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This paper deals with the quasilinear parabolic-elliptic chemotaxis system ut = ∇ • (D(u)∇u) − ∇ • (χu∇v) + µu − µu r , x ∈ Ω, t > 0, τ vt = ∆v − v + u, x ∈ Ω, t > 0, under homogeneous Neumann boundary conditions in a bounded domain Ω ⊂ R n with smooth boundary, where τ ∈ {0, 1}, χ > 0, µ > 0 and r ≥ 2. D(u) is supposed to satisfy D(u) ≥ (u + 1) α with α > 0. It is shown that when µ > χ 2 16 and r ≥ 2, then the solution to the system exponentially converges to the constant stationary solution (1, 1).

The bolt-loosening detection method using vision-based technique is summarized and a new gray gradient enhancement method is proposed to improve the stability of the nut edge detection and bolt-loosening detection. The Influence of the thresholds in Canny edge detector is studied and a new gray gradient enhancement method is proposed to enhance the gray gradient at the pixels on the outer boundary of the nut. Meanwhile, the suggestion on the high threshold value in Canny edge detector is given and can be used to reduce the subjectivity of parameter determination in Canny detector and the interference of uninterested edge lines. The proposed method is verified using a bolt connection in laboratory. The results show that the proposed method can effectively highlight the outer boundary of the nut and improve the stability of the nut edge detection and bolt-loosening detection.