The event camera converts brightness changes into event points through digital circuits. Event points are marked as a tuple of four elements, e = (x, y, t, p). Among them, (x, y) represents the coordinates of an event point, t represents the event time, and p represents the event polarity.

As shown in Figure 4A, the external environment can introduce some sparse noise points through the event camera, but the object’s event points own the advantage of higher density and continuity. Inspired by biological stimulation of neurons, the SNN filter is utilized to remove the aforementioned low-frequency noise. The SNN filter have an event-triggered computation characteristic, and the consecutive excitation of event points will lead to the accumulation of potential energy (Figure 4B). Therefore, the potential energy integration and threshold approach of SNN method can significantly enhance the object features and filter out noisy event points.

In equation 1, P ( x , y ) t P ( x , y ) t represents the potential energy of a certain pixel at time t, and P₀ represents the initial potential energy. Every event point will trigger and increase the potential energy with an increment of ΔP unit, but P ( x , y ) t P ( x , y ) t will also dissipate with a fixed decay factor of γ at the same time. (1) P ( x , y ) t = P 0 + ∑ i = 0 n ( 1 − 1 T ∫ t ( i ) T γdt ) . ΔP

Among them, n represents the total number of event points, T represents the clustering interval, and t(i) represents the time when the i-th event point occurred within the interval T. In equation 2, θ represents the threshold of potential energy, which is determined by experiment. When P^t surpasses the threshold θ, the filtered events will be triggered and recorded. Each filtered event point can be simplified as a 3D spatial distribution point with coordinates (x_i, y_i, t_i), as illustrated in Figure 4C. (2) ε = { { ε ( x , y ) j , ( j = 1 , 2 ⋯ ⋯ , m ) } ∣ P ( x , y ) t > θ }

The filtering operation not only eliminates noise points, but also weakens the edge information of key features. Considering that there are many feature points near the key features, we calculate the sum of ei points on the projection plan to highlight edge features (Figure 4D). The cumulative range is distributed within in ([x − 4, y − 4], [x + 4, y + 4]). The relationship between the events number and pixel values is presented in equation 3. As 0 < ( 1 1 + e − M − 0.5 ) < 0.5 , the pixel value of δ(M) can be constrained within the scope of [0, 255]. (3) { M = ∫ x − 4 x + 4 ∫ y − 4 y + 4 ε ( x , y ) dxdy δ ( M ) = 255 ∗ 2 ∗ ( 1 1 + e − M − 0.5 )

Several existing studies (Chen et al., 2022) employ the Shared Nearest Neighbor (SNN) method. In contrast to their approaches, the SNN-region method defined in Equation 3 was adopted. Following the SNN processing, the cumulative range distribution is constrained within the region ([x − 4, y − 4], [x + 4, y + 4]). Through this method, we enhance the color contrast in salient feature regions. (Figures 4E,F).

An image with stable and significant features is a prerequisite for ensuring detection accuracy. Influenced by the cylinder speed, sea conditions, and irregular surface appearance, the extracted NeuroVI images appear unstable (Figure 5A). Increasing the clustering time interval will extends the features, while reducing the clustering time interval will weaken the features. Besides, the feature positions among adjacent images are nearly identical, so there is no need to worry about positional drift. Therefore, it’s necessary to select the optimal image under a fixed sampling period.

We extract four consecutive images: t − 2Δt, t − Δt, t, and t + Δt, which are represented as slices in Figure 5B. From these four consecutive image slices, our goal is to select the most suitable NeuroVI image that exhibits the most obvious features. Obviously, images with the longest contour line display the most distinct features. Since the number of sift feature points is directly proportional to the length of the contour line, we evaluate and select the best image by calculating the number of sift feature points.

The convolution operation between the image and the Gaussian function can blur images to different degrees. Therefore, a blurred image can be defined as L(x, y, σ) function in Equation 4. Among them, G(x, y, σ) is a scale-changed Gaussian convolution kernel, and I(x, y) is the original image. (x, y) denotes the pixel coordinates, and σ can influence the blurriness degree of the image. (4) { L ( x , y , σ ) = G ( x , y , σ ) ∗ I ( x , y ) G ( x , y , σ ) = 1 2 π σ 2 e − ( x 2 + y 2 ) 2 σ 2

The convolution calculation with two different σ value can blur image with different degrees. Subsequently, the subtraction operation is applied between the two adjacent blurred images (equation 5), resulting in another image, namely the Difference of Gaussians (DOG). To find the local maximum and minimum values, a certain pixel in the DOG needs to be compared with its adjacent pixels. If a pixel owns the highest or lowest value among its neighboring pixels, it is defined as an extreme point in the original image. (5) D ( x , y , σ ) = ( G ( x , y , kσ ) − G ( x , y , σ ) ) ∗ I ( x , y ) = L ( x , y , kσ ) − L ( x , y , σ )

Generally, an ideal extreme point exhibits smaller curvature along the edge and larger curvature in the direction perpendicular to the edge. The application of the DOG operator tends to produce multiple extreme points, some of which may be unstable and required to be eliminated. To achieve this, the Hessian matrix is calculated at each extreme point. The curvature is then derived by evaluating the 2 × 2 Hessian matrix H, as described in equation 6. (6) H = [ D xx D xy D xy D yy ]

At the extreme points, the values of D_xx, D_xy, and D_yy are computed by using the difference method. α denotes the maximum eigenvalue of the matrix, and β denotes the minimum eigenvalue of the matrix. Tr(H) denotes the trace of matrix H, and Det(H) denotes the determinant of matrix H. The relevant calculation relationship is illustrated in Equation 7. (7) { Tr ( H ) = D xx + D yy = α + β det ( H ) = D xx + D yy − D xy 2 = α . β

γ = α/β represents the ratio of the two eigenvalues. The relationship among the trace, determinant and γ is calculated in equation 8. (8) Tr ( H ) 2 det ( H ) = ( α + β ) 2 αβ = ( γβ + β ) 2 γ β 2 = ( γ + 1 ) 2 γ

The reliability of extreme points is associated with the γ value. Usually, a higher γ value indicates smaller curvature along the edge and larger curvature in the direction perpendicular to the edge. To filter out extreme noise points, a threshold is set by using equation 9, and the extreme points with values greater than this threshold are considered reliable. Through experimental evaluation, a threshold value of Tr = 12.1 is finally determined. One example of selection process in a scenario is demonstrated in Figure 6. (9) Tr ( H ) 2 det ( H ) > ( r + 1 ) 2 r = 12.1

At the edge positioning point of the hydraulic cylinder motion mechanism, the moving guide rod is rigidly fixed to the motion plate using high-strength bolts, forming a high-stiffness kinematic pair. The motion process was captured with μs-level temporal precision using a DAVIS346 event camera, generating asynchronous event streams. Subsequently, we employed a SNN filter algorithm to extract images of the moving edge rod, performed precise image annotation, and constructed a specialized dataset. The resulting dataset is illustrated in Figure 7.

After extracting the optimal image, we designed a deep learning detection network (Figure 3). Given the superior inference capability of the Transformer architecture, we adopted it for object and motion detection. The Transformer structure incorporates three feature attention matrixes, namely the Query/Key/Value (Q/K/V) matrices. To reduce the computational overhead of matrix operations during inference, the three layers share the query matrix from the first Transformer layer. Additionally, the query matrix of the first Transformer layer is downscaled while maintaining its original dimensions. Since this approach only detects moving objects, it significantly enhances detection reliability.

Event cameras detect moving objects with microsecond (μs) latency, whereas neural network-based object detection incurs 7–8 millisecond (ms) delays. To enhance real-time processing performance, current event density (spatiotemporal thickness) provides real-time velocity input, and previously estimated object position serves as positional input. Defining the state vector at time k as xk = [dk, vk]T, we design the Kalman filter with state equation 10, measurement equation 11 and covariance matrices equation 12. Δt denote the temporal interval between event-based detections. σa denotes the standard deviation of acceleration noise. σb denotes the standard deviation of displacement noise. F denotes the state transition matrix. H denotes the observation matrix. The Kalman filtering method is shown in Figure 8A. Through experiment, the performance metrics are shown in Figure 8B. (10) { x k ∣ k − 1 = F x k − 1 ∣ k − 1 F = [ 1 Δt 0 1 ] (11) { z k = Hx k + v k H = [ 1 0 ] (12) Q = [ Δ t 4 4 σ a 2 Δ t 3 2 σ a 2 Δ t 3 2 σ a 2 Δ t 2 σ a 2 ] , R = σ z 2

1) Hydraulic system modeling in AMESim

When constructing the hydraulic system model in AMESim, components from different libraries are color-coded for clarity: blue represents hydraulic library elements, red denotes signal library components, and green indicates mechanical library parts. The controller is implemented using the Simulink interface module from the Interface library. The AMESim model of the hydraulic system is illustrated in Figure 9A.

2) Control system modeling in MATLAB/Simulink

Based on the operational principles of wave compensation systems for integrated installation of offshore wind turbine, the control model regulates cylinder displacement by adjusting the proportional directional valve opening. During cylinder extension, the pump and accumulator rapidly replenish hydraulic fluid to maintain flow demand. Conversely, during cylinder retraction, the accumulator absorbs excess fluid to mitigate hydraulic shock. The Simulink implementation of this control system is presented in Figure 9B.

3) Dynamic modeling of wave compensation systems

Heave force analysis and modeling assumptions for integrated installation of offshore wind turbine (Lei, 2015; Zhang and Sheng, 2022):

Assumption 1: The hook, rigging, and turbine share colinear centers of mass along the heave axis, forming a unified rigid body without relative motion.

Assumption 2: Secondary effects are neglected, such as aerodynamic drag forces, self-weight and elastic deformation of lifting assemblies, and friction between compensation cylinders and turbine base.

Simplification basis for wave compensation system dynamics model:

Simplification 1: The vessel’s heave motion induced by waves is idealized as a sinusoidal excitation.

Simplification 2: During turbine lowering, the cables are treated as rigid bodies, and the hook moves downward at a constant velocity (v).

Simplification 3: The wave compensation mechanism is installed on the pile-founded platform, with its key features including mounting atop the pre-installed foundation piles. The compensation system is modeled as a variable spring-damper with equivalent stiffness (k), damping coefficient (c), and turbine displacement (x).

Based on the preceding assumptions and simplifications, the mechanical analysis of the wind turbine hoisting system and the dynamic model of the compensation system are presented in Figures 10A,B.

Based on the established assumptions and dynamic model, the force balance equation for the system’s center of mass is derived as follows (Jia et al., 2017; Niu et al., 2017):

When the turbine descends at constant velocity (a = 0): (13) F 1 + F 2 + ( − G ) + ∑ i = 1 8 F i = 0

Wave-induced acceleration (a ≠ 0) modifies the balance to: (14) Ma = Mg − [ F 1 + F 2 ] − ∑ i = 1 8 F i

In equations 13, 14 F 1 , F 2 represents the tension forces from crane hooks, F i ( i = 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ) represents the thrust forces from 8 compensation cylinders, G = Mg represents total weight of turbine and rigging, where M represents mass.

When the turbine contacts the compensation cylinders, the piston becomes the critical load-bearing component (Liu, 2010; Yao, 2015). The force analysis diagram is shown in Figure 10C. The external load acting on the piston rod is derived as shown in equation 15: (15) F w = Mg − F 1 − F 2

The piston rod and its coupled load exhibit dynamic response shown in equation 16: (16) F a = m d 2 x d t 2

The liquid in the cylinder acts as an equivalent spring. When compressed or stretched, this spring-like medium deforms, with the deformation equal to the piston rod’s displacement within the hydraulic cylinder. The compressed gas in the system tends to restore its original state, generating a restoring force that can be expressed as shown in equation 17: (17) F k = kx

The liquid in the cylinder generates resistance during motion. This resistance force magnitude depends on three key factors: the hydraulic oil flow rate, the oil viscosity, and the resistance coefficient. Their relationship can be expressed as shown in equation 18: (18) f = c · dx dt

In summary, the equation of motion for the hydraulic cylinder piston can be derived as shown in equation 19: (19) m d 2 x dt 2 + kx + c · dx dt = Mg − F 1 − F 2

1) Compensation performance simulation of displacement sensor/NeuroVI camera under step excitation

The target displacement was configured as a unit step input (amplitude = 1). As shown in Figure 11A, the system maintained stability when using the conventional displacement sensor; however, it exhibited an extended settling time. In comparison, the NeuroVI camera-based system demonstrated significantly improved dynamic response, achieving stable-state regulation within 0.3 s—a marked enhancement in transient performance over traditional sensor methods.

2) Compensation performance simulation of displacement sensor/NeuroVI camera under sinusoidal excitation

The target displacement was modeled as a sinusoidal signal with an amplitude of 1, where the ideal output followed a standard sine function. As illustrated in Figure 11B, the displacement signal acquired by the conventional sensor exhibited a noticeable phase lag compared to the target displacement, indicating a slight delay in response. In contrast, the NeuroVI camera-based displacement tracking demonstrated near-perfect alignment with the reference signal, achieving significantly shorter settling time and higher accuracy. This confirms that the NeuroVI camera ensures superior system stability over traditional displacement sensors.

3) Compensation performance simulation of displacement sensor/NeuroVI camera under irregular waves

Ocean waves exhibit high uncertainty and randomness, typically characterized as irregular waves in hydrodynamics (Su et al., 2021). Through extensive experiments and field data analysis, researchers have established spectral wave models, including the Pierson-Moskowitz (P-M) spectrum, ITTC two-parameter spectrum, and JONSWAP spectrum. Among these, the JONSWAP spectrum provides the closest approximation to real-world wind-wave conditions. Thus, this study employs the JONSWAP spectrum to simulate wave profiles under Sea State 4 (Zhao et al., 2024; Yin and Ran, 2023). Using the generated wave profile as the target displacement, the simulation results are presented in Figure 11C. The data demonstrate that the displacement signals acquired by the NeuroVI camera exhibit the highest consistency with the target displacement, achieving significantly superior compensation performance compared to conventional methods.

4) Stability comparison of compensation performance: displacement sensor vs. NeuroVI camera

To simulate the dynamic load during wind turbine lowering, a ramp signal was applied to represent the gradually increasing force on the compensation cylinder. Meanwhile, wave-induced disturbances were modeled as a sinusoidal signal (Huang et al., 2017), replicating realistic marine conditions during integrated installation of offshore wind turbine.

As demonstrated in Figures 11D,E, the velocity response of the compensation cylinder reveals significant performance differences between signal acquisition methods. The NeuroVI camera-based system exhibits superior stabilization, maintaining near-constant cylinder velocity compared to conventional displacement sensors. These results confirm that the proposed NeuroVI-based wave compensation system ensures a safe and stable operational environment for integrated installation of offshore wind turbine.