An Adaptive Calibration Method and Apparatus for HVAC Models Based on Residual Analysis

Abstract

This invention discloses an adaptive calibration method and apparatus for HVAC models based on residual analysis. It collects operating data of HVAC equipment to calculate physical model residuals, identifies periodic residual patterns from the predicted residual sequence to generate periodic residual identifiers, and dynamically adjusts the forgetting factor based on these identifiers to construct a noise baseline and calibration monitoring benchmark. The residual-baseline rate ratio is calculated, and the continuous over-limit trigger density is statistically analyzed to generate parameter update trigger identifiers. Abnormal residual features are extracted to form a calibration feature parameter set. The calibration feature parameter set is then subjected to online parameter identification, and periodic components are removed to generate online calibration parameters. Based on the online calibration parameters, post-calibration residual backtesting is performed to generate calibration validity identifiers. Parameters that pass verification are updated online, outputting adaptive calibration model parameters, thus improving the accuracy of calibration triggering and parameter updates.

Description

Technical Field

[0001] This invention relates to the field of HVAC control technology, and in particular to an adaptive calibration method and apparatus for HVAC models based on residual analysis. Background Technology

[0002] After long-term operation, factors such as heat exchanger scaling, refrigerant leakage, and actuator wear cause the actual performance of the HVAC system to continuously deviate from the assumptions of the physical model. The deviation between the model prediction and the measured value accumulates over time. The current maintenance method that relies on periodic manual parameter tuning is difficult to keep up with the dynamic evolution of the equipment status. The model deviation between two tunings continuously affects the reliability of the control strategy and energy consumption prediction.

[0003] The residuals of the physical model of the HVAC system simultaneously contain periodic fluctuation components and actual parameter drift components. The daytime usage patterns of the building and the group control strategy of the equipment will introduce stable periodic components into the residuals. The existing automatic calibration scheme lacks a mechanism to effectively separate the two types of components. The periodic components are easily misjudged as evidence of parameter drift, leading to deviations in the calibration direction. Furthermore, there is a lack of back-checking and verification after parameter updates. Incorrect parameters written into the physical model will actually exacerbate the deviation. Summary of the Invention

[0004] This invention discloses an adaptive calibration method and apparatus for HVAC models based on residual analysis. It aims to effectively separate periodic fluctuations and parameter drift components from the predicted residuals of physical models. By dynamically adjusting the forgetting factor, an adaptive noise baseline and calibration monitoring benchmark are constructed. The residual-baseline rate ratio drives continuous over-limit trigger density statistics to accurately identify active drift periods. Online calibration parameters are generated through online parameter identification and periodic component stripping. The closed-loop mechanism of residual back-check verification after calibration ensures the continuous reliability of parameter updates, providing accurate and efficient calibration support for the adaptive maintenance of HVAC system models.

[0005] The first aspect of this invention proposes an adaptive calibration method for HVAC models based on residual analysis, comprising the following steps: Collect operating data of HVAC equipment, perform physical model residual calculation based on the operating data to generate a predicted residual sequence, and identify periodic residual patterns from the predicted residual sequence to generate periodic residual identifiers; A noise baseline is generated by dynamically adjusting the exponentially weighted moving average forgetting factor using the predicted residual sequence and the periodic residual identifier. The fluctuation range of the noise baseline is defined to generate a noise tolerance band. A calibration monitoring benchmark is constructed by using the noise tolerance band and the predicted residual sequence. Based on the calibration monitoring benchmark, the residual-baseline rate ratio is calculated for the predicted residual sequence to generate a trigger ratio sequence. The continuous over-limit trigger density is statistically analyzed from the trigger ratio sequence to generate parameter update trigger identifiers. Based on the parameter update trigger identifiers, abnormal residual features for the corresponding time period are extracted from the predicted residual sequence to form a calibration feature parameter group. The calibration feature parameter group is subjected to online parameter identification to generate a drift rate identifier, and the drift rate identifier and the period residual identifier are used to perform period component stripping evaluation to generate online calibration parameters; After calibrating the predicted residual sequence based on the online calibration parameters, the residual back-check verification generates a calibration validity identifier. Based on the calibration validity identifier, the online calibration parameters are updated online to output adaptive calibration model parameters.

[0006] A second aspect of this invention proposes an adaptive calibration device for HVAC models based on residual analysis, comprising: The residual calculation module is used to collect operating data of HVAC equipment, perform physical model residual calculation based on the operating data to generate a predicted residual sequence, and identify periodic residual patterns from the predicted residual sequence to generate periodic residual identifiers. The baseline estimation module is used to dynamically adjust the exponentially weighted moving average forgetting factor using the predicted residual sequence and the periodic residual identifier to generate a noise baseline, define the fluctuation range of the noise baseline to generate a noise tolerance band, and construct a calibration monitoring benchmark by using the noise tolerance band and the predicted residual sequence. The trigger identification module is used to calculate the residual-baseline rate ratio of the predicted residual sequence based on the calibration monitoring benchmark to generate a trigger ratio sequence, statistically analyze the continuous over-limit trigger density from the trigger ratio sequence to generate parameter update trigger identifiers, and extract abnormal residual features of the corresponding time period from the predicted residual sequence based on the parameter update trigger identifiers to form a calibration feature parameter group. An online identification module is used to perform online parameter identification on the calibration feature parameter group to generate a drift rate identifier, and to use the drift rate identifier and the periodic residual identifier to perform periodic component stripping evaluation to generate online calibration parameters; The calibration update module is used to calibrate the predicted residual sequence based on the online calibration parameters, perform residual back-check verification to generate a calibration validity identifier, and update the online calibration parameters online according to the calibration validity identifier to output adaptive calibration model parameters.

[0007] The beneficial effects of this invention are reflected in the following points: 1. By performing spectral decomposition and cross-period peak consistency analysis on the predicted residual sequence to identify stable periodic components, and using periodic residual identifiers to drive dynamic adjustment of the forgetting factor to construct an adaptive noise baseline, and combining an effective offset marker set to apply directional correction to the noise tolerance band to establish a calibration monitoring benchmark, the effective separation of periodic fluctuations and systematic shifts is achieved, reducing the probability of calibration false triggering caused by periodic component interference. 2. At the calibration triggering level, the ratio of the predicted residual change rate to the baseline change rate of the calibration monitoring benchmark is calculated. Through continuous over-limit trigger density statistics, the active period of parameter drift is accurately located. The extraction range of abnormal residual features strictly corresponds to the trigger segment, avoiding the inclusion of normal fluctuations in stable periods in feature estimation, and improving the representativeness of the calibration feature parameter set to the true drift state. 3. To ensure the reliability of calibration parameters, the drift acceleration state is quantified by identifying monotonic drift segments and performing second-order difference analysis. Combined with periodic component stripping, the net parameter drift is obtained and online calibration parameters are generated. Before the calibration parameters are written into the physical model, they are verified by residual back-checking after calibration. Measurement points that fail the validity test retain their original parameter values ​​and trigger re-identification, forming a closed-loop mechanism of calibration-verification-iteration, which ensures the continuous reliability of the adaptive calibration model parameters. Attached Figure Description

[0008] The accompanying drawings illustrate specific examples of the technical solutions described in this invention and, together with the detailed embodiments, form part of the specification, serving to explain the technical solutions, principles, and effects of this invention.

[0009] Figure 1 This is a flowchart illustrating an adaptive calibration method for HVAC models based on residual analysis, as proposed in this invention.

[0010] Figure 2 This is a structural block diagram of an adaptive calibration device for HVAC models based on residual analysis, according to the present invention. Detailed Implementation

[0011] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0012] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0013] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0014] The technical solutions of the embodiments of this application will be described below.

[0015] like Figure 1 As shown, this embodiment of the invention provides an adaptive calibration method for HVAC models based on residual analysis, including the following steps S110-S150: Step S110: Collect HVAC equipment operation data, calculate physical model residuals based on operation data to generate a predicted residual sequence, and identify periodic residual patterns from the predicted residual sequence to generate periodic residual identifiers.

[0016] Specifically, HVAC equipment operation data is collected. This data is acquired in real-time from sensors and controllers of various sub-equipment within the HVAC system. It covers multiple physical quantities, including chilled water supply and return temperatures, cooling water supply and return temperatures, compressor power, chilled water pump and cooling water pump frequencies, expansion valve opening, and indoor and outdoor ambient temperature and humidity. Each physical quantity is grouped according to its acquisition point identifier, and the acquisition cycle is uniformly set to 1 minute. Measurement points with acquisition interruptions exceeding 3 cycles are marked as having missing data, and the corresponding data during the missing period is not included in subsequent calculations. The HVAC equipment operation data is organized hierarchically by subsystem, with data from the chiller unit side and terminal air conditioning unit side grouped separately. The chiller unit side focuses on acquiring compressor operating status and chilled water outlet temperature, while the terminal air conditioning unit side focuses on acquiring supply air temperature and valve opening. The acquisition timestamps for both sides are uniformly calibrated to eliminate data misalignment caused by clock deviations. After the data acquisition is completed, the measured values ​​of each measuring point in the HVAC equipment operation data are checked for validity. The check includes two items: range exceeding the limit and adjacent cycle jump. When the measured value of a measuring point exceeds the upper limit of the sensor range or the change amplitude between two adjacent cycles exceeds the physically achievable rate, it is marked as an abnormal point. Abnormal points are replaced by linear interpolation and an abnormal label is added. Measuring points with an abnormality rate of more than 10% are marked as low quality in the HVAC equipment operation data. The confidence of the residual calculation results of low quality measuring points is reduced accordingly.

[0017] Based on HVAC equipment operating data, a physical model residual calculation is performed to generate a predicted residual sequence. The physical model is based on the thermodynamic equations of the refrigeration system, establishing steady-state mapping relationships between parameters under various operating conditions. The model input includes three main driving variables: outdoor dry-bulb temperature, chilled water supply temperature setpoint, and system load rate. The output is the theoretical power and flow prediction values ​​for each sub-equipment under the corresponding operating conditions. The difference between the measured values ​​at each measuring point in the HVAC equipment operating data and the corresponding predicted values ​​output by the physical model is the residual for that measuring point at that moment. The residual calculation formula is e_k = y_k - y_pred_k, where e_k is the residual of the kth acquisition cycle, y_k is the measured value of the corresponding measuring point in the HVAC equipment operating data, and y_pred_k is the predicted value of the physical model for that measuring point with outdoor dry-bulb temperature, chilled water supply temperature setpoint, and system load rate as input. A positive e_k indicates that the measured value is higher than the model prediction, while a negative e_k indicates that the measured value is lower than the prediction. The larger the absolute value of e_k, the greater the deviation between the actual operating state of the sub-equipment and the model assumption. The e_k values ​​for each acquisition cycle are arranged in chronological order to form a prediction residual sequence. The prediction residual sequence covers all measurement points, and the prediction residual sequence for each measurement point is stored independently. The sequence length is consistent with the number of effective acquisition cycles. Cycles with missing or abnormal HVAC equipment operating data are marked as invalid points at the corresponding positions in the prediction residual sequence. Invalid points do not participate in subsequent periodic residual pattern recognition.

[0018] In some embodiments, the step of identifying periodic residual patterns from the predicted residual sequence and generating periodic residual identifiers includes: performing spectral decomposition on the predicted residual sequence to extract periodic frequency components and generate a residual spectral distribution; performing multi-period spectral peak comparison analysis based on the residual spectral distribution to generate a cross-period peak consistency distribution; using the cross-period peak consistency distribution to identify high-stability peak frequencies and generate an effective periodic candidate set; and calibrating the periodic residual patterns using the effective periodic candidate set to generate periodic residual identifiers.

[0019] The residual spectrum distribution is generated by extracting periodic frequency components from the predicted residual sequence through spectral decomposition. Spectral decomposition employs Fast Fourier Transform (FFT) on the time-domain data of the predicted residual sequence. Before the transform, the sequence is detrended by subtracting the linear fit value. Removing linear drift components allows the spectral decomposition results to better reflect the true periodic fluctuations without being affected by slow drift. The FFT outputs the amplitude and phase spectra of each frequency component. The amplitude spectrum reflects the energy intensity of each frequency component in the predicted residual sequence; a higher amplitude indicates a more significant periodic fluctuation at that frequency. In HVAC systems, compressor power residuals typically exhibit a significant amplitude peak at the daily cycle frequency, reflecting the regular model bias caused by the difference in daytime and nighttime loads. The residual spectrum distribution is composed of the amplitudes of each frequency component in the amplitude spectrum arranged from low to high frequency. The frequency resolution is determined by the time span of the predicted residual sequence; a longer time span results in higher frequency resolution, enabling the differentiation of frequency components with similar daily and weekly cycles. Frequency components in the residual spectrum distribution with amplitudes exceeding the noise floor threshold are extracted as periodic frequency candidate points. The noise floor threshold is determined by adding twice the standard deviation to the mean of the low-amplitude region in the residual spectrum distribution. Amplitudes below this threshold are considered background noise and are not included in subsequent analysis. When the variable frequency speed control strategy of the HVAC system's refrigeration pump switches once per hour, the amplitude at the corresponding frequency is usually significantly higher than the noise floor threshold and is extracted as a candidate point. However, the amplitude of random frequency components introduced by sensor sampling jitter is usually below the threshold and is filtered out. When the number of valid points in the predicted residual sequence is less than one complete period, the reliability of the spectral decomposition results is low, the residual spectrum distribution is marked as insufficient data, and the subsequent peak comparison process is not triggered.

[0020] Multi-period peak frequency comparison analysis based on residual spectral distribution generates a cross-period peak consistency distribution. The multi-period peak frequency comparison uses the noise floor threshold and peak frequency range determined by the residual spectral distribution as reference benchmarks. The predicted residual sequence is divided into multiple subsequences according to time. Each subsequence undergoes independent spectral decomposition to obtain the spectrum of the corresponding time period. The noise floor threshold and candidate frequency range in the subsequence spectral decomposition follow the corresponding settings in the residual spectral distribution. The subsequence length is set to an integer multiple of the period corresponding to the candidate peak frequency with the highest amplitude in the residual spectral distribution to avoid truncation effects introducing spectral leakage. The overlap ratio between adjacent subsequences is set to 50% to improve time period coverage density. The peak frequencies in the spectrum of each time period are extracted as the spectral peak set for that time period. The peak frequency is the frequency point above the noise floor threshold in the residual spectral distribution that forms a local maximum on the frequency axis. When the residual spectral distribution of a certain measurement point in the HVAC system shows the same frequency in the spectral peak sets of multiple consecutive time periods, it indicates that the periodic fluctuation corresponding to that frequency has a stable physical origin and is not a random disturbance. The occurrence consistency of each peak frequency is obtained by dividing the number of times each peak frequency appears in the peak set of the spectrum in different time periods by the total number of time periods. The occurrence consistency of all peak frequency candidate points is arranged by frequency to form a cross-time period peak consistency distribution. In the cross-time period peak consistency distribution, frequency points with high consistency correspond to periodic components that exist stably in the time dimension, while frequency points with low consistency correspond to occasional or brief non-periodic disturbances. When there are no frequency components in the residual spectrum distribution with amplitudes exceeding the noise floor threshold, the cross-time period peak consistency distribution is set to zero, and subsequent extraction of effective periodic candidate sets is not performed.

[0021] High-stability peak frequencies are identified using cross-period peak consistency distributions to generate a candidate set of effective periods. High-stability peak frequencies correspond to frequency points in the cross-period peak consistency distribution where consistency exceeds a stability threshold. A stability threshold of 0.7 indicates that the frequency exhibits a significant peak in more than 70% of the time-period spectrum. Frequency points with consistency higher than 0.7 possess sufficient cross-period reproducibility and can be identified as genuine periodic fluctuation components in the predicted residual sequence. The rationality of the stability threshold is reflected in the operation of HVAC equipment. Genuine periodic deviations originate from physical mechanisms such as equipment aging, control strategy patterns, or load patterns. Residual periods driven by these mechanisms remain stable over long time scales, while frequency components introduced by occasional disturbances or measurement noise typically have consistency below 0.7 across different time periods. The set of high-stability peak frequencies that meet the stability threshold condition constitutes the candidate set of effective periods. Each frequency point in the candidate set of effective periods is accompanied by two attributes: occurrence consistency and average amplitude. Occurrence consistency reflects the robustness of the period in the time dimension, while the average amplitude reflects the contribution of the period to the energy of the predicted residual sequence. These two attributes are used in the subsequent period residual labeling to distinguish between dominant and secondary periods. When the peak consistency distribution across time periods is set to zero, the effective periodic candidate set is empty. The empty set corresponds to the absence of stable periodic fluctuation components in the predicted residual sequence, indicating that the model residual is mainly composed of random noise.

[0022] Periodic residual identifiers are generated by calibrating periodic residual patterns using an effective periodic candidate set. The period duration corresponding to each frequency point in the effective periodic candidate set is determined by the reciprocal of the frequency. The period duration covers multiple scales from hourly to daily cycles. Common cycle scales in HVAC systems include the hourly component of the corresponding equipment start-stop control cycle and the 24-hour component of the corresponding daily load pattern. The physical causes of different cycle scales are different. Hourly cycles are usually related to chiller group control switching strategies, while daily cycles are usually related to load fluctuations caused by building usage patterns. The frequency point with the highest average amplitude in the effective periodic candidate set corresponds to the dominant cycle with the most concentrated energy in the predicted residual sequence. The four values ​​of the dominant cycle—cycle duration, average amplitude, average phase, and occurrence consistency—are extracted as the core fields of the periodic residual identifier. The average phase is determined by taking the circumferential average of the phase spectrum at the dominant cycle frequency in the spectrum of each time period, reflecting the starting offset position of the periodic component on the time axis. The corresponding information of the secondary cycles is added as a supplementary field to the periodic residual identifier. The dominant period duration in the periodic residual identifier reflects the main rhythm of the model residual fluctuations. When this rhythm closely matches the execution cycle of the HVAC control strategy, it indicates a systematic deficiency in the physical model's description of the control dynamic response. When the rhythm matches the building usage pattern, it indicates a regular deviation in the model's load prediction component. When the effective period candidate set is empty, the periodic residual identifier is marked as having no significant period, indicating that the fluctuations in the prediction residual sequence are mainly composed of non-periodic random components, and the model bias originates from random disturbances rather than regular mismatches.

[0023] Step S120: The predicted residual sequence is used to dynamically adjust the exponentially weighted moving average forgetting factor to generate a noise baseline by combining the periodic residual identifier. The fluctuation range of the noise baseline is defined to generate a noise tolerance band. The calibration monitoring benchmark is constructed by the noise tolerance band and the predicted residual sequence.

[0024] In some embodiments, the step of dynamically adjusting the exponentially weighted moving average forgetting factor using the predicted residual sequence in conjunction with the periodic residual identifier to generate a noisy baseline includes: quantizing the periodic intensity of the periodic residual identifier to generate a periodic intensity coefficient; mapping the predicted residual sequence to a forgetting factor using the periodic intensity coefficient to generate a dynamic forgetting factor sequence; performing an exponentially weighted moving average calculation on the predicted residual sequence based on the dynamic forgetting factor sequence to generate a smoothed residual sequence; and determining a baseline estimate based on the smoothed residual sequence to generate a noisy baseline.

[0025] Periodic intensity coefficients are generated by quantifying the periodic residual identifiers. The average amplitude of the dominant period in the periodic residual identifier reflects the energy intensity of the periodic fluctuation, while consistency reflects the temporal stability of the periodic fluctuation. The daily periodic residual amplitude of HVAC systems during peak building usage is usually much higher than that during non-working periods. The quantification results of periodic intensity can accurately distinguish between high-intensity periodic drive and low-intensity random fluctuation. The periodic intensity coefficient is determined by multiplying the normalized value of the instantaneous amplitude of the dominant period by the consistency. The instantaneous amplitude is obtained by extracting the amplitude spectrum peak at the dominant frequency through a sliding short-time Fourier transform with the duration of the dominant period as the window width, periodically. The normalized amplitude, ranging from 0 to 1, is obtained by dividing the instantaneous amplitude by the historical maximum instantaneous amplitude. When secondary periods exist in the periodic residual identifier, the periodic intensity coefficient of the secondary period is calculated separately in the same way. The weighted sum of the periodic intensity coefficients of the dominant period and the secondary period is taken as the comprehensive intensity output. The weight of the dominant period is 0.7, and the weight of the secondary period is 0.3. The upper limit of the weighted sum is truncated to 1 to ensure boundedness. When the periodic residual is marked as having no significant period, the periodic intensity coefficient is assigned a value of 0. In subsequent forgetting factor mapping, the default forgetting factor is used and no dynamic adjustment is performed. The periodic intensity coefficient is updated point-by-point according to the collection cycle. The basic mapping formula between the periodic intensity coefficient and the forgetting factor is λ_base_k = λ_max - (λ_max - λ_min) × C_k, where C_k is the periodic intensity coefficient of the k-th collection cycle, λ_max is the upper limit of the forgetting factor (empirical value 0.98), λ_min is the lower limit of the forgetting factor (empirical value 0.85), and λ_base_k is the basic forgetting factor value directly mapped based on the periodic intensity coefficient.

[0026] For example, the step of using the periodic intensity coefficient to perform forgetting factor mapping on the predicted residual sequence to generate a dynamic forgetting factor sequence includes: performing time-series difference calculation on the periodic intensity coefficient to generate an intensity change rate sequence; identifying intensity rising segments based on the intensity change rate sequence to generate a feedforward trigger set; using the feedforward trigger set and the periodic intensity coefficient to perform forgetting factor feedforward configuration to generate a feedforward forgetting factor group; and performing time-varying mapping on the predicted residual sequence according to the feedforward forgetting factor group to generate a dynamic forgetting factor sequence.

[0027] A time-series difference calculation is performed on the periodic intensity coefficient to generate an intensity change rate sequence. The time-series difference is applied to the time-domain data of the periodic intensity coefficient. The difference between the periodic intensity coefficient values ​​of two adjacent acquisition periods is divided by the acquisition interval to obtain the intensity change rate at that time point. The formula for calculating the intensity change rate is r_k=(C_k-C_{k-1}) / T_s, where r_k is the intensity change rate of the k-th acquisition period, C_k and C_{k-1} are the periodic intensity coefficients of the k-th and (k-1)-th acquisition periods, respectively, and T_s is the acquisition interval. A positive r_k indicates that the periodic intensity is increasing, while a negative r_k indicates that the periodic intensity is decreasing. The larger the absolute value, the more drastic the change in periodic intensity. Approximately 30 minutes before the building is opened, the pre-cooling start of the chiller in the HVAC system causes a rapid increase in the load rate. During this stage, the daily periodic residual component experiences a rapid increase in energy, corresponding to a rapid increase in the periodic intensity coefficient. The intensity change rate sequence shows a continuous large positive value during this period, reflecting that the periodic intensity is in a rapid accumulation phase. The intensity change rate sequence is composed of the difference results from all acquisition cycles arranged chronologically. It is one element shorter than the periodic intensity coefficient sequence. For acquisition cycles with a periodic intensity coefficient of 0, the difference result in the intensity change rate sequence is usually close to zero. However, if the periodic intensity coefficient of an adjacent cycle suddenly increases from zero, it corresponds to a large positive change rate. This jump indicates the sudden appearance of a periodic component. Isolated elements with abnormally large absolute values ​​in the intensity change rate sequence correspond to transient abrupt changes in the periodic intensity coefficient, usually caused by a single measurement anomaly rather than a true change in periodic intensity. Isolated abrupt change elements are identified and labeled using median filtering of adjacent elements. After labeling, they are not included in the determination of subsequent intensity increase segments.

[0028] A feedforward trigger set is generated based on the intensity change rate sequence to identify intensity-increasing segments. An intensity-increasing segment corresponds to a time period in the intensity change rate sequence where the change rate is positive for multiple consecutive acquisition cycles and the mean exceeds a positive threshold. The positive threshold is set as the mean of the historical positive values ​​in the intensity change rate sequence. This threshold filters out weak positive changes and retains segments with a significant upward trend. The determination of continuous positive exceedance of the threshold requires at least three consecutive acquisition cycles to meet this condition. Periods with fewer than three positive exceedances are considered short-lived fluctuations and are not included in the intensity-increasing segment. This length requirement ensures that the identified increasing segments have sufficient persistence to reflect the true strengthening trend of the cyclic intensity rather than random disturbances. During the daily start-up phase of the HVAC system, the cyclic intensity coefficient rapidly rises from a low value to a high value. The corresponding intensity change rate sequence continuously exceeds the positive threshold during this phase. This continuous increasing segment is identified as a trigger record in the feedforward trigger set, indicating that the forgetting factor should be tightened in advance during this phase to prevent the baseline estimate from being skewed when the cyclic component rapidly strengthens. The feedforward trigger set consists of three fields: the start time, the end time, and the mean of the intensity change rate sequence within the entire intensity increase segment. The mean reflects the average enhancement rate of the increase segment. The higher the enhancement rate, the faster the dominance of the periodic component increases, and the corresponding forgetting factor needs to be tightened more quickly. When there are no consecutive positive segments exceeding the threshold in the intensity change rate sequence, the feedforward trigger set is empty, and the subsequent forgetting factor feedforward configuration is not executed.

[0029] A feedforward forgetting factor set is generated by using a feedforward trigger set and a periodic intensity coefficient to perform feedforward configuration of the forgetting factor. The HVAC system pre-cools the building before opening each morning, during which the daily periodic component energy rapidly accumulates. If the forgetting factor is tightened only after the periodic component has fully intensified, the baseline estimate will be skewed. Early intervention ensures the forgetting factor is tightened before pre-cooling begins, thus guaranteeing baseline stability during the rapid intensification phase of the periodic component. The advance amount for feedforward intervention is determined by the average enhancement rate of each segment in the feedforward trigger set. Segments with higher enhancement rates require earlier intervention. The advance amount T_lead = α / v_rise, where α is the feedforward adjustment coefficient (empirical value of 0.5), v_rise is the mean of the intensity change rate sequence within the segment, and the unit of T_lead is consistent with the acquisition interval. The upper limit of T_lead is truncated to the dominant period duration to prevent the advance amount from approaching infinity when v_rise approaches zero. The feedforward forgetting factor values ​​at each time step in the feedforward forgetting factor set are linearly tightened from the default value to the target low value starting from the T_lead time step before the trigger segment of the feedforward trigger set. The tightened target low value is calculated based on the predicted value of the periodic intensity coefficient at the end of the corresponding trigger segment using the aforementioned basic mapping formula. The predicted value of the periodic intensity coefficient at the end of the trigger segment is obtained by linear extrapolation of the periodic intensity coefficient at the start of the segment and the mean of the intensity change rate sequence within the segment. The extrapolation formula is C_pred = C_start + v_rise × T_segment, where C_start is the periodic intensity coefficient at the start of the segment, T_segment is the segment duration, and the upper limit of C_pred is truncated to 1 to ensure boundedness. The calculation result ensures that the forgetting factor reaches the target level after the periodic enhancement is complete when the feedforward is finished. When the feedforward trigger set is empty, the feedforward forgetting factor set has the same forgetting factor value as the one directly mapped based on the periodic intensity coefficient, and no feedforward correction is applied. The feedforward forgetting factor set is output point by point according to the acquisition cycle, with each point corresponding to a forgetting factor value for subsequent time-varying mapping.

[0030] A dynamic forgetting factor sequence is generated by performing a time-varying mapping on the predicted residual sequence based on the feedforward forgetting factor set. The time-varying mapping is based on the forgetting factor values ​​of each acquisition period in the feedforward forgetting factor set, combined with the reactive forgetting factor value obtained from the basic mapping formula using the current period intensity coefficient. The smaller of the two values ​​is taken as the final forgetting factor output for that moment. The logic for taking the smaller value is that if either the feedforward or reactive estimation method determines that the current period component has a strong influence, the forgetting factor should be tightened first. This conservative strategy ensures that the baseline estimation is not skewed by period fluctuations. The feedforward forgetting factor set is tightened in advance before the intensity rises, while the reactive estimation maintains a higher value before the intensity is fully reflected. Taking the smaller value allows the feedforward effect to take effect early in the rising phase. During the daily start-up phase of the HVAC system, while the daily period component is still in the process of strengthening, the feedforward forgetting factor intervenes in advance, keeping the dynamic forgetting factor sequence low during this phase. This improves the sensitivity of the baseline estimation to recent data. The result after taking the smaller value still needs to be smoothed to eliminate the point-by-point jitter that may be introduced during the linear tightening of the feedforward forgetting factor group. The smoothing method is to apply a simple moving average of 3 acquisition cycles to the sequence after taking the smaller value. The smoothed result is the final value of the corresponding time in the dynamic forgetting factor sequence. The dynamic forgetting factor sequence is composed of the final forgetting factor values ​​of all acquisition cycles arranged in chronological order. This sequence integrates both feedforward and reactive information and has a better anticipatory response capability during the period of rapid enhancement of the periodic component compared with the simple reactive mapping.

[0031] A smoothed residual sequence is generated by performing an exponentially weighted moving average on the predicted residual sequence based on the dynamic forgetting factor sequence. The exponentially weighted moving average uses λ_k at each time point in the dynamic forgetting factor sequence as the time-varying weight, and updates the weighted historical mean of the residual point by point. The update formula is S_k = λ_k × S_{k-1} + (1-λ_k) × e_k, where S_k is the smoothed value of the k-th acquisition period, S_{k-1} is the smoothed value of the previous period, and e_k is the residual value of the k-th acquisition period in the predicted residual sequence. The larger λ_k is, the higher the weight of S_{k-1} and the more fully historical information is retained. The smaller λ_k is, the higher the weight of e_k and the more sensitive the response to recent data. During the transition period from full daytime load to light nighttime load in the HVAC system, the unloading of the chiller causes a brief and significant fluctuation in the power residual. During this period, the rapid decrease in the diurnal energy component leads to a larger λ_k in the dynamic forgetting factor sequence, resulting in a higher weight of S_{k-1}. This effectively suppresses the impact of transient residual fluctuations on the smoothed residual sequence, allowing it to transition smoothly rather than exhibiting false jumps due to transient fluctuations. Invalid points in the predicted residual sequence are skipped during processing. When skipped, S_k directly inherits the value of S_{k-1} to maintain the continuity of the smoothed residual sequence. If sensor communication interruption causes consecutive invalid points to span more than one complete dominant cycle, the corresponding segment of the smoothed residual sequence is marked as having low estimation reliability. This marking prevents abrupt changes in the initial data after communication recovery from being misjudged as drift acceleration. The S_k values ​​from all acquisition cycles are arranged in chronological order to form a smoothed residual sequence. The smoothed residual sequence retains the low-frequency trend components of the predicted residual sequence and suppresses high-frequency random noise and periodic fluctuations. When the heat exchanger of the HVAC system is fouled, the heat transfer efficiency continues to decrease. The smoothed residual sequence of the corresponding measurement point increases monotonically over several consecutive acquisition cycles, and the measured power is consistently higher than the model prediction. This unidirectional drift mode is a typical signal that triggers subsequent parameter calibration.

[0032] A noise baseline is generated by determining the baseline estimate based on the smoothed residual sequence. The current value of the smoothed residual sequence in each acquisition period serves as a candidate baseline estimate for that moment. The candidate value must pass a short-term stability test before it can be confirmed as the official baseline. The short-term stability test requires that the change in the smoothed residual sequence value over the most recent 5 acquisition periods does not exceed 20% of the historical standard deviation of the predicted residual sequence. When this condition is met, the current baseline estimate is considered to be in a steady state, and the current smoothed residual sequence value is directly confirmed as the current value of the noise baseline. If the short-term stability test fails, it indicates that the smoothed residual sequence is still in a rapid change phase. During the initial stage of chiller startup, the HVAC system undergoes a thermal equilibrium establishment process. During this process, the smoothed residual sequence continuously changes, and the current value of the noise baseline remains unchanged from the previous steady-state confirmed value until stability is restored and then updated again. This mechanism prevents transient residual fluctuations during the transition process from being incorrectly written into the noise baseline. The historical sequence of the noise baseline retains the daily average of the most recent 7 days to assess the long-term drift trend of the baseline. The slope of the linear fit of the 7-day average reflects the long-term evolution rate of the model bias. A continuous increase in the absolute value of the slope indicates that the drift of the model parameters is accelerating, and the priority of calibration triggering needs to be increased. When the overall effective rate of the smoothed residual sequence is less than 50%, the noise baseline is marked as low reliability. The low reliability noise baseline triggers a conservative estimation strategy in the subsequent noise tolerance band definition.

[0033] A noise tolerance band is generated by defining the fluctuation range of the noise baseline. The noise tolerance band is defined with the noise baseline as the central axis. The upper and lower boundaries are determined by estimating the distribution range of random noise components in the predicted residual sequence. The boundary range reflects the reasonable fluctuation space of the predicted residual sequence around the noise baseline under normal operating conditions. Residual fluctuations within the boundary range are considered normal noise and do not trigger calibration; fluctuations exceeding the boundary are considered abnormal signals and enter subsequent analysis. The deviation of each point in the predicted residual sequence relative to the noise baseline value at the same moment is extracted as the baseline-removed residual sequence. The standard deviation of the baseline-removed residual sequence after removing periodic components is estimated as the random noise intensity. The removal method is to apply band-stop filtering corresponding to the dominant period in the periodic residual identifier to the baseline-removed residual sequence. After band-stop filtering, the remaining components are mainly random noise. The upper boundary of the noise tolerance band is set to the current value of the noise baseline plus twice the random noise intensity, and the lower boundary is set to the current value of the noise baseline minus twice the random noise intensity. Twice the standard deviation covers approximately 95% of the probability range of the normal distribution. During the transitional season when the outdoor temperature fluctuates drastically during the day, the noise measured by the air supply temperature sensor of the terminal air conditioning unit increases significantly. The tolerance band width is adaptively widened according to the current random noise intensity, effectively avoiding misjudging the temporary over-limit caused by environmental disturbances as a systematic offset that requires calibration. The upper and lower boundaries of the noise tolerance band are output together with the noise baseline. The relative positions of the three curves on the time axis intuitively reflect the normal fluctuation space of the current model residual.

[0034] In some embodiments, constructing a calibration monitoring benchmark using the noise tolerance band and the predicted residual sequence includes: generating a residual limit-crossing distribution by performing a point-by-point comparison between the predicted residual sequence and the noise tolerance band; performing upper and lower limit-crossing symmetry analysis on the residual limit-crossing distribution to generate a limit-crossing skewness index; identifying asymmetric limit-crossing intervals based on the limit-crossing skewness index to generate an effective offset marker set; and constructing a calibration monitoring benchmark using the effective offset marker set and the noise tolerance band.

[0035] The residual limit distribution is generated by point-by-point comparison between the predicted residual sequence and the noise tolerance band. The point-by-point comparison compares the residual values ​​of each acquisition period in the predicted residual sequence with the upper and lower boundaries of the noise tolerance band at the same time. A residual value exceeding the upper boundary is marked as an upper limit violation, below the lower boundary as a lower limit violation, and within the boundary range as normal. These three states are assigned values ​​of 1, -1, and 0, respectively. If multiple consecutive periods in the residual limit violation distribution show upper limits violation, it indicates that the predicted residual sequence is consistently higher than the noise tolerance band during that period. This suggests that the HVAC system's refrigeration unit is experiencing a decrease in cooling efficiency due to refrigerant leakage, resulting in a consistently higher measured power value than the model prediction. The corresponding residual limit violation distribution exhibits a typical continuous upper limit violation pattern. Continuous lower limits violation may correspond to sensor zero-point drift or refrigerant overcharging, leading to abnormally high system efficiency. Invalid points in the predicted residual sequence are marked as missing during point-by-point alignment. Missing points are not included in the out-of-limit count but are retained as placeholders to maintain the continuity of the sequence's time axis. The statistical confidence of the corresponding segment in the residual out-of-limit distribution with dense missing points is correspondingly reduced. When the upper and lower out-of-limits alternate densely in the residual out-of-limit distribution, it indicates that the predicted residual sequence is oscillating violently near the boundary of the noise tolerance band. This pattern usually corresponds to increased measurement noise or frequent switching of equipment operating conditions and is not a systematic bias requiring calibration. Identifying this pattern can effectively avoid misjudging measurement disturbances as model drift.

[0036] A symmetry analysis of the upper and lower limits of the residual out-of-limit distribution is performed to generate an out-of-limit skewness index. The symmetry analysis focuses on the relative ratio of the number of upper to lower limits within a statistical period. The statistical period is set to an integer multiple of the dominant period length of the periodic residual identifier to eliminate the interference of periodic fluctuations on the ratio of upper and lower limits. When the periodic residual identifier is marked as having no significant period, the statistical period uses the default value of 24 hours. Setting the period to an integer multiple ensures that the complete waveform of the periodic component is included in the statistics within each statistical period, avoiding the introduction of artificial asymmetry due to truncation effects. The number of upper limits within the statistical period is denoted as N_up, and the number of lower limits is denoted as N_down. The out-of-limit skewness index is determined by the formula Skew=(N_up-N_down) / (N_up+N_down), where Skew ranges from -1 to 1. A positive Skew indicates that the upper limit is dominant, and a negative Skew indicates that the lower limit is dominant. The larger the absolute value of Skew, the more asymmetric the out-of-limit distribution. The time series of the out-of-limit skewness index reflects the evolution of the model bias direction. When the operating efficiency of the chiller in the HVAC system continuously declines due to equipment aging, the power residual remains consistently positive, causing the out-of-limit skewness index to remain positive for a long time, indicating a systematic underestimation in the physical model. Conversely, when the cooling water temperature sensor experiences negative zero-point drift, the measured value remains consistently lower than the true value, corresponding to an out-of-limit distribution where out-of-limit is dominant, and the out-of-limit skewness index remains negative. The two types of directional biases are intuitively distinguished by the sign of the out-of-limit skewness index. When the number of missing points in the statistical period exceeds 30% of the total number of collection points in that period, the out-of-limit skewness index is marked as insufficient data and does not participate in subsequent offset labeling identification. This labeling avoids misjudgment caused by a severe imbalance in the out-of-limit statistical sample due to the concentration of missing points in the out-of-limit period. When both the upper and lower out-of-limit occurrences in the residual out-of-limit distribution are zero, the out-of-limit skewness index is assigned a value of 0, indicating that the predicted residual sequence in the current statistical period is completely within the noise tolerance band, with no signs of systematic offset.

[0037] Asymmetric out-of-limit intervals are identified based on the out-of-limit skewness index, generating a valid offset marker set. An asymmetric out-of-limit interval corresponds to a period where the absolute value of the out-of-limit skewness index consistently exceeds the skewness threshold of 0.4 over multiple consecutive statistical periods. A skewness threshold of 0.4 corresponds to an upper-to-lower limit ratio of 7:3 or higher within a statistical period. This asymmetry exceeds the normal fluctuation range caused by random noise, indicating a genuine systematic shift in the predicted residual sequence in this direction. When evaporator scaling occurs in a HVAC system, the measured chilled water outlet temperature consistently exceeds the model prediction, corresponding to a long-term bias of the out-of-limit skewness index towards the upper out-of-limit side, a typical unidirectional systematic shift scenario. An asymmetric out-of-limit interval is defined as a statistical period exceeding the skewness threshold for at least three consecutive periods. Periods exceeding the threshold for fewer than three statistical periods are considered occasional fluctuations and not included in the marker set. When a short-term external disturbance causes a sudden increase in the out-of-limit skewness index in a single statistical period, followed by a rapid recovery, a valid offset marker is not triggered, ensuring that the valid offset marker set only records persistent systematic shift events. The start and end times of the asymmetric out-of-limit interval and the mean of the out-of-limit skewness index within the interval are extracted as offset label triples. The triples completely describe the time range and intensity of a valid offset event. All offset label triples are summarized to form the valid offset label set. When the out-of-limit skewness index does not exceed the skewness threshold throughout the entire process, the valid offset label set is an empty set. The empty set corresponds to the overall symmetry of the out-of-limit distribution of the current predicted residual sequence, and there is no systematic offset that needs to be labeled.

[0038] A calibration monitoring baseline is constructed using an effective offset marker set and a noise tolerance band. The time interval corresponding to each offset marker triplet in the effective offset marker set is superimposed with an offset correction amount on top of the noise tolerance band. The offset correction amount is determined by the product of the mean of the out-of-limit skewness index within the corresponding interval and the current half-width of the noise tolerance band. The upper limit of the absolute value of the correction amount is truncated to half the width of the noise tolerance band to prevent excessive central axis offset from causing failure in reverse detection. When the mean of the out-of-limit skewness index is positive, the correction amount is offset upwards towards the central axis of the noise tolerance band; when it is negative, it is offset downwards. After correction, the central axis position is closer to the actual distribution center of the predicted residual sequence within that interval. The upper and lower boundaries of the noise tolerance band after offset correction, together with the corrected central axis, constitute the calibration monitoring baseline within that time interval. The calibration monitoring baseline for time intervals not covered by the effective offset marker set directly inherits the upper and lower boundaries of the noise tolerance band without applying offset correction. The upper and lower boundaries of the calibration monitoring benchmark shift entirely within the offset interval compared to the original noise tolerance band. The direction of this shift is consistent with the offset direction recorded in the effective offset marker set. The continuous upward shift caused by the decrease in the cooling efficiency of the HVAC system causes the calibration monitoring benchmark to shift upward as a whole. Based on the corrected boundary judgment, the out-of-limit judgment can effectively distinguish between true model drift and normal periodic noise fluctuations, reducing the probability of falsely triggering calibration. When the effective offset marker set is empty, the calibration monitoring benchmark is completely consistent with the noise tolerance band. After the calibration monitoring benchmark is established, it serves as the basis for subsequent steps to determine whether the predicted residual sequence triggers parameter updates.

[0039] Step S130: Calculate the residual-baseline rate ratio of the predicted residual sequence based on the calibration monitoring benchmark to generate a trigger ratio sequence. Statistically calculate the continuous over-limit trigger density from the trigger ratio sequence to generate a parameter update trigger identifier. Based on the parameter update trigger identifier, extract the abnormal residual features of the corresponding time period from the predicted residual sequence to form a calibration feature parameter group.

[0040] In some embodiments, the step of calculating the residual-baseline rate ratio to generate a trigger ratio sequence based on the calibration monitoring benchmark includes: performing time-series differencing on the predicted residual sequence to generate a residual change rate sequence; extracting the baseline change rate based on the calibration monitoring benchmark to generate a baseline rate reference value; performing rate ratio calculations between the residual change rate sequence and the baseline rate reference value to generate a rate ratio distribution; and performing trigger threshold mapping based on the rate ratio distribution to generate a trigger ratio sequence.

[0041] A residual rate of change sequence is generated by performing time-series differencing on the predicted residual sequence. Time-series differencing is applied to the time-domain data of the predicted residual sequence. The residual values ​​of two adjacent acquisition periods are subtracted and divided by the acquisition interval to obtain the residual rate of change at that time point. The rate of change reflects the dynamic trend of the predicted residual sequence on the time axis rather than its static numerical value. When the chiller efficiency of an HVAC system continuously decreases due to slow refrigerant leakage, the power residual monotonically increases over a longer time scale. The corresponding residual rate of change sequence shows a consistently positive rate with a relatively stable absolute value. This pattern is significantly different from the rate abrupt changes caused by instantaneous disturbances. The difference between two adjacent points is denoted as Δe_k = e_k - e_{k-1}. Dividing Δe_k by the acquisition interval T_s yields the residual rate of change for the k-th acquisition period: v_k = Δe_k / T_s, where T_s is the acquisition interval. A positive rate indicates that the residual is increasing, meaning the measured value is increasingly overestimating the model prediction; a negative rate indicates that the residual is decreasing. The residual rate of change sequence is composed of v_k from all valid acquisition periods arranged in chronological order. It is one element shorter than the predicted residual sequence. Invalid points in the predicted residual sequence are skipped during the difference calculation. The difference results between adjacent valid points on either side of an invalid point are normalized to the actual time interval, ensuring that the rate estimation across missing points does not introduce systematic bias due to uneven time spans. Isolated elements with abnormally large absolute values ​​in the residual rate of change sequence typically correspond to transient abrupt changes in the predicted residual sequence, which are clearly distinguishable from continuous high-rate segments caused by persistent drift. This distinction provides a basis for subsequent trigger determination.

[0042] Baseline rate reference values ​​are generated by extracting the baseline change rate from the calibration monitoring benchmark. The benchmark centerline values ​​for each acquisition period in the calibration monitoring benchmark form a time-series curve on the time axis. The same time-series differencing operation as the predicted residual sequence is performed on this curve to obtain the rate of change of the calibration monitoring benchmark in each acquisition period. This rate reflects the dynamic trend of the calibration monitoring benchmark itself over time. The rate of change of the calibration monitoring benchmark is driven by two parts: the slow drift of the noise baseline and the change in the offset correction amount introduced by the effective offset marker set. The former changes slowly, reflecting the low-frequency drift trend of the physical model, while the latter may show large jumps at the boundaries of the offset interval, indicating the entry or exit of the offset state. The rate of change of the calibration monitoring benchmark is arranged in chronological order and then averaged using a sliding window. The sliding window width is set to one-quarter of the duration of the dominant period of the periodic residual marker. When the periodic residual marker indicates no significant period, the sliding window width uses the default value of 360 acquisition periods. The result after smoothing the window average is used as the baseline rate reference value for each acquisition period. The smoothing operation eliminates the interference of jumps at the offset marker boundaries on the reference value, ensuring that the baseline rate reference value stably reflects the medium- and long-term change trend of the calibration monitoring benchmark. When the baseline rate reference value is close to zero, it indicates that the calibration monitoring benchmark is in a stable stage. When the HVAC system is running under stable conditions, the benchmark centerline does not drift significantly for a long time. At this time, once a large rate value appears in the residual change rate sequence, it can be directly identified as an abnormal signal that the predicted residual sequence deviates from the stable benchmark. It can trigger subsequent judgment without comparing with the benchmark rate. When the absolute value of the baseline rate reference value is large, the two need to be compared to determine whether the change of the predicted residual sequence exceeds the normal evolution range.

[0043] Rate ratio distributions are generated by performing rate ratio calculations on the residual rate of change sequence and the baseline rate reference value. The rate ratio calculation compares the rate value v_k at each time step in the residual rate of change sequence with the baseline rate reference value b_k at the same time step. The ratio R_k = v_k / b_k reflects the multiple relationship between the predicted residual rate of change at that time step and the normal evolution rate of the calibration monitoring benchmark, where b_k is the baseline rate reference value in the k-th acquisition cycle. An absolute value of R_k much greater than 1 indicates that the predicted residual rate of change far exceeds the normal evolution rate of the calibration monitoring benchmark, suggesting a rapid deviation outside the normal range at that time step. Direct division when the baseline rate reference value is close to zero can lead to singular ratios. Therefore, a lower protection limit is set. When the absolute value of the baseline rate reference value is lower than the lower protection limit, the lower protection limit is used instead in the calculation. The lower protection limit is 10% of the standard deviation of the historical rate of the predicted residual sequence, ensuring that the ratio still reflects the absolute magnitude of the residual rate of change sequence during the static phase of the calibration monitoring benchmark. The R_k values ​​for all acquisition cycles are arranged in chronological order to form a rate ratio distribution. When the expansion valve opening parameter of the HVAC system experiences aging drift, the rate of change of the corresponding subsystem power residual is consistently higher than the baseline rate reference value. The period during which R_k is consistently greater than 1 forms a high-value segment in the rate ratio distribution, which is the key detection target for subsequent trigger threshold mapping.

[0044] Trigger ratio sequences are generated by mapping trigger thresholds based on rate ratio distributions. The trigger threshold mapping compares the R_k value of each element in the rate ratio distribution with the trigger threshold T_trig, which is determined by adding twice the standard deviation to the historical statistical mean of the rate ratio distribution. This threshold setting ensures that approximately 95% of rate ratios under normal operating conditions are below the threshold, with only rate ratios that truly deviate from the normal range exceeding the threshold. When the absolute value of R_k in the rate ratio distribution exceeds T_trig, that moment is marked as a trigger moment and assigned a value of 1; when the absolute value of R_k is below T_trig, that moment is marked as a non-trigger moment and assigned a value of 0. The trigger markers from all acquisition cycles are arranged in chronological order to form the trigger ratio sequence. The trigger threshold T_trig is dynamically adjusted every 7 days based on the historical statistical updates of the rate ratio distribution. During the transition between winter and summer operating conditions, the cooling load characteristics differ significantly, and the statistical characteristics of the rate ratio distribution change accordingly. The dynamic threshold avoids the large number of false triggers or missed triggers that would occur after the operating condition transition if a fixed threshold is used. A single isolated trigger moment in the trigger ratio sequence usually corresponds to a transient disturbance rather than a true model drift. The identification condition for an isolated trigger moment is that the two acquisition cycles before and after the moment are both in a non-triggering state. The isolated trigger moment retains its original value in the trigger ratio sequence but is marked as isolated. It is then weighted down when performing subsequent continuous over-limit trigger density statistics.

[0045] In some embodiments, the step of generating parameters to update the trigger identifier by statistically analyzing the continuous over-limit trigger density from the trigger ratio sequence includes: extracting over-limit moments from the trigger ratio sequence to generate an over-limit moment sequence; dividing the over-limit moment sequence into time windows to generate a trigger time window distribution; performing continuous trigger counting within the trigger time window distribution to generate a continuous trigger density distribution; and determining over-limit density based on the continuous trigger density distribution to generate parameters to update the trigger identifier.

[0046] An out-of-limit time sequence is generated by extracting out-of-limit moments from the trigger ratio sequence. In the trigger ratio sequence, acquisition periods with a value of 1 correspond to moments when the rate ratio exceeds the trigger threshold. The timestamps of these moments are extracted from the trigger ratio sequence, and the extraction results are arranged in ascending order of time to form the out-of-limit time sequence. Each element in the out-of-limit time sequence records the occurrence time of a rate anomaly event. The time density reflects the frequency of rate anomalies, and the interval between moments reflects the duration between two adjacent rate anomalies. During periods of frequent operating condition switching in HVAC chiller units, the rate of change of cooling power residuals may frequently and briefly exceed the threshold. The element density corresponding to these periods in the out-of-limit time sequence is high, but the intervals between adjacent elements are short, which differs from the uniform and dense triggering pattern caused by continuous drift of model parameters. Trigger moments with isolated annotations in the trigger ratio sequence are processed with reduced weights when extracting the out-of-limit time sequence. The weighting method is to set the weight of the element corresponding to the isolated trigger moment to 0.5, and the weight of the non-isolated trigger moment to 1. The weight information is attached to each element in the out-of-limit time sequence, and the weights are included in the subsequent time window division and trigger counting statistics to reduce the impact of isolated transient triggers on the final judgment. When the time sequence of the time limit is empty, it means that there is no acquisition period with a value of 1 in the trigger ratio sequence. The rate change of the predicted residual sequence within the current statistical period is generally within the normal range. Subsequent processes will not be executed, and parameter update trigger flags will not be generated.

[0047] Trigger window distribution is generated based on time window segmentation of the out-of-limit time sequence. The time window segmentation is based on the overall time span of the out-of-limit time sequence, dividing the time axis into multiple statistical windows at equal intervals. The width of each statistical window is set to half the duration of the dominant period of the periodic residual identifier. When the periodic residual identifier indicates no significant period, the statistical window width uses a default value of 720 acquisition periods. This setting ensures that each statistical window covers approximately half a period, capturing local trigger density changes within the period without causing the density statistics to lose representativeness due to sparse trigger samples within a single window being too short. The start time of the statistical window is aligned to the first trigger time in the out-of-limit time sequence. This alignment operation ensures that densely triggered sections are not artificially segmented into two adjacent windows due to misaligned window boundaries, thus affecting the integrity of continuous trigger identification. When the performance of the HVAC system heat exchanger continuously deteriorates, leading to abnormally concentrated power residual rates, misalignment of this dense section may cause it to cross the window boundary and be segmented into two low-density windows, resulting in the failure of continuous trigger determination. The sum of the product of the number of out-of-limit time sequence elements contained in each statistical window and their corresponding weights is used as the weighted trigger count for that window. Isolated trigger moments, with a weight of 0.5, contribute little to the window count and are unlikely to cause misjudgments of consecutive trigger segments. Non-isolated trigger moments, with a weight of 1, are fully included in the density statistics. This weighting strategy makes the counting results more accurately reflect the true density of anomalies within the window. The time range of each statistical window and the weighted trigger count together constitute a record of the trigger window distribution. All statistical windows are arranged in chronological order to form the trigger window distribution. Continuous zero-value window segments in the trigger window distribution indicate that the rate of change of the predicted residual sequence is generally within the normal range during that period, representing a relatively stable stage of model operation.

[0048] For example, the step of performing continuous trigger counting within a window to generate a continuous trigger density distribution on the trigger window distribution includes: using the trigger window distribution to align window boundaries to generate an aligned window set; counting the number of trigger events within each window based on the aligned window set to generate an in-window trigger frequency distribution; identifying cross-window continuous trigger segments according to the in-window trigger frequency distribution to generate a continuous trigger segment set; and calculating the average segment density of the continuous trigger segment set to generate a continuous trigger density distribution.

[0049] A set of aligned time windows is generated by aligning window boundaries using a trigger time window distribution. Boundary alignment is performed on each statistical window in the trigger time window distribution. The goal of boundary alignment is to eliminate the misalignment between window boundaries and the natural time scale caused by irregular start times of the out-of-limit time sequence. After alignment, the boundaries of each statistical window fall on integer multiples of the acquisition period, ensuring that subsequent trigger event statistics are not introduced with asymmetric counting errors due to window boundary positions. The boundary alignment method involves rounding the start time of the first window in the trigger time window distribution forward to the nearest integer multiple of the acquisition period. After rounding, the time range of the first window is extended forward, and the extended portion is filled with actual trigger records for the corresponding time period in the out-of-limit time sequence. If a trigger time exists within the extended portion, it is included in the count of the first window; otherwise, the count remains unchanged. When the HVAC system acquisition period is in whole minutes, the start time of each statistical window after boundary alignment is also in whole minutes. The statistical range of trigger events within the window precisely corresponds to the actual time scale, facilitating cross-validation with operating events recorded in whole minutes in the equipment operation log. Each subsequent window is calculated at equal intervals according to the starting time of the first alignment window and the width of the statistical window, forming an equally spaced alignment window sequence that covers the entire time range of the time sequence exceeding the limit. The time range of all alignment windows and the window identifier together constitute the alignment time window set. After the mapping between each statistical window in the trigger time window distribution and the corresponding window in the alignment time window set is completed, all subsequent counting operations are performed based on the alignment time window set.

[0050] The trigger frequency distribution within a window is generated based on the number of triggered events within each window in the aligned time window set. After determining the time range of each window in the aligned time window set, trigger time elements falling within the time range of that window are selected from the out-of-limit time sequence. The weighted count of the selection results is used as the trigger frequency within that window, with isolated trigger times having a weight of 0.5 and non-isolated trigger times having a weight of 1. The trigger frequencies within each window in the aligned time window set are arranged in the window time order to form the trigger frequency distribution within the window. The trigger frequency distribution within the window is a discrete sequence with the statistical window as the time unit, and the value of each element in the sequence reflects the weighted density of rate anomaly events within the corresponding statistical window. When dust accumulates on the filter screen of the air conditioning unit at the end of the HVAC system, the air volume decreases, leading to aggravated power residual fluctuations. The trigger frequency within the corresponding statistical window is continuously high, and the trigger frequency distribution within the window shows a continuously high value segment during this period, which is in stark contrast to the low frequency segment during the normal operation period of the equipment. The windows near which the trigger frequency distribution suddenly increases significantly usually correspond to a sudden change in a certain operating condition. The identification of the jump point is achieved by the frequency difference between adjacent windows exceeding three times the standard deviation of the historical mean. The jump point is marked on the corresponding element of the trigger frequency distribution within the window to support the accurate positioning of subsequent continuous triggering segments. The windows with a value of zero in the trigger frequency distribution within the window correspond to the collection period in which the trigger ratio sequence within the statistical window is not assigned a value of 1.

[0051] Based on the trigger frequency distribution within a window, continuous trigger segments across windows are identified, generating a set of continuous trigger segments. The continuous trigger threshold is set as the mean of the historical non-zero values ​​of the trigger frequency distribution within the window. This threshold identifies windows with trigger frequencies significantly higher than the historical average as densely triggered windows. Starting from the first element of the trigger frequency distribution within the window, the process iterates backward. When a window with a frequency exceeding the continuous trigger threshold is first encountered, the starting window of the segment is recorded. Subsequent consecutive windows exceeding the threshold are all included in the same segment until a window with a frequency below the threshold is encountered, at which point the segment is considered to end. The ending window of the segment is not included in the segment's scope. The starting window identifier and the ending window identifier of the segment jointly determine the time range of the segment. If a single interval window below the threshold exists between two consecutive triggering segments in the window triggering frequency distribution, it is determined as a disturbance interval that does not break the segment continuity. The two segments are merged into a complete segment spanning the disturbance window. When the triggering frequency of a single statistical window is slightly below the threshold due to temporary fluctuations in the HVAC system's operating conditions, the merging operation ensures that this temporary decrease is not misjudged as two independent drift events. The frequency statistics of the merged segment include the triggering events within the interval window. The start and end window identifiers of all consecutive triggering segments and the mean of the window triggering frequency distribution within the segment are summed to form a set of consecutive triggering segments. Each segment in the set of consecutive triggering segments is accompanied by a peak window identifier within the segment. The peak window corresponds to the period when the rate anomaly is most concentrated. When there is no consecutive over-threshold window sequence in the window triggering frequency distribution, the set of consecutive triggering segments is empty.

[0052] The mean density of consecutive triggering segments is calculated to generate a consecutive triggering density distribution. The mean density of each segment in the consecutive triggering segment set is determined by the weighted mean of the in-window trigger frequency distribution of all statistical windows within the segment. The weighted mean is calculated with the time span of each window as the weight. The formula for calculating the mean density is D_seg=Σ(f_j×w_j) / Σw_j, where D_seg is the mean density of the consecutive triggering segment, f_j is the in-window trigger frequency of the j-th statistical window within the segment, and w_j is the time span of the j-th statistical window. Windows with longer time spans contribute more to the mean density. This weighting method avoids the problem of lowering the mean density due to lower frequencies caused by window truncation at the segment boundaries. The physical meaning of the density mean is the average weighted number of triggers per unit time within the continuous triggering segment. A high density mean indicates that the rate of abnormal events within the segment is dense and continuous. When the aging of the cooling tower packing in the HVAC system leads to a long-term high rate of change in the residual temperature of the cooling water outlet, the density mean of the corresponding continuous triggering segment remains high, forming a clear contrast with the low-density segment caused by occasional external disturbances. The density mean of each segment in the continuous triggering segment set is accompanied by the corresponding time range and the peak value of the trigger frequency distribution within the window of the segment. These three values ​​together describe the temporal location, average intensity, and peak intensity of the segment. The density mean of all segments is arranged in the time sequence of the segments to form the continuous triggering density distribution. The high-density segments in the continuous triggering density distribution correspond to the period when the model parameters drift rapidly and continuously, which is the core basis for updating the trigger parameters in the subsequent density over-limit determination. When the continuous triggering segment set is empty, the continuous triggering density distribution is set to zero.

[0053] The trigger density distribution is used to determine if the density exceeds the limit and generate updated trigger identifiers. The density exceedance determination compares the trigger density of each segment in the continuous trigger density distribution with the density exceedance threshold. The density exceedance threshold is determined by adding 1.5 times the standard deviation to the historical mean of the continuous trigger density distribution. This setting identifies segments with trigger densities significantly higher than historical normal levels as exceedance segments. The threshold is dynamically updated based on historical statistical accumulation, avoiding systematic misjudgments caused by changes in density distribution characteristics after switching between winter and summer operating conditions. Segments in the continuous trigger density distribution where the trigger density exceeds the density exceedance threshold are extracted as exceedance segments. When the coefficient of performance (COP) of a HVAC system continuously declines due to long-term aging, the corresponding power residual change rate accumulates over a long time scale. As the trigger density of the continuous trigger density distribution gradually approaches and exceeds the density exceedance threshold, it indicates that the parameter drift has reached a level requiring intervention and calibration. A continuous increase in trigger density and an expanding exceedance further indicates that the drift is accelerating. The parameter update trigger identifier consists of four fields: the start time of the density exceeding the limit section, the end time, the trigger density peak value, and the corresponding measurement point identifier. These four fields together locate the time range, severity, and subsystems involved in the trigger update. The higher the trigger density peak value, the more severe the parameter drift of the corresponding subsystem. In the subsequent calibration feature extraction, the abnormal residual features of this subsystem are processed first. When the density distribution is continuously set to zero, the parameter update trigger identifier is not generated.

[0054] Based on the parameter update trigger identifier, abnormal residual features corresponding to the time period are extracted from the predicted residual sequence to form a calibration feature parameter group. The start time of each trigger entry in the parameter update trigger identifier locates the time period that needs to be analyzed in the predicted residual sequence. Taking the start time as the center, a dominant cycle duration is traced back and extended to the end time of the trigger segment. The predicted residual sequence data within this time range is extracted as the abnormal residual analysis window. After removing the periodic component corresponding to the dominant cycle in the periodic residual identifier from the predicted residual sequence data in the abnormal residual analysis window, the mean and variance of the remaining residual sequence are extracted as abnormal residual features. The mean reflects the current systematic bias level, and the variance reflects the dispersion of residual fluctuations. When the impeller of the chilled water pump in the HVAC system is worn, the flow rate is continuously lower than the design value. The corresponding residual mean is stably biased in the same direction and the variance is small, which can be clearly distinguished from the high variance and low mean pattern caused by random load disturbances caused by building personnel entering and exiting. When the coefficient of performance (COP) of a chiller in an HVAC system drifts, the power residual typically exhibits a combination of a persistently positive mean and a small variance within the anomaly analysis window. This combination is fundamentally different from the high variance and low mean characteristics caused by random noise. When multiple trigger entries exist in the parameter update trigger identifier, each entry corresponds to an independent anomaly residual analysis window. The two statistical features of each window are extracted and grouped according to the trigger entry identifier. The sum of the anomaly residual features corresponding to all trigger entries constitutes the calibration feature parameter group. Entries with higher trigger density peaks correspond to higher feature weights. When no parameter update trigger identifier is generated, the calibration feature parameter group is an empty set.

[0055] Step S140: Online parameter identification is performed on the calibration characteristic parameter group to generate drift rate identifiers. The drift rate identifiers and period residual identifiers are used to perform period component stripping evaluation to generate online calibration parameters.

[0056] In some embodiments, the step of generating a drift rate identifier by online parameter identification of the calibration feature parameter set includes: generating a parameter change rate sequence by performing time-series difference calculation based on the calibration feature parameter set; identifying monotonically drifting segments based on the parameter change rate sequence to generate a monotonically drifting sequence; generating a second-order drift change rate distribution by performing second-order difference calculation using the monotonically drifting sequence; and generating a drift rate identifier by identifying drift trend intensification features through the second-order drift change rate distribution.

[0057] A parameter change rate sequence is generated by time-series difference calculation based on the calibration feature parameter set. The time-series difference is applied to the mean field of each feature item in the calibration feature parameter set. The difference between the means of two adjacent trigger items divided by the time interval between their start times gives the parameter change rate within that time period. The parameter change rate is calculated as p_n=(μ_n-μ_{n-1}) / Δt_n, where p_n is the parameter change rate between the nth trigger item and the (n-1)th trigger item, μ_n and μ_{n-1} are the mean fields of the corresponding trigger items, and Δt_n is the time interval between their start times. The parameter change rate reflects the evolution speed of the calibration feature mean between adjacent trigger events. A continuously positive change rate indicates that the mean extracted at each trigger gradually increases, suggesting that the systematic bias of the corresponding sub-device is accumulating and deepening. In the calibration feature parameter set, the mean field typically exhibits a slow and monotonous trend during normal aging. When the impeller of a chilled water pump in an HVAC system experiences a continuous decrease in head efficiency due to long-term wear, the mean of the corresponding flow residual gradually becomes more negative with each calibration feature extraction. The component of this measurement point in the parameter change rate sequence remains negative, reflecting the cumulative process of head loss. The number of feature entries for each measurement point in the calibration feature parameter set varies depending on the trigger frequency. Measurement points with fewer than 3 entries have insufficient sample size in their parameter change rate sequence, which is marked as sparse data. The confidence level of subsequent drift segment identification conclusions for sparse data measurement points is correspondingly reduced. The difference result of the variance field in the parameter change rate sequence is calculated synchronously and appended to the sequence. A continuous increase in variance indicates that the residual fluctuation of the corresponding measurement point is intensifying.

[0058] Monotonic drift segments are identified and monotonic drift sequences are generated based on the parameter change rate sequence. A monotonic drift segment corresponds to a time period in the parameter change rate sequence where multiple consecutive elements have the same sign and their absolute values ​​all exceed the monotonic threshold. The same sign indicates that the parameter is continuously changing in the same direction during that time period, and the absolute value exceeding the monotonic threshold excludes random walks with excessively small amplitudes. The monotonic threshold is set to the lower quartile of the historical absolute values ​​of the parameter change rate sequence. When the variance field difference result is continuously positive within the corresponding segment, the monotonic threshold is increased to 1.5 times the lower quartile to distinguish between two types of patterns: increased volatility and parameter drift. This setting treats weak changes with a rate of change below the adjusted threshold as background noise and excludes them from the monotonic segment, retaining only meaningful continuous changes. A monotonically drifting segment is defined as having at least three consecutive elements that meet the conditions. If a single element with a reversed sign appears within the segment, but the signs of the two elements before and after it are the same, it is considered a disturbance point and does not break the segment. Single parameter estimation errors caused by HVAC system operating condition switching may produce isolated reversed elements in the parameter change rate sequence. The disturbance tolerance mechanism ensures that this isolated reversed point does not artificially divide the continuous drift process into two segments. The monotonically drifting sequence consists of three fields: the starting trigger entry index, the ending trigger entry index, and the mean change rate within the segment. The mean change rate reflects the average propulsion speed of the drift segment; a larger absolute value of the mean change rate indicates a faster drift speed for the corresponding physical parameter. When there are no consecutively satisfying elements in the parameter change rate sequence, the monotonically drifting sequence is empty, indicating that the characteristic mean change in the calibration characteristic parameter group has no regular trend.

[0059] The second-order rate of change distribution of the drift is generated by second-order difference calculation using a monotonically drifted sequence. The second-order difference is applied to the mean rate of change of each segment in the monotonically drifted sequence. The second-order rate of change is obtained by subtracting the mean rate of change of two adjacent monotonically drifted segments. The formula for calculating the second-order rate of change is a_m = (V_m - V_{m-1}) / Δt_m, where a_m is the second-order rate of change between the m-th and (m-1)-th monotonically drifted segments, V_m and V_{m-1} are the mean rate of change of the corresponding monotonically drifted segments, and Δt_m is the time interval between the center moments of the m-th and (m-1)-th monotonically drifted segments. The second-order rate of change reflects whether the drift velocity itself is accelerating. A positive second-order rate of change in the positive drift direction indicates that the parameter is drifting forward and accelerating, while a negative second-order rate of change in the positive drift direction indicates that the positive drift is decelerating and tending to stabilize. When a small leak of refrigerant in an HVAC system causes a slow decrease in system pressure, the drift rate of the corresponding pressure residual is slow in the initial stage of the leak. As the refrigerant continues to decrease, the drift rate gradually accelerates. The second-order difference value of the corresponding segment in the second-order rate of change distribution remains positive, indicating that the drift is accelerating rather than maintaining a constant speed. This acceleration mode is significantly different from the constant-speed drift caused by equipment wear, and the two correspond to different physical failure mechanisms. If the number of monotonically drift segments in a monotonically drift sequence is less than two, the second-order rate of change distribution cannot be calculated. This is marked as insufficient sample size, and the mean of the first-order rate of change of the monotonically drift segments is directly output for reference in subsequent drift rate label generation. The second-order difference results of all adjacent monotonically drift segments are arranged in chronological order to form the second-order rate of change distribution. High positive value segments in the second-order rate of change distribution correspond to the drift acceleration stage, high negative value segments correspond to the drift deceleration stage, and segments close to zero correspond to the constant-speed drift stage.

[0060] A drift rate identifier is generated by identifying the characteristics of intensified drift trends through the second-order rate of change distribution of the drift. An intensified drift trend is defined as multiple consecutive segments in the second-order rate of change distribution where the second-order difference values ​​are all positive and their absolute values ​​exceed an intensification threshold. The intensification threshold is set as the average of the historical positive values ​​in the second-order rate of change distribution; exceeding this threshold indicates that the drift acceleration has exceeded historical normal levels. An intensified drift trend is determined when at least two segments consecutively meet this condition. When the aging of the cooling tower packing in an HVAC system leads to an accelerated decline in heat exchange efficiency, the drift velocity of the cooling water outlet temperature residual continuously increases in an increasing trend. The corresponding consecutive segments in the second-order rate of change distribution all exceed the intensification threshold, triggering the intensified drift trend determination. The drift rate identifier is composed of the intensified drift trend determination result and the average rate of change of the latest segment in the monotonic drift sequence. The average rate of change is derived from the monotonic drift sequence, and the intensified drift trend determination result is represented by a Boolean value. The average rate of change reflects the absolute velocity of the current drift. Both fields together describe the acceleration state and current intensity of the drift. When there is no continuous over-aggravation threshold segment in the second-order rate of change distribution of drift, the drift trend aggravation judgment result is false. Only the current rate of change mean is retained in the drift rate label, indicating that the current drift is progressing at a constant speed and has not yet entered the acceleration stage. When the monotonic drift sequence is an empty set, the drift rate label is marked as no effective drift, and the subsequent periodic component stripping evaluation is not triggered.

[0061] Online calibration parameters are generated by performing periodic component stripping evaluation using drift rate identifiers and periodic residual identifiers. The goal of periodic component stripping evaluation is to separate the true parameter drift component from the periodic residual component within the abnormal residual features of the calibration feature parameter set, avoiding misidentification of periodic component energy as a parameter drift contribution, which would lead to calibration direction deviation. The amplitude and frequency information of the dominant period in the periodic residual identifier are used to reconstruct the theoretical value of the periodic component for the current time period. Based on the frequency and average phase information of the dominant period in the periodic residual identifier, combined with the time offset of the start time of the time period corresponding to the trigger entry in the calibration feature parameter set relative to the zero phase time corresponding to the average phase in the periodic residual identifier, the phase of the current time period is calculated, and a standard sine component is synthesized. The theoretical value of the synthesized periodic component is subtracted from the mean of the abnormal residual to obtain the net mean of the de-periodized residual. The mean rate of change in the drift rate indicator and the result of the drift trend intensification jointly constrain the mapping of the mean net residual to the change in physical parameters. When refrigerant leakage occurs in the HVAC system and the leakage rate continues to accelerate, the trend in the drift rate indicator intensifies. In this case, the recent mean net residual better reflects the current true degree of drift, and the mapping weight is tilted towards the recent period to allow the calibration parameters to quickly keep up with the accelerating drift trend. Conversely, when the equipment drifts slowly and shows no signs of acceleration in the early stages of normal wear, the historical mean is better at smoothing out the interference of occasional disturbances on the calibration quantity, and the mapping weight is tilted towards the historical period to ensure calibration stability. When the evaporator of the HVAC system scales, the evaporation temperature continues to decrease, and the corresponding mean net residual is continuously positive and the trend in the drift rate indicator intensifies. The mapping weight is tilted towards the recent data to allow the calibration parameters to quickly respond to the current drift state. After weight mapping, the mean net residual yields the calibration correction amount for each physical parameter. The calibration correction amount and the current value of the corresponding parameter in the physical model are superimposed to form the online calibration parameters. Each parameter in the online calibration parameters is accompanied by a confidence assessment. The correction amount for parameters with a confidence level below the threshold is downweighted and not directly written into the physical model.

[0062] Step S150: After calibrating the predicted residual sequence based on the online calibration parameters, the residual back-check verification is performed to generate a calibration validity identifier. Based on the calibration validity identifier, the online calibration parameters are updated online to output the adaptive calibration model parameters.

[0063] Specifically, after calibrating the predicted residual sequence based on online calibration parameters, residual backtesting is performed to generate a calibration validity identifier. The post-calibration residual backtesting involves substituting the online calibration parameters into the physical model to recalculate the predicted values ​​for each measuring point. During recalculation, the online calibration parameters replace the corresponding original parameter values ​​in the physical model, while the rest of the model structure and input driving variables remain unchanged. The updated predicted values ​​are then subtracted from the measured values ​​of the predicted residual sequence within the time period corresponding to the parameter update trigger identifier to obtain the calibrated residual sequence. After calibrating the heat exchange efficiency of the HVAC system chiller, if the mean residual of the corresponding power measuring point falls from a consistently positive bias to near zero, it indicates that the systematic bias of underestimating efficiency has been effectively corrected. If the variance increases significantly after calibration, it indicates that the calibration parameters have introduced new unstable components, requiring a reassessment of whether the periodic component stripping is complete. The calibration validity indicator is determined by two indicators: the reduction ratio of the mean residual after calibration and the change ratio of the variance. The calibration is considered valid when the reduction ratio of the mean exceeds 50% and the change ratio of the variance is within the range of -20% to 20%. When the online calibration parameters involve multiple measurement points, each measurement point is calibrated independently and the residual is checked. The validity judgment results of each measurement point are summarized and the overall pass rate is used to represent the comprehensive rating of the calibration validity indicator.

[0064] Based on the calibration validity indicator, online calibration parameters are updated online to output adaptive calibration model parameters. When the overall rating of the calibration validity indicator exceeds the pass threshold, it indicates that the online calibration parameters are generally valid. The pass threshold is set at a validity pass rate of no less than 80% for each measuring point. Online calibration parameters that reach the pass threshold are directly written into the corresponding parameter positions in the physical model to complete the online update. If the pass threshold is not reached, the online calibration parameter values ​​of the last valid calibration in the historical version of the adaptive calibration model parameters are rolled back and maintained, and the identification process is retried from the calibration feature parameter group extraction stage. When some measuring points in the calibration validity indicator fail the validity judgment, the online calibration parameters of the corresponding measuring points are not written into the physical model. Only the parameters of the measuring points that pass the validity judgment are updated to the model. The measuring points that fail the validity judgment retain their current parameter values ​​and re-extract calibration features in the next trigger cycle. If a measuring point in the HVAC system experiences an abnormal calibration feature extraction due to a temporary sensor failure, the validity judgment of that measuring point fails, but the parameter updates of other normal measuring points are not affected and proceed normally. After the online update is completed, the physical model re-predicts the subsequent data of the predicted residual sequence using the adaptively calibrated model parameters. The new round of residual sequences of the updated predicted values ​​and measured values ​​are continuously input into the S110 process, forming a closed-loop iterative mechanism of calibration-verification-recalibration. The adaptive calibration model parameters consist of all the updated parameter values ​​written into the physical model this time. The historical versions of the adaptive calibration model parameters retain the most recent 10 update records, and if the effect deteriorates after calibration of the current version, it is possible to roll back to a historically valid version.

[0065] To implement the above-described method embodiments, a residual analysis-based adaptive calibration method for HVAC models is proposed to achieve the corresponding functionalities and technical effects. See also... Figure 2 , Figure 2 This paper presents a structural block diagram of an adaptive calibration device 200 for HVAC models based on residual analysis, according to an embodiment of this application. The device includes: The residual calculation module 201 is used to collect operating data of HVAC equipment, perform physical model residual calculation based on the operating data to generate a predicted residual sequence, and identify periodic residual patterns from the predicted residual sequence to generate periodic residual identifiers. The baseline estimation module 202 is used to dynamically adjust the exponentially weighted moving average forgetting factor using the predicted residual sequence and the periodic residual identifier to generate a noise baseline, define the fluctuation range of the noise baseline to generate a noise tolerance band, and construct a calibration monitoring benchmark by using the noise tolerance band and the predicted residual sequence. Trigger identification module 203 is used to calculate the residual-baseline rate ratio of the predicted residual sequence based on the calibration monitoring benchmark to generate a trigger ratio sequence, statistically analyze the continuous over-limit trigger density from the trigger ratio sequence to generate parameter update trigger identifier, and extract abnormal residual features of the corresponding time period from the predicted residual sequence based on the parameter update trigger identifier to form a calibration feature parameter group. Online identification module 204 is used to perform online parameter identification on the calibration feature parameter group to generate a drift rate identifier, and use the drift rate identifier and the period residual identifier to perform period component stripping evaluation to generate online calibration parameters; The calibration update module 205 is used to perform calibration on the predicted residual sequence based on the online calibration parameters, perform residual back-check verification to generate a calibration validity identifier, and perform online update on the online calibration parameters according to the calibration validity identifier to output adaptive calibration model parameters.

[0066] The aforementioned HVAC model adaptive calibration device 200 based on residual analysis can implement an HVAC model adaptive calibration method based on residual analysis as described in the above method embodiments. The options in the above method embodiments are also applicable to this embodiment and will not be detailed here. The remaining content of this application embodiment can be referred to the content of the above method embodiments, and will not be repeated in this embodiment.

[0067] The purpose of the above embodiments is to reproduce and derive the technical solution of the present invention by way of example, and to fully describe the technical solution, purpose and effect of the present invention. The purpose is to enable the public to have a more thorough and comprehensive understanding of the disclosure of the present invention, and not to limit the scope of protection of the present invention.

Claims

1. An adaptive calibration method for HVAC models based on residual analysis, characterized in that, include: Collect operating data of HVAC equipment, perform physical model residual calculation based on the operating data to generate a predicted residual sequence, and identify periodic residual patterns from the predicted residual sequence to generate periodic residual identifiers; A noise baseline is generated by dynamically adjusting the exponentially weighted moving average forgetting factor using the predicted residual sequence and the periodic residual identifier. The noise baseline is then used to define the fluctuation range to generate a noise tolerance band. The noise tolerance band is defined by estimating the distribution range of random noise components in the predicted residual sequence, with the noise baseline as the central axis. A calibration monitoring benchmark is constructed using the noise tolerance band and the predicted residual sequence. Based on the calibration monitoring benchmark, the residual-baseline rate ratio is calculated for the predicted residual sequence to generate a trigger ratio sequence. The continuous over-limit trigger density is statistically analyzed from the trigger ratio sequence to generate parameter update trigger identifiers. Based on the parameter update trigger identifiers, abnormal residual features for the corresponding time period are extracted from the predicted residual sequence to form a calibration feature parameter group. The calibration feature parameter group is subjected to online parameter identification to generate a drift rate identifier, and the drift rate identifier and the period residual identifier are used to perform period component stripping evaluation to generate online calibration parameters; After calibrating the predicted residual sequence based on the online calibration parameters, the residual back-check verification generates a calibration validity identifier. Based on the calibration validity identifier, the online calibration parameters are updated online to output adaptive calibration model parameters.

2. The method according to claim 1, characterized in that, The step of identifying periodic residual patterns from the predicted residual sequence and generating periodic residual identifiers includes: The predicted residual sequence is used to perform spectral decomposition to extract periodic frequency components and generate a residual spectral distribution. Based on the residual spectrum distribution, a multi-period spectrum peak comparison analysis is performed to generate a cross-period peak consistency distribution; The cross-period peak consistency distribution is used to identify highly stable peak frequencies and generate an effective periodic candidate set; Periodic residual identifiers are generated by calibrating periodic residual patterns using the effective periodic candidate set.

3. The method according to claim 1, characterized in that, The step of dynamically adjusting the exponentially weighted moving average forgetting factor using the predicted residual sequence combined with the periodic residual identifier to generate a noisy baseline includes: The periodic residual identifier is subjected to periodic intensity quantization to generate a periodic intensity coefficient; The predicted residual sequence is mapped to a forgetting factor using the periodic intensity coefficient to generate a dynamic forgetting factor sequence; Based on the dynamic forgetting factor sequence, an exponentially weighted moving average is calculated on the predicted residual sequence to generate a smoothed residual sequence; Based on the smoothed residual sequence, a baseline estimate is determined to generate a noisy baseline.

4. The method according to claim 1, characterized in that, The step of constructing a calibration monitoring benchmark by using the noise tolerance band and the predicted residual sequence includes: The residual over-limit distribution is generated by comparing the predicted residual sequence with the noise tolerance band point by point. Perform upper and lower limit symmetry analysis on the residual limit distribution to generate a limit skewness index; Based on the out-of-limit skewness index, identify asymmetric out-of-limit intervals and generate a valid offset marker set; A calibration monitoring benchmark is constructed using the effective offset marker set and the noise tolerance band.

5. The method according to claim 1, characterized in that, The step of generating a trigger ratio sequence by calculating the residual-baseline rate ratio of the predicted residual sequence based on the calibration monitoring benchmark includes: The predicted residual sequence is subjected to time-series differencing to generate a residual change rate sequence; Based on the calibration monitoring benchmark, the baseline change rate is extracted to generate a baseline rate reference value; A rate ratio distribution is generated by performing a rate ratio operation between the residual rate of change sequence and the baseline rate reference value; Trigger ratio sequences are generated by mapping trigger thresholds based on the rate ratio distribution.

6. The method according to claim 1, characterized in that, The step of generating parameters and updating the trigger identifier by statistically analyzing the continuous over-limit trigger density from the trigger ratio sequence includes: The trigger ratio sequence is used to extract out-of-limit moments and generate an out-of-limit moment sequence. Based on the aforementioned time-out sequence, a trigger time window distribution is generated by dividing the time window; Execute continuous trigger counts within the trigger window distribution to generate a continuous trigger density distribution; Based on the continuous trigger density distribution, the density exceeds the limit and parameters are generated to update the trigger identifier.

7. The method according to claim 1, characterized in that, The step of generating drift rate identifiers through online parameter identification of the calibration feature parameter set includes: Based on the calibration feature parameter set, a time-series difference calculation is performed to generate a parameter change rate sequence; Based on the parameter change rate sequence, monotonic drift segments are identified and monotonic drift sequences are generated. The second-order rate of change distribution of the drift is generated by performing second-order difference calculation using the monotonical drift sequence. The drift rate identifier is generated by identifying the characteristics of intensified drift trend through the second-order rate of change distribution of drift.

8. The method according to claim 3, characterized in that, The step of using the periodic intensity coefficient to perform forgetting factor mapping on the predicted residual sequence to generate a dynamic forgetting factor sequence includes: The periodic intensity coefficient is subjected to time-series difference calculation to generate an intensity change rate sequence; Based on the intensity change rate sequence, identify intensity-increasing segments and generate a feedforward trigger set; The feedforward forgetting factor group is generated by performing a feedforward configuration using the feedforward trigger set and the periodic intensity coefficient; A dynamic forgetting factor sequence is generated by performing a time-varying mapping on the predicted residual sequence based on the feedforward forgetting factor set.

9. The method according to claim 6, characterized in that, The step of performing continuous trigger counting within the trigger window distribution to generate a continuous trigger density distribution includes: The window boundary alignment is performed using the aforementioned trigger window distribution to generate an aligned window set; Based on the alignment window set, the number of triggered events in each window is counted to generate the window trigger frequency distribution; Based on the window trigger frequency distribution, identify cross-window continuous trigger segments and generate a continuous trigger segment set; The average segment density is calculated for the set of continuous triggering segments to generate a continuous triggering density distribution.

10. An adaptive calibration device for HVAC models based on residual analysis, characterized in that, include: The residual calculation module is used to collect operating data of HVAC equipment, perform physical model residual calculation based on the operating data to generate a predicted residual sequence, and identify periodic residual patterns from the predicted residual sequence to generate periodic residual identifiers. The baseline estimation module is used to dynamically adjust the exponentially weighted moving average forgetting factor using the predicted residual sequence and the periodic residual identifier to generate a noise baseline, define the fluctuation range of the noise baseline to generate a noise tolerance band, the noise tolerance band is the upper and lower boundaries determined by estimating the distribution range of random noise components in the predicted residual sequence with the noise baseline as the central axis, and construct a calibration monitoring benchmark by using the noise tolerance band and the predicted residual sequence. The trigger identification module is used to calculate the residual-baseline rate ratio of the predicted residual sequence based on the calibration monitoring benchmark to generate a trigger ratio sequence, statistically analyze the continuous over-limit trigger density from the trigger ratio sequence to generate parameter update trigger identifiers, and extract abnormal residual features of the corresponding time period from the predicted residual sequence based on the parameter update trigger identifiers to form a calibration feature parameter group. An online identification module is used to perform online parameter identification on the calibration feature parameter group to generate a drift rate identifier, and to use the drift rate identifier and the periodic residual identifier to perform periodic component stripping evaluation to generate online calibration parameters; The calibration update module is used to calibrate the predicted residual sequence based on the online calibration parameters, perform residual back-check verification to generate a calibration validity identifier, and update the online calibration parameters online according to the calibration validity identifier to output adaptive calibration model parameters.

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