An early warning method for stability of aerobic granular sludge based on dissolved oxygen multifractal analysis

Abstract

The application discloses an early warning method for stability of aerobic granular sludge based on dissolved oxygen multifractal analysis, and the method comprises the following steps: continuously collecting dissolved oxygen data in an aeration stable section, performing sliding window median filtering and first-order difference preprocessing to retain signal intrinsic fluctuations, adopting a multifractal analysis method based on scale transformation to process the dissolved oxygen time series data, and calculating a generalized dimension spectrum D q ( q ) and a singular spectrum f ( α ) ; calculating a generalized dimension D q and a left spectrum width Δα left , respectively, to represent dominant structure and large-amplitude extreme fluctuation intensity of the dissolved oxygen time series fluctuations; an alarm threshold is calibrated through ROC curve analysis to establish a two-step protocol of 'early warning + cause diagnosis', so that identification of the heavy-tailed characteristics of the particle size distribution is realized; the application has the characteristics of significant early warning lead time, zero capital expenditure, strong diagnostic specificity, real-time online, automatic integration and intervention feedback, can warn about structural instability 60 days earlier than traditional indicators, and effectively prevents irreversible disintegration of the granular sludge.

Description

Technical Field

[0001] This invention belongs to the field of wastewater biological treatment technology, and in particular relates to an early warning method for the stability of aerobic granular sludge based on dissolved oxygen multifractal analysis. Background Technology

[0002] Aerobic granular sludge is a highly efficient biological treatment technology with broad application prospects in wastewater treatment. During the operation of an aerobic granular sludge system, the stability of the granular structure directly affects sludge performance and system treatment efficiency. Instability in granular sludge typically manifests as sludge disintegration, deterioration of settling properties, excessive proliferation of filamentous bacteria, and decreased nitrogen and phosphorus removal performance. Even under constant dissolved oxygen conditions during the cultivation of aerobic granular sludge, instability may still occur in the system. For example, as the average particle size of the sludge increases, the diffusion resistance of dissolved oxygen within the granular sludge continuously increases, leading to anaerobic gas production within the granules, sludge breakage and disintegration, or excessive proliferation of filamentous bacteria.

[0003] Traditional descriptive indicators for the stability of aerobic granular sludge include sludge settling ratio (SV) and 30-minute vs. 5-minute SV ratio (SV). 30 / SV5), sludge volume index (SVI), densification time ( t d ) and sorting time ( t s These indicators, such as particle size distribution, are outcome-based and often only show abnormalities after significant degradation of particle structure, exhibiting a clear lag. Particle size distribution detection typically relies on image analysis or laser particle size analyzers, which are costly and difficult to implement for long-term online monitoring. Since conventional online dissolved oxygen monitoring is mainly based on the mean dissolved oxygen or setpoint deviation, which is generally considered constant during operation, existing research and engineering practices focus primarily on the relationship between particle size distribution and sludge stability, lacking in-depth analysis of the relationship between the operating environment parameters dissolved oxygen, particle size distribution, and sludge stability.

[0004] In aerobic granular sludge systems, changes in particle structure affect dissolved oxygen mass transfer resistance and microbial metabolic characteristics, resulting in fluctuations in dissolved oxygen time series and variations in scale structure. This invention, based on the multifractal complexity of dissolved oxygen signals, quantitatively characterizes particle structural heterogeneity, enabling early warning of aerobic granular sludge stability without requiring additional hardware.

[0005] Patent application No. 202310985786.6 discloses a method for detecting the state of activated sludge based on the variation characteristics of texture entropy in settling images. This technology involves capturing sludge settling videos with a fixed camera, extracting data on the variation of image texture entropy over time at different heights, constructing a hologram of settling image entropy changes, and then calculating its slope and aspect to obtain a standardized clarification time. t c Densification time ( t d ) and sorting time ( t s Compared to the limitations of the traditional sludge volume index (SVI), which only reflects the final volume of sedimentation and cannot characterize the dynamic characteristics of the sedimentation process, this method directly provides a description of the microscopic physical and statistical properties of the particle population. It can capture the dynamic characteristics and spatial heterogeneity of particle distribution during sedimentation using only a single visual sensor signal. This technology not only has the advantages of high real-time performance, high automation, and low cost, but also can sensitively diagnose microscopic structural evolution signals such as early particle disintegration and filamentous bacterial growth, thus making up for the lack of intuitive physical description of microstructure in traditional indicators. However, this technical solution relies on additional image acquisition hardware and requires strict monitoring of the entire sludge sedimentation process. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, the present invention aims to provide an early warning method for the stability of aerobic granular sludge based on dissolved oxygen multifractal analysis. By performing multifractal processing on the noisy high-frequency fluctuation signal obtained by conventional dissolved oxygen sensors, the background noise caused by fluid turbulence and other factors, as well as the chaotic signal induced by extreme intermittent events in dissolved oxygen fluctuations, is analyzed. Sensitive indicators characterizing the heterogeneous evolution of particle population structure and particle size distribution are accurately extracted, enabling early and real-time diagnosis of the heavy-tailed characteristics of aerobic granular sludge particle size distribution, and issuing an early warning several tens of days before the macroscopic settling performance deteriorates.

[0007] To achieve the above objectives, the present invention is implemented through the following technical solution: An early warning method for the stability of aerobic granular sludge based on dissolved oxygen multifractal analysis includes the following steps: Step 1, Dissolved oxygen data acquisition stage: During the aeration stabilization stage of the aerobic granular sludge reactor, high-frequency dissolved oxygen time series data are continuously collected in the area above the sludge layer formed by sedimentation and below the liquid surface in the aerobic granular sludge reactor using a dissolved oxygen sensor at sampling intervals of no more than 20 s. Step 2, Multifractal Analysis Stage: Obtaining Dissolved Oxygen Time Series Data to be Analyzed: Perform one or both of the following operations on the raw dissolved oxygen time series data collected in Step 1: denoising and detrending, to obtain the dissolved oxygen time series data to be analyzed; or directly use the raw dissolved oxygen time series data collected in Step 1 as the dissolved oxygen time series data to be analyzed; use a multifractal analysis method based on scaling transformation to process the dissolved oxygen time series data to be analyzed to obtain the quality index. t ( q According to the quality index Calculating the generalized dimension spectrum using the generalized dimension formula D q ( q At the same time, the quality index Singular spectrum obtained by Legendre transform f ( α ); Step 3, Feature Parameter Extraction Stage: Based on the generalized dimension spectrum obtained in Step 2 D q ( q ), select a specific moment order q Corresponding generalized dimension D q The value is used as a characteristic parameter to characterize the dominant structure of dissolved oxygen time series fluctuations; based on the singular spectrum obtained in step 2... f ( α ), calculate the left spectral width Da left , used to characterize the intensity contribution of large-amplitude extreme fluctuations; Step 4, Early Warning and Diagnosis Stage: The generalized dimension obtained in Step 3 is analyzed using Receiver Operating Characteristic (ROC) curve analysis. D q Threshold calibration is performed to determine the alarm threshold; when the generalized dimension D q When the value exceeds the alarm threshold, the system is determined to be in a safe operating zone and no alarm is triggered; when the generalized dimension... D q When the value falls below the alarm threshold, an early alarm signal for structural drift is triggered; this is combined with the left-side spectral width obtained in step 3. D α left For specific diagnosis, when the left spectral width is... Da left When the value increases significantly, it is determined to be due to the deterioration of the heavy-tailed particle size distribution structure caused by the accumulation of extremely large particles; when the left-side spectral width... Da left If the increase is not significant, it is determined to be a disturbance in other processes; Step 5, Early Warning Output Stage: Based on the diagnostic results obtained in Step 4, an alarm diagnostic report is generated for external systems to call or display.

[0008] The multifractal analysis method in step 2 includes any one of the following: box counting, fixed mass method, or wavelet transform modulus maxima method. The calculation process for each method includes: (1) Box counting method: The dissolved oxygen time series data to be analyzed in step 2 are divided into different scales. e Divide the data into multiple boxes, calculate the probability measure within each box, and construct the partition function. X q ( e The quality index is obtained by log-log fitting. t ( q ); (2) Fixed mass method: Using each data point of the dissolved oxygen time series data to be analyzed in step 2 as the center, find the radius containing a fixed probability mass, analyze the scaling relationship between the radius and the total number of samples or the scale, and obtain the mass index. t ( q ); (3) Wavelet transform modulus maxima method: Perform continuous wavelet transform on the dissolved oxygen time series data to be analyzed in step 2, extract the modulus maxima line, construct a partition function based on scale and moment order, and obtain the quality index through scaling relationship. t ( q ); The quality index obtained by any of the above methods t ( q Calculate the generalized dimension spectrum using the generalized dimension formula. D q ( q ); Generalized Dimension Spectrum D q ( q The calculation formula for ) is as follows: The quality index obtained by any of the above methods t ( q Singular spectra obtained through Legendre transform f ( α ); Strange Spectrum f ( α The calculation formula for ) is as follows: In the formula, α It is the singularity index.

[0009] In step 3, the left spectral width Da left The calculation formula is as follows: Δleft= α0 - αmin ⑤ In the formula: α 0 is f ( α The singular index corresponding to the maximum value, α min for f ( α The singularity index corresponding to the left endpoint.

[0010] The early warning and diagnosis stage of step 4 specifically includes: The generalized dimension obtained in step 3 is analyzed using the receiver operating characteristic curve analysis method. D q Threshold calibration was performed, and all dissolved oxygen time-series observation data during the long-term operation of the aerobic granular sludge reactor were merged. Binary classification labels were assigned based on the fitting results of the particle size distribution: states with a Rayleigh distribution were labeled as unstable states, and states with a log-normal, normal, or Cauchy distribution were labeled as stable states; generalized dimension was used as the basis for classification. D q As a continuous scoring variable, an ROC curve is constructed, and the generalized dimension is quantified by the area under the curve (AUC). D q The ability to distinguish between stable and unstable states; by maximizing the Youden exponent. J The alarm threshold can be determined using a hierarchical bootstrap resampling method, with its 95% confidence interval obtained. The Youden index... J The calculation formula is as follows: J = sensitivity + specificity - 1 ⑥ In the formula, sensitivity represents the proportion of unstable state samples that are correctly identified as unstable states out of all unstable state samples; specificity represents the proportion of stable state samples that are correctly identified as stable states out of all stable state samples. Based on this, a two-step alarm diagnostic protocol is established: The first step, generalized dimension D q Used to characterize the dominant structure of dissolved oxygen time series fluctuations; when the generalized dimension D q At higher levels, the dominant structure of dissolved oxygen time series fluctuations tends to be stable and the distribution is relatively symmetrical; when the generalized dimension is high... D qWhen the particle size distribution decreases, it exhibits enhanced heavy-tailed characteristics and an increase in extreme events; threshold optimization based on the ROC curve can achieve quantitative identification of this structural transformation; when the generalized dimension... D q When the temperature remains below the calibrated alarm threshold, an early alarm signal for structural drift is triggered, and the safety zone, transition zone, and alarm zone are divided according to the 95% confidence interval. The second step is to combine the left-side spectral width obtained in step 3. Da left For specific diagnosis: when the left spectral width is... Da left When the value increases significantly, it is determined to be due to the deterioration of the heavy-tailed particle size distribution structure caused by the accumulation of extremely large particles; when the left-side spectral width... Da left If the increase is not significant, it is determined to be a disturbance of other processes.

[0011] In step 4, the specific values ​​of the alarm threshold and diagnostic limit are determined through the following steps: collecting historical operating data under different reactor types, operating conditions, and influent water quality; constructing a dataset containing labels for stable and unstable states; and using ROC curve analysis to determine the maximum Youden index. J Generalized dimension of time D q As an alarm threshold under specific operating conditions.

[0012] Compared with the prior art, the present invention has the following significant advantages: (1) Significant advance in diagnosis This invention combines the alarm threshold calibrated based on the ROC curve in step 5 to increase the generalized dimension. D q It can keenly detect microscopic changes in structural heterogeneity and show a continuous decreasing trend in the early stage of the transition from a nearly symmetrical distribution (log-normal distribution) to a heavy-tailed distribution (Cauchy distribution) in particle size distribution. Experimental verification shows that its early warning signal is more accurate than that of the traditional SVI index and dynamic sedimentation index (densification time). t d Sorting time t s This can be done up to 60 days in advance. This provides ample time for process operators to intervene, fundamentally eliminating the risk of irreversible disintegration of granular sludge.

[0013] (2) Zero capital expenditure In step 1 of this invention, the existing online dissolved oxygen sensor and data acquisition system already standard in wastewater treatment plants are fully utilized. Through algorithmic processing in step 2, the conventional dissolved oxygen time series is transformed into high-value structural diagnostic information without requiring any additional hardware detection units. While achieving high-precision monitoring, this method achieves the engineering goal of zero new investment, making it easily and cost-effectively promoted in existing and newly constructed aerobic granular sludge treatment plants.

[0014] (3) Structurally sensitive and highly specific for diagnosis In step 5 of this invention, the generalized dimension is established. D q Spectral width on the left Da left Two complementary multifractal parameters were used to construct an "early alarm" ( D q + Etiological diagnosis Da left The two-step alarm diagnostic protocol can accurately identify the degradation of the heavy-tailed particle size distribution caused by the accumulation of extremely large particles, and effectively distinguish structural problems from other process disturbances, fundamentally solving the diagnostic limitation of existing technologies that "only know the result, not the cause".

[0015] (4) Real-time online, automatic integration and intervention feedback The two-step alarm diagnosis in step 5 of this invention enables continuous, automated calculation and seamless integration into existing host computer control systems, eliminating the need for offline sampling or cumbersome laboratory biochemical analysis. Generalized Dimension D q Spectral width on the left Da left It has a high sensitivity and reversibility to intervention measures such as particle size management, and can provide real-time feedback on the intervention effect, providing direct quantitative basis for control strategies.

[0016] In summary, this invention addresses the industry challenge of "lagging diagnosis" of aerobic granular sludge stability at the mechanistic level. By deeply mining conventional dissolved oxygen signals into high-value, structure-sensitive diagnostic information, it provides a practical, efficient, and economical new intelligent monitoring method for the long-term stable operation of aerobic granular sludge processes. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the early warning process according to an embodiment of the present invention.

[0018] Figure 2 This is a schematic diagram showing the installation position of the dissolved oxygen sensor 4 in an embodiment of the present invention.

[0019] Figure 3(a) shows the average particle size and SVI of the aerobic granular sludge in Example 1 of the present invention. 30 The time evolution diagram.

[0020] Figure 3(b) is a time evolution diagram of particle size distribution during the aerobic granular sludge cultivation process in Example 1 of the present invention; R1 is the conventional operation, R2 is the floc-particle replacement intervention, and the shaded area represents the floc-particle replacement period in R2.

[0021] Figure 4 The normalized clarification time of dynamic texture entropy in Embodiment 1 of the present invention ( t c Densification time ( t d ), sorting time ( t s (Time evolution diagram)

[0022] Figure 5 The relevant dimensions in the two aerobic granular sludge reactors R1 and R2 in Example 1 of this invention. D 2. Time evolution graph; the black line represents the alarm threshold, and the gray bar chart represents the flocculent particle replacement window in the aerobic granular sludge reactor R2.

[0023] Figure 6 This is a time evolution diagram of the left-side width of the multifractal spectrum in Embodiment 1 of the present invention.

[0024] Figure 7(a) shows the particle size distribution under four different average particle size mixing ratio schemes in Example 2 of the present invention.

[0025] Figure 7(b) is a time series diagram of dissolved oxygen under four different average particle size mixing ratio schemes in Example 2 of the present invention.

[0026] Figure 7(c) shows the relevant dimensions under four different average particle size mixing ratio schemes in Example 2 of the present invention. D 2 and the left spectral width Da left The comparison chart.

[0027] Figure 2 In the middle: 1-SBR reactor, 2-bubble, 3-aerobic granular sludge, 4-dissolved oxygen sensor, 5-host computer, 6-dissolved oxygen sensor installation position: bottom fluorescent film 15-20 cm from the liquid surface. Detailed Implementation

[0028] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0029] like Figure 2As shown, this embodiment employs a laboratory sequencing batch reactor (SBR) system, where 1 is the main body of the SBR reactor, 2 is the air bubbles generated by the bottom aeration device, 3 is the aerobic granular sludge cultivated inside, and 4 is an online dissolved oxygen sensor submerged in the liquid surface, responsible for real-time acquisition of concentration time-series data and transmission to the host computer 5. The host computer 5 executes the algorithm of this invention, and by analyzing the multifractal characteristics of the dissolved oxygen signal, achieves early warning and specific diagnosis of the structural stability of the granular sludge. This embodiment uses aerobic granular sludge in a laboratory SBR reactor as the object to describe in detail the specific implementation process of the early warning method for the stability of aerobic granular sludge based on dissolved oxygen multifractal analysis of this invention.

[0030] like Figure 1 As shown, in step 1, the dissolved oxygen data acquisition stage: In the aerobic granular sludge reactor, a dissolved oxygen sensor 4 is fixedly installed inside the reactor. The sampling interval for dissolved oxygen time series data can be selected according to the reactor size, aeration intensity, and data acquisition equipment performance, preferably not greater than 20 s. In this embodiment, 20 s is selected as the sampling interval for dissolved oxygen time series data, and the aeration stable period is selected as the analysis object. The installation position of the dissolved oxygen sensor 4 is fixed in the area above the aerobic granular sludge bed and below the liquid surface, which can effectively represent the overall dissolved oxygen fluctuation characteristics and particle disturbance signal. It is preferably located from 0.5 m below the liquid surface to 2 / 3 of the effective water depth of the aerobic granular sludge reactor. In this embodiment, the dissolved oxygen sensor 4 is fixedly installed 15-20 cm below the liquid surface inside the aerobic granular sludge reactor. In large-scale engineering reactors, the dissolved oxygen sensor 4 can be arranged at a single point or multiple points.

[0031] Step 2, Multifractal Analysis Stage: In this embodiment, the dissolved oxygen time series data collected in Step 1 is subjected to sliding window mid-range filtering. The window size and threshold multiplier can be selected according to the noise level and signal characteristics. Verified by long-term operation data of the aerobic granular sludge reactor, a window size of 3-10 and a threshold multiplier k of 3-8 are preferred ranges to remove measurement noise and extreme outliers while retaining intrinsic fluctuations reflecting the particle population structure. In this embodiment, the window size is set to 5, and the threshold multiplier k is set to... k The value was set to 5.0; subsequently, first-order differencing was performed on the filtered dissolved oxygen time series data to eliminate the long-term trend of the signal; box counting was used to process the processed dissolved oxygen time series data according to different box scales. e Divided into N For each box, calculate the root mean square value of dissolved oxygen fluctuations. Define probability measure Construct the partition function The quality index was obtained by log-log linear fitting. According to the quality index Calculate the generalized dimension using the generalized dimension formula. D q At the same time, the quality index Singular spectrum obtained by Legendre transform f (α); The specific implementation method of step 2 includes: probability measure The calculation formula is as follows: partition function The calculation formula is as follows: Quality Index The calculation formula is as follows: In the formula, the parameter values ​​can be optimized based on actual process conditions, signal length, and required discrimination accuracy, and the moment order... q The preferred value range is [-5, 5] to [-15, 15]. In this embodiment, the moment order is... q The value range is [-10, 10], and at least 20 values ​​are evenly selected within this range. q The values ​​are calculated, and in this embodiment, 30 are preferred. q Values ​​are calculated, box dimensions e The preferred value range is 5 to 1 / 2 of the length of the dissolved oxygen time series after pretreatment; According to the quality index Calculating the generalized dimension spectrum using the generalized dimension formula D q ( q Generalized dimensional spectrum D q ( q The calculation formula is as follows: At the same time, the quality index Singular spectrum obtained by Legendre transform f (α); Singular spectrum f (α) is calculated using the following formula: Step 3, Feature Parameter Extraction Stage: In this embodiment, based on the generalized dimension spectrum obtained in Step 2... D q ( q ), calculate the relevant dimension D 2. The relevant dimension D 2 is the order of the moment. q Generalized dimension when =2 Dq Values ​​are used to characterize the dominant structure of dissolved oxygen time series fluctuations; based on the singular spectrum obtained in step 2. f ( α ), calculate the left spectral width Da left , used to characterize the intensity contribution of large-amplitude extreme fluctuations; The dominant structure of dissolved oxygen time series fluctuations refers to the dynamic evolution pattern of dissolved oxygen time series data determined by the physicochemical properties of granular sludge itself (such as particle size distribution, porosity, and activity stratification) after removing measurement noise and random disturbances.

[0032] In step 3, the left spectral width Da left The calculation formula is as follows: Δleft= α0 - αmin ⑧ In the formula: α 0 is f ( α The singular index corresponding to the maximum value, α min for f ( α The singularity index corresponding to the left endpoint.

[0033] Step 4, Early Warning and Diagnosis Stage: The relevant dimensions obtained in Step 3 are analyzed using Receiver Operating Characteristic (ROC) curve analysis. D 2. Perform threshold calibration to determine the alarm threshold; when the relevant dimensions D 2. When the value exceeds the alarm threshold, the system is determined to be in a safe operating zone and no alarm is triggered; when the relevant dimension... D 2. When the value is below the alarm threshold, an early alarm signal for structural drift is triggered; combined with the left spectral width obtained in step 3. D α left For specific diagnosis, when the left spectral width is... Da left When the value increases significantly, it is determined to be due to the deterioration of the heavy-tailed particle size distribution structure caused by the accumulation of extremely large particles; when the left-side spectral width... Da left If the increase is not significant, it is determined to be a disturbance in other processes; The early warning and diagnosis stage of step 4 specifically includes: The relevant dimensions obtained in step 3 were analyzed using the receiver operating characteristic curve analysis method. D2. Threshold calibration was performed. All dissolved oxygen time-series observation data during the long-term operation of the aerobic granular sludge reactor were merged, and binary classification labels were assigned based on the fitting results of particle size distribution: states with fitting results of Rayleigh distribution were marked as unstable states, and states with fitting results of log-normal, normal, or Cauchy distribution were marked as stable states; the correlation dimension was used as the basis for classification. D 2. As a continuous rating variable, an ROC curve is constructed, and the correlation dimension is quantified by the area under the curve (AUC). D 2. The ability to distinguish between stable and unstable states; by maximizing the Youden exponent. J The alarm threshold can be determined using a hierarchical bootstrap resampling method, with its 95% confidence interval obtained. The Youden index... J The calculation formula is as follows: J = sensitivity + specificity - 1 ⑨ In the formula, sensitivity represents the proportion of unstable state samples that are correctly identified as unstable states out of all unstable state samples; specificity represents the proportion of stable state samples that are correctly identified as stable states out of all stable state samples. Based on this, a two-step alarm diagnostic protocol is established: The first step is to determine the relevant dimensions. D 2 is used to characterize the dominant structure of dissolved oxygen time series fluctuations; when the relevant dimension D At higher values, the dominant structure of dissolved oxygen time series fluctuations tends to be stable and the distribution is relatively symmetrical; when the correlation dimension is high... D When the value of 2 decreases, the particle size distribution exhibits enhanced heavy-tailed characteristics and an increase in extreme events; threshold optimization based on the ROC curve can achieve quantitative identification of this structural transformation; when the relevant dimension... D 2. When the value remains below the calibrated alarm threshold, an early alarm signal for structural drift is triggered, and the safety zone, transition zone, and alarm zone are divided according to the 95% confidence interval. The second step is to combine the left-side spectral width obtained in step 3. Da left For specific diagnosis: when the left spectral width is... Da left When the value increases significantly, it is determined to be due to the deterioration of the heavy-tailed particle size distribution structure caused by the accumulation of extremely large particles; when the left-side spectral width... Da left If the increase is not significant, it is determined to be a disturbance of other processes.

[0034] Step 5, Early Warning Output Stage: Based on the diagnostic results obtained in Step 4, an alarm diagnostic report is generated for external systems to call or display.

[0035] In step 4, the specific values ​​of the alarm threshold and diagnostic limit are determined through the following steps: collecting historical operating data under different reactor types, operating conditions, and influent water quality; constructing a dataset containing labels for stable and unstable states; and using ROC curve analysis to determine the maximum Youden index. J Time-related dimensions D 2 serves as the alarm threshold under specific operating conditions.

[0036] Example 1 In this embodiment, two sequencing batch reactors (SBRs) with an effective volume of 12.37 L were operated in parallel for 150 days, designated as aerobic granular sludge reactor R1 (conventional operation control group) and aerobic granular sludge reactor R2 (size management experimental group). During the two intervention windows of days 44-98 and 122-135, a 2.5% volumetric floc-particle replacement operation was performed daily in aerobic granular sludge reactor R2 to regulate particle size distribution. To investigate the relationship between the stability of granular sludge and dissolved oxygen fluctuations, a fitting analysis was conducted on the particle size distribution of granular sludge in aerobic granular sludge reactors R1 and R2. The fitting results identified four particle size distribution types: log-normal, normal, Cauchy, and Rayleigh. These different distribution types represent the changes in granular sludge at different stability stages.

[0037] Dissolved oxygen sensor 4, as described in step 1 above, is fixedly installed 15-20 cm above the water column in both aerobic granular sludge reactors R1 and R2, and continuously collects high-frequency data at 20-second sampling intervals. During data processing, only the stable aeration period of each cycle is extracted. After median filtering and first-order difference preprocessing as described in step 2, multifractal analysis is performed using the box counting method as described in step 3, and the relevant dimension is calculated as described in step 4. D 2 and left spectral width Da left .

[0038] Experimental results show that under the normal operating conditions of the aerobic granular sludge reactor R1, the relevant dimension is... D 2. The decline begins around day 30 of cultivation and ends around day 40, when the temperature drops from the safe zone. D 2≥0.75) quickly enter the alarm zone ( D 2≤0.64) (e.g. Figure 5 As shown in the figure, the traditional sludge volume index SVI at this time 30 It remained stable until day 100 of cultivation, when it increased significantly (as shown in Figure 3(a)), indicating the correlation dimension. D 2 compared to SVI 30It exhibits a significant diagnostic lead time of approximately 60 days. Meanwhile, as shown in Figure 3(b), the particle size distribution of the aerobic granular sludge reactor R1 initially follows a log-normal distribution (approximately 0–40 days), exhibiting a relatively symmetrical and concentrated distribution. Subsequently, it gradually transitions to a Cauchy and Rayleigh distribution, characterized by a significant increase in the volume fraction of large particles (>300 µm), a gradually strengthening heavy-tailed characteristic, and a corresponding decrease in the proportion of small particles (<100 µm). This evolution of particle size distribution from near-symmetrical to heavy-tailed is related to… D The descent height of 2 is synchronized: when the distribution is still log-normal or normally oriented, the correlation dimension is... D 2. Maintain a high level; once the heavy-tailed characteristic dominated by the Cauchy distribution appears, the correlation dimension will decrease. D The value of 2 begins to decrease significantly and remains low for a long period during Rayleigh distributions. This is reflected in the enhanced extreme intermittent events in dissolved oxygen fluctuations, which is related to the correlation dimension. D 2. Reduced correlation. Normalized compaction time, a sedimentation kinetic index characterized by dynamic texture entropy. t d With sorting time t s A significant rebound only occurred during the disintegration phase of the Rayleigh distribution on days 90 and 105, respectively (e.g. Figure 4 As shown), this further confirms... D The warning time for 2 is significantly earlier than that for the deterioration index of settlement performance.

[0039] In the size management group of the aerobic granular sludge reactor R2, a near-symmetrical particle size distribution was effectively maintained during the intervention window (days 44–98 and 122–135) through daily floc-particle replacement of 2.5%, as shown in Figure 3(b). The aerobic granular sludge reactor R2 maintained a narrow symmetrical distribution during the intervention period. Correspondingly, the relevant dimensions during the intervention window... D 2. Maintain stability within the safe zone ( D 2≥ 0.75) (e.g. Figure 5 As shown), the relevant dimensions after stopping the intervention. D 2. If it quickly falls back to the 0.4-0.5 range, the relevant dimensions will be updated after intervention is restarted. D 2 shows a clear recovery and partially rebounds to the transition zone, with the left spectral width... Da left It also decreases accordingly (e.g.) Figure 6 As shown in the figure, the real-time response capability and reversibility of the multifractal index to size management measures were verified.

[0040] This embodiment combines 150 days of continuous operation with... Figure 1~Figure 6The system comparison fully verified the early warning capability, threshold applicability, and feedback effect of the method of the present invention in actual aerobic granular sludge processes, providing a reliable implementation basis for zero-capital expenditure online monitoring in engineering sites.

[0041] Example 2 To further verify the direct sensitivity and causal relationship of multifractal indices to particle size distribution structure, a size-controlled mixing experiment was conducted in this embodiment. Mature aerobic granular sludge was taken and separated into small particle groups (average diameter 263 µm) and large particle groups (average diameter 562 µm) using a standard sieve, and then recombine them into four mixing systems according to their mass ratio: Group A: 100% small particles; Group B: 70% small particles + 30% large particles; Group C: 30% small particles + 70% large particles; Group D: 100% large particles.

[0042] Each mixture group was placed in the same reactor for aeration experiments. Dissolved oxygen sensors were fixedly installed as described in step 1 above, and high-frequency dissolved oxygen data were collected at 20-second sampling intervals. After preprocessing as described in step 2, multifractal analysis was performed using the box counting method from step 3, and relevant dimensions were extracted as described in step 4. D 2 and left spectral width Da left .

[0043] The experimental results are shown in Figures 7(a), 7(b), and 7(c): As the proportion of large particles gradually increases from 0% (Group A) to 100% (Group D), the particle size distribution gradually changes from a single-peaked narrow distribution to a multi-peaked heavy-tailed distribution, as shown in Figure 7(a); more frequent and stronger extreme fluctuations appear in the dissolved oxygen time series, as shown in Figure 7(b); the generalized dimension spectrum... D q The curve shows an overall downward shift, as shown in Figure 7(c). Relevant dimensionality. D 2. The spectral width on the left side shows a monotonically decreasing trend as the proportion of large particles increases (from the highest value in group A to the lowest value in group D), while the spectral width on the left side... Da left It then increases monotonically, from about 0.74 to about 0.96, as shown in Figure 7(c).

[0044] This embodiment systematically verifies the correlation dimension of the multifractal index by precisely controlling the particle size composition. D 2 and left spectral width Da left The direct response relationship to the accumulation of extremely large particles and the characteristics of heavy-tailed PSD is the basis for the "early alarm" of this invention. D 2) + Etiological diagnosis ( Daleft The two-step protocol provides strong mechanistic support and further verifies the structural sensitivity and engineering reliability of the method.

[0045] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. An early warning method for the stability of aerobic granular sludge based on dissolved oxygen multifractal analysis, characterized in that, Includes the following steps: Step 1, Dissolved oxygen data acquisition stage: During the aeration stabilization stage of the aerobic granular sludge reactor, high-frequency dissolved oxygen time series data are continuously collected in the area above the sludge layer formed by sedimentation and below the liquid surface in the aerobic granular sludge reactor using a dissolved oxygen sensor at sampling intervals of no more than 20 s. Step 2, Multifractal Analysis Stage: Obtaining Dissolved Oxygen Time Series Data to be Analyzed: Perform one or both of the following operations on the raw dissolved oxygen time series data collected in Step 1: denoising and detrending, to obtain the dissolved oxygen time series data to be analyzed; or directly use the raw dissolved oxygen time series data collected in Step 1 as the dissolved oxygen time series data to be analyzed; use a multifractal analysis method based on scaling transformation to process the dissolved oxygen time series data to be analyzed to obtain the quality index. τ ( q According to the quality index Calculating the generalized dimension spectrum using the generalized dimension formula D q ( q At the same time, the quality index Singular spectrum obtained by Legendre transform f ( α ); Step 3, Feature Parameter Extraction Stage: Based on the generalized dimension spectrum obtained in Step 2 D q ( q ), select a specific moment order q Corresponding generalized dimension D q The value is used as a characteristic parameter to characterize the dominant structure of dissolved oxygen time series fluctuations; Based on the singular spectrum obtained in step 2 f ( α ), calculate the left spectral width Δα left , used to characterize the intensity contribution of large-amplitude extreme fluctuations; Step 4, Early Warning and Diagnosis Stage: The generalized dimension obtained in Step 3 is analyzed using the Receiver Operating Characteristic (ROC) curve method. D q Threshold calibration is performed to determine the alarm threshold; when the generalized dimension D q When the value exceeds the alarm threshold, the system is determined to be in a safe operating zone and no alarm is triggered; when the generalized dimension... D q When the value falls below the alarm threshold, an early alarm signal for structural drift is triggered; this is combined with the left-side spectral width obtained in step 3. Δα left For specific diagnosis, when the left spectral width is... Δα left When the value increases significantly, it is determined to be due to the deterioration of the heavy-tailed particle size distribution structure caused by the accumulation of extremely large particles; when the left-side spectral width... Δα left If the increase is not significant, it is determined to be a disturbance in other processes; Step 5, Early Warning Output Stage: Based on the diagnostic results obtained in Step 4, an alarm diagnostic report is generated for external systems to call or display.

2. The method for early warning of aerobic granular sludge stability based on dissolved oxygen multifractal analysis according to claim 1, characterized in that, The multifractal analysis method in step 2 includes any one of the following: box counting, fixed mass method, or wavelet transform modulus maxima method. The calculation process for each method includes: (1) Box counting method: The dissolved oxygen time series data to be analyzed in step 2 are divided into different scales. ε Divide the data into multiple boxes, calculate the probability measure within each box, and construct the partition function. X q ( ε The quality index is obtained by log-log fitting. τ ( q ); (2) Fixed mass method: Using each data point of the dissolved oxygen time series data to be analyzed in step 2 as the center, find the radius containing a fixed probability mass, analyze the scaling relationship between the radius and the total number of samples or the scale, and obtain the mass index. τ ( q ); (3) Wavelet transform modulus maxima method: Perform continuous wavelet transform on the dissolved oxygen time series data to be analyzed in step 2, extract the modulus maxima line, construct a partition function based on scale and moment order, and obtain the quality index through scaling relationship. τ ( q ); The quality index obtained by any of the above methods τ ( q Calculate the generalized dimension spectrum using the generalized dimension formula. D q ( q ); Generalized Dimension Spectrum D q ( q The calculation formula for ) is as follows: The quality index obtained by any of the above methods τ ( q Singular spectra obtained through Legendre transform f ( α ); Strange Spectrum f ( α The calculation formula for ) is as follows: In the formula, α It is the singularity index.

3. The method for early warning of aerobic granular sludge stability based on dissolved oxygen multifractal analysis according to claim 1, characterized in that, In step 3, the left spectral width Δα left The calculation formula is as follows: In the formula: α 0 is f ( α The singular index corresponding to the maximum value, α min for f ( α The singularity index corresponding to the left endpoint.

4. The method for early warning of aerobic granular sludge stability based on dissolved oxygen multifractal analysis according to claim 1, characterized in that, The early warning and diagnosis stage of step 4 specifically includes: The generalized dimension obtained in step 3 is analyzed using the receiver operating characteristic curve analysis method. D q Threshold calibration was performed, and all dissolved oxygen time-series observation data during the long-term operation of the aerobic granular sludge reactor were merged. Binary classification labels were assigned based on the fitting results of the particle size distribution: states with a Rayleigh distribution were labeled as unstable states, and states with a log-normal, normal, or Cauchy distribution were labeled as stable states; generalized dimension was used as the basis for classification. D q As a continuous scoring variable, an ROC curve is constructed, and the generalized dimension is quantified by the area under the curve (AUC). D q The ability to distinguish between stable and unstable states; by maximizing the Youden exponent. J The alarm threshold can be determined using a hierarchical bootstrap resampling method, with its 95% confidence interval obtained. The Youden index... J The calculation formula is as follows: In the formula, sensitivity represents the proportion of unstable state samples that are correctly identified as unstable states out of all unstable state samples; specificity represents the proportion of stable state samples that are correctly identified as stable states out of all stable state samples. Based on this, a two-step alarm diagnostic protocol is established: The first step, generalized dimension D q Used to characterize the dominant structure of dissolved oxygen time series fluctuations; when the generalized dimension D q At higher levels, the dominant structure of dissolved oxygen time series fluctuations tends to be stable and the distribution is relatively symmetrical; when the generalized dimension is high... D q When the particle size distribution decreases, it exhibits enhanced heavy-tailed characteristics and an increase in extreme events; threshold optimization based on the ROC curve can achieve quantitative identification of this structural transformation; when the generalized dimension... D q When the temperature remains below the calibrated alarm threshold, an early alarm signal for structural drift is triggered, and the safety zone, transition zone, and alarm zone are divided according to the 95% confidence interval. The second step is to combine the left-side spectral width obtained in step 3. Δα left For specific diagnosis: when the left spectral width is... Δα left When the value increases significantly, it is determined to be due to the deterioration of the heavy-tailed particle size distribution structure caused by the accumulation of extremely large particles; when the left-side spectral width... Δα left If the increase is not significant, it is determined to be a disturbance of other processes.

5. The method for early warning of aerobic granular sludge stability based on dissolved oxygen multifractal analysis according to claim 1 or 4, characterized in that, In step 4, the specific values ​​of the alarm threshold and diagnostic limit are determined through the following steps: collecting historical operating data under different reactor types, operating conditions, and influent water quality; constructing a dataset containing labels for stable and unstable states; and using ROC curve analysis to determine the maximum Youden index. J Generalized dimension of time D q As an alarm threshold under specific operating conditions.

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