A near-critical teaching regulation method and system with effectiveness gate constraint

Abstract

The application discloses a kind of effectiveness gate constrained near-critical teaching regulation methods and systems, and the effective boundary of intervention model is determined by multi-scale critical analysis, and three effectiveness gates are formed by index authentication, causal support domain verification and sovereignty constraint verification, and the real-time measurement data is carried out trusted access control.According to risk level, the measurement that passes authentication is executed freezing, limited degradation or hierarchical processing of artificial takeover.When authentication passes, the model predictive controller optimizes the output intervention intensity within the critical intensity interval, forming a closed-loop mechanism of trusted measurement driven control and failed measurement fallback.The application can improve the safety and controllability of the regulation process and the measurement credibility, enhance the generality of the regulation strategy and the stability of the intervention output, and has fault-tolerant fallback capability under abnormal conditions, which can meet the engineering application needs of large-scale online teaching system for near-critical safety control.

Description

Technical Field

[0001] This invention relates to the field of educational control and adaptive intervention technology, and more specifically, to a near-critical teaching control method and system with effectiveness gate constraints. Background Technology

[0002] Closed-loop intervention and control have significant application value in large-scale online education and intelligent teaching systems. By continuously measuring the state indicators of the target group and dynamically adjusting the intervention intensity, the intervention effect can be improved under the constraint of limited control resources, while avoiding the fluctuation of the group state and waste of resources caused by over-intervention. However, the complexity and heterogeneity of the group state pose serious challenges to the accuracy and safety of intervention and control. How to achieve effective and safe intervention in a dynamically changing environment is a key problem in the practice of smart education engineering.

[0003] Existing teaching control methods mainly face the following technical limitations:

[0004] Insufficient control safety: Existing control systems generally assume that measured values ​​are reliable, and the controller directly consumes the latest measurement and executes control logic that increases intervention as the error increases. When measurements fail due to insufficient samples, noise interference, or abnormal acquisition, the system continues to increase intervention, leading to population overload or even control instability, thus limiting control safety.

[0005] Insufficient generalization of regulation: Current solutions often apply the same intervention model directly to groups of different sizes. However, when the model is run at an inapplicable scale, the intervention strategy is mismatched with the characteristics of the group, resulting in insufficient generalization of regulation.

[0006] Limited precision in regulation: When measurement anomalies or model mismatches occur, the intervention and adjustment strategies of existing solutions tend to be uniform, and anomalies of different severity trigger homogeneous handling actions, which limits the precision of regulation and the adaptability to different scenarios. Summary of the Invention

[0007] The purpose of this invention is to provide a near-critical teaching control method and system with effectiveness gate constraints to solve the above-mentioned problems existing in the prior art.

[0008] In a first aspect, embodiments of the present invention provide a near-critical teaching control method for effectiveness gate constraints, comprising:

[0009] S1: Acquire multi-scale intervention response calibration data, current real-time status measurement data, historical operational intervention sequence data, and a first intervention intensity; the first intervention intensity is the intervention intensity of the current control cycle;

[0010] S2: Based on the multi-scale intervention response calibration data, multi-scale critical analysis is performed through scaling and collapse to obtain the critical intensity range, applicable scale range and model mismatch.

[0011] S3: Based on the applicable scale range and the model mismatch, determine the scale applicability of the current real-time state measurement data to obtain scale-applicable data;

[0012] S4: Based on the historical operational intervention sequence data, perform triple verification on the scale-applicable data to obtain a trusted authentication result and a sub-item verification result; the trusted authentication result includes authentication passed and authentication failed;

[0013] S5: If the trusted authentication result is authentication failure, based on the sub-item verification results, the first intervention intensity is gradually downgraded to obtain the second intervention intensity;

[0014] S6: If the trusted authentication result is successful, based on the current real-time state measurement data, the critical intensity range, the applicable scale range, and the first intervention intensity, the second intervention intensity is obtained by rolling optimization through the model prediction controller.

[0015] Optionally, the second intervention intensity output in the current control cycle is used as new data, and the historical intervention sequence is updated according to the rolling window rule; the average mastery of the group collected after the intervention in the current control cycle is used as new data, and the historical state response sequence is updated according to the rolling window rule; the steps described in S101 to S106 are executed to obtain the second intervention intensity of the next control cycle, thereby realizing the closed-loop rolling operation of near-critical teaching regulation.

[0016] Optionally, the multi-scale intervention response calibration data includes datasets of intervention intensity response curves at multiple population sizes; based on the multi-scale intervention response calibration data, multi-scale criticality analysis is performed through scaling and collapse to obtain the critical intensity range, applicable scale range, and model mismatch, including:

[0017] Based on the intervention intensity response curve dataset, the response curves are scaled by scaling and collapse to obtain the collapsed response data.

[0018] The collapsed response data is evaluated level by level to obtain the model mismatch degree corresponding to each group size;

[0019] The critical transition point is identified from the collapsed response data to obtain the critical intensity corresponding to each population size.

[0020] Based on the model mismatch, the applicability of the population size is screened to obtain the applicable size range;

[0021] The critical intensity range is determined based on the critical intensity corresponding to the size of each group.

[0022] Optionally, based on the response curve dataset, a scaling transformation of the response curves is performed through scaling and collapse to obtain the collapsed response data, including:

[0023] The response curve dataset is used to extract response curves based on group size to obtain the mastery and intervention intensity response curves corresponding to each group size.

[0024] Based on the mastery level corresponding to each group size and the response curve of the intervention intensity, parameter estimation is performed through scaling law fitting to obtain the local critical intensity, response scaling index and correlation scaling index;

[0025] The scaling law fitting is specifically defined by the following formula:

[0026]

[0027] in, In order to control the degree, For the intensity of intervention, For group size, For local critical strength, In response to the scaling index, For correlation scaling index, It is a universal function independent of the group size;

[0028] Based on the local critical intensity, the response scaling index, and the correlation scaling index, the mastery and intervention intensity response curves are scaled to obtain the set of transformed coordinate points corresponding to each group size;

[0029] Based on the transformed set of coordinate points, the local critical intensity, the response scaling index, and the correlation scaling index are iteratively adjusted until data points of different population sizes fall into the same universal function, thus obtaining the collapsed response data.

[0030] Optionally, the scale-applicable data includes original state indicators and sovereign compliance attributes; based on the historical operational intervention sequence data, the scale-applicable data undergoes triple verification to obtain trusted authentication results and itemized verification results, including:

[0031] Based on the historical operational intervention sequence data, the original state indicators are certified to obtain the indicator certification results;

[0032] Based on the historical operational intervention sequence data and the original state indicators, causal support domain verification is performed through causal effect estimation to obtain causal verification results.

[0033] Perform sovereignty constraint verification on the aforementioned sovereignty compliance attributes to obtain the sovereignty verification result;

[0034] The authentication results of the indicators, the causality verification results, and the sovereignty verification results are logically merged to obtain the trusted authentication results.

[0035] The results of the indicator authentication, the causal verification, and the sovereignty verification are aggregated separately to obtain the itemized verification results.

[0036] Optionally, the original state indicators include data collected from at least two independent sources; based on the historical operational intervention sequence data, the original state indicators are certified to obtain the certification results, including:

[0037] The original state indicators are subjected to statistical significance testing to obtain the significance determination results;

[0038] Based on the historical operational intervention sequence data, the signal-to-noise ratio (SNR) is calculated using sliding window variance decomposition.

[0039] The signal-to-noise ratio is thresholded to obtain the signal-to-noise ratio determination result;

[0040] Based on the original state indicators, consistency is determined by correlation comparison to obtain the consistency determination result.

[0041] The significance determination result, the signal-to-noise ratio determination result, and the consistency determination result are logically merged to obtain the indicator certification result.

[0042] Optionally, based on the historical operational intervention sequence data and the original state indicators, causal support domain verification is performed through causal effect estimation to obtain causal verification results, including:

[0043] Based on the historical intervention sequence data, the causal effect was estimated using the difference-in-differences method to obtain the average causal effect and confidence interval.

[0044] Based on the original state indicators and the first intervention intensity, the direction and magnitude of the intervention response are determined.

[0045] Based on the average causal effect, the direction of the intervention response is checked for consistency, and the direction check result is obtained.

[0046] Based on the confidence interval, the amplitude of the intervention response is verified to obtain the amplitude verification result;

[0047] The direction verification result and the amplitude verification result are logically merged to obtain the causality verification result.

[0048] Optionally, the sovereignty compliance attributes include data sovereignty flags, privacy budget status, and permission levels; sovereignty constraint verification is performed on the sovereignty compliance attributes to obtain sovereignty verification results, including:

[0049] The data sovereignty marker is subjected to a compliance assessment to obtain a sovereignty compliance assessment result;

[0050] Based on the privacy budget status, the balance is verified using the differential privacy budget accounting method to obtain the privacy budget verification result;

[0051] The permission levels are compared to obtain the permission verification results;

[0052] The sovereignty compliance determination result, the privacy budget verification result, and the permission verification result are logically merged to obtain the sovereignty verification result.

[0053] Optionally, if the trusted authentication result is authentication failure, based on the sub-item verification results, the first intervention intensity is gradually downgraded to obtain a second intervention intensity, including:

[0054] Based on the results of the itemized verification, risk levels are classified to obtain risk level determination results; the risk level determination results include a first risk level, a second risk level, and a third risk level.

[0055] If the risk level determination result is the first risk level, the first intervention intensity will be used as the second intervention intensity;

[0056] If the risk level determination result is the second risk level, the first intervention intensity is adjusted to obtain the second intervention intensity;

[0057] If the risk level assessment result is the third risk level, a manual takeover request is made to obtain the second intervention intensity.

[0058] Optionally, if the trusted authentication result is successful, based on the current real-time state measurement data, the critical intensity range, the applicable scale range, and the first intervention intensity, a second intervention intensity is obtained through rolling optimization using a model prediction controller, including:

[0059] Based on the current real-time state measurement data and the first intervention intensity, multi-step state prediction is performed through the state space model to obtain the predicted state trajectory;

[0060] Based on the predicted state trajectory, the critical intensity range, and the applicable scale range, the intervention intensity sequence with boundary constraints is optimized through the model prediction controller to obtain the optimal intervention intensity sequence.

[0061] The optimal intervention intensity sequence is first extracted to obtain the second intervention intensity.

[0062] Secondly, embodiments of the present invention provide a near-critical teaching control system with effectiveness gate constraints, the system comprising:

[0063] The data acquisition module is used to acquire multi-scale intervention response calibration data, current real-time status measurement data, historical operational intervention sequence data, and the first intervention intensity.

[0064] The multi-scale critical analysis module is used to perform multi-scale critical analysis based on the multi-scale intervention response calibration data by scaling and collapse, to obtain the critical intensity range, applicable scale range and model mismatch.

[0065] The model suitability determination module is used to determine the scale suitability of the current real-time state measurement data based on the applicable scale range and the model mismatch degree, so as to obtain the scale suitability data.

[0066] The trusted authentication module is used to perform triple verification on the scale-applicable data based on the historical operation intervention sequence data to obtain trusted authentication results and item verification results;

[0067] The security downgrade execution module is used to, if the trusted authentication result is authentication failure, gradually downgrade the first intervention intensity based on the sub-item verification results to obtain a second intervention intensity;

[0068] The model prediction control module is used to perform rolling optimization based on the current real-time state measurement data, the critical intensity range, the applicable scale range, and the first intervention intensity, if the trusted authentication result is successful, to obtain the second intervention intensity.

[0069] Thirdly, embodiments of the present invention also provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of any of the methods described above.

[0070] Fourthly, embodiments of the present invention also provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of any of the methods described above.

[0071] Fifthly, embodiments of the present invention also provide a computer program product, including a computer program / instructions, which, when executed by a processor, implement the steps of any of the methods described above.

[0072] Compared with the prior art, the embodiments of the present invention achieve the following beneficial effects:

[0073] This invention also provides a near-critical teaching control method and system with effectiveness gate constraints. First, based on multi-scale intervention response calibration data, it performs multi-scale critical analysis through scaling and collapse, using critical intensity range, applicable scale range, and model mismatch metric to characterize the effective boundary of the intervention model. This ensures that the near-critical control strategy always operates within the model's effective range, significantly improving the generalization and interpretability of the control. More importantly, this method introduces a triple effectiveness gate consisting of indicator verification, causal support domain verification, and sovereign constraint verification before control decisions. Only after real-time measurement data passes the triple verification does it enter subsequent control decisions, strictly limiting the control process to a safe decision space where measurements are reliable and the model is applicable. This avoids the system instability risk caused by the dangerous escalation logic of traditional controllers directly consuming failed measurements and executing interventions with increasing errors. Simultaneously, relying on a gradual degradation mechanism and the rolling optimization of the model predictive controller, it collaboratively ensures the smoothness and resource optimization of the intervention output, solving the problems of singular anomaly handling and limited control precision in existing technologies. Ultimately, without the need for manually pre-setting complex anomaly rules, it achieves near-critical intelligent teaching control with high safety, strong generalization, and smooth controllability. Attached Figure Description

[0074] Figure 1 This is a flowchart of a near-critical teaching control method for effectiveness gate constraints provided in an embodiment of the present invention.

[0075] Figure 2 This is a flowchart of multi-scale critical analysis in a near-critical teaching control method with effectiveness gate constraints provided in an embodiment of the present invention.

[0076] Figure 3 This is a flowchart of the triple validity gate verification in a near-critical teaching control method for validity gate constraints provided in an embodiment of the present invention.

[0077] Figure 4 This is a flowchart of the gradual degradation process in a near-critical teaching control method for effectiveness gate constraints provided in an embodiment of the present invention.

[0078] Figure 5 This is a flowchart of model prediction rolling optimization in a near-critical teaching control method with effectiveness gate constraints provided in an embodiment of the present invention.

[0079] Figure 6 This is a block structure diagram of an electronic device provided in an embodiment of the present invention.

[0080] Icons: 700 - Bus; 701 - Receiver; 702 - Processor; 703 - Transmitter; 704 - Memory; 705 - Bus Interface. Detailed Implementation

[0081] The embodiments of the present invention will be described in detail below with reference to examples. However, those skilled in the art will understand that the following examples are only for illustrating the present invention and should not be regarded as limiting the scope of the present invention.

[0082] The purpose of this application is to overcome the problems of insufficient control security, insufficient generalization of regulation, and limited regulation precision in existing technologies, and to provide a near-critical teaching regulation method and system with effectiveness gate constraints. This application determines the applicable scale and model mismatch through multi-scale critical analysis, applies effectiveness gate constraints to real-time measurements through triple verification of index certification, causal support domain, and sovereign constraints, and gradually reduces the intervention intensity according to the risk level or uses the model predictive controller to continuously optimize the intervention intensity, ultimately achieving reliable, safe, smooth, and controllable near-critical teaching regulation.

[0083] The present invention will now be described in detail with reference to the accompanying drawings.

[0084] Example

[0085] like Figure 1 As shown, this embodiment of the invention provides a near-critical teaching control method for effectiveness gate constraints, the method comprising:

[0086] S101: Obtain multi-scale intervention response calibration data, current real-time status measurement data, historical operational intervention sequence data, and first intervention intensity.

[0087] The multi-scale intervention response calibration data includes datasets of intervention intensity response curves collected at multiple preset group sizes, with the horizontal axis representing intervention intensity and the vertical axis representing the average group mastery. This multi-scale intervention response calibration data is obtained through multi-scale aggregation and mining of historical operational data before system deployment or during periodic updates.

[0088] Specifically, the construction method for multi-scale intervention response calibration data is as follows: Group size levels are determined based on the course teaching plan and stored as size nodes in the calibration database. The system extracts group operation records corresponding to different intervention intensities under each size node from historical operation logs. Using intervention intensity as the horizontal axis and average group mastery as the vertical axis, the intervention intensity is categorized according to a preset step size. The arithmetic mean of the average group mastery of multiple historical records within each intervention intensity level is calculated to obtain the response value corresponding to that intensity point. Connecting these intensity points forms the intervention intensity response curve dataset for that scale.

[0089] In this embodiment, the intervention intensity is a normalized comprehensive control quantity, weighted and synthesized from the amount of practice exercises pushed, the duration of explanations, the frequency of difficulty switching, and the feedback density. When the intervention intensity is at the lower limit of the interval, it corresponds to the minimum intervention configuration, i.e., pushing a basic number of questions per day, no additional explanations, no active switching of difficulty, and only providing feedback on correct and incorrect answers. When the intervention intensity is at the upper limit of the interval, it corresponds to the maximum intervention configuration, i.e., pushing the maximum number of questions per day, providing complete explanation videos, high-frequency switching of difficulty, and providing progressive prompts and feedback. During the teaching operation, the system records the intervention intensity value of the current actual configuration in each control cycle. The average mastery of the group is a state quantity automatically calculated by the teaching platform at the end of each control cycle based on the response data of the target group in the assessment task. It is the ratio of the number of correct responses of all individuals in the target group to the total number of responses, and then the group mean is taken and normalized. The system automatically calculates and records this value at the end of each control cycle.

[0090] In this embodiment, the group size is divided into five tiers: tier 1, tier 2, tier 3, tier 4, and tier 5, centered on {30, 60, 120, 240, 480}. During system operation, the actual group size is mapped to the nearest size node based on proximity: tier 1 corresponds to 1 to 45, tier 2 to 46 to 90, tier 3 to 91 to 180, tier 4 to 181 to 360, and tier 5 to greater than 360. The preset step size for intervention intensity tiering is 0.05. The weights for weighted summation of the amount of practice pushed, explanation duration, difficulty switching frequency, and feedback density in synthesizing intervention intensity are 0.3, 0.3, 0.2, and 0.2, respectively.

[0091] In this embodiment, one control cycle is one teaching week (7 calendar days).

[0092] The current real-time status measurement data includes raw status indicators and sovereignty compliance attributes. Sovereign compliance attributes include data sovereignty flags, privacy budget status, and permission levels. Raw status indicators include knowledge mastery, task participation, error rate, and dwell time. The current real-time status measurement data is collected in real-time through the front-end measurement and collection interface of the teaching platform.

[0093] The acquisition of raw status indicators includes: at the beginning of each control cycle, simultaneously triggering at least two independent acquisition channels. The acquisition results from the two channels are then combined to obtain the raw status indicators.

[0094] Specifically, the first data collection channel automatically collects knowledge mastery, error rate, dwell time, and task participation through the learning management system database. In this embodiment, knowledge mastery is a state quantity automatically calculated by the teaching platform based on the target group's response data in the assessment task, taking the ratio of the number of correct responses from all individuals in the target group to the total number of responses, then taking the group mean and normalizing it. The error rate is a state quantity automatically calculated by the teaching platform based on the target group's response logs in the interactive task, taking the ratio of the number of responses marked as errors to the total number of responses. Dwell time is a state quantity automatically calculated by the teaching platform based on the time interval between each login and logout of the target group, taking the average of the group's single dwell time and normalizing it. Task participation is a state quantity automatically calculated by the teaching platform based on the target group's assignment submission timestamps, taking the ratio of the number of individuals who submitted assignments on time within a preset period to the total number of individuals in the group.

[0095] Specifically, the second data acquisition channel automatically collects group task participation behavior logs through the teaching platform and calculates knowledge mastery, task participation, error rate, and dwell time based on the behavior logs. In this embodiment, task participation is a state quantity obtained by weighted summing the number of times the target group actively asked questions, the proportion of timely homework submissions, and the frequency of classroom discussion participation within a preset period, respectively, after normalization. Knowledge mastery is a state quantity obtained by weighted summing the number of times the target group actively asked questions, the proportion of timely homework submissions, and the frequency of classroom discussion participation, respectively, after normalization. The error rate is a state quantity calculated by the teaching platform based on the ratio of the number of times statements marked as incorrect to the total number of statements in the classroom discussion records. Dwell time is a state quantity obtained by the teaching platform after normalizing the time span from the first statement to the last statement of the target group in the classroom discussion.

[0096] In this embodiment, the preset period is one control period (7 calendar days). In the task participation rate of the second acquisition channel, the weights of the number of times actively asking questions, the proportion of timely assignment submissions, and the frequency of speaking in classroom discussions are set to 0.3, 0.3, and 0.4, respectively. In the knowledge mastery rate of the second acquisition channel, the weights of the number of times actively asking questions, the proportion of timely assignment submissions, and the frequency of speaking in classroom discussions are set to 0.2, 0.5, and 0.3, respectively.

[0097] The collection of sovereignty compliance attributes includes: retrieving the data sovereignty flag from the data metadata corresponding to the target group. This flag records the source organization, collection authorization status, and availability of the data batch, used to confirm whether the current data is permitted for intervention intensity control decisions. The remaining privacy budget is queried from the privacy budget management record, which is calculated based on the cumulative privacy budget consumed in previous measurement data queries. The access permission level for the target group's data is retrieved from the currently logged-in user's identity and permission record, obtaining the permission level. The data sovereignty flag, privacy budget status, and permission level together constitute the sovereignty compliance attribute. The original status indicators and the sovereignty compliance attribute together form the current real-time status measurement data.

[0098] The historical operational intervention sequence data includes historical intervention sequences from multiple historical control cycles and their corresponding historical state response sequences. This data is retrieved from the operational log database. The historical intervention sequence represents the actual intervention intensity values ​​output by the system over several past control cycles, automatically recorded in the operational log by the controller output module after each decision. The historical state response sequence represents the group average mastery sequence acquired after a preset response delay following each intervention execution, acquired and recorded in the operational log by the measurement and acquisition module after a fixed delay following each intervention execution.

[0099] The first intervention intensity is the intervention intensity setpoint held by the system in the current control cycle, serving as the input benchmark for this control decision. The first intervention intensity is a normalized comprehensive control quantity, defined using the same dimensions as the intervention intensity in the multi-scale intervention response calibration data. Its physical meaning is jointly determined by the configuration parameters of four intervention actions: the amount of practice pushed, the duration of explanation, the frequency of difficulty switching, and the feedback density. The system has a pre-set intervention intensity-action mapping table that maps the first intervention intensity to specific teaching action execution parameters.

[0100] In this embodiment, the intervention intensity-action mapping table is divided into ten levels at equal intervals, with each level having a step width of 0.1. The intervention action configuration parameters corresponding to each level are shown in the table below:

[0101] Intervention intensity Push practice volume Explanation duration Difficulty switching frequency Feedback density 0.0 6 dishes / day 0 minutes Do not switch actively Only provide feedback on correctness or error. 0.1 9 dishes / day 0 minutes Switch every 10 questions Only provide feedback on correctness or error. 0.2 12 dishes / day 0 minutes Switch every 8 questions Provide feedback on correct and incorrect answers and error analysis. 0.3 18 dishes / day 5 minutes The question changes every 6 questions. Provide key step tips 0.4 24 dishes / day 8 minutes Switch every 5 questions Provide key step tips 0.5 30 dishes / day 10 minutes Switch every 4 questions Provides key step hints and thought process guidance 0.6 36 dishes / day 15 minutes Switch every 3 questions Provide step-by-step prompts 0.7 42 dishes / day 20 minutes Switch every 2 questions Provide step-by-step prompts 0.8 48 dishes / day 25 minutes Switch to a different question after each question. Provide detailed step-by-step instructions 0.9 54 dishes / day 30 minutes Switch every question. Provide step-by-step prompts and variant associations 1.0 60 dishes / day 30 minutes Switch every question. Provide step-by-step prompts throughout the process.

[0102] In this embodiment, the first intervention strength is read from the output of the previous control cycle. If the controller was optimized normally in the previous cycle through model prediction, the first intervention strength is the second intervention strength output in the previous cycle. If the previous cycle failed to perform a freeze due to trusted authentication failure, the first intervention strength remains the safety action value executed in the previous cycle.

[0103] S102: Based on multi-scale intervention response calibration data, multi-scale critical analysis is performed through scaling and collapse to obtain the critical intensity range, applicable scale range, and model mismatch.

[0104] S103: Based on the applicable scale range and model mismatch, determine the scale applicability of the current real-time state measurement data to obtain scale-applicable data.

[0105] The applicable data for this scale includes original state indicators and sovereign compliance attributes.

[0106] The scale applicability determination specifically involves extracting the group size corresponding to the current real-time state measurement data and comparing this group size with the applicable scale range. If the group size is less than the lower limit or greater than the upper limit of the applicable scale range, the scale is deemed inapplicable. If the group size falls within the applicable scale range, the model mismatch corresponding to this group size is further checked to see if it is less than a preset mismatch threshold. If the model mismatch is greater than or equal to the preset mismatch threshold, the scale is deemed inapplicable. If the model mismatch is less than the preset mismatch threshold, the scale is deemed applicable, and the original state indicators and sovereign compliance attributes in the current real-time state measurement data are merged as the scale-applicable data output.

[0107] Optionally, if the determination scale is not applicable, the current real-time status measurement data will not enter the subsequent triple verification, and the system will trigger the gradual degradation process of the security degradation execution module to maintain the first intervention intensity unchanged.

[0108] In this embodiment, the preset mismatch threshold is set to 0.08. The applicable size range consists of size ranges with a mismatch degree less than the size selection threshold. The preset mismatch threshold is used to perform a secondary review of the current group size that falls within the applicable size range.

[0109] S104: Based on historical operational intervention sequence data, perform triple verification on the applicable scale data to obtain credible authentication results and item verification results.

[0110] The trusted authentication result includes authentication passed and authentication failed.

[0111] Among them, the triple verification constitutes a triple validity gate. This gate is a trusted authentication mechanism set at the controller input end, used to verify the measurement data from three dimensions: statistical validity, causal interpretability, and data compliance before the scale-appropriate data enters the control decision.

[0112] S105: If the trusted authentication result is that the authentication fails, the first intervention intensity is gradually downgraded based on the sub-item verification results to obtain the second intervention intensity.

[0113] S106: If the trusted authentication result is successful, the second intervention intensity is obtained by rolling optimization through the model prediction controller based on the current real-time state measurement data, critical intensity range, applicable scale range and first intervention intensity.

[0114] Optionally, the second intervention intensity output in the current control cycle is used as new data, and the historical intervention sequence is updated according to the rolling window rule. The average mastery level of the group collected after the intervention in the current control cycle is used as new data, and the historical state response sequence is updated according to the rolling window rule. Steps S101 to S106 are executed to obtain the second intervention intensity for the next control cycle, thus achieving closed-loop rolling operation of near-critical teaching regulation.

[0115] By adopting the above scheme, at the multi-scale critical analysis level, scaling transformation and model mismatch assessment are used to quantitatively characterize the effective boundary of the intervention strategy, ensuring that near-critical regulation always operates within the population size range suitable for the model, avoiding strategy mismatch caused by cross-scale application. At the measurement credibility assurance level, a triple validity gate consisting of indicator certification, causal support domain verification, and sovereign constraint verification is used to determine the credibility of real-time measurements from three orthogonal dimensions of statistics, causality, and compliance, preventing the controller from directly consuming failed measurements and triggering escalation of danger. At the safety control decision level, automatic triage is performed based on the credibility certification results. When the measurement is unreliable, the risk level is gradually downgraded or manual takeover is requested. When the measurement is reliable, the model predicts that the controller will continuously optimize within the critical strength and scale constraints, taking into account both the smoothness of the intervention output and resource optimization. Overall, without the need for manually pre-setting complex anomaly rules, a near-critical intelligent teaching regulation closed loop is achieved, which features interpretable boundaries, reliable measurements, fallback control, and smooth output, meeting the engineering application requirements of large-scale online teaching systems for security and generalization.

[0116] Optionally, the multi-scale intervention response calibration data includes datasets of intervention intensity response curves at multiple population sizes. In this embodiment, step S102: Based on the multi-scale intervention response calibration data, multi-scale critical analysis is performed through scaling and collapse to obtain the critical intensity range, applicable scale range, and model mismatch, including the following sub-steps S201~S205, please refer to the relevant documentation. Figure 2 :

[0117] Among them, multi-scale critical analysis is a process of extracting critical features of the intervention model in the group size dimension based on the intervention intensity response curve dataset under multiple group sizes, through scaling law fitting, scaling transformation and critical transition point identification, and determining the effective boundary of the intervention model accordingly.

[0118] S201: Based on the intervention intensity response curve dataset, the response curve is scaled by scaling and collapse to obtain the collapsed response data.

[0119] Among them, scaling collapse is based on the finite scale theory, which maps the intervention intensity response curves under different group sizes to the same universal function that is independent of the group size through scaling transformation, so as to eliminate the dispersion of response curves caused by size differences.

[0120] The specific implementation of step S201 is as follows: Response curves of different group sizes are extracted from the response curve dataset to obtain the mastery and intervention intensity response curves corresponding to each group size. Based on the mastery and intervention intensity response curves corresponding to each group size, parameters are estimated through scaling law fitting to obtain the local critical intensity, response scaling index, and correlation scaling index. Based on the local critical intensity, response scaling index, and correlation scaling index, scaling transformation is performed on the mastery and intervention intensity response curves to obtain the transformed coordinate point set corresponding to each group size. Based on the transformed coordinate point set, the local critical intensity, response scaling index, and correlation scaling index are iteratively adjusted until data points of different group sizes fall into the same universal function, resulting in collapsed response data.

[0121] The scaling law fitting is specifically expressed by the following formula:

[0122]

[0123] in, In order to control the degree, For the intensity of intervention, For group size, For local critical strength, In response to the scaling index, For correlation scaling index, It is a universal function that is independent of the group size.

[0124] Among them, the universal function It is a function with adjustable parameters.

[0125] The scaling transformation specifically involves horizontally scaling the intervention intensity and vertically normalizing the mastery level to obtain the transformed set of coordinate points corresponding to each group size.

[0126] The horizontal scaling is specifically calculated using the following formula:

[0127]

[0128] in, The coordinates are used to scale the intervention intensity.

[0129] Vertical normalization is specifically expressed by the following formula:

[0130]

[0131] in, To scalarize and control the degree coordinates.

[0132] Based on the transformed set of coordinate points, the local critical strength, response scaling index, and correlation scaling index are iteratively adjusted until data points of different population sizes fall into the same universal function, resulting in collapsed response data. Specifically, during iterative adjustment, the convergence criterion is whether data points of different population sizes fall into the same distribution in the transformed coordinate system. If the transformed coordinate points of each size do not coincide on the same curve, the local critical strength, response scaling index, and correlation scaling index are corrected, and the scaling transformation is re-executed until data points of different population sizes fall into the same universal function, resulting in collapsed response data. The collapsed response data includes the scaled set of coordinate points for each population size after scaling transformation, and the universal function curve formed by the overlap of data points from each size. This universal function is a common response skeleton independent of population size, determined by the common distribution formed by the overlap of data points from each size during the iteration process.

[0133] In this embodiment, the universal function adopts a family of saturated S-curve functions, specifically:

[0134]

[0135] in, For saturation amplitude parameters, The slope parameter of the curve. This is the center offset parameter.

[0136] In this embodiment, the iteratively adjusted saturation amplitude parameter is set to 1.2, the curve slope parameter is set to 1.8, and the center offset parameter is set to 0.1. The local critical intensity, response scaling exponent, correlation scaling exponent, and universal function family parameters are automatically iterated using a nonlinear least squares algorithm (Levenberg-Marquardt, LM). The optimization objective is to minimize the sum of squared residuals from the coordinate points after all population scale transformations to the universal function curve. The above parameters are solved simultaneously until the sum of squared residuals converges or the parameter change is less than a preset tolerance. The preset tolerance is set to... .

[0137] S202: Evaluate the response data after collapse on a level-by-level basis to obtain the model mismatch degree corresponding to each group size.

[0138] Specifically, the evaluation is performed sequentially for each group size: the set of data points for that size in the collapsed coordinate system is extracted, the residuals from each data point to the universal function curve are calculated, and the residuals are statistically aggregated to obtain the model mismatch for that size. After the evaluation of all size groups is completed, the model mismatch for each size is obtained.

[0139] In this embodiment, the model mismatch is taken as the root mean square error of the residuals from each data point to the universal function curve.

[0140] S203: Identify the critical transition point of the response data after collapse to obtain the critical intensity corresponding to each population size.

[0141] Specifically, the critical transition point identification includes: analyzing the trend of scaled mastery with scaling intervention intensity for the post-collapse response data corresponding to each population size. The point where the second derivative of the scaled mastery curve reaches its maximum value or the inflection point of the curve is used as the critical transition point. The original intervention intensity coordinates corresponding to this point are extracted and restored to the local critical intensity for each population size through inverse scaling transformation. This identification process is performed sequentially for each size to obtain the critical intensity corresponding to each population size.

[0142] The horizontal scaling is specifically calculated using the following formula:

[0143]

[0144] in, The coordinates of the original intervention intensity after restoration represent the local critical intensity corresponding to this population size range.

[0145] S204: Based on the model mismatch, the applicability of the population size is screened to obtain the applicable size range.

[0146] Specifically, the model mismatch degree corresponding to each group size category is extracted. Size categories with a model mismatch degree greater than or equal to the category selection threshold are removed, while size categories with a model mismatch degree less than the category selection threshold are retained. The minimum group size among the retained size categories is used as the lower limit of the applicable size range, and the maximum group size is used as the upper limit of the applicable size range. The applicable size range is determined by the combination of the lower limit and the upper limit.

[0147] The applicable scale range is updated periodically with the calibration database, and the updated range results are read directly during the operation phase.

[0148] In this embodiment, the gear selection threshold is set to 0.10.

[0149] S205: Determine the critical intensity range based on the critical intensity corresponding to the size of each population.

[0150] Specifically, the critical intensity corresponding to each group size within the applicable scale range is extracted, and the minimum value among them is taken as the lower limit of the critical intensity range, and the maximum value among them is taken as the upper limit of the critical intensity range, thus obtaining the critical intensity range.

[0151] By combining the above methods with scaling transformation, step-by-step evaluation and critical transition point identification, the critical characteristics and applicable boundaries of the intervention model under different population sizes can be quantitatively extracted, avoiding mismatched application across scales and improving the generalization and interpretability of regulation.

[0152] Optionally, the scale-applicable data includes original state indicators and sovereign compliance attributes. In this embodiment, step S104: Based on historical operational intervention sequence data, perform triple verification on the scale-applicable data to obtain trusted authentication results and itemized verification results, including the following sub-steps S401~S405, please refer to the relevant documentation. Figure 3 :

[0153] S401: Based on historical operational intervention sequence data, perform indicator verification on the original state indicators to obtain indicator verification results.

[0154] The specific implementation of step S401 is as follows: A statistical significance test is performed on the original state indicators to obtain a significance determination result. Based on historical operational intervention sequence data, the signal-to-noise ratio (SNR) is calculated using sliding window variance decomposition to obtain the SNR. A threshold determination is performed on the SNR to obtain the SNR determination result. Based on the original state indicators, a consistency determination is performed through correlation comparison to obtain the consistency determination result. The significance determination result, the SNR determination result, and the consistency determination result are logically merged to obtain the indicator certification result.

[0155] The original state indicators are subjected to statistical significance tests to obtain significance determination results. Specifically, the single-sample mean difference significance test is used to conduct a statistical significance test on the knowledge mastery level among the original state indicators, examining whether there is a significant difference between the average knowledge mastery level of the group during this period and the null hypothesis baseline value. The test statistic and its corresponding significance probability value are calculated. If the probability value is less than the preset significance level, it is considered passed; otherwise, it is considered failed.

[0156] Based on historical intervention sequence data, the signal-to-noise ratio (SNR) is calculated using sliding window variance decomposition. Specifically, the population average mastery observations for the most recent control cycles are extracted from the historical state response sequence to construct a time series. A sliding window width is set, and the window slides along the time series with a fixed step size. The sample variance of the data within each window is calculated as a local signal variance estimate, while the sample variance of the remaining data outside the window is calculated as a background noise variance estimate. The ratio of the local signal variance to the background noise variance is converted to decibels (dB) to obtain the SNR at each window position. The arithmetic mean of the SNRs at all window positions is taken as the final SNR.

[0157] The signal-to-noise ratio (SNR) in decibels is obtained using the following calculation method:

[0158]

[0159] in, For local signal variance, For the background noise variance, This represents the signal-to-noise ratio in decibels.

[0160] Based on the original state indicators, consistency is determined through correlation comparison to obtain the consistency judgment result. Specifically, the original state indicators include the knowledge mastery collected by the first acquisition channel and the knowledge mastery calculated by the second acquisition channel. The historical acquisition values ​​of knowledge mastery from the first and second acquisition channels over the most recent control cycles are constructed into two time series, and the Pearson correlation coefficient between the two time series is calculated. If the absolute value of the correlation coefficient is greater than a preset consistency threshold, the consistency judgment result is passed; otherwise, it is failed.

[0161] The Pearson correlation coefficient is obtained as follows:

[0162]

[0163] in, The Pearson correlation coefficient is used. For the first acquisition channel Historical data collected over a control cycle For the second acquisition channel Historical data collected over a control cycle and These are the arithmetic mean of the two sequences (the first acquisition channel sequence and the second acquisition channel sequence), respectively. The sequence length is given.

[0164] The significance, signal-to-noise ratio, and consistency results are logically combined to obtain the indicator certification result. Specifically, a logical AND operation is used for merging: the indicator certification result is passed only if all three results are passed; otherwise, the indicator certification result is failed.

[0165] In this embodiment, the preset significance level is 0.05, the preset consistency threshold is 0.85, and the preset signal-to-noise ratio threshold is set to 3.0 dB. The time series data is constructed by extracting historical observations from the most recent twenty control periods, with a sliding window width of five control periods and a sliding step size of one control period.

[0166] S402: Based on historical operational intervention sequence data and original state indicators, causal support domain verification is performed through causal effect estimation to obtain causal verification results.

[0167] Step S402 is implemented as follows: Based on historical intervention sequence data, causal effect estimation is performed using the difference-in-differences method to obtain the average causal effect and confidence interval. Based on the original state indicators and the first intervention intensity, the direction and magnitude of the intervention response are determined. Based on the average causal effect, the direction of the intervention response is checked for consistency, and the direction check result is obtained. Based on the confidence interval, the magnitude of the intervention response is checked, and the magnitude check result is obtained. The direction check result and the magnitude check result are logically merged to obtain the causal check result.

[0168] Based on historical intervention sequence data, causal effect estimation was performed using the difference-in-differences method to obtain the average causal effect and confidence interval. Specifically, the average group mastery after intervention and the average group mastery before intervention were calculated for the treatment group, yielding the change in the treatment group. The average group mastery after intervention and the average group mastery before intervention were calculated for the control group at the corresponding time periods, yielding the change in the control group. The difference between the changes in the treatment group and the control group was taken as the average causal effect. Confidence interval estimation of the average causal effect was performed using a bootstrap resampling method: the original sample was resampled with replacement, and the resampling operation was repeated a preset number of times. After each resampling, the average causal effect was recalculated, resulting in a distribution composed of multiple resampled average causal effects. The percentile interval corresponding to the preset confidence level in this distribution was taken as the confidence interval of the average causal effect.

[0169] In this embodiment, the preset number of resampling times is set to 1,000, and the preset confidence level is set to 95%.

[0170] Based on the original state indicators and the initial intervention intensity, the direction and magnitude of the intervention response are determined. Specifically, the knowledge mastery level in the current control period is differentially calculated with that in the previous control period to obtain the change in mastery. The initial intervention intensity in the current control period is compared with that in the previous control period. If the initial intervention intensity is greater than that in the previous period, the expected intervention direction is strengthening. If the initial intervention intensity is less than that in the previous period, the expected intervention direction is weakening. If the change in mastery is in the same direction as the expected intervention direction (strengthening intervention corresponds to an increase in mastery, weakening intervention corresponds to a decrease in mastery), the intervention response direction is positive. If they are opposite, the intervention response direction is negative. The absolute value of the change in mastery is taken as the intervention response magnitude.

[0171] Based on the average causal effect, a direction consistency check is performed on the intervention response direction to obtain the direction check result. Specifically, the sign direction of the intervention response direction is compared with that of the average causal effect. If the intervention response direction is positive and the average causal effect is greater than zero, or if the intervention response direction is negative and the average causal effect is less than zero, the direction check result is passed. If the sign directions are inconsistent, the direction check result is failed.

[0172] Based on the confidence interval, an amplitude verification is performed on the intervention response amplitude to obtain the amplitude verification result. Specifically, it is determined whether the confidence interval of the average causal effect covers the intervention response amplitude. If the intervention response amplitude falls within the confidence interval, the amplitude verification result is passed. If the intervention response amplitude exceeds the confidence interval, the amplitude verification result is failed.

[0173] The direction and amplitude verification results are logically combined to obtain the causality verification result. Specifically, a logical AND operation is used for merging: the causality verification result is passed only if both the direction and amplitude verification results are passed. If either result fails, the causality verification result is failed.

[0174] S403: Perform sovereignty constraint verification on sovereignty compliance attributes to obtain sovereignty verification results.

[0175] Among these, sovereign compliance attributes include data sovereignty markers, privacy budget status, and permission levels.

[0176] Step S403 is implemented as follows: A compliance determination is made on the data sovereignty marker to obtain a sovereignty compliance determination result. Based on the privacy budget status, a balance verification is performed using a differential privacy budget accounting method to obtain a privacy budget verification result. Permission levels are compared to obtain permission verification results. The sovereignty compliance determination result, privacy budget verification result, and permission verification result are logically merged to obtain the sovereignty verification result.

[0177] The data sovereignty marker is assessed for compliance, resulting in a sovereignty compliance determination. Specifically, the data sovereignty marker carried by the current real-time status measurement data is extracted and compared with the system's pre-set sovereignty compliance policy library. If the current data sovereignty marker exists in the valid list, the sovereignty compliance determination result is passed; otherwise, it is failed.

[0178] The sovereign compliance policy library is pre-configured by the system administrator in accordance with the requirements of laws and regulations such as the Data Security Law and the Personal Information Protection Law, and contains a list of legal data sovereignty symbols that are allowed to be accessed.

[0179] In this embodiment of the application, the sovereign compliance policy library is set as follows: the data sovereignty flags that are allowed to be accessed include local authorization within China (CN_LOCAL_AUTH) and cross-border compliance authorization within China (CN_CROSS_AUTH), and the data sovereignty flags that are prohibited from being accessed include foreign data of unknown origin (FOREIGN_UNKNOWN) and unauthorized foreign data (FOREIGN_UNAUTH).

[0180] Based on the privacy budget status, a differential privacy budget accounting method is used to verify the balance and obtain the privacy budget verification result. Specifically, a differential privacy mechanism is used to protect the target group data. Each time a batch of data is queried or used, random noise is added to the data, a process that consumes a certain amount of privacy budget. The privacy budget status records the remaining available budget amount for the current batch of data. During balance verification, the remaining privacy budget balance of the batch of data is read, and the privacy budget consumption required for this teaching adjustment calculation is estimated. The remaining balance is compared with the required consumption. If the remaining balance is sufficient to cover the consumption, the privacy budget verification result is passed. If the remaining balance is insufficient, the privacy budget verification result is failed.

[0181] In this embodiment, the initial total privacy budget is set to 100.0. Each time target group data is queried, a privacy budget ranging from 0.1 to 5.0 is consumed, depending on the amount of data queried and the intensity of noise injection. The remaining budget ledger is maintained in real time, and historical cumulative consumption is automatically deducted before each verification. The minimum budget threshold is set to 1.0.

[0182] The logical merge performs a logical AND operation on the sovereignty compliance determination result, privacy budget verification result, and permission verification result. Specifically, if all three verification results pass, the sovereignty verification result is passed. If any one of the three verification results fails, the sovereignty verification result is failed.

[0183] S404: Logically merge the indicator authentication results, causality verification results, and sovereignty verification results to obtain a trusted authentication result.

[0184] The trusted authentication result includes authentication passed and authentication failed.

[0185] Specifically, a logical AND operation is used for merging: the trusted authentication result is passed only when the indicator authentication result, causality verification result, and sovereignty verification result are all passed; otherwise, the trusted authentication result is failed.

[0186] S405: The results of indicator certification, causality verification, and sovereignty verification are aggregated separately to obtain the sub-item verification results.

[0187] The individual verification results are structured data records containing eight independent status fields and one summary status field. The eight independent status fields are: statistical significance determination result, signal-to-noise ratio determination result, consistency determination result, direction verification result, amplitude verification result, sovereignty compliance determination result, privacy budget verification result, and permission verification result. The summary status field is the trusted authentication result, obtained by performing a logical AND operation on the eight independent status fields.

[0188] Specifically, the statistical significance, signal-to-noise ratio, and consistency results in the indicator certification results, the direction and magnitude results in the causality verification results, and the sovereignty compliance, privacy budget, and permission verification results in the sovereignty verification results are summarized and merged to obtain the sub-item verification results.

[0189] By combining the above methods with sliding window variance decomposition, difference-in-differences estimation and differential privacy budget accounting, cross-credibility verification of scale-applicable data is performed from three orthogonal dimensions: statistical significance, causal direction and magnitude, and sovereign compliance. This avoids measurement data that is statistically invalid, causally unexplainable, or compliance-controversial for controller consumption, thereby improving the security and credibility of regulatory decisions.

[0190] Optionally, step S105: If the trusted authentication result is authentication failure, based on the sub-item verification results, the first intervention intensity is gradually downgraded to obtain the second intervention intensity, including sub-steps S501~S504, please refer to the relevant documentation. Figure 4 .

[0191] S501: Based on the results of the itemized verification, risk levels are classified to obtain the risk level determination results.

[0192] The risk level assessment results include the first risk level, the second risk level, and the third risk level.

[0193] Specifically, the process iterates through the eight independent status fields in the itemized verification results, identifies fields with a "failed" status, and obtains a set of failed items. This set of failed items is then categorized according to their respective verification categories, resulting in a set of failure categories. These categories include sovereignty verification, causality verification, and indicator authentication, and the number of failed items is counted. Based on the set of failure categories and the number of failed items, a risk level determination is performed using pre-defined classification rules, yielding the risk level assessment result.

[0194] In this embodiment, the preset classification rule is as follows: If the failure category set includes a sovereignty verification category, then regardless of the number of failures, the risk level determination result is the first risk level. If the failure category set does not include a sovereignty verification category but includes a causal verification category, then the risk level determination result is the second risk level. If the failure category set only includes an indicator authentication category, then the risk level determination result is the third risk level. If the number of failures is greater than or equal to three, then regardless of the category, the risk level determination result is directly the first risk level.

[0195] S502: If the risk level is determined to be the first risk level, the first intervention intensity shall be used as the second intervention intensity.

[0196] In this embodiment, the first risk level represents the highest risk scenario. At this point, any increase in intervention intensity is prohibited; the current intervention intensity is frozen, and the original value of the first intervention intensity is output as the second intervention intensity to maintain the existing safety intervention level unchanged.

[0197] S503: If the risk level assessment result is the second risk level, the first intervention intensity is adjusted to obtain the second intervention intensity.

[0198] Specifically, the restricted adjustment rules are as follows: Based on the first intervention intensity, a candidate intervention intensity is obtained by scaling it according to a preset degradation coefficient. The candidate intervention intensity must not be lower than the preset safe intervention intensity lower limit. If the candidate intervention intensity is lower than the preset safe intervention intensity lower limit, the preset safe intervention intensity lower limit is taken as the second intervention intensity. If the candidate intervention intensity is not lower than the preset safe intervention intensity lower limit, the candidate intervention intensity is taken as the second intervention intensity. During the restricted adjustment process, the second intervention intensity does not exceed the first intervention intensity and does not exceed the preset safe intervention intensity lower limit, ensuring that the degradation range is controlled and the intervention is not interrupted.

[0199] In this embodiment, the preset degradation coefficient is 0.8, and the preset lower limit of security intervention intensity is 0.10.

[0200] S504: If the risk level assessment result is the third risk level, a manual takeover request is made to obtain the second intervention intensity.

[0201] Specifically, the system pushes manual takeover requests and failed indicator certification sub-items from the sub-item verification results to the control personnel's review end in batches. After logging into the review end, the control personnel check the name, judgment threshold, actual calculated value, and corresponding original status indicator source of each failed sub-item. After confirming whether there is statistical distortion or cross-source inconsistency in the current measurement data, they perform a takeover confirmation operation or a rejection operation on the review end. After receiving the takeover confirmation instruction, the system reads the takeover intervention intensity entered by the control personnel on the review end and performs a safety range verification on the input value: the input value must not be lower than the preset safety intervention intensity lower limit and not higher than the preset maximum intervention intensity upper limit. If the verification is successful, the takeover intervention intensity entered by the control personnel is used as the second intervention intensity, and a manual takeover log is generated. The log record includes the takeover personnel's identifier, takeover timestamp, and takeover intervention intensity value. If the verification fails, the control personnel do not perform a confirmation operation within the preset response time, or the control personnel reject the takeover, the system continues to maintain the first intervention intensity as the second intervention intensity.

[0202] In this embodiment, the preset lower limit of safety intervention intensity is 0.10, the preset upper limit of maximum intervention intensity is 1.00, and the preset response time is 60 minutes.

[0203] By combining the above methods with risk level classification, restricted downgrade and manual takeover requests, the system implements graded handling according to the verification category to which the failed item belongs. This avoids measurement data quality defects directly triggering an increase or erroneous adjustment of the intervention intensity, balances security and response efficiency, and improves the rollback and explainability of the control system in the event of certification failure.

[0204] Optionally, step S106: If the trusted authentication result is successful, based on the current real-time state measurement data, critical intensity range, applicable scale range, and first intervention intensity, the model prediction controller performs rolling optimization to obtain the second intervention intensity, including sub-steps S601~S603, please refer to the relevant documentation. Figure 5 .

[0205] S601: Based on the current real-time state measurement data and the first intervention intensity, multi-step state prediction is performed through the state space model to obtain the predicted state trajectory.

[0206] The state-space model takes the form of:

[0207]

[0208]

[0209] in, For the first The state vector of each control cycle For the first Intervention intensity per control cycle, For the first Output of each control cycle Here is the state transition matrix. For the input matrix, This is the output matrix. , , The parameters are obtained by offline system identification of historical operational intervention sequence data.

[0210] The specific method for multi-step state prediction is as follows: using the original state indicators in the current real-time state measurement data as the observed values ​​of the current state vector, and using the first intervention intensity as the input quantity of the current control cycle, the state vectors for several future control cycles are recursively calculated according to the state-space model. During prediction, the intervention intensity of each future control cycle is first used as the baseline input with the first intervention intensity remaining unchanged. The state transition matrix and the input matrix are then applied sequentially to the current state vector and the input quantity, and this process is repeated cycle by cycle to obtain the predicted state trajectory composed of the state vectors of each future control cycle.

[0211] In this embodiment, the state-space model adopts a linear time-invariant discrete state-space model (LTI). It is understood that in other embodiments, the state-space model may also adopt a time-varying state-space model or a nonlinear state-space model, with matrices... , , It can also be estimated from historical operating data using methods such as Kalman filtering and subspace identification.

[0212] In this embodiment, the state transition matrix is ​​specifically as follows:

[0213]

[0214] The input matrix is ​​specifically as follows The output matrix is ​​specifically as follows .

[0215] S602: Based on the predicted state trajectory, critical intensity range, and applicable scale range, the intervention intensity sequence with boundary constraints is optimized through the model predictive controller to obtain the optimal intervention intensity sequence.

[0216] In this embodiment, the model predictive controller employs Quadratic Programming-based Model Predictive Control (QP-MPC), using a state-space model as the internal predictive model, a critical intensity range as the intervention intensity constraint boundary, and an applicable scale range as a prerequisite for controller operation. The optimal intervention intensity sequence is solved by minimizing a quadratic cost function. It is understood that in other embodiments, Nonlinear Model Predictive Control (NMPC) or Explicit Model Predictive Control (EMPC) may also be used.

[0217] Specifically, the cost function for optimizing the intervention intensity sequence is:

[0218]

[0219] in, To predict the length of the time domain, In the first The first control cycle prediction Output of each control cycle To achieve the desired level of knowledge mastery, The first one to be solved Intervention intensity per control cycle, To track error weighting coefficients, To control the incremental weighting coefficients, the first term measures the tracking deviation between the predicted output and the expected knowledge mastery, while the second term suppresses abrupt changes in the intensity of intervention between adjacent control periods.

[0220] The constraints include intervention intensity boundary constraints and intervention intensity change rate constraints. The intervention intensity boundary constraints are as follows: ,in This represents the lower limit of the critical intensity range. This represents the upper limit of the critical intensity range. The constraint on the rate of change of intervention intensity is: ,in This represents the maximum permissible change in intervention intensity between adjacent control cycles.

[0221] In this embodiment, the predicted time domain length is... Set to 5, consistent with the number of steps in the predicted state trajectory. Tracking error weighting coefficient. Set to 1.0 to control the incremental weighting coefficient. Set to 0.5. Expected knowledge mastery level. The value is set at 0.80 according to the pre-set teaching plan. Within the constraint of the rate of change of intervention intensity, Set it to 0.10.

[0222] The aforementioned cost function and constraints are transformed into a standard quadratic programming problem, which is then solved using a quadratic programming solver. Specifically, the intervention intensity sequence to be solved is used as the optimization variable. The cost function is rearranged into a quadratic form with respect to the optimization variable. The boundary constraints and rate of change constraints of the intervention intensity are transformed into linear inequality constraints with respect to the optimization variable. The quadratic programming solver then searches for the intervention intensity sequence that minimizes the cost function within the feasible region; this sequence is the optimal intervention intensity sequence. During the solution process, the predicted state trajectory is obtained periodically from the aforementioned state-space model and substituted into the cost function to calculate the tracking error term.

[0223] In this embodiment, the quadratic programming solver employs the Interior Point Method (IPM). It is understood that in other embodiments, the quadratic programming solver may also be implemented using methods such as the Active-Set Method or the Alternating Direction Method of Multipliers (ADMM).

[0224] S603: Perform the first step extraction on the optimal intervention intensity sequence to obtain the second intervention intensity.

[0225] Specifically, the intervention intensity value corresponding to the first control period is extracted from the optimal intervention intensity sequence and used as the second intervention intensity for the current control period.

[0226] By combining state-space prediction, quadratic programming optimization, and initial extraction, the intervention intensity sequence is continuously optimized within the critical intensity interval boundary. This approach balances the accuracy of knowledge mastery tracking with the smoothness of intervention intensity changes, avoiding short-sighted single-step decision-making and regulatory lag caused by sequence solidification, thereby improving the stability and adaptability of intervention output.

[0227] Combination Figure 1 The near-critical teaching control system with validity gate constraints provided in this application operates as follows when executing the near-critical teaching control method with validity gate constraints:

[0228] Acquire multi-scale intervention response calibration data D_calib, current real-time status measurement data M_curr, historical operational intervention sequence data H_hist, and the first intervention intensity u_first. The current real-time status measurement data M_curr includes the raw status indicator X_raw and the sovereign compliance attribute A_sov. The historical operational intervention sequence data H_hist includes the historical intervention sequence U_hist and the corresponding historical status response sequence Y_hist. The first intervention intensity u_first is the intervention intensity setpoint for the current control cycle.

[0229] The multi-scale intervention response calibration data D_calib performs multi-scale criticality analysis through scaling and collapse, outputting the critical intensity interval I_crit, the applicable scale interval I_scale, and the model mismatch E_mis. Specifically, the critical intensity interval I_crit represents the range of intervention intensity at which a significant change in the intervention response occurs; the applicable scale interval I_scale is the range covered by population size groups where the model mismatch is less than a preset threshold; and the model mismatch E_mis represents the degree of deviation of the data points from the universal function curve after collapse for each size group.

[0230] The current real-time state measurement data M_curr is used to determine its scale suitability based on the applicable scale range I_scale and the model mismatch degree E_mis. The current population size N_curr is compared with the applicable scale range I_scale. If N_curr falls within the applicable scale range, it is further checked whether the model mismatch degree corresponding to the population size is less than a preset mismatch degree threshold. If both conditions are met, the original state indicator X_raw and the sovereign compliance attribute A_sov are merged into the scale suitability data D_suit.

[0231] The scale-applicable data D_suit enters the triple validity gate. Indicator authentication, based on the historical state response sequence Y_hist, sequentially performs significance testing, signal-to-noise ratio calculation, and cross-source consistency judgment on the original state indicator X_raw, yielding the indicator authentication result R_ind. Causality verification, based on the historical intervention sequence U_hist and the historical state response sequence Y_hist, estimates the average causal effect ACE and confidence interval through double difference estimation, and compares it with the current intervention response direction and magnitude, yielding the causality verification result R_cau. Sovereignty verification verifies the data sovereignty flag, privacy budget status, and permission level in the sovereignty compliance attribute A_sov, yielding the sovereignty verification result R_sov. The three results are merged into the trust authentication result R_trust, and the results of each sub-item are aggregated into the sub-item verification result R_item.

[0232] When trusted authentication fails, risk levels are determined based on the itemized verification results R_item. For the first risk level, the first intervention strength u_first is frozen and used as the second intervention strength u_second. For the second risk level, the first intervention strength u_first is scaled using a degradation factor; if the scaling result is lower than the lower limit of the safe intervention strength, the lower limit is used as the second intervention strength u_second. For the third risk level, a manual takeover request is triggered, and the second intervention strength u_second is obtained after verifying the safety range of the manually input takeover intervention strength.

[0233] Upon successful authentication, the original state index X_raw is used as the initial value of the state vector. Multi-step prediction based on the state-space model is performed to obtain the predicted state trajectory. Then, using the critical intensity interval I_crit as boundary constraints and the applicable scale interval I_scale as prerequisites, the optimal intervention intensity sequence U_opt is solved by minimizing the cost function through quadratic programming. The first step is extracted as the second intervention intensity u_second. After the current cycle ends, the second intervention intensity u_second and the average group mastery level collected after the intervention are used to update the historical intervention sequence and historical state response sequence, respectively, before entering the closed-loop rolling operation of the next control cycle.

[0234] Based on the above-described near-critical teaching control method using validity gate constraints, this invention provides a near-critical teaching control system using validity gate constraints to execute the above method. Specifically, the system includes:

[0235] The data acquisition module is used to acquire multi-scale intervention response calibration data, current real-time status measurement data, historical operational intervention sequence data, and the first intervention intensity.

[0236] The multi-scale critical analysis module is used to perform multi-scale critical analysis based on multi-scale intervention response calibration data through scaling and collapse, so as to obtain the critical intensity range, applicable scale range and model mismatch degree.

[0237] The model suitability determination module is used to determine the scale suitability of the current real-time state measurement data based on the applicable scale range and model mismatch, and obtain the scale-suitable data.

[0238] The trusted authentication module is used to perform triple verification on applicable data based on historical operational intervention sequence data, and obtain trusted authentication results and sub-item verification results.

[0239] The security downgrade execution module is used to gradually downgrade the first intervention intensity to obtain the second intervention intensity based on the sub-item verification results if the trusted authentication result is that the authentication failed.

[0240] The model prediction control module is used to obtain the second intervention intensity by rolling optimization based on the current real-time state measurement data, critical intensity range, applicable scale range and first intervention intensity if the credible authentication result is successful.

[0241] In this application, the specific implementation details of the modules in the above-mentioned near-critical teaching control system with validity gate constraints are as described in the steps of the above-mentioned near-critical teaching control method with validity gate constraints. For details, please refer to the detailed steps of the above-mentioned near-critical teaching control method with validity gate constraints, which will not be repeated here.

[0242] By adopting the above scheme, based on multi-scale critical analysis and a triple effectiveness gate, combined with risk grading and degradation and model prediction rolling optimization, safe, reliable, and smooth near-critical teaching regulation was achieved. Its specific beneficial effects are as follows:

[0243] High safety and controllability: Through the synergy of triple effectiveness gates, risk classification and disposal and model prediction control boundary constraints, the intervention intensity is always constrained within the range of credible data and critical intensity from input, decision-making to output, blocking the abnormal adjustment of intervention caused by failure measurement from the source.

[0244] Sufficient trust assurance: Indicator authentication, causal support domain verification, and sovereignty constraint verification cross-certify measurement data from three orthogonal dimensions. The controller only consumes verified measurement data, and control decisions are based on trusted inputs.

[0245] Good generalization of regulation: By scaling and collapse quantization, the critical intensity range and applicable scale range of the intervention model under different group sizes are characterized. The regulation strategy always operates within the effective boundary of the model, avoiding strategy mismatch caused by cross-scale application.

[0246] High intervention stability: The model predicts that the controller is continuously optimized within the critical intensity range. The cost function balances the accuracy of knowledge mastery tracking with the suppression of changes in intervention intensity, thus avoiding sudden changes in intervention intensity due to measurement fluctuations.

[0247] Strong fault tolerance and rollback capability: Through risk level classification and graded handling, it can achieve three levels of safe rollback: freeze and maintain, restricted downgrade, and manual takeover. The adjustment range of intervention intensity is controlled. The system can safely roll back when measurement is abnormal, avoiding the impact of erroneous intervention.

[0248] Regarding the systems and apparatus in the above embodiments, the specific methods by which each module performs its operations have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0249] This invention also provides an electronic device, such as... Figure 6As shown, it includes a memory 704, a processor 702, and a computer program stored in the memory 704 and executable on the processor 702. When the processor 702 executes the program, it implements the steps of the near-critical teaching control method for effectiveness gate constraints described above.

[0250] Among them, Figure 6 In this document, a bus architecture (represented by bus 700) is used. Bus 700 may include any number of interconnected buses and bridges, linking various circuits including one or more processors represented by processor 702 and memory represented by memory 704. Bus 700 may also link various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and therefore will not be described further herein. Bus interface 705 provides an interface between bus 700 and receiver 701 and transmitter 703. Receiver 701 and transmitter 703 may be the same element, i.e., a transceiver, providing a unit for communicating with various other devices over a transmission medium. Processor 702 is responsible for managing bus 700 and general processing, while memory 704 can be used to store data used by processor 702 during operation.

[0251] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the near-critical teaching control method for effectiveness gate constraints described above.

[0252] This invention also provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps of the near-critical teaching control method for effectiveness gate constraints described above.

[0253] The algorithms and displays provided herein are not inherently related to any particular computer, virtual system, or other device. Various general-purpose systems can also be used in conjunction with the teachings herein. The required structure for constructing such systems is apparent from the above description. Furthermore, this invention is not directed to any particular programming language. It should be understood that the contents of the invention described herein can be implemented using various programming languages, and the above description of specific languages ​​is for the purpose of disclosing the best mode of implementation of the invention.

[0254] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0255] The various component embodiments of the present invention can be implemented in hardware, or as software modules running on one or more processors, or a combination thereof. Those skilled in the art will understand that microprocessors or digital signal processors (DSPs) can be used in practice to implement some or all of the functions of some or all of the components in the apparatus according to embodiments of the present invention. The present invention can also be implemented as a device or apparatus program (e.g., a computer program and computer program product) for performing part or all of the methods described herein. Such programs implementing the present invention can be stored on a computer-readable medium or can be in the form of one or more signals. Such signals can be downloaded from an Internet website, provided on a carrier signal, or provided in any other form.

Claims

1. A near-critical teaching control method with effectiveness gate constraints, characterized in that, include: S1: Acquire multi-scale intervention response calibration data, current real-time status measurement data, historical operational intervention sequence data, and the first intervention intensity; The first intervention intensity is the intervention intensity of the current control cycle; S2: Based on the multi-scale intervention response calibration data, multi-scale critical analysis is performed through scaling and collapse to obtain the critical intensity range, applicable scale range and model mismatch. S3: Based on the applicable scale range and the model mismatch, determine the scale applicability of the current real-time state measurement data to obtain scale-applicable data; S4: Based on the historical operation intervention sequence data, perform triple verification on the scale-applicable data to obtain the trusted authentication result and the item verification result; The trusted authentication result includes authentication passed and authentication failed; S5: If the trusted authentication result is authentication failure, based on the sub-item verification results, the first intervention intensity is gradually downgraded to obtain the second intervention intensity; S6: If the trusted authentication result is successful, based on the current real-time state measurement data, the critical intensity range, the applicable scale range, and the first intervention intensity, the second intervention intensity is obtained by rolling optimization through the model prediction controller.

2. The near-critical teaching control method with effectiveness gate constraints according to claim 1, characterized in that, The multi-scale intervention response calibration data includes datasets of intervention intensity response curves for multiple population sizes; Based on the multi-scale intervention response calibration data, multi-scale critical analysis is performed through scaling and collapse to obtain the critical intensity range, applicable scale range, and model mismatch, including: Based on the intervention intensity response curve dataset, the response curves are scaled by scaling and collapse to obtain the collapsed response data. The collapsed response data is evaluated level by level to obtain the model mismatch degree corresponding to each group size; The critical transition point is identified from the collapsed response data to obtain the critical intensity corresponding to each population size. Based on the model mismatch, the applicability of the population size is screened to obtain the applicable size range; The critical intensity range is determined based on the critical intensity corresponding to the size of each group.

3. The near-critical teaching control method with effectiveness gate constraints according to claim 2, characterized in that, Based on the aforementioned response curve dataset, a scaling transformation of the response curves is performed through scaling and collapse to obtain the collapsed response data, including: The response curve dataset is used to extract response curves based on group size to obtain the mastery and intervention intensity response curves corresponding to each group size. Based on the mastery level corresponding to each group size and the response curve of the intervention intensity, parameter estimation is performed through scaling law fitting to obtain the local critical intensity, response scaling index and correlation scaling index; The scaling law fitting is specifically defined by the following formula: in, In order to control the degree, For the intensity of intervention, For group size, For local critical strength, In response to the scaling index, For correlation scaling index, It is a universal function independent of the group size; Based on the local critical intensity, the response scaling index, and the correlation scaling index, the mastery and intervention intensity response curves are scaled to obtain the set of transformed coordinate points corresponding to each group size; Based on the transformed set of coordinate points, the local critical intensity, the response scaling index, and the correlation scaling index are iteratively adjusted until data points of different population sizes fall into the same universal function, thus obtaining the collapsed response data.

4. The near-critical teaching control method with effectiveness gate constraints according to claim 1, characterized in that, Applicable data for this scale includes raw status indicators and sovereign compliance attributes; Based on the historical operational intervention sequence data, the applicable scale data is subjected to triple verification to obtain a trusted authentication result and itemized verification results, including: Based on the historical operational intervention sequence data, the original state indicators are certified to obtain the indicator certification results; Based on the historical operational intervention sequence data and the original state indicators, causal support domain verification is performed through causal effect estimation to obtain causal verification results. Perform sovereignty constraint verification on the aforementioned sovereignty compliance attributes to obtain the sovereignty verification result; The authentication results of the indicators, the causality verification results, and the sovereignty verification results are logically merged to obtain the trusted authentication results. The results of the indicator authentication, the causal verification, and the sovereignty verification are aggregated separately to obtain the itemized verification results.

5. The near-critical teaching control method for effectiveness gate constraints according to claim 4, characterized in that, The raw state indicators include data collected from at least two independent sources; Based on the historical operational intervention sequence data, the original state indicators are certified to obtain the indicator certification results, including: The original state indicators are subjected to statistical significance testing to obtain the significance determination results; Based on the historical operational intervention sequence data, the signal-to-noise ratio (SNR) is calculated using sliding window variance decomposition. The signal-to-noise ratio is thresholded to obtain the signal-to-noise ratio determination result; Based on the original state indicators, consistency is determined by correlation comparison to obtain the consistency determination result. The significance determination result, the signal-to-noise ratio determination result, and the consistency determination result are logically merged to obtain the indicator certification result.

6. The near-critical teaching control method for effectiveness gate constraints according to claim 4, characterized in that, Based on the historical operational intervention sequence data and the original state indicators, causal support domain verification is performed through causal effect estimation to obtain causal verification results, including: Based on the historical intervention sequence data, the causal effect was estimated using the difference-in-differences method to obtain the average causal effect and confidence interval. Based on the original state indicators and the first intervention intensity, the direction and magnitude of the intervention response are determined. Based on the average causal effect, the direction of the intervention response is checked for consistency, and the direction check result is obtained. Based on the confidence interval, the amplitude of the intervention response is verified to obtain the amplitude verification result; The direction verification result and the amplitude verification result are logically merged to obtain the causality verification result.

7. The near-critical teaching control method for effectiveness gate constraints according to claim 4, characterized in that, The sovereign compliance attributes include data sovereignty flags, privacy budget status, and permission levels; sovereignty constraint verification is performed on the sovereign compliance attributes to obtain sovereignty verification results, including: The data sovereignty marker is subjected to a compliance assessment to obtain a sovereignty compliance assessment result; Based on the privacy budget status, the balance is verified using the differential privacy budget accounting method to obtain the privacy budget verification result; The permission levels are compared to obtain the permission verification results; The sovereignty compliance determination result, the privacy budget verification result, and the permission verification result are logically merged to obtain the sovereignty verification result.

8. The near-critical teaching control method for effectiveness gate constraints according to claim 1, characterized in that, If the trusted authentication result is authentication failure, based on the sub-item verification results, the first intervention intensity is gradually downgraded to obtain a second intervention intensity, including: Based on the results of the itemized verification, risk levels are classified to obtain risk level determination results; the risk level determination results include a first risk level, a second risk level, and a third risk level. If the risk level determination result is the first risk level, the first intervention intensity will be used as the second intervention intensity; If the risk level determination result is the second risk level, the first intervention intensity is adjusted to obtain the second intervention intensity; If the risk level assessment result is the third risk level, a manual takeover request is made to obtain the second intervention intensity.

9. The near-critical teaching control method for effectiveness gate constraints according to claim 1, characterized in that, If the trusted authentication result is successful, based on the current real-time state measurement data, the critical intensity range, the applicable scale range, and the first intervention intensity, a second intervention intensity is obtained through rolling optimization using a model prediction controller, including: Based on the current real-time state measurement data and the first intervention intensity, multi-step state prediction is performed through the state space model to obtain the predicted state trajectory; Based on the predicted state trajectory, the critical intensity range, and the applicable scale range, the intervention intensity sequence with boundary constraints is optimized through the model prediction controller to obtain the optimal intervention intensity sequence. The optimal intervention intensity sequence is first extracted to obtain the second intervention intensity.

10. A near-critical teaching control system with effectiveness gate constraints, characterized in that, include: The data acquisition module is used to acquire multi-scale intervention response calibration data, current real-time status measurement data, historical operational intervention sequence data, and the first intervention intensity. The multi-scale critical analysis module is used to perform multi-scale critical analysis based on the multi-scale intervention response calibration data by scaling and collapse, to obtain the critical intensity range, applicable scale range and model mismatch. The model suitability determination module is used to determine the scale suitability of the current real-time state measurement data based on the applicable scale range and the model mismatch degree, so as to obtain the scale suitability data. The trusted authentication module is used to perform triple verification on the scale-applicable data based on the historical operation intervention sequence data to obtain trusted authentication results and item verification results; The security downgrade execution module is used to, if the trusted authentication result is authentication failure, gradually downgrade the first intervention intensity based on the sub-item verification results to obtain a second intervention intensity; The model prediction control module is used to perform rolling optimization based on the current real-time state measurement data, the critical intensity range, the applicable scale range, and the first intervention intensity, if the trusted authentication result is successful, to obtain the second intervention intensity.

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