An industrial equipment fault prediction method and system for a resource-constrained scenario

Abstract

This invention discloses a method and system for predicting industrial equipment failures in resource-constrained scenarios, comprising: S1: deploying lightweight local models on multiple clients; S2: selected clients training their local models using local data and uploading the trained local model parameters and multi-factor index sets to the server; S3: the server standardizing the multi-factor index sets received from all clients and dynamically calculating the aggregate weights of each client based on the standardized indicators using a multi-factor fusion weight calculation function; S4: the server performing a weighted average of the local model parameters of each client according to the aggregate weights to generate an updated global model and distributing the global model to each client. This invention introduces a multi-factor weight calculation mechanism on the server side to dynamically evaluate the contribution of each client to the global model, thereby achieving more stable and efficient joint failure prediction model training and improving the intelligence level of industrial equipment health status monitoring.

Description

Technical Field

[0001] This invention belongs to the field of industrial equipment failure prediction, and specifically relates to a method for industrial equipment failure prediction in resource-constrained scenarios. Background Technology

[0002] With the rapid development of the Industrial Internet, massive amounts of equipment operation data provide a data foundation for fault prediction. However, in resource-constrained industrial scenarios, edge devices often suffer from weak computing power, limited storage space, and insufficient communication bandwidth. Furthermore, due to differences in equipment operating conditions, operating environments, and fault modes, local data at each node often exhibits highly non-independent and identically distributed (Non-IID) characteristics, leading to problems such as client drift, slow convergence speed, and low prediction accuracy when traditional federated learning methods aggregate the global model.

[0003] Existing federated learning aggregation strategies are mostly based on data-weighted averaging (such as FedAvg), failing to comprehensively consider factors such as client data quality, model performance, and training stability. This makes it difficult to achieve efficient and reliable fault prediction under strongly non-IID data distributions. Therefore, there is an urgent need for a federated learning algorithm that can dynamically evaluate client contributions and adaptively adjust aggregation weights to improve the accuracy and reliability of industrial equipment fault prediction in resource-constrained scenarios. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method and system for predicting industrial equipment failures in resource-constrained scenarios. By introducing a multi-factor weighting calculation mechanism on the server side, the contribution of each client to the global model is dynamically evaluated, thereby achieving more stable and efficient joint failure prediction model training and improving the intelligence level of industrial equipment health status monitoring.

[0005] The main technical solution adopted in this invention is as follows:

[0006] A method for predicting faults in industrial equipment under resource-constrained scenarios includes:

[0007] S1: Deploy lightweight local models on multiple clients for fault prediction of industrial equipment;

[0008] S2: The selected client uses local data to train the local model and uploads the trained local model parameters and multi-factor index set to the server;

[0009] S3: The server standardizes the multi-factor index set received from all clients, and dynamically calculates the aggregate weight of each client based on the standardized index using a preset multi-factor fusion weight calculation function.

[0010] S4: The server performs a weighted average of the local model parameters of each client according to the aggregation weight, generates an updated global model, and distributes the updated global model to each client.

[0011] Preferably, in step S1, the local model is a one-dimensional convolutional neural network, which adopts a symmetrical design of the number of convolutional filters and introduces dropout layers and batch normalization layers.

[0012] Preferably, in step S2, a stochastic gradient descent optimizer with Nesterov acceleration momentum is used for local training, and gradient pruning technique is introduced to optimize the model parameters, as follows:

[0013] For client k participating in local training, the local model parameters after the t-th round of local training are... As shown below:

[0014] (1);

[0015] in, Let be the global model parameters for round t. Let be the momentum term for the t-th round;

[0016] And the momentum term in round t The expression is as follows:

[0017] (2);

[0018] In the formula, Let be the learning rate in round t; The momentum coefficient; The loss function;

[0019] When the parameter gradient The L2 norm exceeds the preset threshold At that time, scaling will be performed according to the following rules:

[0020] If (3).

[0021] Preferably, in step S2, a step-wise learning rate decay strategy is adopted, where the learning rate is decreased every fixed number of rounds. Multiply by the attenuation factor The specific formula is as follows:

[0022] (4);

[0023] in, Let t be the learning rate for the current round. The initial learning rate, It is the attenuation factor, and ∈ (0, 1), T is the decay interval round.

[0024] Preferably, in step S2, the multi-factor index set includes local data volume, local validation set accuracy, training loss variance, average validation loss, and data class distribution variance.

[0025] Preferably, in step S3, the multi-factor fusion weight calculation function is as follows:

[0026] (10);

[0027] in, Let K be the aggregate weight of client k, and let the denominator be the normalization factor, satisfying all weights. ; The overall positive score for client k; For the penalty term of client k, This represents the set of clients selected and trained in round t.

[0028] Preferably, the comprehensive positive score Calculated using the following formula:

[0029] (11);

[0030] Where α, β, and γ are linear weights, and satisfy α + β + γ = 1. The standardized sample size for client k. For the client Standardized accuracy of the validation set of the local model; Let k be the recent participation frequency of the client based on the exponential moving average, and its formula is as follows:

[0031] (12);

[0032] Where p is the smoothing coefficient. Indicates client In the Whether a wheel is selected for training is set to 1 if selected, and 0 otherwise. (Initial value) .

[0033] Preferably, the penalty item The formula is as follows:

[0034] (13);

[0035] In the above formula, , , Let V represent the standardized training loss variance, standardized average validation loss, and standardized data class distribution variance for client k, respectively. , These are the corresponding penalty coefficients.

[0036] Preferably, in step S4, the specific formula for generating the updated global model using weighted average is as follows:

[0037] (14);

[0038] in, This represents the global model parameters after the (t+1)th round update. The aggregate weight for client k, For the client Model parameters after the t-th round of local training; Let t be the set of clients selected to participate in training in round t.

[0039] A fault prediction system for resource-constrained industrial equipment includes:

[0040] Multiple client nodes, each deploying a lightweight local model, are used for local training using local data and uploading the trained local model parameters and multi-factor index set.

[0041] Central server, including

[0042] A receiving module is used to receive the multi-factor index set;

[0043] A standardization processing module is used to standardize the multi-factor index set;

[0044] The weight calculation module is used to dynamically calculate the aggregate weight of each client through a preset multi-factor fusion weight calculation function;

[0045] The aggregation module is used to perform a weighted average of the local model parameters of each client according to the aggregation weight to generate an updated global model;

[0046] The distribution module is used to distribute the updated global model to each client node.

[0047] Beneficial effects: This invention provides a method and system for predicting industrial equipment failures in resource-constrained scenarios, which has the following advantages:

[0048] (1) This invention constructs a multi-factor fusion weight calculation function to comprehensively evaluate positive indicators such as client data volume, validation set accuracy, and recent participation frequency, and applies exponential penalties to clients with unstable training or poor data quality to achieve differentiated weighted aggregation. This mechanism can "softly deweight" clients with poor performance, effectively improving the overall model performance while enhancing aggregation fairness.

[0049] (2) This invention effectively reduces the impact of invalid or negative aggregation through a differentiated weighted aggregation mechanism, significantly improves the model convergence efficiency, and greatly reduces the communication overhead in resource-constrained scenarios.

[0050] (3) This invention uses a lightweight one-dimensional convolutional neural network as the local model. The model uses the ReLU activation function to ensure efficient nonlinear expression. Combined with the Dropout and batch normalization dual regularization strategies, it ensures generalization performance while controlling the number of parameters. With the NAG-SGD optimizer, gradient pruning and step-wise learning rate decay strategy, the training stability is further enhanced. It is particularly suitable for edge devices with weak computing power and limited storage space and real-time time series data analysis tasks. Attached Figure Description

[0051] Figure 1 This is a simplified diagram of the Dropout layer structure of the network model of this invention;

[0052] Figure 2 This is a diagram of the PT890 Industrial Internet Intelligent Operation and Maintenance Simulation Test Bench;

[0053] Figure 3 This is a diagram of the CWRU experimental equipment;

[0054] Figure 4 This is a graph showing the data distribution of the present invention in the PT890 dataset;

[0055] Figure 5 This is a diagram showing the data distribution of the present invention in the CWRU dataset;

[0056] Figure 6 This is a curve comparing the accuracy of the present invention on the CWRU dataset;

[0057] Figure 7 This is a comparison curve of the loss function values ​​of this invention on the CWRU dataset;

[0058] Figure 8 This is a curve showing the accuracy of the present invention on the PT890 dataset;

[0059] Figure 9 This is a curve comparing the loss function values ​​of the present invention on the PT890 dataset. Detailed Implementation

[0060] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application are clearly and completely described below. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this application.

[0061] Example 1

[0062] This embodiment proposes a fault prediction method for industrial equipment in resource-constrained scenarios, and the specific steps are as follows:

[0063] Step 1: Deploy a lightweight local model on multiple clients for fault prediction of industrial equipment.

[0064] To adapt to resource-constrained edge devices, this embodiment designs a lightweight one-dimensional convolutional neural network as a client-side local model. This model is deployed on multiple clients for fault prediction of industrial equipment. With lightweight design as its core objective, the model significantly improves computational efficiency while maintaining temporal feature extraction capabilities.

[0065] Specifically, the client-side local model employs a three-layer convolutional-pooling architecture, consisting of three convolutional layers and two max-pooling layers. Each convolutional layer is followed by a ReLU activation function to enhance non-linear feature extraction capabilities, and a batch normalization layer accelerates the training convergence process. To balance model complexity and performance, the number of convolutional filters is designed symmetrically as 8-16-8.

[0066] A Dropout layer with a dropout rate of 0.6 is introduced at the end of the network as a random regularization technique to effectively prevent overfitting by randomly discarding neurons. Its network structure is as follows: Figure 1 As shown in Table 1, the feature map is then converted into a one-dimensional vector through a flattening layer and connected to a fully connected layer with 64 neurons for advanced feature fusion. Finally, a linear classifier outputs multi-class fault prediction results. This model structure ensures the ability to extract temporal features while keeping the total number of parameters at a low level, fully meeting the resource constraints of edge devices. The specific structural parameters of the model are shown in Table 1.

[0067] Step 2: The selected client trains its local model using local data and uploads the trained local model parameters and multi-factor index set to the server. Details are as follows:

[0068] In each round of local training, the client uses a stochastic gradient descent (NAG-SGD) optimizer with Nesterov acceleration momentum to update parameters.

[0069] Suppose there exists a set of local clients , The total number of edge device nodes connected to the central server (50 in this example), and each client k has a local dataset. When the t-th round of global training begins, the central server will send the global model parameters... Distribute to each local client device that will participate in the t-th round of global aggregation.

[0070] For client k participating in local training, its training task is to iteratively optimize its model parameters through T rounds of global aggregation. In this optimization process, the loss value of client k in the t-th round of local training is... It can be represented as Then the local model parameters of node k after the t-th round of local iteration As shown below:

[0071] (1);

[0072] Let be the global model parameters for round t. Let t be the momentum term of the t-th round.

[0073] Among them, the momentum term of round t The expression is as follows:

[0074] (2);

[0075] In the formula, The learning rate in round t, For momentum coefficient, Let be the loss function. By introducing Nesterov momentum, the parameter trajectory can be "predicted" before the update, thereby improving the convergence speed and stability.

[0076] Furthermore, to enhance the numerical stability of the gradient calculation process and effectively suppress gradient explosion, this invention introduces a gradient pruning technique. During each backpropagation process, when the parameter gradient... The L2 norm exceeds the preset threshold At that time, scaling will be performed according to the following rules:

[0077] If (3).

[0078] This embodiment achieves upper limit specification for outlier gradients by imposing constraints on the L2 norm of the parameter gradient.

[0079] After local training is complete, each participating client needs to upload not only the updated local model parameters, but also a set of multi-factor weighted impact metrics for the server to evaluate the client's contribution. This metric set includes: local data volume, local validation set accuracy, etc. Variance of loss per round of local training Average verification loss and the variance of data category distribution .

[0080] In this embodiment, the specific process of local training on the client side is as follows:

[0081] The input is known to be global model parameters. Local training rounds Learning rate

[0082] (a): The client first performs the following initialization operations: sets the initial value of the momentum term to zero: Set the momentum coefficient Create an empty list This is used to record the loss value for each training round; and to calculate the variance of the local data class distribution. It is used to measure the degree to which data are not independently and identically distributed (Non-IID);

[0083] (b): Perform E rounds of local iterative training

[0084] (b1): Calculate the loss value, loss←

[0085]

[0086] Where C represents the total number of fault categories. For real labels, To predict the probability distribution of labels.

[0087] (b2): Add the current loss value to the loss list: loss_list.append(loss)

[0088] (b3): ​​Calculate the gradient of the loss function with respect to the model parameters;

[0089] (b4): Gradient clipping is performed based on formula (3);

[0090] (c): Update momentum term and model parameters

[0091] Update the momentum term using formula (2);

[0092] Update the model parameters using formula (1);

[0093] (d): Calculate the impact of each weighted index, including , , , .

[0094] In one optional embodiment, a stepped learning rate decay strategy is employed. This strategy uses a learning rate adjustment method that gradually decreases as the training progresses. By dynamically reducing the learning rate at different training stages, the client-side local model can quickly approach a better solution in the early stages, while in later stages, weight updates are performed at more granular paces, thereby enhancing the overall training stability and generalization performance. Let the initial learning rate be... After every T training rounds, the learning rate is multiplied by a decay factor. , If ∈ (0, 1), then the learning rate for the current round t is... The expression is:

[0095] (4).

[0096] Step 3: The server standardizes the multi-factor indicator sets received from all clients, and dynamically calculates the aggregate weight of each client based on the standardized indicators using a preset multi-factor fusion weight calculation function.

[0097] Taking the logarithmic standardization of the accuracy metric as an example, the standardization process for the various weights affecting the client-side metrics is explained. The specific process is as follows:

[0098] 3.1 Let For defining the client on the validation set The accuracy of the local model. First, the proportion of each client's accuracy to the total accuracy of all selected clients is calculated to generate a normalized accuracy metric. This metric reflects the relative importance of the accuracy of each client model in the entire population. The specific standardization process is shown in formula (5):

[0099] (5);

[0100] in, This represents the accuracy of each selected client-side local model on the validation set. Represented as client The standardized accuracy is given by K, where K represents the number of clients selected by the central server to participate in the overall training in the current round.

[0101] 3.2 Add offset to ensure numerical stability

[0102] Apply a small positive offset to the normalized accuracy To avoid invalid mathematical operations in subsequent calculations, a tiny constant is added. In this embodiment, to ensure the numerical stability of the calculations, a very small positive number is added to the accuracy of each client. (Pick = 10 −6 The adjustment process is shown in formula (6):

[0103] (6).

[0104] 3.3 Calculating Information Entropy and Information Content

[0105] The concept of information entropy is introduced to quantify the amount of information contained in the accuracy of each client's local model in the current training epoch. (Information content) The calculation method is as follows:

[0106] (7);

[0107] In the formula, Let k represent the normalized precision of client k after offset adjustment, and then the amount of information corresponding to that client. This is represented by the accuracy of the client.

[0108] 3.4 Information content The weight index is converted into a weight that conforms to the form of a probability distribution, and the information content is normalized to satisfy the basic properties of the probability distribution. The specific normalization process is shown in formula (8):

[0109] (8);

[0110] In this embodiment, to ensure the numerical stability of each weighting factor when applied to the contribution function calculation and to reduce the impact of extreme values, the following metrics of the client-side local model must all undergo the above-mentioned logarithmic standardization process: validation set accuracy of the client-side local model. Recent training frequency Variance of loss per round of local training Average verification loss and data category distribution variance .

[0111] Standardization of client data volume: The standardization method is slightly different, directly calculating the proportion of each client's data volume to the total of all selected client data volumes in the weighting function. The standardization process is as shown in formula (9):

[0112] (9).

[0113] in, This indicates the amount of data for client k. This indicates the amount of data in the local model of each selected client.

[0114] While metrics such as the number and quality of client samples, the accuracy of the local model, and the variance of the loss function all influence the iterative optimization of the global model, the degree to which different clients' performance on each metric affects the global model aggregation varies, requiring a comprehensive trade-off. Therefore, this embodiment designs a weight calculation function based on the idea of ​​multi-factor fusion. This function integrates the standardized values ​​of the various weight influencing factors of each client to evaluate the contribution of each client to the global model aggregation and determine its weight in the aggregation process accordingly. The specific weight calculation formula is shown below:

[0115] (10);

[0116] in, The aggregate weights for client k are defined by a normalization factor in the denominator, ensuring that all standardized metric values ​​from the previous training round satisfy all weights. , The overall positive score for client k is used to measure its training quality and data importance; The penalty term is an exponential form of the client k, used to suppress the influence of clients with large training variance, high loss, or uneven class distribution, making the weight calculation more robust. This represents the set of clients selected and trained in round t.

[0117] The formula for calculating the overall positive score is as follows:

[0118] (11);

[0119] Where α, β, and γ are linear weights, and satisfy α + β + γ = 1. The standardized sample size for client k. For the client Standardized accuracy of the validation set of the local model; For client k, the recent participation frequency is based on the exponential moving average.

[0120] Recent participation frequency in standardization The definition is shown in formula (12):

[0121] (12);

[0122] Where p is the smoothing coefficient. Indicates client In the Whether a wheel is selected for training is set to 1 if selected, and 0 otherwise. (Initial value) .

[0123] This design increases the weight of recent training activities, allowing the model to focus on more representative data sources.

[0124] To mitigate the negative impact of clients with unstable training, high loss, or imbalanced data distribution on the global model, this embodiment also introduces an exponential penalty term. As shown in formula (13):

[0125] (13);

[0126] In the above formula, , , Let Vk represent the variance of the standardized loss function, the standardized average validation set loss, and the standardized variance of the data class distribution for each round of local training on client k, respectively. , These are the corresponding penalty coefficients, which control the intensity of the penalty.

[0127] In this invention, suppression in the form of an exponential function can effectively reduce the negative impact of unstable clients on the global model, smoothly reduce the aggregate weight of poorly performing clients, thereby achieving a "soft weighting" effect and avoiding direct data discarding.

[0128] Step 4: The server performs a weighted average of the local model parameters of each client according to the aggregate weight, generates an updated global model, and distributes the updated global model to each client.

[0129] Based on server-wide model parameters for any local client model In this regard, its aggregation formula is:

[0130] (14);

[0131] in, This represents the global model parameters after the (t+1)th round update. For the client Model parameters after t rounds of local training; Let be the set of clients selected to participate in training in round t, and let be the total number of clients multiplied by the participation ratio, which is 10 in this embodiment. The updated global model will be distributed to all clients for the next round of training.

[0132] In this embodiment, the server-side aggregation process is as follows:

[0133] Step a: Reception and Standardization

[0134] After receiving metrics from all participating clients, the server first standardizes each metric. To address the issue of differing metric dimensions, this invention employs logarithmic standardization and information entropy normalization methods:

[0135] Accuracy metrics: The relative weight of the accuracy of each client is calculated according to formula (5), and a small constant is introduced according to formula (6) to ensure numerical stability. The information is quantified by information entropy according to formula (7), and finally normalized according to formula (11).

[0136] Other metrics: Recent participation frequency, loss variance, average validation loss, and class distribution variance were all standardized with reference to the accuracy metrics to obtain the standardized recent participation frequency. Variance of loss per round of local training Average verification loss and data category distribution variance .

[0137] Data volume indicators: Standardized by the proportion of total volume, as shown in formula (9).

[0138] Step b: Calculate the aggregate weights

[0139] The server calculates an aggregate weight for each client using a multi-factor fusion weight calculation function. The weighting function is based on the overall positive score. and exponential form of penalty item It consists of two parts, as shown in formula (10).

[0140] Overall positive score The linear weighted sum of the standardized data volume, validation set accuracy, and recent participation frequency is shown in formula (11).

[0141] Index penalty item : A penalty is imposed on clients with unstable training (large loss variance), high loss, or uneven data distribution, as shown in Equation (13). This mechanism achieves "soft deweighting" of poorly performing clients.

[0142] Step c: Global model aggregation

[0143] The local model parameters uploaded by each client are weighted and aggregated according to formula (14) to obtain the updated global model.

[0144] The above method is applied to a federated learning system for fault prediction in resource-constrained industrial equipment. This system consists of a central server and multiple edge device nodes acting as clients, aiming to jointly train a high-accuracy global fault prediction model through multiple rounds of federated learning iterations. The system includes:

[0145] Multiple client nodes, each deploying a lightweight local model, are used for local training using local data and uploading the trained local model parameters and multi-factor index set.

[0146] Central server, including:

[0147] A receiving module is used to receive the multi-factor index set;

[0148] A standardization processing module is used to standardize the multi-factor index set;

[0149] The weight calculation module is used to dynamically calculate the aggregate weight of each client through a preset multi-factor fusion weight calculation function;

[0150] The aggregation module is used to perform a weighted average of the local model parameters of each client according to the aggregation weight to generate an updated global model;

[0151] The distribution module is used to distribute the updated global model to each client node.

[0152] Experimental verification and effect analysis

[0153] I. Construction of Experimental Dataset

[0154] This embodiment, based on the PT890 Industrial Internet Intelligent Operation and Maintenance Simulation Test Bench, designs and constructs a multi-category, multi-condition industrial equipment fault dataset, providing reliable data support for subsequent research on industrial equipment fault prediction methods for resource-constrained scenarios.

[0155] 1.1 PT890 Industrial Internet Intelligent Operation and Maintenance Simulation Test Bench

[0156] The PT890 Industrial Internet Intelligent Operation and Maintenance Simulation Test Bench is a comprehensive experimental platform that simulates the operation of equipment in an industrial field. Its physical structure is as follows: Figure 2 As shown, the test bench, from left to right, includes: a three-phase variable frequency geared motor, a rotor system, a parallel fault simulation gearbox, a torque-speed meter, a planetary fault simulation gearbox, and a magnetic powder brake load. The three-phase variable frequency geared motor serves as the power source, with precise speed control achieved through a frequency converter; the parallel gearbox and planetary gearbox simulate different types of transmission mechanism faults; the torque-speed meter monitors the torque and speed parameters of the transmission system in real time; and the magnetic powder brake provides adjustable load conditions.

[0157] Regarding sensor deployment, the test bench installed ICP-type vibration acceleration sensors at the 12 o'clock and 6 o'clock positions on four key components (motor output bearing, parallel gearbox, torque tachometer, and planetary gearbox). The sensor sensitivity is 100 mV / g, and the frequency response range is 0.5 Hz-50 kHz. The dataset includes single and compound faults of different components. Bearing faults include inner ring faults, outer ring faults, rolling element faults, and cage faults. Parallel gearbox faults include gear wear, broken teeth, and missing teeth. Planetary gearbox faults include wear of the input sun gear, broken input sun gear, missing input sun gear, and cracks at the root of the planetary gear teeth.

[0158] 1.2 Operating Condition Design and Data Acquisition

[0159] To simulate the fault behavior of industrial equipment under different operating conditions, three typical operating condition combinations were designed for experimental data collection, as shown in Table 2. The main operating condition variables included rotational speed and load. Rotational speed was typically set to three levels: low speed (approximately 800 rpm), medium speed (approximately 1000 rpm), and high speed (approximately 1200 rpm) to examine the influence of changes in rotational inertia on vibration response. Load was divided into three types: light load, rated load, and overload, to analyze the effect of torque changes on the system's energy distribution. Each fault type was repeatedly sampled under different operating conditions to improve the statistical significance and experimental reliability of the samples.

[0160] For each fault condition, one minute of data was collected under three operating conditions, resulting in a total of 180 data samples for each fault condition. Vibration signals from four channels were collected simultaneously at a sampling frequency of 10kHz to ensure the capture of high-frequency fault characteristics during equipment operation.

[0161] 1.3 Data Storage and Organization Structure

[0162] The data files are saved in a standardized format, with each fault state corresponding to a separate .mat data file. The dataset is stored in MATLAB's .mat format, and each file contains 600,000 data records. The data structure includes the following fields:

[0163] Time: The timestamp of data collection, accurate to milliseconds;

[0164] Rotational speed: Real-time rotational speed collected by a torque tachometer;

[0165] Signal data: Acceleration signals acquired by vibration sensors, including synchronization of four channels;

[0166] Data length: The total number of data records in the file, which is fixed at 600,000.

[0167] The directory structure is organized in a three-level hierarchy of "operating condition / fault location / specific fault state," facilitating conditional retrieval and batch processing. The total dataset size is approximately 3.53GB, providing a sufficient data foundation for subsequent model training and algorithm validation.

[0168] II. Experimental Dataset and Preprocessing

[0169] To verify the effectiveness and robustness of the industrial equipment fault prediction method based on FLWAMF (a federated learning algorithm based on multi-factor fusion weighted aggregation) proposed in this invention, this embodiment designed and implemented a series of comparative experiments. The aim is to systematically evaluate the performance of the FLWAMF algorithm in terms of global model convergence speed, prediction accuracy, and stability under resource-constrained scenarios.

[0170] This invention uses the PT890 industrial equipment fault dataset and the Case Western Reserve University Rolling Bearing Fault Dataset (CWRU) for experiments. The descriptions of these two datasets are as follows:

[0171] (1) PT890 Industrial Equipment Fault Dataset

[0172] The aforementioned dataset is self-collected, and its dataset information is as described above.

[0173] (2) CWRU dataset

[0174] The CWRU dataset, released by the Electrical Engineering Laboratory at Case Western Reserve University, is one of the most representative open data resources for rolling bearing experimental research. The experimental system uses accelerometers positioned at the drive end, fan end, and base of the motor body to simultaneously record the vibration response at different locations. The experimental setup is as follows: Figure 3 As shown.

[0175] This invention utilizes vibration samples collected from the drive end under 0HP conditions in this dataset, with a sampling frequency of 12 kHz, i.e., 12,000 data points are collected per second. The experimental platform is set with four basic states: normal bearing, outer ring damage at the 3 o'clock position, inner ring damage, and rolling element damage. Based on these, and according to the different defect sizes, it is further divided into three damage levels: mild, moderate, and severe, with raceway defect diameters of 7 mm, 14 mm, and 21 mm, respectively.

[0176] 2.3 Data Preprocessing

[0177] Before data import, all signal channels were normalized to eliminate the influence of different units on the model learning process. The vibration signals were preprocessed using the Z-Score normalization method.

[0178] (15);

[0179] in, The mean value of the vibration signal. The standard deviation is denoted as . This standardization method can unify vibration signals from different channels and under different operating conditions to the same numerical range, which is beneficial to model convergence and generalization. Simultaneously, a sliding window truncation technique is used to convert continuous time-series data into fixed-length segments for model input.

[0180] The amount of data for different fault types is shown in Table 3. This distribution pattern is highly consistent with the operating characteristics of equipment in actual industrial scenarios, which are "mainly normal operation with occasional faults". The dataset has been divided into 110,000 training samples and 26,000 test samples to ensure that the model can be reliably evaluated based on sufficient training.

[0181] The CWRU dataset is partitioned as shown in Table 4. Each bearing operating state includes 6000 data samples, for a total of 70000 data samples. To ensure the realism of the experiment, the CWRU dataset has been divided into 60000 training samples and 10000 test samples.

[0182]

[0183] III. Data Partitioning Strategy

[0184] Customer data partitioning strategy: This embodiment uses the Dirichlet distribution to partition all training samples to more realistically simulate the non-independent and identically distributed (Non-IID) characteristics of customer data under resource-constrained environments. The Dirichlet distribution is a multivariate continuous probability distribution that produces a proportional vector whose sum of elements equals one, making it particularly suitable for constructing customer datasets where the proportions of samples from different categories vary.

[0185] Partitioning principle: For a dataset containing C fault categories, first sample a scale vector from the Dirichlet distribution for each category c∈{0,1,…,C−1}:

[0186] (16);

[0187] in, This represents the distribution proportion of class c samples in client k. Parameters control the centrality of the distribution: As the size increases, the sample data distribution among participants becomes more similar, especially when... As the range increases (→+∞), the distribution of each client's local data is highly similar to that of the original dataset, exhibiting an independent and identically distributed trend. Conversely, when... When the value is →0, each client contains only samples from one randomly selected category, and the distribution difference between local data on each client is the greatest.

[0188] Division formula: Assign category c to each client according to the sampling ratio. One sample:

[0189] (17);

[0190] in, This represents the number of samples obtained by client k from category c. To more comprehensively represent the degree of dataset personalization among different clients, in this embodiment, the value of α is set to 0.1, thereby simulating a very strong Non-IID data distribution. This invention assumes a total of 50 clients, and the data partitioning of these 50 clients on the two datasets is as follows: Figure 4 and Figure 5 As shown.

[0191] IV. Evaluation Indicators

[0192] The experiments in this invention use accuracy, loss function, and communication cost to evaluate the performance of the model.

[0193] 4.1 Accuracy

[0194] Accuracy measures the overall recognition performance of a model across different fault categories. It is defined as the proportion of correctly predicted samples out of the total number of samples. The calculation formula is as follows:

[0195] (18);

[0196] Where TP represents true positives, TN represents true negatives, FP represents false positives, and FN represents false negatives; ACC represents the model's accuracy.

[0197] 4.2 Cross-entropy loss function

[0198] In addition to accuracy, this invention also utilizes the cross-entropy loss function as a performance metric during model training. A key criterion for evaluating model convergence and generalization ability is that the loss function effectively quantifies the difference between the model's predictions and the true labels. During training, the model's learning progress and optimization stability can intuitively reflect the decreasing trend of the loss function. The entire dataset... There are n samples, and the sample with index i is represented by the feature vector. and one-hot tag vector It consists of two parts. Assume a vector. Let x represent the conditional probability for each class of input x. The log-likelihood is then calculated as follows:

[0199] (19);

[0200] (20);

[0201] According to maximum likelihood estimation, maximizing... This is equivalent to minimizing the negative log-likelihood estimate. For any label y of length q and the predicted result... The cross-entropy loss function is shown in the following formula:

[0202] (twenty one).

[0203] 4.3 Communication costs

[0204] To ensure fair comparisons among different algorithms, this invention uses the number of communication rounds required for a model to reach a specified accuracy as a unified evaluation criterion, and constructs a communication cost metric to reflect the differences in convergence speed among methods. This metric provides a relative cost by comparing the number of communication rounds required for different algorithms to reach the same performance level. For example, if a model achieves 95% accuracy after 100 communication rounds using algorithm A, while algorithm B only requires 90 rounds, then the communication cost of algorithm B can be expressed as 0.9A.

[0205] V. Experiment Setup

[0206] To ensure fair comparisons among different algorithms, this invention uses the number of communication rounds required for a model to reach a specified accuracy as a unified evaluation criterion, and constructs a communication cost metric to reflect the differences in convergence speed among methods. This metric provides a relative cost by comparing the number of communication rounds required for different algorithms to reach the same performance level. For example, if a model achieves 95% accuracy after 100 communication rounds using algorithm A, while algorithm B only requires 90 rounds, then the communication cost of algorithm B can be expressed as 0.9A.

[0207] In this federated learning scenario, this embodiment simulates 50 heterogeneous client nodes to construct a typical distributed model training system. The main hyperparameter settings for the experiment are shown in Table 5.

[0208] The experimental platform utilizes an NVIDIA TITANX graphics processing unit (GPU) and an Intel Core i5-10400F CPU at 2.90GHz, with 16GB of memory. The GPU is primarily used to accelerate model training, while the CPU handles data preprocessing and aggregation calculations on the federated server side. The experiments were conducted on a Windows 10 operating system using Python 3.9. The deep learning framework chosen was PyTorch 1.9.1, which was integrated with the FedML federated learning framework to implement client-side distribution, model synchronization, and global parameter aggregation.

[0209] VI. Experimental Results and Analysis

[0210] This invention systematically verifies the performance of the proposed FLWAMF algorithm under extremely strong Non-IID data distribution conditions. Experiments were conducted on the CWRU bearing fault dataset and the PT890 industrial equipment fault dataset, and the algorithm was compared and analyzed with FedAvg, FedExProx, FedGP, and FedCER in terms of accuracy, convergence speed, and communication cost.

[0211] 6.1 Experimental Results on the CWRU Dataset

[0212] Figure 6 and Figure 7 The accuracy and loss curves of four comparative algorithms and the FLWAMF algorithm proposed in this invention on the CWRU dataset are shown. Under a very strong Non-IID data distribution (α=0.1), the curves are presented.

[0213] like Figure 6 As shown, on the CWRU dataset, the FLWAMF algorithm generally exhibits faster convergence speed and higher accuracy after convergence. FLWAMF's effect on accelerating model convergence is particularly significant. The models trained using the FedAvg, FedExProx, FedGP, and FedCER algorithms achieve accuracies of 94.24%, 96.34%, 96.93%, and 97.80%, respectively, while the model trained using the FLWAMF algorithm proposed in this invention achieves an accuracy of 98.16%. The accuracy of the FLWAMF algorithm proposed in this invention is 3.92% higher than the FedAvg algorithm, 1.82% higher than the FedExProx algorithm, and 1.23% higher than the FedGP algorithm. However, it only improves the accuracy of the model compared to the FedCER algorithm by 0.36%. This is because the FedCER algorithm, through its intelligent joint scheduling, optimizes resource efficiency to the extreme on the relatively simple CWRU dataset.

[0214] 6.2 Experimental Results of PT890 Dataset

[0215] Figure 8 and Figure 9 The accuracy and loss curves of five algorithms on the PT890 dataset under a very strong Non-IID data distribution (α=0.1) are shown.

[0216] Compared to the CWRU dataset, the sample data in the PT890 dataset is more complex, thus requiring more global communication rounds to reach convergence, resulting in greater accuracy differences between algorithms compared to the CWRU dataset. Specifically:

[0217] FedAvg employs a naive aggregation strategy of direct model averaging, which produces significant client drift under highly non-IID data distributions, resulting in a baseline accuracy of only 91.15%.

[0218] While FedExProx alleviated the drift problem by introducing proximal term constraints, achieving an accuracy of 93.68%, its fixed-strength regularization also limited beneficial local updates, creating a performance bottleneck.

[0219] FedGP relies on a globally shared feature extractor, which makes it difficult to adapt to differences in underlying features among clients, resulting in an accuracy rate of only 93.80%.

[0220] FedCER improves generalization ability through consensus constraints, achieving an accuracy of 95.27%. However, the forced consensus mechanism in highly heterogeneous environments may cause the model to learn suboptimal features.

[0221] In contrast, the FLWAMF algorithm proposed in this invention, with its weighting mechanism based on multi-factor fusion, dynamically calculates the aggregate weights during global model updates. Combined with its flexible training framework, it achieves a better balance between global consistency and local adaptation, ultimately achieving a highest accuracy of 97.06% after 150 iterations. This represents an improvement of 5.91%, 3.38%, 3.26%, and 1.79% compared to FedAvg, FedExProx, FedGP, and FedCER, respectively.

[0222] 6.3 Communication Cost Analysis

[0223] Table 6 quantifies the performance of five algorithms on two datasets. Here, Round(Acc) represents the number of communication rounds required for the model to reach its highest accuracy after convergence, Acc is the final accuracy, and C.Cost represents the communication cost (based on FedExProx 1).

[0224] * indicates that the model failed to achieve 95% accuracy within the specified maximum number of communication rounds.

[0225] On the CWRU dataset, the number of communication rounds required for each federated learning algorithm to achieve 95% accuracy varies significantly. FedCER achieves the target accuracy at round 62, FedGP at round 70, while FedExProx requires training up to round 81. FLWAMF performs best, achieving 95% accuracy at round 50, while FedAvg fails to reach this threshold within the maximum number of communication rounds. Using FedExProx as a benchmark, the relative communication costs for the other algorithms are calculated as follows: FedGP 0.86, FedCER 0.77, and FLWAMF 0.62.

[0226] The comparison results on the PT890 dataset show a similar trend. FedCER achieved 95% accuracy in 117 rounds, FLWAMF achieved its goal in 101 rounds, while FedAvg, FedExProx, and FedGP failed to meet the performance requirements within the specified maximum number of communication rounds. Based on the same benchmark, the relative communication cost of FedCER is 0.78, and the relative communication cost of FLWAMF is 0.68.

[0227] In summary, under extremely strong Non-IID data distribution conditions, FLWAMF, compared with FedAvg, FedExProx, FedGP, and FedCER, can effectively improve the convergence speed of the server's global model, reduce communication costs, and has higher fault prediction accuracy.

[0228] This invention addresses the challenges of uneven data distribution and limited computing power in federated learning model aggregation for industrial equipment fault prediction in resource-constrained scenarios. Building upon the FedAvg algorithm, it proposes a federated learning algorithm based on multi-factor fusion weighted aggregation. This algorithm comprehensively considers multiple factors, including local dataset size, model prediction accuracy, and participation frequency, enabling a more comprehensive evaluation of the contributions of each participant during the aggregation process.

[0229] Experimental results show that this method outperforms similar methods in terms of model convergence speed and global prediction performance. It achieves fault prediction accuracy of 98.16% and 97.06% on the CWRU bearing fault dataset and the PT890 industrial equipment fault dataset, respectively. The communication cost is only 62%-68% of that of similar algorithms, which verifies its effectiveness and practical value in fault prediction under resource-constrained environments.

[0230] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should all fall within the scope of protection of the present invention.

Claims

1. A method for industrial equipment failure prediction for resource-constrained scenarios, the method comprising: include: S1: Deploy lightweight local models on multiple clients for fault prediction of industrial equipment; S2: The selected client uses local data to train the local model and uploads the trained local model parameters and multi-factor index set to the server; S3: The server standardizes the multi-factor index set received from all clients, and dynamically calculates the aggregate weight of each client based on the standardized index using a preset multi-factor fusion weight calculation function. S4: The server performs a weighted average of the local model parameters of each client according to the aggregation weight, generates an updated global model, and distributes the updated global model to each client.

2. The method of claim 1, wherein, In step S1, the local model is a one-dimensional convolutional neural network. The one-dimensional convolutional neural network adopts a symmetrical design of the number of convolutional filters and introduces dropout layers and batch normalization layers.

3. The method of claim 2, wherein, In step S2, a stochastic gradient descent optimizer with Nesterov acceleration momentum is used for local training, and gradient clipping is introduced to optimize the model parameters, as follows: For a client k participating in local training, the local model parameters after the t-th round of local training As follows: （1）； wherein, is the global model parameter for the t-th round, is the momentum term for the t-th round. And the momentum term in round t The expression is as follows: （2）； In the formula, Let be the learning rate in round t; The momentum coefficient; The loss function; When the parameter gradient The L2 norm exceeds the preset threshold At that time, scaling will be performed according to the following rules: If (3)。 4. The industrial equipment fault prediction method for resource-constrained scenarios according to claim 3, characterized in that, In step S2, a step-wise learning rate decay strategy is adopted, where the learning rate is decreased every fixed number of rounds. Multiply by the attenuation factor The specific formula is as follows: （4）； in, Let t be the learning rate for the current round. The initial learning rate, It is the attenuation factor, and ∈ (0, 1), T is the decay interval round.

5. The industrial equipment fault prediction method for resource-constrained scenarios according to claim 1, characterized in that, In step S2, the multi-factor index set includes local data volume, local validation set accuracy, training loss variance, average validation loss, and data class distribution variance.

6. The industrial equipment fault prediction method for resource-constrained scenarios according to claim 1, characterized in that, In step S3, the multi-factor fusion weight calculation function is as follows: （10）； in, Let K be the aggregate weight of client k, and let the denominator be the normalization factor, satisfying all weights. ; The overall positive score for client k; For the penalty term of client k, This represents the set of clients selected and trained in round t.

7. The industrial equipment fault prediction method for resource-constrained scenarios according to claim 6, characterized in that, The overall positive score Calculated using the following formula: （11）； Where α, β, and γ are linear weights, and satisfy α + β + γ = 1. The standardized sample size for client k. For the client Standardized accuracy of the validation set of the local model; Let k be the recent participation frequency of the client based on the exponential moving average, and its formula is as follows: （12）； Where p is the smoothing coefficient. Indicates client In the Whether a wheel is selected for training is set to 1 if selected, and 0 otherwise. (Initial value) .

8. The industrial equipment fault prediction method for resource-constrained scenarios according to claim 6, characterized in that, The penalty item The formula is as follows: （13）； In the above formula, , , Let V represent the standardized training loss variance, standardized average validation loss, and standardized data class distribution variance for client k, respectively. , These are the corresponding penalty coefficients.

9. The method for predicting industrial equipment failures in resource-constrained scenarios according to claim 1, characterized in that, In step S4, the specific formula for generating the updated global model using the weighted average is as follows: （14）； in, This represents the global model parameters after the (t+1)th round update. The aggregate weight for client k, For the client Model parameters after the t-th round of local training; Let t be the set of clients selected to participate in training in round t.

10. A fault prediction system for resource-constrained industrial equipment, used to perform the method according to any one of claims 1 to 9, characterized in that, include: Multiple client nodes, each deploying a lightweight local model, are used for local training using local data and uploading the trained local model parameters and multi-factor index set. Central server, including A receiving module is used to receive the multi-factor index set; A standardization processing module is used to standardize the multi-factor index set; The weight calculation module is used to dynamically calculate the aggregate weight of each client through a preset multi-factor fusion weight calculation function; The aggregation module is used to perform a weighted average of the local model parameters of each client according to the aggregation weight to generate an updated global model; The distribution module is used to distribute the updated global model to each client node.

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