Development of Artificial Neural Network Based Metamodels for Inactivation of Anthrax Spores in Ventilated Spaces Using Computational Fluid Dynamics

Figures & data

Table 1. List of variables

	Variable	Symbol	Unit
1	Initial number of the organisms released	N 0	spores/m^3
2	Number of viable organisms in the room after time	N	spores/m^3
3	Length of the room	L	m
4	Width of the room	W	m
5	Height of the room	H r	m
6	Distance between inlet and outlet	I	m
7	Cross-sectional area of the inlet and outlet	A	m^2
8	Velocity of mixture at the inlet	U mix	m/sec
9	Mass fraction of chlorine dioxide
10	Time given for the spores to initially disperse	τ	sec
11	Contact time of spores with chlorine dioxide	τc	sec
12	Inactivation rate of B. anthracis spores	k in	(L/mg)^0.5sec^−1
13	Surface decay rate of chlorine dioxide	k s	sec^−1
14	Bulk decay rate of chlorine dioxide	k b	sec^−1
15	Density of air	ρf	kg/m^3
16	Dynamic viscosity of air	μ	kg/m·sec
17	Density of spore	ρp	kg/m^3
18	Diameter of spore	d p	kg/m^3

Figure 1. Geometry of the room.

Table 2. Range for each of the dimensionless groups

		Groups	Maximum		Minimum
1.		L/W		1.67
2.		L/H r		2.08
3.		I/H r		0.6
4.		WH r/A		15
5.	x 1		2000		500
6	x 2	k sθ	3.64		0.00
7.	x 3	k bθ	0.43		0.01
8.	x 4	k inρ^1/2θ	1051		105
9.	x 5	Q mixρ/Lμ	7550		50
10.		τ/θ		1
11.	x 6	τc/θ	150		3
12.		L/d p		5.00 × 10^6
13.		ρp/ρf		861

Table 3. Design space of the chosen six dimensionless groups

Cases	x 1	k sθ x 2	k bθ x 3	k inρ^1/2θ x 4	Q mixρ/Lμ x 5	τc/θ x 6
1	530	0.73	0.15	191	693	24
2	590	0.91	0.09	376	882	62
3	650	0.40	0.26	815	435	66
4	710	2.91	0.06	526	538	87
5	770	2.27	0.34	143	936	70
6	830	1.37	0.24	332	378	129
7	890	2.32	0.20	933	756	6
8	950	2.33	0.04	260	951	134
9	1010	3.06	0.25	879	473	8
10	1070	0.29	0.17	965	635	49
11	1130	0.03	0.35	370	924	90
12	1190	0.68	0.07	199	670	111
13	1250	0.69	0.21	749	906	132
14	1310	1.02	0.19	876	1120	9
15	1370	1.35	0.06	992	420	30
16	1430	2.16	0.14	543	161	51
17	1490	1.93	0.40	597	658	84
18	1550	2.35	0.13	175	942	93
19	1610	3.35	0.32	820	588	118
20	1670	0.58	0.08	955	1060	112
21	1730	2.39	0.04	973	336	56
22	1790	1.48	0.25	298	714	5
23	1850	0.39	0.37	433	988	136
24	1910	3.49	0.13	569	351	17
25	1970	0.03	0.13	667	843	96

Figure 2. Plot of normalized number of viable particles remaining in the room over time; ClO₂ was injected at 0 sec (case 14).

Figure 3. Plot of normalized number of viable particles remaining in the room over time, ClO₂ injected at 0 sec (case 22).

Figure 4. Linear model results. (a) CFD results against predicted results; (b) standardized residual plot.

Figure 5. Quadratic model results. (a) CFD results against predicted results; (b) standardized residual plot.

Figure 6. Training results (a) for ANN_6-2-1 and (b) for ANN_6-3-1.

Figure 7. Standardized residual plot (a) for ANN_6-2-1 predictions and (b) for ANN_6-3-1 predictions.

Table 4. Change of SSE with increasing number of neurons for architecture with one hidden layer

Neurons	Adjustable Parameters	Training SSE	Cross-validation SSE
1	9	11107	27209
2	17	1583.5	25740
3	25	677.6	22989
4	33	275.2	121780
5	41	209.2	282390

Figure 8. Change of sum of square of errors with increasing number of neurons; architecture with one hidden layer.

Figure 9. Training results (a) for ANN_6-2-2-1 and (b) for ANN_6-3-2-1.

Figure 10. Standardized residual plot (a) for ANN_6-2-2-1 predictions (b) for ANN_6-3-2-1 predictions.

Table 5. Change of SSE with number of neurons (architecture: two hidden layers)

Neurons
First Hidden Layer	Second Hidden Layer	Adjustable Parameters	Training SSE	Cross-validation SSE
1	1	11	10989	65533
2	1	19	1578	58883
2	2	23	649	39165
3	1	27	445	23940
3	2	32	379	16299
3	3	37	308	3.82 × 10^10
4	1	35	287	61222
4	2	41	207	14059
4	3	47	189	15863
4	4	53	161	4.72 × 10^6

Figure 11. Change of sum of square of errors with increasing number of neurons in the second hidden layer; architecture with two hidden layers (number of neurons in the second hidden layer the number of neurons in the first hidden layer).

Figure 12. Plots of sensitivity of the response of the output log(N/N ₀) applying ANN_6-4-3-1.