finally :

d� (21rpNuodt) = y (l -exp ( -a(o,y)fao)) (9)
This equation appears as an intrinsic cutter wear rate, which is function of cutter position on bit profile. For a given rock, this quantity depends on the bit profile and on the bit penetration per revolution o, but not on the location and the number of cutters. (T) = (T)c + (T) f and (W) = (W)c + (W)f [START_REF] Glowka | [END_REF] It is interesting to note with Detournay3, that the global cutting forces applied to the bit do not depend on bit geometry, provided the specific energy be supposed constant for all cutters : [START_REF] Sinor | [END_REF] where (c5R*) is the rock surface swept by the bit in one revolution in a meridian plane and R* radius of the "bit cutter line profile", defined by Detournay_ 3. Indeed, radius R*, which includes existence of external cutters can be replaced by the profile . radius Rb with the maximal relative error of 2� b .

(W)f and (T)f result from summing up friction forces on cutters wear flats :

(T)f = E(yFf) and (W)I = EF1 ( 1
2 )

The cutter friction forces can be expressed as :

F1 = Awf(a) and F/ = p,F1 (13)
where Aw is the wear flat area, which shape is a truncated ellipse, given the cylindrical circular shape of the PDC cutter. This surface can be expressed in terms of the wear depth e in the normal direction to the surface of the rock wall r): with 8, rake angle, de, cutter diameter cCOS e is given from integration of (9)

7 Illustrative examples

For illustration, some simple bit geometries have been considered. Intrinsic wear distribution on the bit profile, according to equation [START_REF] Maitournam | [END_REF], is given in Figure 11 for an elliptic bit profile y2 I R2 + z2 I S2 = 1, with ellipticity Rl S = 0.57; 1; 1.74 corresponding to elongated elliptic, circular, oblate elliptic profile and for two different bit penetretion c5. Notice that for higher c5, a higher wear rate occurs for external cutters, which is currently predicted by other models in literature (Glowka 10) . But for lower c5, a reverse tendency can be noticed for the sharp elliptical profile. The model allows to find again some results observed on laboratory tests (Warren 11, Glowka 10 ) . Wear flat effect results in the upward concave curve T vs. WOB (Figure 12), illustrating the better efficiency of the bit as WOB increases, i.e., as depth of cut increases.

Conclusion

It can be considered that a reasonable understanding of mechanisms on the cutting edge and wear flat of a PDC cutter has been now achieved, so that a better modelling of PDC bit performance and better insight in wear laws can be expected. In this study, the elastoplastic nature of the frictional mechanism has been demonstrated, which expresses as a law relating the frictional stresses on wear flat contact to the movement of the bit, relatively to the rock wall.

A simplified law for this mechanism has been proposed, together with a reasonable wear law for the cutter wear flat. This has allowed to propose a PDC drill bit model which wear evolution is governed by the frictional mechanism which can be called abrasion. This model shows that wear evolution depends on the profile and on the depth of penetration per revolution. In this case, the cutter distribution on the bit has no influence with respect with the frictional wear, unless another wear law be envisaged with respect to the cutting effects.

The next step will be the validation and experimental identification of the

Figure 1 : A PDC bit 2

 12 Figure 1: A PDC bit

Figure 2 :

 2 Figure 2: Forces acting on the worn cutter.

Figure 3 :

 3 Figure 3: helical trajectory of a cutter on a flat nose bit, and a angle

Figure 4 :

 4 Figure 4: Testing apparatus

Figure 5 :

 5 Figure 5: Depth of penetration d versus distance L. a) Cutting mechanism, b) Frictional mechanism

Figure 6 :

 6 Figure 6: Wear flat model This is a frictional unilateral contact problem, with unknown contact length 2a, normal pressure condition p( x) � 0 and shear stress related to normal pressure by a Coulomb's law r(x) = J-tp(x) on contact area [ -a, a]. This problem is resolved by means of an algorithm of contact described in more details in (Geoffroy 7). It has been validated, using an analytical elastic solution of this problem (Adachi 8 ) :The steady motion of the slider is simulated, using a specifi c steady algo rithm in plane strain finite element code. This algorithm allows, in a reference moving with the cutter, to treat the stationary problem on a fixed geometry(Maitournam 9).Two models were used to describe elastoplastic rock mass behaviour. A Von Mises law, as a perfect elastoplastic model, is intended to confirm

Figure 7 :

 7 Figure 7: Evolution of the distribution of normal pressure beneath the punch for different values of penetration angle a.

  40 r-----�------�--�--� Jl�.5 VonMises 0 �------._ ______ ._ ____ �

Figure 8 :

 8 Figure 8: Po(MPa) versus or: Von Mises and Cam-Clay laws

Figure 9 : 4 )

 94 Figure 9: Cam-Clay law ; plastic volumetric zones ; Ji. == 0.5 ; or :::: 0.05 rd

4

 4

  per revo utwn m t e 1t ax1s uectwn u = � .

Figure 10 :

 10 Figure 10: Schematic diagram of bit profile in meridian plane

Awd� 4 . 3

 43 Dip angle of cutter wear fiatsIt now possible to precise angle a as a function of position of the cutter on bit profile and depth of penetration o, according to the hypothesis of wear flat parallel to bit profile (Figure10):

5

  Bit wear evolutionUsing expression (4), rate of wear expresses as:d� J.L F /. J.L<To -= --= -(1-exp(-a(o y)fao)) d[ CAw C '

6

  Global forces on the bitGlobal forces result from local integration of local forces on cutters. With similar notations as for the single cutter, Torque and Weight On Bit write :

d2 1 Aw = 2 si� 8 ( 2

 1282 arccos V(1-4(w-w 2 ))-V(w-9w 2 + 8w3-4w4) (14)w = d e 8

Figure 11 :

 11 Figure 11: Intrinsic wear distribution on the bit profile

 -----------------------


M A Hassan
email: mahssan1@ua.eng.edu

A S Malik

D Fofi

B Karasfi

F Meriaudeau

Towards Health Monitoring Using Remote Heart Rate Measurement Using Digital Camera: A Feasibility Study

Keywords: Heart Rate Measurement, Photoplethysmography, Ballistocardiography, Non-contact, Facial Imaging

The paper presents a feasibility study for heart rate measurement using a digital camera to perform health monitoring. The feasibility study investigates the reliability of the state of the art heart rate measuring methods in realistic situations. Therefore, an experiment was designed and carried out on 45 subjects to investigate the effects caused by illumination, motion, skin tone, and distance variance. The experiment was conducted for two main scenarios; human-computer interaction scenario and health monitoring scenario. The human-computer scenario investigated the effects caused by illumination variance, motion variance, and skin tone variance. The health monitoring scenario investigates the feasibility of health monitoring at public spaces (i.e. airports, subways, malls). Five state of the art heart rate measuring methods were reimplemented and tested with the feasibility study database. The results were compared with ground truth to estimate the heart rate measurement error. The heart rate measurement error was analyzed using mean error, standard deviation; root means square error and Pearson correlation coefficient. The findings of this experiment inferred promising results for health monitoring of subjects standing at a distance of 500 cm.

Introduction

Heart rate is an important parameter to estimate the physiological state of an individual/person. Traditionally electrocardiogram (ECG) and pulse oximeter attached to the fingertips or earlobes were used to measure the heart rate. These methods often caused discomfort to the patient [START_REF] Hassan | Towards health monitoring in visual surveillance[END_REF][START_REF] Poh | Non-contact, automated cardiac pulse measurements using video imaging and blind source separation[END_REF]. The ability to monitor heart rate remotely by non-contact means is a growing interest in healthcare [START_REF] Bauer | Heart rate turbulence: standards of measurement, physiological interpretation, and clinical use: International society for holter and noninvasive electrophysiology consensus[END_REF][START_REF] Zhang | Webcambased, non-contact, real-time measurement for the physiological parameters of drivers[END_REF]. The Research on remote health sensing is more focus towards personal health monitoring. The applications mainly spread through, monitoring of neonatal patients, health monitoring for ergonomics, for driving assistance, monitoring while training/exercising and monitoring during human-computer interaction [START_REF] Lin | Face-based heart rate signal decomposition and evaluation using multiple linear regression[END_REF]. The main aim is to monitor the physiological signals from patient/ individual. The heart rate, respiratory rate, breathing rate, and oxygen saturation are some of the commonly analyzed physiological parameters.

The outbreak of infectious diseases at crowd gathering has been a threat for local and global health care systems. The world health organization (WHO) defines crowd gathering as "sufficient to strain the planning and response resources of the community, state or nation hosting the event" [START_REF] Nsoesie | New digital technologies for the surveillance of infectious diseases at mass gathering events[END_REF]. Crowd gathering is part and parcel of the very existence of our civilization. However, overcrowding brings the risk of importing and exporting or locally spreading infectious diseases. The overcrowding phenomenon is common in world's largest and popular crowd gatherings; Hajj, FIFA world Cup, and Olympics [START_REF] Nsoesie | New digital technologies for the surveillance of infectious diseases at mass gathering events[END_REF].

At present infectious disease monitoring or health monitoring of crowd is performed in the form of contingency approach. Specialist utilizes technology driven modules to perform monitoring. The specialist has used technologies based on Internet-based systems, wireless sensor network, and mobile phone Figure 1: Illustration on the health monitoring methods at public spaces such as airports application and syndromic surveillance system. Fever monitoring using a thermometer or thermal camera are example of some of the common devices used to detect individuals with the infectious disease (see Fig. 1). Change in temperature of the human body is a pathological variation that occurs when the body is affected by a foreign agent (i.e. infectious disease). However, most of the infectious diseases are respiratory or cardiovascular diseases that affects the heart rate and breathing rate [START_REF] Hirsch | Respiratory sinus arrhythmia in humans: how breathing pattern modulates heart rate[END_REF][START_REF] Benkouiten | Circulation of respiratory viruses among pilgrims during the 2012 hajj pilgrimage[END_REF], such as; SARS, H1N1 influenza, swine flu, coronavirus and Ebola.

Therefore the ability to monitor the heart rate of an individual remotely would be ideal to monitor potentially infected persons from mixing with large gatherings. Recently many methods have been proposed to estimate the heart rate remotely. Kranjec et al. [START_REF] Kranjec | Novel methods for noncontact heart rate measurement: a feasibility study, Instrumentation and Measurement[END_REF], in 2014 presented a feasibility study reporting the reliability of different remote heart rate measuring methods such as; Capacitively Coupled ECG (CCECG) [START_REF] Mahdi | Non-contact biopotential sensor for remote human detection[END_REF], Microwave Distance Measurement Method (MDM) [START_REF] Lu | Contact-free measurement of heart rate variability via a microwave sensor[END_REF], and Ultrasound Distance Measurement method (UDM) [START_REF] Obeid | Multitunable microwave system for touchless heartbeat detection and heart rate variability extraction[END_REF], The feasibility study was for a variable distance between 5 cm to 60 cm. Remote heart rate measuring methods have grown rapidly, and many methods using different mediums have emerged. The technological maturity along with the reliability of each of the methods are discussed in detail in [START_REF] Kranjec | Novel methods for noncontact heart rate measurement: a feasibility study, Instrumentation and Measurement[END_REF][START_REF] Hassan | Heart rate estimation using facial video: a review[END_REF].

RGB camera based health monitoring has become one of the interesting avenues for remote health monitoring due to its inexpensive sensor and, low computational and implementation complexity. The proficiency to perform multiple sensing using single sensor has motivated researchers to make this technology sustainable [START_REF] Poh | Advancements in noncontact, multiparameter physiological measurements using a webcam[END_REF][START_REF] Hassan | Towards health monitoring in visual surveillance[END_REF]. The application and maturity of the technology are still in progress. Digital camera based heart rate measurement method operates based on two broad principles, photoplethysmography (PPG), and ballistocardiography (BCG). The digital camera based heart rate measurement method using photoplethysmography extracts physiological signals from the heart by capturing microscopic color variations of the skin, mainly the facial area [START_REF] Verkruysse | Remote plethysmographic imaging using ambient light[END_REF][START_REF] Wang | Algorithmic principles of remote-ppg[END_REF][START_REF] Hassan | Novel health monitoring method an using rgb camera[END_REF]. Ballistocardiography based methods rely on the mechanical motion of the heart. The mechanical motion contributes to a microscopic displacement of the head/face or facial skin [START_REF] Balakrishnan | Detecting pulse from head motions in video[END_REF][START_REF] Hassan | Video-based heartbeat rate measuring method using ballistocardiography[END_REF]. Many digital camera based heart rate measuring methods have been proposed using these two principles; a comprehensive survey and review on the details of the methods can be found in [START_REF] Mcduff | A survey of remote optical photoplethysmographic imaging methods[END_REF][START_REF] Hassan | Heart rate estimation using facial video: a review[END_REF].

RGB camera based heart measuring methods are mostly developed for human compute interaction (HCI) applications and fitness monitoring applications. Most of the existing public databases data are collected under controlled environment with simplistic scenarios which are not as challenging as in real world scenarios. Furthermore, to the best of our knowledge the application of health monitoring for a person from distance is an area that has not been investigated. Therefore, we performed this feasibility study to investigate real world factors that could challenge the reliability of RGB camera based heart rate measuring methods. The study investigates the reliability of the methods for challenges such as; Illumination variance and motion variance, the effects caused by different skin tones and finally, we investigate of distances variance which would be one of the major concerns on deploying RGB camera based methods for health monitoring. The remaining of the paper is discussed as follows; Section 2 describes the methodology involved in collecting the data for the feasibility study. Section 3 provides an overview of the experiment setup and Section 4 discusses the results from the experiments, and finally, the findings of this study are concluded in section 5.

Methodology of the Feasibility Study

This section mainly focuses on the methodology of the feasibility study experiment of heart rate extraction using a digital camera. Previous databases such as MANHOB-HCI database [START_REF] Tarvainen | An advanced detrending method with application to hrv analysis[END_REF], have presented data which exhibit physical motion regarding moving the head while the body remained static. Also, previous database provided emotion variations which also exhibits motion variations only with respect to the muscles movements in the face. Most of the existing databases are compiled under controlled environment. The aim of our study is to generate heart rate measurement database under realistic environment. Our experiment involved various scenarios that were similar to real-world situations emulating a realistic situation.

The database resulting from our experiment intended to investigate the effect of four real-world situations that would help us understand improve reliability of the methods for heath monitoring. The data was collected for two scenarios mainly; human-computer interaction scenario (i.e. a person sitting in front of a compute and interacting with the computer), and health monitoring scenario. The human-computer interaction scenario investigate the feasibility of issues related to real world situations; effect of Illumination variance, motion variance and the effect of different skin tone of the subject. The health monitoring scenario investigate the feasibility of heart rate measurement for subjects from various distances from the camera sensor. The health monitoring scenario was conducted by using a surveillance cameras setup.

During the experiment, 45 healthy subjects were used for data collection. bit RGB camera which records data at 30 fps with a resolution of 1080 × 1920.

The camera was mounted at 240 cm from the ground with 59 0 degree angle.

The camera sensor information is tabulated in Table . 1.

The ground truth heart rate was captured using a pulse oximeter. The Wris-tOx2 model 3150 wrist-worn pulse oximeter by Nonin Medical [22], was used to collect the heart rate (see Fig. 2). The device was highly accurate during clinical tests and during lab tests with a MDA (Medical Device Authority) approved DANTESTT DT-HW5 ECG device. The oximeter was strapped to the wrist of the subject, and the heart rate measuring sensor was attached to the index finger of the subject. The subject was asked to wear the pulse oximeter throughout the experiment, and the heart rate was monitored individually for each session in units of beats per minute (bpm).

Human-computer interaction scenario

The human-computer interaction scenario intended to investigate the feasibility of heart rate extraction at realistic situations. During this scenario we use cam 1 to record the data at 80 cm from the subject (see Fig. 3). This experiment investigated the effects caused by illumination variance, motion variance and the effect of different skin tones of the subject.

Illumination variance session

The change of light intensity of the environment correlates with the quality of the video. A high light intensity would smear an image while at the same time a low light intensity would dim an image. The facility used for data collection was illuminated by fluorescent light and light from the surrounding environment. The fluorescent light consisted of a light spectrum of 400nm to 700nm wave length [START_REF] Bielski | Phototherapy with broad spectrum white fluorescent light: a comparative study[END_REF]. During this session, we collected data considering the effect of global illumination variance, that is about three illumination intensity levels of a room. The luminance level was measured using a luminance meter T-10 [START_REF] Minolta | T-10ma illuminance meters[END_REF] the luminance level was noted as Lux and denoted as lx.

Here we estimated the heart rate for three different illumination levels ranging from 310 lx to 560 lx [START_REF] Pears | Strategic study of household energy and greenhouse issues a report for environment australia, Strategic study[END_REF]. The lighting condition was categorized into high lighting intensity between i.e. 510 to 550 lx, medium lighting intensity 430 to 470 lx and low lighting intensity between 340 to 380 lx. During this session, we used 36 subjects separating 12 subjects for each of the three sessions. The subjects were asked to sit idle with minimum physical movement facing the camera since the objective of the session is to monitor the effects caused by illumination variance. The data collection involved a period of five minutes. Therefore, the amount of melanin present in the skin pigmentation would relate to the conspicuous/ambiguous detection of the microscopic color change.

During this session, 45 subjects were used to collect the data. The subjects were divided into three groups of 15 subjects each by visually inspecting their skin tone. The three groups pertained to three major skin tones: Fair/Pale, Brown, and Black see (Fig. 4). Since the object is to determine the effect caused by the variance of skin tone, the subjects were asked to sit idle with minimum physical movement, facing the camera.

Health Monitoring Scenario

The health monitoring scenario was conducted to investigate the feasibility of health monitoring for individual/crowd at public spaces. The objective of would reduce (see Fig. 5). Therefore, the feasibility of extracting microscopic variations of the features also would reduce, which results in an uncertainty of reliability of the heart rate measuring method. During this session, the cam2 was used to record the data of 45 individuals/subjects from three different distances. The subject was asked to ascend to three distance points from the camera and was asked to stand idle with minimum physical movement, facing the camera. The subject stood idle at three points from the camera at a distance of 500 cm on point A, a distance of 700 cm on point B and a distance of 1000 cm on point C (See Fig. 6).

(a) (b) (c)

Experiment setup

We re-implemented five state of the art digital camera based heart rate measuring methods and tested them on our experimental data. The experiment consisted of two parts; Benchmarking and Feasibility study. The sensor parameters and the experimental parameters of all the session and datasets are tabulated in Table . 2 for convenient data visualization. The re-implemented 2015 [START_REF] Feng | Motion-resistant remote imaging photoplethysmography based on the optical properties of skin, Circuits and Systems for Video Technology[END_REF]. The overall experiment setup is described using a block diagram in

Benchmarking

The benchmarking of the methods were performed on two data sets; 1.

MANHOB-HCI database [START_REF] Tarvainen | An advanced detrending method with application to hrv analysis[END_REF], and 2. Neutral session of feasibility study database.

The purpose of checking the methods on MANHOB-HCI database is to demonstrate that we have correctly re-implemented the state of the art methods. Therefore, we used simplistic data of 27 subjects under a neutral condition with minimum physical movements. MAHNOB-HCI consisted of two main experiments, 'emotion elicitation'experiment, and 'implicit tagging'experiment.

During this study, we used the 'emotion elicitation'experiment since this experiments consist of sessions of longer duration.

We used the data recorded by the color camera of 61 fps (frames processed per second) at a resolution of 780 × 580. The camera was positioned in front of the subject at a distance of 40 cm. The ECG signal was recorded using three

Feasibility Study

The feasibility study experiment was conducted to investigate the main objective of this study, that is, the feasibility of the state of the art methods to operate under realistic environments. During this experiment session, the reliability of the heart rate measuring methods for illumination variance, motion variance, and skin tone variance and distance variance are investigated. The data of the 45 subjects were separated into different groups and sessions as described in the experiment design section. The effects of motion variance sessions were expressed in comparison to the reliability of neutral session of the feasibility study database for the human computer interaction scenario. The effect of skin tone variance was investigated for the human computer interaction scenario. The effect of distance variance was investigated for 45 subjects of three different distance points for the health monitoring scenario. implemented by extracting the initial frame and segmenting the foreground by using active contour model [START_REF] Chan | Active contours without edges[END_REF] to extract a binary silhouette. The color image was cropped using the binary silhouette of the detected foreground object to to the segmented image to extract the feature points. After that, the feature points were used for the face detection method that operated on the remaining of the incoming frames to reduce the face detection.

Data Preprocessing

(a) (b) (c) (d) (e) (f) (g) (h) (i)

Evaluation Metric

The

HR e (i) = |HR video (i) -HR gt (i)| (1)
Me HR = 1 N N i=1 HR e (i) (2)
SDe HR = 1 N -1 N i=1
(HR e (i) -Me HR ) 2 (3)

RMSE = N n=1 (HR e (i)) 2 N (4) r = N HR video HR gt -HR video HR gt [ NHR 2 video -( HR video ) 2 ] • 1 NHR 2 gt -( HR gt ) 2 (5)
Where N is the total number of samples and i is the sample at an instance.

HR video is the sum of the measured heart rate and HR gt is the sum of the actual heart rate and HR video HR gt is the sum of the products of the paired scores.

Results and Discussion

Reliability is an important aspect of the development of a health monitoring method. Heart rate measurement error within five bpm is an acceptable error margin [START_REF] Cecconi | A prospective study to evaluate the accuracy of pulse power analysis to monitor cardiac output 625 in critically ill patients[END_REF]. Feasibility of a method to operate at realistic situations would enable the method to be sustainable. The experiment was conducted to investigate the effect of four real-world situations; effect of Illumination variance, motion variance, and the effect of different skin tones of the subject and finally to verify the feasibility to perform health monitoring for surveillance purpose. The MANHOB-HCI database was used to benchmark the methods and to demonstrate that the methods were correctly re-implemented by us. The neutral session of the feasibility study database was used to investigate the reliability of the methods, operating from a controlled environment to realistic environment.

Benchmarking

The benchmarking of the methods using MANHOB-HCI database shows that the results reported in our experiment (see Table . 3) mainly the RMSE were similar to the results reported in [START_REF] Li | Remote heart rate measurement from face videos under realistic situations[END_REF][START_REF] Tulyakov | Selfadaptive matrix completion for heart rate estimation from face videos under realistic conditions[END_REF][START_REF] Lam | Robust heart rate measurement from video using select random patches[END_REF], therefore, demonstrating that we have correctly re-implemented the state of the art method. Measured heart rate of each of the methods was validated with the actual heart rate. The measured heart rate was estimated by extracting the power spectral density (PSD) of the PPG or BCG signal. The first harmonic of the PSD was extracted as the heart rate frequency. The heart rate frequency was multiplied by 60 to estimate the heart rate for beats per minute (bpm).

Feng et al. [START_REF] Feng | Motion-resistant remote imaging photoplethysmography based on the optical properties of skin, Circuits and Systems for Video Technology[END_REF] reported the lowest error by a mean error of 6.64 bpm with a standard deviation of 8.01 bpm. Feng et al. [START_REF] Feng | Motion-resistant remote imaging photoplethysmography based on the optical properties of skin, Circuits and Systems for Video Technology[END_REF], also reported the highest correlation coefficient between actual heart rate and the measured heart rate.

Balakrishnan et al. [START_REF] Balakrishnan | Detecting pulse from head motions in video[END_REF], reported the highest error rate by a mean error of 17 bpm with a standard deviation of 14.66 bpm. Poh et al. [START_REF] Poh | Advancements in noncontact, multiparameter physiological measurements using a webcam[END_REF] heart rate measuring method based on BSS did not perform well as to the other PPG methods heart rate error, RMSE -the root is mean square error and r-Pearson correlation coefficient [START_REF] Li | Remote heart rate measurement from face videos under realistic situations[END_REF][START_REF] Feng | Motion-resistant remote imaging photoplethysmography based on the optical properties of skin, Circuits and Systems for Video Technology[END_REF]. However, [START_REF] Poh | Advancements in noncontact, multiparameter physiological measurements using a webcam[END_REF], reported a correlation coefficient of 0.44, while conced-325 ing a high mean error. The correlation coefficient shows that [START_REF] Poh | Advancements in noncontact, multiparameter physiological measurements using a webcam[END_REF] extracted an accurate heart rate for 44% of the experiments while conceding higher error rate for the remaining experiments.

The accuracy of the heart rate measuring method reduced under the realistic environment (see Table .4) of the feasibility study database. Feng et al.

330 [START_REF] Feng | Motion-resistant remote imaging photoplethysmography based on the optical properties of skin, Circuits and Systems for Video Technology[END_REF], proposed method using adaptive green, red differentiation approach reported a mean error of 10.14 bpm and standard deviation of 11.51 bpm. The method also reported person correlation coefficient of 0.41, which shows that the 41% of the measurements were accurate. Li et al. [START_REF] Li | Remote heart rate measurement from face videos under realistic situations[END_REF] conceded a higher error rate during the feasibility study experiment. The illumination compensation method by using adaptive filter method based on the illumination of the background could be the cause of the high error rate.

The background of the controlled environment used by the MAHNOB database varies with the backdrop of the realistic environment. Therefore the assumption made by [START_REF] Li | Remote heart rate measurement from face videos under realistic situations[END_REF] for illumination compensation may not be valid for a realistic environment. The performance of the PPG methods reduced at the realistic environment. The approach of extracting the spatial mean from the ROI to generate the raw PPG signal could have contributed to the change in accuracy.

Under the realistic situation, illumination is not controlled. Therefore, it can be seen that there was a variance of the illumination intensity present at different parts of the face/ ROI (see Fig. 10(a)), compared to the illumination intensity distribution of the controlled environment (see Fig. 10(b)).

The BCG based approach of Balakrishnan et al. [START_REF] Balakrishnan | Detecting pulse from head motions in video[END_REF], method based on motion features performed better at the feasibility study database. The improvement in the correlation coefficient indicates that [START_REF] Balakrishnan | Detecting pulse from head motions in video[END_REF] method performed better under realistic conditions. The usage of motion feature compared to the gradient features may have improved the accuracy under illumination varying conditions. However [START_REF] Balakrishnan | Detecting pulse from head motions in video[END_REF] reported a high error rate. The PCA based blind source separation of the tracked features of the KLT may have contributed to the uncertainty of the accuracy. Since [START_REF] Balakrishnan | Detecting pulse from head motions in video[END_REF] extracts the BCG signal from the first five principal components and the prospective BCG signal may result in any n principle component of the n number of tracked features.

Illumination variance

The results of the illumination variance session showed that the PPG-based heart rate measuring method performed better under high lighting intensity (i.e. 510 to 550 lx) and the performance reduced as the lighting intensity reduced. Feng et al. [START_REF] Feng | Motion-resistant remote imaging photoplethysmography based on the optical properties of skin, Circuits and Systems for Video Technology[END_REF] performed well under high lighting intensity. The adaptive green and red differencing method reported the lowest mean error of 9.61 bpm (see Table . 5) with a standard deviation of 8.65 bpm. Whereas, the error rate increased as the lighting intensity decreased. The method reported a mean error of 10.86 with a standard deviation of 11.59 (see Table 6) for the medium light intensity of (i.e. 430 to 470 lx), increasing the mean error by ≈ 1 bpm with a standard deviation of ≈ 4 bpm.

For the low lighting (i.e. 340 to 380 lx) session, the method reported the highest error rate by a mean error of 13.13 bpm with a standard deviation of 12.74 bpm (see Table . 7). The results showed an increment of the error rate by a mean error of ≈ 3 bpm with a standard deviation of ≈ 3 bpm, compared to the error rate reported in the high lighting intensity session. As mentioned earlier the method [START_REF] Balakrishnan | Detecting pulse from head motions in video[END_REF] suffers in the BCG signal extraction approach after BSS. However, the Pearson correlation coefficient shows that the motion feature based method [START_REF] Balakrishnan | Detecting pulse from head motions in video[END_REF] did not exhibit any major change in accuracy during the global illumination variance experiment.

Motion variance

The motion variance experiment was highly challenging for the ROI tracking of the heart rate measuring methods. The free rigid and non-rigid motion of the person increased the error rate of the heart rate measurement. The adap- Similarly the green spectrum based PPG method [START_REF] Li | Remote heart rate measurement from face videos under realistic situations[END_REF] also failed to track the ROI at nine sessions.

The motion feature based method of [START_REF] Balakrishnan | Detecting pulse from head motions in video[END_REF] failed the most by not being able to detect the ROI at 23 sessions. The ROI loss was mainly due to rigid motion variance caused by posture variation. The motion feature based method mainly failed due to loss of feature points. The rise of the error rate for Feng et al. [START_REF] Feng | Motion-resistant remote imaging photoplethysmography based on the optical properties of skin, Circuits and Systems for Video Technology[END_REF], and Li et al. [START_REF] Li | Remote heart rate measurement from face videos under realistic situations[END_REF], was due to ROI drift (See Fig. 11). These methods used KLT feature tracking algorithm to track the detected ROI, however as the subject moved the ROI shift and the tracking algorithm failed to track the ROI to the actual location, causing ROI drift.

Also, the results showed that Li et al. [START_REF] Li | Remote heart rate measurement from face videos under realistic situations[END_REF] performed better under motion variance session compare to the neutral session by reporting a lower error rate. The temporal pruning based motion artifact removal method operated efficiently during motion variance. However, the uncertainty in the accuracy may have raised due to the PPG signal reconstruction approach used after the

Skin tone variance

The effect of skin tone variance may have a direct relationship to the nature of the feature that is used to compute the PPG or BCG signals. The adaptive green and red differencing approach of [START_REF] Feng | Motion-resistant remote imaging photoplethysmography based on the optical properties of skin, Circuits and Systems for Video Technology[END_REF], performed similarly to fair (see Table. 9) and dark skin tones (see Table. 11). The Error rate and the Pearson correlation coefficients did not vary largely for different skin tones. However the green spectrum based PPG method [START_REF] Li | Remote heart rate measurement from face videos under realistic situations[END_REF] showed an increment in error rate with a reducing Pearson correlation coefficient for the skin tones from fair to dark. Also, it was noticeable that Poh et al. [START_REF] Poh | Advancements in noncontact, multiparameter physiological measurements using a webcam[END_REF], showed a higher correlation between the actual heart rate and the measured heart rate for fair skin (0.48), brown skin (0.26) and black skin (0.31).

The BSS based approach [START_REF] Poh | Advancements in noncontact, multiparameter physiological measurements using a webcam[END_REF] using all three RGB spectral information was better compared to the signal spectral method of [START_REF] Li | Remote heart rate measurement from face videos under realistic situations[END_REF] while measuring PPG signal from different skin tones. The change in skin tone surprisingly affects the motion feature based BCG method [START_REF] Balakrishnan | Detecting pulse from head motions in video[END_REF]. The BCG based method reported a

Pearson correlation coefficient of 0.22 for fair skin, 0.25 for brown skin and 0.18 for dark skin. The usage of KLT to track the feature points may have resulted in the change in accuracy for dark skin tone since KLT tracks the motion of feature points based on the pixel intensity variation of the neighboring pixels of the feature point. The feasibility of health monitoring experiment for health monitoring was performed by measuring the heart rate, while the subject stood at different distances from the camera. The results of this experiment showed that the reliability of the heart rate measuring methods reduced as the distance of the subject from the camera increased. The lowest error rate was measured by Feng et al. [START_REF] Feng | Motion-resistant remote imaging photoplethysmography based on the optical properties of skin, Circuits and Systems for Video Technology[END_REF], the method reported a mean error of 15.32 bpm with a standard deviation of 10.11 for point A (i.e. 500 cm) (see Table . 12) and mean error of 18.23 bpm with a standard deviation of 14.24 (see Table . 13) for point B (i.e. 700 cm) and mean error of 24.06 bpm with a standard deviation of 12.84 (see Table .     14) for point C (i.e. 1000 cm).

Similarly, the Pearson correlation coefficient also reduced from 0.39 for point A (i.e. 500 cm) (see Table . 12) and 0.12 (see Table . 13) for point B (i.e. 700 cm) and 0.09 (see Table.

Conclusion

This paper presented a feasibility study on health monitoring using a digital camera. The study was mainly carried out to understand the effects of realistic conditions for the application of health monitoring which deals with health monitoring at public spaces (i.e. airports, subways, malls). The experiment was conducted on 45 subjects to assess four issues that could affect the reliability of the heart rate measuring methods at realistic situations. The feasibility was evaluated for illumination variance, motion variance, and skin tone variance and distance variance. The results were analyzed and discussed for each experiment. Five heart rate measuring methods based on five different feature selection methods were re-implemented and tested for these scenarios.

We tested the methods on the neutral session of the MANHOB-HCI database to verify that the state of the art methods were re-implemented correctly.

The methods were then tested on the data of the feasibility study. The results of the first experiment (i.e. neutral session), showed that the reliability of the methods was highly affected by the diversity of the realistic environment.

A preprocessing foreground selection step was included to all the heart rate measuring methods to narrow the ROI to operate at the realistic environment.

The reliability was mainly affected by motion artifact caused by the spatial illumination variance of the face. The experiments of the illumination variance session showed that the reliability of heart rate measuring methods based on PPG is directly proportional to the illumination level of the room. However, the motion feature based BCG method showed that the BCG based approach is invariant to illumination variance and can measure heart rate under low illumination levels.

The motion variance session was mainly affected by ROI loss and ROI drift, the face detection methods used by the heart rate measuring methods failed to detect the face during rigid motion variation and failed to track the face consistently while the body was moving. The effect of skin tone variance was significant for the PPG-based method. The BSS approach of using RGB spec-trum was able to perform better in measuring the heart rate from all three skin tones. However, the results derived from the green spectrum based method did not perform well as the other PPG method. Therefore the idea of using a function of two spectra or all three spectra may be useful in measuring the heart rate across different skin tones.

The results of the health monitoring experiment showed that the reliability of the heart rate is inversely proportional to the distance of the subject from the camera. As the subject was further apart from the camera; the size of the ROI reduced greatly. This affected the heart rate measuring methods since most of the methods generate the raw signal by estimating the spatial mean of the ROI.

Thus smaller ROI leading to poor spatial mean estimation. Also the methods were affected by the clarity of the facial features of the face while standing at a distance. This is mainly use to the camera hardware specifications, specifically the focal length. The methods were not able to operate at many sessions due to ROI loss and ROI drift issues. However, the heart rate measurement by The main idea of this study is to understand the effect of the realistic situation while measuring heart rate remotely. The heart rate measurement is performed by remotely extracting the physiological signals (BCG/PPG) from the human body. Understanding heart rate variability of these physiological signals can further derive respiratory and autonomic nervous system functions of the human body. Therefore the application of RGB camera based health monitoring would be encouraging as, developing a remote health monitoring method to monitor the physiological state of people in public spaces would prevent fatalities, the spread of communicable disease.

Figure 3 :

 3 Figure 3: Experiment setup for Human-computer interaction scenario

2. 1 . 2 .

 12 Motion variance session Motion variance from facial images related to the muscle movements within the face and change of body posture. Motion variance due to muscle movements within the face is called non-rigid motion variance and often caused by talking, smiling, yawning and expression of other facial emotions. Motion variance caused by body movement is due to changing the head orientation or by changing the posture of the body is called rigid motion variance. Either of these scenarios, results in changing the illumination level on the face and fluctuation of the ROI, ROI drift and loss of ROI. During this session, the data were collected from 45 subjects for two scenarios; During the first scenario, the subject is asked to be idle with minimum physical movement facing the camera. The second scenario, the subject was requested to use the computer and

Figure 4 :

 4 Figure 4: Description on the three different skin tones

Figure 5 :

 5 Figure 5: Description on the effect of distance for the health monitoring experiment, (A) when subject at point A, (B) when subject at point B and (C) when subject at point C

Figure 6 :

 6 Figure 6: Experiment setup for Health monitoring scenario

Fig 7 .

 7 Fig 7.

Figure 7 :

 7 Figure 7: Illustration on the overview of the experiment

  Data preprocessing was used to reduce the false positive/negative detection of the face detection algorithms used by the state of the art methods, mainly Viola-Jones face detector and Discriminative Response Map Fitting (DRMF) based face detector. The data collected for the feasibility study emulated a realistic situation and environment. Therefore, the face detector methods which

Figure 8 :

 8 Figure 8: Illustration on the diversity of the two database (a) & (b) shows the detected faces of the feasibility study, (c) shows the detected faces of the MANHOB-HCI database

Figure 9 :

 9 Figure 9: Illustration on ROI detection before and after preprocessing, (a) & (d) are the original images (g) is the preprocessed image, (b) & (c) are the face detection results of Viola-Jones & DRMF face detectors for HCI databse. (e) & (f) are the face detection results of Viola-Jones & DRMF face detectors for Feasibility databse. (h) & (i) are the face detection results of Viola-Jones & DRMF face detectors after preprocessing

Figure 10 :

 10 Figure 10: Illustration on the distribution on the illumination intensity values across the face, (a) MANHOB-HCI database & (b) Feasibility study database

Figure 11 :

 11 Figure 11: Illustration on the issue of ROI drift for the motion variance session

Figure 12 :

 12 Figure 12: Illustration on clarity of the face while object is standing at a distance (a)detected face at point A, (b) detected face at point B & (c) detected face at point C

  14) for point C (i.e. 1000 cm). The drop in the correlation coefficient can relative to average face size of the subjects varied from 25 × 90 (see Fig. 12(a)) for point A, 25 × 50 for point B (see Fig. 12(b)) and 20 × 35 for point C (see Fig. 12(c)). The methods were also affected significantly by the issues of poor ROI tracking. The methods failed to detect the ROI at many sessions causing ROI loss, and ROI drift. The number of ROI loss and ROI drift for each session is tabulated

Feng

  et al.[START_REF] Feng | Motion-resistant remote imaging photoplethysmography based on the optical properties of skin, Circuits and Systems for Video Technology[END_REF], at 500 cm point was promising. The re-implemented methods that were tested in this study were developed for controlled environments. By incorporating the ideas and the feature selection methods used by each of the methods; one can further improve the reliability of heart rate measurement for uncontrolled realistic environments.In conclusion, the computer vision aspect of selection of ROI, ROI detection, ROI loss and ROI drift and rigid motion variation and spatial illumination variance appeared to be the main problem for heart rate measuring methods to operate at the realistic environment. Future research should be conducted to address these issue. An interesting direction would be to incorporate advanced computer vision and deep learning based method to perform face/landmark detection and tracking in realistic environments. Remote health monitoring using RGB camera would provide a cheap yet highly efficient solution for health monitoring of crowd. One could perform health monitoring at bottleneck locations of public spaces (e.g. exit and entrance of train stations, malls, and airport) or by using multiple RGB cameras at checkpoints (e.g. immigration checkpoint or ticket counters) to perform individual health monitoring.

Table 1 :

 1 Camera specification of the feasibility study

	Camera	Cam1	Cam2
	Specification
	Color filter	Bayer mosaic	Bayer mosaic
	Color model	24 bit RGB 24 bit RGB
	Frame processing speed	30 fps	30 fps
	Resolution	1080×1920 1080×1920
	Focal length	3.67 mm	3.8 mm
	Auto focus	Disabled	Disabled
	Mounting hight (from ground)	120 cm	240 cm
	Mounting angle	90

o 59 o Figure 2: WristOx2 pulse oximeter

  heart rate measured by the state of the art methods were derived in terms of absolute heart rate measurement error HR e . Heart rate measurement error is a function of the absolute difference (See Eq.1) between the heart rate measured HR video and corresponding ground truth heart rate HR gt . The ground truth was extracted from a device that is clinically approved. For MANHOB-HCI database we used the heart rate computed from the ECG signal and for the feasibility study database the heart rate was obtained from the pulse oximeter. The heart rate measurement error was validated using four statistical operators; Mean of the heart rate error Me HR (see Eq. 2), standard deviation of the heart rate error SDe HR (see Eq. 3), the root is mean square

Table 2 :

 2 Description of the Database and datasets that is used for the experiment The results were computed from the difference between the actual heart rate and measured heart rate. The Mean heart rate error signifies the overall/average accuracy limit of the heart rate measurement model regarding bpm.The standard deviation gives an overview of the fluctuation of the heart rate measurement from the mean heart rate error regarding bpm. The RMSE measures the standard deviation of the residual (i.e. the spread of the points about

	Database	Dataset	Session	Camera Specification	No. of subjects	Table No.
				Frame speed 61 fps
				Resolution 780×580
	MANHOB-HCI	Emotion elicitation Neutral	24-bit RGB		IV
				distance from subject -40
				cm
			Neutral			V
			Illumination variance -high			VI
			Illumination variance -medium			VII
		Human-computer	Illumination variance -low	Frame speed 30 fps Resolution 1080×1920		VIII
		interaction		24-bit RGB
		scenario	Motion variance	distance from subject -80		IX
				cm
			Skin tone variance -Fair			X
			Skin tone variance -Brown			XI
	Feasability study		Skin tone variance -Black			XII
				Frame speed 30 fps
				Resolution 1080×1920
			Distance point A	24-bit RGB		XIII
				distance from subject -
				500 cm
				Frame speed 30 fps
		Health monitoring scenario	Distance point B	Resolution 1080×1920 distance from subject -24-bit RGB		XIV
				700 cm
				Frame speed 30 fps
				Resolution 1080×1920
			Distance point C	24-bit RGB		XV
				distance from subject -
				1000 cm

the fitted regression line) regarding bpm. Therefore, providing an estimate of the noise that is generated by the methods. Finally, the Pearson correlation coefficient provides the linear correlation between the actual heart rate and measured heart rate by a measure of 0 to 1, where 1 been the highest correlation.

Table 3 :

 3 Performance validation of the methods for the neutral session of MANHOB-HCI database

	Method	M eHR (bpm)	SD eHR (bpm)	RMSE (bpm)	r
	Poh et al. 2010	15.24	12.82	21.08 0.34
	Poh et al. 2011	10.00	12.66	14.01 0.44
	Balakrishnan et al. 2013	17.00	14.66	22.01 0.14
	Xiaobai et al. 2014	7.14	9.53	12.47 0.53
	Feng et al. 2015	6.64	8.01	10.12 0.64
	M -mean of the heart rate error, SD -standard deviation of eHR eHR
	heart rate error, RMSE -the root is mean square error and
	r-Pearson correlation coefficient

Table 4 :

 4 Performance validation of the methods for the neutral session of Feasibility study database

	Method	M eHR (bpm)	SD eHR (bpm)	RMSE (bpm)	r
	Poh et al. 2010	31.57	23.77	39.01 0.19
	Poh et al. 2011	22.57	21.15	32.75 0.26
	Balakrishnan et al. 2013	32.57	26.10	50.48 0.23
	Li et al. 2014	23.33	18.10	36.34 0.32
	Feng et al. 2015	10.14	11.51	16.94 0.41
	M -mean of the heart rate error, SD -standard deviation of eHR eHR

Table 5 :

 5 Performance validation of the methods for the illumination variance (high) session of

	Feasibility study database
	Method	M eHR (bpm)	SD eHR (bpm)	RMSE (bpm)	r
	Poh et al. 2010	31.99	24.03	38.87 0.25
	Poh et al. 2011	26.06	28.96	37.41 0.35
	Balakrishnan et al. 2013	28.42	27.04	41.92 0.33
	Li et al. 2014	21.01	22.48	34.86 0.53
	Feng et al. 2015	9.61	8.65	13.98 0.74

Table 6 :

 6 Performance validation of the methods for the illumination variance (medium) session of

	Feasibility study database
	M
	eHR
	Method

Table 7 :

 7 Performance validation of the methods for the illumination variance (low) session of Fea-

	r

Table 8 :

 8 Performance validation of the methods for the motion variance session of Feasibility study tive green and red differentiation approach to compensate motion variance performed better compared to other PPG methods (see Table. 8).However, the overall accuracy of the heart rate measurement did reduce as indicated by the Pearson correlation coefficients of Table. 4 and Table. 8. The BSS based meth-

	database
	Method	M eHR (bpm)	SD eHR (bpm)	RMSE (bpm)	r
	Poh et al. 2010	60.69	45.99	75.74 0.11
	Poh et al. 2011	62.05	59.48	85.34 0.15
	Balakrishnan et al. 2013	85.93	56.29	102.39 0.14
	Xiaobai et al. 2014	45.02	48.35	65.54 0.06
	Feng et al. 2015	20.65	13.15	24.38	0.1

ods

[START_REF] Poh | Non-contact, automated cardiac pulse measurements using video imaging and blind source separation[END_REF][START_REF] Poh | Advancements in noncontact, multiparameter physiological measurements using a webcam[END_REF]

suffered largely due to failure in ROI tracking. The Viola-Jones face detector based face tracking method failed to track the face at 17 occasions.

Table 9 :

 9 Performance validation of the methods for the skin tone variance (fair) session of Feasibil-

	ity study database
	Method	M eHR (bpm)	SD eHR (bpm)	RMSE (bpm)	r
	Poh et al. 2010	72.83	54.32	89.69 0.11
	Poh et al. 2011	59.13	54.02	78.78 0.48
	Balakrishnan et al. 2013	92.47	56.38	107.25 0.02
	Xiaobai et al. 2014	60.96	52.40	79.16 0.29
	Feng et al. 2015	14.37	10.80	17.75 0.49

Table 10 :

 10 Performance validation of the methods for the skin tone variance (brown) session of

	Feasibility study database
	Method	M eHR (bpm)	SD eHR (bpm)	RMSE (bpm)	r
	Poh et al. 2010	29.45	25.72	37.99 0.14
	Poh et al. 2011	24.18	28.63	36.29 0.26
	Balakrishnan et al. 2013	36.76	31.45	54.14 0.25
	Li et al. 2014	26.80	22.36	34.33 0.24
	Feng et al. 2015	11.00	13.65	17.10 0.41

Table 11 :

 11 Performance validation of the methods for the skin tone variance (black) session of Fea-

	sibility study database Method Poh et al. 2010 Poh et al. 2011 Balakrishnan et al. 2013 Li et al. 2014 Feng et al. 2015	M eHR (bpm) 26.86 21.32 32.92 25.28 12.95	SD eHR (bpm) 20.96 20.33 25.65 27.51 9.37	RMSE (bpm) 36.50 0.17 r 32.65 0.31 48.71 0.18 37.36 0.19 16.49 0.44

Table 12 :

 12 Performance validation of the methods for the distance variance (point A) session of

	Feasibility study database
	Method	M eHR (bpm)	SD eHR (bpm)	RMSE (bpm)	r
	Poh et al. 2010	29.83	20.29	38.33	0.16
	Poh et al. 2011	31.27	19.81	35.90	0.22
	Balakrishnan et al. 2013	32.11	28.11	53.23	0.18
	Li et al. 2014	27.71	22.32	39.95	0.24
	Feng et al. 2015	15.32	10.11	19.51	0.39

Table 13 :

 13 Performance validation of the methods for the distance variance (point B) session of

		Feasibility study database
			M	SD	RMSE
			eHR	eHR
		Method				r
			(bpm)	(bpm)	(bpm)
		Poh et al. 2010	29.25	29.23	50.72	0.07
		Poh et al. 2011	28.78	24.21	49.11	0.09
		Balakrishnan et al. 2013	33.47	27.40	54.97	0.04
		Li et al. 2014	30.64	23.25	46.70	0.09
		Feng et al. 2015	18.23	14.24	23.14	0.12
		in Table. 15. As the distance from the camera increased the credibility of the
		face detection methods reduced in detecting facial features therefore, causing
		ROI loss and ROI drift. Also, the distance, reduce the clarity of the pixel values,
		therefore, baffling the microscopic color changes that amount to the PPG signal
	450	generation. Similarly the motion feature based method [18], also conceded a
		high error rate and reported a low Pearson correlation coefficient. The BCG
		based approach could have also been affected by the size of the ROI. Since
		the KLT feature tracking algorithm would not be able to track the microscopic
		motion of the head as the subject, descend further from the camera.

Table 14 :

 14 Performance validation of the methods for the distance variance (point C) session of

	Feasibility study database
	Method	M eHR (bpm)	SD eHR (bpm)	RMSE (bpm)	r
	Poh et al. 2010	35.41	29.11	59.25 0.05
	Poh et al. 2011	32.32	28.55	53.07 0.09
	Balakrishnan et al. 2013	40.19	26.39	58.81 0.02
	Li et al. 2014	32.19	24.74	44.67 0.09
	Feng et al. 2015	24.06	12.84	27.19 0.09

Table 15 :

 15 Tabulation of the number of ROI loss and ROI drift occurrence for the health monitoring

	experiment
	Session Method	ROI loss ROI drift
		Poh et al 2010	16	0
		Poh et al. 2011	16	0
	Point A	Balakrishnan et al. 2014	19	9
		Li et al. 2014	13	5
		Feng et al. 2015	13	5
		Poh et al 2010	21	0
		Poh et al. 2011	21	0
	Point B	Balakrishnan et al. 2014	13	5
		Li et al. 2014	5	10
		Feng et al. 2015	5	10
		Poh et al 2010	23	0
		Poh et al. 2011	23	0
	Point C	Balakrishnan et al. 2014	21	4
		Li et al. 2014	13	6
		Feng et al. 2015	13	6

Acknowledgment

This experiment is supported by the graduate assistance scheme of University Teknologi PETRONAS.


Mahmoud Ali

Thomas Sayet

Alain Gasser

Eric Blond

Thermomechanical Modelling of Refractory Mortarless Masonry Wall Subjected to Biaxial Compression

Mortarless refractory masonry is widely used in the steel industry for the linings of high-temperature components such as steel ladles and furnaces. Successful design of these large-sized structures requires a proper understanding of the interaction between material discontinuity introduced by the presence of mortarless joints, joints closure and reopening due to loading/unloading, and their effect on the thermomechanical response of the structure. In the present study, 3D thermomechanical models have been developed to analyze the effects of joints reopening on the thermomechanical behavior of mortarless masonry walls. Four joint patterns, with their corresponding equivalent elastic properties, have been defined based on the state of head and bed joints (open or closed). The effective elastic properties of each joint pattern have been calculated with the help of the finite element method and the strain energy-based homogenization technique. The joints reopening and closure criteria have been defined as a function of macroscopic stresses and strains. The developed material model has been implemented in a commercial finite element software and then used to analyze the thermomechanical behavior of refractory masonry walls. The numerical model has been validated by comparing the numerical results with experimental data (biaxial compression test of a flat wall). Both results are in good agreement.

Introduction

Refractory masonry is widely used in the steel industry for the linings of large-sized hightemperature components such as steel ladles and furnaces. In order to design and optimize these components, suitable numerical models are required. In previous research works, two modeling approaches of masonry with mortar joints have been developed: micro modeling and macro modeling [START_REF] Blond | New trends in the analysis of masonry structures[END_REF] , 2) . Micro-modeling approach is based on modeling the bricks and the joints separately, using different behavior laws. The mechanical properties for each constituent are usually obtained from experimental tests. The main drawback of this approach is that it  mahmoud.ali@univ-orleans.fr (Mahmoud ALI) requires large computation time and high cost and, therefore, it is suitable for small sized structures.

Regarding the second approach (macro modeling), the masonry structure (brick, mortar and brickmortar interface) is considered as a homogeneous medium. The mechanical properties are determined from experimental tests. A macro model is very effective from the computation time point of view. However, it is often not suitable to describe the micromechanics occurring at the local scale.

In case of mortarless masonry structures, very few numerical and/or analytical studies exist. Most of them are based on detailed micro modeling approach. However, previous numerical models are not suitable for modeling the linings of large-sized structures such as steel ladle and furnaces due to high computation time and cost. For example, Thanoon et al. [START_REF] Thanoon | Finite element analysis of interlocking mortarless hollow block masonry prism[END_REF] developed a micro numerical model to investigate the effects of dry joints imperfections and progressive contact on the mechanical behavior of a hollow mortarless concrete masonry block. Similarly, Ngapeya et al. [START_REF] Chewe Ngapeya | Impact of the height imperfections of masonry blocks on the load bearing capacity of drystack masonry walls[END_REF]) developed a 3D micro numerical model to study the effects of height imperfection on the load-bearing capacity of a mortarless stack masonry wall.

The present work is a continuity of previous works carried out by Gasser et al. [START_REF] Gasser | Modelling of joint effects on refractory lining behaviour[END_REF] and Nguyen et al. [START_REF] Nguyen | Mechanical homogenisation of masonry wall without mortar[END_REF] on mechanical homogenization and modeling of masonry systems with dry joints. The main objective is to develop an equivalent material model whose mechanical properties depend on the state of bed and head joints and to define suitable joint closure and reopening criteria. The developed material model has been implemented in Abaqus software and used to simulate a masonry wall under biaxial compression.

Methodology 2.1 Effective elastic properties

In order to determine the effective elastic properties, four possible joint patterns (also called jont states) are defined based on the status of bed and head joints as follows (see Fig. In case of joint pattern 1, 2 and 4, it is possible to define the mechanical properties directly from those of the brick. However, in case of joint pattern 3, the mechanical properties have been determined thanks to the homogenization technique and the Finite Element Method 'FEM'.

In order to determine the mechanical constants of joint pattern 3, a Representative Elementary Volume (REV) is chosen (see Fig. 2), then symmetric and periodic boundary conditions are applied. For the considered homogenization problem, in the linear elastic range, the macroscopic stress (  ), strain ( E ) and constitutive law can be written as follows:

1 d V V V    = =  (1) 1 d V EV V   ==  (2)
A  Σ = E (3)
Where , , , * , A V   are the local stress, local strain, volume of the representative element, the average operator, and macroscopic elasticity tensor, respectively. The number of bars above the symbol denotes the rank of the tensor. The local stress and strain in the REV with volume (V) and subjected to macroscopic strain (E) can be obtained by solving the following equations [START_REF] Cecchi | Validation of analytical multiparameter homogenization models for out-of-plane loaded masonry walls by means of the finite element method[END_REF] :

* ( ) ( ), 1 ( ( )) ( ( ) ( )) 2 ( ( )), ( ) 0, ( ) ( ) , t u x E x u x x V u x u x u x E x u x x V div x V x a y x V     =  +   =  +  =  +   =   =                (4)
A finite element software (Abaqus) has been used to solve the homogenization problem given by Eq. ( 4) and to obtain the mechanical constants. Table 1 summarizes the mechanical properties of the equivalent homogeneous material.

Table 1 mechanical properties of equivalent homogeneous material 1 .

Patte rn

1 E 2 E 3 E 12  13  23  12 G 13 G 23 G 1 0 0 b E 0 0 0 0 b G b G 2 b E 0 b E 0 b  0 0 b G b G 3 h E b E b E h  h  b  h G h G b G 4 b E b E b E b  b  b  b G b G b G

Joints closure and reopening criteria

When the masonry structure is subjected to mechanical or thermal loading, it will change from one joint pattern to another. For instance, when joint pattern 1 is subjected to compression load in direction 1, the thickness of head joints will decrease gradually until reaching zero. Then, the structure will change to pattern 2 (see Fig. 1). The corresponding joint is considered to be closed when [START_REF] Nguyen | Mechanical homogenisation of masonry wall without mortar[END_REF] :

T ij ij m E g =  (5)
Where ij m is a proportional coefficient, T ij E is the macroscopic total strain and g is the initial joint thickness. In the linear elastic range, the macroscopic total strain can be expressed as:

.

T e th E E E =+ (6)

Where e E and

. th E are the macroscopic elastic and thermal strains. After joints closure and during thermal or mechanical unloading joints can reopen if the normal stress to the joint surface is higher than zero. Head

A E A E A E A E A E A E

 = + +    = + +   (7)
Where ijkl A are the macroscopic elastic constants determined by the homogenization technique. The above-described material model has been implemented in a commercial finite element software by means of UMAT subroutine and then used to analyze the thermomechanical behavior of refractory masonry walls.

Results and Discussions

Figure 3 presents the numerical results of a masonry wall subjected to axial loading and unloading. In the beginning, bed and head joints are open and the masonry structure is in state 1. During loading, joints thickness will decrease gradually till reaching zero and masonry will change to either state 2 (X-loading) or state 3 (Y-loading). During unloading, some joints will reopen and change back to state 1. After reopening the final joint thickness is usually less than the initial one.

Figure 4 shows the biaxial compression test setup at RHI Magnesita technology center (Leoben, Austria). The test device is composed of four ceramic plates, masonry test field and four linear variable differential transformers (LVDTs). Two of the ceramic plates are fixed and the others are moving thanks to two hydraulic pistons. The pistons can either provide a constant increase in displacement or in force. Four LVDTs have been used to measure the displacement in two directions (horizontal and vertical).

A commercial finite element code (Abaqus) has been used to simulate the experimental test. Figure 5 depicts the solution domain of the experimental test. The four ceramic plates, as well as the support device, have been modeled as rigid plates. Two of them are fixed while displacement boundary conditions have been applied to the other two. The friction between the bricks and the rigid plates and between the bricks and the support device have been considered. During the first few millimeters, the LVDTs will not predict any displacement. So, a preload, in the two directions, has been applied till the sensors detect a displacement. Then, loads have been applied in both directions.

After applying the preload, the four joint patterns will be present in the masonry structure as follow (see Fig. 5): pattern 1, in all masonry far away from the moving plates, pattern 2 near the moving plate in direction 1, pattern 3 near the moving plate in direction 2, and pattern 4 near the intersection between the two moving plates.

Figure 6 shows a comparison between experimental and numerical results. As can be seen from the figure, both numerical and experimental results are in good agreement. The overall behavior of the masonry is orthotropic and nonlinear due to the gradual closure/reopening of the joints and changing from one joint pattern to another. The reaction forces, in the two directions, increase with the increase of the applied displacement due to the gradual closure of the joints and the increase of material stiffness with joints closure. The displacement in direction 2 is higher than that in direction 1 as the number of joints in direction 2 is higher than in direction 1 (13 bed joints in direction 2 and 8 head joints in direction 1). After unloading, the masonry structure will not return back to the initial configuration and there is always a permanent deformation in both directions. This can be attributed to that the final joint thickness in both directions is less than the initial one.

Conclusion

Three-dimensional thermomechanical models have been developed to analyze the effects of joints closure/reopening on the mechanical behavior of mortarless masonry walls. Four joint patterns, with their corresponding equivalent elastic properties, have been defined based on the state of head and bed joints.

The overall behavior of the masonry is orthotropic and nonlinear due to the gradual closure of joints and changing from one joint pattern to another. After unloading the final joint thickness is usually lower than the initial one and there will be a permanent deformation in both directions.

  1): Pattern 1: bed and head joints are open. Pattern 2: bed joints are open and head joints are closed. Pattern 3: bed joints are closed and head joints are open. Pattern 4: bed and head joints are closed.

1 E

 1 Youngs modulus, ν Poisson's ratio and G shear modulus. The subscript b refers to brick and h refers to computed by homogenization technique.

  *

Fig. 1 Fig. 2

 12 Fig. 1 Possible joint patterns and joint closure /reopening criteria.

Fig. 3

 3 Fig. 3 Joints closure and reopening due to X (A) and Y (B) loading and unloading.

Fig. 4 Fig. 5 Fig. 6

 456 Fig. 4 Biaxial compression test setup 6) .

Acknowledgments

This work was supported by the funding scheme of the European commission, Marie Skłodowska Curie Actions Innovative Training Networks in the frame of the project ATHOR -Advanced Thermomechanical mOdelling of Refractory linings 764987 Grant.

The authors are thankful to the Artemis cluster of Centre Val de Loire region (France) for the computation time.