A deep-sea mining system time domain prediction method based on physical information and uncertainty quantification

Abstract

The application discloses a deep-sea mining system time domain prediction method based on physical information and uncertain quantification, and belongs to the technical field of intelligent prediction of deep-sea mining equipment. First, an input vector is constructed based on the working condition parameters in the training set, triangular function coding and ship-environment hydrodynamic coupling interaction items. A physical information uncertain quantification network is constructed by introducing a heteroscedastic double-head output layer, wherein the mean head and the variance head both adopt MC-Dropout layers, and the variance head introduces a deep perception prior to modulate the spatial and temporal characteristics of the variance channel. A compound loss function containing mean square error and Gaussian negative log likelihood is constructed to train the model. The prediction result is decomposed for uncertainty, and the corresponding confidence interval is solved by superimposing the total variance and combining the prediction mean. The application considers the prediction accuracy and uncertainty description, provides a physically consistent depth-dependent confidence interval, and is suitable for deep-sea mining hoisting system design verification, safety evaluation and risk warning scenes.

Description

Technical Field

[0001] This invention belongs to the field of intelligent prediction technology for deep-sea mining equipment, specifically involving a time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification. Background Technology

[0002] Deep-sea polymetallic nodules contain strategic metal resources such as manganese, nickel, cobalt, and copper, making them an important target for future mineral resource development. Hydraulic lifting systems, as the primary technology for transporting ore from the seabed to surface mining vessels, typically consist of subsystems including a surface support vessel, a lifting riser with pumps, a relay station, and a seabed ore collection vehicle. During operation, the lifting riser simultaneously withstands coupled dynamic loads from waves, currents, wind loads, ship heave, and internal slurry flow, exhibiting a complex time-varying stress distribution along the pipeline. Accurate and efficient prediction of dynamic stress responses at multiple monitoring depths is crucial for ensuring structural integrity and operational safety in complex marine environments.

[0003] Numerical simulation methods based on finite element method (FEM) and multibody dynamics have been widely used to study the dynamic behavior of deep-sea mining hoisting systems. While these methods can provide high-fidelity predictions, transient simulations of a single deep-sea mining system often require hours of computation, making parameterization studies across hundreds of environmental configurations computationally unfeasible and failing to meet the demands of real-time monitoring and rapid decision-making. Data-driven surrogate modeling offers a feasible approach to accelerate such predictions. Deep learning architectures such as Long Short-Term Memory (LSTM) networks and gated recurrent units (GRUs) are highly capable of capturing nonlinear input-output mappings and have been widely used in sequence modeling tasks. However, purely data-driven models are prone to producing predictions that violate known physical laws when training data is limited. Existing deep learning prediction studies for deep-sea mining systems mostly focus on stress prediction at a single cross-section, failing to achieve simultaneous multi-output mapping from environmental parameters to multi-depth temporal responses.

[0004] Most existing prediction models lack the ability to quantify uncertainty. In safety-critical marine engineering applications, providing only point predictions is insufficient; decision-makers need reliable confidence intervals and information about the sources of prediction uncertainty. The homogeneous variance assumption fails to characterize the spatial variation noise characteristics experienced by monitoring points from near-surface to deep water, and it fails to explicitly decompose uncertainty into interpretable accidental and cognitive components. There is an urgent need for a time-domain prediction method for deep-sea mining systems that can simultaneously meet the following requirements: integrating hydrodynamic priors into the input space through physical information feature encoding; achieving multi-output mapping from low-dimensional static environmental parameters to multi-depth high-dimensional stress time series; providing physically consistent, depth-dependent uncertainty quantification; and decomposing the total uncertainty into accidental and cognitive components. Summary of the Invention

[0005] The purpose of this invention is to provide a time-domain prediction method, system, medium, and product for deep-sea mining systems based on physical information and uncertainty quantification. Through the collaborative design of physical information feature encoding, a hierarchical multi-resolution prediction architecture, a depth-aware heteroscedastic dual-head output layer, and multi-source uncertainty decomposition, rapid, accurate, and probabilistic prediction of the stress response at multiple monitoring depths in deep-sea mining hoisting systems is achieved, providing physically consistent depth-dependent confidence intervals.

[0006] This invention provides a time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification, comprising the following steps:

[0007] A coupled time-domain dynamic model of a deep-sea mining hoisting system was established; the maximum von Mises stress time series data along multiple monitoring depths of the hoisting pipe under various working conditions were acquired, and a training set was constructed.

[0008] A physical information uncertainty quantification network is constructed by introducing a deep-aware heteroscedastic dual-head output layer. After extracting spatiotemporal features from the input vector using the physical information uncertainty quantification network, the features are input into the deep-aware heteroscedastic dual-head output layer. Both the mean head and variance head adopt MC-Dropout layers. The variance head incorporates deep-aware priors to modulate the spatiotemporal features of the variance path. Finally, the dual-head outputs the mean and log-variance of the stress response prediction. Based on Monte Carlo Dropout multiple forward sampling, the uncertainty of the prediction results is decomposed.

[0009] A composite loss function consisting of a weighted combination of mean square error and heteroscedastic Gaussian negative log-likelihood is constructed to train a network for quantifying the uncertainty of physical information.

[0010] The target working condition parameters are input into the trained physical information uncertainty quantification network, and the stress response prediction results of the deep-sea mining hoisting system at multiple monitoring depths are output. The uncertainty of the prediction results is decomposed, and the corresponding confidence interval is solved by superimposing the total variance and combining it with the prediction mean.

[0011] Furthermore, the deep-sea mining hoisting system includes a surface support vessel, a hoisting riser, a booster pump, a relay station, a flexible hose with a buoyancy module, and a mining vehicle; the dynamic model is modeled using the lumped mass method, the hydrodynamic loads are calculated using the Morison formula, the environmental conditions include wave, current, and wind loads, and the six-degree-of-freedom motion of the vessel is synthesized with the target spectrum through frequency domain RAO and applied as the displacement boundary condition of the top of the hoisting riser.

[0012] Furthermore, an input vector is constructed by cascading the operating parameters and their trigonometric function encodings with the ship-environment hydrodynamic coupling interaction term. :

[0013]

[0014] in, For the sake of righteousness, the waves rise high. For the spectral peak period, For the ship's forward speed, , , These are the wave direction angle, wind direction angle, and ocean current direction angle, respectively. The component of the ship's velocity projected along the direction of wave propagation; The component of ship velocity projected along the direction of the coastal current;

[0015]

[0016]

[0017] Furthermore, the input vector is sequentially passed through an adaptive multi-resolution feature fusion module, a hierarchical prediction module with sequence correction, and a dual-path spatiotemporal attention module to extract spatiotemporal features that are both temporally dependent and spatially correlated. The adaptive multi-resolution feature fusion module inputs the expanded normalized input vector into three parallel one-dimensional convolutional branches, which are then cascaded along the channel dimension and processed by a squeeze-excitation block to obtain the channel-recalibrated features.

[0018] Furthermore, the hierarchical prediction module with sequence correction employs two fully connected layers with Dropout to encode the flattened features into high-information-density features, which are then linearly projected and reshaped to form a coarse prediction matrix. This coarse prediction matrix serves as the input sequence for the bidirectional gated recurrent unit layer at each time step. The forward GRU and backward GRU are computed independently respectively; the forward and backward hidden states are concatenated and normalized to obtain bidirectional temporal features.

[0019] Furthermore, the spatiotemporal attention module of the pathway sequentially includes a temporal attention pathway and a spatial attention pathway; the temporal attention pathway extracts features through a multi-head self-attention module, fuses the bidirectional temporal features as residual branches with the attention output, and then outputs them after layer normalization; the spatial attention pathway reweights the temporal features using channel attention weights, adds and fuses the calibrated features with the temporal attention output through a second residual connection, and then outputs them after layer normalization.

[0020] Furthermore, the mean head forms point predictions by performing residual correction on the coarse predictions, first mapping the spatiotemporal features to the time mean through a temporal distribution hidden layer with MC-Dropout;

[0021]

[0022] in, This refers to the MC-Dropout rate; , All are learnable weight matrices; , All are learnable parameters;

[0023] A rough prediction using time-mean correction is as follows:

[0024]

[0025] in, This is a coarse prediction matrix; This is a mean forecast.

[0026] Furthermore, the variance header uses a fully connected layer with MC-Dropout to generate the log-variance of the depth modulation, specifically:

[0027] Step 1: Construct the normalized deep encoding vector:

[0028]

[0029] in, For the first The physical depth of each monitoring point This represents the maximum depth of the system.

[0030] Step 2: Project the deep encoded vector through a learnable embedding layer and convert it into a gated signal:

[0031]

[0032]

[0033] in, For deep embedding dimensions;

[0034] Step 3: The spatiotemporal characteristics of the variance path are modulated by affine transformation of the depth-sensing gated signal:

[0035]

[0036] in, To control the scaling factor of the depth prior modulation intensity;

[0037] Step 4: Input the modulated features into a fully connected layer with MC-Dropout, and output the features after random feature masking regularization.

[0038]

[0039] in, For MC-Dropout probability;

[0040] Step 5: Then process it through a fully connected layer containing a second MC-Dropout layer:

[0041]

[0042] Step 6: The final log-variance output is generated by linear projection of the time distribution:

[0043] .

[0044] Furthermore, the composite loss function is:

[0045]

[0046] in, These are the weighting coefficients for the NLL terms; This is the mean square error loss; For heteroscedastic Gaussian negative log-likelihood loss;

[0047]

[0048] in, The number of training samples, For the first Each sample at time step With monitoring points The normalized truth value; and These are the predicted mean and variance, respectively.

[0049] Furthermore, the total variance is the sum of the random uncertainty estimate and the cognitive uncertainty estimate; the random uncertainty estimate is the average of the sampling variances; and the cognitive uncertainty estimate is the variance using the mean.

[0050] The confidence interval for:

[0051]

[0052] in, It is the upper part of the standard normal distribution quantiles; In time step With monitoring points The point prediction mean; In time step With monitoring points The total variance of the total forecast uncertainty.

[0053] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification described above.

[0054] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification as described above.

[0055] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification as described above.

[0056] The beneficial effects of this invention are as follows:

[0057] (1) The method of the present invention eliminates the discontinuity of the periodic boundary of the direction angle by trigonometric function encoding, and introduces the ship-environment hydrodynamic coupling interaction term to explicitly embed the hydrodynamic prior into the input space, thereby improving the physical consistency of the prediction and the stability of the training.

[0058] (2) The method of the present invention achieves simultaneous multi-output mapping from low-dimensional static environmental parameters to multi-depth high-dimensional stress time series through adaptive multi-resolution feature fusion, hierarchical prediction with sequence correction and dual-path spatiotemporal attention. The average absolute percentage error is only 1.33% across 6 monitoring depths.

[0059] (3) The method of the present invention achieves high-precision point prediction and reliable uncertainty estimation in a single unified architecture by using a deep-perception heteroscedastic dual-head output layer and an asymmetric structure, and by using a composite loss including a mean square error term and a heteroscedastic Gaussian negative log-likelihood term, thereby avoiding the computational overhead of traditional ensemble methods.

[0060] (4) The method of the present invention decomposes the total prediction uncertainty into two interpretable components, random uncertainty and cognitive uncertainty, by using the law of total variance, providing actionable information for risk informed decision-making: when the random component dominates, it means that the uncertainty is due to the intrinsic variability of the working conditions and is difficult to reduce by improving the model; when the cognitive component dominates, it means that the training data coverage is insufficient and can be improved by supplementing key working condition data. Attached Figure Description

[0061] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0062] Figure 2 A schematic diagram of the components of a deep-sea mining system;

[0063] Figure 3 This is a schematic diagram showing the actual stress time series values, predictions, and uncertainty quantification results of PIUQ-Net (33m monitoring point).

[0064] Figure 4 This is a schematic diagram of the actual stress time series values, predictions, and uncertainty quantification results of PIUQ-Net (543m monitoring point).

[0065] Figure 5 This is a schematic diagram showing the actual stress time series values, predictions, and uncertainty quantification results of PIUQ-Net (1053m monitoring point).

[0066] Figure 6 This is a schematic diagram of the actual stress time series values, predictions, and uncertainty quantification results of PIUQ-Net (1563m monitoring point).

[0067] Figure 7 This is a schematic diagram of the actual stress time series values, predictions, and uncertainty quantification results of PIUQ-Net (2073m monitoring point).

[0068] Figure 8 This is a schematic diagram showing the actual stress time series values, predictions, and uncertainty quantification results of PIUQ-Net (2873m monitoring point).

[0069] The attached diagram is labeled as follows: 1. Surface support vessel, 2. Lifting riser, 3. Booster pump, 4. Relay station, 5. Flexible hose, 6. Mining vehicle. Detailed Implementation

[0070] The present invention will be further described below with reference to the accompanying drawings. The embodiments are only used to explain the present invention and are not intended to limit the scope of protection of the present invention.

[0071] This invention discloses a time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification, comprising the following steps:

[0072] S1. Establish a coupled time-domain dynamic model of the deep-sea mining hoisting system, acquire the maximum von Mises stress time series data at multiple monitoring depths along the hoisting pipe under multiple working conditions, and construct a training set;

[0073] S2. Physical information feature encoding is performed on environmental and operational parameters. Trigonometric function encoding is used to eliminate the discontinuity of the periodic boundary of the direction angle, and a ship-environment hydrodynamic coupling interaction term is introduced to obtain a physical information enhanced input vector.

[0074] S3. Construct a physical information uncertainty quantification network, which consists of an adaptive multi-resolution feature fusion module, a hierarchical prediction module with sequence correction, a dual-path spatiotemporal attention module, and a deep-perception heteroscedastic dual-head output layer connected in series.

[0075] S4. In the depth-aware heteroscedastic dual-head output layer, the mean head forms point predictions by performing residual correction on the coarse predictions, while the variance head generates the depth-modulated log-variance for uncertainty estimation. Both heads retain Monte Carlo dropout (MC-Dropout) and remain active during the inference phase.

[0076] S5. Based on Monte Carlo Dropout multiple forward sampling, the total prediction uncertainty is decomposed into random uncertainty and cognitive uncertainty;

[0077] S6. Construct a composite loss function composed of a weighted combination of mean square error and heteroscedastic Gaussian negative log-likelihood, and train the physical information uncertainty quantification network with the goal of minimizing the composite loss function to obtain the trained prediction model.

[0078] S7. Input the target working condition parameters into the trained prediction model and output the stress response prediction time series and its confidence interval for the deep-sea mining hoisting system at multiple monitoring depths.

[0079] Example 1

[0080] This embodiment presents a time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification, such as... Figure 1 As shown, it includes the following steps:

[0081] S1. System Dynamics Modeling and Data Acquisition

[0082] like Figure 2 As shown, the deep-sea mining system includes a surface support vessel, a riser, a booster pump, a relay station, a flexible hose with a buoyancy module, and a mining vehicle. In this embodiment, the riser is 5490m long and adopts a seven-segment stepped structure, with the wall thickness decreasing with depth. The relay station is modeled as a 6-DOF floating body, with an overall length of 10m, a diameter of 5m, a dry weight of 80,000kg, and a drainage volume of 10.19m³. The flexible hose extends from 5490m to 6000m, with a buoyancy module configured in the middle section to control curvature. The top connection of the riser moves with the surface support vessel in six-DOF motion. The vessel's motion time history is synthesized from the frequency domain RAO and the target spectrum and applied as a boundary condition for the riser top displacement. The tensioner system consists of 12 parallel steel wire ropes, each with a stroke of ±7.62m, and its stiffness is determined by the wet weight of the suspension system.

[0083] The lumped mass method was used to perform time-domain discrete modeling of the riser, relay station, flexible hose and mining vehicle. The hydrodynamic load was calculated using the Morison formula. Environmental conditions included wave, ocean current and wind loads.

[0084] This embodiment is designed for sea conditions with active ship movement, and the environmental parameter is fixed as significant wave height. m, spectral peak period s. Consider two ship forward speeds. m / s. For each ship speed, the directional parameter space is systematically sampled through three environmental configurations: (i) collinear loading (three directional angles are the same); (ii) wave-current alignment with wind direction variation; (iii) wave-wind alignment with current direction variation.

[0085] The surrogate model outputs the maximum von Mises stress time history at six monitoring depths along the riser. Monitoring points were selected at key structural locations: the 33m location is below the ship-riser interface, capturing wave-excited dynamic loads transmitted through the interface; the 543m, 1053m, 1563m, and 2053m locations are near the four tandem booster pumps, corresponding to stress concentration areas caused by concentrated mass and geometric discontinuities; the 2873m location is in the deep-water transition zone, capturing the response characteristics during the transition from wave-dominated to current-dominated loading. Stress time series were sampled every 15 seconds, and each channel generated... There are several time steps, therefore the complete output of each operating condition is a spatiotemporal matrix. Dataset The samples were randomly divided into training and testing sets at a ratio of 85:15, resulting in approximately 331 training samples and 59 testing samples.

[0086] S2, Physical Information Feature Encoding

[0087] The original input to the prediction task is a six-dimensional parameter vector representing a given working condition:

[0088] (1)

[0089] in, For the sake of righteousness, the waves rise high. For the spectral peak period, For the ship's forward speed, These are the wave direction angle, wind direction angle, and ocean current direction angle, respectively.

[0090] S21, Trigonometric Function Encoding

[0091] The three direction parameters are essentially periodic angle quantities. Directly feeding the angle values ​​into the network introduces discontinuities at the angle boundaries, causing two physically consistent directions to be mapped to the two values ​​with the largest numerical differences, violating the smoothness assumption required by gradient-based optimization. Therefore, for each direction angle... ( Perform trigonometric function decomposition:

[0092] (2)

[0093] In this process, angles are first converted from degrees to radians. This mapping projects the angular quantities onto the unit circle, maintaining the continuous metric relationship between directions and eliminating boundary artifacts.

[0094] S22, Hydrodynamic Coupling Interaction Term

[0095] In addition to trigonometric function encoding, two physically driven interactive features are introduced to capture the coupling relationship between ship kinematics and directional environmental loads. In marine hydrodynamics, the effective wave encounter frequency and the relative flow velocity in the pipe both depend on the projection of the ship's velocity vector onto the corresponding load direction. Therefore, the ship-environment hydrodynamic coupling interaction term is defined as follows:

[0096] (3)

[0097] (4)

[0098] in, It represents the ship's velocity component projected along the direction of wave propagation. It determines the two navigation conditions of heading into the waves and sailing with the waves, and directly affects the frequency of encountering waves. This represents the ship velocity component projected along the direction of the coastal current, which affects the effective drag force distribution along the riser.

[0099] These interactive features embed directional periodicity and first-order hydrodynamic physics into the input space. Concatenating the aforementioned scalar parameters, trigonometric function encodings, and coupled interaction terms yields a complete physical information-enhanced input vector:

[0100] (5)

[0101] Reshape the normalized input vector into a tensor. ( Each feature is treated as a single-channel position on the feature axis.

[0102] S31, Adaptive Multi-Resolution Feature Fusion Module

[0103] Input tensor Mapped to a higher-dimensional space through a dense time-distribution transformation:

[0104] (6)

[0105] in, and For learnable parameters, For the input vector dimension, To expand the dimensionality, this operation transforms each scalar feature into a rich feature embedding while preserving the unique physical properties of each input parameter.

[0106] The expanded representation indicates that the input consists of three parallel one-dimensional convolutional branches with kernel sizes of [sizes to be filled in]. Each branch applies the same number of filters, ReLU activation function, and batch normalization (BN).

[0107] (7)

[0108] Where BN is the batch normalization operation, and the number of filters in each branch is... Conv1D is a 1D convolution.

[0109] Concatenate the three branch outputs along the channel dimension:

[0110] (8)

[0111] in, This indicates channel cascading.

[0112] Adaptive recalibration of the channels is performed using squeeze-excitation (SE) blocks. The squeeze operation generates channel descriptors through global average pooling.

[0113] (9)

[0114] The incentive operation generates channel attention weights through a two-layer bottleneck structure:

[0115] (10)

[0116] in, and For learnable weight matrix, The compression ratio is... It is the sigmoid activation function; and These are learnable parameters.

[0117] The characteristics after channel recalibration are:

[0118] (11)

[0119] in, This represents the element-wise product of elements broadcast along the characteristic axis.

[0120] S32, Hierarchical prediction module with sequence correction

[0121] A core design principle of PIUQ-Net is to decompose the complex mapping from low-dimensional static input to high-dimensional temporal output. Coarse prediction establishes a global baseline through dense layers, followed by temporal corrections learned by a bidirectional recurrent network. Finally, residual connections form the final prediction, allowing the refinement branch to capture only small temporal corrections without processing the complete output signal.

[0122] Flatten the recalibrated features:

[0123] (12)

[0124] in, This is a function for reducing the dimensionality of multidimensional arrays.

[0125] The flattened features are encoded into a compact representation through two fully connected layers with Dropout:

[0126] (13)

[0127] (14)

[0128] in, and These are the hidden dimensions of two fully connected layers. This represents the Dropout probability.

[0129] A coarse prediction matrix is ​​formed through linear projection and reshaping:

[0130] (15)

[0131] in, For time steps, Number of monitoring points; The function gives an array a new shape without changing the data.

[0132] rough prediction As the input sequence for the Bidirectional Gated Recurrent Unit (BiGRU) layer, for each time step Calculated independently by the forward GRU and backward GRU respectively:

[0133] (16)

[0134] (17)

[0135] (18)

[0136] (19)

[0137] in, for Coarse prediction vector at time step To update the door, To reset the door, In the candidate hidden state, All are learnable parameters;

[0138] The backward GRU processes the same sequence with independent parameters along the reverse time direction to obtain... The process is the same as the forward process.

[0139] Cascade the forward and backward hidden states:

[0140] (20)

[0141] in, Number of hidden units per direction;

[0142] After layer normalization, a stable bidirectional time series representation is obtained:

[0143] (twenty one)

[0144] S33, Dual-path spatiotemporal attention module

[0145] Normalized BiGRU output Further processing is performed by the Spatiotemporal Attention Module (STAM), simultaneously capturing long-range temporal correlations and cross-channel spatial relationships. STAM consists of a temporal self-attention path and a spatial channel attention path, each accompanied by residual connectivity and layer normalization, capturing both long-range temporal correlations and cross-channel spatial relationships. The temporal self-attention mechanism allows each time step to attend to all other time steps and learn their importance weights, enabling the model to capture global temporal patterns throughout the simulation, such as resonance phenomena, transient stress peaks, and slowly varying load envelopes. Along the temporal attention path, a channel attention mechanism is applied to recalibrate the feature dimensions, thereby modeling inter-channel correlations related to different monitoring depths.

[0146] Temporal attention pathway:

[0147] Apply multi-head scaled dot product attention along the time dimension. For the input... ( ), No. The query, key, and value matrix for each attention head is as follows:

[0148] (twenty two)

[0149] in, and For learnable projection matrices, For key dimensions.

[0150] No. The scaling dot product attention of the size is:

[0151] (twenty three)

[0152] Each head output is cascaded and linearly projected:

[0153] (twenty four)

[0154] in, For the number of attention heads, This is for outputting the projection matrix.

[0155] The temporal attention representation is obtained through residual connections and layer normalization:

[0156] (25)

[0157] Spatial channel attention pathway:

[0158] The channel descriptor is obtained by averaging over the time dimension:

[0159] (26)

[0160] Channel attention weights are calculated using the bottleneck structure:

[0161] (27)

[0162] in, and It forms a two-layer structure of compression and excitation.

[0163] Spatial reweighting calculates temporal features using an element-wise method and combines them with the temporal attention output through a second residual connection. The spatially recalibrated representation is then fused with the residual to obtain a joint spatiotemporal representation.

[0164] (28)

[0165] (29)

[0166] The resulting tensor integrates temporal self-attention and spatial channel attention, and serves as the shared input for the dual-head output layer.

[0167] S34, Depth-Aware Heteroscedastic Dual-Head Output Layer

[0168] A key design feature of this invention is its asymmetric dual-head output architecture, where the mean prediction head and variance prediction head follow structurally different computational paths and employ different regularization strategies. This asymmetry is structural: the mean head forms point predictions by performing residual correction on coarse predictions, while the variance head generates deeply modulated log-variance for uncertainty estimation. Both heads retain Monte Carlo dropout (MC-Dropout) and remain active during the inference phase.

[0169] Spatiotemporal features are mapped to the time mean through a time distribution hidden layer with MC-Dropout:

[0170] (30)

[0171] in, This is the MC-Dropout rate. The final mean forecast adds this correction to the coarse forecast via residual connections.

[0172] The final mean prediction is obtained by adding the residuals and the coarse prediction:

[0173] (31)

[0174] Variance firstly for the same spacetime representation Monte Carlo Dropout (MC-Dropout) is applied, and MC-Dropout remains active during the inference phase.

[0175] First, construct the normalized deep encoding vector:

[0176] (32)

[0177] in, For the first The physical depth of each monitoring point This represents the maximum depth of the system.

[0178] Then, using the depth information monitored, these spatiotemporal features are modulated based on depth perception priors. This normalized vector is projected through a learnable embedding layer and converted into a gated signal:

[0179] (33)

[0180] (34)

[0181] in, For deep embedding dimensions.

[0182] The variance path characteristics of the depth-sensing gated signal modulated by affine transformation are as follows:

[0183] (35)

[0184] in, To control the scaling factor of the depth prior modulation intensity; the multiplicative form encourages deeper monitoring points to generate greater learning uncertainty, with additive unit terms. It maintains the ability to estimate baseline variance when the contribution of depth is small.

[0185] Apply a fully connected MC-Dropout layer to the STAM output:

[0186] (36)

[0187] in, The probability is MC-Dropout, which remains active during both training and inference.

[0188] After the first regularization, the features are processed through a fully connected layer containing a second MC-Dropout layer:

[0189] (37)

[0190] The final log-variance output is generated by linear projection of the time distribution:

[0191] (38)

[0192] in, This is the bias term. This initialization ensures that the variance head starts with a small uncertainty estimate and gradually learns to an appropriate magnitude during training.

[0193] The complete output is a concatenated prediction of the mean and log-variance along the channel dimension:

[0194] (39)

[0195] S4. Multi-source uncertainty decomposition

[0196] The dual-head architecture allows the total prediction uncertainty to be decomposed into two physically interpretable components: random uncertainty and cognitive uncertainty. Random uncertainty captures inherent, unreducible noise in the data, stemming from turbulent fluctuations, numerical discretization effects in hydrodynamic simulations, and the intrinsic randomness of environmental load processes. This component is directly estimated by the heteroscedastic variance head, learning the variances related to input, time, and depth. Cognitive uncertainty captures knowledge gaps in the model due to insufficient training data coverage or model capacity. This component is further decomposed by… During each inference iteration, random forward propagation estimation is performed, with the MC-Dropout layer in the variance head sampling different subnetwork configurations at each propagation.

[0197] Based on the theoretical framework that interprets MC-Dropout as approximate Bayesian inference, this component performs [something] during the inference phase. The estimation is performed using random forward propagation. Since both the mean path and variance path preserve MC-Dropout, each iteration... Each time a mean prediction value is generated. sum of variance predicted values .

[0198] The point prediction is the mean of the predictions over all iterations:

[0199] (40)

[0200] The random uncertainty is estimated as the average of the sample variances:

[0201] (41)

[0202] Cognitive uncertainty is estimated as the variance of the sample mean:

[0203] (42)

[0204] At this point, the variance is strictly positive. The total forecast uncertainty is obtained by adding these two components according to the law of total variance:

[0205] (43)

[0206] Given the total forecast standard deviation The stress response at each time step and monitoring depth The prediction interval is:

[0207] (44)

[0208] in, It is the upper part of the standard normal distribution Quantiles. For the 95% prediction interval, .

[0209] This decomposition provides actionable information for engineering decisions: if the accidental component dominates, the uncertainty stems from the intrinsic variability of the operating conditions and cannot be reduced by improving the model; if the cognitive component dominates, the uncertainty reflects insufficient training coverage, indicating that adding simulation data to relevant regions of the input space can improve prediction confidence.

[0210] S5. Composite Loss Function and Training Strategy

[0211] The training objective of PIUQ-Net is a weighted combination of mean squared error (MSE) and heteroscedastic Gaussian negative log-likelihood (NLL). The MSE component drives the prediction accuracy, while the NLL component calibrates the learning uncertainty estimate.

[0212] The mean square error term is:

[0213] (45)

[0214] in, The number of training samples, For the first Each sample at time step With monitoring points The normalized truth value, This is for predicting the mean.

[0215] The heteroscedastic Gaussian negative log-likelihood term is:

[0216] (46)

[0217] in, The number of training samples, For the first Each sample at time step With monitoring points The normalized truth value, and These are the predicted mean and variance, respectively.

[0218] The composite training loss is defined as a weighted sum:

[0219] (47)

[0220] in, These are the weighting coefficients for the NLL terms; Taking the smaller value ensures that the MSE term dominates the optimization objective, thus prioritizing the accuracy of mean prediction. The NLL term, as a secondary objective, progressively calibrates the variance head without interfering with the convergence of the mean head. This asymmetric weighting strategy avoids the mean-variance coupling problem commonly found when heteroscedastic NLL loss is used alone.

[0221] S6. Model Implementation and Hyperparameter Configuration

[0222] PIUQ-Net receives enhanced physical information input After passing through a series of interconnected modules—an adaptive multi-resolution feature fusion module, a hierarchical prediction module with sequence correction, a dual-path spatiotemporal attention module, and a depth-aware heteroscedastic dual-head output layer—the spatiotemporal tensor is output. The first six channels represent the predicted mean stress response at each monitoring depth, while the last six channels represent the corresponding predicted log-variance. In the adaptive multi-resolution feature fusion module, the feature embedding dimension is taken sequentially. The kernel sizes of the three parallel one-dimensional convolution branches are respectively Number of filters SE block compression ratio In the hierarchical prediction module with sequence correction, the hidden dimensions of the two fully connected layers are respectively... , Standard Dropout probability Number of hidden units per direction in BiGRU The number of multi-head self-attention heads in a dual-path spatiotemporal attention module. Key Dimension Spatial channel attention adopts a compression-excitation bottleneck structure In the deep-perception heteroscedastic dual-head output layer, the mean path has a dense temporal distribution layer of 64 units; the variance path has MC-Dropout probability. Deeply embedded dimensions Deep prior modulation coefficients The logarithmic variance output is initially biased. With the clipping range Ensure numerical stability.

[0223] The model is trained using the Adam optimizer with an initial learning rate of [missing information]. Gradient clipping The upper bound of the norm is To suppress gradient explosion that may occur in the loop layer; batch size is taken as... Maximum number of training rounds The loss function is the composite loss defined in equation (47), with NLL weighting coefficients. The ground truth tensor of the training samples is dimensional by Fill to To align with the dual-head output, loss calculation is based only on the first... One channel.

[0224] To improve training stability and generalization performance, three callback mechanisms are introduced to adjust the training dynamics: when the validation loss is continuously... If the learning rate does not decrease within a certain number of rounds, the lower bound is halved. When the verification loss is continuous Early stopping is triggered if there is no improvement within a certain number of rounds to avoid overfitting; the model checkpoint mechanism saves the optimal weights on the validation set in real time. After training, the network parameters are restored to their optimal state. The input parameters are fitted on the training set using MinMaxScaler and applied to both the training and test sets to eliminate scale differences between features of different dimensions.

[0225] During the inference phase, Monte Carlo Dropout is used for multiple forward sampling to estimate uncertainty. Specifically, both heads retain Monte Carlo Dropout (MC-Dropout) and keep it active during the inference phase. Execution The second independent forward pass yields... The sample consists of a set of logarithmic variance samples. The final predicted mean can be obtained by performing mean aggregation and variance decomposition on the samples according to formulas (43)-(46). Accidental uncertainty Cognitive uncertainty With total forecast uncertainty And then in Output the stress response prediction time series and its confidence interval at each monitoring depth at the confidence level.

[0226] In particular, in some preferred embodiments of the present invention, a computer device is also provided, including a memory and a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification described in any of the above embodiments.

[0227] In some other preferred embodiments of the present invention, a computer-readable storage medium is also provided, on which a computer program is stored, which, when executed by a processor, implements the steps of the time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification described in any of the above embodiments.

[0228] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the above embodiments of the time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification, which will not be repeated here.

[0229] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0230] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0231] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0232] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification, characterized in that, Includes the following steps: A coupled time-domain dynamic model of a deep-sea mining hoisting system was established; the maximum von Mises stress time series data along multiple monitoring depths of the hoisting pipe under various working conditions were acquired, and a training set was constructed. A physical information uncertainty quantification network is constructed by introducing a deep-aware heteroscedastic dual-head output layer. Using this network, spatiotemporal features are extracted from the input vector incorporating the ship-environment hydrodynamic coupling interaction term, and then input into the deep-aware heteroscedastic dual-head output layer. Both the mean head and variance head employ MC-Dropout layers. The variance head incorporates deep-aware priors to modulate the spatiotemporal features of the variance path. The dual-head output layer ultimately measures the mean and logarithmic variance of the predicted stress response. Uncertainty decomposition of the prediction results is performed based on multiple forward sampling using Monte Carlo Dropout. A composite loss function consisting of a weighted combination of mean square error and heteroscedastic Gaussian negative log-likelihood is constructed to train a network for quantifying the uncertainty of physical information. The target working condition parameters are input into the trained physical information uncertainty quantification network, and the stress response prediction results of the deep-sea mining hoisting system at multiple monitoring depths are output. The uncertainty of the prediction results is decomposed, and the corresponding confidence interval is solved by superimposing the total variance and combining it with the prediction mean.

2. The time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification according to claim 1, characterized in that, The deep-sea mining hoisting system includes a surface support vessel, a hoisting riser, a booster pump, a relay station, a flexible hose with a buoyancy module, and a mining vehicle. The dynamic model is modeled using the lumped mass method, the hydrodynamic loads are calculated using the Morison formula, and the environmental conditions include wave, current, and wind loads. The six-degree-of-freedom motion of the vessel is synthesized with the target spectrum through frequency domain RAO and applied as the displacement boundary condition at the top of the hoisting riser.

3. The time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification according to claim 1, characterized in that, Based on the cascading of operating parameters and their trigonometric function encodings, and ship-environment hydrodynamic coupling interaction terms, an input vector is constructed. : in, For the sake of righteousness, the waves rise high. For the spectral peak period, For the ship's forward speed, , , These are the wave direction angle, wind direction angle, and ocean current direction angle, respectively. The component of the ship's velocity projected along the direction of wave propagation; The component of ship velocity projected along the direction of the coastal current; 4. The time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification according to claim 1, characterized in that, The input vector is sequentially passed through an adaptive multi-resolution feature fusion module, a hierarchical prediction module with sequence correction, and a dual-path spatiotemporal attention module to extract spatiotemporal features that are both temporally dependent and spatially correlated. The adaptive multi-resolution feature fusion module inputs the expanded normalized input vector into three parallel one-dimensional convolutional branches, which are then cascaded along the channel dimension and processed by a squeeze-excitation block to obtain the channel-recalibrated features.

5. The time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification according to claim 4, characterized in that, The hierarchical prediction module with sequence correction employs two fully connected layers with Dropout to encode flattened features into high-information-density features, which are then linearly projected and reshaped to form a coarse prediction matrix. This coarse prediction matrix serves as the input sequence for the bidirectional gated recurrent unit layer at each time step. The forward GRU and backward GRU are computed independently respectively; the forward and backward hidden states are concatenated and normalized to obtain bidirectional temporal features.

6. The time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification according to claim 5, characterized in that, The spatiotemporal attention module of the pathway includes a temporal attention pathway and a spatial attention pathway. The temporal attention pathway extracts features through a multi-head self-attention module, fuses the bidirectional temporal features as residual branches with the attention output, and then outputs them after layer normalization. The spatial attention pathway reweights the temporal features using channel attention weights, adds and fuses the calibrated features with the temporal attention output through a second residual connection, and then outputs them after layer normalization.

7. The time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification according to claim 1, characterized in that, The mean head forms point predictions by performing residual correction on coarse predictions. First, the spatiotemporal features are mapped to the time mean through a time distribution hidden layer with MC-Dropout. in, This refers to the MC-Dropout rate; , All are learnable weight matrices; , All are learnable parameters; A rough prediction using time-mean correction is as follows: in, This is a coarse prediction matrix; This is a mean forecast.

8. The time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification according to claim 1, characterized in that, The variance header uses a fully connected layer with MC-Dropout to generate the log-variance of depth modulation, specifically: Step 1: Construct the normalized deep encoding vector: in, For the first The physical depth of each monitoring point This represents the maximum depth of the system. Step 2: Project the deep encoded vector through a learnable embedding layer and convert it into a gated signal: in, For deep embedding dimensions; Step 3: The spatiotemporal characteristics of the variance path are modulated by affine transformation of the depth-sensing gated signal: in, To control the scaling factor of the depth prior modulation intensity; Step 4: Input the modulated features into a fully connected layer with MC-Dropout, and output the features after random feature masking regularization. in, For MC-Dropout probability; Step 5: Then process it through a fully connected layer containing a second MC-Dropout layer: Step 6: The final log-variance output is generated by linear projection of the time distribution: 。 9. The time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification according to claim 1, characterized in that, The composite loss function is: in, These are the weighting coefficients for the NLL terms; This is the mean square error loss; For heteroscedastic Gaussian negative log-likelihood loss; in, The number of training samples, For the first Each sample at time step With monitoring points The normalized truth value; and These are the predicted mean and variance, respectively.

10. The time-domain prediction method for deep-sea mining systems based on physical information and uncertainty quantification according to claim 1, characterized in that, The total variance is the sum of the random uncertainty estimate and the cognitive uncertainty estimate; the random uncertainty estimate is the average of the sampled variances; the cognitive uncertainty estimate is the variance using the mean. The confidence interval for: in, It is the upper part of the standard normal distribution quantiles; In time step With monitoring points The point prediction mean; In time step With monitoring points The total variance of the total forecast uncertainty.

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