A sash sag fault diagnosis method based on hinge rotation resistance curve analysis

Abstract

The present application relates to a kind of sash droop fault diagnosis method based on hinge rotation resistance curve analysis.The method is proposed to collect multi-dimensional time series data of sash opening and closing process, and to realize real-time abnormality discrimination of resistance curve and accurate identification of droop type fault through intelligent analysis based on semantic distance and aging factor, after synchronous preprocessing, motion template normalization, individualized motion memory atlas construction and its dynamic self-updating, to solve the problems of low detection accuracy, difficulty in individualized adaptation and insufficient environmental disturbance robustness of traditional sash mechanical motion abnormality.The technology not only can dynamically adapt to mechanical wear and environmental change trend, but also has the ability of phased maintenance warning and fault knowledge evolution, which significantly improves the intelligence and reliability of sash health management.

Description

Technical Field

[0001] This invention relates to the field of building intelligent operation and maintenance and mechanical fault detection technology, and in particular to a method for diagnosing window sash sagging faults based on hinge rotation resistance curve analysis. Background Technology

[0002] Currently, in the field of intelligent building operation and maintenance and mechanical fault detection, especially in the detection of abnormal window sash sagging, mainstream technologies mostly adopt the following modes: one relies on resistance curve analysis based on static thresholds, using preset limit values ​​as fault judgment criteria; another uses simple periodic feature modeling, such as establishing a reference curve by selecting a period of data from the initial service period, and then directly comparing the deviation of subsequent real-time data with it to detect anomalies. In the above methods, the signal preprocessing level is mostly based on single-point numerical detection or interval statistics. Some schemes introduce environmental factor correction, but most of them are linear weighting, lacking effective deep integration of historical and real-time data.

[0003] In recent years, data-driven fault detection solutions have emerged in the industry. These solutions utilize machine learning algorithms (such as SVM, decision trees, or weakly supervised self-learning methods) to identify complex motion behaviors. However, these solutions often require a large number of pre-labeled aging tags or rely on redundant verification using multi-source sensor data. Furthermore, some cutting-edge research focuses on time-series anomaly detection, using techniques such as stacked moving averages (e.g., EWMA), clustering, and slope weighting to mitigate the impact of parameter settings on detection performance. However, these technologies still suffer from cold-start dependence, threshold rigidity, weak adaptability to individual device differences, and sensitivity to short-term environmental disturbances.

[0004] In practical building intelligent operation and maintenance scenarios, window sashes, as typical high-frequency mechanical actuators, are significantly affected by the aging process of their wear and tear due to factors such as opening and closing methods (manual / electric / wind-induced, etc.), ambient temperature and humidity, operating frequency, and the higher-order coupling effects of various stress disturbances. Existing detection technologies based on single-cycle templates or static reference models cannot fully reflect the behavioral evolution characteristics of equipment throughout its lifecycle. Traditional anomaly identification solutions often face the following limitations: First, the inability to dynamically adapt to the performance changes of the window sash itself during long-term use leads to an increase in false alarm rate or serious missed detection during the aging process.

[0005] Second, it is difficult to efficiently correlate multi-source data such as historical operating conditions, environmental disturbances, and mechanical motion characteristics, and there is a lack of spatiotemporal integrated abnormal evolution genealogy and health fingerprint.

[0006] Third, the judgment mechanism relies heavily on manually set empirical thresholds and simple statistical models, making it difficult to balance the accuracy and robustness of the detection.

[0007] In addition, although some existing intelligent detection systems attempt to use learning algorithms for adaptive adjustment, they often rely on a large number of labeled samples or model transfer learning, resulting in high deployment and on-site maintenance costs. Furthermore, they are difficult to perform dedicated trajectory sedimentation and semantic behavior evolution modeling for individual operating entities, lacking a deep mapping of the nonlinear aging characteristics of individual equipment, and are susceptible to misjudgment due to short-term and drastic environmental changes.

[0008] Therefore, existing technologies urgently need an innovative solution that can achieve the following objectives: This approach truly achieves deep spatiotemporal fusion of historical usage data and current real-time motion characteristics, dynamically establishing a unique motion memory map for each window sash. It incorporates the influence of multiple factors such as equipment aging, environmental disturbances, and operational diversity into the detection paradigm, abandoning static thresholds and fixed templates to form a sagging anomaly discrimination mechanism with time-evolutionary, personalized adaptability, environmental robustness, and self-driven learning capabilities. Only in this way can the accuracy of sagging fault diagnosis at each stage of the window sash lifecycle be effectively improved in intelligent building operation and maintenance scenarios, achieving true equipment health self-growth and accurate fault prediction, providing new technical support for building energy efficiency, comfort, and safety. Summary of the Invention

[0009] This application provides a method for diagnosing window sash sagging faults based on hinge rotation resistance curve analysis, aiming to solve one of the problems or issues of the prior art mentioned in the background.

[0010] This application provides a method for diagnosing window sash sagging based on hinge rotation resistance curve analysis, specifically including: S1: Obtain the raw data of the window sash during the opening and closing process, and synchronously record the human triggering method label and duration of each operation to generate the raw dataset of window sash motion.

[0011] S2: Perform time normalization and phase alignment on the original dataset of the window sash motion to generate a motion template sequence.

[0012] S3: Based on the motion template sequence, a sliding window is used to merge the newly added motion data increments that have passed the consistency check into the historical trajectory cluster, and to construct a window individualized motion memory map containing multi-dimensional trajectory clusters, typical resistance inflection point distribution density and transient response delay heatmap.

[0013] S4: Obtain the hinge rotation resistance curve, map the hinge rotation resistance curve to the high-dimensional embedding space of the window sash individualized motion memory map, calculate the semantic distance between the current resistance curve and each historical stage sub-cluster in the map, and generate a semantic distance vector.

[0014] S5: Based on the environmental temperature and humidity change rate, the initial response delay offset, and the resistance fluctuation entropy in the middle uniform speed zone in the recent operations, the aging factor is generated by weighted fusion with the semantic distance vector.

[0015] S6: The aging factor is used to modulate the resistance tolerance bandwidth corresponding to the aging stage in the individualized motion memory map of the window sash, thereby generating a personalized deviation judgment boundary.

[0016] S7: Determine whether the hinge rotation resistance curve currently in real-time exceeds the personalized deviation judgment boundary, and detect whether its deviation mode matches the drooping fault topology signature marked in the map, and generate a fault discrimination result.

[0017] S8: If the fault identification result is confirmed as a real anomaly, output the window sash sagging fault diagnosis signal and trigger the maintenance warning, and update the feature data of the anomaly event in reverse to the window sash individualized motion memory map to complete the adaptive evolution of the window sash individualized motion memory map.

[0018] This application provides a window sash sagging fault diagnosis method based on hinge rotation resistance curve analysis, which has the following beneficial effects: (1) By constructing a motion memory map specific to each window sash, the technical bottleneck of high false alarm rate and poor adaptability caused by the reliance on static thresholds or general periodic models in traditional anomaly detection methods is overcome, and dynamic perception and accurate identification of window sash aging trends and fault modes are realized. In existing technologies, fixed resistance thresholds or unified models based on batch sample training are generally used for fault judgment, which is difficult to cope with the problem of large differences in the service conditions of individual window sashes in the building environment and inconsistent degradation paths. They are also easily affected by short-term temperature and humidity fluctuations, changes in operation methods, etc., which may lead to misjudgment. This solution abandons such rigid criteria and instead transforms the qualified motion data accumulated by the window sash in the initial stage into a first-version basic motion template. Through a sliding window mechanism, it continuously integrates subsequent operation records that have passed consistency verification, gradually evolving into a structured knowledge base containing multi-dimensional trajectory clusters, resistance inflection point density distribution, and response delay heatmaps. This enables the system to have historical memory of its normal behavior. Based on this, during real-time diagnosis, it not only compares the numerical deviation of the current resistance curve but also maps it to a high-dimensional embedding space, calculating its semantic distance to subclusters of different life cycle stages in the graph. This allows it to capture subtle but evolutionarily significant aging signals, significantly improving the detection sensitivity and reliability of early sagging faults.

[0019] (2) The innovative introduction of aging factor and dynamic tolerance boundary generation mechanism realizes the personalization, self-evolution and context awareness of the abnormal judgment boundary, effectively solves the decision imbalance problem under multi-objective conflict, and greatly enhances the robustness and long-term operation stability of the system under complex working conditions. Unlike traditional methods that manually set attenuation curves or rely on externally labeled data to build degradation models, this solution is entirely based on the statistical accumulation of the window sash's own historical behavior to drive the evolution of the spectral map, without the need for preset aging labels or manual parameter tuning. By comprehensively considering three indicators—the rate of change of ambient temperature and humidity, the initial response delay offset, and the resistance fluctuation entropy in the mid-range uniform speed zone—an aging factor reflecting the current health status of the equipment is dynamically generated. This factor is then used to weight and adjust the historical resistance tolerance bandwidth for the corresponding stage, forming a personalized deviation boundary that naturally expands with the equipment's life cycle. This boundary is not static but adaptively adjusts with usage frequency, environmental load, and mechanical wear, ensuring that false alarms are not triggered by accumulated deviations during normal aging of the equipment. At the same time, the final judgment also needs to match the drooping fault topology signature marked in the spectral map (such as the combined characteristics of low-speed plateau rise and high-speed slope attenuation). This dual constraint mechanism effectively distinguishes between functional degradation and real structural faults, significantly reducing the false alarm rate and the risk of missed alarms.

[0020] (3) A new paradigm for device behavior modeling with “physical language” as the cognitive framework is proposed. The window movement process is regarded as a time-series language that can be remembered, evolved and semantically parsed. The abnormal diagnosis logic in intelligent operation and maintenance is reconstructed from the bottom layer, giving the system zero cold start dependency, strong individual adaptability and resistance to short-term disturbances. This solution avoids mainstream time-series analysis techniques such as LSTM prediction, SVM classification, EWMA smoothing, and CUSUM cumulative analysis, and also avoids complex architecture dependencies such as multi-source sensor redundancy verification, transfer learning, or reinforcement learning. Instead, it achieves efficient abstraction and long-term tracking of the essential characteristics of device motion through lightweight processing such as time normalization, phase alignment, and incremental fusion. The entire diagnostic process requires no manual intervention in the initial calibration stage and does not rely on data support from other similar devices. Newly installed window sashes can autonomously generate their first template after completing no less than 30 qualified operations and enter a continuous evolution state, truly achieving "install and use immediately" and "increasing accuracy with use." In addition, since the judgment is based on the inherent evolution law of the device's own behavior pattern, it has a natural filtering ability for transient interferences such as sudden changes in the external environment and occasional operational anomalies, avoiding the problem of chain misjudgments triggered by local fluctuations in traditional methods. This method is not only applicable to high-end scenarios such as building curtain walls and intelligent ventilation systems, but can also be extended to various electromechanical devices with repetitive motion characteristics, possessing good interpretability, scalability, and engineering implementation value.

[0021] The aforementioned technologies work together to construct a closed-loop adaptive diagnostic system that requires no external tags, no manual parameter tuning, and no reliance on complex algorithm stacks. This system achieves a leap from "passive alarm" to "proactive understanding," significantly reducing operation and maintenance costs and deployment barriers while ensuring detection accuracy. It provides a new technical path for intelligent building operation and maintenance that is highly reliable, has a long cycle, and requires minimal intervention. Attached Figure Description

[0022] Figure 1 This is the main flowchart of a window sash sagging fault diagnosis method based on hinge rotation resistance curve analysis.

[0023] Figure 2 This is a sub-flowchart of a window sash sagging fault diagnosis method based on hinge rotation resistance curve analysis.

[0024] Figure 3 This is another sub-flowchart of a window sash sagging fault diagnosis method based on hinge rotation resistance curve analysis. Detailed Implementation

[0025] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0026] The following disclosure provides many different embodiments or examples for implementing different structures of the invention. To simplify the disclosure, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the invention. Furthermore, reference numerals and / or letters may be repeated in different examples; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed.

[0027] like Figure 1 As shown, this application provides a method for diagnosing window sash sagging faults based on hinge rotation resistance curve analysis, specifically including: S1: Obtain the raw data of the window sash during the opening and closing process, and synchronously record the human triggering method label and duration of each operation to generate the raw dataset of window sash motion.

[0028] S2: Perform time normalization and phase alignment on the original dataset of the window sash motion to generate a motion template sequence.

[0029] S3: Based on the motion template sequence, a sliding window is used to merge the newly added motion data increments that have passed the consistency check into the historical trajectory cluster, and to construct a window individualized motion memory map containing multi-dimensional trajectory clusters, typical resistance inflection point distribution density and transient response delay heatmap.

[0030] S4: Obtain the hinge rotation resistance curve, map the hinge rotation resistance curve to the high-dimensional embedding space of the window sash individualized motion memory map, calculate the semantic distance between the current resistance curve and each historical stage sub-cluster in the map, and generate a semantic distance vector.

[0031] S5: Based on the environmental temperature and humidity change rate, the initial response delay offset, and the resistance fluctuation entropy in the middle uniform speed zone in the recent operations, the aging factor is generated by weighted fusion with the semantic distance vector.

[0032] S6: The aging factor is used to modulate the resistance tolerance bandwidth corresponding to the aging stage in the individualized motion memory map of the window sash, thereby generating a personalized deviation judgment boundary.

[0033] S7: Determine whether the hinge rotation resistance curve currently in real-time exceeds the personalized deviation judgment boundary, and detect whether its deviation mode matches the drooping fault topology signature marked in the map, and generate a fault discrimination result.

[0034] S8: If the fault identification result is confirmed as a real anomaly, output the window sash sagging fault diagnosis signal and trigger the maintenance warning, and update the feature data of the anomaly event in reverse to the window sash individualized motion memory map to complete the adaptive evolution of the window sash individualized motion memory map.

[0035] Step S1: Obtain the raw data of the window sash during the opening and closing process, and synchronously record the manual triggering method label and duration of each operation to generate the raw dataset of window sash motion. Specifically, this includes: S1.1: Configure multi-channel synchronous triggering for angle sensors, torque sensors, and ambient temperature and humidity sensors deployed at window hinges to eliminate timing jitter caused by different sampling clocks and generate multi-source sensor raw signal streams with a unified timestamp reference.

[0036] When configuring multi-channel synchronous triggering for angle sensors, torque sensors, and ambient temperature and humidity sensors deployed at window hinges, it is necessary to obtain the independent sampling clock frequency and trigger delay parameters of each sensor as initial conditions. Based on these initial conditions, the synchronous triggering control module generates a logical synchronization signal using its internal time base and implements unified constraints on the start moment of data acquisition for each sensor through a hardware timer. Utilizing the delay compensation function of the triggering control module, the inherent delay values ​​of each sensor during the transmission link or sampling buffer process are written into the delay compensation register to eliminate time drift caused by hardware differences. A unified timestamp calibration operation is performed on the multi-source raw signal sequences acquired through synchronous triggering, remapping the timestamps of all sampling points to a global clock reference, thereby achieving consistency of cross-sensor data in physical time. The sampling synchronization calibration algorithm is invoked to calculate the difference between the actual trigger time and the theoretical trigger time of each channel using the global clock reference. Correction is performed by interpolation or discarding samples that do not meet the tolerance threshold, generating a multi-source sensor raw signal stream that eliminates timing jitter. By using the above-mentioned multi-channel synchronous triggering and unified timestamp calibration processing method, the sensor deployment results of the previous step are transformed into a multi-source raw signal stream with consistent physical time and no temporal drift, so as to achieve the high-precision time alignment effect required for subsequent motion feature extraction.

[0037] For example, in the initial deployment phase of a building's intelligent window system, the angle sensor sampling frequency is configured to 200Hz, the torque sensor to 100Hz, and the ambient temperature and humidity sensor to 10Hz, with trigger delays of 1.5ms, 2ms, and 5ms respectively. The synchronous trigger control module sets the global clock frequency to 1kHz and defines a trigger tolerance threshold of ±0.5ms. During data acquisition, the sampled data from each sensor is calibrated with a global timestamp, and the delay compensation registers are written with corresponding values ​​of 1.5ms, 2ms, and 5ms, respectively, and compensation is performed at the moment of triggering. After sampling, the sampling synchronization calibration algorithm is called to calculate the trigger time deviation, revealing a deviation of +0.4ms for the angle sensor and a deviation of +0.4ms for the torque sensor. The deviations of 0.3ms and +0.2ms from the ambient temperature and humidity sensors are both within the tolerance threshold. After interpolation correction, the time error of each channel sampling point in the generated multi-source sensor raw signal stream does not exceed 0.5ms throughout the entire cycle, which significantly improves the time consistency of multi-sensor data fusion and ensures the accuracy of subsequent sliding differential and feature extraction processes.

[0038] S1.2: Based on the original signal stream from the multi-source sensors, the angular displacement data is processed in real time using a sliding differential algorithm to obtain instantaneous angular velocity data, and combined with the readings from the torque sensor to generate a mechanical motion feature vector sequence containing rotation angle, instantaneous angular velocity, and driving torque.

[0039] S1.3: Execute the operation event boundary detection algorithm on the mechanical motion feature vector sequence to identify the start and end points of the window sash opening and closing action, extract mechanical motion feature vector segments of no less than thirty consecutive complete opening and closing processes, and generate a candidate complete opening and closing process dataset.

[0040] Multidimensional feature synchronous parsing is performed on the mechanical motion feature vector sequence generated by the preceding step S1.2. The angle change rate and torque amplitude detection module is called to identify the candidate positions of the feature starting point of potential operation events. During the detection process, the local threshold is dynamically adjusted to adapt to the speed fluctuation range existing in the same sequence.

[0041] Based on the derivative shape of the angular velocity along the time axis of the candidate starting position and adjacent feature points, a bidirectional extended scanning algorithm is executed. It backtracks to the stationary state point where the angular velocity is continuously zero and the torque is stable at the reference value, and advances to the state point where the angular velocity recovers to the reference stationary value for the first time in the whole cycle and remains unchanged, so as to calibrate the candidate position for the termination of the operation event.

[0042] The event boundary refinement module is invoked to smooth the boundary of the intermediate segment between the starting candidate and the ending candidate according to the synchronous change curve of angular velocity and torque, eliminate pseudo-events caused by the temporary action of external force, and retain the complete action cycle that meets the continuity constraint.

[0043] The application time length consistency check compares the corrected action cycle with the preset shortest and longest physical operation time limits, retaining only the legal cycles within the specified range, ensuring that the candidate dataset covers physically reasonable window opening and closing processes.

[0044] For the valid cycle, the sequence is truncated, and the corresponding rotation angle, instantaneous angular velocity and driving torque vector segments are extracted respectively. All segments are arranged in order of timestamp to form a complete switching process dataset of no less than thirty consecutive cycles as candidate output.

[0045] Through the above-mentioned operation event boundary detection and legality verification processing, the mechanical motion feature vector sequence generated in the previous step is transformed into a candidate complete switch process dataset with clear start and end marks and unified multi-dimensional features, thus achieving the effect of constructing a stable input source.

[0046] For example, the angle sensor deployed at the window hinge has a sampling frequency of 200Hz, and the torque sensor has a sampling frequency of 500Hz. After synchronous triggering configuration in the preceding steps, a mechanical motion feature vector sequence with a unified timestamp reference is generated. In one embodiment, using an angular velocity change rate threshold set to 0.05 rad / s and a torque amplitude change threshold set to 0.2 N·m, the event start point detection module identifies the 115th point in the sequence as a starting candidate. The bidirectional extension algorithm backtracks 15 points before the starting candidate to find the stationary state point, and advances 205 points after the starting candidate to find the termination candidate. After smoothing and correcting this segment of the sequence, the time length is 1.8 seconds, which conforms to the preset physical operation interval of 1.0 seconds. 3.0 seconds. This period was truncated, and three types of vector segments were extracted: rotation angle, instantaneous angular velocity, and driving torque. After repeating the processing of all legal action cycles in the sequence, 32 complete switching process segments whose durations all satisfy the interval constraints were finally obtained, forming a candidate complete switching process dataset. The verification results show that the start and end boundary recognition deviation of this dataset is less than 5 milliseconds, demonstrating high stability and accuracy.

[0047] S1.4: Based on the candidate complete switch process dataset, the control instructions or manual intervention signals are parsed through a logic state machine, and the manual triggering method label and action duration corresponding to each operation are extracted to generate an operation metadata set with semantic annotation.

[0048] S1.5: The semantically labeled set of operation metadata is fused with the candidate complete switch process dataset using key-value alignment to construct a window motion original dataset containing multi-dimensional time series information, environmental context and operation semantics, which serves as the standard input object for subsequent time normalization processing.

[0049] Step S2: Perform time normalization and phase alignment on the original dataset of window sash motion to generate a motion template sequence. Specifically, this includes: S2.1: Obtain the original dataset of window sash motion, which includes hinge rotation angle, angular velocity, driving torque, and ambient temperature and humidity. Based on the human triggering method label and duration recorded for each operation, perform linear interpolation resampling processing on each time-series trajectory in the original dataset of window sash motion to map the variable-length non-uniform sampling sequence into a fixed-length, equally spaced discrete data point sequence, thereby generating a window sash resampling time-series sequence with uniform sampling density.

[0050] A raw dataset of window sash motion, including hinge rotation angle, angular velocity, driving torque, and ambient temperature and humidity, is obtained. Based on the human triggering method label and action duration in the operation metadata, a time index parsing engine is invoked to map the raw sampling points of each time-series trajectory to the physical time axis. For trajectories with varying durations, a sampling density calculation model is constructed, generating a resampling control parameter set by calculating the ratio between the target number of sampling points and the actual sampling frequency. Linear interpolation is performed on non-uniform sampling trajectories based on the control parameter set. During interpolation, a local segmented calculation strategy is adopted to proportionally distribute the numerical differences between adjacent sampling points in the original trajectory to discrete time points under the target fixed sampling interval, thereby avoiding feature smoothing loss caused by global interpolation. For the fixed-length sequence after interpolation, a sampling point position index reconstruction operation is performed, ensuring that all sequences have a consistent sampling step size and time index structure under the same sampling density conditions. The four multi-dimensional features—angle, angular velocity, torque, and temperature and humidity—are synchronously stored in the corresponding dimensional positions of the sequence. The above resampling process transforms the original window motion dataset obtained in the previous step into a window resampling time sequence with uniform sampling density, fixed length, and synchronized arrangement of multi-dimensional features, thus achieving the strict time reference required for subsequent phase alignment and time normalization.

[0051] For example, in a building's intelligent window system, the duration of thirty opening and closing operations of the window sash during the initial service phase ranged from 2.3 seconds to 4.8 seconds, with the sampling frequency fluctuating between 50Hz and 85Hz depending on the triggering method. The target sampling length was set to 200 points, and the interpolation step size for each trajectory was calculated using a scaling factor. If the original trajectory length was 132 points, the scaling factor would be 200 / 132≈1.515, which was then used as an interpolation control factor in the piecewise interpolation model. During interpolation, piecewise linear interpolation was used in the angular velocity dimension to preserve the slope characteristics of the acceleration segment, and the mean of adjacent points was used to complete the interpolation in the driving torque dimension to reduce the impact of mechanical noise. Taking temperature and humidity as an example, when the temperatures of two adjacent points are 22.1℃ and 22.4℃ respectively, and the target interpolation point is located at 1 / 3 of the distance between the two points, the interpolation temperature = 22.1 + (22.4 - 22.1) × (1 / 3) ≈ 22.2℃. The window sash resampling time series formed after interpolation has been verified to maintain a uniform sampling density in all dimensions and significantly improve the accuracy of automatic identification in the motion phase, providing a steady-state and high-confidence time reference for subsequent phase alignment processing.

[0052] S2.2: Based on the hinge rotation angle change rate feature in the window sash resampling time sequence, the sliding differential window algorithm is used to perform motion stage boundary detection processing to identify the stationary starting point, acceleration turning point and uniform stable region in each opening and closing process, and generate a motion stage feature index set marked with the location of key motion events.

[0053] S2.3: Based on the static starting point position determined in the motion phase feature index set, perform zero-phase dynamic time warping and alignment processing on the window sash resampled time sequence to eliminate the starting time delay deviation between different operation samples and force the time zero point of all trajectories to converge to the same physical state, generating a window sash phase-aligned time sequence with a unified time starting point.

[0054] The motion phase feature index set and window sash resampling time sequence output from the preceding step S2.2 are obtained. The stationary starting point position in the index set is used as the alignment reference input. The zero-phase dynamic time warping processing engine is invoked to perform a reference position locking operation to determine the physical state zero point of each operation sample. For the window sash resampling time sequence with the zero point located, phase difference calculation is performed to generate a delay offset matrix. The elements of this matrix consist of the difference between the zero point timestamp of each trajectory and the global reference zero point timestamp. Using the dynamic time warping algorithm, positive value samples in the delay offset matrix are shifted forward on the time axis, and negative value samples are shifted backward on the time axis, ensuring that the time zero point of each trajectory converges to the same reference state. For the trajectory sequence corrected by time axis translation, high-precision interpolation synchronization operation is performed to generate a complete set of multi-dimensional feature values ​​at a unified time zero point, including hinge rotation angle, angular velocity, and driving torque, ensuring physical state consistency. The zero-phase calibration module is invoked to perform global consistency verification, and the trajectory alignment error is calculated using the following standardized residual square formula: in, For the first Each sample at the normalized time point angular velocity at that point The angular velocity of the reference trajectory at the corresponding time point. Where is the total number of samples, and is Trajectory alignment error is addressed to ensure that the aligned trajectory error meets a preset threshold. A zero-phase dynamic time warping alignment process is used to transform the resampled sequence from the previous step into a window-phase aligned time series with a unified time starting point. This eliminates differences in the starting times across samples and provides a standardized benchmark for subsequent time-scale normalization.

[0055] For example, in the operation and maintenance scenario of an office building's smart window system, a window sash resampling time sequence of length 1024 points is obtained. The static starting point indices are point 15 of sample 1, point 18 of sample 2, and point 12 of sample 3, with point 15 set as the global zero point. The delay offsets of the three trajectories are 0, 3, and... At point 3, a dynamic time warping algorithm is used to shift the time axis of the second trajectory forward by 3 points and the time axis of the third trajectory backward by 3 points. Linear interpolation of angle and angular velocity features is performed at the zero point of time to obtain a multi-dimensional feature set at the same zero point. When calculating the sum of squared residuals, N=1024 is set, and the angular velocity value is substituted into the formula, yielding an alignment error E=0.0025, far below the set threshold of 0.01, verifying the accuracy of phase alignment. After this processing, all trajectories are completely consistent at the physical state zero point, significantly improving the performance of subsequent time scale normalization and template construction, and greatly enhancing trajectory alignment stability.

[0056] S2.4: Based on the angular velocity distribution statistics in the window sash phase alignment time sequence, a normalized time axis mapping function is constructed and a nonlinear time scale transformation is performed on the window sash phase alignment time sequence to compress or stretch the intermediate process time period under different operating speeds and make the percentage of motion progress within the whole cycle strictly correspond, thereby generating a window sash normalized motion trajectory cluster with a standard time dimension.

[0057] S2.5: Perform multidimensional arithmetic averaging on the hinge rotation angle, angular velocity and driving torque values ​​corresponding to all samples in the normalized motion trajectory cluster of the window sash at the same normalized time point, so as to integrate the common features of multiple operations and remove random noise interference, and generate a motion template sequence that characterizes the standard motion behavior of the window sash.

[0058] It should be noted that the motion template sequence can constitute a three-dimensional data structure. The first dimension can be a normalized time point, with a total of 200 equally spaced points, corresponding to the 0% to 100% motion progress of the entire window opening and closing cycle. The second dimension can be a feature type, including hinge rotation angle (unit: degrees), angular velocity (unit: degrees / second), and driving torque (unit: Newton-meter). The third dimension can be the corresponding feature value.

[0059] like Figure 2 As shown, step S3 involves: based on the motion template sequence, using a sliding window to fuse newly added motion data increments that have passed consistency verification into the historical trajectory cluster, constructing a window sash individualized motion memory map containing multi-dimensional trajectory clusters, typical resistance inflection point distribution density, and transient response delay heatmaps. Specifically, this includes: S3.1: Obtain the motion template sequence and the collected motion data to be fused, and use the sliding time window algorithm to perform time-series slicing processing on the motion data to be fused to generate standardized motion data segments with fixed time lengths.

[0060] The motion template sequence and the collected motion data to be fused are used as input conditions to ensure consistency in sampling density and time reference, so that subsequent slicing and verification operations are comparable. The latest collected motion data to be fused is loaded into the sliding time window algorithm execution module, and a fixed time window scale and sliding step size parameters are set according to the standard period length of the motion template sequence. Continuous window scanning operation is performed on the motion data to be fused. Each scan extracts a time segment that strictly matches the window length and adds a global timestamp index to preserve the original positional relationship. Boundary coverage detection is performed on the extracted time segments to remove segments with insufficient window coverage, missing sampling points, or abnormal jumps across periods, so as to ensure the integrity and steady-state characteristics of the sliced ​​data. For time segments that meet the coverage requirements, signal amplitude normalization processing is performed to map the values ​​of rotation angle, angular velocity, and driving torque to the same numerical range as the basic motion template to eliminate amplitude offset caused by sensor drift and differences in environmental conditions. The output consists of standardized motion data segments with uniform time length, uniform sampling density, and amplitude standardization characteristics. These segments serve as the basic input for consistency verification. Through the aforementioned sliding window slicing and standardization processing, the basic motion template sequence results from the previous step are transformed into qualified data units that can be directly used for dynamic envelope overlap calculation, thereby achieving the expected technical effects of improved trajectory fusion accuracy and verification efficiency.

[0061] For example, in a smart building operation and maintenance scenario, a motion template sequence is acquired with a period length of 2.0 seconds and a sampling frequency of 100Hz. The total duration of the latest acquired motion data to be fused is 60 seconds, with the same sampling frequency of 100Hz. The sliding time window algorithm module sets the window length parameter to 200 points (corresponding to 2.0 seconds) and the sliding step size to 50 points (corresponding to 0.5 seconds), and continuously performs scanning operations, extracting a total of 116 original slices. The boundary coverage detection threshold is set to 95%, and 6 slices with missing sampling points due to sensor malfunctions are removed, retaining 110 qualified segments. Amplitude normalization is performed on each segment. After normalization, all rotation angle feature values ​​are mapped to the [0,1] interval, and angular velocity and driving torque also maintain the same interval distribution. The standardized motion data segments output by this processing flow have strict duration consistency and numerical interval uniformity, which significantly improves the matching accuracy in subsequent dynamic envelope overlap calculations and effectively reduces misjudgments caused by amplitude drift.

[0062] S3.2: Based on the standardized motion data fragments and the current motion template sequence, perform a dynamic envelope overlap calculation operation to filter out qualified motion data fragments with key feature point deviations lower than the preset confidence level, thereby generating a high-confidence incremental dataset that has been confirmed by consistency verification.

[0063] S3.3: Perform multidimensional trajectory clustering and fusion processing on the high-confidence incremental dataset, and use the kernel density estimation algorithm to update the spatial distribution probability of the historical trajectory clusters to generate updated multidimensional trajectory clusters.

[0064] It should be noted that the historical trajectory clusters refer to multiple datasets formed by unsupervised clustering of historically valid motion data based on feature similarity. Each cluster represents a typical motion pattern of a window sash at a certain stage of its life cycle (e.g., initial service period, mild wear period, moderate aging period), with the cluster center being the average feature vector of all valid samples at that stage, and the cluster boundary determined by the statistical distribution range of the samples. The multidimensional trajectory clusters refer to the geometric distribution of the aforementioned clusters in a high-dimensional embedding space.

[0065] The input conditions for performing multidimensional trajectory clustering and fusion processing on the high-confidence incremental dataset confirmed by consistency verification are time series segments containing multidimensional features such as hinge rotation angle, angular velocity, driving torque and ambient temperature and humidity, and have a unified time reference and precise alignment of feature points.

[0066] The high-confidence incremental dataset is used to construct a feature matrix according to multi-dimensional feature dimensions, and each dimension is standardized to eliminate dimensional differences.

[0067] Based on the standardized feature matrix, a kernel density estimation algorithm is invoked to perform probability estimation of the feature space distribution of each historical trajectory cluster, where the probability density function is: in, For the sample size, For bandwidth parameters, For kernel function types (such as Gaussian kernel). For feature vectors, For the first The feature vector of each sample For the feature vector The probability density estimate.

[0068] The trajectory cluster affiliation probability is calculated for the feature vector of each sample in the high-confidence incremental dataset to obtain its membership degree distribution in each historical trajectory cluster, and the fusion position is determined according to the principle of maximum membership degree.

[0069] After determining the fusion location, the incremental sample is merged with the sample set of the corresponding trajectory cluster, and the spatial distribution probability of the trajectory cluster is re-estimated to reflect the evolution of the center position and shape of the trajectory cluster over time.

[0070] Through the above fusion and update operations, the spatial distribution probability of all trajectory clusters is remodeled to form an updated multidimensional trajectory cluster containing the latest long-term motion habit features, thus establishing the skeleton structure of the window sash individualized motion memory map.

[0071] By using multidimensional trajectory clustering fusion and kernel density estimation, the results of the previous step are transformed into a spatial distribution probability model of trajectory clusters, thereby accurately depicting the long-term motion habit evolution of window sashes.

[0072] For example, the high-confidence incremental dataset contains 100 standardized time-series samples, each a 4-dimensional feature vector. The features are, in order, hinge angle (degrees), angular velocity (degrees / second), driving torque (Newton-meters), and ambient temperature and humidity (%). Z-score standardization is applied to each feature dimension to achieve a mean of 0 and a standard deviation of 1. Kernel density estimation using a Gaussian kernel function is employed, with the bandwidth parameter h set to 0.5. The probability distribution of each trajectory cluster is calculated using the formula described above. The maximum membership degree of the incremental sample in trajectory cluster A is 0.76, therefore it is incorporated into trajectory cluster A, triggering a re-estimation of the spatial probability of trajectory cluster A. The updated trajectory cluster center position shifts by +0.12 in the angular velocity dimension and +0.08 in the torque dimension, with the maximum probability density decreasing by 0.05, indicating a slight increase in torque during the low-speed phase of motion. The updated multi-dimensional trajectory cluster output significantly improves the stability of subsequent inflection point distribution statistics and delay trend mapping.

[0073] S3.4: Based on the resistance change nodes in the updated multidimensional trajectory cluster, perform inflection point statistical distribution modeling, calculate the resistance mutation frequency and amplitude variance within a unit angle interval, and generate a typical resistance inflection point distribution density matrix.

[0074] Based on the updated multidimensional trajectory cluster's resistance change nodes, the node detection results are used as input to perform quantitative statistical calculations on the rotation angle intervals corresponding to each node, ensuring that the node coverage within each unit angle interval is strictly defined. For each unit angle interval, a dual-feature evaluation method based on the resistance mutation amplitude and the number of node occurrences is adopted to classify high-amplitude mutations and low-amplitude mutations separately, establishing a classification label index. Using the classification label index, amplitude variance is calculated, and the resistance mutation frequency F and amplitude variance V within the unit angle interval are calculated using the following formulas: in, The frequency of sudden changes in resistance within a unit angle interval. For the first The abrupt change in resistance at each resistance-changing node. The threshold for determining sudden changes in resistance. As an indicator function, when the absolute value of the sudden change in resistance is greater than If the value is 1, then the value is 0; otherwise, the value is 0.

[0075] in, For amplitude variance, This represents the mean of the abrupt change in resistance within this angular interval. This represents the total number of abrupt change nodes within the interval. Using a joint matrix of frequency and variance, the local wear characteristics of each unit angle interval are mapped to a two-dimensional matrix, forming a typical resistance inflection point distribution density matrix. Normalization is performed on the matrix to ensure comparability of data from different angle intervals in subsequent comparisons. Through the above statistical distribution modeling and matrix construction methods, the updated multidimensional trajectory cluster results from the previous step are transformed into a visualized and quantifiable typical resistance inflection point distribution density matrix, achieving accurate characterization of local mechanical wear features.

[0076] For example, in the monitoring of a hinged window sash, the updated multidimensional trajectory cluster contains 720 nodes showing resistance changes. The rotation angle of each node ranges from 0 to 90 degrees, divided into unit angle intervals, with each interval containing 8 node data points. The resistance mutation threshold τ is set to 0.15 N·m. The mutation frequency F and amplitude variance V are calculated for the node data in the 35th to 36th degree interval. The node data shows that 5 nodes in this interval have absolute resistance mutation values ​​greater than τ, therefore F = 5. Simultaneously, the mean resistance mutation value μ in this interval is measured to be 0.18 N·m. Substituting each mutation value into the variance formula, V = 0.004 N²·m² is obtained. The F and V values ​​for all angle intervals are combined into a two-dimensional matrix, with the row representing the frequency and the column representing the variance. After multiplying the matrix by a global normalization coefficient of 0.05, the output matrix is ​​used for subsequent construction of a transient response delay heatmap. The application effect of this matrix is ​​that it can significantly improve the accuracy of identifying local wear-sensitive locations in maintenance diagnosis, especially in the high-frequency node range, achieving a significant increase in the anomaly detection rate.

[0077] S3.5: Using the typical resistance inflection point distribution density matrix and the timestamp information of the high-confidence incremental dataset, perform transient response delay spatiotemporal mapping operation to construct a delay cumulative frequency model on an angle-time two-dimensional grid, so as to generate a transient response delay heatmap that intuitively shows the degradation trend of the window sash start-stop characteristics, and construct the individualized motion memory map of the window sash.

[0078] Obtain the timestamp information of the typical resistance inflection point distribution density matrix and the high-confidence incremental dataset generated by the preceding sub-step S3.4, and use them as the dual input reference for the transient response delay spatiotemporal mapping operation.

[0079] Based on timestamp information, a triplet mapping table containing the operation start time, resistance inflection point time, and corresponding angle is constructed to establish the timing anchor point for delay calculation.

[0080] For each resistance inflection point event, a time difference calculation is performed. The difference between the actual occurrence time and the corresponding theoretical occurrence time in the template is taken as the delay amount, and the hinge rotation angle value corresponding to the delay amount is recorded to form a local delay data point.

[0081] Using a set of delayed data points, coordinate mapping is performed on a two-dimensional angle-time grid. The delay is used as the third dimension of data. The delayed events in each grid cell are weighted and counted through cumulative frequency statistics to construct a cumulative frequency model of delay.

[0082] A two-dimensional thermal mapping transformation is performed on the delay cumulative frequency model to map the frequency values ​​into color gradient values, and the trend of start-stop characteristic degradation with the period is presented in the direction of the time axis to generate a transient response delay heatmap.

[0083] By using matrix mapping and heatmap construction, the statistical results of the resistance inflection point in the previous step are transformed into two-dimensional visualization data that intuitively reflects the degradation trend of the window sash start-stop characteristics, thereby realizing the full construction of motion memory maps and enhancing the readability of time series.

[0084] For example, this step is deployed in a building smart window system. A typical resistance inflection point distribution density matrix comprises nine evenly spaced segments with angles ranging from 0° to 90°, and the frequency of resistance abrupt changes in each segment is statistically between 5 and 20. The high-confidence incremental dataset contains timestamps of the most recent 180 seconds of operation records, with calculated latency values ​​ranging from 0.05s to 0.35s. A two-dimensional grid is constructed with an angle step size of 10° and a time step size of 0.1s. For each grid cell, the following formula is used... Calculate the cumulative frequency, where The values, after normalization to the delay, range from 0.8 to 1.2. The values ​​range from 3 to 15 in each grid cell. The mapping results show that the delay frequency is significantly increased in the low-angle segment from 0° to 20°, and the color gradient of the heat map changes from light yellow to dark red, reflecting a clear trend of increasing mechanical clearance during the start-up and shutdown phases. The verification results show that this heat map can significantly improve the positioning accuracy and trend perception ability of maintenance personnel for the degradation of start-up and shutdown characteristics.

[0085] like Figure 3 As shown, step S4 involves: obtaining the hinge rotation resistance curve, mapping the hinge rotation resistance curve to the high-dimensional embedding space of the individualized motion memory map of the window sash, calculating the semantic distance between the current resistance curve and each historical stage sub-cluster in the map, and generating a semantic distance vector. Specifically, this includes: S4.1: Perform timestamp alignment and noise filtering on the raw data of the hinge rotation resistance curve currently running in real time to eliminate sampling jitter and environmental transient interference, and generate a standardized resistance curve sequence with a unified time series reference.

[0086] S4.2: Extract multidimensional dynamic feature vectors based on the standardized resistance curve sequence, calculate local slope, curvature and energy distribution indices using the sliding window statistical method, and generate structured feature descriptors.

[0087] The standardized resistance curve sequence output from the preceding step S4.1 is subjected to multidimensional dynamic feature vector extraction under a unified time reference condition.

[0088] The standardized resistance curve sequence is divided into sliding windows of fixed length. The window length and sliding step size are set according to the statistical distribution of the hinge rotation period to ensure that each window segment covers the complete local dynamic change process.

[0089] Within each window segment, the difference between adjacent sampling points of the drag curve is taken and divided by the sampling interval to calculate the local slope parameter, forming a time-domain gradient feature component that reflects the rate of change of drag with angle.

[0090] The slope sequence within each window segment is subjected to second-order difference processing and divided by the square of the sampling interval to calculate the local curvature parameter of the resistance curve, characterizing the polygonal or smooth degree of the transient resistance waveform.

[0091] Within each window segment, a local energy distribution index is generated based on the integral of the squared magnitude of the drag data, calculated using the following formula: in, This is an index of the local energy distribution within the window segment. This represents the amplitude of the resistance curve within the window segment. The window duration. This is the window's initial time.

[0092] The aforementioned local slope parameters, local curvature parameters, and local energy distribution indices are concatenated according to window order and feature dimensions to form a multidimensional dynamic feature vector matrix.

[0093] Normalization is used to eliminate the dimensional differences between the feature components, ensuring a balanced contribution of different dimensions in the subsequent high-dimensional embedding mapping.

[0094] By using a sliding window statistical method, the standardized resistance curve sequence is transformed into a structured feature descriptor, thereby mapping the time series signal into a feature data form that facilitates spatial matching operations.

[0095] For example, in a real-time diagnostic scenario of a building's intelligent window system, the sampling frequency is set to 100Hz, the sliding window length is 1.0 second, the sliding step size is 0.2 seconds, and each window contains 100 data sampling points for the resistance curve. In the local slope calculation, the average resistance difference between adjacent sampling points is 0.05Nm, and the sampling interval is 0.01 seconds, resulting in an average local slope of 5.0Nm / s. In the local curvature calculation, the average second-order difference result is 0.002Nm, and the square of the sampling interval is 0.0001s², resulting in an average local curvature of 20.0Nm / s². In the local energy distribution calculation, the cumulative value of the square integral of the resistance amplitude is 0.25Nm²·s, and the window length... If the interval is 1.0 second, the local energy distribution index value is 0.25 Nm². The slope, curvature, and energy features extracted from all window segments are Z-score normalized and then concatenated sequentially to obtain a horizontally balanced structured feature descriptor matrix. This matrix significantly improves the matching accuracy of drag curve patterns in subsequent high-dimensional embedding mapping.

[0096] S4.3: Based on the structured feature descriptor, call the pre-constructed high-dimensional embedding mapping function to project the low-dimensional feature space data to the high-dimensional embedding space where the individualized motion memory map of the window sash is located, and generate the high-dimensional embedding coordinate points of the current resistance curve.

[0097] When calling the pre-constructed high-dimensional embedding mapping function based on the structured feature descriptor, the components of the descriptor vector are first arranged according to the predefined feature domain order, and normalization is performed to eliminate the dimensional differences of different physical quantities on a numerical scale. The feature domain weight matrix is ​​then called on the normalized vector, and matrix multiplication is performed to highlight the contribution of key features to the localization in the embedding space, while weakening the influence of non-key features. A kernel function mapping is then applied to the weighted vector, using radial basis functions to construct a nonlinear mapping kernel that maps points in the low-dimensional feature space to the high-dimensional manifold structure. The following function expression is used in this process: in, The output is a radial basis function mapping. The feature vector after weight adjustment. For the coordinates of the center point of the mapping, The scaling parameter is used. A multi-kernel concatenation operation is performed on all mapping kernel output vectors, preserving the global feature representation of the combined kernel space. The orthogonalization projection matrix is ​​then applied to the concatenated high-dimensional representation, ensuring the embedded coordinates satisfy the constraints of orthogonal axes and balanced variance distribution in the high-dimensional space. Sparse encoding is then performed on the orthogonalized coordinates, reducing redundant dimensions by limiting the number of non-zero components, ultimately forming the set of coordinate points of the current drag curve in the high-dimensional embedding space of the window sash individualized motion memory map. Through this processing, the structured feature descriptor from the previous step is transformed into high-dimensional embedded coordinates, achieving precise spatial positioning of the drag curve in the evolution map.

[0098] For example, in a building intelligent window operation and maintenance system, the collected structured feature descriptors are 12-dimensional, including three types of indicators: local slope, curvature, and energy distribution, each with 4-dimensional components. Each component is normalized to compress the numerical range to between 0 and 1. The feature domain weight matrix is ​​configured with a weight of 0.4 for the local slope component, 0.35 for the curvature component, and 0.25 for the energy distribution component. The weighted vector is then mapped using the radial basis function, with σ set to 0.5 and c representing the center point of the corresponding historical normal phase. The kernel function values ​​of each component are calculated according to the formula and combined into a high-dimensional vector. The kernel outputs of three different scale parameters (σ=0.3, 0.5, 0.8) are concatenated into a 36-dimensional combined kernel space representation. This is then projected using the orthogonalized projection matrix generated by the decomposition of the historical trajectory cluster covariance matrix, ensuring that the variance of each axis is balanced between 0.05 and 0.07. The projected vectors are sparsely encoded, limiting the number of non-zero components to no more than 10. The output high-dimensional embedded coordinates represent the spatial location of the sub-clusters near the early aging stage in the map. Subsequent similarity matching shows that the distance between these coordinates and the corresponding historical stage is significantly shortened, and the positioning accuracy is significantly improved.

[0099] S4.4: Using the high-dimensional embedded coordinate points, traverse the centers of each historical stage sub-cluster in the individualized motion memory map of the window, perform a similarity matching operation based on manifold distance metric, and generate an initial distance set between the current resistance curve and each historical stage sub-cluster.

[0100] It should be noted that the semantic distance refers to the similarity measure between the high-dimensional embedded coordinates of the current resistance curve and the centers of each historical stage sub-cluster, specifically calculated using the manifold distance algorithm. Here, "semantic" refers to the mechanical characteristics implied by the current motion state (e.g., healthy, slightly worn, severely aged). The smaller the semantic distance, the closer the current motion state is to the mechanical characteristics represented by that historical stage sub-cluster; the larger the semantic distance, the greater the degree to which the current motion state deviates from the normal pattern of that historical stage. After calculating the semantic distance for all historical stage sub-clusters sequentially, all distance components are combined into a one-dimensional vector according to the sub-cluster index order, which is the semantic distance vector.

[0101] The high-dimensional embedded coordinates of the current resistance curve generated in step S4.3 are used as the calculation benchmark. The historical stage sub-cluster indices and center position data of each sub-cluster in the individualized motion memory map of the window sash are then retrieved. Coordinate difference calculations are performed on the center of each historical stage sub-cluster to obtain a sequence of component differences between the current coordinates and the sub-cluster center in the high-dimensional embedded space. This sequence of component differences is input into a manifold-based distance metric model. Local manifold projection reconstruction is performed on each component difference using an adjacency weight matrix to ensure that the distance calculation takes into account the nonlinear spatial curvature factor. Based on the reconstructed coordinates, a weighted Euclidean distance calculation is performed, and the manifold distance between each sub-cluster center and the current coordinate point is expressed as... in, The manifold distance between the current coordinate point and the center of the historical subcluster. For the dimension of the high-dimensional embedded space, These are the local weighting coefficients of the manifold. Let be the coordinate component of the sub-cluster center in the i-th dimension. For the current embedding point at the th The coordinate components of the dimension are calculated. The above distance calculation is then performed sequentially on all historical stage subclusters to generate a complete initial distance set. Through the manifold distance-based matching process described above, the embedded coordinates obtained in the previous step are transformed into quantifiable distance metrics, enabling accurate assessment of the similarity between the current resistance curve and the historical stage subclusters.

[0102] For example, in a smart window maintenance scenario of a building, the high-dimensional embedding space is set to 12 dimensions. The adjacency weight matrix is ​​constructed from K nearest neighbors (k=5) and reduced to a local subspace that maintains 90% variance using local PCA. The current resistance curve embedding coordinate point is [1.2,0.5,3.1,2.9,1.8,0.4,0.7,2.0,1.5,0.9,1.1,0.6], and the sub-cluster center of a certain historical stage is [1.0,0.4,3.0,3.0,2.0,0.5,0.5,2.1,1.4,1.0,1.2,0.5]. The manifold local weight coefficient is preset to 1. Inputting this coordinate difference into the formula, the sum of squared component differences is calculated to be 0.14, and the square root distance is 0.374, indicating that the sub-cluster center has a high similarity to the current embedding point. After performing the same calculation on all subclusters, an initial distance set [0.374, 0.612, 0.890, 0.450, ...] is generated. It has been verified that this set can significantly improve the resolution of the deviation metric during the subsequent S4.5 weighted aggregation, ensuring that the anomaly detection is more sensitive to changes in the aging stage.

[0103] S4.5: Perform weighted aggregation and normalization on the initial distance set, and combine the time decay weight factors of each historical stage sub-cluster to generate the semantic distance vector.

[0104] Step S5: Based on the environmental temperature and humidity change rate, initial response delay offset, and mid-range uniform velocity zone resistance fluctuation entropy from the most recent operations, a weighted fusion is performed using the semantic distance vector to generate an aging factor. Specifically, this includes: S5.1: Obtain the original time-series data of environmental temperature and humidity from the most recent operation records, and use the sliding difference algorithm to perform first-order derivative calculation on the original time-series data of environmental temperature and humidity to eliminate the difference in absolute numerical benchmarks and extract the trend features, and generate an environmental temperature and humidity change rate vector that represents the severity of environmental disturbance.

[0105] S5.2: Based on the operation time window corresponding to the environmental temperature and humidity change rate vector, extract the standard start time in the motion template sequence and the actual start time in the actual collected data, perform timestamp difference calculation to quantify the response lag caused by the expansion of mechanical transmission clearance, and generate a scalar of the start response delay offset that characterizes the degree of mechanical loosening.

[0106] Based on the operation time window corresponding to the environmental temperature and humidity change rate vector, the standard start time data in the motion template sequence is called as the time reference signal.

[0107] The start-up time data of the resistance curves of the most recent ten switching processes are synchronously read on the time reference signal to form a paired sample set containing dual timestamps.

[0108] The timestamp difference operation is performed on the paired sample set, and the response delay offset is calculated using the difference. The calculated delay offset sequence is input into the mechanical transmission clearance amplification effect model, and the linear amplification factor is calculated to distinguish the delay caused by wear from the transient response fluctuation caused by the rate of change of ambient temperature and humidity.

[0109] The mean extraction and outlier removal processes are performed on the delay offset after amplification factor correction to obtain a single scalar output that stably represents the degree of mechanical loosening.

[0110] By using the above processing method, the difference between the environmental temperature and humidity change rate in the previous step and the window sash start-up time is quantified into a scalar of the initial response delay offset that reflects the change in transmission gap, thereby achieving accurate quantification of the mechanical loosening state.

[0111] For example, in a building's intelligent window system, the operation time window for the environmental temperature and humidity change rate vector is the most recent number of opening and closing processes. The standard start time is determined by the motion template sequence as 0.00 seconds, while the actual collected start times range from 0.05 seconds to 0.12 seconds. An offset is calculated for each start time; for example, if the actual start time is 0.08 seconds, the offset is 0.08 seconds. The offset sequence is input into a transmission gap amplification effect model, with an environmental correction coefficient set to 0.85, resulting in a corrected delay offset of 0.068 seconds. The mean of the corrected sequence is extracted, and outliers exceeding ±0.02 seconds are removed, ultimately yielding a stable scalar of 0.071 seconds as an indicator of mechanical loosening. This indicator serves as a crucial input in subsequent aging factor calculations, significantly improving the accuracy of mechanical degradation assessment. In practical applications, it enables early detection of minor loosening, effectively enhancing the real-time performance and targeted nature of maintenance warnings.

[0112] S5.3: Extract the data segment in the uniform motion stage from the current real-time running resistance curve, and use the Shannon entropy calculation formula to measure the amplitude distribution disorder of the data segment in the uniform motion stage, so as to quantify the complexity of resistance fluctuation caused by uneven hinge wear, and generate the resistance fluctuation entropy value of the middle uniform zone that characterizes the deterioration state of the friction surface.

[0113] Extract the data segment in the uniform motion phase of the current real-time running resistance curve, accurately locate the start and end time boundaries of the phase based on the phase feature index set generated in the previous steps, and extract the corresponding resistance amplitude sequence as the analysis object.

[0114] The resistance amplitude sequence is subjected to amplitude discretization processing, and the continuous resistance values ​​are divided into a finite number of amplitude levels according to a preset amplitude resolution, so as to construct an amplitude level distribution set that can be used for statistical frequency.

[0115] In the set of amplitude level distributions, the frequency of occurrence of each amplitude level is counted to form a normalized probability distribution sequence, which serves as the input probability vector for Shannon entropy calculation.

[0116] By applying the Shannon entropy calculation formula, an unordered metric operation is performed on the normalized probability distribution sequence: in, Let Shannon's entropy be the value. The number of amplitude levels. For the first The sum of the probabilities corresponding to each amplitude level reflects the degree of uncertainty of the current resistance fluctuation.

[0117] The calculated entropy value is subjected to amplitude correction processing. An amplitude sensitivity coefficient matrix is ​​constructed using the average resistance value and resistance standard deviation statistically obtained during the uniform speed stage. The entropy value is multiplied by this coefficient matrix to enhance the weight of wear unevenness characteristics in the entropy value.

[0118] By using the above processing method, the resistance curve data of the uniform speed stage in the previous step is transformed into the resistance fluctuation entropy value of the middle uniform speed zone, which characterizes the deterioration state of the friction surface, thereby realizing a quantitative assessment of the complexity of resistance fluctuation.

[0119] For example, when detecting the resistance curve of an aluminum alloy window sash installed for more than five years during the uniform speed phase, the duration of this phase was recorded as 2.4 seconds, the sampling frequency was 100Hz, and the total number of sampling points was 240. The resistance value was discretized into 10 amplitude levels, and the frequency of occurrence of each level was statistically analyzed to obtain a probability distribution vector: [0.05, 0.08, 0.12, 0.10, 0.15, 0.14, 0.10, 0.09, 0.09, 0.08]. Substituting this probability vector into the Shannon entropy formula, the intermediate entropy value was calculated to obtain 2.28. Under the conditions that the average resistance value of this phase is 4.6N and the standard deviation of resistance is 0.7N, an amplitude sensitivity coefficient matrix was constructed (averaging the coefficients for each level), with a coefficient of 1.12. After entropy correction, the final resistance fluctuation entropy was output as 2.554. The verification results show that the window sash resistance fluctuation entropy is significantly higher than that in the initial service stage, indicating that the wear of the hinge friction surface is significantly uneven. This value will then be used as an input feature for the generation of subsequent aging factors.

[0120] S5.4: Call the semantic distance vector generated in the previous step as the benchmark deviation metric, construct a multivariate feature input matrix containing the environmental temperature and humidity change rate vector, the initial response delay offset scalar, and the resistance fluctuation entropy value of the middle uniform speed zone, and use an adaptive weight allocation algorithm to perform a weighted fusion operation on the multivariate feature input matrix to balance the impact of environmental transient disturbances and long-term mechanical degradation on the state assessment, and generate a preliminary aggregated degradation index.

[0121] It should be noted that the weighted fusion refers to the linear weighted summation of the environmental temperature and humidity change rate vector, the initial response delay offset scalar, the mid-range uniform velocity zone resistance fluctuation entropy value, and the semantic distance vector after assigning preset weight coefficients to each. The recommended values ​​for each weight coefficient in this embodiment are: environmental temperature and humidity change rate weight 0.2, initial response delay offset weight 0.3, mid-range uniform velocity zone resistance fluctuation entropy weight 0.3, and semantic distance vector weight 0.2. The sum of these weight coefficients is 1, and can be adaptively adjusted according to the window sash installation model, usage environment (such as coastal high-humidity areas or inland dry areas), and historical fault data.

[0122] S5.5: Perform nonlinear normalization mapping on the preliminary aggregated degradation index, constrain its numerical range to a continuous interval from zero to one to match the life cycle percentage definition, and finally output an aging factor that reflects the degree of evolution of the window sash from its initial healthy state to its current aging state.

[0123] Based on the preliminary aggregation degradation index obtained from the previous steps, the nonlinear normalization mapping function module is invoked, and this index is used as an input scalar into the normalization pipeline. The slope of the mapping curve is controlled by setting the shape parameter of the normalization mapping function, ensuring that the sensitivity differences in degradation levels across different intervals are reasonably adjusted. During the mapping process, interval pruning is first performed to limit the preliminary aggregation degradation index value within the physically permissible range, thus avoiding the impact of outliers on normalization accuracy. Subsequently, a piecewise nonlinear function is used to scale the index, where a gradual increase function is used in the low degradation range to suppress misjudgments caused by small fluctuations, and a steep increase function is used in the high degradation range to strengthen its weight in the judgment. This piecewise nonlinear transformation can be expressed by the following MathML formula: in, This is a preliminary aggregation degradation index. This is the curve slope adjustment coefficient. The mapping center point is used. The mapping result undergoes numerical constraint processing, precisely limiting the output to a continuous closed interval between 0 and 1 to conform to the standard format defined by the life cycle percentage. Through this processing method, the multivariate fusion degradation index of the previous step is transformed into a single scalar life cycle percentage aging factor, achieving accurate characterization of the degree of evolution of the window sash from its initial healthy state to its current aging state.

[0124] For example, in a building intelligent operation and maintenance scenario, the initial aggregated degradation index is calculated to be 0.37. The nonlinear normalization mapping function is set to k=8 and x0=0.5, with the curve rising sharply near x0.5 to improve sensitivity in the medium-to-high degradation zone. Substituting x=0.37 into the formula, the normalized value is obtained: The calculated value is 0.305, and after interval constraint processing, the output is also 0.305, which serves as the final value of the aging factor. Under this configuration, the suppression effect in the low degradation zone is significant, avoiding false alarms caused by environmental fluctuations. When the index value approaches or exceeds 0.5, the steep rise of the mapping curve can significantly improve the sensitivity of the detection to true aging, thereby optimizing the fault judgment capability of the anomaly detection module in the early and late stages of the window sash's life cycle.

[0125] Step S6: Modulate the resistance tolerance bandwidth corresponding to the aging stage in the individualized motion memory map of the window sash using the aging factor to generate a personalized deviation judgment boundary. Specifically, this includes: S6.1: Obtain the aging factor generated by the previous steps, which reflects the degree of degradation of the window sash throughout its life cycle. Based on this aging factor, perform a nonlinear mapping function operation to convert the scalar degradation index into a drag bandwidth adjustment coefficient vector that characterizes the intensity of local deformation in the spectral space, so as to establish the quantitative driving basis for subsequent bandwidth modulation.

[0126] The aging factor output from the previous steps is obtained as an input scalar. The nonlinear mapping function module is then used to perform curve fitting parameterization on this scalar, transforming the degradation index in the form of a lifespan percentage into a function input variable. A hybrid mapping function model, incorporating polynomial piecewise and exponential asymptotic segments, is constructed to enhance the sensitivity of local regulation for different aging stages. The mapping function is calculated in interval segments. In the initial degradation interval, a quadratic polynomial mapping is used to maintain slow bandwidth changes, while an exponential amplification term is introduced in the mid-to-high degradation interval to strengthen bandwidth compression control in sensitive directions. Numerical iterative methods are used to solve for the output value of the mapping function at each normalized degradation index position, and this output value is used as the basis for constructing the components of the drag bandwidth adjustment coefficient. Vector assembly operations are used to combine the adjustment coefficients calculated in different degradation intervals into a drag bandwidth adjustment coefficient vector, achieving a multidimensional quantitative characterization of the local deformation intensity in the spectral space.

[0127] in, For normalized aging factors, , , These are the function parameters fitted based on historical performance data. This represents the drag bandwidth adjustment coefficient. The k value calculated using the above formula exhibits a controllable nonlinear variation trend within different I intervals. This transforms the result of the previous step into a quantitative vector of the local deformation intensity in the spectral space, providing a quantitative driving basis for personalized drag tolerance bandwidth modulation.

[0128] For example, in a smart window sash that has been in service for eight years, the aging factor collected is 0.65, and the mapping model parameters are configured as a=0.5, b=0.8, and c=1.2. Using the above formula, the first term is calculated to be 0.21125, and the second term to be 1.6576, resulting in a resistance bandwidth adjustment coefficient of approximately 1.86885. This coefficient vector is applied to the local region of the sub-cluster corresponding to the aging stage in the spectrum, automatically expanding the tolerance range by approximately 1.87 times in the direction of accelerated aging, while proportionally compressing the boundary in the direction of anomaly sensitivity. Experimental results show that this modulation coefficient significantly improves the adaptability of anomaly detection to resistance drift in the later stages of the life cycle, while maintaining stable judgment performance under environmental disturbances.

[0129] S6.2: Based on the resistance bandwidth adjustment coefficient vector and the historical stage sub-cluster index in the individualized motion memory map of the window sash, perform a spatiotemporal correlation matching operation to locate the specific historical stage sub-cluster corresponding to the current aging factor and its distribution area in the high-dimensional embedding space of the map, and generate the target scope set of the resistance tolerance bandwidth to be modulated.

[0130] It should be noted that the resistance tolerance bandwidth refers to the normal resistance value fluctuation range of each historical stage sub-cluster in the individualized motion memory map of the window sash. This bandwidth consists of an upper limit boundary and a lower limit boundary, and its physical unit is Newton-meter (N·m).

[0131] S6.3: For the original resistance tolerance bandwidth baseline data within the target domain set, perform anisotropic scaling transformation processing using the resistance bandwidth adjustment coefficient vector, automatically expand the tolerance range according to the aging acceleration direction and compress the safety boundary according to the abnormal sensitivity direction, and generate a dynamic resistance tolerance bandwidth candidate set after preliminary geometric deformation correction.

[0132] Based on the target domain set located in the previous steps and its corresponding original resistance tolerance bandwidth baseline data, the component values ​​in the resistance bandwidth adjustment coefficient vector are first called and indexed and matched with the baseline data in the same high-dimensional embedding space coordinates to confirm the adjustment direction and magnitude of each tolerance bandwidth segment.

[0133] Based on the completed matching, a vector decomposition operation is performed on each segment, splitting the adjustment coefficient vector into two orthogonal components along the aging aggravation principal axis and the abnormal sensitivity principal axis, which serve as the driving parameters for the anisotropic scaling transformation.

[0134] For the component along the aging acceleration direction, a bandwidth amplification function is constructed, and the tolerance range is automatically expanded through an exponential scaling transform. The calculation formula is as follows: in, The transformed bandwidth, For the original bandwidth, This is the magnification factor. This is the adjustment coefficient component.

[0135] For the component along the abnormally sensitive direction, a bandwidth compression function is constructed, and the security boundary is shrunk through a linear reduction transformation. The calculation formula is as follows: in, The compression factor is 1. For the adjustment coefficient component, The transformed bandwidth, This represents the original bandwidth.

[0136] The transformation results in the two directions are superimposed on the corresponding coordinate axes to form a candidate set of dynamic resistance tolerance bandwidths after preliminary geometric deformation correction, while maintaining the topological continuity of each segment in the spectral space to avoid misjudgment caused by bandwidth abrupt changes.

[0137] Through the above anisotropic scaling transformation process, the target domain set and the original bandwidth baseline data in the previous step are transformed into a dynamic resistance-tolerant bandwidth candidate set with aging sensitivity and abnormal response capability, so as to realize the adaptive scaling adjustment of bandwidth during the life cycle evolution process.

[0138] For example, in a window hinge system that has been in service for 8 years, the original resistance tolerance bandwidth W is set to 3.2 N·m, and the principal component α of the resistance bandwidth adjustment coefficient vector is 0.15 in the aging direction and 0.08 in the anomaly-sensitive direction. Along the aging acceleration direction, the amplification factor k is set to 0.5, and substituting into the above formula, the expanded bandwidth is calculated to be approximately 3.44 N·m. Along the anomaly-sensitive direction, the compression factor β is set to 1.2, and substituting into the above formula, the contracted bandwidth is calculated to be approximately 3.104 N·m. In the two-dimensional embedding space, the two transformation results are applied to the corresponding axes to generate the bandwidth distribution within the candidate set. During verification, this candidate set shows enhanced tolerance in the aging direction and improved sensitivity response in the anomaly direction, significantly improving the accuracy and robustness of anomaly detection.

[0139] S6.4: Based on the aforementioned dynamic resistance tolerance bandwidth candidate set, a material thermal expansion and contraction compensation term caused by the rate of change of ambient temperature and humidity is introduced for secondary superposition correction calculation to eliminate the instantaneous influence of environmental disturbances on the mechanical resistance benchmark, and generate a final personalized resistance tolerance bandwidth envelope with environmental robustness.

[0140] Based on the aforementioned dynamic resistance tolerance bandwidth candidate set, the environmental temperature and humidity change rate vector generated in the previous steps is used as the basis for quantifying the interference source. Parametric error modeling of material thermal expansion and contraction is performed on the angular intervals of each data point within the candidate set, establishing a transient offset function for the mechanical resistance benchmark caused by environmental changes. This offset function is used to calculate the corresponding deformation compensation at each candidate bandwidth boundary point, and it is mapped to the high-dimensional embedding space of the individualized motion memory map of the window sash to maintain the spatiotemporal consistency of environmental compensation. A weighted superposition operation is performed on the mapped compensation, with the weights determined based on the degree of matching between the severity of environmental disturbance and the abnormally sensitive direction of the candidate bandwidth in the current aging stage, thus achieving quantitative correction of the bandwidth by the compensation.

[0141] The calculated environmental compensation is applied to the upper and lower boundary points of the dynamic drag tolerance bandwidth candidate set, and geometric offset operations are performed outward and inward respectively to eliminate the transient impact of environmental changes on the mechanical drag reference. Through this processing method, the dynamic bandwidth candidate set of the previous step is transformed into a final personalized drag tolerance bandwidth envelope with environmental robustness, realizing an adaptive stability improvement of the anomaly detection threshold to short-term environmental disturbances.

[0142] S6.5: The final personalized resistance tolerance bandwidth envelope is fused and reconstructed with the topology of the window sash individualized motion memory map to generate a personalized deviation judgment boundary, which serves as the sole dynamic reference standard for judging whether the current real-time running resistance curve is abnormal.

[0143] The final personalized resistance tolerance bandwidth envelope with environmental robustness and the topological structure of the window sash individualized motion memory map are used as the two input objects for fusion processing. A high-dimensional topology fusion algorithm is called to analyze the geometric correspondence between the two in the embedding space and generate a preliminary fusion topology mapping matrix.

[0144] A node-level bandwidth binding operation is performed on the preliminary fusion topology mapping matrix to map the numerical boundaries of the local resistance tolerance interval in the envelope to the node attributes of the corresponding historical stage subclusters in the graph, so as to establish the physical meaning of the resistance tolerance bandwidth in the multidimensional trajectory space.

[0145] A topological connectivity correction is introduced onto the mapped node attribute set. The edge connection strength function is used to smoothly distribute local bandwidth variations according to neighborhood correlation coefficients, forming a complete... Figure 1 A resistance tolerance gradient distribution model.

[0146] Based on the gradient distribution model, the envelope surface reconstruction operation is performed. A personalized deviation judgment surface that runs through the entire life cycle stage is generated through three-dimensional surface fitting and curvature constraint algorithms, upgrading the original two-dimensional resistance tolerance envelope shape into a dynamic judgment boundary that can be matched in a high-dimensional space.

[0147] The graph consistency verification module is called to calculate the global overlap between the reconstructed decision surface and the existing trajectory cluster topology. If the global overlap is lower than the preset threshold, local iterative compensation is performed to ensure the balance between the decision boundary in terms of life cycle adaptability and fault sensitivity.

[0148] Through the above-mentioned fusion and reconstruction process, the final bandwidth envelope result of the previous step is transformed into a personalized deviation judgment dataset with time evolution capability in a high-dimensional topology, realizing a unique dynamic reference standard that changes with the life cycle.

[0149] For example, after completing the final personalized resistance tolerance bandwidth envelope output by S6.4, a building intelligent window sash system inputs it into a high-dimensional topology fusion algorithm in the form of a three-dimensional matrix. The envelope boundary points are 300, and the individualized motion memory map of the window sash contains 5 historical stage sub-clusters, each with 120 nodes. In the fusion mapping stage, a Gaussian weighting function with a neighborhood radius of 0.15 is used to smoothly bind the bandwidth value. In the connectivity correction stage, the bandwidth change is smoothly allocated through an edge connection strength function; in the surface reconstruction stage, a curvature constraint value of 0.05 is used to ensure the smoothness of the lifecycle surface. The final reconstructed judgment surface achieves a global overlap of 0.92, higher than the preset threshold of 0.9, verifying the balanced effect of the fusion reconstruction judgment boundary in terms of adaptability and sensitivity. The output personalized deviation judgment dataset achieves significantly improved judgment accuracy in subsequent S7 fault judgment.

[0150] Step S7: Determine whether the hinge rotation resistance curve currently in real-time exceeds the personalized deviation judgment boundary, and detect whether its deviation pattern matches the drooping fault topology signature already marked in the atlas, generating a fault discrimination result. Specifically, this includes: S7.1: Obtain the hinge rotation resistance curve currently running in real time and the personalized deviation judgment boundary generated by the previous steps. Use the point-by-point envelope comparison algorithm to perform full-cycle scanning processing on the hinge rotation resistance curve to identify the set of discrete abnormal data points that exceed the upper or lower limit of the personalized deviation judgment boundary, and generate a preliminary abnormal candidate sequence marked with out-of-bounds position information.

[0151] The sagging fault refers to a mechanical failure type in which the window sash sags when closed and experiences abnormally increased resistance during opening due to wear, deformation, or loosening of the hinges caused by long-term use. Typical mechanical characteristics of sagging faults include: in the low-speed start-up zone (hinge rotation angle between 0° and 15°), the resistance curve plateau shows a significant rise relative to the healthy state baseline; in the medium-to-high-speed operation zone (hinge rotation angle between 30° and 60°), the slope of the resistance curve shows a significant decrease relative to the healthy state baseline. The topological signature refers to a feature vector template composed of the two key characteristic parameters mentioned above (the rise in resistance plateau in the low-speed zone and the decrease in slope ratio in the high-speed zone). This template is pre-stored in the window sash's individualized motion memory map and used for morphological matching with abnormal feature segments in real-time operation. Only when the deviation pattern of the real-time resistance curve and the topological signature simultaneously satisfy both the low-speed zone rise and high-speed zone decrease conditions is it determined to be a genuine sagging fault event.

[0152] S7.2: Based on the set of discrete abnormal data points in the preliminary abnormal candidate sequence, perform continuous segment clustering and noise removal operations to merge temporally adjacent and amplitude-continuous boundary points into abnormal duration intervals with clear start and end angles, and generate structured abnormal feature segments that characterize the true deviation behavior.

[0153] S7.3: Call the drooping fault topology signature template pre-stored in the individualized motion memory map of the window sash, and use a multi-dimensional morphological matching algorithm to calculate the geometric similarity between the structured abnormal feature fragment and the drooping fault topology signature template in terms of the rise amplitude of the resistance platform in the low-speed zone and the slope attenuation ratio in the high-speed zone, and generate a topology matching score that reflects the degree of fault mode matching.

[0154] Obtain the structured anomaly feature fragments generated by the preceding step S7.2 as the input object for the matching calculation.

[0155] The pre-stored drooping fault topology signature template in the individualized motion memory map of the window sash is invoked to map the input abnormal feature fragments to the low-speed and high-speed segmentation feature space defined by the template.

[0156] Within the low-speed region feature space, the average resistance platform value of abnormal feature segments is extracted and compared with the corresponding average resistance platform value in the template. The amplitude difference is calculated and normalized to eliminate the reference deviation caused by different equipment specifications.

[0157] A geometric similarity matching algorithm is used, taking the difference in the rise of the resistance platform in the low-speed region and the difference in the slope attenuation ratio in the high-speed region as the input of a two-component vector, calculating the Euclidean distance of the feature vectors and generating a matching score through a similarity conversion formula.

[0158] The formula is as follows: in, Score the topology matching degree. The difference component between the low-speed and high-speed regions is the Euclidean distance, and the denominator contains... Ensure that the scores are continuously distributed between zero and one.

[0159] A threshold constraint is applied to the matching score, so that when the score is lower than a certain value, it is directly marked as a low similarity state, thus avoiding misjudgment caused by accidental environmental interference.

[0160] By executing a multidimensional morphological matching algorithm, the abnormal feature fragments from the previous step are transformed into quantified topological matching scores, thereby enabling a measurable assessment of the degree of fit for drooping fault modes.

[0161] For example, in a single test of a smart building window sash system, the average resistance plateau value in the low-speed zone of the structured anomalous feature segment was 15.2 N·m, and the template value was 14.0 N·m. The slope attenuation ratio in the high-speed zone was 0.78, and the template value was 0.72. The amplitude difference in the low-speed zone was calculated to be 1.2 N·m and normalized to 0.085, and the slope difference in the high-speed zone was calculated to be 0.06 and normalized to 0.083. The Euclidean distance calculation formula is as follows: in, The difference in the rise of the resistance plateau in the low-speed region after normalization. This represents the difference in slope attenuation ratio in the high-speed region after normalization. Substituting this into the formula yields the calculated result. The Euclidean distance is approximately 0.118. Substituting the Euclidean distance into the matching scoring formula generates a score of 0.895, which is significantly higher than the set fault confirmation threshold of 0.85. The topological matching score output by the matching algorithm confirms that the abnormal segment highly conforms to the characteristics of the drooping fault mode, which assists in the subsequent fault validity judgment.

[0162] S7.4: Perform logical threshold decision processing based on the topology matching score and a pre-set fault confirmation threshold. Only when the structured abnormal feature fragment simultaneously meets the boundary conditions and the topology matching score is higher than the fault confirmation threshold is it determined to be a valid fault event, generating a fault validity confirmation flag containing a Boolean state identifier. Obtain the boundary condition judgment results of the topology matching score and structured abnormal feature fragment output from the previous steps, and establish the input matrix for the logical threshold decision operation. Call the fault confirmation threshold storage unit, read the matching degree critical value set for drooping faults, and use this threshold as a comparison benchmark. Perform the first comparison operation, calculate the numerical difference between the topology matching score and the fault confirmation threshold, and generate a matching degree exceeding limit Boolean flag. Perform the second comparison operation, parse the boundary condition judgment result of the structured abnormal feature fragment into Boolean values, and generate a boundary condition satisfied Boolean flag. Call the logical AND operation module, perform a bitwise logical multiplication operation on the matching degree exceeding limit Boolean flag and the boundary condition satisfied Boolean flag to form a joint fault validity judgment Boolean value. The joint Boolean value is encapsulated as a fault validity confirmation flag, and a timestamp and source identification information are attached to ensure the traceability of subsequent confidence fusion. Through the above logical threshold decision processing, the topology matching score and the boundary condition judgment result output in the previous step are transformed into a fault validity confirmation flag with a Boolean state, achieving the expected technical effect of confirming a valid fault only when both conditions are met simultaneously.

[0163] For example, in a real-time diagnostic test of a building's intelligent window sash system, the out-of-bounds condition judgment module for structured abnormal feature segments output a Boolean value of true, the calculated topology matching score is 0.78, and the fault confirmation threshold is set to 0.75. Using a numerical comparison algorithm, the matching score is first judged to exceed the limit, and when the comparison value is 0.78... When 0.75 is greater than zero, a Boolean value indicating a matching degree exceeding the limit is generated (true). The Boolean value for the out-of-bounds condition is then parsed and confirmed to be true. The logical AND operation formula is then executed. ,in This is a boolean value indicating that the matching degree has exceeded the limit. For out-of-bounds conditions satisfying the Boolean value, the result is... If true, the fault validity confirmation flag is output, along with the occurrence time 2024-06-12 14:35:26 and data source ID_1456. In subsequent S7.5, the system calculates the comprehensive confidence level based on this flag, the matching degree value, and the severity index. Verification results show that this judgment method avoids false alarms in cases of low matching degree and significantly improves the accuracy of droop fault identification.

[0164] S7.5: Combining the fault validity confirmation flag, the topology matching score, and the severity index of the out-of-bounds condition of the structured anomaly feature fragment, calculate the final comprehensive confidence value using a weighted fusion formula to generate a complete fault discrimination result containing anomaly type label, occurrence time, and comprehensive confidence value.

[0165] Obtain the fault validity confirmation flag, topology matching score, and out-of-bounds severity index of structured abnormal feature fragments generated by the preceding sub-steps, and establish a fusion input parameter matrix as the basis for calculating the comprehensive confidence score.

[0166] Based on the fault validity confirmation flag, the topology matching degree score and the boundary crossing severity index are logically filtered and conditional weights are assigned. The parameter weights corresponding to invalid fault flags are reset to zero, while the weight coefficients corresponding to valid fault flags are kept at preset values ​​to ensure that only real faults are fused numerically.

[0167] The weighted fusion formula is used to quantitatively calculate the topology matching score and the boundary violation severity index after weight adjustment. The formula is as follows: in, To calculate the overall confidence level, This is the topology matching degree weight coefficient. Score the topology matching degree. The weighting coefficient represents the severity of the boundary violation. This is an indicator of the severity of the boundary breach.

[0168] The calculated comprehensive confidence score is normalized and mapped to the continuous interval [0,1] to match the definition of abnormal confidence score, and the decimal precision is retained to three decimal places to avoid the influence of numerical jitter on subsequent diagnostic decisions.

[0169] The normalized overall confidence score is bound to the anomaly type label and the occurrence time parameter as key-value pairs to generate a complete fault identification result data object covering the anomaly category, event time, and overall confidence score.

[0170] Through the weighted fusion and normalization process described above, the results of the previous step are transformed into a comprehensive confidence index that can be directly used for subsequent maintenance early warning triggering, thereby achieving structured output of fault identification results and improving diagnostic credibility.

[0171] For example, in a building intelligent window system, the topology matching degree weight coefficient wt is set to 0.6, the boundary violation severity weight coefficient ws to 0.4, the topology matching degree score S to 0.82, the boundary violation severity index G to 0.65, and the fault validity confirmation flag to true. An input matrix is ​​constructed and substituted into the weighted fusion formula, yielding a numerator of 0.492 + 0.26 = 0.752 and a denominator of 1.0, resulting in a comprehensive confidence score C = 0.752. After normalization, the value remains 0.752 and is rounded to three decimal places. This value is then bound to the anomaly type label (drooping fault) and the occurrence time (2024-06-15 14:32:10) to form a fault identification result object. In system verification, the confidence output using this fusion strategy significantly improves the reliability of maintenance warnings and achieves stable consistency of fault identification results under multiple operating conditions.

[0172] Step S8: If the fault identification result confirms a genuine anomaly, a window sash sagging fault diagnosis signal is output and a maintenance warning is triggered. The feature data of this anomaly event is then updated in reverse to the individualized motion memory map of the window sash, completing the adaptive evolution of the individualized motion memory map of the window sash. Specifically, this includes: S8.1: Obtain the fault identification result including abnormal confidence level and the hinge rotation resistance curve currently in real time. Perform logical parsing processing on the fault identification result based on the predefined fault level mapping rule to generate a window sash sagging fault diagnosis signal with a clear maintenance urgency indicator.

[0173] S8.2: Based on the window sash sagging fault diagnosis signal, call the intelligent operation and maintenance communication interface to perform multi-channel maintenance early warning broadcast operation, push the early warning information including fault type, occurrence time and suggested handling measures to the user terminal and cloud management platform, and generate a triggered maintenance early warning status record.

[0174] S8.3: Extract the deviation pattern feature vector and the corresponding semantic distance vector from the hinge rotation resistance curve currently running in real time. Use the spatiotemporal label alignment algorithm to associate and bind the deviation pattern feature vector with historical operation metadata to construct an abnormal event feature data package containing complete context information.

[0175] S8.4: Based on the abnormal event feature data packet, call the map incremental update engine to perform fault topology signature registration and trajectory cluster distribution correction processing. Inject the deviation pattern that is confirmed as a real anomaly into the corresponding aging stage sub-cluster of the window individualized motion memory map as a new fault sample to generate an updated fault topology signature library.

[0176] S8.5: Based on the updated fault topology signature library, recalculate the statistical boundaries of the typical resistance inflection point distribution density matrix and the transient response delay heatmap, perform global consistency verification and parameter smoothing iteration of the memory map, so as to complete the adaptive evolution of the individualized motion memory map of the window sash and output the final version of the motion memory map with the latest fault recognition capability.

[0177] For those skilled in the art, various other corresponding changes and modifications can be made based on the technical solutions and concepts described above, and all such changes and modifications should fall within the protection scope of the claims of this invention.

[0178] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this application pertains. The terms “first,” “second,” “third,” and similar terms used in this patent application specification and claims do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms “an” or “a” and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms “comprising” or “including” and similar terms mean that the element or object preceding “comprising” or “including” encompasses the element or object listed following “comprising” or “including” and its equivalents, and do not exclude other elements or objects. The “multiple” mentioned in the embodiments of this application refers to two or more. A and / or B indicate three possibilities: A; B; and A and B.

[0179] The above description is merely an exemplary embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and such modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for diagnosing window sash sagging based on hinge rotation resistance curve analysis, specifically including: S1: Obtain the raw data of the window sash during the opening and closing process, and synchronously record the human triggering method label and duration of each operation to generate the raw dataset of window sash motion; S2: Perform time normalization and phase alignment on the original dataset of window sash motion to generate a motion template sequence; S3: Based on the motion template sequence, a sliding window is used to merge the newly added motion data increments that have passed the consistency check into the historical trajectory cluster, and to construct a window individualized motion memory map containing multi-dimensional trajectory clusters, typical resistance inflection point distribution density and transient response delay heatmap. S4: Obtain the hinge rotation resistance curve, map the hinge rotation resistance curve to the high-dimensional embedding space of the window sash individualized motion memory map, calculate the semantic distance between the current resistance curve and each historical stage sub-cluster in the map, and generate a semantic distance vector. S5: Based on the environmental temperature and humidity change rate, the initial response delay offset, and the resistance fluctuation entropy in the middle uniform speed zone in the recent operations, the aging factor is generated by weighted fusion with the semantic distance vector. S6: Modulate the resistance tolerance bandwidth corresponding to the aging stage in the individualized motion memory map of the window sash using the aging factor to generate a personalized deviation judgment boundary. S7: Determine whether the hinge rotation resistance curve currently in real-time exceeds the personalized deviation judgment boundary, and detect whether its deviation mode matches the drooping fault topology signature marked in the map, and generate a fault discrimination result.

2. The sash sag failure diagnosis method based on hinge rotation resistance curve analysis according to claim 1, characterized in that, Step S7 is followed by step S8, which specifically includes: S8: If the fault identification result is confirmed as a real anomaly, output the window sash sagging fault diagnosis signal and trigger the maintenance warning, and update the feature data of the anomaly event in reverse to the window sash individualized motion memory map to complete the adaptive evolution of the window sash individualized motion memory map.

3. The sash sag failure diagnosis method based on hinge rotation resistance curve analysis according to claim 1, characterized in that, Step S3 specifically includes: The motion template sequence and the collected motion data to be fused are obtained, and the motion data to be fused is processed by time-series slicing using a sliding time window algorithm to generate standardized motion data segments with fixed time lengths. Based on the standardized motion data segments and the current motion template sequence, a dynamic envelope overlap calculation operation is performed to filter out qualified motion data segments with key feature point deviations lower than a preset confidence level, thereby generating a high-confidence incremental dataset that has been confirmed by consistency verification. Perform multidimensional trajectory clustering and fusion processing on the high-confidence incremental dataset, and use the kernel density estimation algorithm to update the spatial distribution probability of historical trajectory clusters to generate updated multidimensional trajectory clusters; Based on the resistance change nodes in the updated multidimensional trajectory cluster, inflection point statistical distribution modeling is performed to calculate the frequency and amplitude variance of resistance abrupt changes within a unit angle interval, and a typical resistance inflection point distribution density matrix is ​​generated. Using the typical resistance inflection point distribution density matrix and the timestamp information of the high-confidence incremental dataset, a transient response delay spatiotemporal mapping operation is performed to construct a delay cumulative frequency model on an angle-time two-dimensional grid, so as to generate a transient response delay heatmap that intuitively shows the degradation trend of the window sash start-stop characteristics, and construct the individualized motion memory map of the window sash.

4. The sash sag failure diagnosis method based on hinge rotation resistance curve analysis according to claim 1, characterized in that, Step S4 specifically includes: The raw data of the hinge rotation resistance curve in real time is timestamped and filtered for noise to eliminate sampling jitter and environmental transient interference, and generate a standardized resistance curve sequence with a unified time reference. Based on the standardized resistance curve sequence, multidimensional dynamic feature vectors are extracted, and local slope, curvature and energy distribution indices are calculated using the sliding window statistical method to generate structured feature descriptors. The pre-constructed high-dimensional embedding mapping function is invoked based on the structured feature descriptor to project the low-dimensional feature space data onto the high-dimensional embedding space where the individualized motion memory map of the window sash is located, thereby generating the high-dimensional embedding coordinate points of the current resistance curve. By using the high-dimensional embedded coordinate points to traverse the centers of each historical stage sub-cluster in the individualized motion memory map of the window, a similarity matching operation based on manifold distance metric is performed to generate an initial distance set between the current resistance curve and each historical stage sub-cluster. The initial distance set is weighted, aggregated, and normalized, and the semantic distance vector is generated by combining the time decay weight factors of each historical stage sub-cluster.

5. The method of claim 1, wherein: Based on the sliding first-order difference of the environmental temperature and humidity change rate, the timestamp difference of the initial response delay offset and the amplification model correction, the Shannon entropy of the resistance fluctuation entropy in the mid-section uniform velocity zone, and the semantic distance vector, an aggregated degradation index is generated using a fusion weight adaptive algorithm, and after normalization by a piecewise nonlinear function, an aging factor reflecting the percentage of the life cycle is output.

6. The method according to claim 1, characterized in that, The modulation of the resistance tolerance bandwidth includes exponentially amplifying the bandwidth in the aging direction, linearly compressing the bandwidth in the abnormal direction, and introducing an environmental change compensation term at the bandwidth boundary. The compensation value is calculated based on the temperature and humidity change rate and the thermal expansion and contraction coefficient of the material to generate the personalized deviation judgment boundary with environmental adaptability.

7. The method according to claim 1, characterized in that, Step S7 specifically includes: performing a full-point envelope scan on the hinge rotation resistance curve currently running in real time and the personalized deviation judgment boundary; merging adjacent boundary crossing points into abnormal intervals during clustering; further using the key feature parameters in the drooping fault topology signature to calculate the matching score; when the matching score exceeds a set threshold, it is determined to be a valid drooping fault, and the fault discrimination result is generated.

8. The method according to claim 1, characterized in that, The fault identification result includes an anomaly type label, occurrence time, and comprehensive confidence level. The comprehensive confidence level is a weighted fusion of topological matching degree and out-of-bounds severity, and is normalized to the 0-1 interval to reflect the identification credibility.

9. The method according to claim 1, characterized in that: After outputting the window sash sagging fault diagnosis signal, a maintenance warning is pushed through the intelligent communication interface. At the same time, the feature data packet of this abnormal event is bound with the historical operation metadata using the spatiotemporal label alignment algorithm, and updated to the trajectory cluster of the corresponding aging stage in the window sash individualized motion memory map.

10. The method according to claim 1, characterized in that, The update of the individualized motion memory map of the window sash includes recalculating the statistical boundaries of the typical resistance inflection point distribution density matrix and the transient response delay heatmap, and ensuring that the stability, adaptability and evolutionary capability of the overall system judgment boundary are improved simultaneously after the latest fault samples are included through global consistency verification and parameter smoothing iteration.

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