Knowledge-ability-competence triple map-based new engineering course teaching evaluation method

Abstract

The application discloses a kind of new engineering course teaching evaluation methods based on knowledge-ability-quality triple spectrum, belong to wisdom education and intelligent control technical field.Data of three dimensions of student knowledge, ability and quality are collected to construct a unified state vector, and the dynamic evolution of the learning process is described by combining the state update and prediction model of residual network;Multi-cell filtering method is used for state set estimation, and in the prediction step, linear propagation and residual local linearization are combined, and the safety and reliability of state interval estimation are guaranteed by using Lipschitz upper bound to circumscribe the nonlinear residual;In the update step, the set is tightened by the intersection of the prediction strip and the generator contraction, the coverage calibration based on quantile is introduced to ensure the confidence level of set estimation.The application can dynamically, stably and explainably estimate the learning state of students, and realize accurate and efficient course adjustment optimization, with good application prospect and popularization value.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of educational informatization, intelligent control and data processing, and involves the application of student learning state estimation, membership filtering and model predictive control (MPC) in course teaching. Specifically, it is a teaching evaluation method for new engineering courses based on a knowledge-ability-quality triple graph. Background Technology

[0002] With the rapid advancement of digitalization and intelligentization in education, accurately characterizing students' knowledge acquisition, ability development, and comprehensive qualities during the learning process has become an important research direction for smart education and educational management. Traditional teaching evaluation methods mostly rely on mid-term and final exams or periodic tests. While these methods can reflect some knowledge acquisition, they often have the following shortcomings: poor timeliness, failing to track students' dynamic changes in the learning process in real time; single-dimensional approach, focusing on knowledge assessment while neglecting the comprehensive improvement of abilities and qualities; and lack of uncertainty representation, with evaluation results usually providing single-value scores, making it difficult to quantify potential fluctuations and reliable ranges, resulting in insufficient precision and robustness of teaching interventions.

[0003] In recent years, data-driven learning analytics methods have gradually emerged. Researchers have attempted to introduce deep learning, graph modeling, and temporal prediction to model and predict students' learning trajectories. Deep learning automatically extracts students' learning features through multi-layered neural networks, achieving efficient learning and prediction. Graph modeling represents students' behavior, interests, and interactions as nodes and edges in a graph, capturing relationships and behavioral patterns among students. Temporal prediction utilizes students' historical behavioral data (such as learning time, grades, and behavioral patterns) for modeling and prediction, aiming to achieve personalized teaching and adaptive scheduling. However, the complex network structure and numerous parameters in deep neural networks make their decision-making process difficult to interpret. Furthermore, the complex internal mechanisms and lack of modularity result in outputs lacking causal relationships. In addition, deep neural networks are highly dependent on the training data, making them vulnerable to adversarial attacks, and they can also suffer from overfitting during training. Their application is limited in scenarios requiring transparency and traceability, such as educational evaluation. Furthermore, deep models typically provide point estimates, thus ignoring internal uncertainties, data noise, and model structure. They lack effective descriptions of external disturbances, sample differences, and model uncertainties, making it difficult to guarantee the robustness of prediction results.

[0004] On the other hand, set-membership filtering methods have been extensively studied in the fields of control and signal processing. These methods, by maintaining a feasible set of system states during the prediction and update steps, can provide interval estimates of the state under conditions of "unknown but bounded noise." In particular, zonotope representations, due to their advantages such as high computational efficiency, good closure, and the ability to compactly characterize uncertain sets, have been applied in fault detection, robust control, and state estimation. Compared with traditional ellipsoidal algorithms, zonotope filtering performs better in terms of set shrinkage and robustness, providing less conservatism.

[0005] However, directly applying multi-cell filtering to educational scenarios still faces several challenges: First, the knowledge-ability-quality triple graph in the educational process has strong nonlinearity, cross-dimensional coupling, and feedback loop characteristics. The three elements influence and constrain each other, forming a complex system with complex positive and negative feedback; relying solely on linear models is insufficient to accurately describe this. Second, significant individual differences among students make it difficult for a single deterministic model to capture diverse learning trajectories. Third, educational interventions are characterized by limited resources, prerequisites, and multi-objective optimization, necessitating a comprehensive planning approach that combines predictive models with optimal scheduling methods.

[0006] In summary, existing methods either over-rely on static, fractionalized evaluations, lacking characterization of dynamic processes and uncertainties; or, while incorporating deep learning models, struggle to guarantee interpretability and confidence levels. In the context of smart education and precision teaching, there is an urgent need for a new method that combines the nonlinear fitting capabilities of deep learning with the ensemble estimation capabilities of multicell filtering. This method should accurately model student learning states, provide reliable intervals and confidence information, and further integrate with model predictive control (MPC) to achieve optimal scheduling of teaching interventions. This is precisely the problem that the technical solution proposed in this invention aims to solve. Summary of the Invention

[0007] To address the aforementioned problems in existing technologies, this invention provides a teaching evaluation method for new engineering courses based on a triple graph of knowledge, ability, and competence. This method includes: constructing a state update and prediction model by combining a deep residual network; designing a fully symmetric multicell set-membership filter to estimate the state in intervals; adjusting the uncertainty boundary through a coverage calibration mechanism to calibrate the coverage between the predicted output and the actual prediction; and finally optimizing the scheduling through model prediction control to output the final scheduling result.

[0008] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0009] Step 1: Collect data on students' knowledge, abilities, and qualities across three dimensions to represent their learning status, and represent these data as a state vector. ;

[0010] Data on students' knowledge, abilities, and qualities are collected to construct a three-dimensional vector representing students' learning status. The expression for the state vector representing students' learning status is as follows:

[0011]

[0012] in, The knowledge dimension measures students' mastery of the core theories and fundamental knowledge of the course, and its evaluation results reflect whether students have met the pre-set syllabus requirements. Predictive indicators for this dimension include: chapter quiz scores, accuracy rate in answering key concept questions, homework completion, and time spent reading course materials.

[0013] Chapter quiz scores refer to the scores students obtain through periodic quizzes or unit tests at the end of each knowledge unit or chapter; key concepts refer to the fundamental principles, theorems, definitions, or professional terms that are central to the course; key concept answer accuracy refers to the percentage of students who answer correctly in specific questions or assessments that include key concepts; homework completion status refers to the scores students receive on their assignments; course materials refer to various learning aids provided by teachers on online platforms or resource management systems, such as textbook chapters, handouts, PPTs, lab guides, references, course videos, etc.; course material reading time is the cumulative browsing / study time students spend on course materials on online learning platforms or resource management systems.

[0014] This is the competency dimension, used to characterize students' ability to transfer and apply learned knowledge to practical problems, particularly their level of solving complex tasks, designing experiments, and completing interdisciplinary projects. Predictive indicators for this dimension include: experiment completion rate, course design task grades, pass rate for programming or modeling problems, and role fulfillment in team projects.

[0015] Experiment completion rate refers to the score students receive for completing experimental operations and experimental reports; course design task grade refers to the score students receive for comprehensive design or research tasks assigned in the course; the pass rate for programming or modeling problems refers to the percentage of students who complete programming implementation, numerical modeling, or simulation tasks in course assessments or competitions; and role performance in team projects refers to the score students receive for completing tasks individually in group collaborations or interdisciplinary team projects.

[0016] This is a competency dimension used to reflect students' attitudes, sense of responsibility, teamwork, and overall personality traits during the learning process. It is a comprehensive measure of learning behavior and soft skills. Predictive indicators for this dimension include: classroom participation, number of discussions and interactions, teamwork efficiency, performance of innovative thinking, and punctuality and integrity records.

[0017] Classroom participation refers to the number of times students actively answer questions during classroom teaching; discussion interaction frequency refers to the frequency of student interaction in course discussion areas, classroom group discussions, or online learning platforms; teamwork efficiency refers to the proportion of individual task completion in group tasks or interdisciplinary team projects to the total task volume; innovative thinking performance refers to the score of students in learning or project tasks; punctuality and integrity record refers to the score of students in adhering to time arrangements and academic norms during the learning process.

[0018] After all components are collected, they need to be normalized to [0, 1], where 0 represents not fully mastered / achieved, and 1 represents fully mastered / achieved.

[0019] Step 2: Construct a course teaching evaluation system, which includes a data acquisition module, a status update and prediction model, a coverage calibration module, a multi-cell filtering module, and an MPC scheduling module.

[0020] The data acquisition module collects predictive data related to students' knowledge, abilities, and qualities, and transmits the collected data to the state update and prediction model. The state update and prediction model predicts the state vector of students' learning status and transmits the prediction results to the coverage calibration module. The coverage calibration module updates the uncertainty boundary and outputs the update results to the multi-cell filtering module. The multi-cell filtering module performs prediction and update and reduces the generator order, then feeds the output results back to the state update and prediction model. The state update and prediction model receives the feedback and regenerates the prediction results, which are transmitted to the MPC scheduling module. After optimization, the optimal class scheduling intervention is output.

[0021] The state update and prediction model are overlaid with a deep residual network, and its expression is:

[0022]

[0023] in, This refers to the amount of teaching intervention input, which is all the teaching interventions and resource inputs that educators give to students, including knowledge input from courses, guidance and feedback input from tutors, laboratory platforms, and resource input from competition opportunities; Represents contextual features; This indicates the linear dependence between the three graphs, such as the influence of knowledge on ability and ability on quality. This represents the direct gain of the intervention input on each dimension; Evaluation metrics representing state mappings, such as quiz scores, experiment pass rates, and project scores; The direct gain of the input on the output; represent OK The real vector space of columns; These are predictable quantities obtained from exams, projects, experiments, and competency assessments. Represents process noise, Represents measurement noise; This represents a vector of nonlinear effects, used to characterize nonlinear effects that are not covered by traditional linear state-space models. Represents an individual difference vector; used to characterize individual differences that traditional linear state-space models fail to cover.

[0024] The knowledge input for the course refers to the ratio of the number of new knowledge points taught in this term to the total number of knowledge points in the syllabus; the guidance and feedback input from the tutor refers to the number of weekly face-to-face meetings; the laboratory platform refers to the ratio of equipment usage time to equipment open time; the competition opportunity resource input refers to the ratio of the number of competition slots or preparation support funds and venues that can be obtained by the team or individual to the total funds and venues.

[0025] The training data for deep residual networks comes from multi-dimensional data during the course operation, including knowledge, ability, quality, intervention input, and contextual information; before training, the above data is cleaned, missing values ​​are handled, and 0-1 normalized.

[0026] The deep residual network structure is a small residual network LSTM, which includes: an input layer, hidden layers, activation function layers and an output layer;

[0027] The input to the input layer includes the center of the fully symmetric multicellular body. Input volume of teaching intervention With context features The hidden layers consist of 2–3 fully connected and LSTM layers, with 64–128 nodes per layer; the activation function layers are ReLU or Tanh, used to add the network output to the linear model prediction residuals, ensuring that it degenerates into a linear model when there is no nonlinearity; the output layer outputs a vector of nonlinear effects. Individual difference vector .

[0028] The deep residual network is trained using the Adam optimizer, with mean squared error (MSE) as the loss function, i.e.:

[0029]

[0030] in, Represents the number of samples;

[0031] The data is divided into training, validation, and test sets according to the semester and week. The training set is used for parameter updates, the validation set is used for hyperparameter tuning, and the test set is used for performance evaluation.

[0032] Step 3: Use the multicell filtering module to perform interval estimation on the prediction and update steps of the state update and prediction model to obtain preliminary evaluation results, specifically including:

[0033] Using the fully symmetric multicell in the set-member algorithm Represents a set of states, based on the current time. The state variables are estimated for the next time step, thus obtaining... The expression for the fully symmetric multicellular body that encapsulates the true state at time t. express Predict the center of a fully symmetrical multicell at all times. This represents the generating matrix of the fully symmetric multicell;

[0034] For the prediction step of the state update and prediction model, the linear principal term is:

[0035]

[0036] in, This is the process noise generator matrix;

[0037] Next, the deep learning residuals are locally linearized, and their expression is:

[0038]

[0039] in, ;

[0040] The linear approximation error of the residuals satisfies the expression:

[0041]

[0042] in, , The Lipschitz constant is obtained through spectral norm regularization or network analysis.

[0043] Therefore, the residual set is obtained as follows:

[0044]

[0045] in, Represents a value centered at 0 with a radius of . hypercube;

[0046] The prediction set is obtained by linearizing and combining the linear principal terms and the residual set. , where the prediction set The expression is:

[0047] .

[0048] For the state update and the update step of the prediction model, the residual is defined as:

[0049]

[0050] in, Represents the residual input. exist The linearized form is obtained, and its expression is:

[0051]

[0052] Intersect the prediction set and the prediction band, and obtain the updated set through shape matrix reduction operation. ;

[0053] The expression for the prediction band is:

[0054]

[0055] in, The nonlinear residual term represents the first... The local linearization correction matrix at time step 1. Represents a constant bias term. This represents the upper bound of the predicted noise. It is the upper bound of the linearized remainder term;

[0056] The expressions for the state estimation center points of the updated set and the generation matrix of the updated set are as follows:

[0057]

[0058]

[0059] in, The expression representing the update gain of a fully symmetric multicellular body is as follows:

[0060]

[0061] Step 4: Perform coverage calibration on the preliminary evaluation results obtained in Step 3 to update the noise boundary, and then transmit the updated noise boundary to the multi-cell filtering module. This specifically includes:

[0062] Based on historical inconsistency Coverage calibration is performed on the maximum deviation between the predicted output and the actual observation, where historical inconsistency is considered. The expression is:

[0063]

[0064] Through historical inconsistency Find the minimum threshold This makes at least one (90%) of the samples fell into Within this range, coverage calibration can be achieved;

[0065] Take the empirical quantile:

[0066]

[0067] Predict the upper bound of noise Adjusted to To ensure that the coverage of the prediction set reaches the confidence level .

[0068] Step 5: Based on the updated multicell filter module obtained in Step 4, perform interval estimation on the output of the state update and prediction model, and transmit the evaluation results of the output to the MPC scheduling module.

[0069] Step Six: Optimize the evaluation results output from Step Five using the MPC scheduling module, and output the final class rescheduling intervention, specifically including:

[0070] The MPC scheduling module optimizes scheduling by considering target deviation, uncertainty width, and intervention cost, and outputs the optimal class rescheduling intervention plan.

[0071] Under the constraints of target state and resources, we construct a model predictive control (MPC) optimization problem that aims to ensure students achieve the preset knowledge, ability and quality goals while avoiding the waste of teaching resources and the burden on students caused by excessive intervention.

[0072] Therefore, the cost function is defined as follows:

[0073]

[0074] in, Represents the target state. The deviation from the target is used to measure the gap between the student's current state and the target state, ensuring that the student can gradually approach the established training objectives. The representative represents the weighting coefficient of the uncertainty width contraction term, used to adjust the balance between "estimation robustness" and "target tracking" in the cost function. The larger the value, the greater the proportion of "estimated robustness". The smaller the value, the larger the proportion of "target tracking"; The uncertainty width term corresponds to the width of the multicell filter estimation set, reflecting the confidence interval of the state estimation. By shrinking and optimizing it, the reliability and robustness of the evaluation results can be improved. This is the cost of intervention.

[0075] Under the constraint , Under the conditions, among which For dimensions and Find identical column vectors all equal to 1; solve. This will allow us to obtain the optimal teaching intervention for the following week. The teaching intervention is then applied to the following week's teaching, and this process is repeated iteratively to complete the state vector of the student's learning state under the triple graph. With teaching intervention Adaptive scheduling.

[0076] The beneficial effects of this application are:

[0077] This invention provides a new engineering curriculum teaching evaluation method based on a knowledge-ability-quality triple graph. By unifying the modeling of knowledge, ability, and quality into a single dimension, and constructing a state update and prediction model incorporating a deep residual network, combined with multi-cell filtering, it achieves dynamic interval estimation of students' learning states, balancing interpretability and confidence in educational scenarios. Compared to traditional methods relying on static score evaluation or using only point predictions from deep models, this invention not only accurately depicts the evolution of states but also reflects uncertainty in a set form, making the teaching evaluation more robust. Through local linearization and the introduction of Lipschitz upper bounds, the nonlinear prediction results of the deep model are strictly externalized, avoiding the opacity of black-box models and ensuring statistically verifiable confidence levels for the estimation results. This invention combines set estimation with model predictive control, comprehensively considering target deviation, uncertainty contraction, and intervention costs under limited resources and multiple constraints, to achieve optimal scheduling of teaching interventions, making curriculum arrangement more targeted and efficient. This method enables dynamic updates and rolling optimization in the actual educational process, which not only improves the scientific nature of teaching decisions but also ensures the robustness and traceability of student development evaluation, thus providing a new solution for smart education and precision teaching that has both theoretical value and application prospects. Attached Figure Description

[0078] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0079] Figure 1 This is a flowchart of a new engineering course teaching evaluation method based on a knowledge-ability-quality triple graph provided in Embodiment 1 of the present invention;

[0080] Figure 2 This is a schematic diagram of the course teaching evaluation system in the new engineering course teaching evaluation method based on the knowledge-ability-quality triple map provided in Embodiment 1 of the present invention;

[0081] Figure 3 This is a schematic diagram of the membership filtering results of the knowledge dimension in a new engineering course teaching evaluation method provided in Embodiment 2 of the present invention;

[0082] Figure 4 This is a schematic diagram of the membership filtering results of the knowledge dimension after intervention in a new engineering course teaching evaluation method provided in Embodiment 2 of the present invention;

[0083] Figure 5 This is a schematic diagram of the mean trajectory changes of the three dimensions of knowledge, ability, and quality before and after intervention in a new engineering course teaching evaluation method provided in Embodiment 2 of the present invention.

[0084] Figure 6 This is a schematic diagram showing the change curve of students' final exam pass rate before and after intervention in a new engineering course teaching evaluation method provided in Embodiment 2 of the present invention;

[0085] Figure 7 This is a schematic diagram of the change curve of the total uncertainty width under the weekly average member estimation before and after intervention in a new engineering course teaching evaluation method provided in Embodiment 2 of the present invention. Detailed Implementation

[0086] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0087] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0088] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0089] Example 1

[0090] This embodiment provides a new engineering course teaching evaluation method based on a knowledge-ability-quality triple map. The process of this method is as follows: Figure 1 As shown, the method includes: first, collecting state data of students' knowledge, ability and quality in three dimensions, and normalizing them to represent them as state vectors; then, constructing a state update and prediction model combined with a deep residual network; then, using a fully symmetric multicell filtering method to achieve dynamic interval estimation of students' learning state; then, using a coverage calibration mechanism to adjust the uncertainty boundary; and finally, using a model predictive control method to optimize the output results, ultimately outputting the optimal scheduling scheme.

[0091] Step 1: Collect data on students' knowledge, abilities, and qualities across three dimensions to represent their learning status, and represent these data as a state vector. ;

[0092] Data on students' knowledge, abilities, and qualities are collected to construct a three-dimensional vector representing students' learning status. The expression for the state vector representing students' learning status is as follows:

[0093]

[0094] in, The knowledge dimension measures students' mastery of the core theories and fundamental knowledge of the course, and its evaluation results reflect whether students have met the pre-set syllabus requirements. Predictive indicators for this dimension include: chapter quiz scores, accuracy rate in answering key concept questions, homework completion, and time spent reading course materials.

[0095] Chapter quiz scores refer to the scores students obtain through periodic quizzes or unit tests at the end of each knowledge unit or chapter; key concepts refer to the fundamental principles, theorems, definitions, or professional terms that are central to the course; key concept answer accuracy refers to the percentage of students who answer correctly in specific questions or assessments that include key concepts; homework completion status refers to the scores students receive on their assignments; course materials refer to various learning aids provided by teachers on online platforms or resource management systems, such as textbook chapters, handouts, PPTs, lab guides, references, course videos, etc.; course material reading time is the cumulative browsing / study time students spend on course materials on online learning platforms or resource management systems.

[0096] This is the competency dimension, used to characterize students' ability to transfer and apply learned knowledge to practical problems, particularly their level of solving complex tasks, designing experiments, and completing interdisciplinary projects. Predictive indicators for this dimension include: experiment completion rate, course design task grades, pass rate for programming or modeling problems, and role fulfillment in team projects.

[0097] Experiment completion rate refers to the score students receive for completing experimental operations and experimental reports; course design task grade refers to the score students receive for comprehensive design or research tasks assigned in the course; the pass rate for programming or modeling problems refers to the percentage of students who complete programming implementation, numerical modeling, or simulation tasks in course assessments or competitions; and role performance in team projects refers to the score students receive for completing tasks individually in group collaborations or interdisciplinary team projects.

[0098] This is a competency dimension used to reflect students' attitudes, sense of responsibility, teamwork, and overall personality traits during the learning process. It is a comprehensive measure of learning behavior and soft skills. Predictive indicators for this dimension include: classroom participation, number of discussions and interactions, teamwork efficiency, performance of innovative thinking, and punctuality and integrity records.

[0099] Classroom participation refers to the number of times students actively answer questions during classroom teaching; discussion interaction frequency refers to the frequency of student interaction in course discussion areas, classroom group discussions, or online learning platforms; teamwork efficiency refers to the proportion of individual task completion in group tasks or interdisciplinary team projects to the total task volume; innovative thinking performance refers to the score of students in learning or project tasks; punctuality and integrity record refers to the score of students in adhering to time arrangements and academic norms during the learning process.

[0100] All components need to be normalized to [0, 1] after collection, where 0 represents not mastering / achieving at all, and 1 represents mastering / achieving at all.

[0101] Step Two: Construct a course evaluation system, such as... Figure 2 As shown, the course evaluation system includes a data acquisition module, a state update and prediction model, a coverage calibration module, a multi-cell filtering module, and an MPC scheduling module.

[0102] The data acquisition module collects predictive data related to students' knowledge, abilities, and qualities, and transmits the collected data to the state update and prediction model. The state update and prediction model predicts the state vector of students' learning status and transmits the prediction results to the coverage calibration module. The coverage calibration module updates the uncertainty boundary and outputs the update results to the multi-cell filtering module. The multi-cell filtering module performs prediction and update and reduces the generator order, then feeds the output results back to the state update and prediction model. The state update and prediction model receives the feedback and regenerates the prediction results, which are transmitted to the MPC scheduling module. After optimization, the optimal class scheduling intervention is output.

[0103] The state update and prediction model are overlaid with a deep residual network, and its expression is:

[0104]

[0105] in, This refers to the amount of teaching intervention input, which is all the teaching interventions and resource inputs that educators give to students, including knowledge input from courses, guidance and feedback input from tutors, laboratory platforms, and resource input from competition opportunities; Represents contextual features; This indicates the linear dependence between the three graphs, such as the influence of knowledge on ability and ability on quality. This represents the direct gain of the intervention input on each dimension; Evaluation metrics representing state mappings, such as quiz scores, experiment pass rates, and project scores; The direct gain of the input on the output; represent OK The real vector space of columns; These are predictable quantities obtained from exams, projects, experiments, and competency assessments. Represents process noise, Represents measurement noise; This represents a vector of nonlinear effects, used to characterize nonlinear effects that are not covered by traditional linear state-space models. Represents an individual difference vector; used to characterize individual differences that traditional linear state-space models fail to cover.

[0106] The knowledge input for the course refers to the ratio of the number of new knowledge points taught in this term to the total number of knowledge points in the syllabus; the guidance and feedback input from the tutor refers to the number of weekly face-to-face meetings; the laboratory platform refers to the ratio of equipment usage time to equipment open time; the competition opportunity resource input refers to the ratio of the number of competition slots or preparation support funds and venues that can be obtained by the team or individual to the total funds and venues.

[0107] The training data for deep residual networks comes from multi-dimensional data during the course operation, including knowledge, ability, quality, intervention input, and contextual information; before training, the above data is cleaned, missing values ​​are handled, and 0-1 normalized.

[0108] The deep residual network structure is a small residual network LSTM, which includes: an input layer, hidden layers, activation function layers and an output layer;

[0109] The input to the input layer includes the center of the fully symmetric multicellular body. Input volume of teaching intervention With context features The hidden layers consist of 2–3 fully connected and LSTM layers, with 64–128 nodes per layer; the activation function layers are ReLU or Tanh, used to add the network output to the linear model prediction residuals, ensuring that it degenerates into a linear model when there is no nonlinearity; the output layer outputs a vector of nonlinear effects. Individual difference vector .

[0110] The deep residual network is trained using the Adam optimizer, with mean squared error (MSE) as the loss function, i.e.:

[0111]

[0112] in, Represents the number of samples;

[0113] The data is divided into training, validation, and test sets according to the semester and week. The training set is used for parameter updates, the validation set is used for hyperparameter tuning, and the test set is used for performance evaluation.

[0114] Step 3: Use the multicell filtering module to perform interval estimation on the prediction and update steps of the state update and prediction model to obtain preliminary evaluation results, specifically including:

[0115] Using the fully symmetric multicell in the set-member algorithm Represents a set of states, based on the current time. The state variables are estimated for the next time step, thus obtaining... The expression for the fully symmetric multicellular body that encapsulates the true state at time t. express Predict the center of a fully symmetrical multicell at all times. This represents the generating matrix of the fully symmetric multicell;

[0116] For the prediction step of the state update and prediction model, the linear principal term is:

[0117]

[0118] in, This is the process noise generator matrix;

[0119] Next, the deep learning residuals are locally linearized, and their expression is:

[0120]

[0121] in, ;

[0122] The linear approximation error of the residuals satisfies the expression:

[0123]

[0124] in, , The Lipschitz constant is obtained through spectral norm regularization or network analysis.

[0125] Therefore, the residual set is obtained as follows:

[0126]

[0127] in, Represents a value centered at 0 with a radius of . hypercube;

[0128] The prediction set is obtained by linearizing and combining the linear principal terms and the residual set. , where the prediction set The expression is:

[0129] .

[0130] For the state update and the update step of the prediction model, the residual is defined as:

[0131]

[0132] in, Represents the residual input. exist The linearized form is obtained, and its expression is:

[0133]

[0134] Intersect the prediction set and the prediction band, and obtain the updated set through shape matrix reduction operation. ;

[0135] The expression for the prediction band is:

[0136]

[0137] in, The nonlinear residual term represents the first... The local linearization correction matrix at time step 1. Represents a constant bias term. This represents the upper bound of the predicted noise. It is the upper bound of the linearized remainder term;

[0138] The expressions for the state estimation center points of the updated set and the generation matrix of the updated set are as follows:

[0139]

[0140]

[0141] in, The expression representing the update gain of a fully symmetric multicellular body is as follows:

[0142]

[0143] Step 4: Perform coverage calibration on the preliminary evaluation results obtained in Step 3 to update the uncertainty boundary, and then transmit the updated uncertainty boundary to the multicell filtering module. Specifically, this includes:

[0144] Based on historical inconsistency Coverage calibration is performed on the maximum deviation between the predicted output and the actual observation, where historical inconsistency is considered. The expression is:

[0145]

[0146] Through historical inconsistency Find the minimum threshold This makes at least one (90%) of the samples fell into Within this range, coverage calibration can be achieved;

[0147] Take the empirical quantile:

[0148]

[0149] Predict the upper bound of noise Adjusted to To ensure that the coverage of the prediction set reaches the confidence level .

[0150] Step 5: Based on the updated multicell filter module obtained in Step 4, perform interval estimation on the output of the state update and prediction model, and transmit the evaluation results of the output to the MPC scheduling module.

[0151] Step Six: Optimize the evaluation results output from Step Five using the MPC scheduling module, and output the final class rescheduling intervention, specifically including:

[0152] The MPC scheduling module optimizes scheduling by considering target deviation, uncertainty width, and intervention cost, and outputs the optimal class rescheduling intervention plan.

[0153] Under the constraints of target state and resources, we construct a model predictive control (MPC) optimization problem that aims to ensure students achieve the preset knowledge, ability and quality goals while avoiding the waste of teaching resources and the burden on students caused by excessive intervention.

[0154] Therefore, the cost function is defined as follows:

[0155]

[0156] in, Represents the target state. The deviation from the target is used to measure the gap between the student's current state and the target state, ensuring that the student can gradually approach the established training objectives. The representative represents the weighting coefficient of the uncertainty width contraction term, used to adjust the balance between "estimation robustness" and "target tracking" in the cost function. The uncertainty width term corresponds to the width of the multicell filter estimation set, reflecting the confidence interval of the state estimation. By shrinking and optimizing it, the reliability and robustness of the evaluation results can be improved. This is an intervention cost item, representing resources and teaching burden, to avoid wasting educational resources and student stress due to excessive intervention.

[0157] Under the constraint , Under the conditions, among which For dimensions and Find identical column vectors all equal to 1; solve. This will allow us to obtain the optimal teaching intervention for the following week. The teaching intervention is then applied to the following week's teaching, and this process is repeated iteratively to complete the state vector of the student's learning state under the triple graph. With teaching intervention Adaptive scheduling.

[0158] Example 2

[0159] This embodiment provides a new engineering course teaching evaluation method. This method is based on the course teaching evaluation system constructed in Embodiment 1. The method inputs the collected student data into the course teaching evaluation system and outputs the evaluation.

[0160] The trend of the center plus lower bound of students' knowledge dimension before and after intervention is as follows: Figure 3 and Figure 4 As shown; by Figure 3 It can be seen that the result of set membership filtering can completely encompass the state center, providing a reference interval and offering more flexible information for decision-making; while by Figure 4 It can be seen that after the intervention is applied, the reference interval shrinks and has less uncertainty.

[0161] A schematic diagram illustrating the changes in the mean trajectories of students' knowledge, abilities, and overall qualities before and after the intervention. Figure 5It can be seen that the controlled curves of the three dimensions of knowledge, ability and quality are all higher than the baseline, and the gap continues to widen in the middle and later stages. This proves that the knowledge-ability-quality triple map constructed in this application plus closed-loop intervention can accurately locate the weak dimension and achieve the earlier and faster rise of the group trajectory.

[0162] Figure 6 A comparison chart of student end-of-term achievement rates before and after the intervention, from... Figure 6 As can be seen, after the intervention, the controlled distribution shifted to the right, indicating that the students' final exam pass rate was higher overall, with more students passing and fewer students scoring low, thus proving the effectiveness of the proposed scheme.

[0163] Each student's weekly average uncertainty width under the estimated group size before and after intervention, for example... Figure 7 As shown, after intervention, the controlled weekly average total width is lower and converges faster, indicating a narrower estimation interval, less fluctuation, and more controllable individual differences, proving that the course teaching evaluation method provided in this application can significantly improve students' performance.

[0164] Some steps in the embodiments of the present invention can be implemented using software, and the corresponding software program can be stored in a readable storage medium, such as an optical disc or a hard disk.

[0165] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A teaching evaluation method for new engineering courses based on a triple map of knowledge, ability, and competence, characterized in that, The evaluation methods include: Step 1: Collect data on students' knowledge, abilities, and qualities in three dimensions and construct a state vector; Step 2: Construct a course teaching evaluation system, which includes a data acquisition module, a state update and prediction model, a coverage calibration module, a multi-cell filtering module, and an MPC scheduling module; Step 3: Use the multicell filtering module to perform interval estimation on the prediction step and update step of the state update and prediction model to obtain preliminary evaluation results; Step 4: Perform coverage calibration on the preliminary evaluation results obtained in Step 3 to update the uncertainty boundary, and then transmit the updated uncertainty boundary to the multicell filtering module; Step 5: Based on the updated multicell filter module obtained in Step 4, perform interval estimation on the output of the state update and prediction model, and output the evaluation results; Step Six: Optimize the evaluation results output from Step Five using the MPC scheduling module, and output the final class adjustment intervention. The multi-cell filtering module in step three includes a fully symmetric multi-cell set-membership filter. This fully symmetric multi-cell set-membership filter performs interval estimation of the prediction and update steps of the state update and prediction model. Specifically, it includes: Through fully symmetrical multicellular bodies Let represent the set of states, where express The center of a fully symmetrical multicellular body at any given time. This represents the generating matrix of the fully symmetric multicell; In the prediction step of the state update and prediction model, the linear principal term is: in, This is the process noise generator matrix; The deep residual network is then locally linearized, and its expression is: in, A state vector representing the student's learning state. ; The linear approximation error of deep residual networks satisfies the following expression: in, , The Lipschitz constant is obtained through spectral norm regularization or network analysis; Therefore, the residual set is obtained as follows: in, Represents a value centered at 0 with a radius of . hypercube; The prediction set is obtained by linearizing and combining the linear principal term and the residual set, and its expression is as follows: in Represents the prediction set; Step four involves adjusting the uncertainty boundary using a coverage calibration mechanism, specifically including: Coverage calibration is performed based on the maximum deviation between the model's predicted output and actual observations, using historical inconsistency as the basis. The expression is: Historical inconsistency Find the minimum threshold This makes at least one The sample falls within; Take the empirical quantile: Predict the upper bound of noise Adjusted to To ensure that the coverage of the prediction set reaches the confidence level ; Step five involves optimizing the scheduling and output of the teaching intervention plan by comprehensively considering target deviation, uncertainty width, and intervention cost. Specifically, this includes: Given the objective state and resource constraints, design a model predictive control optimization problem and define the cost function: in, Represents the target state. For deviation target deviation term; The representative represents the weighting coefficient of the uncertainty width contraction term; This is the uncertainty width term, corresponding to the width of the multicell filter estimation set, reflecting the confidence interval of the state estimation; For intervention costs; Under the constraint , Under the conditions, among which For dimensions and Find identical column vectors all equal to 1; solve. This will allow us to obtain the optimal teaching intervention for the following week. The teaching intervention is then applied to the following week's teaching, and this process is repeated iteratively to complete the state vector of the student's learning state under the triple graph. With teaching intervention Adaptive scheduling.

2. The evaluation method according to claim 1, characterized in that, The course evaluation system in step two: The data acquisition module is used to collect observational data related to students' knowledge, abilities, and qualities, and transmit the collected data to the state update and prediction model. The state update and prediction model is used to predict the state vector of the student's learning state and transmit the prediction result to the coverage calibration module. The coverage calibration module updates the uncertainty boundary and outputs the update result to the multicell filtering module; The multicell filtering module receives the update results output by the coverage calibration module and performs interval estimation on the state update and prediction model; The state update and prediction model regenerates the evaluation results based on the updated multicell filter module and transmits the evaluation results to the MPC scheduling module. The MPC scheduling module optimizes the evaluation results and ultimately outputs a class rescheduling intervention.

3. The evaluation method according to claim 2, characterized in that, The state update and prediction model are superimposed with a deep residual network, and its expression is: in, Representing a moment, This represents the input vector for instructional intervention; Represents contextual features; This indicates the linear dependence between the triple graphs; This represents the direct gain of the intervention input on each dimension; Evaluation metrics representing state mapping; The direct gain of the input on the output; represent OK The real vector space of columns; These are predictable quantities obtained from exams, projects, experiments, and competency assessments. Represents process noise, Represents measurement noise; Represents the vector of nonlinear effects. This represents an individual difference vector.

4. The evaluation method according to claim 3, characterized in that, In the state update and prediction model update step, the residual is defined as: in, Represents the residual input. exist The linearized form is obtained, and its expression is: The prediction set and prediction band are intersected, and then the updated set is obtained through shape matrix reduction. The expression for the prediction band is: in, The nonlinear residual term represents the first... The local linearization correction matrix at time step 1. Represents a constant bias term. Represents the upper bound of the predicted noise. It is the upper bound of the linearized remainder term; The resulting updated set is The expressions for the state estimation center points of the updated set and the generation matrix of the updated set are respectively: in, The expression representing the update gain of a fully symmetric multicellular body is as follows: 。 5. The evaluation method according to claim 4, characterized in that, In step one, a three-dimensional vector is constructed by collecting data on students' knowledge, abilities, and qualities to represent their learning status. The expression for the state vector representing the student's learning status is as follows: in, From the knowledge dimension, From the perspective of capability, For the quality dimension; after all the components of the dimension are collected, they need to be normalized to [0, 1], where 0 represents not mastering / achieving at all, and 1 represents mastering / achieving at all.

6. The evaluation method according to claim 5, characterized in that, The training data for the deep residual network comes from multi-dimensional data during the course operation, including knowledge, ability, quality, intervention input, and contextual information. Before training, the above data was cleaned, missing values ​​were removed, and 0-1 normalization was performed. The deep residual network structure is a small residual network LSTM, which includes: an input layer, a hidden layer, an activation function layer, and an output layer; The input to the input layer includes the center of the fully symmetric multicellular body. Input volume of teaching intervention With context features The hidden layers consist of 2–3 fully connected and LSTM layers, with 64–128 nodes per layer. The activation functions are ReLU or Tanh, used to add the network output to the linear model's prediction residuals, ensuring that it degenerates into a linear model when there is no nonlinearity. The output layer outputs a vector of nonlinear effects. Individual difference vector ; The deep residual network is trained using the Adam optimizer, with mean squared error as the loss function, and its expression is as follows: in, This represents the number of samples.

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