Refrigerator life prediction method based on adaptive physical information recurrent neural network

Abstract

The invention discloses a refrigerator life prediction method based on an adaptive physical information recurrent neural network, and the method comprises the steps: extracting multi-source statistical health features through a steady-state control window, capturing time sequence dependence through a recurrent neural network, and generating a degeneration state estimator; embedding the estimator into a stochastic differential equation driven by a Wiener stochastic process to enable a drift term to reflect a deterministic degradation mechanism and a diffusion term to quantify the uncertainty of a working condition; based on data deviation, equation residual and monotonicity violation, multi-constraint joint loss is constructed, Bayesian uncertainty estimation is adopted to dynamically optimize each loss weight, and adaptive balance of physical consistency and observation fitting is realized. According to the method, residual life prediction with probability distribution is output, and the precision and robustness of refrigerator health management under complex working conditions are effectively improved.

Description

Technical Field

[0001] This invention relates to the field of industrial equipment health management technology, and in particular to a method for predicting the lifespan of a refrigeration unit based on an adaptive physical information recurrent neural network. Background Technology

[0002] In modern industrial systems, refrigeration machines, as core elements driving production and maintaining system operation, play a vital role through their stable and long-term operation and efficient energy conversion. Refrigeration machines are widely used in various fields, such as manufacturing, food processing, chemical industry, and air conditioning systems, ensuring precise temperature control and stable operation in industrial processes. They not only maintain the necessary working environment in industrial production but also play a crucial role in many demanding fields, such as cryogenic storage, precision manufacturing, and cold chain logistics. Therefore, the efficient operation and long-term reliability of refrigeration machines are directly related to production efficiency and safety.

[0003] During actual use, the overall performance of a refrigeration unit gradually declines. Failure to monitor and intervene in this decline not only affects its lifespan but may also pose potential safety hazards. In refrigeration unit performance mechanism research, efficiency is widely used as a physical quantity to measure the current performance state. By comparing it with the initial efficiency, the health status is derived; it is a relative state quantity measuring the health of the refrigeration unit. Accurately assessing the health status of the refrigeration unit and predicting its remaining lifespan is one of the core tasks of a refrigeration unit management system.

[0004] Traditional health status estimation methods primarily rely on physical models and data-driven models. Physical models describe the refrigeration system's degradation process through thermodynamic equations and heat transfer models. While these models offer theoretical accuracy, their practical application is limited due to the complexity of the physical mechanisms and high computational costs. On the other hand, data-driven models such as Support Vector Machines (SVM), Random Forests (RF), and Deep Neural Networks (DNN) offer high accuracy and efficiency when dealing with large-scale datasets, but often lack interpretable physical meaning and are heavily dependent on the quality and quantity of training data.

[0005] In recent years, Physical Information Neural Networks (PINNs), as an innovative approach combining physical knowledge and deep learning, have gradually attracted the attention of researchers. PINNs attempt to embed physical information into neural networks and express it in the form of a loss function. PINN methods can achieve effective modeling and estimation even with scarce data, while embedding physical information ensures the physical consistency and interpretability of the model. In recent years, PINNs have also been widely applied in the fields of refrigerator health status estimation and remaining service life prediction. In various refrigerator experiments, PINNs have demonstrated the ability to accurately capture complex refrigerator degradation mechanisms and have made progress in improving estimation and prediction accuracy, enhancing model generality and stability.

[0006] Early PINN methods incorporated physical priors into neural network training, significantly improving prediction accuracy and plausibility under small sample conditions. Subsequently, the STA-HPINN architecture was proposed, combining attention mechanisms with depthwise separable convolutions to extract spatiotemporal features and implicit decay physics, thereby enhancing the modeling of decay behavior under complex operational conditions. Based on this, PhyCRNet was proposed, employing an autoregressive time-stepping strategy to improve the spatiotemporal modeling of complex decay processes. Further development led to PhyICNet, which introduced an interactive time feedback mechanism and a pseudo-mesh structure to enhance extrapolation capabilities. Furthermore, the PI-LSTM framework embeds structural dynamics equations into LSTM training, improving physical consistency and robustness while maintaining prediction accuracy.

[0007] While PINNs offer significant advantages in integrating prior physical knowledge, recent research has primarily focused on how to embed physical information more efficiently, such as by improving the design of loss functions to enhance the embedding effect of physical constraints (e.g., conservation laws and boundary conditions). However, in practical engineering implementation, current research faces three main problems: insufficient embedding of temporal information, poor interpretability, and poor model transferability across different devices.

[0008] To address these issues, this invention proposes a PINN framework based on recurrent neural networks (RNNs). This framework incorporates the time memory capability of RNNs into the modeling of the solution function, thereby better capturing the time dependence of the refrigerator's degradation process. Furthermore, considering the need for interpretability in practical engineering for remaining lifetime prediction, a Wiener stochastic process is introduced to describe the dynamics of the refrigerator's degradation behavior, enhancing interpretability in the modeling. In addition, to improve the model's ability to transfer between different batches of refrigerators, Bayesian estimation is introduced to dynamically adjust the weights between the partial differential equation loss terms and other loss terms in the neural network, forming a general model for predicting the remaining lifetime of refrigerators under complex operating conditions. Summary of the Invention

[0009] Therefore, the present invention provides a method for predicting the lifespan of a refrigerator based on an adaptive physical information recurrent neural network, in order to solve the aforementioned problems existing in the prior art.

[0010] To achieve the above objectives, this invention provides a method for predicting the lifespan of a refrigerator based on an adaptive physical information recurrent neural network, comprising:

[0011] Step S1: Obtain multi-source data of the chiller, extract statistical health features based on the steady-state control window, and construct a time-series degradation feature vector;

[0012] Step S2: Input the time series degradation feature vector into a recurrent neural network, and map it into a time-varying hidden state through a recurrent neural network structure to generate a degradation state estimate;

[0013] Step S3: Embed the degradation state estimate into a stochastic differential equation model to construct a degradation state evolution equation that includes drift and diffusion terms;

[0014] Step S4: Obtain measured degradation data. Based on the deviation between the degradation state estimate and the measured degradation data, the residual of the degradation state evolution equation, and the degree of monotonicity violation of the degradation state estimate at adjacent time points, construct data consistency term, physical constraint term, and monotonic prior term respectively, and then obtain the multi-constraint joint loss function.

[0015] Step S5: Using the Bayesian uncertainty estimation method, the weights of each loss term are dynamically optimized based on the online statistical characteristics of the data consistency term, the physical constraint term, and the monotonic prior term to obtain the target recurrent neural network.

[0016] Step S6: Predict the health status trajectory based on the target recurrent neural network, and calculate the remaining service life in combination with the preset failure threshold.

[0017] Furthermore, the process of step S2 includes:

[0018] The time-series degradation feature vector is input into the recurrent neural network in chronological order. After initializing the initial hidden state, the time-varying hidden state at each time step is calculated by using the hidden state at the previous time step and the input features at the current time step through a gated nonlinear mapping function. The mapping function is controlled by the update gate and the forget gate.

[0019] The time-varying hidden state is mapped through the output layer to generate a degenerate state estimate.

[0020] Furthermore, the degradation state estimate includes one or a combination of the following two forms:

[0021] (1) The time-varying hidden state is mapped through the output layer to generate the health status index of the refrigerator, which is used to construct the data consistency loss and physical constraint residual;

[0022] (2) The time-varying hidden state is mapped through the output layer to generate a time-varying mechanism parameter vector, which is used to modulate the drift term and diffusion term of the stochastic differential equation in step S3 to realize memory-driven stochastic dynamic evolution.

[0023] Furthermore, the process of step S3 includes:

[0024] ,

[0025] in, This represents the degradation state variable of the refrigeration unit at continuous time t. Let be the drift function, representing the average evolution rate and nonlinear mechanism of degradation; Let be the diffusion function, representing the intensity of random fluctuations and how they change with state / operating condition; For exogenous input;

[0026] The structural parameters of the drift function and the diffusion function are modulated by a time-varying mechanism parameter vector.

[0027] Furthermore, the process of step S4 includes:

[0028] ,

[0029] in, For multi-constraint loss functions, , Represents physical constraint terms. Let t represent time, x represent the state / operating condition input of the refrigerator, H(⋅) be the residual operator constructed from the degradation dynamics equation (i.e., the deviation obtained by substituting the network output into the control equation), and N be the total number of sampling points. , Indicates data consistency items, This represents the observed degradation or health index of the refrigeration unit at the i-th sampling point. This represents the estimate of the degraded state. , Let j represent the monotonic prior term, j represent the j-th refrigerator or the j-th degenerate sequence, and k be the time index within the sequence. This represents the estimate of the degenerate state at time k. The linear rectified function with the positive part is used, and this term achieves monotonicity constraint by penalizing the increase in the predicted value at adjacent time steps. This represents the learnable weight coefficient for the corresponding item.

[0030] Furthermore, the process of step S5 includes:

[0031] The data consistency term, physical constraint term, and monotonic prior term are treated as noisy statistical constraints, and a corresponding precision parameter is introduced for each loss term. At the same time, a prior distribution is set for each precision parameter.

[0032] Based on the online statistical characteristics of the data consistency term, physical constraint term, and monotonic prior term, Bayesian updates are performed on each precision parameter to obtain the corresponding posterior precision distribution.

[0033] The weights of each loss term are set to be proportional to the expected posterior accuracy to obtain the original weight vector;

[0034] The original weight vector is normalized, and preset lower and upper limits are applied to obtain normalized constraint weights.

[0035] The loss statistic is smoothed using the exponential moving average method to obtain a smoothed loss statistic.

[0036] In each training iteration, the data consistency term, physical constraint term, and monotonic prior term are calculated based on the smoothing loss statistic. The smoothing loss statistic is used to update each precision parameter and obtain the corresponding normalized constraint weights. Then, backpropagation is performed through the updated multi-constraint joint loss function to update the recurrent neural network parameters. The above iterative process is repeated until the network converges, thereby obtaining the target recurrent neural network.

[0037] Furthermore, the process of setting the weights of each loss term to be proportional to the expected posterior accuracy to obtain the original weight vector includes:

[0038] Based on the prior accuracy distribution and the online statistical characteristics, the posterior accuracy distribution corresponding to each loss term is calculated using Bayes' formula.

[0039] The expected value of the posterior accuracy distribution is determined as the original weight of each loss term, and the original weight is proportional to the expected posterior accuracy.

[0040] Furthermore, step S6 includes the following process:

[0041] Based on the target recurrent neural network, a health status prediction sequence at discrete time points is generated, and a failure threshold is preset;

[0042] The health state prediction sequence is interpolated to obtain a continuous health state trajectory;

[0043] The continuous health status trajectory is detected against the failure threshold, and the moment when the predicted health trajectory first reaches the threshold is determined as the failure moment;

[0044] The difference between the failure time and the current assessment time is calculated as the estimated value of the remaining useful life.

[0045] By using the diffusion term in the degradation state evolution equation to perform multiple random samplings, a degradation trajectory sample set is generated, and the probability distribution and confidence interval of the remaining lifetime are obtained.

[0046] Furthermore, the process of step S1 includes:

[0047] In the operating data of the refrigeration unit, a steady-state control window is identified. The current, cooling duration and transition cold plate temperature of the refrigeration unit are extracted from the steady-state control window to form a first time-series curve. The temperature, pressure difference or flow rate of the hot end are extracted to form a second time-series curve.

[0048] The mean, standard deviation, skewness, kurtosis, duration, cumulative amount, slope and entropy are calculated for the first time series curve and the second time series curve respectively, and a sixteen-dimensional feature vector is constructed.

[0049] The sixteen-dimensional feature vector is normalized to obtain the time series degradation feature vector.

[0050] Compared with existing technologies, the beneficial effects of this invention are as follows: By dynamically embedding the temporal degradation features extracted by a recurrent neural network into stochastic differential equations, the drift term adaptively reflects the deterministic degradation mechanism of piston wear and working fluid contamination, while the diffusion term quantifies the uncertainty introduced by fluctuations in operating conditions and measurement noise. This constructs a degradation evolution model that couples physical laws and data features in both directions. Furthermore, the invention uses Bayesian uncertainty estimation to evaluate the credibility of three loss terms: data fitting, physical constraints, and monotonic priors. The weights of each loss term are dynamically adjusted based on their actual performance, achieving an optimal balance between physical mechanisms and observed data at the gradient level. Finally, the invention outputs a remaining life prediction with probabilistic distribution significance. Its point estimate captures the main degradation trends, and the confidence interval reflects the prediction uncertainty. Engineers can use this to formulate more accurate maintenance strategies, avoiding premature or late maintenance due to a single empirical threshold, and significantly improving the efficiency of refrigeration unit health management and operational reliability. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating the refrigerator life prediction method based on an adaptive physical information recurrent neural network provided in an embodiment of the present invention.

[0052] Figure 2 This is a flowchart illustrating step S5 in the refrigerator life prediction method based on adaptive physical information recurrent neural network provided in an embodiment of the present invention.

[0053] Figure 3This is a flowchart illustrating step S6 in the refrigerator life prediction method based on adaptive physical information recurrent neural network provided in this embodiment of the invention. Detailed Implementation

[0054] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0055] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0056] It should be noted that in the description of this invention, the terms "upper", "lower", "left", "right", "inner", "outer", etc., which indicate directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings. This is only for the convenience of description and is not intended to indicate or imply that the device or element must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of this invention.

[0057] Furthermore, it should be noted that, in the description of this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0058] Please see Figure 1 As shown, this invention provides a method for predicting the lifespan of a refrigerator based on an adaptive physical information recurrent neural network, comprising:

[0059] Step S1: Obtain multi-source data of the chiller, extract statistical health features based on the steady-state control window, and construct a time-series degradation feature vector;

[0060] Specifically, in the chiller operation data stream, the steady-state control window is identified based on the feedback signal of the chiller control system.

[0061] Specifically, step S1 includes the following process:

[0062] In the operating data of the refrigeration unit, a steady-state control window is identified. The current, cooling duration and transition cold plate temperature of the refrigeration unit are extracted from the steady-state control window to form a first time-series curve. The temperature, pressure difference or flow rate of the hot end are extracted to form a second time-series curve.

[0063] Specifically, the steady-state start point is defined as when the refrigerator enters a temperature lockout state and the control deviation remains within ±0.5°C for more than 5 minutes; the steady-state end point is defined as when the control deviation exceeds ±1°C or the refrigerator switches operating modes. The continuous data segment extracted in this way is the steady-state control window, and each window has a length of no less than 300 seconds of sampled data.

[0064] Specifically, piston wear leads to increased friction and pressure drop, resulting in a decrease in effective cooling capacity. To maintain the set temperature, it is usually necessary to increase the input power, manifested as an increase in the refrigerator's current / power level. Working fluid contamination introduces driving energy fluctuations and operational instability, manifested as increased current / power fluctuations, intermittent anomalies, and changes in spectral composition. Deterioration of the operating thermal environment increases the thermal resistance of the heat dissipation and regeneration links, reduces heat dissipation capacity, leads to decreased cooling efficiency, and causes deterioration of temperature control indicators. Typical manifestations include an increased time required to reach the target temperature (increased cooling time) and a gradual rise in the temperature of key hot nodes such as the transition cold plate. Therefore, within each steady-state control window, two types of time-series curves are extracted from the refrigerator's sensor data:

[0065] The first type of curve is the core health observation measurement, including the refrigerator operating current, cooling duration (cumulative time from start-up to the current moment), and transition cold plate temperature (temperature measurement point located between the evaporator and the load).

[0066] The second type of curve provides a supplementary characterization of the thermal environment, including hot-end temperature (condenser outlet temperature), system pressure difference (pressure difference between compressor inlet and outlet), and working fluid mass flow rate.

[0067] The mean, standard deviation, skewness, kurtosis, duration, cumulative amount, slope and entropy are calculated for the first time series curve and the second time series curve respectively, and a sixteen-dimensional feature vector is constructed.

[0068] Specifically, the mean and standard deviation are used to characterize the average level and stability of energy consumption and thermodynamic state; skewness and kurtosis are used to characterize changes in the distribution pattern of fluctuations (more sensitive when degradation leads to "skewed" or "sharpened" control outputs); window duration τ is used to characterize the ease or difficulty of maintaining steady state under the same control objective; cumulative quantities (such as cumulative power consumption within the window) are used to characterize resource consumption per unit steady-state period; curve slope or trend term (such as the slope obtained by first-order fitting of the curve within the window) is used to characterize slow drift within the steady-state segment; and curve entropy (which can be discretized Shannon entropy or spectral entropy) is used to quantify the complexity of control fluctuations.

[0069] The sixteen-dimensional feature vector is normalized to obtain the time series degradation feature vector.

[0070] Specifically, the eight statistical features of the first type of curve and the eight statistical features of the second type of curve are concatenated sequentially to form a sixteen-dimensional feature vector. This sixteen-dimensional feature vector is then normalized using the minimum and maximum values ​​from the training set, scaling each feature dimension to the range of -1 to +1. For real-time data, fixed minimum and maximum values ​​from the training set are used for normalization to avoid data leakage.

[0071] Step S2: Input the time series degradation feature vector into a recurrent neural network, and map it into a time-varying hidden state through a recurrent neural network structure to generate a degradation state estimate;

[0072] Specifically, a recurrent neural network (RNN) is used as the gating unit to construct the temporal memory enhancement module. The network contains a single recurrent layer, with the hidden state dimension set to 64 dimensions, and the input dimension corresponding to the 16-dimensional feature vector output in step S1. The initial hidden state h0 is initialized as a trainable variable with the same dimension as the hidden state, and the initial value is a zero tensor, which is automatically optimized through backpropagation during training.

[0073] Specifically, step S2 includes the following process:

[0074] The time-series degradation feature vector is input into the recurrent neural network in chronological order. After initializing the initial hidden state, the time-varying hidden state at each time step is calculated by using the hidden state at the previous time step and the input features at the current time step through a gated nonlinear mapping function. The mapping function is controlled by the update gate and the forget gate.

[0075] Specifically, the time series degradation feature vector is divided into time windows with a batch size of 32 and a sequence length of 50, arranged chronologically. For each time window, a forward recursion is performed: at discrete time t_k, the current input feature x_k and the hidden state h_{k-1} from the previous time step are input into the RNN unit. The current hidden state h_k is calculated using a nonlinear activation mechanism with update and forget gates, and the mapping relationship is expressed as h_k = f_θ(h_{k-1}, x_k). The gating structure regulates the information flow, ensuring that the hidden state retains both long-term degradation trends and robustness to short-term measurement noise.

[0076] The time-varying hidden state is mapped through the output layer to generate a degenerate state estimate.

[0077] Specifically, the degradation state estimate includes one or a combination of the following two forms:

[0078] (1) The time-varying hidden state is mapped through the output layer to generate the health status index of the refrigerator, which is used to construct the data consistency loss and physical constraint residual;

[0079] Specifically, the first type of output is the degradation state estimate, denoted as ẑ_k, defined as the refrigerator health index SOH. This output is generated by mapping through a fully connected output layer with a dimension of 1, using a linear activation function, and its value range is normalized to the [0,1] interval by the training data, which is used to subsequently construct the data consistency loss and physical constraint residuals.

[0080] (2) The time-varying hidden state is mapped through the output layer to generate a time-varying mechanism parameter vector, which is used to modulate the drift term and diffusion term of the stochastic differential equation in step S3 to realize memory-driven stochastic dynamic evolution.

[0081] Specifically, the second type of output is a time-varying mechanism parameter vector, denoted as... The output is generated by mapping through another parallel fully connected output layer with a dimension of 4 and using the tanh activation function. Its four components correspond to the degradation rate coefficient and temperature sensitivity coefficient in the drift function, and the fluctuation reference strength and operating condition coupling coefficient in the diffusion function, respectively. These components are used to modulate the drift and diffusion terms of the stochastic differential equation in step S3 to achieve memory-driven stochastic dynamic evolution.

[0082] Specifically, in practical implementations, the two output formats described above can be used in combination. For example, the recursive representation module can simultaneously output a SOH sequence and a time-varying parameter vector sequence, which are used to construct different loss terms and drive different dynamic components, respectively. This allows the model to both directly predict the health state and impart the dynamic change capability of the degradation process through time-varying parameters.

[0083] Specifically, the recurrent neural network is fully differentiable with respect to its parameter θ and supports end-to-end training. During training, the Adam optimizer is used with an initial learning rate of 0.001 and a gradient clipping threshold of 1.0 to prevent gradient explosion. Dropout regularization is applied to the hidden states with a dropout rate of 0.2 to enhance generalization ability. The loss function is the multi-constraint joint loss constructed in step S4, which synchronously updates the network weights, initial hidden state h0, and output layer parameters through backpropagation until training terminates when the loss on the validation set no longer decreases for 10 consecutive rounds, resulting in the optimized recurrent neural network parameters.

[0084] Step S3: Embed the degradation state estimate into a stochastic differential equation model to construct a degradation state evolution equation that includes drift and diffusion terms;

[0085] Specifically, step S3 includes the following process:

[0086] ,

[0087] in, This represents the degradation state variable of the refrigeration unit at continuous time t. Let be the drift function, representing the average evolution rate and nonlinear mechanism of degradation; Let be the diffusion function, representing the intensity of random fluctuations and how they change with state / operating condition; For exogenous input;

[0088] Specifically, the degradation process of the refrigeration unit is modeled as a stochastic differential equation, where the degradation state variable represents the health level of the equipment at the current moment, and its evolution is driven by both drift and diffusion terms. The drift function adopts a parameterized structure with physical semantics, including monotonically decreasing constraints, exponential degradation rate, and temperature-dependent sensitivity coefficients; the diffusion function adopts a time-varying structure coupled with operating conditions, including fluctuation baseline strength and load modulation coefficients. The standard Wiener process W(t) is used to capture accumulated random disturbances.

[0089] The structural parameters of the drift function and the diffusion function are modulated by a time-varying mechanism parameter vector.

[0090] Specifically, all structural parameters in the drift function and diffusion function are dynamically modulated by a time-varying mechanism parameter vector, which is generated in real time by the output layer of the recurrent neural network in step S2. The four components are mapped to: the degradation rate coefficient (control index degradation rate) and temperature sensitivity coefficient (modulation temperature influence strength) in the drift function, and the fluctuation reference strength (determining the basic uncertainty level) and operating condition coupling coefficient (reflecting the modulation effect of the load on the fluctuation strength) in the diffusion function. This modulation mechanism is implemented through a fully connected layer, and the modulated drift function and diffusion function have operating condition adaptive capabilities.

[0091] Specifically, in the discrete implementation process, initial conditions are first given. At discrete sampling time At this point, the Euler–Maruyama method is used to numerically advance the stochastic differential equations:

[0092]

[0093] Calculate the drift term at the current time. and diffusion terms ,in The exogenous inputs at the current moment (including ambient temperature, load power, and speed). For random items, where Set to a fixed time step (1 hour). It is sampled from the standard normal distribution N(0,1). Through this discretization method, the current state is obtained. Calculate the state at the next time step The time series of the degradation trajectory is generated.

[0094] The above update generates a set of degenerate trajectory samples and yields a conditional distribution at each time step (the mean is dominated by the drift term, and the variance by the diffusion term). When observations exist... Then, an observation equation can be further introduced:

[0095]

[0096] in To measure noise, a likelihood term is constructed based on this observation equation, which aligns the model with the observation data in a statistical sense and enhances uncertainty calibration.

[0097] Step S4: Obtain measured degradation data. Based on the deviation between the degradation state estimate and the measured degradation data, the residual of the degradation state evolution equation, and the degree of monotonicity violation of the degradation state estimate at adjacent time points, construct data consistency term, physical constraint term, and monotonic prior term respectively, and then obtain the multi-constraint joint loss function.

[0098] Specifically, step S4 includes the following process:

[0099] ,

[0100] in, For multi-constraint loss functions, , Represents physical constraint terms. Let t represent time, x represent the state / operating condition input of the refrigerator, H(⋅) be the residual operator constructed from the degradation dynamics equation (i.e., the deviation obtained by substituting the network output into the control equation), and N be the total number of sampling points. , Indicates data consistency items, This represents the observed degradation or health index of the refrigeration unit at the i-th sampling point. This represents the estimate of the degraded state. , Let j represent the monotonic prior term, j represent the j-th refrigerator or the j-th degenerate sequence, and k be the time index within the sequence. This represents the estimate of the degenerate state at time k. The linear rectified function with the positive part is used, and this term achieves monotonicity constraint by penalizing the increase in the predicted value at adjacent time steps. This represents the learnable weight coefficient for the corresponding item.

[0101] Specifically, obtain measured degradation data of the refrigeration unit. 1This data represents normalized performance degradation metrics, including normalized coefficient of performance (COP), cooling capacity retention rate, or energy consumption offset. The data sampling interval is aligned with the steady-state control window of step S1. The degradation state estimate generated in step S2 is then used... 1 Measured data u from the same sampling point 1 The L2 norm squared deviation is calculated, and the data consistency term is obtained by summing the deviations over all N sampling points. In the implementation, this term is calculated for each batch of data, and a time-weighted strategy is used to assign higher weights to recent sampling points to enhance the model's fitting accuracy to the current degradation state.

[0102] Specifically, selecting collocation points (t) within the spatiotemporal domain i , x i N collocation points are uniformly sampled from the training set. The degenerate state estimate is input into the stochastic differential equation residual operator H(·), and the squared value of the equation residual at each collocation point is calculated. The residual operator H is implemented using automatic differentiation technology. The network output is differentiated with respect to time and then input into the left-hand side of the stochastic differential equation. The difference between this left-hand side and the drift and diffusion terms is calculated. The summation of the squared residuals over all collocation points yields the physical constraint term. This term is activated gradually in the early stages of training, with the weight coefficients used in the first 10 rounds. Set it to 0.1 to avoid initial oscillations, and then restore it to the dynamically optimized value.

[0103] Specifically, the degradation sequences of all M refrigerators are processed separately: for the degradation sequence of the j-th refrigerator, the degradation state estimate of its time index k from 1 to N_j is extracted. Calculate the difference between adjacent time points. The ReLU activation function is applied to the difference to extract the positive part, i.e., only the positive value portion of the predicted value that violates monotonicity is retained. The squared values ​​of the retained values ​​are then summed over the entire sequence. The results of M refrigerators are accumulated to obtain the monotonic prior term. In the implementation, the tolerance threshold ε is set to 1×10⁻⁴. When the value is less than ε, it is considered numerical noise and not penalized, thus avoiding excessive suppression of small fluctuations.

[0104] Specifically, a phased training strategy is adopted in the implementation: In the first phase, the physical constraint terms are frozen, and only the data consistency term and the monotonic prior term are trained for 30 epochs to allow the network to initially fit the degradation trend; in the second phase, all three terms are unfrozen and trained jointly, and the gradient magnitudes of the three losses are ensured to be of the same order of magnitude through weight normalization. The final L_total is used as the objective function input to the backpropagation algorithm to update the parameters of the recurrent neural network.

[0105] Step S5: Using the Bayesian uncertainty estimation method, the weights of each loss term are dynamically optimized based on the online statistical characteristics of the data consistency term, the physical constraint term, and the monotonic prior term to obtain the target recurrent neural network.

[0106] Specifically, such as Figure 2 As shown, the process of step S5 includes:

[0107] Step S51: Treat the data consistency term, physical constraint term, and monotonic prior term as noisy statistical constraints, introduce a corresponding precision parameter for each loss term, and set a prior distribution for each precision parameter.

[0108] Specifically, the data consistency term, physical constraint term, and monotonic prior term are treated as independent statistical constraints, and corresponding precision parameters λ_data, λ_PDE, and λ_mono are introduced for each term. The Gamma distribution is used as the prior distribution for each precision parameter, i.e., λ_i~Gamma(α_i, β_i), where the concentration parameter α_i and the rate parameter β_i are both initialized to 1.0, so that the mean and variance of the prior distribution are 1, ensuring that the initial weights of the three loss terms are in a balanced state during the early stage of training.

[0109] Step S52: Based on the online statistical characteristics of the data consistency term, physical constraint term, and monotonic prior term, perform Bayesian update on each precision parameter to obtain the corresponding posterior precision distribution.

[0110] Specifically, in each training batch, the online statistical properties of three losses are calculated: the average of the data consistency loss over all samples in the current batch is used to obtain L_data_batch, and similarly, L_PDE_batch and L_mono_batch are obtained. Bayesian updates are performed using conjugate prior properties, treating the statistic of the sum of squared losses as observational evidence for the accuracy parameter. The posterior accuracy distribution update formula is:

[0111]

[0112]

[0113] Where N_batch is the number of valid samples in the current batch, and Li_batch is the batch mean of the corresponding loss term. This yields the posterior precision distribution λ_i|D ~ Gamma(α_i', β_i').

[0114] Step S53: Set the weights of each loss term to be proportional to the expected posterior accuracy to obtain the original weight vector;

[0115] Specifically, the process of setting the weights of each loss term to be proportional to the expected posterior accuracy to obtain the original weight vector includes:

[0116] Based on the prior accuracy distribution and the online statistical characteristics, the posterior accuracy distribution corresponding to each loss term is calculated using Bayes' formula.

[0117] Specifically, the expected value of the posterior accuracy distribution is calculated as E[λ_i] = α_i' / β_i', which reflects the quantitative assessment of the credibility of each loss term in the current training phase.

[0118] The expected value of the posterior accuracy distribution is determined as the original weight of each loss term, and the original weight is proportional to the expected posterior accuracy.

[0119] Specifically, the original weights w_i_raw of each loss term are set to be proportional to the expected posterior accuracy: w_i_raw = E[λ_i] / Σ_j E[λ_j], thus obtaining the three-dimensional original weight vector [w_data_raw, w_PDE_raw, w_mono_raw]. This proportional relationship ensures that loss terms with lower uncertainty (higher posterior accuracy) receive larger weights, thereby adaptively dominating the training process.

[0120] Step S54: Normalize the original weight vector and apply preset lower and upper limits to obtain normalized constraint weights.

[0121] Specifically, L1 norm normalization is performed on the original weight vector: w_i = w_i_raw / Σ_j w_j_raw, ensuring that the sum of the three weights is always 1. Strict upper and lower bound constraints are imposed: w_i ∈ [0.05, 0.9]. Weights below the lower bound are increased to 0.05, and weights above the upper bound are decreased to 0.9 through a truncation operation, before renormalization. This constraint prevents any single loss term from becoming too small, leading to vanishing gradients, or too large, causing training failure, and especially ensures that the physical constraint term maintains an effective gradient flow even when data is scarce.

[0122] Step S55: The loss statistic is smoothed using the exponential moving average method to obtain a smoothed loss statistic.

[0123] Specifically, an exponential moving average (EMA) is applied to the batch loss statistic Li_i_batch to suppress weight fluctuations caused by operating condition switching, with the smoothing coefficient γ fixed at 0.9. The smoothing update formula is:

[0124] L_i_smooth = γ × L_i_smooth + (1 - γ) × L_i_batch

[0125] Li_i_smooth is initialized as the mean of the losses from the first three rounds of the training set and is dynamically updated in each subsequent batch. This smoothing statistic replaces the original batch statistics in the Bayesian update, giving the weight adjustment inertia and avoiding drastic fluctuations caused by anomalous data in a single batch.

[0126] Step S56: In each training iteration, the data consistency term, physical constraint term, and monotonic prior term are calculated based on the smoothing loss statistic. The smoothing loss statistic is used to update each precision parameter and obtain the corresponding normalized constraint weights. Then, backpropagation is performed through the updated multi-constraint joint loss function to update the recurrent neural network parameters. The above iterative process is repeated until the network converges, thereby obtaining the target recurrent neural network.

[0127] Step S6: Predict the health status trajectory based on the target recurrent neural network, and calculate the remaining service life in combination with the preset failure threshold.

[0128] Specifically, such as Figure 3 As shown, the process of step S6 includes:

[0129] Step S61: Generate a health status prediction sequence at discrete times based on the target recurrent neural network, and preset a failure threshold;

[0130] Specifically, the real-time operating data of the refrigerator to be predicted is input into the target recurrent neural network trained in step S5, and the prediction length is set to 1.5 times the remaining lifespan (not exceeding 500 hours). The network generates discrete-time health status prediction sequences using a forward propagation method. Each element is a normalized health index value in the interval [0,1], where 1 represents a brand new state and 0 represents complete failure. The failure threshold u_fail is set according to engineering specifications, specifically 0.2 (corresponding to performance degradation to 80%) or calibrated based on historical failure data: analyze the distribution of health indicators before historical failures of the same model of refrigeration unit, and take the 95th percentile of the index value at the time of failure as the threshold to ensure that the threshold has consistency across models.

[0131] Step S62: Interpolate the health state prediction sequence to obtain a continuous health state trajectory;

[0132] Specifically, a linear function is established between adjacent discrete points (t_k, û_k) and (t_{k+1}, û_{k+1}): û(t) = û_k + (û_{k+1} - û_k) × (t - t_k) / (t_{k+1} - t_k). The interpolation time resolution is set to 0.1 hours (i.e., 6 minutes), which strikes a balance between computational efficiency and trajectory accuracy. The interpolated trajectory covers the entire prediction time domain and is used to accurately detect threshold crossing times.

[0133] Step S63: Detect the continuous health status trajectory and the failure threshold, and determine the moment when the predicted health trajectory first reaches the threshold as the failure moment;

[0134] Specifically, starting from the current evaluation time t_current, the continuous trajectory is traversed forward along the time axis, detecting the moment when the predicted health status value first becomes less than or equal to the failure threshold. The determination condition is:

[0135]

[0136] If the condition is still not met after traversing the entire prediction sequence, then output a warning flag and set... .

[0137] Step S64: Calculate the difference between the failure time and the current assessment time as the estimated value of the remaining useful life.

[0138] Specifically, the difference between the failure time and the current assessment time is used as the remaining useful life point estimate: RUL_point = t_fail - t_current. This value is output in hours, retaining two decimal places of precision. If no threshold crossing is detected after traversing the entire prediction sequence, a warning flag "Out of prediction range" is output, and RUL is set to the upper limit of the prediction time domain (500 hours) to remind maintenance personnel to extend the observation period.

[0139] Step S65: Use the diffusion term in the degradation state evolution equation to perform multiple random samplings to generate a degradation trajectory sample set, and obtain the probability distribution and confidence interval of the remaining lifetime.

[0140] Specifically, the diffusion term in the degradation state evolution equation is subjected to Monte Carlo random sampling. The number of sampling iterations is set to 1000, with each sampling generating an independent degradation trajectory:

[0141] For each sampling path m (m=1..1000), at each discrete time t_k, a random increment is independently sampled from the standard normal distribution N(0,1). The state evolution is calculated according to the Euler-Maruyama update formula in step S3 to obtain the trajectory { For each trajectory, perform threshold detection steps S2 to S4 to obtain the corresponding failure time. .

[0142]

[0143] Threshold detection is performed on each trajectory to obtain failure time samples. This leads to the construction of a RUL sample set:

[0144]

[0145] The empirical distribution function was calculated based on 1000 RUL sample values, and its 5th and 95th quantiles were taken as the 95% confidence interval.

[0146] For a dataset containing N evaluation points, calculate the mean absolute percentage error (MAPE) and root mean square error (RMSE):

[0147]

[0148]

[0149] The final output includes the remaining useful life point estimate, probability density function curve, confidence interval, and the aforementioned performance evaluation metrics.

[0150] Specifically, this invention dynamically embeds temporal degradation features extracted by a recurrent neural network into stochastic differential equations. This allows the drift term to adaptively reflect the deterministic degradation mechanism of piston wear and working fluid contamination, while the diffusion term quantifies the uncertainty introduced by fluctuations in operating conditions and measurement noise. This constructs a degradation evolution model that couples physical laws and data features. Furthermore, it uses Bayesian uncertainty estimation to online evaluate the reliability of three loss terms: data fitting, physical constraints, and monotonic priors. The weights of each loss term are dynamically adjusted based on their actual performance, achieving an optimal balance between physical mechanisms and observed data at the gradient level. Finally, it outputs a remaining life prediction with probabilistic distribution significance. The point estimate captures the main degradation trends, and the confidence interval reflects the prediction uncertainty. Engineers can use this to formulate more accurate maintenance strategies, avoiding premature or late maintenance due to a single empirical threshold, and significantly improving the efficiency of refrigeration unit health management and operational reliability.

[0151] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

[0152] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting the lifespan of a refrigerator based on an adaptive physical information recurrent neural network, characterized in that, include: Step S1: Obtain multi-source data of the chiller, extract statistical health features based on the steady-state control window, and construct a time-series degradation feature vector; Step S2: Input the time series degradation feature vector into a recurrent neural network, and map it into a time-varying hidden state through a recurrent neural network structure to generate a degradation state estimate; Step S3: Embed the degradation state estimate into a stochastic differential equation model to construct a degradation state evolution equation that includes drift and diffusion terms; Step S4: Obtain measured degradation data. Based on the deviation between the degradation state estimate and the measured degradation data, the residual of the degradation state evolution equation, and the degree of monotonicity violation of the degradation state estimate at adjacent time points, construct data consistency term, physical constraint term, and monotonic prior term respectively, and then obtain the multi-constraint joint loss function. Step S5: Using the Bayesian uncertainty estimation method, the weights of each loss term are dynamically optimized based on the online statistical characteristics of the data consistency term, the physical constraint term, and the monotonic prior term to obtain the target recurrent neural network. Step S6: Predict the health status trajectory based on the target recurrent neural network, and calculate the remaining service life in combination with the preset failure threshold.

2. The method for predicting the lifespan of a refrigerator based on an adaptive physical information recurrent neural network according to claim 1, characterized in that, The process of step S2 includes: The time-series degradation feature vector is input into the recurrent neural network in chronological order. After initializing the initial hidden state, the time-varying hidden state at each time step is calculated by using the hidden state at the previous time step and the input features at the current time step through a gated nonlinear mapping function. The mapping function is controlled by the update gate and the forget gate. The time-varying hidden state is mapped through the output layer to generate a degenerate state estimate.

3. The method for predicting the lifespan of a refrigerator based on an adaptive physical information recurrent neural network according to claim 2, characterized in that, The degradation state estimate includes one of the following two forms or a combination thereof: (1) The time-varying hidden state is mapped through the output layer to generate the health status index of the refrigerator, which is used to construct the data consistency loss and physical constraint residual; (2) The time-varying hidden state is mapped through the output layer to generate a time-varying mechanism parameter vector, which is used to modulate the drift term and diffusion term of the stochastic differential equation in step S3 to realize memory-driven stochastic dynamic evolution.

4. The refrigerator life prediction method based on adaptive physical information recurrent neural network according to claim 3, characterized in that, The process of step S3 includes: ， in, This represents the degradation state variable of the refrigeration unit at continuous time t. Let be the drift function, representing the average evolution rate and nonlinear mechanism of degradation; Let be the diffusion function, representing the intensity of random fluctuations and how they change with state / operating condition; For exogenous input; The structural parameters of the drift function and the diffusion function are modulated by a time-varying mechanism parameter vector.

5. The method for predicting the lifespan of a refrigerator based on an adaptive physical information recurrent neural network according to claim 4, characterized in that, The process of step S4 includes: ， in, For multi-constraint loss functions, , Represents physical constraint terms. Let t represent time, x represent the state / operating condition input of the refrigerator, H(⋅) be the residual operator constructed from the degradation dynamics equation (i.e., the deviation obtained by substituting the network output into the control equation), and N be the total number of sampling points. , Indicates data consistency items, This represents the observed degradation or health index of the refrigeration unit at the i-th sampling point. This represents an estimate of the degraded state. , Let j represent the monotonic prior term, j represent the j-th refrigerator or the j-th degenerate sequence, and k be the time index within the sequence. This represents the estimate of the degenerate state at time k. The linear rectified function with the positive part is used, and this term achieves monotonicity constraint by penalizing the increase in the predicted value at adjacent time steps. This represents the learnable weight coefficient for the corresponding item.

6. The method for predicting the lifespan of a refrigerator based on an adaptive physical information recurrent neural network according to claim 5, characterized in that, The process of step S5 includes: The data consistency term, physical constraint term, and monotonic prior term are treated as noisy statistical constraints, and a corresponding precision parameter is introduced for each loss term. At the same time, a prior distribution is set for each precision parameter. Based on the online statistical characteristics of the data consistency term, physical constraint term, and monotonic prior term, Bayesian updates are performed on each precision parameter to obtain the corresponding posterior precision distribution. The weights of each loss term are set to be proportional to the expected posterior accuracy to obtain the original weight vector; The original weight vector is normalized, and preset lower and upper limits are applied to obtain normalized constraint weights. The loss statistic is smoothed using the exponential moving average method to obtain a smoothed loss statistic. In each training iteration, the data consistency term, physical constraint term, and monotonic prior term are calculated based on the smoothing loss statistic. The smoothing loss statistic is used to update each precision parameter and obtain the corresponding normalized constraint weights. Then, backpropagation is performed through the updated multi-constraint joint loss function to update the recurrent neural network parameters. The above iterative process is repeated until the network converges, thereby obtaining the target recurrent neural network.

7. The method for predicting the lifespan of a refrigerator based on an adaptive physical information recurrent neural network according to claim 6, characterized in that, The process of setting the weights of each loss term to be proportional to the expected posterior accuracy to obtain the original weight vector includes: Based on the prior accuracy distribution and the online statistical characteristics, the posterior accuracy distribution corresponding to each loss term is calculated using Bayes' formula. The expected value of the posterior accuracy distribution is determined as the original weight of each loss term, and the original weight is proportional to the expected posterior accuracy.

8. The method for predicting the lifespan of a refrigerator based on an adaptive physical information recurrent neural network according to claim 7, characterized in that, The process of step S6 includes: Based on the target recurrent neural network, a health status prediction sequence at discrete time points is generated, and a failure threshold is preset; The health state prediction sequence is interpolated to obtain a continuous health state trajectory; The continuous health status trajectory is detected against the failure threshold, and the moment when the predicted health trajectory first reaches the threshold is determined as the failure moment; The difference between the failure time and the current assessment time is calculated as the estimated value of the remaining useful life. By using the diffusion term in the degradation state evolution equation to perform multiple random samplings, a degradation trajectory sample set is generated, and the probability distribution and confidence interval of the remaining lifetime are obtained.

9. The method for predicting the lifespan of a refrigerator based on an adaptive physical information recurrent neural network according to claim 8, characterized in that, The process of step S1 includes: In the operating data of the refrigeration unit, a steady-state control window is identified. The current, cooling duration and transition cold plate temperature of the refrigeration unit are extracted from the steady-state control window to form a first time-series curve. The temperature, pressure difference or flow rate of the hot end are extracted to form a second time-series curve. The mean, standard deviation, skewness, kurtosis, duration, cumulative amount, slope and entropy are calculated for the first time series curve and the second time series curve respectively, and a sixteen-dimensional feature vector is constructed. The sixteen-dimensional feature vector is normalized to obtain the time series degradation feature vector.

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