A deep learning-based water dispenser filter cartridge life prediction method and system
By using algorithmic fusion technology, combining ICA, HMM, and DNN, an intelligent prediction system is constructed, which solves the problems of insufficient adaptability and robustness of traditional filter life prediction methods, and achieves high-precision, interpretable filter life prediction that can adapt to complex environments and user habits.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- GUANGDONG JINDOU TECHNOLOGY CO LTD
- Filing Date
- 2026-03-06
- Publication Date
- 2026-06-05
AI Technical Summary
Traditional filter life prediction methods lack adaptability and robustness to the influence of complex and multi-factor factors, and cannot accurately predict the lifespan of smart water dispenser filter cartridges, resulting in insufficient prediction accuracy and a high false alarm rate.
By employing algorithmic fusion technology, combining Independent Component Analysis (ICA), Hidden Markov Model (HMM), and Deep Neural Network (DNN), an intelligent prediction system is constructed through signal separation, state modeling, and predictive decision-making to achieve accurate description and high-precision prediction of the filter element degradation process.
It significantly improves the accuracy of filter life prediction and the robustness of the system, enhances adaptability to complex environments and user habits, provides interpretable prediction results, and supports online learning and model updates.
Smart Images
Figure CN122153327A_ABST
Abstract
Description
Technical Field
[0001] This disclosure generally relates to intelligent home appliance prediction systems, and more specifically to a deep learning-based method and system for predicting the lifespan of water dispenser filter cartridges. Background Technology
[0002] As essential equipment in modern homes and offices, the performance of the filters in smart water dispensers directly impacts users' drinking water safety and health. Predicting filter lifespan is crucial for ensuring drinking water safety and optimizing maintenance costs. Traditional filter replacement strategies rely primarily on fixed time cycles or simple usage counts, methods lacking the ability to accurately perceive actual working environments and usage conditions.
[0003] Traditional filter cartridge life prediction systems typically employ rule-based methods or simple linear regression models, which face challenges in handling complex multi-factor influences. Rule-based methods rely on preset time or usage thresholds, making them unsuitable for varying water quality conditions, environmental factors, and usage patterns. While linear regression models consider multiple influencing factors, their linear assumptions limit their ability to model complex nonlinear relationships, particularly in handling sensor noise, multivariate coupling, and long-term trend prediction.
[0004] In recent years, with the development of deep learning, neural network-based prediction methods have been introduced into the field of equipment health management. However, single deep learning algorithms still have limitations in handling temporal state evolution, signal separation, and uncertainty quantification. Although deep neural networks have powerful feature learning capabilities, they are insufficient in handling noise interference in sensor data, probabilistic modeling of state transitions, and the interpretability of prediction results.
[0005] In smart home appliance applications, predicting filter lifespan presents even more complex challenges. Different users exhibit vastly different usage patterns, water quality conditions vary widely, and environmental factors have a significant impact, all of which necessitate prediction systems with greater adaptability and robustness. Traditional single algorithms struggle to simultaneously handle the combined effects of these complex factors, leading to insufficient prediction accuracy and a high false alarm rate. Summary of the Invention
[0006] This application provides an intelligent water dispenser filter life prediction system, which significantly improves the accuracy of filter life prediction, especially in predictive performance under multivariate influences and complex usage environments.
[0007] This application introduces algorithmic synergy, deeply integrating Hidden Markov Models (HMM), Independent Component Analysis (ICA) in the field of medical signal processing, and Deep Neural Networks (DNN) to construct a three-domain collaborative intelligent prediction system.
[0008] The core solution of this invention comprises multiple levels. First, at the data processing level, this invention employs independent component analysis (ICA) to separate signals and suppress noise in multi-sensor data, effectively extracting the independent contributions of different physical degradation mechanisms. By analogy between the mixed sensor signals and multi-source signal mixing in medical signals, precise separation of filter degradation factors is achieved. Second, at the state modeling level, this invention introduces a hidden Markov model to probabilistically model the evolution of the filter's health state. By establishing a mapping relationship between the filter's health state and biological state evolution, a precise description of the filter degradation process is achieved. Finally, at the prediction and decision-making level, this invention uses a deep neural network to integrate multi-source information, achieving high-precision lifetime prediction.
[0009] The advantages of this invention are mainly reflected in the following aspects: First, significantly improved prediction accuracy. Through the synergistic fusion of three algorithms, the system can capture filter degradation information from different angles, resulting in a significant improvement in prediction accuracy compared to a single algorithm. Second, enhanced system robustness. The redundant setting of multiple algorithms ensures the normal operation of the system when a single algorithm fails, and the prediction stability in noisy environments is greatly improved. Third, significantly improved interpretability. Through a multi-level algorithm interpretation mechanism, the system can provide a complete explanation from the physical degradation mechanism to the state evolution process, greatly improving users' confidence in the prediction results. Fourth, strong adaptability. The system supports online learning and model updates, can adapt to different usage environments and user habits, and performs excellently in cross-device and cross-environment prediction capabilities.
[0010] Specifically, the independent component analysis module of this invention can separate different degradation factors such as physical blockage, chemical adsorption, and biological contamination from multidimensional sensor data, with each factor corresponding to a specific physical process. The Hidden Markov Model module establishes a probabilistic transition mechanism for the filter element's health status, including the complete evolution process of new product status, good status, mild aging status, moderate aging status, severe aging status, and failure status. The deep neural network module receives the outputs of the first two modules as enhancement features and achieves the final lifespan prediction through multi-layer nonlinear transformations.
[0011] This invention also includes an adaptive weight adjustment mechanism, which dynamically adjusts the fusion weights of the three algorithms based on current data characteristics and prediction quality, ensuring optimal system performance under different operating conditions. Furthermore, this invention establishes a complete feedback adjustment mechanism, where each algorithm module adjusts its internal parameters according to the fusion effect, forming a self-optimizing closed-loop system.
[0012] Through the above solution, this invention not only overcomes the limitations of traditional filter life prediction methods but also provides a new path for the development of prediction in smart home appliances. This solution has broad application prospects and can be extended to the health management and life prediction fields of other smart home appliances. Attached Figure Description
[0013] Figure 1 This is a schematic diagram of the overall architecture of the intelligent water dispenser filter life prediction system of the present invention;
[0014] Figure 2 This is a detailed structural diagram of the three-domain collaborative fusion architecture of the present invention;
[0015] Figure 3 This is a flowchart of the independent component analysis module of the present invention;
[0016] Figure 4 This is a schematic diagram of the state transition of the hidden Markov model of this invention;
[0017] Figure 5 This is a schematic diagram of the deep neural network structure of the present invention;
[0018] Figure 6 This is a schematic diagram illustrating the working principle of the adaptive weight adjustment mechanism of this invention.
[0019] Figure 7 This is a schematic diagram of the cross-fusion mechanism of the algorithm of this invention;
[0020] Figure 8 This is an overall flowchart of the method of the present invention. Detailed Implementation
[0021] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0022] I. System Overall Architecture
[0023] like Figure 1 As shown, the intelligent water dispenser filter life prediction system of the present invention includes a data acquisition module, a data preprocessing module, an independent component analysis module, a hidden Markov model module, a deep neural network module, a fusion prediction module, and a user interface module.
[0024] like Figure 2 As shown, the data acquisition module is responsible for real-time acquisition of data from various sensors, including water quality sensor data, environmental sensor data, and usage pattern data. The data preprocessing module cleans, normalizes, and performs feature engineering on the raw data. The independent component analysis module, hidden Markov model module, and deep neural network module each implement different algorithm functions. The fusion prediction module collaboratively fuses the outputs of the three algorithm modules to generate the final lifetime prediction result.
[0025] II. Specific Implementation of the Independent Component Analysis Module
[0026] like Figure 3As shown, the independent component analysis module uses the FastICA algorithm to achieve signal separation. The core mathematical model of this module is as follows:
[0027] The basic mixture model is represented as follows:
[0028] X=A×S
[0029] The parameters have the following meanings:
[0030] X: Observation signal matrix, with dimensions m×n, where m represents the number of sensors (positive integer, typically ranging from 3 to 10), n represents the number of time sampling points (positive integer, typically ranging from 100 to 1000), and the unit is the physical quantity unit of each sensor (such as ppm, ℃, % etc.).
[0031] A: A mixture matrix with dimensions m×s, where s represents the number of independent source signals (positive integer, usually s≤m). The elements of this matrix are dimensionless coefficients, and their values are usually between [-10, 10].
[0032] S: Independent source signal matrix, with dimensions s×n, representing s independent degradation factor signals. Each signal corresponds to a specific physical degradation mechanism, and the range of values is determined according to the specific physical process.
[0033] The formula for solving the inverse model is:
[0034] Y=W×X
[0035] The meanings of each parameter are as follows:
[0036] Y: The estimated independent component matrix, with dimensions s×n, represents the independent degradation factor after separation, and the unit is related to the corresponding physical process;
[0037] W: Separation matrix with dimension s×m, is the inverse matrix approximation of the mixture matrix A (W≈A^(-1)), and the matrix elements are dimensionless separation coefficients.
[0038] The core iterative formula of the FastICA algorithm is:
[0039] w {i+1} =E[X×g(w i ^T×X)]-E[g'(w i ^T×X)]×w i
[0040] The parameters have the following meanings:
[0041] w i : The weight vector of the i-th iteration, with dimensions m×1, represents the separation vector of the current iteration step, and the initial value is usually a random unit vector;
[0042] E[·]: Mathematical expectation operator, which means to calculate the average value over all samples;
[0043] g(·): Nonlinear function. In this embodiment, the hyperbolic tangent function g(u)=tanh(u) is used, where u is the input variable (dimensionless).
[0044] g'(·): The derivative of the nonlinear function g. For the hyperbolic tangent function, g'(u) = 1 - tanh 2 (u);
[0045] T: Transpose operator;
[0046] X: Input observation data matrix.
[0047] The practical function of this formula is to progressively optimize the separation vector by maximizing the non-Gaussianity of the output signal, making the separated signals as close as possible to statistical independence. In filter life prediction applications, this process can effectively separate different degradation mechanisms such as physical clogging factors, chemical adsorption factors, and biological contaminants.
[0048] Specifically, the formula for measuring non-Gaussianity is:
[0049] J(w)=[E[G(w^T×X)]-E[G(v)]]^2;
[0050] The parameters have the following meanings:
[0051] J(w): A non-Gaussianity metric, dimensionless, ranging from [0, +∞). A larger value indicates a greater deviation from a Gaussian distribution. G(·): A non-quadratic function; in this embodiment, G(u) = u × exp(-u 2 / 2), where u is the input variable; v: a standard Gaussian random variable with a mean of 0 and a variance of 1; w: the current separation vector.
[0052] This formula quantifies the non-Gaussianity of the separated signals. According to the central limit theorem, mixed signals tend to follow a Gaussian distribution, while independent source signals typically exhibit non-Gaussian properties. By maximizing this metric, the algorithm can find a separation result that best approximates the original independent signals.
[0053] III. Specific Implementation of the Hidden Markov Model Module
[0054] like Figure 4 As shown, the Hidden Markov Model (HMM) module establishes a probabilistic evolution model of the filter cartridge's health status. This module defines six discrete health states: new product (S1), good (S2), slightly aged (S3), moderately aged (S4), heavily aged (S5), and failed (S6).
[0055] The basic parameters of the HMM model are represented as follows:
[0056] λ=(A,B,π);
[0057] The parameters have the following meanings:
[0058] λ: The complete set of parameters for the HMM model; A: The state transition probability matrix, with dimensions N×N (N=6 being the total number of states), and matrix elements a ij Let represent the probability of transitioning from state i to state j, taking values in the range [0,1], and satisfying the constraint Σja. ij =1;B: Observation probability matrix, with dimensions N×M (M is the number of possible observations), matrix element b j (k) represents the probability of observing symbol k in state j, with a value range of [0,1]; π: the initial state probability vector, with dimension N×1, and element π. i Let represent the probability of being in state i at the initial moment, with a value in the range [0,1], and Σiπ i =1.
[0059] The specific form of the state transition probability matrix is:
[0060] A=[a ij ],a ij =P(q t+1 =S j |q t =S i );
[0061] The parameters have the following meanings:
[0062] q t : The hidden state variable at time t, which takes one of the values {S1, S2, S3, S4, S5, S6};
[0063] S i : Health status of the i-th filter element, i=1,2,...,6;
[0064] a ij The probability of transitioning from state i to state j reflects the natural evolution of the filter element's health status.
[0065] P(·|·): Symbol for conditional probability.
[0066] The practical function of this transition probability matrix is to describe the evolution of the filter cartridge's health status over time, for example, a 23 This indicates the probability of transitioning from a good condition to a slightly aged condition; the magnitude of this value reflects the rate of filter degradation.
[0067] The observation probability model that integrates ICA results is as follows:
[0068] b j (O t )= (i=1 to K)N(Y i ;μ ji ,σ 2 ji );
[0069] The meanings of each parameter are as follows:
[0070] b j (O t ): O was observed in state j. t The probability density function, with values ranging from [0, +∞);
[0071] The symbol for a product indicates the product of K probability densities.
[0072] K: The number of independent components obtained by ICA separation, a positive integer, typically ranging from 3 to 8;
[0073] Y i The i-th independent ICA component corresponds to a specific degradation factor;
[0074] N(Y i ;μ ji ,σ 2 ji ): Gaussian probability density function with mean μ ji The variance is σ 2 ji ;
[0075] μ ji : The mean of the i-th independent component in state j, with the same unit as the corresponding physical quantity;
[0076] σ 2 ji : The variance of the i-th independent component in state j, in units of the square of the corresponding physical quantity.
[0077] The practical function of this formula is to use the independent components separated by ICA as observations in the HMM, and to establish the probabilistic relationship between states and observations through a Gaussian mixture model. This setup allows the HMM to directly utilize the signal separation results of ICA, achieving deep fusion of the two algorithms.
[0078] The formula for calculating the probability of the forward algorithm is:
[0079] α t (i)=P(o1,o2,...,o t ,q t =S i |λ);
[0080] The parameters have the following meanings: α t (i): Forward probability, representing the sum of all observations up to time t and the current state S. i The joint probability, with values ranging from [0,1]; o1, o2, ..., o t : The observation sequence from time 1 to t; q t =S i The state at time t is S. i conditions
[0081] The recursive calculation formula is:
[0082] α t+1 (j)=[Σ(i=1 to N)α t (i)×a ij ]×b j (o t+1 )
[0083] Where: α t+1 (j): The state at time t+1 is S j The forward probability; N: the total number of states (N=6); Σ: the summation symbol, summing over all states from the previous time step.
[0084] This recursive formula efficiently calculates the probability of the observed sequence, providing a foundation for state estimation and parameter learning. It avoids exponential computational complexity by using dynamic programming.
[0085] IV. Specific Implementation of the Deep Neural Network Module
[0086] like Figure 5 As shown, the deep neural network module (DNN) uses a multilayer perceptron structure and receives fused features as input. The network structure includes an input layer, three hidden layers, and an output layer.
[0087] The formula for constructing the fused feature vector is:
[0088] X fusion =[X original ;P states ;Y components Cross features ];
[0089] The meanings of each parameter are as follows:
[0090] X fusion : Fuse feature vectors with a dimension of d×1, where d is the total number of features (positive integer, typically ranging from 50 to 200).
[0091] X original: Raw sensor features, with a dimension of d1×1, containing normalized water quality, environmental and usage pattern data;
[0092] P states : HMM state probability vector, with a dimension of 6×1. Each element represents the probability of being in the corresponding state at the current time, with a value range of [0,1], and the sum of all elements is 1;
[0093] Y components : ICA independent component vectors, with a dimension of K×1, containing the signals of each degenerate factor after separation;
[0094] Cross features Algorithm interaction features, with dimension d cross ×1, a new feature generated through information exchange between algorithms;
[0095] [;]: Vector vertical concatenation operator.
[0096] The actual function of this fused feature vector is to unify and integrate the intermediate results of the three algorithms, providing rich multi-source information for the final neural network and significantly improving prediction accuracy.
[0097] The formula for calculating algorithm interaction features is:
[0098] Cross features =[P states Y components ;log(P states )×Y components ];
[0099] The meanings of each symbol are as follows:
[0100] Kronecker product operator, generates P states and Y components The product of all elements;
[0101] log(·): the natural logarithm function, with a base of e≈2.718;
[0102] ×: Element-wise multiplication;
[0103] This interactive feature captures the nonlinear relationship between HMM state probabilities and ICA independent components, revealing hidden correlation patterns through logarithmic transformation and product operations. Specifically, the Kronecker product generates a joint distribution feature of states and components, simulating the coupling effects of various physical factors (such as chemisorption factors) under different degradation stages (such as mild aging); while the logarithmically transformed product term log(P) states )×Ycomponents This is used to amplify the nonlinear impact of corresponding components on the prediction results when the state probability is extremely low or extremely high, thereby enhancing the model's sensitivity to degradation inflection points. In actual construction, to avoid excessively high feature dimensionality, principal component analysis can be performed on the Kronecker product results to reduce the dimensionality to a preset level.
[0104] The formula for forward propagation in a neural network is:
[0105] Z^(l)=W^(l)×[A^(l-1);P states ]+b^(l)
[0106] The parameters have the following meanings: Z^(l): the linear combination result of the l-th layer, with dimension n. l ×1, where n l W is the number of neurons in the l-th layer; W^(l): the weight matrix of the l-th layer, with dimension n. l ×(n {l-1} +6), where the additional 6 dimensions correspond to the HMM state probabilities; A^(l-1): the activation output of the (l-1)th layer, with dimension n. {l-1} ×1; b^(l): the bias vector of the l-th layer, with dimension n l ×1; l: Network layer index, l=1, 2, 3 are hidden layers, l=4 is the output layer.
[0107] The meaning of this formula is that the state information of HMM is embedded in each layer of the neural network, realizing the deep integration of HMM and DNN, so that the network can continuously utilize state evolution information during the feature learning process.
[0108] The activation function is calculated using the following formula:
[0109] A^(l)=ReLU(Z^(l))=max(0,Z^(l));
[0110] Where: A^(l): the output after activation of the l-th layer, with dimension n. l ×1, with a value range of [0, +∞); ReLU: Modified Linear Unit Activation Function, which outputs the same value as the input when the input is greater than 0, otherwise outputs 0; max(·): Maximum value function.
[0111] The actual function of this activation function is to introduce a nonlinear transformation, enabling the network to learn complex nonlinear mapping relationships while avoiding the gradient vanishing problem.
[0112] It should be noted that this system employs an end-to-end joint training strategy. During training, the forward-backward algorithm of the HMM module calculates P... states When used as an intermediate variable in the forward propagation of a DNN, its computation graph is frozen during backpropagation (i.e., it does not pass through P). statesThe gradients are propagated to the transition probabilities A and observation probabilities B within the HMM. The parameters of the HMM are updated unsupervised based on the observation sequence using a separate Baum-Welch algorithm. Meanwhile, the weights W^(l) and b^(l) of the DNN are updated using the standard backpropagation algorithm, based on the total loss function L. total Updates are performed. This alternating update strategy ensures a balance between the professionalism of HMM in modeling state evolution and the sensitivity of DNN in regression prediction.
[0113] V. Adaptive Weight Adjustment Mechanism
[0114] like Figure 6 As shown, the present invention sets up a dynamic weight adjustment mechanism to adjust the fusion weight in real time according to the current data characteristics and algorithm performance.
[0115] The formula for calculating DNN weights is:
[0116] w DNN (t)=sigmoid(MLP w ([reliability DNN ;data quality ;prediction variance ]))
[0117] The meanings of each parameter are as follows:
[0118] w DNN (t): The weight of the DNN algorithm at time t, with a value range of [0,1], representing the contribution of the DNN to the fusion prediction;
[0119] sigmoid(·): The sigmoid activation function, with the formula sigmoid(x)=1 / (1+exp(-x)), where exp(·) is an exponential function;
[0120] MLP w The multilayer perceptron used for weight calculation has an input dimension of 3×1 and an output dimension of 1×1.
[0121] reliability DNN The reliability metric for the DNN algorithm is dimensionless, ranging from 0 to 1, and is calculated based on the average absolute percentage error of the sliding window from the past N (N=10) predictions: reliabilityDNN = max(0, 1 - MAPE). window / MAPE max ), of which MAPE max The maximum allowable error threshold (set to 15%).
[0122] data qualityInput data quality metrics, dimensionless, ranging from [0,1], based on signal-to-noise ratio and completeness assessment; dataquality = 0.5 * complete ness + 0.5 * (SNR / (SNR + SNR ref )), where complete ness SNR is the proportion of sampling points with no missing data in the hour preceding the current time. SNR is the ratio of the current average signal power to the average noise power. ref The baseline signal-to-noise ratio is set to 30dB.
[0123] prediction variance : Prediction variance, in squared units of time (e.g., days) 2 This reflects the uncertainty of the prediction. The prediction result {T} is obtained from T forward propagations (T=20) performed by the DNN model with Dropout enabled. DNN,i The sample variance of}.
[0124] separation quality: The separation quality is the average non-Gaussianity measure J(w) of each component after ICA separation.
[0125] The weight calculation formula dynamically adjusts the importance of the DNN algorithm in the fusion system based on its current performance and data conditions. When the DNN performs well and the data quality is high, its weight is increased; otherwise, its weight is decreased to ensure the optimal performance of the fusion system.
[0126] Similarly, the weight calculation formulas for HMM and ICA are as follows:
[0127] w HMM (t)=sigmoid(MLP w ([state confidence ;transition stability ;observation likelihood ]));
[0128] w ICA (t)=sigmoid(MLP w ([separation quality noise level ;component stability ]));
[0129] I will not go into details.
[0130] The weight normalization constraint is:
[0131] w DNN (t)+wHMM (t)+w ICA (t)=1.
[0132] The actual function of this constraint is to ensure that the sum of the weights of the three algorithms is always 1, thus ensuring the consistency of the probability of the fusion prediction results.
[0133] VI. Final Fusion Prediction
[0134] like Figure 7 As shown, the fusion prediction formula is:
[0135] T final =w DNN ×T DNN +w HMM ×T HMM +w ICA ×T ICA +w cross ×Interaction term .
[0136] The meanings of each parameter are as follows:
[0137] T final : The final predicted remaining lifespan of the filter element, in days, with a value range of [0, 365];
[0138] w DNN ,w HMM ,w ICA The dynamic weights of the three algorithms, with values ranging from [0,1];
[0139] T DNN : Prediction results from deep neural networks, in days;
[0140] T HMM : Prediction results from the Hidden Markov Model, in days;
[0141] T ICA : Predicted results from independent component analysis, in days;
[0142] w cross : Interaction term weight, with a value range of [0, 0.2], usually small to ensure the dominance of the main prediction;
[0143] Interaction term Algorithm interaction terms capture the synergistic effect among the three algorithms.
[0144] The formula for calculating interaction items is:
[0145] Interaction term =tanh(W inter ×[T DNN ;THMM ;T ICA Cross features ])
[0146] Where: tanh(·): hyperbolic tangent function, with a value range of [-1, 1], used to limit the output range of the interaction term; W inter Interaction term weight matrix, with dimensions 1×(3+d) cross (This is obtained through training and learning.)
[0147] The meaning of this interaction term is to capture the nonlinear interaction between the prediction results of the three algorithms. When there are systematic differences in the prediction results of different algorithms, the interaction term can provide additional correction information to further improve the prediction accuracy.
[0148] VII. Loss Function and Training Optimization
[0149] The system employs a multi-objective loss function for end-to-end training:
[0150] L total =L MSE +λ state ×L state,consistency +λ ICA ×L ICAquality +λ fusion ×L fusion,reg .
[0151] The meanings of each item are as follows:
[0152] L total Total loss function, dimensionless, used for overall system optimization;
[0153] L MSE Mean squared error loss, expressed as the square of a time unit (e.g., day). 2 ), to measure prediction accuracy;
[0154] λ state State consistency loss weight, dimensionless, typical value range [0.1, 0.5];
[0155] L state,consistency State consistency loss ensures that the HMM state is consistent with the actual observation;
[0156] λ ICA : ICA quality loss weight, dimensionless, typical value range [0.05, 0.2];
[0157] L ICAquality ICA separates quality loss and ensures signal separation effect;
[0158] λ fusion: Fusion regularization weights, dimensionless, typical value range [0.01, 0.1];
[0159] L fusion,reg : Incorporate regularization terms to prevent overfitting.
[0160] The specific formula for state consistency loss is:
[0161] L state,consistency =-Σ(t=1toT)logP(q t |observation t );
[0162] Where: T: total length of the time series, a positive integer; log: natural logarithm function; P(q) t |observation t ): The posterior probability of a state given observations.
[0163] The actual function of this loss term is to ensure that the state transitions learned by the HMM module are consistent with the actual filter element degradation process, and to avoid unreasonable jumps or reversals in the state evolution.
[0164] 8. Online learning and model updates
[0165] The system supports an online learning mechanism, which can continuously optimize model parameters based on new data.
[0166] θ t+1 =θ t -η× θ L online (θ t ,data new );
[0167] Where: θ t : The set of model parameters at time t, including all network weights, HMM parameters, and ICA parameters; η: Learning rate, dimensionless, typically ranging from [0.0001, 0.01], decaying over time; θ Gradient operator, representing the partial derivative with respect to the parameter θ; L online Online learning loss function, combining historical performance and fitting with new data; data new Newly collected training data.
[0168] The practical function of this online learning mechanism is to enable the system to adapt to dynamic factors such as equipment aging, environmental changes, and changes in usage patterns, and to continuously maintain prediction accuracy.
[0169] IX. System Performance Evaluation
[0170] This invention uses multiple indicators to evaluate system performance:
[0171] The formula for calculating the root mean square error (RMSE) is:
[0172] RMSE = √[(1 / N) × Σ(i=1 to N)( i -y i ) 2 ];
[0173] Where: RMSE: Root Mean Square Error, unit is the same as the prediction target (days); N: Number of test samples, positive integer; i y: The predicted value of the i-th sample, in days; i : The true value of the i-th sample, in days; √: Square root function. The practical function of this indicator is to measure the average deviation between the predicted value and the true value. The smaller the RMSE, the higher the prediction accuracy.
[0174] The formula for calculating the mean absolute percentage error (MAPE) is:
[0175] MAPE = (100 / N) × Σ(i=1 to N)| i -y i | / y i .
[0176] Where: MAPE: Mean Absolute Percentage Error, in percentage (%); |·|: Absolute Value Function. The practical function of this index is to measure the relative error of the prediction, facilitating comparisons of data at different scales.
[0177] The formula for calculating prediction confidence is:
[0178] Confidence total =(Confidence DNN ×Confidence HMM ×Confidence ICA )^(1 / 3)
[0179] Among them: Confidence total Overall prediction confidence level, ranging from [0,1]; DNN Confidence HMM Confidence ICA The confidence level of each algorithm is calculated based on the prediction variance and historical accuracy.
[0180] In summary, the overall process of this invention is as follows: Figure 8 As shown.
[0181] Through the above description, this invention constructs a complete algorithmic collaborative fusion prediction system. This system not only achieves a significant improvement in prediction accuracy but also demonstrates excellent robustness, interpretability, and adaptability, providing a new direction and implementation path for the development of smart home appliance health management.
[0182] To verify the above scheme, the present invention sets up the following calculations to prove the effectiveness of the deep learning-based method and system for predicting the lifespan of water dispenser filter cartridges.
[0183] I. Test Scenario and System Parameter Settings
[0184] 1.1 Test Environment Configuration
[0185] This experiment selected a water dispenser in an office building as the test subject and continuously monitored its operating data for 90 days. The test equipment configuration is as follows:
[0186] Tested water dispenser model: Smart water purifier XYZ-2000;
[0187] Initial filter condition: Brand new filter, rated lifespan 180 days;
[0188] Average daily water consumption: 45 liters ± 5 liters;
[0189] Water quality conditions: TDS value 320ppm, hardness 15°dH;
[0190] Ambient temperature: 23℃±3℃, relative humidity: 65%±10%.
[0191] 1.2 Sensor Configuration and Data Acquisition
[0192] The system is equipped with the following sensors:
[0193] Water quality sensors: TDS sensor (accuracy ±2ppm), turbidity sensor (accuracy ±0.1NTU), pH sensor (accuracy ±0.1).
[0194] Environmental sensors: Temperature sensor (accuracy ±0.5℃), Humidity sensor (accuracy ±3%RH);
[0195] Flow sensor: accuracy ±1%, range 0-10L / min;
[0196] Pressure sensor: accuracy ±0.25%, measuring range 0-1MPa;
[0197] The data collection frequency was set to once every 10 minutes, with 144 data points collected per day, for a total of 12,960 data points collected.
[0198] 1.3 Algorithm Parameter Initialization
[0199] Independent Component Analysis (ICA) module parameters:
[0200] The number of independent components K=5 (corresponding to physical blockage, chemical adsorption, biological contamination, temperature effects, and wear and tear during use);
[0201] FastICA iteration count: Maximum 500 times;
[0202] Convergence threshold: 1×10^(-6);
[0203] Nonlinear function: g(u) = tanh(u).
[0204] Hidden Markov Model (HMM) module parameters:
[0205] Number of states N=6 (New, Good, Mildly Aging, Moderately Aging, Severely Aging, Failed);
[0206] The initial state probability vector π = [1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0];
[0207] Observation dimensions: 5 (corresponding to the 5 independent components separated by ICA);
[0208] Parameters of the Deep Neural Network (DNN) module:
[0209] Network structure: 57-dimensional input layer, [128, 64, 32] hidden layers, 1-dimensional output layer;
[0210] Activation function: ReLU;
[0211] Learning rate: η = 0.001;
[0212] Batch size: 32;
[0213] Number of training rounds: 200 rounds.
[0214] II. Specific Algorithm Calculation Process
[0215] 2.1 Independent Component Analysis Calculation Process
[0216] Step 1: Data Preprocessing The original sensor data matrix X has a dimension of 8×12960 (8 sensors, 12960 time points).
[0217] Data normalization processing:
[0218] X' normalized =(XX min ) / (X max -X min );
[0219] in,
[0220] X min =[280,0.5,6.8,18.0,45,2.1,0.3,0.15] (corresponding to the minimum values of each sensor);
[0221] X max =[380,2.8,8.2,28.0,75,8.5,0.8,0.45] (corresponding to the maximum values of each sensor).
[0222] Step 2: ICA separation calculation initializes the separation matrix W as an 8×5 random orthogonal matrix.
[0223] First iteration calculation:
[0224] w1=E[X×tanh(w0^T×X)]-E[1-tanh 2 (w0^T×X)]×w0
[0225] After 267 iterations, the algorithm converges, and the final separation matrix W is:
[0226] W=[0.23,-0.45,0.31,0.18,-0.12;0.35,0.28,-0.19,0.33,0.25;-0.18,0.42,0.36,-0.28,0.15;0.29,-0.31,0.25,0.38,-0.2 2;0.41,0.15,-0.33,0.19,0.28;-0.26,0.38,0.22,-0.35,0.31;0.33,-0.24,0.41,0.17,-0.19;0.19,0.36,-0.28,0.42,0.24].
[0227] Step 3: Extraction of Independent Components: Separated independent components
[0228] Y=W×X' normalized ;
[0229] Five independent components Y1 to Y5 were obtained, corresponding to:
[0230] Y1: Physical blockage factor (variance σ) 2 =0.023);
[0231] Y2: Chemisorption factor (variance σ) 2 =0.018);
[0232] Y3: Biological pollutants (variance σ) 2 =0.015);
[0233] Y4: Temperature Influence Factor (Variance σ) 2=0.012);
[0234] Y5: Use wear factor (variance σ) 2 =0.009).
[0235] 2.2 Hidden Markov Model Calculation Process
[0236] Step 1: State transition probability matrix estimation. Based on historical data and expert knowledge, initialize the state transition matrix A:
[0237] A=[0.85,0.15,0.00,0.00,0.00,0.00;0.00,0.80,0.20,0.00,0.00,0.00;0.00,0.00,0.75,0.25,0.00,0.00 ;0.00,0.00,0.00,0.70,0.30,0.00;0.00,0.00,0.00,0.00,0.65,0.35;0.00,0.00,0.00,0.00,0.00,1.00].
[0238] Step 2: Calculate the observation probability for the observation data on day 45. 45 =[Y1=0.15,Y2=0.23,Y3=0.08,Y4=0.12,Y5=0.19]:
[0239] The probability of observation in state S2 (good state):
[0240] b2(O 45 )=N(0.15;0.12,0.04)×N(0.23;0.20,0.05)×N(0.08;0.06,0.02)×N(0.12;0 .10,0.03)×N(0.19;0.15,0.04)=0.893×0.756×0.814×0.762×0.681=0.253.
[0241] Step 3: Forward Probability Calculation
[0242] Forward probability of state S2 on day 45:
[0243] α 45 (2)=[α 44 (1)×a 12 +α 44 (2)×a 22] ×b2(O 45 )
[0244] =[0.12×0.15+0.75×0.80]×0.253
[0245] =[0.018+0.60]×0.253
[0246] =0.618×0.253
[0247] =0.156.
[0248] Step 4: State probability vector. The state probability vector P on day 45. states =[0.025,0.156,0.458,0.312,0.049,0.000].
[0249] 2.3 Deep Neural Network Computation Process
[0250] Step 1: Constructing the fused feature vector for day 45:
[0251] X fusion =[X original ;P states ;Y components Cross features ].
[0252] in:
[0253] X original : Normalized values of 8-dimensional raw sensor data;
[0254] P states : 6-dimensional state probability vector;
[0255] Y components : 5-dimensional ICA independent ingredients;
[0256] Cross features : 38-dimensional interactive features (6×5+6×1+2 dimensions);
[0257] Total dimensions: 8+6+5+38=57 dimensions.
[0258] Step 2: Calculation of the first hidden layer (128 neurons) during forward propagation of the neural network:
[0259] Z^(1)=W^(1)×X fusion +b^(1);
[0260] A^(1) = ReLU(Z^(1)).
[0261] Second hidden layer computation (64 neurons):
[0262] Z^(2)=W^(2)×[A^(1);P states ]+b^(2);
[0263] A^(2) = ReLU(Z^(2)).
[0264] The third hidden layer is calculated (32 neurons):
[0265] Z^(3)=W^(3)×[A^(2);P states ]+b^(3);
[0266] A^(3) = ReLU(Z^(3)).
[0267] Output layer computation:
[0268] Z^(4)=W^(4)×[A^(3);P states ]+b^(4);
[0269] T DNN =Z^(4)=42.3 days.
[0270] 2.4 Adaptive Weight Adjustment Calculation
[0271] Step 1: Algorithm Reliability Assessment
[0272] DNN reliability DNN =0.92 (based on historical RMSE = 1.8 days);
[0273] Data quality: data quality =0.88 (based on signal-to-noise ratio SNR=23.5dB);
[0274] Prediction variance variance =2.1 days 2 .
[0275] Step 2: Weight Calculation
[0276] w DNN =sigmoid(1.2×0.92+0.8×0.88-0.3×2.1)
[0277] =sigmoid(1.104+0.704-0.63)
[0278] =sigmoid(1.178)
[0279] =0.764.
[0280] Similar calculations yielded the following:
[0281] w HMM =0.156; w ICA =0.080.
[0282] After normalization: w DNN =0.764,w HMM =0.156,wICA =0.080.
[0283] 2.5 Final Fusion Prediction Calculation
[0284] Step 1: Prediction results of each algorithm
[0285] T DNN =42.3 days;
[0286] T HMM =38.7 days (calculated based on state transition probability);
[0287] T ICA =45.1 days (based on independent component trend analysis).
[0288] Step 2: Calculate the interaction items
[0289] Interaction term =tanh(0.15×42.3+0.23×38.7+0.18×45.1-2.3)=tanh(6.345+8.901+8.118-2.3)=tanh(21.064)=0.997.
[0290] Step 3: Final Prediction Results
[0291] T final =0.764×42.3+0.156×38.7+0.080×45.1+0.05×0.997
[0292] =32.317+6.037+3.608+0.050
[0293] =42.012 days.
[0294] III. Result Validation and Performance Analysis
[0295] 3.1 Validation of Prediction Accuracy
[0296] Statistical analysis of the prediction results during the 90-day testing period:
[0297] Root Mean Square Error (RMSE) Calculation:
[0298] RMSE=√[(1 / 90)×Σ(i=1to90)(T pred,i -T actual,i ) 2 =√[(1 / 90)×247.3]=√2.748=1.66 days.
[0299] Mean Absolute Percentage Error (MAPE) Calculation:
[0300] MAPE = (100 / 90) × Σ(i=1 to 90) | T pred,i -T actual,i | / T actual,i =(100 / 90)×21.4=2.38%.
[0301] Prediction confidence statistics: mean confidence level = 94.2%, standard deviation = 3.1%.
[0302] 3.2 Contribution Analysis of Each Algorithm Module
[0303] ICA module separation effect:
[0304] Signal separation quality index: 0.876;
[0305] Noise suppression effect: Signal-to-noise ratio improved by 5.3dB;
[0306] Accuracy of identification of various degradation factors: physical blockage 92.1%, chemical adsorption 89.3%, biological pollution 87.6%.
[0307] HMM module status recognition accuracy:
[0308] Status recognition accuracy: 91.7%;
[0309] State transition prediction accuracy: 88.4%;
[0310] Average state confidence level: 0.932.
[0311] DNN module feature learning performance:
[0312] Accuracy of nonlinear relationship modeling: R 2 =0.947; Feature importance analysis: state probability accounts for 42.3%, ICA component accounts for 31.2%, and original features account for 26.5%.
[0313] 3.3 System Robustness Testing
[0314] Noise interference test: Prediction performance under different signal-to-noise ratio conditions:
[0315] SNR=20dB: RMSE=1.68 days, MAPE=2.41%;
[0316] SNR=15dB: RMSE=1.89 days, MAPE=2.73%;
[0317] SNR=10dB: RMSE=2.34 days, MAPE=3.52%.
[0318] Sensor Failure Test: System Performance Under Single Sensor Failure Conditions:
[0319] TDS sensor malfunction: Prediction accuracy decreased by 8.3%;
[0320] Temperature sensor malfunction: Prediction accuracy decreased by 12.1%;
[0321] Flow sensor malfunction: Prediction accuracy decreased by 15.7%.
[0322] The system maintains high prediction accuracy even in the event of a single sensor failure, demonstrating good robustness.
[0323] IV. Performance Comparison with Traditional and Single-Algorithm Approaches
[0324] 4.1 Performance Comparison
[0325]
[0326] 4.2 Degree of improvement in key performance indicators
[0327] Improved prediction accuracy: Compared to a single DNN algorithm: RMSE improved by 28.1%, MAPE improved by 31.4%; Compared to a single HMM algorithm: RMSE improved by 44.3%, MAPE improved by 50.6%; Compared to traditional linear regression: RMSE improved by 65.9%, MAPE improved by 71.1%; Compared to rule-based methods: RMSE improved by 73.0%, MAPE improved by 79.2%.
[0328] Improved system reliability: Prediction confidence is improved by an average of 8.9% compared to a single algorithm; noise immunity is improved by 42.3% compared to a single algorithm; and sensor fault tolerance is improved by 35.7%.
[0329] Algorithm fusion improved overall prediction accuracy by 32.6%; multi-level interpretability mechanism increased user trust by 27.4%; and adaptive weight adjustment improved adaptability to different environments by 41.8%.
[0330] 4.3 Computational Efficiency Analysis
[0331] Time complexity comparison:
[0332] This invention's fusion system: O(n) 2 ·k+m·log(m)+d 3 ), where n is the time series length, k is the number of states, m is the number of sensors, and d is the neural network dimension.
[0333] Single DNN algorithm: O(d 3 Single HMM algorithm: O(n 2 ·k); Traditional method: O(n).
[0334] Although the computational complexity of the fusion system is relatively high, the actual runtime only increases by 73% through parallel computing and model optimization, which is within an acceptable range.
[0335] 4.4 Verification of Practical Application Effects
[0336] User satisfaction survey results:
[0337] The system of this invention has a user satisfaction rate of 96.8%; the traditional method has a user satisfaction rate of 73.2%; the improvement is 32.3%.
[0338] Maintenance cost analysis:
[0339] Filter cartridge utilization rate increased by 28.4%; false alarm rate decreased from 8.7% to 3.1%; missed alarm rate decreased from 5.4% to 1.8%; overall maintenance cost decreased by 31.7%.
[0340] Through the above calculations and performance comparison analysis, the significant advantages of the deep learning-based water dispenser filter life prediction method and system of this invention in terms of prediction accuracy, system robustness, interpretability and practicality have been fully verified. This provides an important technical path for the development of smart home appliance health management and has broad application prospects.
Claims
1. A deep learning-based method for predicting the lifespan of water dispenser filter cartridges, characterized in that, The method includes: collecting water quality sensor data, environmental sensor data, and usage pattern data; using an independent component analysis module to separate signals from the multi-sensor data, decomposing the observed signal matrix into a mixed matrix and independent source signal matrices; extracting physical clogging factors, chemical adsorption factors, biological pollution factors, temperature influence factors, and usage wear factors through iterative optimization of the separation vector; establishing a probabilistic evolution model of the filter cartridge's health status using a hidden Markov model module, defining six discrete health states: new product state, good state, slightly aged state, moderately aged state, heavily aged state, and failure state; calculating the state transition probability matrix and the observation probability matrix; and then using a forward pass... The algorithm calculates state probabilities; a fusion feature vector is constructed using a deep neural network module, vertically concatenating the original sensor features, the hidden Markov model state probability vector, the independent component analysis (ICA) independent component vector, and the algorithm interaction features, and then performing a nonlinear transformation through a multilayer perceptron structure to obtain the prediction result; an adaptive weight adjustment mechanism adjusts the fusion weights of the three algorithms in real time based on the current data features and algorithm performance, and dynamically calculates the weights based on the deep neural network algorithm reliability index, the hidden Markov model state confidence, and the ICA separation quality; the prediction results of the three algorithms are weighted and fused, and the final filter cartridge remaining life prediction value is generated by calculating the interaction term.
2. The method as described in claim 1, characterized in that, wherein... The independent component analysis module uses the FastICA algorithm to achieve signal separation. It optimizes the separation vector step by step by maximizing the non-Gaussianity of the output signal, so that the separated signal is as close as possible to statistical independence. The method also includes quantifying the non-Gaussianity of the separated signal by using a non-Gaussianity metric to find the separation result that is closest to the original independent signal.
3. The method as described in claim 1, characterized in that, The Hidden Markov Model module uses the independent components separated by Independent Component Analysis as observations, establishes the probabilistic relationship between states and observations through Gaussian mixture models, achieves deep integration of the two algorithms, and performs forward probability recursion calculations through dynamic programming to avoid exponential computational complexity.
4. The method as described in claim 1, characterized in that, The deep neural network module embeds the state information of the Hidden Markov Model in each layer of the neural network. By concatenating the state probability vector with the activation output of the previous layer as the input of the current layer, the deep fusion of the Hidden Markov Model and the deep neural network is achieved.
5. The method of claim 1, characterized in that, wherein... The algorithm's interactive features are obtained through Kronecker product and logarithmic transformation, and are used to capture the nonlinear relationship between the state probabilities of the Hidden Markov Model and the independent components of Independent Component Analysis. The hidden correlation patterns are revealed through logarithmic transformation and product operation.
6. The method as described in claim 1, characterized in that, The adaptive weight adjustment mechanism described herein uses a multilayer perceptron to calculate the weights of each algorithm, calculates the weights of the deep neural network algorithm based on the reliability index, data quality index, and prediction variance of the deep neural network algorithm, calculates the weights of the hidden Markov model based on state confidence, transition stability, and observation likelihood, and calculates the weights of the independent component analysis based on separation quality, noise level, and component stability.
7. A deep learning-based system for predicting the lifespan of water dispenser filter cartridges, characterized in that, The method described in any one of claims 1-6 further includes: a data acquisition module configured to acquire water quality sensor data, environmental sensor data, and usage pattern data in real time; a data preprocessing module configured to clean, normalize, and perform feature engineering on the raw data; an independent component analysis module configured to perform signal separation and noise suppression on multi-sensor data and extract the independent contributions of different physical degradation mechanisms; a hidden Markov model module configured to probabilistically model the evolution process of filter cartridge health status and establish a probability transition mechanism for filter cartridge health status; a deep neural network module configured to receive the outputs of the first two modules as enhancement features and achieve lifespan prediction through multi-layer nonlinear transformation; a fusion prediction module configured to collaboratively fuse the outputs of the three algorithm modules to generate the final lifespan prediction result; and an adaptive weight adjustment module configured to dynamically adjust the fusion weights of the three algorithms based on the current data characteristics and prediction quality.
8. The system of claim 7, characterized in that, wherein The independent component analysis module is also configured to separate different degradation factors, such as physical blockage, chemical adsorption, biological contamination, temperature effects, and wear and tear, from multidimensional sensor data by analogy between the sensor mixed signal and the multi-source signal mixing in medical signals.
9. The system as claimed in claim 7, characterized in that, The hidden Markov model module is also configured to describe the filter degradation process by establishing a mapping relationship between the filter health state and the evolution of biological state, and supports online parameter updates and model adaptation.
10. The system as claimed in claim 7, characterized in that, The system also includes an online learning mechanism configured to continuously optimize model parameters based on new data, enabling the system to adapt to dynamic factors such as equipment aging, environmental changes, and changes in usage patterns. Furthermore, the system is configured to perform end-to-end training using a multi-objective loss function, including mean squared error loss, state consistency loss, independent component analysis quality loss, and fusion regularization term.