Intelligent household electrical appliance fault detection method based on multi-sensor fusion

Abstract

The invention provides an intelligent household electrical appliance fault detection method based on multi-sensor fusion, relates to the field of fault detection, and provides a FUSION-Net fault detection model for multi-source intelligent household electrical appliance data, and the FUSION-Net fault detection model is composed of a multi-scale constraint module, an abnormal wave resistance module and a fault judgment module. The multi-scale constraint module realizes smooth alignment and dynamic stability of multi-scale features and improves abnormal change capture precision and model robustness, and a cross-scale response vector set generated by the abnormal wave resistance module realizes high-sensitivity detection of abnormal fluctuations, so that the accuracy and anti-interference capability of fault identification are improved, and the fault identification efficiency is improved. The fault judgment module can accurately distinguish normal and abnormal states, and the real-time performance and stability of fault recognition are improved.

Description

Technical Field

[0001] This invention belongs to the field of fault detection, specifically relating to a method for detecting faults in smart home appliances based on multi-sensor fusion. Background Technology

[0002] With the in-depth application of IoT and AI technologies, smart home appliance systems have evolved from single control units to multi-module collaborative systems encompassing sensing, communication, control, and learning capabilities. Home appliances are simultaneously affected by multiple factors, including electrical, mechanical, thermal, and environmental factors, during operation. Traditional single-sensor monitoring methods struggle to fully reflect the true state of the equipment. Minor current fluctuations, temperature anomalies, and vibration anomalies in home appliance compressors may be misjudged as normal fluctuations under single-channel observation, thus delaying the warning of potential faults. Multi-sensor fusion technology, by integrating multi-source data such as current, voltage, temperature, vibration, noise, and air pressure, provides a higher-dimensional and more robust perception foundation for the operating status of home appliances, representing a key path to solving the problem of hidden fault detection in complex systems.

[0003] The sensing layer of smart home appliances often contains sensors of different types and accuracy levels. These sensors differ in time synchronization, dimensional scale, and noise characteristics. Relying on a single signal can easily lead to local sensitivity or false alarms. Multi-sensor fusion can coordinate data at both the temporal and spatial levels. In the time domain, it enables dynamic correlation modeling of multi-channel signals and extracts cross-modal anomaly patterns. In the spatial domain, it achieves complementary information through feature-level and decision-level fusion, thereby improving the distinguishability and robustness of fault characteristics.

[0004] As home appliances evolve towards self-adaptation, energy efficiency, and remote operation and maintenance, users are placing higher demands on the system's autonomous perception, real-time early warning, and intelligent maintenance capabilities. Multi-sensor fusion provides the technological foundation for achieving this goal. By using deep learning methods to uniformly model the temporal characteristics, correlation characteristics, and abnormal patterns of various sensor signals, it is possible to instantly identify early degradation, component aging, or abnormal energy consumption in equipment. Summary of the Invention

[0005] This invention provides a fault detection method for smart home appliances based on multi-sensor fusion. For multi-source smart home appliance data, a FUSION-Net fault detection model is proposed, which consists of a multi-scale constraint module, an abnormal wave impedance module, and a fault judgment module.

[0006] The technical solution adopted by the present invention to achieve the above objectives specifically includes the following steps:

[0007] Collect data related to smart home appliances, construct a dataset, and preprocess and divide the dataset;

[0008] Construct a multi-scale constraint module: Segment smart home appliance data, use average pooling sampling, perform multi-scale sequence segmentation and embedding operations to obtain multi-scale embedding;

[0009] Input the multi-scale embedding design potential function, define the gradient equilibrium condition based on the potential function, and calculate the new multi-scale embedding sequence;

[0010] Extract scale nodes from the new multi-scale embedding sequence, construct local curvature factors, and build cross-scale mapping weights;

[0011] The cross-scale mapping weights are combined into a cross-scale mapping weight matrix as the input of the cross-scale potential energy function. Smooth equilibrium conditions are constructed, and after discretization, the cross-scale aligned set is obtained.

[0012] Construct an abnormal wave impedance module: map the cross-scale aligned set to the frequency domain, calculate the smart home appliance periodic sequence, generate a decision vector through a fully connected layer, calculate the query vector, divide the cross-scale aligned set into local subsequences, introduce disturbance terms and control parameters, and calculate the smart home appliance query vector;

[0013] The energy inter-mapping function is designed using smart home appliance query vectors and embedding centers, and a cross-scale response vector set is constructed based on the energy inter-mapping function.

[0014] Construct a fault diagnosis module: input a set of cross-scale response vectors to obtain the average cross-scale response vector, calculate the deviation value and time difference value, linearly combine them into a comprehensive judgment index, set threshold parameters to perform fault diagnosis, and output the fault detection results of smart home appliances.

[0015] Preferably, data related to smart home appliances are collected, including voltage, current, temperature, vibration, and power data of smart home appliances during the instantaneous power-on state, and a raw dataset is constructed for data preprocessing, and the dataset is divided in a 7:1:2 ratio.

[0016] Preferably, input smart home appliance data. , in length The sliding window is used to divide the sequence into segments, resulting in the sequence within the current window. ,in For the original scale, Using the starting time position of this window, average pooling downsampling with m different kernel sizes yields a multi-scale sequence from coarse to fine. The sequence time length satisfies T i <T i+1 Then, the multi-scale sequence is segmented, and embedding operations are performed using fully connected layers and positional encoding to obtain the embedded data. splicing fragments into multi-scale embeddings The specific mathematical model is as follows:

[0017] ;

[0018] In the formula, The number of time steps contained in each segment. The dimensions are mapped after each segment is embedded through a fully connected layer.

[0019] Preferably, the potential function of design time point t and neighboring time point k is... At scale i, multi-scale embeddings are input at intervals t and k. Through the time decay coefficient Construct the exponential decay term and simultaneously calculate the embedding. domain embedding The square of the Euclidean distance as an energy variable Substituting into the nonlinear potential energy response function Constructing the potential energy response term, we combine the exponential decay term with the potential energy response term to form the potential function. The specific mathematical model is as follows:

[0020] ;

[0021] In the formula, For the exponentially decaying term, where It is an exponentially decaying function. For the potential energy response term, where This is the operation of squaring the Euclidean distance. The potential energy response function has the following specific mathematical model:

[0022] ;

[0023] In the formula, The potential energy decay coefficient controls the rate of potential energy decay. Then, based on the potential function, a gradient equilibrium condition is defined to ensure that the sum of the embedding gradients at each time point is zero, thus constraining the symmetric equilibrium of potential energy between neighborhoods. The specific mathematical model is as follows:

[0024] ;

[0025] In the formula, For embedding The gradient operator is then introduced, followed by the introduction of an implicit weighting coefficient matrix. The change with embedding difference and time decay is defined by an implicit equation, and the specific mathematical model is as follows:

[0026] ;

[0027] Using the implicit weighted coefficient matrix as weights, and through neighborhood embedding... By performing a weighted solution, a balanced embedding is obtained. A perturbation gradient flow update rule is introduced, and a local energy term is defined. The difference is represented by the squared Euclidean distance between the embedded and balanced embedded systems, and combined with the energy terms of adjacent time steps, the neighborhood energy coupling coefficient is used to represent the difference. By modulating the influence of the neighborhood energy term, a perturbation gradient flow is formed. The specific mathematical model is as follows:

[0028] ;

[0029] In the formula, The energy terms are the energy terms for consecutive time steps, and then determined by the self-constraint coefficients. By controlling the propagation amplitude of the gradient flow, the update amount is superimposed on the current embedding to obtain a new balanced embedding. This process is repeated at all time points, and new balanced embeddings are sequentially combined to form new multi-scale embedding sequences. .

[0030] Preferably, the input is a new multi-scale embedding sequence. Embedded sequences at adjacent scales are extracted as fine-scale nodes. With coarse-scale nodes Construct cross-scale mapping weights Based on the ratio of the time length of the new multi-scale embedded sequence to the embedded sequences at its adjacent scales Calculate the scale ratio, and then construct the local curvature factor in the local neighborhood of each fine-scale node using the second-order difference between neighboring nodes. The specific mathematical model is as follows:

[0031] ;

[0032] In the formula, For Euclidean norm operations, To maintain stability and prevent the denominator from being zero, a topological curvature adjustment coefficient is introduced. This is combined with the local curvature factor to obtain the curvature adjustment term, and a topological distance term based on the node index difference is established, introducing an exponential decay coefficient. A weighted modulation kernel is constructed, and multiplied by the curvature adjustment term to form a cross-scale mapping weight. The specific mathematical model is as follows:

[0033] ;

[0034] In the formula, For weighted modulation kernel, where It is an exponentially decaying function. For topological distance, These are the fine-scale node index and the coarse-scale node index, respectively. This is the curvature adjustment term.

[0035] Preferably, the cross-scale mapping weights among all nodes are... Combined into a cross-scale mapping weight matrix As a subsequent cross-scale potential function The input, specifically the mathematical model, is as follows:

[0036] ;

[0037] In the formula, This represents the number of nodes at the coarse scale. For fine-scale nodes. For coarse-scale nodes, These are the fine-scale node indices and the coarse-scale node indices, respectively. The gradient term is obtained by calculating the partial derivative of the potential function with respect to the cross-scale potential at the fine-scale nodes, while a smoothing coefficient is introduced. The second-order difference term is computed at the fine-scale node index, and the gradient term is combined with the second-order difference term to form a smooth equilibrium condition. The specific mathematical model is as follows:

[0038] ;

[0039] In the formula, For smoothing coefficients, For gradient terms, For the second-order difference term, the smooth equilibrium condition is discretized, and the gradient term is discretized into a sum of weighted differences between nodes. The difference between each fine-scale node and a coarse-scale node is weighted by cross-scale mapping weights, and the second-order difference term is discretized into a second-order difference form. An update step size parameter is then introduced. and The specific mathematical model is as follows:

[0040] ;

[0041] In the formula, For the updated fine-scale nodes, combine the updated fine-scale nodes to obtain a cross-scale aligned set. .

[0042] Preferably, the input is a cross-scale aligned set. Mapping the set to the frequency domain using the frequency decomposition operator Extract the amplitude of each frequency component. With phase Based on the magnitude of the amplitude, the K main frequency components with the highest energy proportion are selected. Then, the selected main frequency amplitude and phase are inversely transformed to obtain the smart home appliance cycle sequence. The specific mathematical model is as follows:

[0043] ;

[0044] In the formula, For smart home appliances, a cyclical sequence The selected dominant frequency amplitude is then mapped and nonlinearly transformed through two fully connected layers to generate a decision vector. For the cross-scale aligned set, a sliding window is used to divide the local subsequences, and a query vector is calculated for each subsequence. Each query vector corresponds to a decision vector, and then a perturbation term following a log-Weiber distribution is introduced. With control parameters The decision vector and disturbance term are combined, and the normalized exponent weights are calculated. Then, all query vectors are weighted and summed to determine the smart home appliance query vector. The specific mathematical model is as follows:

[0045] ;

[0046] In the formula, It is an exponential function. The number of query vectors, This is a query vector for smart home appliances. For index parameters.

[0047] Preferably, the amplitude of the frequency component With phase Weighted average, to obtain the smart home appliance embedded center Design energy mapping function Introducing an exponential decay coefficient And with smart home appliance embedding center and smart home appliance query vector The square of the Euclidean distance between them is taken as input, and the oscillation frequency parameter is used as input. right and The inner product is used for periodic modulation, and the specific mathematical model is as follows:

[0048] ;

[0049] In the formula, Let be the energy mapping function between the s-th smart home appliance query vector and the k-th smart home appliance embedding center at time step t. It is an exponentially decaying function. The inner product of the smart home appliance embedding center and the smart home appliance query vector. Using the squared Euclidean distance as the basis, and based on the energy reciprocity function, the embedded centers of smart home appliances are weighted and aggregated to generate a unified cross-scale response vector. This constitutes a set of cross-scale response vectors. .

[0050] Preferably, the input is a set of cross-scale response vectors. Calculate the modulus and obtain the average cross-scale response vector using the number of vectors as the statistical range. The specific mathematical model is as follows:

[0051] ;

[0052] In the formula, The number of response vectors across scales. The cross-scale response vectors are then compared with the average cross-scale response vector to calculate the deviation value. The time difference value is calculated by comparing the magnitudes of the cross-scale response vectors corresponding to adjacent time steps t and t−1. Weighted parameters are used to control the relative influence of deviation values ​​and time difference values. A comprehensive judgment index is generated through linear combination. The specific mathematical model is as follows:

[0053] ;

[0054] In the formula, For weighted parameters, To comprehensively evaluate the indicators, threshold parameters are set. When the comprehensive index exceeds the threshold parameter, the current smart home appliance is determined to be faulty, and the smart home appliance fault detection result is output.

[0055] The advantages of the technical effects provided by the present invention in the above technical solution are as follows:

[0056] This invention achieves hierarchical modeling of smart home appliance operation data through multi-scale decomposition and embedding in the multi-scale constraint module, taking into account both global trends and local fluctuations. By constraining the embedding symmetry through potential functions and gradient balance conditions, it avoids mismatch between scales. Combined with perturbation gradient flow update and curvature adjustment mechanism, it achieves smooth alignment and dynamic stability of multi-scale features, improving the accuracy of abnormal change capture and model robustness.

[0057] This invention significantly enhances abnormal signals by mapping a cross-scale aligned set to the frequency domain in the abnormal wave impedance module, extracting the dominant frequency component and suppressing high-frequency noise. By combining the disturbance term and control parameters to construct an adaptive query vector, it can highlight the characteristics of weak abnormal waveforms. By establishing a periodic modulation relationship between the embedding center and the query vector through an energy cross-mapping function, it enables the coordinated representation of information in the frequency domain and time domain. The resulting cross-scale response vector set achieves highly sensitive detection of abnormal fluctuations, thereby improving the accuracy of fault identification and anti-interference capability.

[0058] This invention constructs a comprehensive judgment index that takes into account both static deviation and dynamic change by statistically analyzing cross-scale response vectors in the fault judgment module, calculating the average response quantity, deviation degree, and time difference degree. The influence intensity of both is adjusted by weighting parameters, and a threshold is set for adaptive fault judgment, realizing closed-loop discrimination from response characteristics to decision output. This module can accurately distinguish between normal and abnormal states, improving the real-time performance and stability of fault identification. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating the steps of a smart home appliance fault detection method based on multi-sensor fusion.

[0060] Figure 2 This is a diagram of a multi-scale constraint module.

[0061] Figure 3 This is a diagram of an abnormal wave impedance module.

[0062] Figure 4 This is an error distribution diagram of the FUSION-Net fault detection model.

[0063] Figure 5 This is a screenshot of the FUSION-Net fault detection model.

[0064] Figure 6 This is a histogram showing the distribution of comprehensive judgment indicators for the FUSION-Net fault detection model. Detailed Implementation

[0065] This invention proposes a fault detection method for smart home appliances based on multi-sensor fusion, the steps of which are as follows: Figure 1As shown, a FUSION-Net fault detection model is proposed for multi-source smart home appliance data. It consists of a multi-scale constraint module, an anomaly impedance module, and a fault judgment module. The multi-scale constraint module achieves hierarchical modeling of smart home appliance operation data through multi-scale decomposition and embedding, taking into account both global trends and local fluctuations. It avoids inter-scale mismatch by constraining embedding symmetry through potential functions and gradient balance conditions. Combined with perturbation gradient flow updates and curvature adjustment mechanisms, it achieves smooth alignment and dynamic stability of multi-scale features, improving the accuracy of anomaly capture and model robustness. The anomaly impedance module significantly enhances anomaly signals by mapping cross-scale aligned sets to the frequency domain, extracting the dominant frequency component, and suppressing high-frequency noise. It also constructs an adaptive fault detection model by combining perturbation terms and control parameters. The query vector can highlight the characteristics of weak abnormal waveforms. By establishing a periodic modulation relationship between the embedding center and the query vector through an energy cross-mapping function, the information in the frequency domain and time domain is represented in a coordinated manner. The resulting set of cross-scale response vectors enables highly sensitive detection of abnormal fluctuations, thereby improving the accuracy and anti-interference capability of fault identification. The fault judgment module performs statistical analysis on the cross-scale response vectors, calculates the average response, deviation, and time difference, and constructs a comprehensive judgment index that takes into account both static deviation and dynamic changes. By adjusting the influence intensity of both through weighted parameters and setting thresholds for adaptive fault judgment, a closed-loop discrimination from response characteristics to decision output is achieved. This module can accurately distinguish between normal and abnormal states, improving the real-time performance and stability of fault identification.

[0066] Collect data related to smart home appliances, construct a dataset, and preprocess and divide the dataset.

[0067] Furthermore, data acquisition for smart home appliances is conducted using a synchronous sampling and multi-channel fusion design to ensure high-precision capture and time consistency of smart home appliance signals during the power-on transient phase. The data acquisition system consists of five types of sensing units: voltage, current, temperature, vibration, and power. Voltage acquisition uses a Lem LV25-P differential sensor with a range of 0~250V, a bandwidth of 100kHz, and an accuracy of ±0.5%; current acquisition uses a Lem LA55-P Hall sensor with a range of 0~30A and a bandwidth of 50kHz; temperature acquisition uses a K-type thermocouple and a MAX6675 amplification module with a range of 0~400°C and a resolution of 0.25°C; vibration acquisition uses a triaxial accelerometer ADXL356 with a range of ±20g and a bandwidth of 2kHz; and power acquisition uses a PZEM-004T sensor. The v3.0 module has a measurement range of 0–5000W. All signals are time-stamped through a unified main control acquisition module with a time synchronization error of less than 1ms. The sampling frequency is set to 20kHz. Each channel uses a 24-bit ADC for sampling and is filtered and denoised at 10kHz. Each acquisition lasts for 10s, covering the first 2s before power-on, the 3s of startup transient, and the 5s of the stabilization phase. Data is divided into sliding windows with a window length of L=200ms and a step size of S=50ms. The acquisition phase includes 10 sets of normal operation samples and 5 sets of fault conditions, each lasting 10s. The acquired data is stored in CSV format. Each record contains a timestamp, voltage, current, temperature, triaxial vibration, power, and label fields. The experimental environment temperature is maintained at 25±2°C, humidity at 50±5%, and power supply voltage stability not exceeding ±1%. Zero drift calibration is performed before acquisition, and time synchronization verification and signal amplitude verification are executed. Each round of sampling outputs approximately 200,000 time steps of high-frequency data.

[0068] Construct multi-scale constraint modules, such as Figure 2 As shown, the module is: segmenting smart home appliance data, using average pooling sampling, performing multi-scale sequence segmentation and embedding operations to obtain multi-scale embedding.

[0069] Furthermore, input smart home appliance data , in length The sliding window is used to divide the sequence into segments, resulting in the sequence within the current window. ,in For the original scale, Using the starting time position of this window, average pooling downsampling with m different kernel sizes yields a multi-scale sequence from coarse to fine. The sequence time length satisfies T i <T i+1 Then, the multi-scale sequence is segmented, and embedding operations are performed using fully connected layers and positional encoding to obtain the embedded data. splicing fragments into multi-scale embeddings The specific mathematical model is as follows:

[0070] ;

[0071] In the formula, The number of time steps contained in each segment. The dimensions are mapped after each segment is embedded through a fully connected layer.

[0072] In this embodiment, the sliding window segmentation length is set to 2000. This value ensures that a single window can contain the complete electrical fluctuations of the startup transient without introducing redundant steady-state data. The average number of pooling kernels is set to 4, and four-scale fusion can effectively describe the asynchronous dynamics of multi-source signals.

[0073] Input the multi-scale embedding design potential function, define the gradient balance condition based on the potential function, and calculate the new multi-scale embedding sequence.

[0074] Furthermore, the potential function of time point t and its neighboring time point k is designed. At scale i, multi-scale embeddings are input at intervals t and k. Through the time decay coefficient Construct the exponential decay term and simultaneously calculate the embedding. domain embedding The square of the Euclidean distance as an energy variable Substituting into the nonlinear potential energy response function Constructing the potential energy response term, we combine the exponential decay term with the potential energy response term to form the potential function. The specific mathematical model is as follows:

[0075] ;

[0076] In the formula, For the exponentially decaying term, where It is an exponentially decaying function. For the potential energy response term, where This is the operation of squaring the Euclidean distance. The potential energy response function has the following specific mathematical model:

[0077] ;

[0078] In the formula, The potential energy decay coefficient controls the rate of potential energy decay. Then, based on the potential function, a gradient equilibrium condition is defined to ensure that the sum of the embedding gradients at each time point is zero, thus constraining the symmetric equilibrium of potential energy between neighborhoods. The specific mathematical model is as follows:

[0079] ;

[0080] In the formula, For embedding The gradient operator is then introduced, followed by the introduction of an implicit weighting coefficient matrix. The change with embedding difference and time decay is defined by an implicit equation, and the specific mathematical model is as follows:

[0081] ;

[0082] Using the implicit weighted coefficient matrix as weights, and through neighborhood embedding... By performing a weighted solution, a balanced embedding is obtained. A perturbation gradient flow update rule is introduced, and a local energy term is defined. The difference is represented by the squared Euclidean distance between the embedded and balanced embedded systems, and combined with the energy terms of adjacent time steps, the neighborhood energy coupling coefficient is used to represent the difference. By modulating the influence of the neighborhood energy term, a perturbation gradient flow is formed. The specific mathematical model is as follows:

[0083] ;

[0084] In the formula, The energy terms are the energy terms for consecutive time steps, and then determined by the self-constraint coefficients. By controlling the propagation amplitude of the gradient flow, the update amount is superimposed on the current embedding to obtain a new balanced embedding. This process is repeated at all time points, and new balanced embeddings are sequentially combined to form new multi-scale embedding sequences. .

[0085] In this embodiment, the time decay coefficient is set to 0.015. This setting is based on the extremely short interval between adjacent time steps at a sampling rate of 20kHz. This value can form a significant exponential decay gradient within the 0.1s transient interval, and the influence of distant time points decays rapidly, which helps to suppress the noise influence caused by long-term historical dependence, thereby focusing on the active dynamic changes of the initiation transient. The potential energy decay coefficient is set to 0.35 to control the nonlinear convergence speed of the potential energy response function. This value can achieve a balance between the high-frequency oscillation of the electrical signal and the slow change of the temperature signal, so that the potential energy function maintains a relatively smooth gradient transition in the multimodal characteristic space, avoiding out-of-range... Numerical oscillations caused by sudden energy changes are addressed. The neighborhood energy coupling coefficient is set to 0.42, reflecting the synergy between energy terms in adjacent time steps. This value allows the neighborhood energy to form a weak coupling band within 3 to 5 time steps, maintaining dynamic consistency while preventing excessive mutual reinforcement between adjacent energy terms, thus stabilizing the propagation of the perturbation gradient flow. The self-constraint coefficient is set to 0.68, which controls the amplitude of the gradient flow propagation. Its value is slightly higher than the neighborhood energy coupling coefficient, giving local energy differences a certain degree of dominance during updates. This promotes rapid convergence to equilibrium after local perturbations, achieving self-adjustment of the feature distribution between different sensing channels.

[0086] Extract scale nodes from the new multi-scale embedding sequence, construct local curvature factors, and build cross-scale mapping weights.

[0087] Furthermore, input new multi-scale embedding sequences Embedded sequences at adjacent scales are extracted as fine-scale nodes. With coarse-scale nodes Construct cross-scale mapping weights Based on the ratio of the time length of the new multi-scale embedded sequence to the embedded sequences at its adjacent scales Calculate the scale ratio, and then construct the local curvature factor in the local neighborhood of each fine-scale node using the second-order difference between neighboring nodes. The specific mathematical model is as follows:

[0088] ;

[0089] In the formula, For Euclidean norm operations, To maintain stability and prevent the denominator from being zero, a topological curvature adjustment coefficient is introduced. This is combined with the local curvature factor to obtain the curvature adjustment term, and a topological distance term based on the node index difference is established, introducing an exponential decay coefficient. A weighted modulation kernel is constructed, and multiplied by the curvature adjustment term to form a cross-scale mapping weight. The specific mathematical model is as follows:

[0090] ;

[0091] In the formula, For weighted modulation kernel, where It is an exponentially decaying function. For topological distance, These are the fine-scale node index and the coarse-scale node index, respectively. This is the curvature adjustment term.

[0092] In this embodiment, the stability constant is set to 1×10⁻⁶. -6 This value maintains sufficient numerical safety margin and resolution without amplifying or distorting the actual curvature value. The topological curvature adjustment coefficient is set to 0.27 to regulate the sensitivity of local curvature to cross-scale nodes. This value amplifies the second-order difference of local nodes in high curvature regions and suppresses it in smooth regions, thereby enhancing the structural identification capability of anomalous regions. The exponential decay coefficient is set to 0.45 to ensure effective coupling when there is an index difference between fine-scale and coarse-scale nodes, while rapidly decaying to below 0.1 after exceeding this range. This ensures that the cross-scale mapping weights are concentrated in locally adjacent regions, effectively preventing excessive coupling of distant nodes.

[0093] The cross-scale mapping weights are combined into a cross-scale mapping weight matrix, which is used as the input to the cross-scale potential function. Smooth equilibrium conditions are constructed, and after discretization, the cross-scale aligned set is obtained.

[0094] Furthermore, the cross-scale mapping weights among all nodes are... Combined into a cross-scale mapping weight matrix As a subsequent cross-scale potential function The input, specifically the mathematical model, is as follows:

[0095] ;

[0096] In the formula, This represents the number of nodes at the coarse scale. For fine-scale nodes. For coarse-scale nodes, These are the fine-scale node indices and the coarse-scale node indices, respectively. The gradient term is obtained by calculating the partial derivative of the potential function with respect to the cross-scale potential at the fine-scale nodes, while a smoothing coefficient is introduced. The second-order difference term is computed at the fine-scale node index, and the gradient term is combined with the second-order difference term to form a smooth equilibrium condition. The specific mathematical model is as follows:

[0097] ;

[0098] In the formula, For smoothing coefficients, For gradient terms, For the second-order difference term, the smooth equilibrium condition is discretized, and the gradient term is discretized into a sum of weighted differences between nodes. The difference between each fine-scale node and a coarse-scale node is weighted by cross-scale mapping weights, and the second-order difference term is discretized into a second-order difference form. An update step size parameter is then introduced. and The specific mathematical model is as follows:

[0099] ;

[0100] In the formula, For the updated fine-scale nodes, combine the updated fine-scale nodes to obtain a cross-scale aligned set. .

[0101] In this embodiment, the smoothing coefficient is set to 0.32. Setting it to 0.32 ensures that the gradient change of a node between adjacent scales maintains approximately 30% of the energy transfer ratio, thus maintaining the smoothing constraint while preserving local abrupt changes, allowing the potential function to exhibit a continuous transition in multi-scale mapping; update step size Setting it to 0.04 controls the magnitude of cross-scale gradient correction during discrete updates of the gradient term. This value corresponds to an energy decrease of approximately 3%–4% per iteration, ensuring sufficient gradient direction updates without exceeding limits, and adjusting the update step size. Setting it to 0.015 is used for discrete smoothing updates of the second-order difference term. When the value is small, it can stably constrain second-order oscillations, causing the differences between nodes to converge to a low-oscillation state. When the two are combined, the design of η1 > η2 can form a dynamic balance relationship of dominant adjustment and fine correction. That is, directional updates are first achieved with a larger gradient step size, and then the differential smoothing is stabilized with a smaller second-order step size, avoiding excessively fast energy propagation or over-smoothing.

[0102] Constructing an abnormal wave impedance module, such as Figure 3 As shown, the module is as follows: mapping the cross-scale aligned set to the frequency domain, calculating the smart home appliance periodic sequence, generating a decision vector through a fully connected layer, calculating a query vector, dividing the cross-scale aligned set into local subsequences, introducing perturbation terms and control parameters, and calculating the smart home appliance query vector.

[0103] Furthermore, input cross-scale aligned sets Mapping the set to the frequency domain using the frequency decomposition operator Extract the amplitude of each frequency component. With phase Based on the magnitude of the amplitude, the K main frequency components with the highest energy proportion are selected. Then, the selected main frequency amplitude and phase are inversely transformed to obtain the smart home appliance cycle sequence. The specific mathematical model is as follows:

[0104] ;

[0105] In the formula, For smart home appliances, a cyclical sequence The selected dominant frequency amplitude is then mapped and nonlinearly transformed through two fully connected layers to generate a decision vector. For the cross-scale aligned set, a sliding window is used to divide the local subsequences, and a query vector is calculated for each subsequence. Each query vector corresponds to a decision vector, and then a perturbation term following a log-Weiber distribution is introduced. With control parameters The decision vector and disturbance term are combined, and the normalized exponent weights are calculated. Then, all query vectors are weighted and summed to determine the smart home appliance query vector. The specific mathematical model is as follows:

[0106] ;

[0107] In the formula, It is an exponential function. The number of query vectors, This is a query vector for smart home appliances. For index parameters.

[0108] In this embodiment, the shape and size of the perturbation term, which follows a log-Weiber distribution, are set to 1. The value of this perturbation term can obtain a standardized, smooth, differentiable, and stable random perturbation term, ensuring that the perturbation energy is directly compatible with the model weight space without the need for normalization or numerical correction. The control parameter is set to 0.37, which can form an optimal balance between perturbation intensity and energy concentration, so that the decision vector corresponding to the main frequency obtains a weighting ratio of about 70%, thereby maintaining a consistent energy response ratio across different signal channels.

[0109] The energy inter-mapping function is designed using smart home appliance query vectors and embedding centers, and a cross-scale response vector set is constructed based on the energy inter-mapping function.

[0110] Furthermore, the amplitude of the frequency components With phase Weighted average, to obtain the smart home appliance embedded center Design energy mapping function Introducing an exponential decay coefficient And with smart home appliance embedding center and smart home appliance query vector The square of the Euclidean distance between them is taken as input, and the oscillation frequency parameter is used as input. right and The inner product is used for periodic modulation, and the specific mathematical model is as follows:

[0111] ;

[0112] In the formula, Let be the energy mapping function between the s-th smart home appliance query vector and the k-th smart home appliance embedding center at time step t. It is an exponentially decaying function. The inner product of the smart home appliance embedding center and the smart home appliance query vector. Using the squared Euclidean distance as the basis, and based on the energy reciprocity function, the embedded centers of smart home appliances are weighted and aggregated to generate a unified cross-scale response vector. This constitutes a set of cross-scale response vectors. .

[0113] In this embodiment, the exponential attenuation coefficient is set to 0.45 as above, and the oscillation frequency parameter is set to 1.57. This value can establish a moderate periodic modulation intensity in the energy distribution of multi-channel characteristics, so that the energy inter-band functions of different frequency bands have distinguishable peak intervals, thereby improving the distinguishability of abnormal energy patterns.

[0114] Construct a fault diagnosis module: input a set of cross-scale response vectors to obtain the average cross-scale response vector, calculate the deviation value and time difference value, linearly combine them into a comprehensive judgment index, set threshold parameters to perform fault diagnosis, and output the fault detection results of smart home appliances.

[0115] Input cross-scale response vector set Calculate the modulus and obtain the average cross-scale response vector using the number of vectors as the statistical range. The specific mathematical model is as follows:

[0116] ;

[0117] In the formula, The number of response vectors across scales. The cross-scale response vectors are then compared with the average cross-scale response vector to calculate the deviation value. The time difference value is calculated by comparing the magnitudes of the cross-scale response vectors corresponding to adjacent time steps t and t−1. Weighted parameters are used to control the relative influence of deviation values ​​and time difference values. A comprehensive judgment index is generated through linear combination. The specific mathematical model is as follows:

[0118] ;

[0119] In the formula, For weighted parameters, To comprehensively evaluate the indicators, threshold parameters are set. When the comprehensive index exceeds the threshold parameter, the current smart home appliance is determined to be faulty, and the smart home appliance fault detection result is output.

[0120] In this embodiment, the weighting parameters The values ​​were set to 0.62 and 0.38 respectively. The weight of deviation was slightly higher than that of time difference, indicating that the system pays more attention to the deviation of the modulus of the cross-scale response in fault identification than to short-term fluctuations, thereby improving the sensitivity to structural anomalies. The threshold parameter was set to 0.73. This value is located between the mean and the upper bound of the standard deviation of the index distribution under normal operating conditions, which can effectively distinguish between stable and abnormal states.

[0121] Furthermore, the FUSION-Net fault detection model was written in Python, and the experiments were run on a Windows operating system. PyTorch was used as the framework in the CUDA 11.27 environment, and training was performed on a GeForce RTX 3090. The optimizer was Adam, the initial learning rate was set to 0.001, the training batch size was set to 64, the training period was set to 100, and the dataset consisted of 60 days of smart home appliance-related data, which was preprocessed and then input into the FUSION-Net fault detection model.

[0122] Furthermore, the error distribution plot, performance graph, and comprehensive judgment index distribution histogram of the FUSION-Net fault detection model are shown below. Figure 4 , 5 As shown in Figure 6, Figure 4 The horizontal axis represents the prediction error, the vertical axis represents the probability density of the error, the gray histogram represents the discrete statistical results of the error probability density, and the black smooth curve is the kernel density estimation curve based on the Gaussian kernel function. As can be seen from the figure, the overall error distribution is approximately normal, with the center concentrated near zero. This indicates that the prediction output of the FUSION-Net model after multi-sensor signal fusion is highly consistent with the actual measured value, and the model prediction bias is small and the convergence is stable. Figure 5 The horizontal axis represents the sample index, and the vertical axis represents the comprehensive judgment index. In the figure, gray dots represent samples that the model identifies as being in a normal state, black solid dots represent samples that are detected as being in an abnormal state, hollow circles with black outer rings represent external samples that are judged by the system as being in a faulty or stopped state, and dashed lines represent the judgment threshold lines, which are used to distinguish between normal and abnormal samples. As can be seen from the figure, the detection results of the FUSION-Net model after multi-sensor signal fusion are clearly distributed. Abnormal samples form obvious clusters above the threshold, while normal samples are mainly concentrated in the low value region, indicating that the model has strong fault separation ability and robustness. Figure 6 The horizontal axis represents the comprehensive judgment index value, and the vertical axis represents the number of samples in the corresponding interval. The light gray area in the figure represents the distribution of normal samples, and the dark gray area represents the distribution of abnormal samples. The dashed line is the judgment threshold line, which is used to distinguish between normal operation and abnormal operation. It can be seen from the figure that the comprehensive judgment index of normal samples is mainly concentrated in the low value range of 0 to 0.5, showing a clear left-skewed distribution, while the index of abnormal samples is distributed in the high value range and forms a cluster to the right of the threshold. This shows that the FUSION-Net model can effectively distinguish between normal and abnormal states based on the comprehensive judgment index.

Claims

1. A method for fault detection of smart home appliances based on multi-sensor fusion, characterized in that, Includes the following steps: Collect data related to smart home appliances, construct a dataset, and preprocess and divide the dataset; Construct a multi-scale constraint module: Segment smart home appliance data, use average pooling sampling, perform multi-scale sequence segmentation and embedding operations to obtain multi-scale embedding; Input the multi-scale embedding design potential function, define the gradient equilibrium condition based on the potential function, and calculate the new multi-scale embedding sequence; Extract scale nodes from the new multi-scale embedding sequence, construct local curvature factors, and build cross-scale mapping weights; The cross-scale mapping weights are combined into a cross-scale mapping weight matrix as the input of the cross-scale potential energy function. Smooth equilibrium conditions are constructed, and after discretization, the cross-scale aligned set is obtained. Construct an abnormal wave impedance module: map the cross-scale aligned set to the frequency domain, calculate the smart home appliance periodic sequence, generate a decision vector through a fully connected layer, calculate the query vector, divide the cross-scale aligned set into local subsequences, introduce disturbance terms and control parameters, and calculate the smart home appliance query vector; The energy inter-mapping function is designed using smart home appliance query vectors and embedding centers, and a cross-scale response vector set is constructed based on the energy inter-mapping function. Construct a fault diagnosis module: input a set of cross-scale response vectors to obtain the average cross-scale response vector, calculate the deviation value and time difference value, linearly combine them into a comprehensive judgment index, set threshold parameters to perform fault diagnosis, and output the fault detection results of smart home appliances.

2. The intelligent home appliance fault detection method based on multi-sensor fusion according to claim 1, characterized in that, Input smart home appliance data , in length The sliding window is used to divide the sequence into segments, resulting in the sequence within the current window. ,in For the original scale, Using the starting time position of this window, average pooling downsampling with m different kernel sizes yields a multi-scale sequence from coarse to fine. The sequence time length satisfies T i <T i+1 Then, the multi-scale sequence is segmented, and embedding operations are performed using fully connected layers and positional encoding to obtain the embedded data. splicing fragments into multi-scale embeddings The specific mathematical model is as follows: ； In the formula, The number of time steps contained in each segment. The dimensions are mapped after each segment is embedded through a fully connected layer.

3. The intelligent home appliance fault detection method based on multi-sensor fusion according to claim 2, characterized in that, Potential functions at design time point t and neighboring time point k At scale i, multi-scale embeddings are input at intervals t and k. Through the time decay coefficient Construct the exponential decay term and simultaneously calculate the embedding. domain embedding The square of the Euclidean distance as an energy variable Substituting into the nonlinear potential energy response function Constructing the potential energy response term, we combine the exponential decay term with the potential energy response term to form the potential function. The specific mathematical model is as follows: ； In the formula, For the exponentially decaying term, where It is an exponentially decaying function. For the potential energy response term, where This is the operation of squaring the Euclidean distance. The potential energy response function has the following specific mathematical model: ； In the formula, The potential energy decay coefficient controls the rate of potential energy decay. Then, based on the potential function, a gradient equilibrium condition is defined to ensure that the sum of the embedding gradients at each time point is zero, thus constraining the symmetric equilibrium of potential energy between neighborhoods. The specific mathematical model is as follows: ； In the formula, For embedding The gradient operator is then introduced, followed by the introduction of an implicit weighting coefficient matrix. The change with embedding difference and time decay is defined by an implicit equation, and the specific mathematical model is as follows: ； Using the implicit weighted coefficient matrix as weights, and through neighborhood embedding... By performing a weighted solution, a balanced embedding is obtained. A perturbation gradient flow update rule is introduced, and a local energy term is defined. The difference is represented by the squared Euclidean distance between the embedded and balanced embedded systems, and combined with the energy terms of adjacent time steps, the neighborhood energy coupling coefficient is used to represent the difference. By modulating the influence of the neighborhood energy term, a perturbation gradient flow is formed. The specific mathematical model is as follows: ； In the formula, The energy terms are the energy terms for consecutive time steps, and then determined by the self-constraint coefficients. By controlling the propagation amplitude of the gradient flow, the update amount is superimposed on the current embedding to obtain a new balanced embedding. This process is repeated at all time points, and new balanced embeddings are sequentially combined to form new multi-scale embedding sequences. .

4. The intelligent home appliance fault detection method based on multi-sensor fusion according to claim 3, characterized in that, Input new multi-scale embedding sequence Embedded sequences at adjacent scales are extracted as fine-scale nodes. With coarse-scale nodes Construct cross-scale mapping weights Based on the ratio of the time length of the new multi-scale embedded sequence to the embedded sequences at its adjacent scales Calculate the scale ratio, and then construct the local curvature factor in the local neighborhood of each fine-scale node using the second-order difference between neighboring nodes. The specific mathematical model is as follows: ； In the formula, For Euclidean norm operations, To maintain stability and prevent the denominator from being zero, a topological curvature adjustment coefficient is introduced. This is combined with the local curvature factor to obtain the curvature adjustment term, and a topological distance term based on the node index difference is established, introducing an exponential decay coefficient. A weighted modulation kernel is constructed, and multiplied by the curvature adjustment term to form a cross-scale mapping weight. The specific mathematical model is as follows: ； In the formula, For weighted modulation kernel, where It is an exponentially decaying function. For topological distance, These are the fine-scale node index and the coarse-scale node index, respectively. This is the curvature adjustment term.

5. The intelligent home appliance fault detection method based on multi-sensor fusion according to claim 4, characterized in that, Cross-scale mapping weights among all nodes Combined into a cross-scale mapping weight matrix As a subsequent cross-scale potential function The input, specifically the mathematical model, is as follows: ； In the formula, This represents the number of nodes at the coarse scale. For fine-scale nodes. For coarse-scale nodes, These are the fine-scale node indices and the coarse-scale node indices, respectively. The gradient term is obtained by calculating the partial derivative of the potential function with respect to the cross-scale potential at the fine-scale nodes, while a smoothing coefficient is introduced. The second-order difference term is computed at the fine-scale node index, and the gradient term is combined with the second-order difference term to form a smooth equilibrium condition. The specific mathematical model is as follows: ； In the formula, For smoothing coefficients, For gradient terms, For the second-order difference term, the smooth equilibrium condition is discretized, and the gradient term is discretized into a sum of weighted differences between nodes. The difference between each fine-scale node and a coarse-scale node is weighted by cross-scale mapping weights, and the second-order difference term is discretized into a second-order difference form. An update step size parameter is then introduced. and The specific mathematical model is as follows: ； In the formula, For the updated fine-scale nodes, combine the updated fine-scale nodes to obtain a cross-scale aligned set. .

6. The intelligent home appliance fault detection method based on multi-sensor fusion according to claim 1, characterized in that, Input cross-scale aligned sets Mapping the set to the frequency domain using the frequency decomposition operator Extract the amplitude of each frequency component. With phase Based on the magnitude of the amplitude, the K main frequency components with the highest energy proportion are selected. Then, the selected main frequency amplitude and phase are inversely transformed to obtain the smart home appliance cycle sequence. The specific mathematical model is as follows: ； In the formula, For smart home appliances, a cyclical sequence The selected dominant frequency amplitude is then mapped and nonlinearly transformed through two fully connected layers to generate a decision vector. For the cross-scale aligned set, a sliding window is used to divide the local subsequences, and a query vector is calculated for each subsequence. Each query vector corresponds to a decision vector, and then a perturbation term following a log-Weiber distribution is introduced. With control parameters The decision vector and disturbance term are combined, and the normalized exponent weights are calculated. Then, all query vectors are weighted and summed to determine the smart home appliance query vector. The specific mathematical model is as follows: ； In the formula, It is an exponential function. The number of query vectors, This is a query vector for smart home appliances. For index parameters.

7. The intelligent home appliance fault detection method based on multi-sensor fusion according to claim 6, characterized in that, The amplitude of the frequency component With phase Weighted average, to obtain the smart home appliance embedded center Design energy mapping function Introducing an exponential decay coefficient And with smart home appliance embedding center and smart home appliance query vector The square of the Euclidean distance between them is taken as input, and the oscillation frequency parameter is used as input. right and The inner product is used for periodic modulation, and the specific mathematical model is as follows: ； In the formula, Let be the energy mapping function between the s-th smart home appliance query vector and the k-th smart home appliance embedding center at time step t. It is an exponentially decaying function. The inner product of the smart home appliance embedding center and the smart home appliance query vector. Using the squared Euclidean distance as the basis, and based on the energy reciprocity function, the embedded centers of smart home appliances are weighted and aggregated to generate a unified cross-scale response vector. This constitutes a set of cross-scale response vectors. .

8. The intelligent home appliance fault detection method based on multi-sensor fusion according to claim 7, characterized in that, Input cross-scale response vector set Calculate the modulus and obtain the average cross-scale response vector using the number of vectors as the statistical range. The specific mathematical model is as follows: ； In the formula, The number of response vectors across scales. The cross-scale response vectors are then compared with the average cross-scale response vector to calculate the deviation value. The time difference value is calculated by comparing the magnitudes of the cross-scale response vectors corresponding to adjacent time steps t and t−1. Weighted parameters are used to control the relative influence of deviation values ​​and time difference values. A comprehensive judgment index is generated through linear combination. The specific mathematical model is as follows: ； In the formula, For weighted parameters, To comprehensively evaluate the indicators, threshold parameters are set. When the comprehensive index exceeds the threshold parameter, the current smart home appliance is determined to be faulty, and the smart home appliance fault detection result is output.

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