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Expected Performance of a Mobile e-nose platform for Real Time Victim Localization

In this paper it is presented an analysis for the performance of the sensors of a mobile e-nose system that measures the atmospheric air, gas components’ concentrations (actually CO2 and O2), into a rubble void, where humans are entrapped, after a disastrous event that caused the collapsing of a building/construction. In this case, the entrapped humans in the void, they affect the air composition and temperature into the void. The existence of human(s) creates CO2 source(s), O2 sink(s), and heat source(s) as well (from body temperature). The existence of the entrapped humans constantly affect the air composition and temperature into the void and makes gas components’ concentrations dynamic. There will be presented the human CO2 source(s), and O2 sink(s) inside a cavity. The final goal is to estimate the concentrations of CO2 and O2 into the cavity as a function of time, having as parameters the number of entrapped humans. Estimating the concentrations it will enable the operator of a mobile e-nose system with sensors of a specific sensitivity and specificity, to determine the possibilities of detecting the presence of humans in a rubble void, nevertheless without considering the effect of weather conditions.


Introduction
Urban Search and Rescue (USaR), operations, take place after a disaster that involves partial or complete collapse of an urban structure and results in the entrapment of people-victims. The cause can be a natural disaster such as an earth quake, explosion because of equipment failure, or a terrorist action. The victims are trapped in poorly ventilated confined spaces with limited or no space to move around. A number of technologies are being used to assist, complement, or even replace the trained search and rescue dogs [1]. An e-nose system is based on surrounding air sampling and the measurement of its composition for specific gases, indicating human presence. Such an e-nose system is specifically targeted for use in confined and narrow spaces where the detecting conditions are more favourable. It takes advantage of the small air refreshing rate in the confined spaces of the rubble that allows for the existence of large variations of the air composition when a human is present in a survival space-void. Specifically, CO2 concentration it is approximately 400ppm in the atmosphere and 46.000ppm in the exhaled human breath. Concerning O2, atmospheric air has 20,946% and exhaled breath 16%. Thus at a collapsed site's cavity, when humans are trapped inside, it is expected to affect the levels of the CO2 and O2 concentrations since they could be considered as sources of CO2 and sinks of O2, thus changing the composition of the air inside the void. The number of victims in a cavity and their weight, as well as their metabolic state, they define the CO2 supply rate in the cavity (source), and also the O2 absorption rate (sink). Additionally the entire cavity where a victim is entrapped, it is not sealed. In the general case it is expected to be ventilated, allowing the escape of target particles (CO2 and O2), and the renewal of the gas mixture inside the void with fresh atmospheric air. The ventilation of a cavity, with air sources outside (could be fresh air, or, air from an adjacent cavity), is influenced by the openings of the cavity. A human detection e-nose system to be efficient in rescue operations, proper estimation of the concentrations of the target gases/substances to be detected in a specific cavity, it is crucial. Various sensor technologies have different limits of detection (noise floor of the sensors). The differentiation of the concentrations of CO2 and O2 inside the void, in comparison with those in fresh atmospheric air, should be above the e-nose sensors' noise floors, so to be feasible to reveal information about the presence of victims inside a cavity under investigation. Section 2 of the paper formulates the problems that have to be solved and section 3 estimates the anticipated concentration of CO2 and O2 into a void/cavity as a function of time (in the rest of the paper the terms void and cavity are used as equivalent). Section 4 examines the anticipated performance of an e-nose system considering various cases of entrapped humans in a void, the characteristics of the CO2 and O2 sensors and their noise floor detection limits. Section 5 concludes the paper.

Formulation of the problems to solve
In this section we discuss how to formulate the problem and get the individual mathematical representation to solve. The entire void is considered as a confined space of constant volume Vc. Entrapped humans, will be considered as sources of exhaled air and sinks of cavity's air at the same time. Taking into account those sources and sinks of air of the void, and assuming that the movement of air molecules inside of it creates a uniform distribution, then the mean concentrations of CO2 and O2 inside the void, could be estimated. Assuming that all air inside the void is mixed perfectly within the entire volume of it and that all particles have a uniform distribution, it is sufficient to estimate theoretically the concentration mean values for CO2 and O2 inside the void and then by comparing them with the sensors' noise floor, to decide about investigating further a cavity. The sampled and measured air (near the air entrance of the e-nose system), could be assumed that represents all the air in the cavity under investigation and the differentiation of the concentrations of CO2 and O2 inside the void, has to be higher than the e-nose system's detection limits, so to be detectable.

Estimation of mean concentrations in a cavity as function of time
There had to be studied CO2 and O2 sources and sinks to estimate the mean concentrations as a function of time. Concerning the initial conditions of the problem, after the collapsing of a building because of an abrupt catastrophic event, the composition of the atmospheric air inside the created voids/cavities in the rubble, it is assumed to be near the same composition as that of the atmospheric air out of the cavities (400ppm for CO2 and 20,946% for O2). In case, that there will be entrapped humans in the void, then its air composition will be affected. The problem is to estimate how these factors are combined and how they affect CO2 and O2 mean concentrations in the void, as a function of time.

Mean Concentrations Equations
The mean concentration Cx of CO2 or O2 ( 2 or 2 respectively), inside a room or a cavity of volume VC, is given by the expression = ℎ ℎ ℎ ( ). Since cavity's volume VC, remains unchanged, also the total number of air molecules in the cavity for a specific temperature could be considered unchanged. In a cavity that has a number of openings for entering fresh atmospheric air, and with entrapped humans, assuming that before the entrapment of the humans the space was filled with fresh atmospheric air, the following parameters would influence the number of molecules of CO2 or O2 in the cavity :  The concentration Cxf of this specific gas component in the fresh atmospheric air and the concentration Cxe in human's exhaled breath, along with the fresh air flow rate (lit/min) into the room/cavity Ff and the exhaled breath flow rate Fe.  The concentration Cxc of this specific gas component in the air going out from the openings of the room/cavity and its outgoing flow rate (lit/min) Fc.  The concentration Cxc of this specific gas component in cavity's air, inhaled by the entrapped persons in the room/cavity (outgoing from the cavity to humans' lungs), flow rate (lit/min) Fi. Temperature difference between Tc and Tf, (temperature inside the room/cavity Tc, and outside Tf), might increase or decrease the temperature into the cavity from Tc to T'c and change the total number of air molecules in the cavity. Nevertheless this change doesn't affect the concentration of any of the air components as far as the concentration expression refers to volume ratio (air component partial volume), or mole fraction/ratio (ppm or %). According to gas laws the proportionalities among air components molecules and thus partial volumes will remain the same. Assuming that when fresh air enters the void its temperature in very short time becomes the same as the temperature inside the void, the principle used to estimate mean concentration of CO2 or O2 inside the cavity, is that cavity's volume and pressure, remain unchanged and thus airflows coming into the cavity must be balanced with the exhaust flows. Airflows are considered for a specific opening (humans are handled as openings), as positive when they enter into the cavity and negative when they are going out of it. Then ∑ = 0 ⇒ + − − = 0. Additionally because the inhaled and exhaled air flow rates are the same ( = ), it results that = . The change of the partial volume of an air component x in the cavity, within a very small fraction of time dt, it would be : = ( * + * − * − * ) * Also the concentration change is given by : The solution of the above differential equation is as follows: Substituting the solution into the differential equation we get : Taking into account the initial conditions at time t=0 (when happened the catastrophic event) and = (0) = , Ko is calculated as follows : The mean concentration of CO2 or O2 in the cavity, as a function of time, is given by the formula below : Defining as = _ , then, Also defining as = _ , then, Verifying the above formula of ( ), we get (0) = , as expected and that for → ∞, ).

Air sources and sinks inside a rubble cavity and anticipated performance of the e-nose system.
Exhaled air from the entrapped human(s), contains increased concentration of CO2 (as part of human metabolic process), in comparison with the CO2 of the fresh atmospheric air outside the rubble. Specifically exhaled air composition, according to literature, [1][2][3][4] ( 2 ) ≈ 40.000 − 53.000 . Fluctuations are also significant depending on the person's characteristics and physical condition [2]. The dry air of normal atmospheric air, contains roughly ( 2 ) = 405 − 420 CO2, [4]. It is meaningless to use higher accuracy concentrations measurements since the fluctuations in a period of few days or in different nearby places might be significant [4], and also increasing every year. Concerning O2, exhaled air contains decreased concentration levels in comparison to the O2 in the fresh atmospheric air. Exhaled air contains ( 2 ) ≈ 13,6% − 16,0% [2,3,5], and dry air of normal atmospheric air, contains roughly ( 2 ) ≈ 20,536% − 20,946% , [4,6]. Also for oxygen it is meaningless to use higher accuracy concentrations measurements since there are fluctuations as well [4]. Comparing the concentrations of exhaled and fresh air for CO2 and O2, we get respectively, ( 2 ) ≈ _ ( 2 ) ≈ 0,008 − 0,011, and ( 2 ) ≈ _ ( 2 ) ≈ 1,2835 − 1,5401.
Concerning the exhaled air flow rate, for each victim depends actually on their weight. There have to be defined the number of breaths for a specific time period and also the volume of the average breath of a person, to estimate the exhaled air flow rate. The flow rate of exhaled air in litres per minute, results as : Specifically for the respiratory rate, for adults is usually 12-20 breaths per minute [7,8]. Elderly people may have a slower breathing rate (10-18 breaths per minute) [8]. Children have a faster breathing frequency reaching up to 25-40 breaths per minute for infants [9], as shown in Table 1. About the volume of the average breath (tidal volume), of an adult or elderly person, it is estimated between, approximately 390 (women) and 500ml (men) [10]. Infants' and children's tidal volume is between 0,1 and 0,2 litres (Table 1). However, in absolute terms, the amount of air a person needs is determined by the mass of the person. On average a person requires 7ml/kg of body mass [10]. So an average male adult weighting 75kg would have a tidal volume of 0.525lt and as such an exhaled air flow rate of = 6.3 − 10,5lt/min. Below in Table 1, are calculated the exhaled air flow rates for individuals at different ages [11][12][13]. Table 1   Inspiration's flow rate it is considered the same as exhalation = , and the concentration of the cavity's inhaled air in CO2 or O2 is denoted as ( 2 ) and ( 2 ) , respectively.

Mean Concentrations and sensor measurements noise floor
E-nose systems usually they use both, high speed and lower speed sensors. High speed sensors, like non-dispersive infrared absorption sensors, they ensure a fast detection method, but they have low accuracy (~5%). Sensors using less rapid technologies, like fluorescent light, they have higher precision (~2.7%), but their response is really slow [14]. Fast sensors are more preferable for e-nose systems targeted to USaR operations. The main reason is because they deliver data fast enough (up to a 2 Hz), to detect a point of interest during rubble searches. On average this is adequate to detect a change in concentration between 2 adjacent points in a cavity (about 1cm distance for a robotic platform with typical speed 3cm/sec). Nevertheless the accuracy of 5% on top of the picked-up noise, can further distort the signal and rise it up to 15%. There are alternatives adopted by such systems [14], and by using concurrently higher precision but slower sensors to complement the weakness of the low accuracy of the high speed sensors. In an attempt to evaluate CO2 and O2 sensors in an e-nose system for [15], the noise picked up for both categories of sensors has been measured and showed that CO2 was in the range of 380-420ppm (average 406ppm), and O2 percentage ranges were between 20.67%-20.8% (average=20.72%). Measurements of sensors' performance showed that particularly CO₂ sensor picks up a lot of noise. The O₂ sensor, on the other hand, is much more accurate and due to the nature of its detection method, provides a much smoother result. In order for an e-nose system used for USaR operations to detect victims with enough certainty and without creating false alarms to the rescue teams, the raw value acquired from the sensors should be at least two standard deviations away from the mean values of the fresh air outside the rubble. Using the values of standard deviation estimated for the e-nose system in [15], the "alarm" CO₂ concentration should be when ( 2 ) ≥ 1.10798 * ( 2 ) . Similarly the "alarm" O₂ concentration should be if ( 2 ) ≤ 0.9995 * ( 2 ) . These threshold values are the worst case scenario. If more than one measurements from the e-nose system are used for the decision making, particularly with filtering/averaging performed on a window of values, the limits of detection can be significantly reduced. The costs are response time and consequently in search/scanning speed.

Mean Concentrations in equilibrium and human detection limits
In section 3.1, it was shown that for → ∞ the concentration of CO2 or O2 in a cavity/void converges to , = * ( ).
( 2 ) ≈ _ ( 2 ) ≈ 0,008 − 0,011, and ( 2 ) ( 2 ) ≈ _ ( 2 ) ≈ 1,2835 − 1,5401. Also it was shown that ranges from = 2.0lt/min, up to = 10.5lt/min, which results that the ratio = _ . Finally in section 4.1, was found that "alarm" CO₂ and O₂ concentrations are ( 2 ) ≥ 1.10798 * ( 2 ) and ( 2 ) ≤ 0.9995 * ( 2 ) . Thus clarifying further the "alarm" point for CO2 it results the following inequality : Considering the most difficult case where the concentration of CO2 in the exhaled breath is minimum ( ( 2 ) ≈ 40.000 ), and in fresh air maximum ( ( 2 ) = 420 ), thus _ ( 2 ) ≈ 0,011, then the "alarm" point for CO2, becomes : This finding shows that in case that the flow rate of the fresh air Ff, is ≥ _ * = 830,06 * , then the CO2 sensor of the e-nose system will not be able to detect a victim. Specifically for a child 3 years old alone in a void if ≥ 2 3 / it will not be detected, and for an adult male also alone in a void if ≥ 7 3 / . Similarly, clarifying further the "alarm" point for O2 : For O2, the most difficult case is when the concentration in the exhaled breath is maximum ( ( 2 ) ≈ 16%), and maximum as well in fresh air ( ( 2 ) = 20,946%), thus _ ( 2 ) ≈ 1,309125, and the "alarm" point for O2, becomes : Analyzing this finding as well it is shown that in case that the flow rate of the fresh air Ff, is ≥ _ * = 471,26 * , O2 sensor will not be able to detect a victim. Specifically for a child 3 years old alone in a void if ≥ 1,2 3 / it will not be detected, and for an adult male also alone in a void if ≥ 4 3 / . Assuming that rescue teams need to evaluate about the probability of detecting humans in a cavity, under certain conditions (cavity openings and estimated fresh air flow rate), then by using the "alarm" points estimated above, it is possible to define the "resolution" of the e-nose system, i.e. the minimum number of humans that the system would detect under those specific conditions. Nevertheless further details for weather conditions should be known and taken into account and finally decide about the worthiness to investigate a void.  Analyzing the results presented in the above table, it is revealed that within less than 4 hours even in a large cavity where there fit even 15 people, the e-nose system would be able to detect a 3 years old child, assuming that the weather conditions do not create fresh air flow rate more than 1,2m 3 /min ( = _ * ). Weather conditions and their influence to the flow rate of fresh air coming into the cavity, they are analyzed in another paper.

Conclusions
In this paper, the performance of a mobile e-nose system was studied. The targeted e-nose system it measures the atmospheric air gas components' concentrations (actually CO₂ and O₂), into a rubble void, where humans are entrapped, after a disastrous event that caused the collapsing of a building/construction. The performance of the sensors of the system was formulated to determine the equations calculating the anticipated concentration of CO2 and O2 into a void/cavity as a function of time. Then the anticipated performance of such a system was examined considering various cases with parameters like the kind of entrapped humans in a void, the characteristics of the CO2 and O2 sensors