Abnormal driving behavior detection based on an improved ant colony algorithm

Figures & data

Figure 1. The process of simplicial algorithm.

Figure 2. The fitting process of driving behavior.

Figure 3. Trajectory correction based on yaw velocity.

Figure 4. The process of detection model.

Table 1. The details of the five testing functions.

Function	Expression	Searching space	Accuracy	Globally optimal solution
Sphere	$f_1(x)=\sum _{i=1}^n{x}_i^2$	[−100,100]n	0.01	[0,0, … … ,0]
Rosenbrock	$f_2\left(x\right)=\sum _{i=1}^{n-1}\left(100{\left(x_i^2-x_{i+1}^2\right)}^2+{\left(x_i-1\right)}^2\right)$	[−2.048,2.048]n	100	[1,1, … … ,1]
Ackley	$f_3(x)=-20exp(-0.2\sqrt{\frac{1}{n}\sum _{i=1}^n{x}_i^2})-exp(\frac{1}{n}\sum _{i=1}^{n}cos\left(2\pi x_i\right))+20+e$	[−30,30]n	100	[0,0, … … ,0]
Griewanks	$f_4\left(x\right)=\sum _{i=1}^n\frac{x_i^2}{4000}-\prod _{i=1}^{n}cos\left(\frac{x_i}{\sqrt{i}}\right)+1$	[−600,600]n	0.1	[1,1, … … ,1]
Rastrigin	$f_5\left(x\right)=\sum _i^n(x_i-10cos(2\pi x_i)+10)$	[−5.12,5.12]n	100	[0,0, … … ,0]

Table 2. The testing result of the two algorithm.

Function	FP-ACO		Conventional ACO
	mean	standard deviation	mean	standard deviation
Sphere	2.73×10^−14	4.88×10^−15	5.83×10^−5	8.33×10^−5
Rosenbrock	16.77	8.66	47.33	22.58
Ackley	7.43×10^−15	3.23×10^−16	7.49×10^−7	4.74×10^−8
Griewanks	5.28×10^−6	6.77×10^−7	5.27×10^−2	2.49×10^−3
Rastrigin	4.66×10^−3	2.82×10^−4	23.66	14.69
Ackley*	4.72×10^−13	1.64×10^−15	6.73×10^−9	3.51×10^−10
Griewanks*	7.22×10^−8	4.30×10^−9	6.23×10^−4	3.14×10^−4
Rastrigin*	1.68×10^−6	4.37×10^−7	7.47×10^−1	8.64×10^−3

Table 3. The value of SR and the mean of FEs of 50 independent experiments.

	Ackley		Griewanks		Rastrigin		Ackley*		Griewanks*		Rastrigin*
	SR	FEs	SR	FEs	SR	FEs	SR	FEs	SR	FEs	SR	FEs
FP-ACO	92%	17643	84%	15732	87%	16463	91%	25462	82%	19654	87%	22780
ACO	68%	26880	54%	21346	48%	19722	46%	29661	26%	37349	31%	30411

Table 4. The specific information of each kind of driving operation.

Driving operation	Category and range
Left steering angle (°)	${\theta }_{l_1}$: 0–15	${\theta }_{l_2}$:15–30	${\theta }_{l_3}$:45–60	${\theta }_{l_4}$:60–75	${\theta }_{l_5}$:75–90
Right steering angle (°)	${\theta }_{r_1}$:0–15	${\theta }_{r_2}$:15–30	${\theta }_{r_3}$:45–60	${\theta }_{r_4}$:60–75	${\theta }_{r_5}$:75–90
Acceleration (Km/h)	$w_{u_1}$:0–20	$w_{u_2}$:20–40	$w_{u_3}$:40–60	$w_{u_4}$:60–80	$w_{u_5}$:80–100
Deceleration (Km/h)	$w_{d_1}$:0–20	$w_{d_2}$:20–40	$w_{d_3}$:40–60	$w_{d_4}$:60–80	$w_{d_5}$:80–100
Yaw(rad/s)	Yaw1:5–10	Yaw2:10–15	Yaw3:15–20	Yaw4:20–25	Yaw5:25–30

Figure 5. The details of the experiment dataset.

Table 5. The conversion probability between different driving operations.

	${\theta }_{l_1}$	${\theta }_{l_2}$	${\theta }_{l_3}$	${\theta }_{l_4}$	${\theta }_{l_5}$	${\theta }_{r_1}$	${\theta }_{r_2}$	${\theta }_{r_3}$	${\theta }_{r_4}$	${\theta }_{r_5}$	$w_{u_1}$	$w_{u_2}$	$w_{u_3}$	$w_{u_4}$	$w_{u_5}$	$w_{d_1}$	$w_{d_2}$	$w_{d_3}$	$w_{d_4}$	$w_{d_5}$
${\theta }_{l_1}$	0.63	0.27	0.02			0.74	0.56	0.13			0.91	0.83	0.37	0.16	0.09	0.77	0.82	0.57	0.24	0.05
${\theta }_{l_2}$	0.12	0.04				0.83	0.71	0.25			0.69	0.53	0.11	0.06	0.01	0.62	0.47	0.16	0.03	0.01
${\theta }_{l_3}$	0.09	0.03				0.23	0.10	0.01			0.86	0.69	0.37	0.12		0.69	0.23	0.06	0.01
${\theta }_{l_4}$	0.01					0.14	0.05	0.01			0.57	0.32	0.15	0.01		0.37	0.26	0.15	0.04
${\theta }_{l_5}$						0.19	0.01				0.31	0.23	0.03			0.29	0.17	0.08
${\theta }_{r_1}$	0.86	0.63	0.14	0.01		0.42	0.19	0.03			0.47	0.29	0.11	0.01		0.82	0.84	0.37	0.06	0.01
${\theta }_{r_2}$	0.90	0.76	0.06			0.16	0.04	0.01			0.52	0.18	0.03	0.01		0.93	0.59	0.18	0.01	0.01
${\theta }_{r_3}$	0.29	0.04	0.01			0.08	0.01				0.29	0.06	0.01			0.84	0.28	0.04	0.01
${\theta }_{r_4}$	0.37	0.03	0.01			0.02					0.36	0.69	0.01			0.22	0.13	0.01
${\theta }_{r_5}$	0.29	0.06									0.16	0.07	0.01			0.13	0.04	0.01
$w_{u_1}$	0.86	0.77	0.44	0.23	0.09	0.72	0.81	0.52	0.20	0.07	0.93	0.84	0.14	0.02		0.56	0.27	0.28	0.19	0.01
$w_{u_2}$	0.82	0.57	0.55	0.15	0.05	0.50	0.56	0.23	0.11	0.07	0.46	0.18	0.03			0.58	0.32	0.09	0.01
$w_{u_3}$	0.78	0.32	0.12	0.06	0.01	0.25	0.27	0.13	0.09		0.17	0.09	0.01			0.47	0.16	0.03
$w_{u_4}$	0.64	0.32	0.07	0.01		0.31	0.15	0.05	0.02		0.08	0.03				0.35	0.23	0.05
$w_{u_5}$	0.22	0.16	0.02			0.22	0.09	0.04			0.06	0.02				0.23	0.16	0.03
$w_{d_1}$	0.92	0.87	0.36	0.15	0.06	0.84	0.63	0.34	0.11	0.06	0.56	0.37	0.04			0.69	0.57	0.13	0.03
$w_{d_2}$	0.74	0.59	0.21	0.10	0.03	0.81	0.44	0.13	0.08	0.07	0.61	0.12	0.01			0.44	0.15	0.07	0.04
$w_{d_3}$	0.61	0.47	0.19	0.07	0.02	0.45	0.17	0.08	0.02		0.28	0.05	0.01			0.53	0.17	0.03	0.01
$w_{d_4}$	0.25	0.12	0.01			0.31	0.16	0.01			0.07	0.01				0.32	0.11	0.03
$w_{d_5}$	0.27	0.09	0.01			0.13	0.06	0.01			0.14	0.01				0.11	0.04	0.02

Figure 6. The result of anomaly detection.

Figure 7. The result of comparison experiment.

Figure 8. The result of following experiment.

Figure 9. The detection result after improvement.

Data Availability Statement

Data will be provided upon request to the authors.