Underwater Moving Target Localization Based on High-Density Pressure Array Sensing

Abstract

The artificial lateral line sensing principle provides a promising approach for underwater target perception and the navigation of underwater vehicles in complex flow environments. However, the highly nonlinear hydrodynamic mechanisms in complex flow fields make it difficult to establish accurate analytical models, which limits the development of high-precision perception and localization methods for underwater moving targets. In this study, a high-fidelity simulation model is established to characterize the pressure field variations induced by a moving source on an artificial lateral line pressure array. The influences of source velocity and sensing distance on the sensitivity and discretization characteristics of the pressure array are systematically investigated. Simulation results indicate that the sensor density of the pressure array is strongly correlated with the spatial resolution of the acquired pressure data, and a resolution of 50 sensors per meter is selected as the best-performing configuration by balancing sensing accuracy and sensor quantity. Under this configuration, the pressure distribution induced by the moving source exhibits clear and distinguishable spatiotemporal features, making it suitable for deep learning-based modeling. Furthermore, a large-scale temporal pressure dataset is constructed based on high-fidelity simulations under multiple motion directions and velocity conditions, and a spatiotemporal neural network is employed to predict the position of the underwater moving source. Experimental results demonstrate that, for straight-line underwater motion scenarios, the average localization error is within 7 cm, and a classification accuracy of 71% is achieved in practical engineering experiments. These results indicate that the proposed artificial lateral line pressure array design and deep learning-based prediction framework provide a feasible and effective solution for underwater target perception and localization in complex flow environments.

1. Introduction

Underwater exploration and inspection tasks have become increasingly demanding with the rapid expansion of offshore infrastructure, such as subsea pipelines, renewable energy installations, and coastal monitoring systems. In diverse operational scenarios, unmanned underwater vehicles (UUVs)—including autonomous underwater vehicles (AUVs) and remotely operated vehicles (ROVs)—are frequently required to navigate in shallow waters, confined spaces, or in close proximity to man-made structures. In these settings, hydrodynamic disturbances and complex boundary interactions significantly complicate the local flow field [1,2]. Under such challenging conditions, conventional long-range sensing modalities, such as sonar and optical imaging, often suffer from acoustic multipath effects, environmental noise, or severely limited visibility [3]. Consequently, there is a critical need for reliable near-field perception mechanisms capable of detecting local flow variations, which are essential for precise navigation, obstacle avoidance, and target localization in complex underwater environments.

As a near-field sensing modality, the biological lateral line system of fish is insensitive to complex acoustic and optical environments and enables the rapid perception of environmental disturbances, supporting behaviors such as obstacle avoidance, prey capture, predator evasion, and schooling. Consequently, bio-inspired lateral line sensing is expected to provide a robust alternative for near-field perception, localization, and navigation of UUVs in complex flow environments, offering situational awareness inputs for near-field sensing, obstacle avoidance, and navigation control.

Inspired by the unique near-field sensing capability of the fish lateral line system, researchers have sought to replicate this biological sensing mechanism in engineering applications by developing biomimetic artificial lateral line arrays for unmanned underwater vehicles (UUVs). The objective is to endow UUVs with perception and maneuverability comparable to those of fish, which has become a prominent research topic in the field of biomimetic engineering [4,5,6]. In 2007, Liu et al. developed a biomimetic artificial lateral line array using improved flow sensors as the basic sensing units [7,8]. The overall configuration adopted a cross-shaped layout, in which direction-sensitive flow sensors were alternately arranged in orthogonal orientations along the surface of a cylindrical structure. Experimental studies involving the localization of a dipole source and a crayfish were conducted to validate the sensing performance of the proposed artificial lateral line system. Furthermore, by mimicking the canal lateral line structure, the sensors were encapsulated inside perforated ducts, leading to the development of a canal-type artificial lateral line array [9], in which a flow sensor was placed within the duct between adjacent pores. The sensing direction of the sensors was aligned with the axial direction of the duct, and the additional canal structure was shown to significantly suppress noise.

Abdulsadda and Tan proposed a flow sensing unit based on the sensing characteristics of ionic polymer metal composites (IPMCs) and developed artificial lateral line arrays for underwater robots and vehicles [10,11]. The spacing between adjacent sensors was set to 2 cm, under which the array achieved relatively optimal dipole source localization performance [12]. In 2015, the same research group developed an artificial lateral line system with combined sensing capabilities by integrating flow and pressure sensing characteristics [13], enabling the perception of inflow velocity magnitude and direction, as well as the relative position of upstream obstacles, thereby achieving rheotaxis and station-keeping control of a fish-shaped underwater vehicle. In 2018, Sharif et al. proposed a novel differential pressure sensor design method based on canal lateral line pressure sensing principles [14]. Subsequently, Sharif et al. introduced a differential pressure sensor structure integrated into the vehicle body [15], providing insights into the integrated design of artificial lateral line systems for underwater vehicles.

Wang et al. installed an artificial lateral line system based on pressure sensor arrays on a boxfish-inspired robotic fish, enabling swimming speed estimation [16] and mutual perception between neighboring robotic fish [17]. Zhou et al. deployed pressure sensor arrays on both sides of a robotic fish to perceive flow velocity [18], which were further applied to propulsion and station-keeping control [19]. Hu et al. applied empirical mode decomposition (EMD) and support vector machines (SVMs) to achieve the intelligent detection of artificial lateral line signals in a bio-inspired robotic fish [20].

Martiny constructed an autonomous underwater vehicle that mimicked the passive sensing function of the fish lateral line system by using hot-wire anemometers to measure local flow velocities around the hull, enabling object detection, localization, and avoidance [21]. Dagamseh employed bio-inspired artificial hair sensors arranged in a lateral line configuration, combined with beamforming techniques, to localize dipole sources in air [22]. Abdulsadda et al. achieved near-field dipole source localization using multilayer perceptron neural networks [10]. Wolf et al. compared the performance of various neural networks for near-field target localization [23,24]. Liu et al. applied feedforward neural networks for multi-parameter estimation and reported an estimation accuracy of up to 93% [25]. Tuhtan et al. proposed a flow velocity estimation algorithm combining the Pearson product-moment correlation coefficient with multilayer perceptron neural networks [26], while Lakkam et al. explored the application of artificial neural networks in target shape recognition [27]. Wolf et al. proposed a two-dimensional sensitive artificial lateral line composed of eight all-optical flow sensors, which was used to measure the hydrodynamic velocity distribution along the sensor array in response to nearby moving objects and subsequently reconstructed the object position using feedforward and recurrent neural networks [28].

The literature survey reveals that most existing studies focus either on lateral line sensors themselves or on lateral line sensing algorithms in isolation, while relatively few investigations address lateral line sensing from a system-level application perspective. In this work, single-point lateral line sensors (pressure sensors) are analogized to “pressure pixels” in visual perception. By optimizing the arrangement of high-density pressure pixels and combining spatiotemporal neural network models, moving targets are perceived based on the spatiotemporal variations of the pressure pixels, providing a new perspective and paradigm for near-field perception of underwater vehicles. The main contributions of this paper are summarized as follows:

(1) A high-density pressure-sensing hydrodynamic simulation model is established, in which the topology of the pressure sensor arrangement is optimized by considering the spatiotemporal sensitivity of the “pressure pixels” and the deployment cost. Through orthogonal experimental design and CFD simulations, the fluid velocity and pressure at the locations of artificial lateral line pressure sensing units are computed under different angles of attack, inflow velocities, and pressure pixel densities, and the sensor array density is optimized using spatiotemporal sensitivity metrics.

(2) A dataset is constructed based on scanning data acquired using the optimal pressure pixel array density. A spatiotemporal neural network is employed to develop a near-field perception algorithm that enables the artificial lateral line array to more closely emulate the environmental information sensing mechanism of biological lateral lines. A dataset is constructed based on scanning data acquired using the selected best-performing pressure pixel array density. A spatiotemporal neural network is employed to develop a near-field perception algorithm that enables the artificial lateral line array to better emulate the environmental sensing mechanism of biological lateral lines. The proposed approach is applied to localize moving targets in simulation environments and to accurately classify the positions of oscillating excitation sources upstream, providing both theoretical support and an engineering demonstration for near-field perception based on high-density pressure pixels.

2. Fluid Dynamics Simulation Model of Pressure Array

2.1. Simulation Model Construction

The simulation experiment is designed to be conducted in a stationary water domain for a two-dimensional simulation, where the artificial lateral line localizes moving targets in the near field. The perception range of the artificial lateral line is primarily located in the local flow region of the near field. While the local flow field is independent of frequency, the acoustic field is frequency dependent, and thus, the wavelength can be used to measure the specific range of different flow regions. The dipole flow generated by a circular target source moving at a constant speed has a range approximately equal to $\lambda /2\pi$ from the center (where $\lambda$ is the wavelength of underwater sound).

Along the axis of motion of the dipole-like source and in the perpendicular plane, particle movement radiates completely from the center, resulting in an infinite range for the dipole flow. However, the acoustic field generally forms completely only at distances greater than one wavelength. Therefore, the detection of surrounding targets by the artificial lateral line mainly occurs within the dipole flow region in the local flow area. The effective range of the artificial lateral line’s target perception is roughly the local flow region near the target, with the size of this region being approximately $\lambda /2\pi$ from the target’s center as shown in Figure 1a.

Figure 1. (a) Lateral line sensing range. (b) Schematic of the experimental setup. (c) Pressure and flow field disturbances caused by a moving source passing over the artificial lateral line array.

For example, for targets moving below 100 $\mathrm{Hz}$, the theoretical range of the dipole flow field can reach at least 240 $\mathrm{c}$$\mathrm{m}$. However, in real environments, the target’s flow field is influenced by factors such as the motion intensity of the target, flow field diffusion characteristics, fluid viscosity, and complex water flow disturbances. As a result, the actual effective sensing range of the lateral line is generally smaller than the theoretical value. In the experiment, a rectangular water domain of 200 $\mathrm{c}$$\mathrm{m}$ in width and 150 $\mathrm{c}$$\mathrm{m}$ in height is designed. Its four walls are set as open boundaries to prevent boundary effects on the sensor data. A row of pressure sensors representing the artificial lateral line array is placed centered at 25 $\mathrm{c}$$\mathrm{m}$ above the bottom wall. To observe a more pronounced effect, the sensor array is designed to be 100 $\mathrm{c}$$\mathrm{m}$ in length. A circular moving source with a diameter of 5 $\mathrm{c}$$\mathrm{m}$ is placed in the near field above the sensor array, moving at different speeds from various starting positions.

The artificial lateral line array captures the pressure variations caused by the movement of the source, simulating the working environment of the real artificial lateral line in natural conditions. The schematic of the experimental setup is shown in Figure 1b.

The simulation experiment is conducted using the COMSOL Multiphysics^® software, version 6.2 (COMSOL Multiphysics^®, https://www.comsol.com), with the geometric model configured as described in the experimental design, centered at (0, 0). To study pressure data under various conditions, the position of the circular moving source is adjustable within the geometry. To closely simulate the real environment, the material of the moving target is chosen as aluminum with solid physical parameters, rather than the movement of the boundary of the fluid domain. The velocity of the moving target is set to match that of the source. The domain is set to specify the velocity of the moving target source. The fluid domain is configured for laminar flow, and the pressure in COMSOL fluid simulations refers to the pressure drop, also known as relative pressure. Therefore, a reference point for pressure must be set within the fluid domain. We set the lower-left corner of the rectangular fluid domain as the pressure constraint point. Furthermore, the four boundaries of the rectangular domain are configured as open boundaries, not only to prevent the effects of walls on the simulation but also to save computational resources at the boundary. In addition, multiple domain point pressure probes are placed at predetermined locations to simulate pressure sensors, which capture the pressure data of the fluid. The pressure and flow field disturbances when the moving source passes over the artificial lateral line array are shown in Figure 1c.

2.2. Mesh Independence Verification

The accuracy obtained from any finite element analysis model is directly related to the finite element mesh used. The finite element mesh is employed to divide the CAD model into many smaller domains, referred to as elements, and a set of equations is solved on these elements. These equations are approximated using a set of polynomial functions defined on each element. As the mesh is refined, the elements become smaller, making the solution progressively closer to the true solution. The construction of the mesh plays a crucial role in the computational process of finite element models. In this experiment, to ensure the validity of the high-density sensor array data, the mesh refinement level is set to be finer, with a simulation duration of 1 s and a time step of 0.1 s.

We selected mesh element sizes as fine and ultra-fine for comparison as shown in Figure 2. The pressure averages at the last time step for the pressure probes at the two ends and the center of the array were chosen, as these three datasets are representative in artificial lateral line sensor arrays with different densities. Additionally, these provide more diverse data, and the mesh calculation at the last time step is the most stable, producing the most significant pressure changes. The moving source is still a circular geometry with a diameter of 5 cm, initially positioned at (−50, 0). The movement speeds are 0.1, 0.5, and 1 m/s, and three comparisons are made in the same environment. Table 1 presents the experimental results for mesh independence verification.

Figure 2. Mesh comparison: (a) Fine mesh with 2433 elements; (b) Ultra-fine mesh with 22,674 elements.

Table 1. Comparison of pressure averages and their absolute errors under different meshes.

Speed (m/s)	Pressure Average (Pa)		Absolute Error (Pa)
	Fine Mesh	Ultra-Fine Mesh
0.1	0.000183	0.002858	0.002675
0.5	0.380474	0.267606	0.112868
1.0	−2.576490	−2.052960	0.523530

From Table 1, it can be seen that the maximum error caused by the mesh is within 0.5 Pa, thus verifying that the differences in experimental results due to mesh refinement are negligible. The experiment is independent of the mesh refinement level.

3. Pressure Pixel Sensitivity Definition and Evaluation Indicators

Acquiring flow field information is a fundamental prerequisite and a key step for underwater near-field target localization. The spatial distribution of fish lateral line sensors across different parts of the body is the result of long-term natural evolution, enabling fish to robustly adapt to complex flow field environments. However, for underwater vehicles with diverse geometries and operational requirements, such biologically evolved distributions are not necessarily optimal under all scenarios. Therefore, this study conducts a metric-based parametric investigation of artificial lateral line array configurations for underwater near-field target localization. Considering the practicality and manufacturability of engineering implementations, particular attention is given to uniform linear array configurations. The effectiveness of uniform linear arrays with different sensor element densities is systematically analyzed using defined quantitative performance indicators to assess their near-field flow sensing and target localization capabilities.

3.1. Experimental Design and Simulation Conditions

This study uses a uniform linear array artificial lateral line as the research object, defining the array resolution as the average number of sensors distributed within the sensor length range. Four cases are considered with $N=10,20,50,100$. The array range is set from $(-50,0)$ to $(50,0)$. The target moves at speeds of $0.1\mathrm{m}/\mathrm{s}$, $0.5\mathrm{m}/\mathrm{s}$, and $1.0\mathrm{m}/\mathrm{s}$, starting from different initial positions at $(-50,10)$ and $(-50,100)$, and moves at a constant speed along the x-axis. The experiment lasts for 8 s, collecting pressure data from the array at different resolutions and operating conditions.

The raw pressure data recorded by the artificial lateral line array were organized in matrix form. After removing the time columns, only the synchronized pressure signals from all sensors were retained. Each row represents a discrete sampling time step, and each column corresponds to one sensor in the array.

Table 2 presents a representative excerpt of the processed pressure matrix for $N=20$, with the target starting from $(-50,10)$ and moving at $0.1\mathrm{m}/\mathrm{s}$.

Table 2. Representative pressure matrix for $N=20$ (excerpt, 80 time steps).

Time Step	P1 (Pa)	P2 (Pa)	P3 (Pa)	⋯	P20 (Pa)
1	− 2.6823	−2.0042	−0.6980	⋯	−0.1245
2	−2.6468	−1.5061	0.2464	⋯	0.3158
3	−2.5105	−1.9338	−0.0414	⋯	0.0872
⋮	⋮	⋮	⋮	⋱	⋮
78	0.044155	0.063329	0.089017	⋯	0.98287
79	0.042538	0.061572	0.086391	⋯	0.99044
80	0.040839	0.060030	0.083740	⋯	0.99121

3.2. Performance Evaluation Indicators

To comprehensively evaluate the performance of the artificial lateral line array, this paper introduces three types of indicators: array sensitivity (AS), pressure variance (Var), and maximum adjacent pressure difference ($\Delta p_{max}$). These indicators reflect the array’s performance in terms of response sensitivity, result dispersion, and neighboring distinguishability, respectively.

3.2.1. Array Sensitivity (AS)

Sensitivity is a core indicator of sensor performance, representing the ratio of the output increment to the input increment.Array sensitivity is used to measure the contribution of pressure changes between adjacent sensors to the overall array output. It is defined as follows:

$$\mathrm{AS}={\displaystyle \frac{1}{N-1}}\sum _{n=0}^{N-1}{\displaystyle \frac{\left|P_{n+1}-P_n\right|}{\Delta S}}$$

(1)

where N is the array resolution (number of sensors), $\Delta S$ is the sensor spacing, and $P_n$ is the pressure value at the n-th sensor. A higher AS value indicates that the array responds more sensitively to external disturbances.

3.2.2. Pressure Variance (Var)

To reflect the dispersion of data collected by different sensors, this paper introduces the pressure variance indicator to measure the fluctuation of the array’s overall measurement results. It is defined as follows:

$$\mathrm{Var}={\displaystyle \frac{1}{N}}\sum _{n=1}^N{\left(p_n-\overline{p}\right)}^2$$

(2)

where $\overline{p}$ is the mean value of the data collected by the sensors. A larger Var value indicates greater fluctuation in the array’s results and stronger ability to differentiate flow field variations.

3.2.3. Maximum Adjacent Pressure Difference ($\Delta p_{max}$)

When the array density is excessively high or the effective resolution is insufficient, the measurements of adjacent sensors may become very close or even identical. This not only increases manufacturing cost but also makes it difficult to satisfy the accuracy requirements of the sensing system. To address this issue, a maximum adjacent pressure difference indicator is introduced to quantify the distinguishability between neighboring sensors. The indicator is defined as follows:

$$\Delta p_{max}\left(t\right)=\underset{1\le n\le N-1}{max}\left|p_{n+1}\left(t\right)-p_n\left(t\right)\right|$$

(3)

where $p_n\left(t\right)$ is the pressure value at the n-th sensor at time t. $\Delta p_{max}\left(t\right)$ represents the maximum pressure difference between adjacent sensors at time t, and a larger value indicates stronger distinguishability of the array at that time.

3.3. The Impact of Array Density on Sensitivity

Based on the above design and indicators, this paper plots the time series curves of array sensitivity (AS), variance (Var), and maximum adjacent pressure difference ($\Delta p_{max}$) under different resolutions, target speeds, and observation distances, as shown in Figure 3 and Figure 4. By comparing the trends of the three indicators under different conditions, the array’s sensitivity, stability, and distinguishability are analyzed, leading to the identification of the best-performing array layout density within the tested parameter range.

Figure 3. Variation curves of array sensitivity (AS) at distances of 10 cm and 100 cm from the artificial lateral line array in the y-axis direction with different speeds. (a) Speed of 0.1 m/s. (b) Speed of 0.5 m/s. (c) Speed of 1 m/s. Variation curves of variance (VAR) at distances of 10 cm and 100 cm with different speeds. (d) Speed of 0.1 m/s. (e) Speed of 0.5 m/s. (f) Speed of 1 m/s.

Figure 4. Maximum adjacent pressure difference (max $\Delta p$) curves of the artificial lateral line sensor array under different conditions: (a) Distance = 10 cm, $V=0.1$ m/s; (b) Distance = 10 cm, $V=0.5$ m/s; (c) Distance = 10 cm, $V=1.0$ m/s; (d) Distance = 100 cm, $V=0.1$ m/s; (e) Distance = 100 cm, $V=0.5$ m/s; (f) Distance = 100 cm, $V=1.0$ m/s.

As shown in Figure 3, when the speed is low and the distance is short, the AS and Var of the array with lower resolution fluctuate significantly over time. The array with higher resolution has smoother curves, making it easier to capture features in the time series. When the speed remains constant and the distance increases, the array with higher resolution exhibits a significantly higher AS than the array with lower resolution when the target exceeds the length of the sensor array. Once the target surpasses the near-field perception range of the artificial lateral line, the effect of resolution becomes negligible as the distance increases and the speed increases. It is evident that the higher the resolution, the higher the sensitivity, the more diverse the data, and the smoother the time series curve, preserving the time series features effectively. Furthermore, the curves for the arrays with a resolution of 50 and 100 are very close to each other.

According to Figure 4, within the effective sensing range, arrays with resolutions of 10, 20, and 50 all achieve the accuracy requirement of the maximum adjacent pressure difference (max $\Delta p$), indicating that an appropriately selected resolution is sufficient to meet sensor accuracy constraints. Although the array with a resolution of 100 exhibits excellent performance in terms of AS and VAR, its max $\Delta p$ is excessively small. As a result, a large number of measurements become numerically indistinguishable, leading to increased data acquisition cost and power consumption, as well as a substantial computational burden for subsequent predictive algorithms. In comparison, the array with a resolution of 50 produces AS and VAR curves that closely approximate those of the array with a resolution of 100 under various operating conditions, while its max $\Delta p$ generally satisfies the sensor accuracy requirement. This configuration therefore achieves high sensing accuracy without unnecessary resource expenditure. Experimental results demonstrate that the sensor array exhibits the best overall performance at a resolution of 50 among the tested configurations. Consequently, to balance the sensing accuracy and system cost, the resolution of the artificial lateral line array sensor is set to 50.

4. ConvLSTM Model Construction for Moving Target Localization Using Artificial Lateral Line Array Simulations

4.1. Dataset Construction

4.1.1. Experimental Design

In this study, a spherical target is adopted as the moving object model due to its geometric symmetry and well-characterized hydrodynamic behavior. The spherical geometry generates stable and reproducible flow disturbance patterns, which are suitable for systematically evaluating the sensing performance of the artificial lateral line array without introducing additional complexities from irregular target shapes. Due to the limitations of target ball motion conditions in practical engineering experiments, it is difficult to implement the experiment. To validate whether the lateral line array can recognize a moving ball under different flow velocities, a two-dimensional ideal fluid simulation environment was constructed based on COMSOL Multiphysics to collect pressure signal data induced by the target motion. The simulation region was set as a rectangular water domain of $150\times 120\mathrm{cm}$, with an artificial lateral line array placed at the bottom to simulate the measurement process of multi-point pressure sensors. The target was a circular ball with a radius of $2.5\mathrm{cm}$.

In the simulation, the ball moved at a constant speed, with a speed range from $0.1\mathrm{m}/\mathrm{s}$ to $1.0\mathrm{m}/\mathrm{s}$, in steps of $0.1\mathrm{m}/\mathrm{s}$. The movement direction was set in multiples of 45°, with eight directions in total (0°, 45°, 90°, …, 315°) as shown in Figure 5a. At the geometric center of the ball, domain point probes were placed to collect its position information. The sampling duration was $1\mathrm{s}$, with a time step of $0.1\mathrm{s}$, totaling 10 time steps. Each combination of starting point and direction corresponds to an independent simulation, resulting in a total of 14,400 spatiotemporal pressure data samples.

Figure 5. (a) Schematic of the linear motion ball position recognition simulation in eight directions. (b) Time-domain pressure response of the artificial lateral line sensor array. (c) Frequency-domain representation of the sensor array’s pressure response.

4.1.2. Data Preprocessing

Since network training requires a well-structured dataset, during the simulation process, the target may pass through the grid where the sensor probes are located, resulting in some missing pressure data (NaN). Additionally, there may be disturbance signals with very low amplitudes that have no physical significance. If these issues are not addressed, they may affect the subsequent model training and prediction accuracy. Therefore, the raw data undergoes preprocessing as the first step.

For NaN data, interpolation is performed using the median value of adjacent sensors. For array endpoints, the data from the previous time step is used. For points where the pressure amplitude is less than $0.01\mathrm{Pa}$, the value is replaced with 0 to filter out small disturbances that are physically negligible. Since the data is generated in an ideal fluid environment with no random noise interference, no additional denoising process was applied. The processed data more accurately reflects the dynamic pressure changes caused by the target’s movement.

4.1.3. Feature Analysis

To analyze the characteristics of the pressure signals measured by the array, both time-domain and frequency-domain analyses were conducted on the collected data as shown in Figure 5. Figure Figure 5b shows the time-domain pressure response, where it can be observed that the pressure signal amplitude increases significantly when the target approaches the sensor array. Figure 5c shows its spectral distribution, with the main energy concentrated in the range of 5–$15\mathrm{Hz}$, corresponding to the periodic disturbances caused by the target’s uniform motion.

From the feature analysis results, it can be seen that the array pressure data exhibits dynamic disturbances caused by the target’s motion in the time dimension, and amplitude differences across different sensor locations in the spatial dimension. This data has significant spatiotemporal features, making it suitable for modeling and recognition using Convolutional Long Short-Term Memory Networks (ConvLSTM).

4.2. Prediction Model and Experimental Results

While simpler signal processing methods and traditional machine learning models (such as SVR) were initially considered, they proved insufficient in handling the complex spatiotemporal coupling of the sensor array data. Consequently, a deep learning approach was prioritized. In deep learning, selecting an appropriate network architecture based on data characteristics is crucial. Convolutional Long Short-Term Memory (ConvLSTM) is a hybrid model that integrates convolutional neural networks (CNNs) and Long Short-Term Memory (LSTM) networks, specifically designed to handle data with spatiotemporal dependencies, such as video sequences and meteorological data. Unlike traditional LSTM, ConvLSTM replaces the fully connected operation with convolutional operations, allowing it to capture both spatial features and temporal dynamics simultaneously.

4.2.1. Convolutional Long Short-Term Memory Network (ConvLSTM) Principle

Figure 6 illustrates the internal structure of ConvLSTM and its temporal information transmission mechanism. Unlike traditional LSTM, ConvLSTM replaces matrix multiplication of the input and hidden states with convolution operations (∗) to capture spatiotemporal correlations. The model controls information updates and transmission through the forget gate $f_t$, input gate $i_t$, and output gate $o_t$. The cell state $C_t$ stores long-term dependencies, while the hidden state $H_t$ outputs the feature response at the current time step. The complete computational process is given in Equations (4)–(9).

Figure 6. Computational structure of the ConvLSTM model.

The input gate computation is given by

$$i_t=\sigma (W_{xi}\ast X_t+W_{hi}\ast H_{t-1}+b_i)$$

(4)

where ∗ denotes the convolution operation, $W_{xi}$ and $W_{hi}$ are convolutional kernel weights, and $b_i$ is the bias term.

The forget gate computation is given by

$$f_t=\sigma (W_{xf}\ast X_t+W_{hf}\ast H_{t-1}+b_f)$$

(5)

The candidate cell state is computed as

$${\tilde{C}}_t=tanh(W_{xc}\ast X_t+W_{hc}\ast H_{t-1}+b_c)$$

(6)

The cell state update formula is

$$C_t=f_t\circ C_{t-1}+i_t\circ {\tilde{C}}_t$$

(7)

where ∘ denotes element-wise multiplication.

The output gate computation is given by

$$o_t=\sigma (W_{xo}\ast X_t+W_{ho}\ast H_{t-1}+b_o)$$

(8)

Finally, the hidden state $H_t$ is computed as

$$H_t=o_t\circ tanh\left(C_t\right)$$

(9)

4.2.2. ConvLSTM Model Construction and Training

In this paper, the ConvLSTM model is built using the PyTorch software, version 2.1.0 (https://pytorch.org/) deep learning framework, with the core structure, Convolutional Long Short-Term Memory Unit (ConvLSTM Cell), implemented first. To prevent overfitting due to an overly deep network, both two-layer and three-layer architectures were tested. The results indicated that the two-layer model performed better on the validation set, so a two-layer ConvLSTM was selected as the backbone architecture. Considering that the experimental data comes from a single operating condition and the sample distribution is concentrated, the batch size was set to 4 to ensure training stability and generalization ability.

During the model training, the dataset was split into training and validation sets in a 7:3 ratio for model learning and performance evaluation. To accelerate convergence and suppress oscillations, a warm-up with decay learning rate strategy was employed. Initially, a smaller learning rate was used during the warm-up phase, then gradually increased to the target value, and subsequently reduced in the later stages.

The training task of the model is to predict the continuous position of the target in the temporal pressure field, which is a typical regression learning problem. The loss function used is Mean Squared Error (MSELoss), which measures the prediction deviation by averaging the squared differences between predicted and true values. This function smoothly reflects the overall error in regression tasks and provides stable gradients during training, which is beneficial for model convergence.

The formula for the Mean Squared Error loss (MSELoss) is

$$\mathrm{MSEloss}={\displaystyle \frac{1}{N}}\sum _{i=0}^N\left({(x_{pi}-x_{ti})}^2+{(y_{pi}-y_{ti})}^2\right)$$

(10)

where N is the training batch size, and $x_{pi},y_{pi}$ are the predicted coordinates of the target, while $x_{ti},y_{ti}$ are the true coordinates of the target.

The initial learning rate was set to $0.01$, and the convergence curve of the loss function after 300 epochs is shown in Figure 7.

Figure 7. Training loss curve of the ConvLSTM network during 300 epochs of training.

To quantitatively evaluate the prediction accuracy of the model, the average Euclidean distance metric (DS) is introduced, and its computation formula is as follows:

$$\overline{DS}={\displaystyle \frac{1}{N}}\sum _{i=0}^N\left(\sqrt{{(x_{pi}-x_{ti})}^2+{(y_{pi}-y_{ti})}^2}\right)$$

(11)

Based on the analysis of the validation results, the ConvLSTM network achieves rapid convergence, with the validation loss stabilizing at approximately 39 within a small number of training epochs. Correspondingly, the average Euclidean distance satisfies $\overline{DS}<7\mathrm{cm}$. Considering that the actual spatial extent of the circular target source is larger than its center coordinates, a prediction error of approximately $7\mathrm{cm}$ indicates that the estimated position is very close to the true target location. These results demonstrate that the ConvLSTM network exhibits strong predictive performance for moving target localization using artificial lateral line array sensor data.

5. Experimental Validation of ConvLSTM-Based Oscillatory Moving Target Localization Using an Artificial Lateral Line Array

To verify the positioning and identification capability of the artificial lateral line array in real underwater environments, this section establishes an excitation source position classification experimental platform in a recirculating water tank. The platform is combined with a spatiotemporal Convolutional Long Short-Term Memory network (ConvLSTM) to classify and analyze the performance of different excitation source positions.

5.1. Experimental Platform and System Construction

The experimental platform is shown in Figure 8. A reciprocating motor is used as the excitation source to generate stable and controllable periodic water waves. The device consists of a servo motor, a link mechanism, and an aluminum paddle. The motor drives the paddle to swing in the water at a set angle, with a swing amplitude of $\pm$30° and a paddle size of $20\mathrm{cm}\times 10\mathrm{cm}$. The paddle is submerged about $5\mathrm{cm}$ below the water surface to ensure a stable wave pattern and minimal bubble interference.

Figure 8. Excitation motor device and working process: (a) reciprocating motor structure; (b) paddle installation diagram; (c) paddle reciprocating motion.

The relationship between the swing frequency and input voltage is shown in Table 3. The experiment mainly uses a $12\mathrm{V}$ voltage, which corresponds to an excitation frequency of $1.58\mathrm{Hz}$, a frequency that produces stable and regular wave patterns.

Table 3. Excitation motor input voltage and swing frequency relationship.

Gear	Input Voltage (V)	Excitation Frequency (Hz)
1	9.0	1.08
2	10.5	1.31
3	12.0	1.58

The hardware configuration of the artificial lateral line pressure array is depicted in Figure 9. As shown in Figure 9a–c, the system features a planar “artificial skin” architecture, where 200 pressure sensor nodes are uniformly integrated onto a $400\mathrm{mm}\times 200\mathrm{mm}$ stainless-steel substrate. With a spatial density of 50 units/m in both longitudinal and transverse directions, this bio-inspired design captures high-fidelity, spatially distributed hydrodynamic signatures, providing a robust data foundation for localization algorithms.

Figure 9. Overall system configuration of the artificial lateral line pressure array: (a) experimental setup; (b) front view; (c) rear view; (d) internal electronic configuration; (e) modular flexible pressure sensor components.

The system utilizes a modular FPC-based architecture (Figure 9d,e), which facilitates scalable configuration and simplifies maintenance. To emulate biological neuromasts, high-precision commercial absolute pressure sensors (MSPC15M-ADS1) were employed. Each sensing element integrates a MEMS piezoresistive transducer with a 24-bit Sigma-Delta ASIC, delivering calibrated ${\mathrm{I}}^2\mathrm{C}$ outputs with a resolution of $0.1\mathrm{Pa}$ and a measurement range up to $1.5\mathrm{MPa}$. Housed in a compact $2.7\times 2.7\times 1.77\mathrm{mm}$ metal-lid package, these sensors ensure high-speed acquisition (6 ms response time) with minimal thermal drift, capturing both static and dynamic pressure variations effectively.

Figure 10a,b illustrate the experimental configuration and coordinate system for the perception tests. The artificial lateral line array is installed horizontally at a depth of $15\mathrm{cm}$ below the water surface. As defined in the schematic, the coordinate origin is located at the center of the array’s trailing edge, with the longitudinal axis (Y-axis) aligned parallel to the flow direction. The excitation source, comprising a reciprocating motor and a partially submerged blade, is positioned upstream to generate hydrodynamic disturbances that propagate toward the sensing nodes.

Figure 10. Excitation source perception experiment. (a) Schematic of the excitation source perception setup. (b) Layout of excitation source positions.

The arrangement of excitation source positions is summarized in Table 4. Taking the center of the array tail as the coordinate origin, three distances of 60, 70, and $80\mathrm{cm}$ are defined along the x-axis, while six positions of $-30$, $-20$, $-10$, 0, 10, and $20\mathrm{cm}$ are defined along the y-axis, resulting in a total of 18 excitation source locations.

Table 4. Relative positions between the array board and the paddle oscillation centerline.

Axis	Distance from Excitation Source to Array Tail Center ($\mathbf{cm}$)
X-axis	60, 70, 80
Y-axis	−30, −20, −10, 0, 10, 20

5.2. Data Acquisition and Model Training Method

To ensure experimental repeatability and provide a reference baseline, background pressure signals were collected in advance under non-excitation conditions at different flow velocities. A total of 100 samples were recorded and used as baseline data.

The pressure signals collected by the array board are first processed using smoothing filtering and bidirectional Butterworth bandpass filtering (0.5–3 Hz), and subsequently fed into a ConvLSTM-based spatiotemporal classification network for excitation source position recognition.

Since the excitation source locations are discrete points, the position recognition task is essentially a multi-class classification problem. A ConvLSTM classification network with a spatiotemporal convolutional structure is employed in this study. The final layer of the network adopts a softmax activation function to output the probability distribution over 18 excitation source classes. The cross-entropy loss function is used as the optimization objective, defined as

$$L=-{\displaystyle \frac{1}{n}}\sum _{i=1}^n\sum _{j=1}^C{y}_{i,j}log\left({\widehat{y}}_{i,j}\right)$$

(12)

where n denotes the number of samples, C represents the total number of classes, $y_{i,j}$ is the ground-truth label of the i-th sample in one-hot encoding, and ${\widehat{y}}_{i,j}$ is the predicted probability of class j. To alleviate overfitting and mitigate class imbalance, label smoothing and class weighting strategies are incorporated during training.

The experimental data are divided into 18 classes according to the excitation coordinates. For each class, pressure signals with a duration of $1\mathrm{s}$ are extracted from the raw data at fixed intervals, resulting in $14,400$ samples per class. The dataset is split into training and validation sets with a ratio of $7:3$. The correspondence between class labels and excitation coordinates is shown in Table 5.

Table 5. Correspondence between class labels and excitation source coordinates (partial).

Class	0	1	⋯	16	17
Excitation source coordinate	(60, −30)	(60, −20)	⋯	(80, 10)	(80, 20)

During training, the batch size is set to 4, and the initial learning rate is $0.01$. The model is trained for a total of 300 epochs. The convergence curves of the loss function and classification accuracy are shown in Figure 11.

Figure 11. Convergence analysis of the ConvLSTM model during training: (a) convergence curves of training and validation loss; (b) convergence curves of training and validation classification accuracy.

5.3. Experimental Results Analysis

Analysis of the validation results indicates that the artificial lateral line array can effectively predict the approximate position of the excitation source within a certain spatial range. The model converges to a stable state after approximately 200 epochs, achieving a final validation classification accuracy of about $71\%$. Among the $14,400$ samples, 3018 are correctly classified, demonstrating that the proposed ConvLSTM network can extract key spatiotemporal features from underwater periodic flow fields and effectively discriminate excitation source positions.

As shown in Figure 12, the classification results exhibit a certain degree of neighborhood confusion, where misclassifications are more likely to occur between adjacent excitation positions, while confusion between non-adjacent regions is relatively limited. Overall, the classification accuracy decreases as the distance between the excitation source and the array board increases, and higher accuracy is achieved when the source is located closer to the array. This indicates that the artificial lateral line array based on a spatiotemporal convolutional structure is more sensitive to flow disturbances in the near field, whereas signals from distant targets experience amplitude attenuation, phase variation, and reflection interference during propagation, leading to reduced feature separability.

Figure 12. Confusion matrix heatmap.

From a fluid dynamics perspective, the paddle excitation generates more concentrated wave energy in the near-field region, resulting in stronger signal intensity and higher array response amplitudes. Consequently, the classification accuracy in near-field regions is significantly higher than that in far-field regions. Overall, the experimental results validate the feasibility and distance-dependent characteristics of the ConvLSTM-based artificial lateral line array for underwater excitation source localization.

6. Discussion

This study presents an exploratory investigation into the configuration design and performance evaluation of artificial lateral line pressure arrays for underwater moving target localization. The results demonstrate the feasibility of the proposed array design methodology and confirm the effectiveness of the ConvLSTM-based spatiotemporal framework for near-field target localization under controlled conditions. Although promising results have been obtained, several limitations remain and warrant further improvement.

First, the physical modeling in this study is primarily based on the laminar flow regime to investigate the fundamental mechanisms of pressure disturbances under low-speed navigation conditions. At the relatively low Reynolds numbers ($Re$) associated with these velocities, the laminar model effectively captures the core perturbation patterns while avoiding the stochastic noise inherent in fully turbulent simulations. This choice also enabled the execution of large-scale orthogonal experiments within a practical computational timeframe, which would be prohibitively expensive using high-fidelity turbulence closure models (e.g., LES or DNS). Furthermore, since the experimental point-source sensor array effectively captures time-averaged pressure distributions, the laminar-based simulation provides sufficient theoretical guidance that aligns with the dynamic perturbation (dynamic component) extraction logic used in our signal processing. Nevertheless, we acknowledge that in higher-speed engineering practices, turbulent fluctuations and nonlinear fluid–structure interactions become non-negligible. Future work will incorporate turbulence models to evaluate localization robustness under more complex hydrodynamic environments.

Second, the scope of this study is restricted to single targets undergoing linear motion within the near-field region. More complex scenarios, including curvilinear motion, multi-target environments, and three-dimensional localization, have not yet been systematically investigated. These motion patterns may introduce additional ambiguity in pressure field interpretation and increase the difficulty of spatiotemporal feature extraction.

Third, regarding the learning model, while simpler signal processing and traditional machine learning methods (such as Support Vector Regression, SVR) were preliminarily evaluated, they struggled to simultaneously capture the complex inter-sensor spatial correlations and intra-sensor temporal dependencies. Moreover, continuous regression models for coordinate prediction exhibited poor convergence and suboptimal precision given the high-dimensionality of the spatiotemporal features. Consequently, a block-based classification framework was adopted to ensure localization robustness. However, the current ConvLSTM network still remains dependent on training data volume and has not been fully optimized for real-time deployment. Future research will focus on developing high-precision continuous regression models and optimizing computational efficiency for practical underwater robotic systems.

Finally, in the engineering experiments, there remains room for improvement in excitation source localization accuracy. The experimental results are influenced by factors such as environmental conditions, sensor precision, positioning calibration accuracy, and sample size, which introduce uncertainties that are not fully reflected in simulation-based evaluations. Notably, the “no excitation” case was utilized as a baseline calibration in experiments to isolate dynamic signals via Butterworth filtering, a process that ensures consistency with the zero-initial-pressure assumption in simulations.

7. Conclusions

This study investigates the configuration design and performance evaluation of sensor layouts for artificial lateral line pressure arrays, as well as the localization of underwater moving targets. First, a high-fidelity pressure-field simulation model based on a moving source was established. An evaluation method centered on array sensing sensitivity and data acquisition performance was proposed, enabling a quantitative relationship between sensor layout parameters and array sensing performance to be derived. For a one-dimensional uniform linear pressure array, a rational design methodology was further presented. Simulation results demonstrate that, while satisfying data acquisition accuracy requirements, the proposed method can effectively reduce the number of sensors and achieve optimized array configurations, thereby verifying the effectiveness and feasibility of the proposed approach.

Building upon this foundation, the study further addresses the localization of linearly moving targets in the underwater near-field region. Using the selected best-performing pressure array configuration, a temporal pressure dataset was constructed, and a ConvLSTM spatiotemporal convolutional neural network was introduced to learn and predict target positions. Experimental results indicate that the proposed model exhibits good stability and localization accuracy, with an average positioning error of approximately 5–7 cm. Moreover, the localization accuracy shows a linear degradation trend as the distance between the target and the array center increases. In addition, in an engineering excitation source localization experiment, the proposed method achieved a classification accuracy of 71% in position recognition tasks, further demonstrating the potential of artificial lateral line pressure arrays combined with deep learning methods for practical underwater applications.

Future work will focus on extending the present framework toward more realistic and complex underwater environments. In particular, high-fidelity turbulence models and flow-field disturbances will be incorporated to better reflect practical engineering conditions, addressing the limitations of the current laminar-based modeling in high-speed regimes. To further improve localization precision, we will transition from the current block-classification approach to continuous coordinate regression models optimized for high-dimensional spatiotemporal data. Furthermore, more complex motion patterns, including curvilinear trajectories, multi-target scenarios, and three-dimensional localization, will be investigated to enhance system adaptability. From a modeling perspective, lightweight spatiotemporal architectures and model compression techniques will be explored to reduce computational latency and facilitate real-time deployment on underwater robotic platforms. Finally, additional engineering validation experiments under diverse and noisy environmental conditions will be conducted to further strengthen the practical feasibility of artificial lateral line pressure arrays.