Oxygen concentrator life prediction method and system based on multi-scale convolutional network
Patent Information
- Application Number
- CN202611262788.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-19
- Publication Date
- 2026-10-27
AI Technical Summary
[0004]本发明的目的在于提供一种基于多尺度卷积网络的氧气浓缩器寿命预测方法及系统,以解决现有技术中仅依据单一性能指标建模、未纳入多维环境因素,使模型无法随环境自适应更新、导致剩余寿命预测精度不足的问题
通过融合多维环境参数与性能退化指标,使模型得以捕捉外部环境变化对退化速率的影响,克服单一性能指标建模信息不足的局限。经验模态分解将信号分解为不同尺度的本征模态函数,多维度统计特征的提取进一步丰富了退化信息表征,从而提升了模型对退化状态的感知能力。以各本征模态函数为通道维度构建多通道输入张量,使网络能够并行处理不同尺度的退化特征,相较于单一尺度卷积结构,对复杂退化规律的拟合能力更强。通道注意力模块沿多维特征向量的维度聚合后对通道间依赖关系建模,使模型能够聚焦于对寿命退化贡献更显著的本征模态函数通道,实时环境条件的变化可通过多通道输入张量直接反映至模型前端,网络据此动态调整各通道注意力权重,从而实现模型参数随环境条件的自适应更新,最终使剩余寿命预测精度得到显著提升。
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Figure CN122986702A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of airborne equipment condition monitoring technology, and in particular to a method and system for predicting the lifespan of an oxygen concentrator based on a multi-scale convolutional network. Background Technology
[0002] The airborne oxygen concentrator is a core component of the aircraft's environmental control system. Its function, based on the principle of pressure swing adsorption (PSA), is to separate nitrogen from engine bleed air to obtain oxygen-enriched air, providing a continuous and stable oxygen supply to the cockpit and cabin, while also participating in cabin pressure regulation. The health of the oxygen concentrator is directly related to flight safety and the lives of the crew. However, during long-term service, the molecular sieve material inside the oxygen concentrator undergoes gradual performance degradation due to the combined effects of complex environmental factors such as air humidity, temperature fluctuations, vibration, shock, and pressure cycling, manifesting as decreased oxygen concentration and insufficient oxygen partial pressure. When the remaining service life of the oxygen concentrator is insufficient to support a complete flight mission, failure to provide timely warnings and replacement will seriously threaten the execution of the flight mission and crew safety. Therefore, conducting online monitoring of the oxygen concentrator's degradation trend and accurate prediction of its remaining service life is of great significance for rationally planning maintenance and replacement schedules and ensuring flight safety.
[0003] Existing methods for predicting the lifespan of oxygen concentrators mainly rely on single performance degradation indicators such as oxygen partial pressure and oxygen concentration, establishing degradation trajectories through statistical modeling and extrapolating predictions. For example, fuzzy C-means clustering is used to segment oxygen partial pressure degradation data and establish multi-stage dynamic regression models; some studies also utilize Kalman filtering to estimate the state and predict trends of the degradation process of oxygen concentrators. However, existing methods have significant limitations: on the one hand, statistical degradation models based on oxygen partial pressure or oxygen concentration can only reflect the macroscopic trends of performance indicators and are difficult to capture the dynamic impact of environmental factors on the degradation rate; on the other hand, the actual service environment of airborne oxygen concentrators is highly time-varying and uncertain. External factors such as temperature, humidity, and vibration can affect the adsorption efficiency and aging rate of molecular sieves in real time, while traditional statistical models are mostly established offline with fixed parameters, unable to adaptively update model parameters according to real-time environmental conditions. Therefore, their accuracy is insufficient in on-board online prediction scenarios, making it difficult to meet the needs of practical engineering applications. Summary of the Invention
[0004] The purpose of this invention is to provide a method and system for predicting the remaining life of an oxygen concentrator based on a multi-scale convolutional network, in order to solve the problem that the existing technology only models based on a single performance index and does not incorporate multi-dimensional environmental factors, which makes the model unable to adapt to the environment and results in insufficient accuracy in predicting the remaining life.
[0005] To achieve the above objectives, the present invention adopts the following technical solution: This invention discloses a method for predicting the lifetime of an oxygen concentrator based on a multi-scale convolutional network, comprising: Acquire multi-source sensor signals of the working environment and performance degradation of the oxygen concentrator, and preprocess the multi-source sensor signals; Empirical mode decomposition is performed on the preprocessed multi-source sensing signal to obtain several intrinsic mode components. Energy, root mean square, kurtosis, and skewness are extracted from the intrinsic mode components to obtain a multidimensional feature vector for each intrinsic mode component; Using each of the intrinsic mode components as the channel dimension, the corresponding multidimensional feature vectors are combined into a multichannel input tensor; A multi-scale convolutional neural network is constructed using convolutional layers and channel attention modules to acquire historical multi-source sensing signals with remaining lifetime labels; The multi-scale convolutional neural network is trained based on the multi-channel input tensor of the historical multi-source sensor signals to obtain the remaining lifetime prediction model. The multi-channel input tensor of the multi-source sensor signal to be tested is input into the remaining lifetime prediction model, and the remaining lifetime prediction value of the oxygen concentrator to be tested is output.
[0006] Optionally, the step of performing empirical mode decomposition on the preprocessed multi-source sensing signal to obtain several intrinsic mode components includes: The preprocessed multi-source sensing signal is used as the current signal to be decomposed. The mean envelope of the current signal to be decomposed is removed to obtain the modal components to be acquired. The modal components that satisfy the preset screening criteria are taken as the first-order intrinsic modal components, and the first-order intrinsic modal components are separated from the current signal to be decomposed to obtain the residual components. The residual components are used as the current signal to be decomposed, and the intrinsic mode components of multiple orders are repeatedly acquired until the remaining residual components become monotonic functions or constants. The functional expression for the empirical mode decomposition of the multi-source sensing signal is as follows:
[0007] In the formula, Indicates the signal to be decomposed. Represents the decomposition of the first... Each intrinsic mode component Represents the residual component. This represents the total number of intrinsic mode components after decomposition. This represents the index of the intrinsic mode components after decomposition. Represents a time variable.
[0008] Optionally, the step of removing the mean envelope from the current signal to be decomposed to obtain the desired modal components includes: The maximum and minimum points of the current signal to be decomposed are obtained, and interpolation fitting is performed on each of the maximum and minimum points to obtain the upper envelope and lower envelope respectively. The mean envelope is calculated based on the upper envelope and the lower envelope. The function expression for calculating the mean envelope is:
[0009] In the formula, Represents the mean envelope. Indicates the upper envelope. Indicates the lower envelope; The mean envelope is removed from the current signal to be decomposed to obtain the desired modal components. The function expression for removing the mean envelope is:
[0010] In the formula, This represents the intrinsic mode components that are yet to be determined.
[0011] Optionally, the oxygen concentrator life prediction method further includes, after obtaining the modal components to be acquired, screening the modal components, including: If the obtained modal components satisfy the preset screening criteria, then the modal components are taken as the intrinsic modal components of the current stage. If the obtained modal component does not meet the preset screening criteria, the modal component is taken as the new current signal to be decomposed, and the modal component corresponding to the current signal to be decomposed is repeatedly obtained until the modal component meets the preset screening criteria.
[0012] Optionally, the construction of the multi-scale convolutional neural network using convolutional layers and channel attention modules includes: A multi-scale convolutional layer is configured, which includes multiple convolutional branches and a fusion layer. Each convolutional branch is configured with at least one convolutional layer, and the convolutional layers of different convolutional branches have different convolutional kernel sizes. The input of the fusion layer is connected to the output of each convolutional branch. A multi-channel attention module is connected to the output of the fusion layer. The multi-channel attention module includes an aggregation layer, a global average pooling layer, and a weight generation layer connected in sequence. The weight generation layer includes a first fully connected layer, a ReLU activation layer, a second fully connected layer, and a Sigmoid activation layer connected in sequence. A pooling layer is configured, and the input of the pooling layer is connected to the output of the weight generation layer. A third fully connected layer is provided, and the input of the third fully connected layer is connected to the output of the pooling layer.
[0013] Optionally, the step of inputting the multi-channel input tensor of the multi-source sensor signal to be measured into the remaining lifetime prediction model and outputting the remaining lifetime prediction value of the oxygen concentrator to be measured includes: The multi-channel input tensor of the multi-source sensor signal to be measured is input into the multi-scale convolutional layer of the remaining lifetime prediction model to obtain multi-scale convolutional features. The functional expression of the convolution operation is:
[0014] In the formula, Indicates the first The height of the feature map output by each convolutional branch. Indicates the index of the convolution branch. This represents the height of the multi-channel input tensor. Indicates the first The kernel size of the convolutional layer in each convolutional branch, Indicates the filling parameter. Indicates the first The width of the feature map output by each convolutional branch This represents the width of the multi-channel input tensor. Indicates the step size parameter; The multi-scale convolutional features are input into the aggregation layer of the multi-channel attention module to obtain the aggregated value of each channel along the dimension of the multi-dimensional feature vector. The function expression for the aggregation operation is:
[0015] In the formula, Indicates the first The aggregate value corresponding to each channel Indicates the index of the channel, and , This represents the number of features in a multidimensional feature vector. Represents the index of a feature in a multidimensional feature vector. Represents multi-scale convolutional features. Indicates the total number of channels. This represents all elements of the first dimension in a multi-scale convolutional feature vector, and the first element in the multi-dimensional feature vector. The first feature, the first The values corresponding to each channel; A priori weight is introduced for the aggregate value corresponding to each channel. The aggregate value is weighted according to the priori weight, and the weighted aggregate values of each channel are combined into an aggregate vector. The aggregation vector is sequentially input into the global average pooling layer and the weight generation layer of the multi-channel attention module to generate importance weights for each channel. The function representing the importance weights is as follows:
[0016] In the formula, This indicates the importance weight corresponding to each channel. This represents the Sigmoid activation function. and Indicates the weights of the fully connected layer. This represents the activation function. Represents an aggregate vector; The importance weights are applied to the corresponding channels to output the weighted multi-scale convolutional features. The weighting function for the multi-scale convolutional features is expressed as follows:
[0017] In the formula, This represents the weighted multi-scale convolutional features. This indicates a channel-wise weighted operation; The weighted multi-scale convolutional features are input into the pooling layer for dimensionality reduction, and the output is the pooled features. The function of the pooling operation is expressed as:
[0018] In the formula, This represents the pooling feature of the output. Indicates a pooling type function. and This represents the output value of adjacent neurons input to the pooling layer. This represents the index of the output neuron of the pooling layer. This represents the index of adjacent neurons input to the pooling layer; The pooling features are input into the fully connected layer. After fully connected linear processing and activation, the output features corresponding to each lifetime category of the oxygen concentrator under test are obtained. The function expression of the fully connected linear processing is as follows:
[0019] In the formula, This represents the linear output of the fully connected layer. This represents the weight matrix of the fully connected layer. This represents the pooling features input to the fully connected layer. Indicates the bias term; The output features of the oxygen concentrator under test for each lifespan category are converted into a probability distribution. The category with the highest probability is taken as the predicted remaining lifespan of the oxygen concentrator under test. The function for the probability distribution conversion is expressed as:
[0020] In the formula, Indicates the first The predicted probabilities of each category, The category index representing the currently calculated probability. Represents the first linear output value. Values for each category, Indicates the input value Perform nonlinear transformation, This indicates the total number of categories.
[0021] Optionally, the step of introducing prior weights to the aggregated values corresponding to each of the channels, and weighting the corresponding aggregated values according to the prior weights, includes: A priori weight is introduced for the aggregate value corresponding to each of the aforementioned channels. The function of the priori weight is expressed as:
[0022] In the formula, Indicates the first Prior importance weights for each channel, The parameter that controls the magnitude of the weights. Represented by natural constant An exponential function with base 0. The parameter that controls the rate of weight decay. Indicates the index of the preset key channel; The aggregated values are weighted according to the prior weights, and the weighting function is expressed as follows:
[0023] In the formula, Indicates the first The aggregate value after weighting each channel.
[0024] Optionally, the oxygen concentrator life prediction method further includes obtaining the confidence level and decision information of the remaining life prediction value after obtaining the probability distribution of each life category corresponding to the oxygen concentrator under test, including: Based on the probability distribution of each lifespan category of the oxygen concentrator under test, the maximum predicted probability is calculated. The function for calculating the maximum predicted probability is expressed as:
[0025] In the formula, This represents the maximum predicted probability in the predicted probability distribution. This represents a function that transforms linear output values into a predicted probability distribution; The confidence level of the remaining life prediction value is determined based on the maximum prediction probability, and the corresponding decision information is output based on the confidence level.
[0026] The present invention also discloses a prediction system employing the above-described oxygen concentrator life prediction method, the prediction system comprising: The signal preprocessing module is used to acquire multi-source sensor signals of the working environment and performance degradation of the oxygen concentrator, and to preprocess the multi-source sensor signals. The signal decomposition module is used to perform empirical mode decomposition on the preprocessed multi-source sensing signal to obtain several intrinsic mode components. The feature extraction module is used to extract energy, root mean square, kurtosis and skewness from the intrinsic mode components respectively, to obtain a multidimensional feature vector for each intrinsic mode component; The feature combination module is used to combine the corresponding multidimensional feature vectors into a multichannel input tensor, with each of the intrinsic mode components as the channel dimension. A neural network building module is used to construct a multi-scale convolutional neural network using convolutional layers and channel attention modules, and to acquire historical multi-source sensing signals with remaining lifetime labels; The neural network training module is used to train the multi-scale convolutional neural network based on the multi-channel input tensor of the historical multi-source sensor signals to obtain the remaining lifetime prediction model. The lifetime prediction module is used to input the multi-channel input tensor of the multi-source sensor signal to be tested into the remaining lifetime prediction model, and output the remaining lifetime prediction value of the oxygen concentrator to be tested.
[0027] The present invention also discloses a storage medium storing a computer program thereon, which, when executed by a processor, implements the above-described method for predicting the lifespan of an oxygen concentrator.
[0028] Compared with the prior art, the beneficial effects of the oxygen concentrator lifetime prediction method and system based on multi-scale convolutional networks provided by the embodiments of the present invention are as follows: By integrating multidimensional environmental parameters and performance degradation indices, the model can capture the impact of external environmental changes on the degradation rate, overcoming the limitations of insufficient information in modeling with a single performance index. Empirical Mode Decomposition (EMD) decomposes the signal into intrinsic mode functions (EMFs) at different scales, and the extraction of multidimensional statistical features further enriches the representation of degradation information, thereby improving the model's ability to perceive the degradation state. A multi-channel input tensor is constructed using each EMF as a channel dimension, enabling the network to process degradation features at different scales in parallel. Compared to single-scale convolutional structures, this provides a stronger ability to fit complex degradation patterns. The channel attention module aggregates along the dimensions of the multidimensional feature vectors to model the dependencies between channels, allowing the model to focus on EMF channels that contribute more significantly to lifetime degradation. Changes in real-time environmental conditions can be directly reflected in the model front end through the multi-channel input tensor. The network dynamically adjusts the attention weights of each channel accordingly, thereby achieving adaptive updates of model parameters with environmental conditions, ultimately significantly improving the accuracy of remaining lifetime prediction. Attached Figure Description
[0029] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 A schematic block diagram illustrating the steps of the oxygen concentrator life prediction method provided in this embodiment of the invention; Figure 2 Histogram of life prediction error for an airborne oxygen concentrator provided in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the lifespan prediction results of an airborne oxygen concentrator provided in an embodiment of the present invention. Detailed Implementation
[0030] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
[0031] This invention discloses a method for predicting the lifetime of an oxygen concentrator based on a multi-scale convolutional network, such as... Figure 1 The following are included: S1. Acquire multi-source sensor signals of the working environment and performance degradation of the oxygen concentrator, and preprocess the multi-source sensor signals. S2. Perform empirical mode decomposition on the preprocessed multi-source sensing signal to obtain several intrinsic mode components. S3. Extract energy, root mean square, kurtosis and skewness from the intrinsic mode components to obtain the multidimensional feature vector of each intrinsic mode component; S4. Using each intrinsic mode component as the channel dimension, combine the corresponding multi-dimensional feature vectors into a multi-channel input tensor; S5. Construct a multi-scale convolutional neural network using convolutional layers and channel attention modules, and acquire historical multi-source sensing signals with remaining lifetime labels; S6. Train a multi-scale convolutional neural network based on the multi-channel input tensor of historical multi-source sensor signals to obtain the remaining lifetime prediction model. S7. Input the multi-channel input tensor of the multi-source sensor signal to be tested into the remaining lifetime prediction model, and output the remaining lifetime prediction value of the oxygen concentrator to be tested.
[0032] By implementing the above-mentioned oxygen concentrator life prediction method, firstly, environmental parameters such as pressure, temperature, humidity, and vibration, along with performance degradation parameters such as oxygen partial pressure and oxygen concentration, can be incorporated into multi-source sensor signals. By fusing external environmental change information with internal performance degradation information, the shortcomings of traditional methods that rely solely on a single indicator such as oxygen partial pressure or oxygen concentration for degradation statistical modeling are overcome, enabling the subsequent modeling process to simultaneously perceive the impact of environmental factors on the degradation rate and the macroscopic degradation trend of performance indicators.
[0033] Secondly, empirical mode decomposition (EMD) is performed on the preprocessed multi-source sensor signals. This can adaptively decompose the nonlinear and non-stationary original signals into several intrinsic mode components that reflect local feature information at different time scales. This effectively separates the multi-scale degradation information that is coupled in the original signals, providing a structured data foundation for subsequent characterization of degradation features at different scales.
[0034] Furthermore, by extracting statistical features of four dimensions—energy, root mean square (RMS), kurtosis, and skewness—from each intrinsic mode component, energy reflects the trend of signal intensity change, RMS reflects the effective value level of the signal, kurtosis reflects the sensitivity of the signal's impulse characteristics to the degradation process, and skewness reflects the asymmetry of the signal distribution, these four statistical features jointly characterize the degradation information of each intrinsic mode component from different perspectives. This enhances the feature representation capability of a single intrinsic mode component and avoids the problem of insufficient descriptive power of a single statistical quantity. Subsequently, using each intrinsic mode component as a channel dimension, the corresponding multidimensional feature vectors are combined into a multi-channel input tensor, so that each channel independently carries the multidimensional statistical features of an intrinsic mode component. This maintains the independent and orderly organization of the originally scattered degradation information at each scale within the tensor structure, while preserving the inherent scale order relationship between different intrinsic mode components. This facilitates differentiated processing of features at different scales in subsequent processing by the network.
[0035] Furthermore, a multi-scale convolutional neural network constructed using convolutional layers and channel attention modules is employed. For example, multiple convolutional branches with different kernel sizes extract local spatial features from multi-channel input tensors in parallel under different receptive fields. This enables the network to simultaneously capture degradation patterns at different time scales, addressing the problem that single-scale convolutional neural networks can only extract local fixed-scale features and cannot adequately capture degradation patterns at different scales. The channel attention module aggregates each channel along the dimensions of the multi-dimensional feature vector and models the inter-channel dependencies. This allows the network to adaptively learn the differentiated contributions of different intrinsic modal components to remaining lifetime prediction. The impact of environmental changes is directly reflected in the network front end through the multi-channel input tensor. Based on this, the network assigns higher weights to channels of intrinsic modal components that contribute significantly, achieving a dynamic response of the model to environmental changes and overcoming the shortcomings of traditional statistical models whose parameters are fixed and cannot be adaptively updated according to real-time environmental conditions.
[0036] By training the network with historical multi-source sensor signals tagged with remaining lifetime, a nonlinear mapping relationship between the multi-source sensor signals and the remaining lifetime is established. The multi-source sensor signals to be measured are then processed through the same process and input into the trained model to output a predicted remaining lifetime value. This achieves online adaptive prediction based on real-time environmental conditions and higher remaining lifetime prediction accuracy than traditional statistical models. This provides a reliable basis for decision-making regarding the maintenance and replacement of oxygen concentrators, ensuring the smooth execution of flight missions and the safety of onboard personnel.
[0037] Preferably, preprocessing of multi-source sensor signals may include: (1) Data Standardization: Due to the different signal dimensions and amplitude ranges of different sensors, directly inputting the data into the network can lead to unstable training and slow convergence. Therefore, the signal data collected by each sensor is first adjusted to a uniform range to eliminate the impact of dimensional differences on subsequent analysis. In one possible implementation, the standard score method can be used for data standardization, specifically based on the mean and standard deviation of all data from each sensor. The standard score method converts the original data into standardized data with a mean of 0 and a standard deviation of 1, ensuring that the signals from different sensors are on the same scale, which facilitates the stable execution of subsequent empirical mode decomposition and feature extraction. The mean and standard deviation of each sensor can be obtained statistically from historical data.
[0038] The standard score method can be used for data standardization, and its function expression is as follows:
[0039] In the formula, Indicates the first The sensor collects the data. The data after standardization. Indicates the sensor index, This represents the index of the collected data. Indicates the first The data collected by the first sensor One set of raw data, Indicates the first The mean of all raw data from each sensor. Indicates the first The standard deviation of all raw data from each sensor.
[0040] (2) Outlier Detection and Processing: During long-term service, sensors may generate abnormal data due to equipment failure, electromagnetic interference, or sudden environmental changes. If these outliers are not processed, they will seriously interfere with the envelope fitting accuracy of empirical mode decomposition, leading to distortion of the decomposition results. Therefore, outlier detection and processing are performed on the standardized signals to identify and correct abnormal jump points and outliers in the signals, ensuring the continuity and smoothness of the input signals and avoiding false extreme points from interfering with the empirical mode decomposition results.
[0041] (3) Data Augmentation: Due to the high cost of collecting degradation data from airborne oxygen concentrators during actual service, and the limited number of effective samples showing performance degradation, directly using the original samples to train the neural network can easily lead to overfitting, resulting in insufficient model generalization ability. Therefore, data augmentation is performed on the outlier-processed signals to expand the sample data. In one possible implementation, at least one of the following methods can be used for data augmentation: adding random noise, time offset, and amplitude scaling. The method for adding random noise is as follows: by simulating various random disturbances to the signal in the real service environment, random noise is superimposed on the original signal to generate new training samples. The function for adding random noise is:
[0042] In the formula, This represents the sensor signal after adding random noise. Indicates the sampling point index. This represents the initial sensor signal collected. This represents a noise intensity parameter used to control the amplitude of the added noise. Represents a random noise function. Represents a time variable.
[0043] The time-shifting method simulates the temporal uncertainty of the degradation process by shifting the original signal along the time axis, while the amplitude scaling method simulates the changes in signal strength under different operating conditions by adjusting the signal amplitude ratio. Data augmentation, without altering the inherent degradation characteristics of the signal, expands the number of high-quality training samples by simulating the diverse variations of signals in real-world service environments. This alleviates the constraints of the small sample size problem on model performance and enhances the network's robustness to noise interference and signal fluctuations.
[0044] Furthermore, empirical mode decomposition is performed on the preprocessed multi-source sensing signal to obtain several intrinsic mode components, including: The preprocessed multi-source sensing signal is used as the current signal to be decomposed. The mean envelope of the current signal to be decomposed is removed to obtain the modal components to be acquired. The modal components that meet the preset screening criteria are taken as first-order intrinsic modal components, and the first-order intrinsic modal components are separated from the current signal to be decomposed to obtain the residual components. Using the residual components as the current signal to be decomposed, and repeatedly acquiring multiple eigenmode components until the remaining residual components become monotonic functions or constants, the functional expression for the empirical mode decomposition of the multi-source sensor signal is:
[0045] In the formula, Indicates the signal to be decomposed. Represents the decomposition of the first... Each intrinsic mode component Represents the residual component. This represents the total number of intrinsic mode components after decomposition. This represents the index of the intrinsic mode components after decomposition. Represents a time variable.
[0046] Furthermore, the mean envelope of the current signal to be decomposed is removed to obtain the modal components to be acquired, including: Obtain the maximum and minimum points of the current signal to be decomposed, and perform interpolation fitting on each maximum and minimum point to obtain the upper envelope and lower envelope respectively; The mean envelope is calculated based on the upper and lower envelopes. The function expression for calculating the mean envelope is:
[0047] In the formula, Represents the mean envelope. Indicates the upper envelope. Indicates the lower envelope; The mean envelope is removed from the current signal to be decomposed to obtain the desired modal components. The function expression for removing the mean envelope is:
[0048] In the formula, This represents the intrinsic mode components that are yet to be determined.
[0049] Furthermore, the oxygen concentrator life prediction method also includes, after obtaining the required modal components, screening the modal components, including: If the obtained modal components meet the preset screening criteria, the modal components are taken as the intrinsic modal components of the current stage. If the obtained modal components do not meet the preset screening criteria, the modal components are taken as the new current signals to be decomposed, and the modal components corresponding to the current signals to be decomposed are repeatedly obtained until the modal components meet the preset screening criteria.
[0050] By implementing the above-described oxygen concentrator life prediction method, firstly, empirical mode decomposition (EMD) is performed on the preprocessed multi-source sensor signal. Based on the inherent time-scale characteristics of the signal itself, the nonlinear and non-stationary original signal can be adaptively decomposed layer by layer into multiple intrinsic mode components (IMCs). Each IMC reflects the local oscillation information of the original signal at different frequency scales. This adaptive decomposition method does not require pre-setting the basis function or the number of decomposition layers, overcoming the limitations of traditional time-frequency analysis methods that introduce spurious components or lose key degradation information due to improper basis function selection. It is particularly suitable for separating the degradation characteristics of nonlinear and non-stationary multi-source sensor signals generated by airborne oxygen concentrators under complex service environments such as humidity, temperature, and vibration.
[0051] Secondly, obtaining the maxima and minima of the signal to be decomposed is a fundamental operation in empirical mode decomposition (EMD) to characterize the local oscillations of the signal. The maxima and minima represent the local extreme positions of the signal's upward and downward fluctuations at different times, respectively. The distribution density and amplitude variations of these extreme points directly reflect the intensity of the signal's oscillations at different time scales. By interpolating and fitting each maxima and minima, upper and lower envelopes are obtained. The specific implementation of envelope fitting can employ piecewise cubic Hermitian interpolation. This method constructs a cubic polynomial within each sub-interval using the function values and derivatives of the endpoints. While maintaining the continuity and differentiability of the interpolation curve, it effectively avoids overshoot and oscillation problems, ensuring that the fitted envelope accurately passes through all extreme points and has a natural and smooth shape. The upper envelope connects all local maxima of the signal, reflecting the boundary of the signal's upward fluctuations; the lower envelope connects all local minima of the signal, reflecting the boundary of the signal's downward fluctuations. The two envelopes together define the instantaneous oscillation amplitude range of the signal at each moment.
[0052] In terms of dimensional analysis, the upper envelope and lower envelope All are derived from the original signal The extreme points were obtained by interpolation fitting, and the two were compared with... They have the exact same physical dimensions; the pressure signal corresponds to the unit Pa, the temperature signal to the unit K, and the vibration acceleration signal to the unit [missing unit]. Therefore, the mean envelope Dimensions and original signal Complete consistency ensures the dimensional validity of subsequent subtraction operations. The mean envelope is the average of the upper and lower envelopes at each time step, representing the local average trend of the signal at that moment. Removing the mean envelope from the current signal to be decomposed yields the desired modal components. This subtraction operation requires… and Since the dimensions are consistent, therefore Dimensions and original signal Maintaining consistency is crucial. Removing the mean envelope essentially separates the slowly changing low-frequency components from the rapidly changing high-frequency components in the signal. The retained modal components reflect the high-frequency oscillation information of the signal at the current scale. The calculation of the mean of the upper and lower envelopes, as well as the subsequent subtraction operation, are dimensionally consistent, ensuring the mathematical rigor and physical rationality of the decomposition operation.
[0053] Furthermore, the obtained modal components are screened. Modal components that meet the preset screening criteria are taken as the intrinsic modal components of the current stage, while modal components that do not meet the preset screening criteria are taken as new current signals to be decomposed, and modal components are repeatedly acquired until the preset screening criteria are met. The specific determination method of the preset screening criteria is as follows: count the total number of all extreme points and the total number of all zero crossing points of the current modal component. If the two are equal or differ by at most one, the modal component is determined to meet the narrowband characteristic requirement. At the same time, calculate the mean of the upper envelope fitted by the maximum point and the lower envelope fitted by the minimum point of the modal component at each time step. If the mean approaches zero at all time steps, the modal component is determined to meet the local symmetry requirement. Only when both conditions are met is the modal component determined to have passed the screening. For modal components that do not meet the screening criteria, they are treated as new current signals to be decomposed and the extreme point extraction, envelope fitting, and mean envelope removal operations are re-executed. This allows the modal components to gradually approach the definition requirements of the intrinsic mode function in multiple iterations. This iterative strategy of multiple screening effectively eliminates the interference of spurious modal components on the accuracy of subsequent feature extraction and lifetime prediction.
[0054] The residual component is obtained by separating the first-order intrinsic mode components from the current signal to be decomposed. The first-order intrinsic mode components represent the highest frequency components in the signal, reflecting the fastest oscillation changes in the multi-source sensing signal. The residual component retains the signal trend at lower frequencies after removing the high-frequency components. The residual component is used as the new current signal to be decomposed to repeatedly obtain multi-order intrinsic mode components. Each round of decomposition strips the highest-frequency intrinsic mode component from the current residual signal, realizing a complete decomposition process of stripping away layers from high frequency to low frequency. When the residual component becomes a monotonic function or a constant, there is no longer any local oscillation information in the signal, and it is impossible to continue to extract new intrinsic mode components with physical meaning, so the decomposition process naturally terminates. A monotonic function means that the signal is monotonically increasing or monotonically decreasing over the entire time range. At this time, the signal does not have any local extrema, and it is impossible to construct a new envelope. The mean of a constant is itself, and it becomes zero after removing the mean, so no effective mode components can be obtained.
[0055] After decomposition, the original multi-source sensing signal is expressed as a superposition of all intrinsic mode components and residual components. In terms of dimensional analysis, the intrinsic mode components... From the original signal The residual components were obtained through layer-by-layer decomposition. The original signal is obtained by subtracting all intrinsic mode components from the original signal; both are similar to the original signal. Having the same physical dimensions, the intrinsic mode components are arranged in descending order of frequency, and the residual components represent the long-term trend of the signal. The physical meaning of this function is that all the oscillation and trend information of the original signal is completely decomposed into the intrinsic mode components and residual components, without information loss or introduction of additional information during the decomposition process. Through this decomposition, the multi-scale degradation features generated by the coupling of complex factors such as environmental humidity, temperature, and vibration in multi-source sensor signals are effectively separated and arranged in an orderly manner according to frequency scale. This provides a clear and complete data foundation for subsequent extraction of multi-dimensional statistical features such as energy, root mean square, kurtosis, and skewness from different scales. It avoids interference caused by the overlapping of degradation information at different scales, enabling the multi-scale degradation features contained in multi-source sensor signals to be fully utilized by subsequent multi-scale convolutional neural networks.
[0056] Preferably, during empirical mode decomposition, the decomposition process terminates when the residual components can no longer extract new intrinsic mode components. Theoretically, this termination condition can be described as "the residual components become monotonic functions or constants." However, in actual numerical calculations, due to the presence of signal noise and discrete sampling errors, monotonicity in a strict sense is difficult to determine through visual judgment or qualitative description. Therefore, a quantifiable judgment criterion based on numerical calculations needs to be provided.
[0057] The possible determination method is as follows: perform point-by-point differencing on the current residual component and calculate the difference value sequence between adjacent sampling points. If the difference value sequence is all greater than zero or all less than zero (i.e., the difference values of all adjacent points have the same sign), then the residual component is determined to be a monotonically increasing or monotonically decreasing function. If the difference value sequence contains both positive and negative values, then the residual component still contains oscillatory information and has not yet met the termination condition, requiring the next round of decomposition. In numerical implementation, to avoid interference from local small fluctuations caused by noise on the monotonicity judgment, the residual component can be pre-smoothed, or a tolerance threshold can be set. When the absolute value of the difference value is less than the preset threshold, the difference value is treated as zero.
[0058] Another feasible approach is to count the number of extreme points in the current residual components. The existence of extreme points (including maxima and minima) is a direct indicator of local oscillations in the signal—if there is oscillation in the signal, there must be extreme points; if the signal becomes a monotonic function, then the signal has no extreme points within its defined interval. Therefore, the monotonicity condition can be determined by checking whether the total number of maxima and minima in the current residual components is less than 2. When the total number of extreme points is less than 2, the residual components only have a monotonically increasing or monotonically decreasing trend, and an envelope cannot be constructed, thus terminating the decomposition process. This determination method is consistent with the preconditions for envelope construction in empirical mode decomposition—if at least one maxima and one minima cannot be obtained, an upper and lower envelope cannot be constructed, and naturally, intrinsic mode components cannot be further extracted. In practical implementation, extreme points can be identified by comparing the amplitude relationship between each sampling point and its neighboring points. A maximum point is defined as a sampling point whose amplitude is simultaneously greater than its left and right neighboring points, while a minimum point is defined as a sampling point whose amplitude is simultaneously less than its left and right neighboring points. For continuous points of equal value (multiple adjacent sampling points with the same amplitude), the midpoint or endpoint of the flat interval in which it lies can be taken as a representative point, or the point can be ignored and not included in the statistics as an extreme point. The above two methods can be used in combination to improve robustness to noise and numerical errors.
[0059] Furthermore, a multi-scale convolutional neural network is constructed using convolutional layers and channel attention modules, including: A multi-scale convolutional layer is set up, which includes multiple convolutional branches and a fusion layer. Each convolutional branch is configured with at least one convolutional layer, and the convolutional layers of different convolutional branches have different convolutional kernel sizes. The input of the fusion layer is connected to the output of each convolutional branch respectively. The multi-channel attention module is connected to the output of the fusion layer. The multi-channel attention module includes a sequentially connected aggregation layer, a global average pooling layer, and a weight generation layer. The weight generation layer includes a sequentially connected first fully connected layer, a ReLU activation layer, a second fully connected layer, and a Sigmoid activation layer. Set up a pooling layer, and connect the input of the pooling layer to the output of the weight generation layer; Set up a third fully connected layer, and connect the input of the third fully connected layer to the output of the pooling layer.
[0060] By implementing the above-described method for predicting the lifetime of an oxygen concentrator, firstly, a multi-scale convolutional layer is set up, which includes multiple convolutional branches and a fusion layer. Convolutional branches with different kernel sizes correspond to different receptive field sizes. Smaller kernels can capture high-frequency degradation features with short durations and fast change rates in multi-source sensor signals, while larger kernels can capture low-frequency degradation trends with longer durations and slow change rates. Each convolutional branch extracts local spatial features of different scales in parallel, which are then converged by the fusion layer, enabling the network to simultaneously acquire the ability to perceive multi-scale degradation features in a single structure.
[0061] Airborne oxygen concentrators are subjected to the combined effects of multiple environmental factors such as humidity, temperature, and vibration during service. The degradation information in their multi-source sensor signals is distributed across different time scales. Convolutional layers with a single kernel size can only cover a fixed receptive field, failing to capture both rapidly fluctuating high-frequency degradation information and slowly evolving low-frequency degradation trends. Multi-scale convolutional layers, through parallel processing of multiple convolutional branches with different kernel sizes, overcome the limitation of a single receptive field in matching multi-scale degradation features in the signal. The kernel size of different convolutional branches is configured according to the sampling frequency of the multi-source sensor signals and the time scale range of the degradation features. Smaller kernels can be designed to cover several sampling points to capture local transient changes, while larger kernels can be designed to cover tens to hundreds of sampling points to capture long-term evolution trends. The feature maps output by each branch are stitched together along the channel dimension in the fusion layer. The fused feature map contains multi-scale spatial feature information from different receptive fields.
[0062] A multi-channel attention module is configured, comprising a sequentially connected aggregation layer, a global average pooling layer, and a weight generation layer. In a convolutional neural network, the feature map output by the fusion layer contains multiple channels, each corresponding to a specific spatial feature extracted by a convolutional kernel. However, different channels exhibit significantly different importance for the oxygen concentrator lifetime prediction task. The aggregation layer aggregates each channel along the dimension of the multi-dimensional feature vector, condensing the information of each channel along the multi-dimensional feature vector into an aggregated value, thus quantifying the overall activity of each channel. The global average pooling layer performs a global average of the aggregated values of each channel along the spatial dimension, outputting a global descriptive vector for each channel. The weight generation layer generates importance weights for each channel based on this global descriptive vector. These importance weights reflect the relative importance of each channel to the current input multi-source sensor signal in the remaining lifetime prediction task.
[0063] Preferably, the dimension of the multidimensional feature vector is the dimension formed by the four statistical features corresponding to each intrinsic mode component: energy, root mean square, kurtosis, and skewness (F=4). The value distribution of each channel along this dimension reflects the activity level of the degradation features at different scales under the corresponding statistical indicators. By summing and averaging the four feature values of each channel along this dimension, the aggregated value comprehensively reflects the overall activity level of that channel under the current input.
[0064] For multi-source sensor signals from airborne oxygen concentrators under different service stages and environmental conditions, the distribution of degradation information in different channels dynamically changes. The multi-channel attention module can adaptively adjust the weight allocation of each channel according to the feature distribution of the current input signal, enabling the network to focus on the most relevant degradation feature channel under different operating conditions. In the weight generation layer, the Sigmoid activation layer maps the output value to the interval between 0 and 1, ensuring that the importance weights of each channel are positive and have a clear relative magnitude relationship, making the weight allocation interpretable. The first and second fully connected layers form a bottleneck structure, first reducing dimensionality and then increasing it, reducing computational complexity while retaining the ability to model the dependencies between channels. The ReLU activation layer introduces nonlinearity between the two fully connected layers, enabling the weight generation layer to learn the complex nonlinear dependencies between channels.
[0065] A pooling layer is set up, with its input connected to the output of the weight generation layer. This pooling layer downsamples the weighted feature map, compressing its spatial size while preserving significant feature information. This reduces the number of parameters and computational complexity of subsequent network layers, while also expanding the receptive field of subsequent operations. A third fully connected layer is then set up, with its input connected to the output of the pooling layer. This layer flattens the multi-dimensional features output by the pooling layer into a one-dimensional feature vector, which is then linearly transformed and mapped to the output space corresponding to the number of oxygen concentrator lifetime categories. This integrates the multi-scale spatial features extracted from the preceding layers and the weighted features after channel recalibration into the final lifetime prediction result.
[0066] Through the above-mentioned structural design of multi-scale convolutional layers, multi-channel attention modules, pooling layers, and a second fully connected layer, the network can extract degradation features distributed across different time scales in the multi-source sensor signals of the airborne oxygen concentrator in parallel, and adaptively allocate weights according to the contribution of each channel feature to lifetime prediction. This enables the network to effectively focus on the most relevant degradation information under different service environments and different degradation stages, thereby improving the accuracy of remaining lifetime prediction.
[0067] Preferably, training a multi-scale convolutional neural network based on the multi-channel input tensor of historical multi-source sensor signals includes: Step 1: Obtain historical multi-source sensor signal samples and the remaining lifetime label corresponding to each historical multi-source sensor signal sample. After processing each historical multi-source sensor signal sample according to the process of empirical mode decomposition, multidimensional statistical feature extraction and multi-channel input tensor construction, the multi-channel input tensor corresponding to each historical multi-source sensor signal sample is obtained. Each multi-channel input tensor carries the corresponding remaining lifetime label.
[0068] Step 2: Divide all multi-channel input tensors carrying remaining lifetime labels into training set, test set and validation set, where 70% of all samples are used as training samples, 20% as test samples and 10% as validation samples.
[0069] Step 3: Input the multi-channel input tensor from the training set into the constructed multi-scale convolutional neural network for training.
[0070] Step 4: Validate the multi-scale convolutional neural network trained by inputting the multi-channel input tensors in the validation set. Adjust the multi-scale convolutional neural network model according to the parameters corresponding to the multi-scale convolutional neural network model with the highest validation accuracy.
[0071] Step 5: Test the multi-scale convolutional neural network with adjusted multi-channel input tensors in the test set to obtain the final oxygen concentrator life prediction model.
[0072] Furthermore, the multi-channel input tensor of the multi-source sensor signal to be measured is input into the remaining lifetime prediction model, and the output is the predicted remaining lifetime value of the oxygen concentrator to be measured, including: The multi-channel input tensor of the multi-source sensor signal to be tested is input into the multi-scale convolutional layer of the remaining lifetime prediction model to obtain multi-scale convolutional features. The functional expression of the convolution operation is:
[0073] In the formula, Indicates the first The height of the feature map output by each convolutional branch. Indicates the index of the convolution branch. This represents the height of the multi-channel input tensor. Indicates the first The kernel size of the convolutional layer in each convolutional branch, Indicates the filling parameter. Indicates the first The width of the feature map output by each convolutional branch This represents the width of the multi-channel input tensor. Indicates the step size parameter; Dimensional analysis: and The height and width of the multi-channel input tensor are expressed in units of discrete sampling points and are denoted as [L]. The kernel size is [L], expressed in units of discrete sampling points. The filling parameter, in units of discrete sampling points, is denoted as [L]; The step size parameter, expressed in units of discrete sampling points, is denoted as [L]. Molecular The units are additions and subtractions of lengths, with dimensions [L]; the denominator is... The dimension is [L]; the ratio is dimensionless; after adding 1... and The dimension of is the number of discrete points [L], which is consistent with the dimensions of the height and width of the input tensor.
[0074] The multi-scale convolutional features are input into the aggregation layer of the multi-channel attention module to obtain the aggregated value of each channel along the dimension of the multi-dimensional feature vector. The function expression for the aggregation operation is as follows:
[0075] In the formula, Indicates the first The aggregate value corresponding to each channel Indicates the index of the channel, and , This represents the number of features in a multidimensional feature vector. Represents the index of a feature in a multidimensional feature vector. Represents multi-scale convolutional features. Indicates the total number of channels. This represents all elements of the first dimension in a multi-scale convolutional feature vector, and the first element in the multi-dimensional feature vector. The first feature, the first The values corresponding to each channel; Dimensional analysis: The output of the convolutional layer is the activation intensity after the activation function, expressed as a dimensionless numerical value, denoted as [1]; the summation symbol The F eigenvalues are summed, and the units of the summation remain the same [1]; the coefficients Since it is a dimensionless reciprocal, therefore The dimension of is [1].
[0076] Prior weights are introduced for the aggregate values corresponding to each channel. The aggregate values are weighted according to the prior weights, and the weighted aggregate values of each channel are combined into an aggregate vector. The aggregated vector is sequentially input into the global average pooling layer and weight generation layer of the multi-channel attention module to generate importance weights for each channel. The function representing the importance weights is as follows:
[0077] In the formula, This indicates the importance weight corresponding to each channel. This represents the Sigmoid activation function. and Indicates the weights of the fully connected layer. This represents the activation function. Represents an aggregate vector; Dimensional analysis: The aggregate value of each element is dimensionless, with dimensions [1]; Let be the weight matrix of the first fully connected layer. The elements of the weight matrix are the connection weights, which are dimensionless and denoted as [1]. For matrix multiplication, the dimension is [1]; The function is an activation function, and its output has the same dimensions as the input, which are [1]; is the weight matrix of the second fully connected layer, which is dimensionless; The dimension is [1]; The Sigmoid activation function outputs a probability value between 0 and 1, which is dimensionless and denoted as [1]; therefore The dimension of is [1].
[0078] The importance weights are applied to the corresponding channels, and the weighted multi-scale convolutional features are output. The weighted function of the multi-scale convolutional features is expressed as:
[0079] In the formula, This represents the weighted multi-scale convolutional features. This indicates a channel-wise weighted operation; Dimensional analysis: The activation intensity of the output of the convolutional layer after the activation function is dimensionless and is denoted as [1]; The importance weight is dimensionless and ranges from 0 to 1, denoted as [1]; channel-by-channel weighted operation The feature map of each channel is multiplied by its corresponding scalar weight. The weights are dimensionless, the feature map elements are dimensionless, and the product has a dimension of [1]. Therefore, The dimension of is [1].
[0080] The weighted multi-scale convolutional features are input into the pooling layer for dimensionality reduction, and the output is the pooled features. The function of the pooling operation is expressed as:
[0081] In the formula, This represents the pooling feature of the output. Indicates a pooling type function. and This represents the output value of adjacent neurons input to the pooling layer. This represents the index of the output neuron of the pooling layer. This represents the index of adjacent neurons input to the pooling layer; Dimensional analysis: The activation intensity of the weighted multi-scale convolutional features after passing through the activation function is dimensionless and denoted as [1]; pooling type function For maximum value selection or average value calculation, the maximum value is chosen from two input values, and the output dimension is consistent with the input dimension. For average value calculation, the two values with the same dimension are added together and then divided by 2, keeping the dimension unchanged. Therefore... The dimension of is [1].
[0082] Pooling features are input into a fully connected layer, and after fully connected linear processing and activation, the output features corresponding to each lifetime category of the oxygen concentrator under test are obtained. The function representation of the fully connected linear processing is as follows:
[0083] In the formula, This represents the linear output of the fully connected layer. This represents the weight matrix of the fully connected layer. This represents the pooling features input to the fully connected layer. Indicates the bias term; Dimensional analysis: The pooling feature is input to the fully connected layer. After flattening, the feature is a one-dimensional vector, and each element is the activation intensity output by the pooling layer. It is dimensionless and denoted as [1]. is the weight matrix of the fully connected layer, where each element is a connection weight, which is dimensionless and denoted as [1]; For matrix multiplication, the dimension is [1]; As a bias term, its dimensions must be the same as the bias term to make the addition operation valid. Since they are consistent, the dimension of b is [1]; is the linear output of the fully connected layer, with dimensions [1].
[0084] The output features of the oxygen concentrator under test for each lifespan category are converted into a probability distribution. The category with the highest probability is taken as the predicted remaining lifespan of the oxygen concentrator under test. The function for the probability distribution transformation is expressed as:
[0085] In the formula, Indicates the first The predicted probabilities of each category, The category index representing the currently calculated probability. Represents the first linear output value. Values for each category, Indicates the input value Perform nonlinear transformation, This indicates the total number of categories.
[0086] Dimensional analysis: The linear output value of the fully connected layer has dimensions [1]; the exponential function The exponent of a dimensionless numerical value is taken, and the input of the exponential function is required to be a dimensionless pure numerical value, and the output is a dimensionless positive value, denoted as [1]; the denominator The sum of m positive values of the same dimension has a dimension of [1]; the ratio is dimensionless; therefore, the predicted probability is... The dimension of is [1], which meets the requirement that the probability value is a dimensionless scalar in the definition of probability.
[0087] By implementing the above-described method for predicting the lifetime of an oxygen concentrator, firstly, the multi-channel input tensor of the multi-source sensor signal to be measured is input into the multi-scale convolutional layer of the remaining lifetime prediction model. The output size transformation of the convolution operation ensures that the feature maps output by each convolutional branch have a clear size correspondence in the spatial dimension. By adjusting the padding and stride parameters, even if different convolutional branches have different kernel sizes, the feature maps output by each branch can still maintain a consistent spatial size before fusion, enabling the fusion layer to stitch multi-scale features along the channel dimension without additional size alignment operations. After the multi-scale features extracted by each convolutional branch are fused, a single multi-scale convolutional feature tensor simultaneously contains degradation information from different receptive fields. The downstream multi-channel attention module and pooling layer only need to process one fused feature tensor, eliminating the need to design and maintain independent processing paths for features of different scales, thereby reducing the structural complexity of the model.
[0088] Secondly, after the multi-scale convolutional features are input into the aggregation layer of the multi-channel attention module, the aggregation operation condenses the activation intensity values of each channel across multiple feature dimensions into a single scalar aggregated value. Since each channel in the multi-scale convolutional features corresponds to a specific scale feature extracted by a specific convolutional kernel, the aggregated value comprehensively reflects the overall activity level of that channel under the current input. Prior weights are introduced into the aggregated values corresponding to each channel, and weighting is performed based on these prior weights. The weighted aggregated value incorporates prior scale order information while retaining the original activity information of each channel. These prior weights are calculated based on the distance between the channel index and the preset key channel index. Channels with closer distances receive higher prior weights, enabling channels corresponding to the preset key scale to receive higher initial attention in subsequent weight generation.
[0089] Next, the weighted aggregated values of each channel are combined into an aggregated vector. The element order of the aggregated vector is consistent with the channel index order, preserving the scale order information of each channel. This allows the global average pooling layer and the weight generation layer to model the inter-channel dependencies based on the ordered channel representation. After the global average pooling layer performs a global average on the aggregated vector, the first fully connected layer in the weight generation layer performs a linear dimensionality reduction operation to compress the dimension of the aggregated vector, reducing subsequent computation and forcing the network to learn a compact representation between channels. The ReLU activation layer introduces non-linearity, enabling the network to capture non-linear dependencies between channels. The second fully connected layer restores the feature dimension to the original number of channels, and the Sigmoid activation layer maps the output to the 0-1 interval to generate the importance weights of each channel.
[0090] This process dynamically calculates importance weights based entirely on the multi-scale convolutional features of the current input. Different inputs correspond to different distributions of multi-scale convolutional features, and the generated importance weights change dynamically accordingly. After multiplying the importance weights with the multi-scale convolutional features channel by channel, the channel weights enhance the feature expression of channels that contribute more to the current input, while suppressing the feature expression of channels that contribute less or carry redundant information. The weighted multi-scale convolutional features output achieve adaptive recalibration of the channel dimensions while preserving the original multi-scale information.
[0091] The weighted multi-scale convolutional features are reduced in dimensionality by pooling layers to output pooled features. Pooling layers compress the spatial size of the feature map by selecting representative values within local regions. The dimensionality reduction effect of pooling significantly reduces the dimension of the flattened one-dimensional feature vector, decreasing the number of parameters in the weight matrix of the fully connected layer. After the pooled features are input into the fully connected layer, matrix multiplication in the fully connected linear processing maps the pooled features to an output space with a dimension equal to the number of lifespan categories. A bias term provides an offset for each output neuron, giving the activation intensity of each lifespan category an adjustable baseline in the output space. The linear output is then nonlinearly introduced through an activation function to obtain the output features for each lifespan category. The Softmax function performs exponential and normalization operations on the output features. The exponential operation converts the linear output values to positive values and amplifies the differences between categories, while the normalization process ensures that the sum of the predicted probabilities of all categories is 1, forming an interpretable probability distribution.
[0092] The lifetime interval corresponding to the category with the highest probability is the remaining lifetime prediction value output by the model, completing the end-to-end mapping from multi-channel input tensors to specific lifetime prediction values. The entire prediction process, from multi-scale feature extraction and channel adaptive recalibration to probability output, is interconnected, enabling online prediction of the remaining lifetime of the oxygen concentrator under test based on real-time acquired multi-source sensor signals.
[0093] Preferably, the lifespan categories are defined as follows: the remaining lifespan of the oxygen concentrator, from zero to its design lifespan, is divided into multiple lifespan intervals according to a preset time interval. Each lifespan interval corresponds to a category, and the categories are arranged in order of remaining lifespan length. In one possible implementation, if the design lifespan of the oxygen concentrator is 1000 hours, dividing the lifespan intervals into 100-hour intervals results in 10 lifespan categories. The first category corresponds to a remaining lifespan of 0 to 100 hours, the second category corresponds to a remaining lifespan of 100 to 200 hours, and so on, with the tenth category corresponding to a remaining lifespan of 900 to 1000 hours. During prediction, the Softmax function converts the output features of each lifespan category from the third fully connected layer into a probability distribution. The category with the highest probability is the lifespan interval to which the model predicts the remaining lifespan. The median or lower endpoint of this lifespan interval can be used as the specific remaining lifespan prediction value output. The number of lifespan intervals and the time intervals can be adjusted according to the design lifespan and maintenance replacement cycle of the oxygen concentrator in the actual application scenario. The finer the division, the higher the prediction resolution, but at the same time, it requires a sufficient number of samples of each category in the training data; the coarser the division, the more concentrated the distribution of samples of each category, and the higher the stability of the model prediction.
[0094] Using the above remaining life prediction model, the life prediction results of the oxygen concentrator under test are obtained, such as... Figure 2 The figure shows a histogram of the prediction error distribution between the sample size and the lifetime prediction results, reflecting the relationship between the prediction accuracy and the error distribution. Figure 2 As can be seen, the accuracy is highest when the sample size is 1600, which can meet the sample requirements.
[0095] Furthermore, prior weights are introduced for the aggregate values corresponding to each channel, and the corresponding aggregate values are weighted according to these prior weights, including: A priori weight is introduced for the aggregate value corresponding to each channel. The function of the priori weight is expressed as:
[0096] In the formula, Indicates the first Prior importance weights for each channel, The parameter that controls the magnitude of the weights. Represented by natural constant An exponential function with base 0. The parameter that controls the rate of weight decay. Indicates the index of the preset key channel; The aggregated values are weighted according to the prior weights, and the weighting function is expressed as follows:
[0097] In the formula, Indicates the first The aggregate value after weighting each channel.
[0098] By implementing the above-described method for predicting the lifespan of an oxygen concentrator, firstly, a priori weights are introduced for the aggregate value corresponding to any channel. The function expression of the priori weights is exponentially decaying, and its independent variable is the absolute value of the distance between the channel index and the preset critical channel index. The assignment logic of the priori weights is as follows: channels whose channel index is closer to the preset critical channel index receive higher priori importance weights, and channels whose channel index is farther from the preset critical channel index receive lower priori importance weights. The characteristic of this exponential decay function is that when the channel index coincides with the preset critical channel index, the absolute value of the distance is zero, and the weight reaches its maximum value; as the absolute value of the distance increases, the weight decays exponentially, and the weight of channels farther away decreases faster. The exponential decay form gives the weight allocation a clear directionality and concentration, focusing on channels near the preset critical channel.
[0099] In terms of dimensional analysis, channel index and preset key channel index Both are dimensionless index numbers, denoted as [1]; the difference between them is a dimensionless difference, denoted as [1]; the parameter controlling the weight decay rate. Multiplying by the distance value is necessary to maintain the requirement that the independent variable of the exponential function be dimensionless. The dimensions must be [1]; exponential function The output is a dimensionless positive value, denoted as [1]; the parameter controlling the weight magnitude Multiply by the output of the exponential function, The dimensions must be [1]; therefore, the prior importance weights The dimension of is [1], which is a dimensionless scalar value.
[0100] The aggregated values are weighted according to the prior weights. This weighting operation multiplies the prior importance weight of each channel with the original aggregated value of that channel, so that the weighted aggregated value includes both the original overall activity information of the channel and the prior importance information based on the distance between the channel index and the preset key channel index.
[0101] In terms of dimensional analysis, aggregate value The dimensionless scalar value of each channel aggregated along the dimensions of the multidimensional feature vector is denoted as [1]; prior importance weight The dimensionless scalar value is denoted as [1]; the dimension of the product of the two is [1], and the aggregate value is [1]. The dimensions are kept consistent.
[0102] The weighted aggregated values are numerically recalibrated by prior weights. Channels with indices close to the preset key channel indices have their weighted aggregated values amplified and occupy a larger proportion in subsequent aggregated vectors; channels with indices far from the preset key channel indices have their weighted aggregated values compressed and their proportion in subsequent aggregated vectors reduced. Since the arrangement order of each channel in the multi-scale convolutional features is consistent with the splicing order of the feature maps output by each convolutional branch, the channel indices indirectly correspond to degradation information at different scales. The prior weights are allocated based on the distance between the channel indices and the preset key channel indices, so that the integration of prior knowledge does not depend on specific numerical features, but is based on the arrangement position and scale correspondence of the channels.
[0103] Parameters that control the magnitude of the weights And parameters that control the rate of weight decay All are adjustable hyperparameters. Among them, the parameter that controls the weight magnitude... A parameter used to adjust the maximum value of the prior weights at preset key channels, controlling the weight decay rate. This is used to adjust the rate at which the prior weight decreases as the channel index moves away from the preset key channel. In practical implementation, The value range of can be determined based on the maximum amplitude of the prior weights expected to be obtained at the preset key channels. In one possible implementation, The value range is [0.5, 2.0], with a typical value of 1.0; when it is necessary to enhance the attention of preset key channels, the value can be... Setting it to a value greater than 1.0 is useful when it's necessary to weaken the overall influence of prior weights. Set to a value less than 1.0. The value range can be determined based on the attenuation rate requirement of the distance between the channel index and the preset key channel index. In one possible implementation, The value range is [0.1, 1.0], with a typical value between 0.2 and 0.5. The larger the value, the faster the prior weight decays with increasing distance, and the lower the weight obtained by channels whose channel indexes are far away from the preset key channel. The smaller the value, the slower the prior weight decays with increasing distance, and channels far from the preset key channel can still obtain relatively high prior weights. and The specific value can be determined by conventional hyperparameter optimization methods such as cross-validation or grid search, based on the importance of the preset key channels in the actual application scenario and the contribution distribution requirements of the surrounding channels to lifetime prediction.
[0104] In the aggregate vector composed of the weighted aggregate values, the order of each element is still arranged according to the channel index, which preserves the scale order information of each channel, enabling the subsequent global average pooling layer and weight generation layer to model the inter-channel dependencies based on the ordered channel representation.
[0105] Furthermore, the oxygen concentrator life prediction method also includes obtaining the confidence level and decision information of the remaining life prediction value after obtaining the probability distribution of each life category corresponding to the oxygen concentrator under test, including: Based on the probability distribution of each lifespan category of the oxygen concentrator under test, the maximum predicted probability is calculated. The function for calculating the maximum predicted probability is expressed as:
[0106] In the formula, This represents the maximum predicted probability in the predicted probability distribution. This represents a function that transforms linear output values into a predicted probability distribution; The confidence level of the remaining life prediction is determined based on the maximum prediction probability, and the corresponding decision information is output based on the confidence level.
[0107] By implementing the above-described method for predicting the lifespan of oxygen concentrators, the maximum predicted probability is calculated based on the probability distribution of each lifespan category corresponding to the oxygen concentrator under test. The magnitude of the maximum predicted probability directly reflects the model's confidence in the prediction results. The closer the maximum predicted probability is to 1, the more concentrated the probability mass is in a certain category, and the higher the model's certainty in predicting the results; in this case, the prediction results are more reliable. Conversely, the closer the maximum predicted probability is to a uniform distribution, the more dispersed the probability mass is across multiple categories, and the lower the model's certainty in predicting the results; in this case, the prediction results are less reliable.
[0108] The confidence level of the remaining life prediction is determined based on the maximum predictive probability. For example: When the maximum predicted probability is ≥0.95, it is judged as a high confidence level, indicating that the model has a high degree of confidence in the prediction results, and the prediction results can be directly used for subsequent automatic decision-making.
[0109] When the maximum predicted probability is ≥0.70 and <0.95, it is judged as a medium confidence level, indicating that the model has a certain degree of uncertainty in the prediction results, and needs to be confirmed by manual review or other auxiliary verification methods.
[0110] When the maximum predicted probability is less than 0.70, it is judged as a low confidence level, indicating that the model has a high degree of uncertainty about the prediction results, and the credibility of the prediction results is insufficient to support direct decision-making.
[0111] Output the corresponding decision information based on the confidence level, for example: When the confidence level is high, the decision information that can be automatically executed is output, corresponding to level 1 (confidence). The decision information is automatically classified and recorded.
[0112] When the confidence level is medium confidence level, the decision information that triggers an alert and recommends manual review is output, corresponding to level 2 (suspicious). The decision information is marked as pending review and pushed to the expert system.
[0113] When the confidence level is low, the output is a decision message indicating uncertainty and initiating a backup detection process, corresponding to level 3 (unreliable). The decision message is to trigger data resampling, sensor self-test, or switch to a conservative strategy.
[0114] Through the aforementioned confidence level determination and decision information output process, the remaining life prediction value output by the model is accompanied by a confidence level label, providing auxiliary basis for the maintenance and replacement decision of the oxygen concentrator in addition to the predicted value, enabling the decision-making process to adopt differentiated processing strategies according to different confidence levels.
[0115] like Figure 3 The comparison chart of the predicted lifespan and the actual lifespan of the airborne oxygen concentrator shown in the figure demonstrates that the confidence interval of the prediction is 95%, which verifies the effectiveness of the method of the present invention.
[0116] This invention also discloses a prediction system that employs the aforementioned oxygen concentrator life prediction method. The prediction system includes: The signal preprocessing module is used to acquire multi-source sensor signals of the working environment and performance degradation of the oxygen concentrator, and to preprocess the multi-source sensor signals. The signal decomposition module is used to perform empirical mode decomposition on the preprocessed multi-source sensor signal to obtain several intrinsic mode components. The feature extraction module is used to extract energy, root mean square, kurtosis and skewness from the intrinsic mode components, respectively, to obtain a multidimensional feature vector for each intrinsic mode component; The feature combination module is used to combine the corresponding multi-dimensional feature vectors into a multi-channel input tensor, with each intrinsic mode component as the channel dimension. The neural network building module is used to construct a multi-scale convolutional neural network using convolutional layers and channel attention modules, and to acquire historical multi-source sensing signals with remaining lifetime labels. The neural network training module is used to train a multi-scale convolutional neural network based on the multi-channel input tensor of historical multi-source sensor signals to obtain a remaining lifetime prediction model. The lifetime prediction module is used to input the multi-channel input tensor of the multi-source sensor signal to be tested into the remaining lifetime prediction model, and output the remaining lifetime prediction value of the oxygen concentrator to be tested.
[0117] The present invention also discloses a storage medium on which a computer program is stored, which, when executed by a processor, implements the above-described method for predicting the lifespan of an oxygen concentrator.
[0118] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0119] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0120] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0121] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0122] It should be understood that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Those skilled in the art can modify the technical solutions described in the above embodiments, or make equivalent substitutions for some of the technical features; and all such modifications and substitutions should fall within the protection scope of the appended claims of the present invention.
Claims
1. A method for predicting the lifetime of an oxygen concentrator based on a multi-scale convolutional network, characterized in that, The oxygen concentrator life prediction method includes: Acquire multi-source sensor signals of the working environment and performance degradation of the oxygen concentrator, and preprocess the multi-source sensor signals; Empirical mode decomposition is performed on the preprocessed multi-source sensing signal to obtain several intrinsic mode components. Energy, root mean square, kurtosis, and skewness are extracted from the intrinsic mode components to obtain a multidimensional feature vector for each intrinsic mode component; Using each of the intrinsic mode components as the channel dimension, the corresponding multidimensional feature vectors are combined into a multichannel input tensor; A multi-scale convolutional neural network is constructed using convolutional layers and channel attention modules to acquire historical multi-source sensing signals with remaining lifetime labels; The multi-scale convolutional neural network is trained based on the multi-channel input tensor of the historical multi-source sensor signals to obtain the remaining lifetime prediction model. The multi-channel input tensor of the multi-source sensor signal to be tested is input into the remaining lifetime prediction model, and the remaining lifetime prediction value of the oxygen concentrator to be tested is output.
2. The oxygen concentrator life prediction method according to claim 1, characterized in that, The empirical mode decomposition of the preprocessed multi-source sensing signal yields several intrinsic mode components, including: The preprocessed multi-source sensing signal is used as the current signal to be decomposed. The mean envelope of the current signal to be decomposed is removed to obtain the modal components to be acquired. The modal components that satisfy the preset screening criteria are taken as the first-order intrinsic modal components, and the first-order intrinsic modal components are separated from the current signal to be decomposed to obtain the residual components. The residual components are used as the current signal to be decomposed, and the intrinsic mode components of multiple orders are repeatedly acquired until the remaining residual components become monotonic functions or constants. The functional expression for the empirical mode decomposition of the multi-source sensing signal is as follows: In the formula, Indicates the signal to be decomposed. Represents the decomposition of the first... Each intrinsic mode component Represents the residual component. This represents the total number of intrinsic mode components after decomposition. Indicates the index of the intrinsic mode component after decomposition. Represents a time variable.
3. The oxygen concentrator life prediction method according to claim 2, characterized in that, The step of removing the mean envelope from the current signal to be decomposed to obtain the desired modal components includes: The maximum and minimum points of the current signal to be decomposed are obtained, and interpolation fitting is performed on each of the maximum and minimum points to obtain the upper envelope and lower envelope respectively. The mean envelope is calculated based on the upper envelope and the lower envelope. The function expression for calculating the mean envelope is: In the formula, Represents the mean envelope. Indicates the upper envelope. Indicates the lower envelope; The mean envelope is removed from the current signal to be decomposed to obtain the desired modal components. The function expression for removing the mean envelope is: In the formula, This represents the intrinsic mode components that are yet to be determined.
4. The oxygen concentrator life prediction method according to claim 2, characterized in that, The oxygen concentrator life prediction method further includes, after obtaining the required modal components, screening the modal components, including: If the obtained modal components satisfy the preset screening criteria, then the modal components are taken as the intrinsic modal components of the current stage. If the obtained modal component does not meet the preset screening criteria, the modal component is taken as the new current signal to be decomposed, and the modal component corresponding to the current signal to be decomposed is repeatedly obtained until the modal component meets the preset screening criteria.
5. The oxygen concentrator life prediction method according to claim 1, characterized in that, The construction of a multi-scale convolutional neural network using convolutional layers and channel attention modules includes: A multi-scale convolutional layer is configured, which includes multiple convolutional branches and a fusion layer. Each convolutional branch is configured with at least one convolutional layer, and the convolutional layers of different convolutional branches have different convolutional kernel sizes. The input of the fusion layer is connected to the output of each convolutional branch. A multi-channel attention module is connected to the output of the fusion layer. The multi-channel attention module includes an aggregation layer, a global average pooling layer, and a weight generation layer connected in sequence. The weight generation layer includes a first fully connected layer, a ReLU activation layer, a second fully connected layer, and a Sigmoid activation layer connected in sequence. A pooling layer is configured, and the input of the pooling layer is connected to the output of the weight generation layer. A third fully connected layer is provided, and the input of the third fully connected layer is connected to the output of the pooling layer.
6. The oxygen concentrator life prediction method according to claim 5, characterized in that, The step of inputting the multi-channel input tensor of the multi-source sensor signal to be measured into the remaining lifetime prediction model and outputting the remaining lifetime prediction value of the oxygen concentrator to be measured includes: The multi-channel input tensor of the multi-source sensor signal to be measured is input into the multi-scale convolutional layer of the remaining lifetime prediction model to obtain multi-scale convolutional features. The functional expression of the convolution operation is: In the formula, Indicates the first The height of the feature map output by each convolutional branch Indicates the index of the convolution branch. This represents the height of the multi-channel input tensor. Indicates the first The kernel size of the convolutional layer in each convolutional branch, Indicates the filling parameter. Indicates the first The width of the feature map output by each convolutional branch This represents the width of the multi-channel input tensor. Indicates the step size parameter; The multi-scale convolutional features are input into the aggregation layer of the multi-channel attention module to obtain the aggregated value of each channel along the dimension of the multi-dimensional feature vector. The function expression for the aggregation operation is: In the formula, Indicates the first The aggregate value corresponding to each channel Indicates the index of the channel, and , This represents the number of features in a multidimensional feature vector. This represents the index of a feature in a multidimensional feature vector. Represents multi-scale convolutional features. Indicates the total number of channels. This represents all elements of the first dimension in a multi-scale convolutional feature vector, and the first element in the multi-dimensional feature vector. The first feature, the first The values corresponding to each channel; A priori weight is introduced for the aggregate value corresponding to each channel. The aggregate value is weighted according to the priori weight, and the weighted aggregate values of each channel are combined into an aggregate vector. The aggregation vector is sequentially input into the global average pooling layer and the weight generation layer of the multi-channel attention module to generate importance weights for each channel. The function representing the importance weights is as follows: In the formula, This indicates the importance weight corresponding to each channel. This represents the Sigmoid activation function. and Indicates the weights of the fully connected layer. This represents the activation function. Represents an aggregate vector; The importance weights are applied to the corresponding channels to output the weighted multi-scale convolutional features. The weighting function for the multi-scale convolutional features is expressed as follows: In the formula, This represents the weighted multi-scale convolutional features. This indicates a channel-wise weighted operation; The weighted multi-scale convolutional features are input into the pooling layer for dimensionality reduction, and the output is the pooled features. The function of the pooling operation is expressed as: In the formula, This represents the pooling feature of the output. Indicates a pooling type function. and This represents the output value of adjacent neurons input to the pooling layer. This represents the index of the output neuron of the pooling layer. This represents the index of adjacent neurons input to the pooling layer; The pooling features are input into the fully connected layer. After fully connected linear processing and activation, the output features corresponding to each lifetime category of the oxygen concentrator under test are obtained. The function of fully connected linear processing is expressed as: In the formula, This represents the linear output of the fully connected layer. This represents the weight matrix of the fully connected layer. This represents the pooling features input to the fully connected layer. Indicates the bias term; The output features of the oxygen concentrator under test for each lifespan category are converted into a probability distribution. The category with the highest probability is taken as the predicted remaining lifespan of the oxygen concentrator under test. The function for the probability distribution conversion is expressed as: In the formula, Indicates the first The predicted probabilities of each category, The category index representing the currently calculated probability. Represents the first linear output value. Values for each category, Indicates the input value Perform nonlinear transformation, This indicates the total number of categories.
7. The oxygen concentrator life prediction method according to claim 6, characterized in that, The step of introducing prior weights to the aggregated values corresponding to each of the channels, and weighting the corresponding aggregated values according to the prior weights, includes: A priori weight is introduced for the aggregate value corresponding to each of the aforementioned channels. The function of the priori weight is expressed as: In the formula, Indicates the first Prior importance weights for each channel, The parameter that controls the magnitude of the weights. Represented by natural constant An exponential function with base 0. The parameter that controls the rate of weight decay. Indicates the index of the preset key channel; The aggregated values are weighted according to the prior weights, and the weighting function is expressed as follows: In the formula, Indicates the first The aggregate value after weighting each channel.
8. The oxygen concentrator life prediction method according to claim 6, characterized in that, The oxygen concentrator life prediction method further includes obtaining the confidence level and decision information of the remaining life prediction value after obtaining the probability distribution of each life category corresponding to the oxygen concentrator under test, including: Based on the probability distribution of each lifespan category of the oxygen concentrator under test, the maximum predicted probability is calculated. The function for calculating the maximum predicted probability is expressed as: In the formula, This represents the maximum predicted probability in the predicted probability distribution. This represents a function that transforms linear output values into a predicted probability distribution; The confidence level of the remaining life prediction value is determined based on the maximum prediction probability, and the corresponding decision information is output based on the confidence level.
9. A prediction system, characterized in that, The oxygen concentrator life prediction method according to any one of claims 1-8, wherein the prediction system comprises: The signal preprocessing module is used to acquire multi-source sensor signals of the working environment and performance degradation of the oxygen concentrator, and to preprocess the multi-source sensor signals. The signal decomposition module is used to perform empirical mode decomposition on the preprocessed multi-source sensing signal to obtain several intrinsic mode components. The feature extraction module is used to extract energy, root mean square, kurtosis and skewness from the intrinsic mode components respectively, to obtain a multidimensional feature vector for each intrinsic mode component; The feature combination module is used to combine the corresponding multidimensional feature vectors into a multichannel input tensor, with each of the intrinsic mode components as the channel dimension. A neural network building module is used to construct a multi-scale convolutional neural network using convolutional layers and channel attention modules, and to acquire historical multi-source sensing signals with remaining lifetime labels; The neural network training module is used to train the multi-scale convolutional neural network based on the multi-channel input tensor of the historical multi-source sensor signals to obtain the remaining lifetime prediction model. The lifetime prediction module is used to input the multi-channel input tensor of the multi-source sensor signal to be tested into the remaining lifetime prediction model, and output the remaining lifetime prediction value of the oxygen concentrator to be tested.
10. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the oxygen concentrator life prediction method according to any one of claims 1-8.