Flame detection by heat from the infrared spectrum: Optimization and sensitivity analysis

detection strategies based on three or four optical low-pass filters. The optimal wavelengths are reported along with the sensitivity of the detection signal to the filter non-ideality. Our results give guidelines for design of efficient and highly selective flame-radiation-based fire detection sensors.


Introduction
Fast and selective detection of flames is essential for the success of fire suppression, and loss prevention in many industrial applications, such as air hangars [1] and in the chemical industry.While there are several conventional ways for detecting fire, such as detecting smoke or heat, modern fire-detecting technology includes video-image flame detection [2][3][4] and sensors detecting combustion or hot gases before or precisely when combustion starts [5].Indeed, it is not difficult to build detection systems that respond to the smallest signatures of a flame, heat, or gases.The main problem is to avoid false alarms while providing reliable detection of actual fires.False alarms should be avoided as they may cause significant costs through emergency service deployment, damage through the unnecessary activation of suppression systems, and interruption of the normal activities.For instance, in Finland, rescue services are alerted to about 23 000 fires every year.In about 12 000 of these cases, the issue is just checking or resetting the automatic fire detection system or home smoke alarm [6].Intelligent multi-sensors are being designed to detect and process heat, smoke [7], * Corresponding author.E-mail address: hadi.bordbar@aalto.fi(H.Bordbar).
hot gases [8], and carbon monoxide [9], utilizing intelligent algorithms to distinguish between fire and false alarms.
Thermal radiation plays an essential role in the heat transfer and spread of fires due to the relatively high temperatures involved [10].In addition to being able to pass information without any significant delay, the electromagnetic spectrum of the hydrocarbon flame has a unique spectral feature in the infrared regime that can be utilized in an intelligent detection algorithm [11,12].To avoid false alarms, any radiation-based detection algorithm must distinguish the radiation spectra of the flame from other sources such as hot objects or solar radiation.In engineering applications of flame radiation, the dependence of emission and transfer on wavelength is commonly ignored (i.e., the gray assumption), but the dominance of the CO 2 and H 2 O emissions can be used as a flame fingerprint.This is the principle of the infrared detectors that unambiguously distinguish flames from hot surfaces.When the flame is still small and optically thin, it can be detected by comparing the emission intensity at 4. 4  Though detecting a fire through its unique radiative characteristics is a well-established technology, there is no detailed insight into the detection method and especially the spectral characteristics in the open literature.This is the motivation for the current work.The present work provides detailed insight into the characteristics of fire spectral emission that should serve as the spectral signature of a flame.Moreover, we discuss the details of the efficiency of the infrared spectrum-based detection strategy.This work presents an optimized flame detection strategy by analyzing the recently published high-resolution spectra of fire [13][14][15] by computing the corresponding spectra for blackbody emitters, as observed over a finite distance of water-vapor-containing air.In the present work we use high-precision data that were available for carrying out the optimization.The non-ideality of optical filters would also allow data with less frequency resolution but we do not consider this question here.The feasibility of fire detection by three or four low-pass optical filters is studied.The optimized cutoff wavenumbers of the optical filters are obtained by the Pattern Search optimization algorithm of Matlab.Our choice of the optimization method was based on its easy availability, numerical efficiency, and convenience when varying the system parameters.Utilizing a numerical parameter for the detection confidence, we evaluate the effects of the fire size (optical thickness), and filter quality on the possibility of distinguishing flames from other hot objects.Moreover, we provide a sensitivity analysis of the performance of optical filters used in fire flame detectors and its effect on the strength of the detection signals.

Flame and blackbody radiation spectra
Recent improvements in computational power pave the way for more accurate modeling of wild and unwanted fires, leading to more effective mitigating and extinguishing.Fire contains complex, coupled physical processes such as combustion, hydrodynamics, and heat transfer which can be solved with computational fluid dynamics (CFD) in principle.Radiation heat transfer is among the most challenging physical phenomena to solve because in addition to its spatial dependence, the radiative transfer equation has directional and spectral dependence [16,17].Thus, it makes an accurate solution of thermal radiation difficult and costly [18].
To include the spectral dependence in solving the total (i.e., spectrally integrated) radiative heat loss and radiative heat flux, global models such as FSCK [19,20] and WSGG [21] give excellent performance.However, to obtain the fire emission spectra needed for the present research, the radiative transfer equation needs to be solved for a finely discretized spectrum representing millions of monochromic electromagnetic waves.
Circular pool fires are a typical industrial fire scenario, and their consequences are commonly analyzed using CFD [22,23].Bordbar et al. [14] have reported a numerical methodology to obtain line-byline radiation spectra of large-scale pool fires.They first simulated semi-steady circular kerosene pool fires using a CFD model built in Fire Dynamic Simulator (FDS) [24].The CFD model [14] was built following the common practices of industrial fire analyses [22,23], such as an open atmosphere, empirically specified fuel-mass-flow boundary condition, Large Eddy-Simulation-based turbulence modeling, mixingcontrolled combustion model, and a radiation transport model with gray properties.From the CFD solutions they extracted the detailed temporal profiles of gas compositions, soot concentration, and temperature along a sensor's line of sight, to be used for the line-by-line radiation calculation.The gas concentrations of different gas species and soot in fires have been widely reported in the literature, see for instance [14,25,26].It should be noted that the fire emission spectra are affected by the concentration of all the gas species and the temperature.The spectral radiative heat transfer along the sensor's line of sight was then solved using high-resolution absorption spectra of combustion gases and soot by line-by-line calculations.Fig. 1 shows a schematic of the CFD model used in Ref. [14] and a typical spectral intensity profile obtained for large pool fires.The fire spectra obtained numerically with this methodology agree well with the available experimental data with coarser resolution as shown in [14] and Fig. 1.
Comparing fire spectra with a hot blackbody emitter, there is a unique emission peak at ≈ 2000 − 2200 cm −1 .It is due to the strong emission by hot CO 2 in a fire.Moreover, the strong absorption by cold atmospheric CO 2 between a fire and a sensor causes a large absorption valley at ≈ 2200 − 2400 cm −1 .This unique behavior is due to a change in the strength and location of the absorption band of CO 2 with temperature [14].Bordbar et al. [14] showed that by increasing temperature, the center of the band shifts toward smaller wavenumbers and the width of the band shrinks.A wider range of emission spectra for large pool fires and a close-up view of the main CO 2 band have been given in [14].Moreover, the absorption strength of the gas is much larger at lower temperatures.Hence, the hot CO 2 in fire causes an emission peak at smaller wavenumbers.On the other hand, the cold CO 2 between a fire and a sensor causes a strong absorption valley at larger wavenumbers.
The reported numerical results provide high fidelity information about how fire radiation intensity changes with the wavenumber.However, they are relevant for large pool fires representing the most challenging fire scenario for spectral detection.Such pool fires contain a high load of soot, and therefore their spectral behavior is almost gray, making them difficult to differentiate from the radiation of hot objects.Nonetheless, large fires are naturally easy to detect by other means.Moreover, an improved fire detection method should be done at the beginning stages when the fire is relatively small.Hence, in the present work, we use high-resolution spectra of Kerosene pool fires of various sizes (30, 70, and 100 cm) measured by FTIR spectroscopy at a distance of several meters.The spectra are presented in Section 3.1 and details of the measurements are discussed elsewhere [13].
An ideal detector should perfectly differentiate between the radiative intensity spectrum of fire and hot objects to avoid false alarms.To study this issue, we numerically obtained the radiative spectra of some typical hot blackbody emitters.We solved for the radiation transfer along the line of sight of a sensor facing the hot surfaces at a 23 m distance.The high-resolution line-by-line absorption spectra of H 2 O, CO 2 , and CO were obtained from HITEMP 2010 spectral database [27].The details of line-by-line calculations were discussed in our previous works [14,21].The calculated spectra of blackbody emitters are reported in Section 3.1 and Fig. 6.

Detection strategy
As previously reported [14], spectral fire detection should be based on a signal comparing the intensity associated with the emission peak of hot CO 2 with some other parts of the spectrum which remain unchanged by fire.Hence, we need to design a sensor to detect this peak.In measuring radiative heat flux, we need to have several low-pass (with respect to frequency or wavenumber) optical filters to measure the radiative heat flux passing through this part of the spectrum.Here we study the feasibility of this detection by using three or four low-pass optical filters.It is worth noting that the terms low-pass and highpass are used in the literature of Optics with respect to frequency, while wavenumber is the common parameter in spectral radiation modeling in combustion systems.Nonetheless, a low-pass filter allows transmission of all the electromagnetic waves with lower frequencies (wavenumbers) than the filter's cutoff frequency (wavenumber) and blocks electromagnetic waves with higher frequencies (wavenumbers).Moreover, although we obtain three or four band-cut limits for our detection schemes, the proposed ones can be equivalently implemented using two band-pass filters with the same cutoff limits.

Detection strategy with four low-pass filters
We need to obtain the radiative energy passing through two bands as shown by gray and red in Fig. 2.This can be done using four different low/high-pass filters or using two bandpass filters.Either way, the main challenge remains in obtaining the optimal wavenumbers for the bandpass parameters that produce the strongest detection signal.This optimization problem will be formulated in the next section.Having ideal optical low-pass filters with transmissivity changing from one to zero at a distinct wavenumber   , the energy received at wavenumbers below   is and the energy within a wavenumber band The ratio of incident energies within two wide bands (b1 and b2) is where As shown in Fig. 2,  b1 ,  b2 , and  are the centers of two bands and their identical bandwidths, respectively.A fire can be differentiated from a hot object if the ratio  f ire ( b1 ,  b2 , ) corresponding to the fire is greater than that of a hot blackbody object  BB ( b1 ,  b2 , ) such that where  is the detection threshold.The larger the  the better the accuracy of the fire detection.

Detection strategy with three low-pass filters
Alternatively, we also consider the feasibility of fire detection by using three low-pass filters.Fig. 3 schematically shows the fire detection strategy with three optical filters.It is based on comparing the signal of the comparative intensity of two neighboring bands.The ratio of incident energies within two adjacent wide bands is The two neighboring wide bands are schematically shown in Fig. 4, assuming a constant bandwidth of Again, a fire can be differentiated from a hot object if the ratio  f ire ( 2 , ) is greater than the ratio of a hot blackbody object  BB ( 2 , ) such that where  is the detection threshold.

Optimization of four filters detection plan
To obtain the best detection scheme for the proposed strategy with four low-pass filters, we need to get the optimal combination of  b1 ,  b2 , and  to maximize .The objective function to be maximized is defined as: The quantity  represents the ratio of the radiative energy of the two bands as in Eq. ( 3).The variables  b1 ,  b2 , and  represent the centers of two bands and their identical bandwidths, respectively, and  f ire and  BB denote the number of fire and blackbody-emitter spectra used in optimization, respectively.The overbar represents an average over the spectra.Using the experimentally measured normalized fire spectra of three Kerosene pool fires [13] shown in Fig. 5 and the numerically calculated normalized radiative spectra of the hot blackbody for nine evenly spaced temperatures between 400 − 1200 K (Fig. 6), we implement the Pattern Search module of Matlab R2021a to obtain the optimal combination of  b1 ,  b2 and .The radiative intensity profiles have been normalized by their maximum values to give balanced contributions to the optimization process.The calculations were performed on a Dell Precision 5820 Tower Windows computer (6 core 3.60 GHz Intel Xeon).The default settings of the Matlab R2021's Pattern Search solver have been used for the optimization, including mesh tolerance of 10 −6 , maximum iteration of 100×{number of variables}, and function tolerance of 1e-6.Using normalized intensity makes the weight of all the fire and blackbody emitters the same in the final optimized solution.Inspecting normalized intensity of three pool fires shown in Fig. 5, we found  b1 = 2232.8cm −1 to be optimal for catching the characteristics of the emission peak of hot CO 2 and thus fixed its value.It was found by averaging of the spectral ranges of the fire spectra with normalized intensity larger than 0.95.Hence, the optimization of the parameters in Eq. ( 9) is done only for two parameters of  and  b2 in the following ranges: 30 cm −1 <  < 300 cm −1 ; 2395 cm −1 <  b2 < 2800 cm −1 .These ranges were selected based on investigating the normalized intensity spectra of fire and blackbody emitters shown in Figs. 5 and 6 and are in line with previously reported data [10].Using the pattern search algorithm, the best optimal combination for the proposed four-filter detection plan is:    With this combination, the values of  (cf.Eq. ( 3)) are found as listed in Table 1.The values of  for the fires are larger than those of blackbody emitters which confirms strong detection signals for fires.As the size of the fire increases, the detection signal strength decreases.In fact, the larger optical thickness of larger fires, which is due to larger soot volume fraction and larger flame width, makes their radiation spectra closer to that of a blackbody emitter.Note that since the normalized solar intensity spectrum is relatively small and smooth in these two bands, the  for solar spectrum will be around unity and is weaker than the  of the fire.

Optimization of three-filter detection scheme
For the detection scheme with three optical filters, the optimal combination of  2 and  to maximize  (see Eq. ( 8)) should be determined.Similar to the four-filter detection scheme, the objective function to be maximized is defined as: Following the same optimization methodology and spectral data as for the four-filter detection scheme, we again implemented the Pattern Search optimization module of Matlab R2021a to find the optimal combination of  2 and  in the following ranges for  2 and : The above ranges were selected by investigating the fire and blackbody spectra shown in Figs. 5 and 6.Optimizing the detection signal with the pattern search algorithm, we found out that  (  2 ,  ) is maximum with  2 = 2102.55cm −1 (4.756 μm) and  = 217.72 cm −1 .This gives  1 = 1884.83cm −1 (5.3055 μm) and  3 = 2320.27cm −1 (4.3098 μm).With these optimized cutoffs, the calculated ratio of the radiative heat energy of two neighboring wide bands for various fires and blackbodies are listed in Table 2.
As seen in Table 2, the values of  with the optimal combination of  2 and  are around 0.5 for the spectra of blackbody emitters while they are always larger than one for the fire spectra.It is also clearly seen that the smaller fire causes larger  which means a stronger signal.In other words, the smaller the flame, the more distinguishable its spectrum is from the blackbody spectrum.
Emission and absorption of carbon dioxide, carbon monoxide, and water vapor existing in the air between a fire and a sensor may affect the detection signal.This depends on gas concentrations, thermal conditions, and the distance between the fire and the sensor.For instance, air conditioning or different stages of sprinklers affect the water vapor's concentration, and therefore may alter the radiative heat transfer from the fire to the sensor.While the unique feature of the fire spectrum is the emission peak of CO 2 , located beside the absorption dominant region caused by cold atmospheric CO 2 , the water vapor content of the ambient air between the sensor and fire primarily affects the absorption of other parts of the spectrum.Bordbar et al. [14] reported that ambient relative humidity has a negligible effect on the form of the spectrum at large distances.However, at close distances, the main impact of relative humidity is seen in the absorption bands of H 2 O. High relative humidity causes a large deviation from blackbody spectrum.However, the distance and relative humidity seem to have a negligible effect on the absorption/emission peak of CO 2 at ≈ 2000 − 2200 cm −1 (see Table 3).

Effect of the filter non-ideality
The filters in the preceding sections were assumed to behave as step functions with a sharp transition from fully opaque to fully transparent.This represents an ideal filter with zero-step width, which is not feasible in practice.Non-ideality can be present in the step width, step height, and other deviations from the ideal design.Here we consider filters with a non-zero step width with a transmittance defined by a cumulative normal distribution with standard deviation () and average equivalent to the three optimum values of   .The performance of a detector made of three filters with (arbitrary)  = 100 cm −1 is visualized in Fig. 7.
Fig. 8 shows the intensity ratio  of a three-filter detector made of non-ideal filters with 0 ≤  ≤ 1500 cm −1 and radiation coming from the kerosene pool fires or blackbody sources with various temperatures.The ideal case, i.e. a step function with zero width, is equivalent to zero standard deviation.Increasing the step width initially decreases  for the kerosene pool fire spectra and increases it for the blackbody spectra.
The three-filter detection strategy will work if the value of  is above a threshold sensitivity value.Even without specifying an exact

Table 3
The obtained optimal cutoffs for the 3-and 4-filter detection plan.
The optimal 3-filter plan Wavenumber (cm threshold, we can see from Fig. 8 that the signals from the pool fires and blackbody sources with highest temperatures approach each other when  ≥ 200 cm −1 .On the other hand, the difference between the fire and the blackbody spectra remains relatively large up to about 800 cm −1 when the blackbody temperature is low (≤ 600 K).This means that the detection strategy is more likely to distinguish between fire spectra and low temperature black bodies.Interestingly, while  is largest for small fires in ideal filters, the situation is different for non-ideal filters with large step widths.This situation occurs because the  for the 100 cm kerosene fire reaches a minimum at  = 91 cm −1 and thereafter increases above the  for the 30 cm and 70 cm kerosene fires.

Outlook on using metal particle-silica composite filters
The increasing attention towards utilizing mid-IR radiation in various applications within the energy, medical and communication industries has increased the need for developing spectrally functional optical filters.The types of optical filters are numerous, and their transmittance can be adjusted by the refractive index, sub-layer thickness, etc.The mid-IR optical filters are usually designed by applying the Fresnel effect in bulky multilayered dielectric films which limits their application in compact optical devices [28].The development of the nanofabrication techniques, where metasurface materials are used to engineer the optical response [29,30], has helped in reaching compact optical devices.One type of optical filter for this application is based on diffuse reflectance by layers embedded with particles.The transmittance of the layer is influenced by the particle and medium material properties, the layer thickness, particle size and volume fraction, porosity, and surface roughness [31].It may be possible to shift the transmittance cutoff of layers embedded with semiconductor particles by adjusting the particle size and shape or the semiconductor's band gap [32].The layers embedded with semiconductors may have a more sustained reflectance at higher temperatures than metallic particles [33].A silica layer embedded with micron-sized silicon particles was recently estimated to have a step width of about 100 cm −1 [34].Bandgap engineering semiconductors, such as Ge, SiGe, PbS, PbSe, may provide more alternatives for optimizing   .

Conclusions
In the present work we have analyzed experimentally obtained radiation spectra of three different pool fires and compared them to  numerically obtained line-by-line based radiation spectra of blackbody emitters at various temperatures.In this way we have been able to present optimized plans for detecting fire by sensing the unique feature of radiation intensity spectra related to hot CO 2 in the flame zone.The optimized detection plans can be implemented using three or four optical filters to quantify the amounts of radiative heat passing through two spectral bands, one around the emission peak of CO 2 and another outside it.
We have further optimized the cut-off wavelengths for three and four-filter detector designs using a pattern search algorithm.The target of the optimization was to maximize the difference between the detection signals resulting from three pool fires and blackbody emitters between 400 K and 1100 K.With the optimal filter designs, the fireinduced detection signals were found to be 49% to 514% stronger than

Fig. 1 .
Fig. 1.(a) An illustration of the FDS model used in [14].(b) Radiative intensity  as a function of wavenumber from a hot blackbody (BB) object compared to the one from a large Kerosene pool fire.Source: Both figures are adapted from Ref. [14].

Fig. 2 .
Fig. 2. Radiation intensity  as a function of wavenumber  for the detection scheme with four low-pass optical filters.The left side shows the emission spectra of 30 cm Kerosene pool fire measured at a 23 m distance.The radiative energy passing bands 1 and 2 should be measured and compared with those of a blackbody emitter.A sample of emission spectra of a blackbody emitter at 1100 K reaching a sensor at the same distance is shown in the right panel.See text for the definitions of the parameters .

Fig. 5 .
Fig.5.The experimental normalized radiative intensity spectra reported in[13] for Kerosene pool fires. represents the diameters of the three pool fires.

Fig. 6 .
Fig. 6.The numerically calculated normalized radiative intensity spectra reaching a sensor from blackbody emitters of various temperatures at 23 m distance.

Fig. 7 .
Fig. 7. Top panel: The relative extinction as a function of the wavenumber for three fictitious filters with the optimum values of  2 and  from Section 3.2, i.e. the cutoff averages are 1884.83,2102.55,2320.27cm −1 .The filters have a non-ideal step width characterized by a standard deviation  = 100 cm −1 .Bottom panel: Spectral intensity  from a 100 cm kerosene pool fire and the filtered spectra for the three fictitious filters.

Fig. 8 .
Fig. 8.The effect of a non-ideal step width () on the parameter  for kerosene pool fire spectra and a blackbody spectra.The three-filter strategy is used with the optimum values of  2 and  from Section 3.2.
μm representing the emission band of CO 2 to that at 3.8 μm, which is outside of the https://doi.org/10.1016/j.firesaf.2022.103673Received 8 March 2022; Received in revised form 17 August 2022; Accepted 12 September 2022 emission band.The signal in this comparison is much stronger for fire than for other hot emitters.

Table 1
Values of  for the optimized combination of  b1 ,  b2 , and  in the four-filter detection plan.

Table 2
Values of  for the optimized combination of  2 and  in the three-filter detection plan.