Multi-modal uncertainty perception mechanical life prediction method based on random model updating

Abstract

A multi-modal uncertainty perception mechanical life prediction method based on random model updating comprises the steps that firstly, a drift network is constructed, a representation extraction block RDB comprises four layers including a data structure DS, short-term local feature refinement, long-term time trend development and down-sampling, and residual connection is used for capturing cross-layer information and promoting gradient flow; a diffusion network is constructed, Lipschitz continuity is followed, and ReLU is selected as an activation function; then each subnet is trained, the first two parts of a target function of the subnet are regression terms of a distributed drift network and an adjustment diffusion network, and the latter component belongs to an OOD sample; then, the uncertainty of each subnet is quantified, and finally, multi-modal fusion is carried out based on the respective uncertainty; according to the method, modeling is carried out on the uncertainty of each mode through the fractional order stochastic differential equation sub-network, dynamic fusion is carried out according to the uncertainty of modal characteristics, and a final prediction result and the corresponding uncertainty are obtained through regression reasoning.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical remaining life prediction, and specifically relates to a multi-modal uncertainty-aware mechanical life prediction method based on random model updating. Background Art

[0002] As industrial demands continue to increase, mechanical equipment has become increasingly complex, which has also triggered widespread concern about potential equipment failures and operation and maintenance (O&M) costs. Fault prediction and health management (PHM) strategies, especially remaining useful life (RUL) prediction, provide an effective solution. RUL prediction is a method of analyzing the health status of a machine and estimating its remaining useful life by monitoring sensor data. Deep learning technology has shown great potential in this field due to its excellent feature extraction and generalization capabilities. However, most existing deep learning methods rely on degradation information extracted from a single-type data source. Single-type data can only provide a limited and biased health monitoring perspective, which may ignore the key features of the machine's health status and fail to fully reflect the degradation process of the equipment. In addition, single-type data is easily affected by external interference, and its effectiveness is highly dependent on the sensitivity and characteristics of the sensor.

[0003] In order to solve these problems, multimodal monitoring has gradually attracted attention and made significant progress in applications. Multimodal monitoring (Wang Y, Lei Y, Li N, et al. Deep multisource parallel bilinear-fusion network for remaining useful life prediction of machinery [J]. Reliability Engineering & System Safety, 2023, 231: 109006.) can obtain more comprehensive machine health information by collecting multimodal data from different types of sensors, thereby providing a broader perspective for the model. However, this method can often only provide point predictions and does not consider the uncertainty of the prediction results, which may cause the model to produce wrong but blindly confident prediction results. Even in the face of unknown out-of-distribution (OOD) data, the model also gives a confident prediction output, which makes the prediction results output by the model difficult to believe in practical applications, resulting in the inability of the prediction model to be directly applied in many fields, especially in some industries that require strict safety assurance. The existence of this uncertainty may lead to serious economic losses and casualties. Therefore, how to enable the model to quantify the uncertainty of the prediction and provide feedback when an accurate prediction cannot be made has become an important issue that needs to be solved urgently. Summary of the invention

[0004] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a multi-modal uncertainty-aware mechanical life prediction method based on random model updating, which models the uncertainty of each mode through a fractional-order stochastic differential equation (FSDE) sub-network, dynamically fuses the uncertainties of the modal characteristics, and obtains the final prediction result and its corresponding uncertainty through regression reasoning.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A multimodal uncertainty-aware mechanical life prediction method based on stochastic model updating includes the following steps:

[0007] 1) Constructing a drift network: The drift network mines the health status of the monitored object. Its representation and refinement block RDB includes four layers: data structure DS, short-term local feature refinement, long-term time trend development and downsampling. The residual connection is used to capture cross-layer information and promote gradient flow.

[0008] Multiple RBDs gradually refine the health status information embedded in the monitoring data. Subsequently, an MLPs-based module is used to smooth the extracted representation and project it into a lower dimensional space.

[0009] 2) Constructing a diffusion network: Based on the MLP backbone, the diffusion network follows Lipschitz continuity and selects ReLU as the activation function. In addition, the maximum output of the diffusion network uses the sigmoid function and the hyperparameter ε max To regulate, the diffusion network is defined as exist Initially set ε max Set it to 0.1 and increase it to 0.5 at epoch 30;

[0010] 3) Training each subnet: The objective function of the subnet consists of three parts. The first two parts are the regression terms of the in-distribution drift network and the regulated diffusion network, and the last component belongs to the OOD sample;

[0011] 4) Uncertainty quantification of each subnet: Monitoring data from each mode is processed using custom subnets, each of which performs RUL prediction and quantitative uncertainty modeling;

[0012] 5) Multimodal fusion based on respective uncertainties: A fusion method based on Lagrange multipliers is proposed, which is obtained through explicit numerical derivation. For each modality-specific feature, an MLP-based regression module is used to calculate the prediction within each subnet and its corresponding uncertainty. In the multimodal fusion process, the original modality features are directly fused.

[0013] Step 1) A data sequence is organized by the DS layer and then standardized to a comparable scale, which is mathematically expressed as:

[0014]

[0015] Where ⊙ represents the Hadamard product operation, and are the mean and standard deviation of the small batch δ samples, γ scale ,γ shift The scale and shift parameters learned during training have the same shape as x;

[0016] Subsequently, the short-term local feature refinement layer extracts fine-grained, discriminative features. Mathematically, ResNet decomposes the function into:

[0017] f(x)=x+κ(x) (2)

[0018] The decomposition results in a linear term and a nonlinear term for coarse feature extraction, and also expands the information to capture more terms. For the inference function f(x) at the point x=x0, Taylor expansion is applied to obtain:

[0019]

[0020] f(x) is decomposed into higher-order terms, mapping x to its transformed value through a series of functions, which are:

[0021] x→[x,f1(x),f2([x,f1(x)]),…] (4)

[0022] Where [;] represents the connection operation, all functions are combined by a multi-layer perceptron (MLP) to produce the final feature set, using 1×1 convolution and pooling operations to reduce model complexity, these functions are implemented by wavelet convolution; mathematically, for a small batch input δ, the output c out The j-th channel is calculated as:

[0023]

[0024] Where W represents the wavelet kernel weight, * d represents the dilated convolution with a dilation coefficient of d, ψ(·) is the wavelet basis function, c in and c out are the number of input and output channels, respectively, a is the size factor in wavelet transform, b is the time shift factor, and t represents the time step;

[0025] The long-term time trend development layer is designed to track the evolution of monitoring data over time, including changes in degradation patterns; the computation flow is controlled in a gated manner, for the input value x at time step tt , the output is as follows:

[0026]

[0027] where y t-1 is the output of the previous time step, z t In the following description, is a memory state that integrates multi-resolution and attention mechanisms to effectively capture long-range context clues and is calculated as follows:

[0028]

[0029] Where Conv 1×1 (·) represents a 1×1 convolution operation, pe is a position encoding term, and HAP(·) represents a hierarchical attention pooling (HAP) operation; the input feature map is divided into b branches, each of which is processed using self-attention and then aggregated through a linear transformation; mathematically, for a feature map δ,

[0030]

[0031] in, are learnable parameters in the linear transformation, ω1,…,ω b The calculation is divided into ω = softmax (QK T )V,Q,K,V are index, key and value respectively, softmax(·) represents the softmax activation function;

[0032] In equations (6) and (7), z t and r t is a gate that performs convex combinations within (0,1) and is calculated as:

[0033]

[0034] In the formula is the sigmoid activation function, represents a convolution operation with a step size of s=2 and a kernel size of 3×3, and W represents the corresponding weight matrix;

[0035] The last layer of the RDB structure is downsampling, which aggregates the information in each RDB and is performed on the divided region R as follows:

[0036]

[0037] in For each (i,j)∈{1,…,γ out} 2 , and operates with a special random step size that depends on the target output size.

[0038] Step 3) The objective function is:

[0039]

[0040] Where θ1 and θ2 are the learnable weights of the drift network and the diffusion network, L is the total number of layers in the subnet, and P ID and P OOD They are ID and OOD samples respectively. For the loss function f acting on the drift network, RUL is selected as the loss function.

[0041] Step 4) For the m-training subnet, its prediction for:

[0042]

[0043] Where S is the number of random forward passes during the test. is the mean of each prediction of the m-th mode;

[0044] For uncertainty quantification, it is divided into two types: AU and EU; AU is calculated as:

[0045]

[0046] Another uncertainty EU is the variance of the final solution, expressed as:

[0047]

[0048] Step 5) For the mth modality, its modality-specific subnet provides a prediction and an associated uncertainty value u m , uncertainty value u m for:

[0049]

[0050] The α and β scaling factors are adjusted according to the application and are uniformly expressed as:

[0051]

[0052] where ω m is the weight of the mth mode, satisfying

[0053] According to the calculation law of uncertainty propagation, when the measured values ​​of each sensor are independent of each other, the final predicted uncertainty uΔ is calculated as:

[0054]

[0055] where u1,u2,…,u M is the uncertainty of each mode;

[0056] The goal is to minimize u Δ ; Using the Lagrange multiplier method, we get:

[0057]

[0058] Among them, λ is the Lagrange multiplier;

[0059] Then by M The optimized weights are derived from the partial derivatives of and set to zero, so the weight of each mode is:

[0060]

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] 1) The present invention quantifies the inherent uncertainty of RUL prediction for each mode through random model updating. The framework models the forward transformation of a deep neural network as the state evolution of a nonlinear random dynamical system over time. Fractional Brownian motion (FBM) is specifically used to capture correlated noise effects. These design choices make the framework easy to implement, computationally efficient, and does not require the specification of a priori distribution of model parameters.

[0063] 2) This paper proposes a mode-specific FSDE subnet parallel processing strategy, where each modal data is processed separately for specific degradation pattern recognition while explicitly quantifying uncertainty; two types of embedded uncertainty sources are identified to facilitate on-site detection and positioning.

[0064] 3) The multimodal fusion module based on Lagrange multiplier uncertainty in this invention has two main advantages: first, it allows the model to have a more comprehensive understanding of the health status of the machine; second, under the guidance of modality-specific uncertainty and clear optimization objectives, clear multimodal fusion is achieved, making the fusion process physically interpretable.

[0065] In summary, the present invention has significant application value and broad promotion prospects in the field of machinery remaining life prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 The figure is a flow chart of a method according to an embodiment of the present invention.

[0067] Figure 2 The prediction results and corresponding prediction intervals under each working condition of the embodiment are shown, and the detected abnormal intervals are highlighted. DETAILED DESCRIPTION

[0068] The present invention is further described in detail below in conjunction with embodiments and drawings.

[0069] like Figure 1 As shown, a multimodal uncertainty-aware mechanical life prediction method based on stochastic model updating includes the following steps:

[0070] 1) Constructing drift network: The drift network is the main processing flow within the subnet, which is used to mine the health status of the monitored object. Its core unit, the representation refinement block (RDB), is specially designed. RDB consists of four layers: data structure (DS), short-term local feature refinement, long-term time trend development and downsampling. Residual connection is used to capture cross-layer information and promote gradient flow. First, a data sequence is organized by the DS layer, and then the comparable scale is standardized to enhance convergence and reduce the overfitting trend. Mathematically expressed as:

[0071]

[0072] Where ⊙ represents the Hadamard product operation, and are the mean and standard deviation of the small batch δ samples, γ scale ,γ shift The scale and shift parameters learned during training have the same shape as x;

[0073] Subsequently, the short-term local feature refinement layer enables the model to extract fine-grained, discriminative features. Mathematically, ResNet decomposes the function into:

[0074] f(x)=x+κ(x) (2)

[0075] This decomposition obtains a linear term and a nonlinear term in an additive manner for coarse feature extraction; in addition to simple addition, the information capture is expanded to include more terms. For the inference function f(x) at the point x = x0, Taylor expansion is applied to obtain:

[0076]

[0077] f(x) is decomposed into higher-order terms, so that x can be mapped to its transformed value through a series of increasingly complex functions, which are:

[0078] x→[x,f1(x),f2([x,f1(x)]),…] (4)

[0079] Where [;] represents the concatenation operation, all functions are combined by a multi-layer perceptron (MLP) to produce the final feature set, using 1×1 convolution and pooling operations to reduce model complexity, and these functions are implemented by wavelet convolution. Mathematically, for a small batch input δ, the output c out The j-th channel is calculated as:

[0080]

[0081] Where W represents the wavelet kernel weight, * d represents the dilated convolution with a dilation coefficient of d, ψ(·) is the wavelet basis function, c in and c out are the number of input and output channels, respectively, a is the size factor in wavelet transform, b is the time shift factor, and t represents the time step;

[0082] The long-term time trend development layer aims to track the evolution of monitoring data over time, including changes in degradation patterns; specifically, the computation flow is controlled in a gated manner, and for the input value x at time step t t , the output is as follows:

[0083]

[0084] where y t-1 is the output of the previous time step, z t In the following description, is a memory state that integrates multi-resolution and attention mechanisms to effectively capture long-range context clues and is calculated as follows:

[0085]

[0086] Where Conv 1×1 (·) represents a 1×1 convolution operation, pe is a position encoding term, and HAP(·) represents a hierarchical attention pooling (HAP) operation, which expands the receptive field and enables the model to integrate information from a wider context window. First, it divides the input feature map into b branches, each of which is processed using self-attention and then aggregated through a linear transformation; mathematically, for the feature map δ,

[0087]

[0088] in, are learnable parameters in the linear transformation, ω1,…,ω b The calculation is divided into ω = softmax (QK T )V,Q,K,V are index, key and value respectively, and softmax(·) represents the softmax activation function.

[0089] In equations (6) and (7), z t and r t is a gate that performs convex combinations within (0,1) and is calculated as:

[0090]

[0091] In the formula is the sigmoid activation function, represents a convolution operation with a step size of s=2 and a kernel size of 3×3, and W represents the corresponding weight matrix;

[0092] The last layer of the RDB structure is downsampling, which aggregates the information in each RDB to make the block sensitive to the entire input while retaining the processing advantages of the middle layer. It is performed on the divided area R as follows:

[0093]

[0094] in For each (i,j)∈{1,…,γ out} 2 , and operates with a special random step size that depends on the target output size;

[0095] Multiple RBDs constitute the core module of DriftNet, which gradually refines the health status information embedded in the monitoring data. Subsequently, the extracted representation is smoothed and projected into a lower dimensional space using a module based on MLPs.

[0096] 2) Constructing the diffusion network: It is built on the MLP backbone, which makes the OOD samples have high uncertainty and is subject to the Lipschitz maximum limit. The diffusion network follows Lipschitz continuity, which requires Lipschitz-compliant nonlinear activation, so ReLU is selected as the activation function. In addition, in order to prevent the value of the OOD sample from being too large, which may cause instability during the optimization process, the output maximum value of the diffusion network is maximized using the sigmoid function and the hyperparameter ε max To regulate, the diffusion network is defined as exist Initially set ε max Set it to 0.1 and increase it to 0.5 at epoch 30;

[0097] 3) Training each subnet: To simplify the training of each FSDE subnet, the objective function of the subnet consists of three parts. The first two parts are the regression terms of the in-distribution drift network and the regulated diffusion network. In addition to the conventional loss minimization, they are designed to minimize the uncertainty estimate of these samples. The latter component belongs to the OOD samples and is designed to remind the model of its limited knowledge of them, thereby encouraging high uncertainty outputs; specifically, the objective function is

[0098]

[0099] Where θ1 and θ2 are the learnable weights of the drift network and the diffusion network, L is the total number of layers in the subnet, and P ID and P OOD They are ID and OOD samples respectively. For the loss function f acting on the drift network, RUL is selected as the loss function;

[0100] 4) Uncertainty quantification of each subnet: In the constructed framework, a custom subnet is used to process the monitoring data from each mode. Each subnet performs RUL prediction and quantitative uncertainty modeling; specifically, for the m-training subnet, its prediction for

[0101]

[0102] Where S is the number of random forward passes during the test. is the mean of each prediction of the m-th mode;

[0103] For uncertainty quantification, it is divided into two types: AU and EU; AU is calculated as:

[0104]

[0105] Another uncertainty EU is the variance of the final solution, expressed as:

[0106]

[0107] 5) Multimodal fusion based on respective uncertainties: A fusion method based on Lagrange multipliers is proposed. This fusion method is obtained through explicit numerical derivation, which makes the fusion process interpretable. For each modality-specific feature, an MLP-based regression module is used to calculate the prediction within each subnet and its corresponding uncertainty. In the multimodal fusion process, the original modality features are directly fused.

[0108] For the mth modality, its modality-specific subnetwork provides a prediction and an associated uncertainty value u m, the uncertainty value can be obtained by:

[0109]

[0110] The α and β scaling factors can be adjusted according to the application to reflect the relative importance of the maintenance technicians, so that a unified expression can be obtained as:

[0111]

[0112] where ω m is the weight of the mth mode, satisfying

[0113] According to the calculation law of uncertainty propagation, when the measurement values ​​of each sensor are independent of each other, the final predicted uncertainty uΔ can be calculated as

[0114]

[0115] where u1,u2,…,u M is the uncertainty of each mode;

[0116] The goal is to minimize u Δ ; In order to simplify the calculation, using the Lagrange multiplier method, we can get:

[0117]

[0118] Among them, λ is the Lagrange multiplier;

[0119] Then by M The optimized weights can be derived from the partial derivatives of and set to zero, so the weight of each mode is:

[0120]

[0121] The embodiment applies the experimental data set of the robot harmonic reducer (HDRs) accelerated life test to verify the feasibility of the present invention. During the experiment, 5 types of monitoring data were collected. The internal current data was collected in the form of data tracking through the Omron NJ3011100 programmable logic controller (PLC); the external signals included three-axis vibration acceleration data (PCB 356A15), torque data (LONGLV WTQ1050B), three-phase current data (WBI411N95); dual-channel acoustic emission (AE) data (PACWD). During the monitoring data collection process, the external data was sampled at 25.6kHz, the sampling time was 2.56 seconds, and the sampling interval was 1 minute; the internal and acoustic emission data were sampled continuously: the internal data sampling frequency was 2kHz, the duration was 1 second, and the acoustic emission data sampling frequency was 1MHz, and the duration was 0.1 seconds.

[0122] In the data processing pipeline, the collected data and labels are first preprocessed using min-max normalization and health normalization techniques, respectively. Then, each modality is trained in parallel through its own subnet. During the training process, popular community techniques such as early stopping, weight decay, and gradient clipping are used to prevent overfitting and improve training efficiency. The momentum of the Adam optimizer is 0.9, the weight decay is 5×10-4, the mini-batch size is 64, and the training lasts 200 times. The initial learning rate of the drift network is set to 1e -4 , which decreases after epoch 50, while the learning rate of the diffusion network is set to 1e -3 ; The scaling factors in formula (17) are set to 0.6 and 0.4 respectively.

[0123] According to the above settings, the proposed network is verified on three working conditions and five modal data in the accelerated life test dataset of robot harmonic reducers (HDRs). Figure 2 The results for each condition are described in Figure 2 In the paper, the RUL prediction and corresponding uncertainty of each time step are first given. The results show that: 1) the proposed network has satisfactory regression performance and achieves effective uncertainty quantified RUL prediction under various working conditions. 2) During the prediction process of each sample, as the model receives more information about the health status and degradation clues of the monitored object, its prediction performance improves over time. In the critical final stage, the model's estimate is close to the actual RUL curve, helping operation and maintenance participants to plan effectively. (3) Comparing the prediction results under different working conditions, compared with working condition 1, the prediction results under working condition 2 are more accurate, with less uncertainty, and have better generalization ability under data-rich working conditions. Comparing the predictions under working conditions 2 and 3, it can be found that when the number of samples is sufficient, the longer prediction span poses a higher challenge to the model's continuous prediction ability.

[0124] The beneficial effect of this embodiment is that this embodiment proposes a new multimodal uncertainty-aware RUL prediction framework, which is developed through random model updating; in this framework, data from each mode is processed in parallel using a customized FSDE subnet; each FSDE subnet regards the DNN transformation as the state evolution within the random dynamical system, extending the model update from the deterministic domain to the random domain; it identifies different sources of uncertainty as AU and EU, and introduces the FBM term to capture the EU; then, based on the uncertainty of these modal features, a multimodal fusion module based on Lagrange multipliers is used for fusion. The final prediction, as well as the corresponding uncertainty estimate, is generated through regression inference and verified using an experimental dataset of accelerated life tests of robotic harmonic reducers (HDRs). The results confirm the effectiveness of the framework in RUL prediction under multimodal monitoring data, demonstrating its uncertainty quantification capabilities in each modality and the final prediction.

[0125] The present invention is not limited to the RUL prediction of industrial robot harmonic reducers, but can also be extended to other automation equipment and systems. It should be pointed out that the adjustments and modifications made without departing from the concept of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. A multimodal uncertainty-aware mechanical life prediction method based on stochastic model updating, characterized in that: The following steps are involved: 1) Constructing a drift network: The drift network mines the health status of the monitored object. Its representation and refinement block RDB includes four layers: data structure DS, short-term local feature refinement, long-term time trend development and downsampling. The residual connection is used to capture cross-layer information and promote gradient flow. Multiple RBDs gradually refine the health status information embedded in the monitoring data. Subsequently, an MLPs-based module is used to smooth the extracted representation and project it into a lower dimensional space. 2) Constructing a diffusion network: Based on the MLP backbone, the diffusion network follows Lipschitz continuity and selects ReLU as the activation function. In addition, the maximum output of the diffusion network uses the sigmoid function and the hyperparameter ε max To regulate, the diffusion network is defined as exist Initially set ε max Set it to 0.1 and increase it to 0.5 at epoch 30; 3) Training each subnet: The objective function of the subnet consists of three parts. The first two parts are the regression terms of the in-distribution drift network and the regulated diffusion network, and the last component belongs to the OOD sample; 4) Uncertainty quantification of each subnet: Monitoring data from each mode is processed using custom subnets, each of which performs RUL prediction and quantitative uncertainty modeling; 5) Multimodal fusion based on respective uncertainties: A fusion method based on Lagrange multipliers is proposed, which is obtained through explicit numerical derivation. For each modality-specific feature, an MLP-based regression module is used to calculate the prediction within each subnet and its corresponding uncertainty. In the multimodal fusion process, the original modality features are directly fused.

2. The method according to claim 1, characterized in that: Step 1) A data sequence is organized by the DS layer and then standardized to a comparable scale, which is mathematically expressed as: Where ⊙ represents the Hadamard product operation, and are the mean and standard deviation of the small batch δ samples, γ scale ,γ shift The scale and shift parameters learned during training have the same shape as x; Subsequently, the short-term local feature refinement layer extracts fine-grained, discriminative features. Mathematically, ResNet decomposes the function into: f(x)=x+к(x) (2) The decomposition results in a linear term and a nonlinear term for coarse feature extraction, and also expands the information to capture more terms. For the inference function f(x) at the point x=x0, Taylor expansion is applied to obtain: f(x) is decomposed into higher-order terms, mapping x to its transformed value through a series of functions, which are: x→[x,f1(x),f2([x,f1(x)]),…] (4) Where [;] represents the connection operation, all functions are combined by a multi-layer perceptron (MLP) to produce the final feature set, using 1×1 convolution and pooling operations to reduce model complexity, these functions are implemented by wavelet convolution; mathematically, for a small batch input δ, the output c out The j-th channel is calculated as: Where W represents the wavelet kernel weight, * d represents the dilated convolution with a dilation coefficient of d, ψ(·) is the wavelet basis function, c in and c out are the number of input and output channels, respectively, a is the size factor in wavelet transform, b is the time shift factor, and t represents the time step; The long-term time trend development layer is designed to track the evolution of monitoring data over time, including changes in degradation patterns; the computation flow is controlled in a gated manner, for the input value x at time step t t , the output is as follows: where y t-1 is the output of the previous time step, z t In the following description, is a memory state that integrates multi-resolution and attention mechanisms to effectively capture long-range context clues and is calculated as follows: Where Conv 1×1 (·) represents a 1×1 convolution operation, pe is a position encoding term, and HAP(·) represents a hierarchical attention pooling (HAP) operation; the input feature map is divided into b branches, each of which is processed using self-attention and then aggregated through a linear transformation; mathematically, for a feature map δ, in, are learnable parameters in the linear transformation, ω1,…,ω b The calculation is divided into ω = softmax (QK T )V,Q,K,V are index, key and value respectively, softmax(·) represents the softmax activation function; In equations (6) and (7), z t and r t is a gate that performs convex combinations within (0,1) and is calculated as: In the formula is the sigmoid activation function, represents a convolution operation with a step size of s=2 and a kernel size of 3×3, and W represents the corresponding weight matrix; The last layer of the RDB structure is downsampling, which aggregates the information in each RDB and is performed on the divided region R as follows: in For each (i,j)∈{1,…,γ out } 2 , and operates with a special random step size that depends on the target output size.

3. The method according to claim 1, characterized in that: Step 3) The objective function is: Where θ1 and θ2 are the learnable weights of the drift network and the diffusion network, L is the total number of layers in the subnet, and P ID and P OOD They are ID and OOD samples respectively. For the loss function f acting on the drift network, RUL is selected as the loss function.

4. The method according to claim 1, characterized in that: Step 4) For the m-training subnet, its prediction for: Where S is the number of random forward passes during the test. is the mean of each prediction of the m-th mode; For uncertainty quantification, it is divided into two types: AU and EU; AU is calculated as: Another uncertainty EU is the variance of the final solution, expressed as:

5. The method according to claim 1, characterized in that: Step 5) For the mth modality, its modality-specific subnet provides a prediction and an associated uncertainty value u m , uncertainty value u m for: The α and β scaling factors are adjusted according to the application and are uniformly expressed as: where ω m is the weight of the mth mode, satisfying According to the calculation law of uncertainty propagation, when the measured values ​​of each sensor are independent of each other, the final predicted uncertainty uΔ is calculated as: where u1,u2,…,u M is the uncertainty of each mode; The goal is to minimize u Δ ; Using the Lagrange multiplier method, we get: Among them, λ is the Lagrange multiplier; Then by M The optimized weights are derived from the partial derivatives of and set to zero, so the weight of each mode is:

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