Visual chart system for analyzing test question quality and test object ability

Abstract

The invention relates to the technical field of education, in particular to a visual chart system for analyzing test question quality and test object ability, which comprises a dynamic data preprocessing module, a sliding window adaptive adjustment module, a multi-axis fluctuation intensity analysis module, a group trend disassembly module and an abnormal test question judgment module. According to the method, a difference absolute value algorithm is adopted to construct an adjacent test question physical correlation model, a test question serial number is mapped as a time axis variable to generate a thermodynamic diagram, the time-space continuity of score fluctuation is captured, a sliding window algorithm is adopted to establish dynamic correlation between window density and fluctuation amplitude, and normalized parameter difference degree is matched with sampling frequency and data features. A three-axis direction change rate is defined to construct a three-dimensional radar coordinate system, Kriging interpolation is combined to generate a distribution cloud picture, group trend departure and standard deviation distribution difference are analyzed, spatial autocorrelation modeling is used to enhance the anomaly recognition capability, and time sequence modeling, dynamic feedback and spatial vector analysis are used to cooperatively improve the detection and evaluation precision and reduce the misjudgment risk.

Description

Technical Field

[0001] The present invention relates to the field of educational technology, and in particular, to a visual chart system for analyzing the quality of test questions and the abilities of test takers. Background Art

[0002] The field of educational technology includes system design for assisting teaching processes by means of informatization, learning evaluation methods, educational management support, etc. Its core contents include intelligent allocation of learning resources, collection and analysis of students' learning behavior data, process monitoring of teaching activities, multi-dimensional evaluation of learning outcomes, etc. By combining computer technology, big data analysis methods and human-computer interaction methods, this technical field systematically constructs an overall educational information processing architecture suitable for personalized learning and dynamic evaluation, which is widely applied in various scenarios such as basic education, higher education and vocational training, and promotes the improvement of educational fairness and teaching efficiency.

[0003] Among them, the visual chart system refers to a chart generation and management method for graphically presenting students' learning performance, statistical characteristics of test questions and evaluation data. This system mainly focuses on data processing matters involved in the evaluation of test question quality and the analysis of test taker abilities, covering technical contents such as numerical collation of students' answering situations, extraction of parameters for the discrimination and difficulty of different test questions, and division of ability levels of the performance of the learning group. It is usually completed by combining a graphic drawing instruction set with a data scale matching method, extracts evaluation results through a standardized data interface, and then completes the visual expression of information through chart drawing methods such as bar charts, line charts or radar charts.

[0004] In the prior art, the data interception method based on fixed time nodes has multi-dimensional technical defects. The traditional method intercepts data at discrete time nodes, breaking the temporal physical continuity of test question answering, resulting in the inability to effectively capture the score jump characteristics between adjacent test questions. For example, a bar chart can only reflect the average score of a single question and cannot model the dynamic impact of the answering order on ability fluctuations. At the same time, the artificially preset sliding window parameters lack a dynamic feedback mechanism. When the test question difficulty distribution shows non-linear fluctuations, a phase deviation occurs between the fixed window width and the data change frequency, resulting in the omission of key fluctuation nodes. In addition, the existing group statistical models use overall mean comparison analysis, ignoring the standard deviation distribution differences between high and low score groups and the physical separation phenomenon of reverse trends, resulting in a reduction in the statistical significance of test question discrimination evaluation. More seriously, the traditional plane superposition technology is limited by the two-dimensional space modeling ability and cannot analyze complex abnormal patterns under the coupling action of multiple parameters, making it difficult to accurately quantify the dynamic characteristics of parameter interaction effects. Summary of the Invention

[0005] The purpose of the present invention is to solve the defects existing in the prior art, and to propose a visual chart system for analyzing the quality of test questions and the abilities of test takers.

[0006] To achieve the above object, the present invention adopts the following technical solution: A visualization chart system for analyzing the quality of test questions and the abilities of test takers includes: A dynamic data preprocessing module, which is used to extract the score difference between adjacent test questions, call the differential absolute value algorithm to generate a heat distribution diagram of test question jumps, count the jump frequency to generate a scatter diagram of fluctuation frequencies, calculate the sliding average offset rate to generate a line time series diagram of offset rates, and transmit them to the sliding window adaptive adjustment module; A sliding window adaptive adjustment module, which is used to compare window parameters through the received heat distribution diagram of test question jumps, the scatter diagram of fluctuation frequencies, and the line time series diagram of offset rates, adjust the boundary to generate a dynamic coverage area diagram of the sliding window, and transmit it to the multi-axis fluctuation intensity analysis module; A multi-axis fluctuation intensity analysis module, which is used to calculate the upward slope within the received dynamic coverage area diagram of the sliding window to generate the coordinates of a three-axis radar chart, count the ratio of downward frequencies, calculate the recovery period to generate a three-dimensional distribution cloud diagram of fluctuation intensity, and transmit it to the population trend decomposition module and the abnormal test question determination module; A population trend decomposition module, which is used to divide high and low score groups to generate a column chart comparing population standard deviations, count the frequency of reverse trends to generate a density diagram of trend direction deviation, superimpose charts to generate a heat distribution diagram of resolution failure distribution, and transmit it to the abnormal test question determination module.

[0007] As a further solution of the present invention, the dynamic coverage area diagram of the sliding window includes window coverage density, boundary threshold interval, and dynamic weight coefficient. The coordinates of the three-axis radar chart specifically refer to the extreme value of the upward slope, downward frequency clustering, and recovery period span. The three-dimensional distribution cloud diagram of fluctuation intensity includes intensity gradient layer, frequency aggregation node, and period distribution contour line. The column chart comparing population standard deviations is specifically the difference in standard deviations between high and low score groups, the cumulative value of trend reversal, and the ratio of population dispersion. The density diagram of trend direction deviation includes the difference in standard deviation comparison, trend deviation density, and heat overlay area. The heat distribution diagram of resolution failure distribution covers the resolution attenuation area, population offset overlap band, and standard deviation imbalance node.

[0008] As a further solution of the present invention, the differential order of the differential absolute value algorithm is the first-order differential, and the color scale encoding value mapping rule is to proportionally map the absolute value of the difference to the 0-255 gray scale interval; The normalization calculation model for the window parameter comparison is window parameter difference degree = 0.4 × color scale difference + 0.3 × scatter density difference + 0.3 × ratio difference; The calculation basis for the upward slope is the ratio of the change rate of the horizontal axis to the change rate of the time axis, where the change rate of the horizontal axis = Δx / Δt, and the change rate of the time axis = Δy / Δt; The generation logic of the dynamic weight coefficient is the reciprocal of the product of the window coverage density and the boundary threshold interval; The recovery period span is the weighted sum of the mean and standard deviation of the difference in adjacent hierarchical heights.

[0009] As a further solution of the present invention, the dynamic data preprocessing module includes: The jump heat distribution sub-module obtains the adjacent test question score sequence, calls the differential absolute value algorithm to calculate the absolute value of the adjacent score difference item by item, arranges the differences in sequence according to the test question number as a continuous sequence, converts the difference sequence into a color scale coded value through color mapping, and at the same time constructs a two-dimensional coordinate point set based on the test question number and the color scale coded value to generate a test question jump heat distribution map; The mapping rule of the color scale coded value is to map the absolute value of the difference proportionally to the 0-255 gray scale interval; The fluctuation frequency statistics sub-module sets a jump amplitude reference value based on the jump amplitude value of the test question jump heat distribution map, counts the cumulative number of times that the jump amplitude at multiple test question positions exceeds the reference value, connects the test question number and the cumulative number to generate scatter coordinates, and outputs a fluctuation frequency scatter plot; The jump amplitude reference value is the 75th percentile of all test question jump amplitude values; The offset rate time series generation sub-module calls the jump amplitude sequence of the test question jump heat distribution map, divides it into equal-length window segments, calculates the difference ratio between the mean value within the window and the global mean value, and connects the window center time point and the ratio value to generate an offset rate line time series graph; The calculation formula of the difference ratio is ratio = (window mean - global mean) / global mean × 100%.

[0010] As a further solution of the present invention, the sliding window adaptive adjustment module includes: The parameter comparison sub-module calls the color scale coded value of the test question jump heat distribution map, extracts the difference between the maximum and minimum values of the color scale, and at the same time calls the scatter density value of the fluctuation frequency scatter plot, extracts the difference between the maximum and minimum values of the density, and calls the ratio value of the offset rate line time series graph, extracts the difference between the peak and valley values of the ratio, and inputs the three differences into the normalization calculation model to generate the window parameter difference degree; The weighting coefficients of the normalization calculation model are the color scale difference weight of 0.4, the scatter density difference weight of 0.3, and the ratio difference weight of 0.3; The boundary adjustment sub-module sets a horizontal coverage threshold and a vertical expansion reference based on the window parameter difference degree, screens the window numbers with a difference degree exceeding the threshold, and adjusts the expansion amplitude of the left and right boundaries and the expansion amplitude of the upper and lower boundaries of the window to generate dynamic window boundary parameters; The horizontal coverage threshold is 1.5 times the mean of the window parameter difference degree, and the vertical expansion reference is 0.8 times the standard deviation of the difference degree; The dynamic coverage construction sub-module calls the dynamic window boundary parameters, extracts the window boundary coordinates, calculates the difference in the spacing between adjacent windows, fills the difference through interpolation to generate a continuous trajectory, and outputs a sliding window dynamic coverage area map; The algorithm for filling the difference through interpolation is the cubic spline interpolation method.

[0011] As a further solution of the present invention, the multi-axis fluctuation intensity analysis module includes: The radar chart coordinate calculation sub-module calls the coverage trajectory coordinates of the sliding window dynamic coverage area map, extracts the differences in the horizontal axis, vertical axis, and time axis coordinates between the starting point and the ending point of the trajectory, calculates the ratio of the change rates in the three-axis directions, maps the change rate of the horizontal axis to the polar radius length, maps the change rate of the vertical axis to the angle increment, and maps the change rate of the time axis to the hierarchical height to generate three-axis radar chart coordinates; The calculation formula for the ratio of the change rates in the three-axis directions is: change rate of the horizontal axis = Δx / Δt, change rate of the vertical axis = Δy / Δt, change rate of the time axis = Δz / Δt; The downlink frequency analysis sub-module, based on the polar radius length of the three-axis radar chart coordinates, sets the downlink fluctuation reference value to 50% of the average value of the polar radius length, counts the cumulative number of times the polar radius length is lower than the reference value, calculates the ratio of the cumulative number of times to the total number of trajectory points, and generates a downlink frequency ratio; The calculation formula for the downlink fluctuation reference value is: reference value = average value of the polar radius length × 0.5; The cloud map generation sub-module calls the hierarchical height of the three-axis radar chart coordinates and the downlink frequency ratio, extracts the difference in adjacent hierarchical heights to calculate the average recovery period, and inputs the hierarchical height, frequency ratio, and average recovery period into a three-dimensional interpolation model to generate a three-dimensional distribution cloud map of the fluctuation intensity; The three-dimensional interpolation model is the Kriging interpolation algorithm.

[0012] As a further solution of the present invention, the group trend decomposition module includes: The group division sub-module calls the original score data, extracts the score data in the high score threshold interval and the low score threshold interval, calculates the standard deviations of the scores of multiple test questions in the two intervals, aligns the two standard deviations according to the test question numbers, and calculates the absolute value of the difference in the standard deviations of the high and low score groups under the same test question number to generate a group standard deviation comparison value; The high score threshold interval is the score data of the top 30% of the total scores, and the low score threshold interval is the score data of the bottom 30% of the total scores; The trend frequency analysis sub-module, based on the group standard deviation comparison value, sets the quantile parameter as the percentage of the comparison value interval, counts the number of test questions with a comparison value lower than the parameter, calculates the quantity ratio, and generates a trend reverse frequency rate; The quantile parameter is the 25% quantile of the group standard deviation comparison value interval; The trend layer synthesis sub-module calls the population standard deviation comparison value and the trend reverse frequency rate, maps the comparison value to the column height of the bar chart, maps the frequency rate to the heat color scale, aligns the coordinate axes to generate a composite layer, and outputs a heat map of the resolution failure distribution; The mapping rule of the heat color scale is to map the frequency rate proportionally to the red-blue gradient color.

[0013] As a further solution of the present invention, the system further includes: An abnormal test question determination module, which is used to perform spatial superposition on the received three-axis radar chart coordinates, the three-dimensional distribution cloud map of the fluctuation intensity, and the heat map of the resolution failure distribution, screen the regions of three-axis instability and reverse offset in the heat map, and generate a distribution map of abnormal points of test question quality and a correlation matrix map of candidate ability fluctuations; The distribution map of abnormal points of test question quality includes abnormal clustering regions, offset correlation nodes, and instability coordinate mappings. The correlation matrix map of candidate ability fluctuations specifically includes ability fluctuation trajectories, abnormal test question correlation degrees, and group offset synchronization rates.

[0014] As a further solution of the present invention, the abnormal test question determination module includes: The spatial superposition sub-module calls the hierarchical height parameters of the three-axis radar chart coordinates, the intensity distribution surface data of the three-dimensional distribution cloud map of the fluctuation intensity, and the heat color scale parameters of the heat map of the resolution failure distribution, aligns the three types of data according to the spatial coordinates, and superimposes the layers through a coordinate system fusion algorithm to generate a multi-source spatial superposition map; The coordinate system fusion algorithm is an affine transformation algorithm, and the alignment parameters include a translation matrix and a scaling factor; The abnormal screening sub-module is based on the multi-source spatial superposition map, sets the three-axis instability threshold as the quantile of the hierarchical height fluctuation interval, defines the reverse offset benchmark of the heat map as the percentage of the color scale intensity interval, screens the coordinate point set with the hierarchical height exceeding the threshold and the color scale intensity lower than the benchmark, and generates a candidate set of abnormal points; The three-axis instability threshold is the 90% quantile of the hierarchical height fluctuation interval, and the reverse offset benchmark is the 20% quantile of the heat color scale intensity interval; The result generation sub-module calls the coordinate numbers of the candidate set of abnormal points and the intensity mean value of the three-dimensional distribution cloud map of the fluctuation intensity, calculates the candidate ability fluctuation amplitude corresponding to each coordinate number, maps the abnormal points according to the spatial coordinates to generate a distribution map, constructs a matrix relationship between the coordinate numbers and the fluctuation amplitudes, and generates a distribution map of abnormal points of test question quality and a correlation matrix map of candidate ability fluctuations; The calculation formula for the candidate ability fluctuation amplitude is fluctuation amplitude = intensity mean value × hierarchical height.

[0015] Compared with the prior art, the advantages and positive effects of the present invention are: In the present invention, first, a physical correlation model of adjacent test questions is constructed using the differential absolute value algorithm. The question numbers are mapped to time-axis variables and a heat distribution map is generated to dynamically capture the spatio-temporal continuity of score fluctuations for real-time detection of abnormal jump characteristics. Second, an adaptive adjustment algorithm based on a sliding window is used to establish a dynamic correlation between the window coverage density and the data fluctuation amplitude, and the sampling frequency and data characteristics are automatically matched through the normalization calculation of the parameter difference degree to improve the capture accuracy of key nodes. Further, a three-dimensional radar coordinate system is constructed by defining the change rates in three-axis directions (the change rates in the horizontal axis, vertical axis, and time axis), and a distribution cloud map is generated in combination with the Kriging interpolation algorithm to analyze the group trend deviation and standard deviation distribution difference under the coupling action of multiple parameters. Finally, a spatial autocorrelation feature modeling technology is used to enhance the abnormal pattern recognition ability. Through the technical collaboration of time-series modeling, dynamic feedback, and spatial vector analysis, this system significantly improves the sensitivity of test question quality detection and the accuracy of candidate ability assessment, effectively reduces the risk of misjudgment of group trends, and provides highly robust technical support for educational evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is the system flow chart of the present invention; Figure 2 is the flow chart of the dynamic data preprocessing module of the present invention; Figure 3 is the flow chart of the sliding window adaptive adjustment module of the present invention; Figure 4 is the flow chart of the multi-axis fluctuation intensity analysis module of the present invention; Figure 5 is the flow chart of the group trend decomposition module of the present invention; Figure 6 is the flow chart of the abnormal test question determination module of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0017] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0018] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention. In addition, in the description of the present invention, the meaning of "a plurality of" is two or more, unless otherwise specifically defined.

[0019] Embodiment 1: Please refer to Figure 1 , a visualization chart system for analyzing the quality of test questions and the abilities of test takers includes: A dynamic data preprocessing module, which is used to extract the score difference between adjacent test questions, call the differential absolute value algorithm to generate a heat distribution map of test question jumps, statistically calculate the jump frequency to generate a scatter plot of fluctuation frequencies, calculate the sliding average offset rate to generate a line time series diagram of offset rates, and transmit them to the sliding window adaptive adjustment module; A sliding window adaptive adjustment module, which is used to compare window parameters through the received heat distribution map of test question jumps, scatter plot of fluctuation frequencies, and line time series diagram of offset rates, adjust the boundaries to generate a dynamic coverage area map of the sliding window, and transmit it to the multi-axis fluctuation intensity analysis module; A multi-axis fluctuation intensity analysis module, which is used to calculate the upward slope within the received dynamic coverage area map of the sliding window to generate the coordinates of a three-axis radar chart, statistically calculate the ratio of downward frequencies, calculate the recovery period to generate a three-dimensional distribution cloud map of fluctuation intensities, and transmit it to the population trend decomposition module and the abnormal test question determination module; A population trend decomposition module, which is used to divide high and low score groups to generate a bar chart comparing population standard deviations, statistically calculate the frequency of trend reversals to generate a density map of trend direction deviations, superimpose the charts to generate a heat distribution map of resolution failure distributions, and transmit it to the abnormal test question determination module; An abnormal test question determination module, which is used to spatially superimpose the received coordinates of the three-axis radar chart, three-dimensional distribution cloud map of fluctuation intensities, and heat distribution map of resolution failure distributions, screen the areas of three-axis instability and reverse offsets in the heat distribution map, and generate a distribution map of abnormal points of test question quality and a correlation matrix map of the ability fluctuations of examinees.

[0020] The sliding window dynamic coverage area diagram includes window coverage density, boundary threshold interval, and dynamic weight coefficient. The three-axis radar chart coordinates specifically refer to the upward slope extreme value, downward frequency clustering, and recovery period span. The three-dimensional distribution cloud chart of fluctuation intensity includes intensity gradient layer, frequency aggregation node, and periodic distribution contour line. The population standard deviation comparison bar chart specifically refers to the difference in standard deviation between high and low groups, the cumulative value of trend reversal, and the population dispersion ratio. The trend direction deviation density chart includes the difference in standard deviation comparison, trend deviation density, and thermal overlay area. The resolution failure distribution heat map covers the resolution attenuation area, population offset overlap band, and standard deviation imbalance node. The distribution map of abnormal points in test question quality includes abnormal clustering area, offset correlation node, and instability coordinate mapping. The candidate ability fluctuation correlation matrix diagram specifically refers to the ability fluctuation trajectory, abnormal test question correlation degree, and population offset synchronization rate.

[0021] The difference order of the differential absolute value algorithm is the first-order difference, and the color scale encoding value mapping rule is to map the absolute value of the difference proportionally to the 0 - 255 gray scale interval. The normalization calculation model for window parameter comparison is window parameter difference degree = 0.4×color scale difference + 0.3×scatter point density difference + 0.3×ratio difference. The calculation basis of the upward slope is the ratio of the horizontal axis change rate to the time axis change rate, where the horizontal axis change rate = Δx / Δt and the time axis change rate = Δy / Δt. The generation logic of the dynamic weight coefficient is the reciprocal of the product of window coverage density and boundary threshold interval. The recovery period span is the weighted sum of the mean and standard deviation of the difference in adjacent hierarchical heights.

[0022] Please refer to Figure 2 , the dynamic data preprocessing module includes: The jump thermal distribution sub-module obtains the adjacent test question score sequence, calls the differential absolute value algorithm to calculate the absolute value of the adjacent score difference item by item, arranges the differences in a continuous sequence according to the test question number, converts the difference sequence into a color scale encoding value through color mapping, and at the same time constructs a two-dimensional coordinate point set based on the test question number and color scale encoding value to generate a test question jump thermal distribution map. The color scale encoding value mapping rule is to map the absolute value of the difference proportionally to the 0 - 255 gray scale interval. The jump thermal distribution sub-module obtains the adjacent question score sequences of the specified question numbers from the student's answer dataset. For example, for 5 consecutive questions numbered from 1 to 5, the specific scores of each student for each question are called one by one from the student exam result database, and the score sequences of each student are compared one by one. First, the scores of student A in questions 1 to 5 are extracted as 3, 5, 4, 2, and 6 points respectively. Then, the absolute value of the score difference between adjacent questions is calculated item by item. The absolute value of the score difference between questions 1 and 2 is |5 - 3| = 2 points, between questions 2 and 3 is |4 - 5| = 1 point, between questions 3 and 4 is |2 - 4| = 2 points, and between questions 4 and 5 is |6 - 2| = 4 points. Another example, if the scores of student B in the same question numbers are 6, 5, 5, 3, and 1 points respectively, the absolute values of the score differences between adjacent questions are calculated as |5 - 6| = 1 point, |5 - 5| = 0 point, |3 - 5| = 2 points, and |1 - 3| = 2 points. Then, by analogy, the absolute values of the score differences of all students are merged and summarized to obtain the overall sequence of the absolute values of the differences for each question number position. For example, the sequence of the absolute values of the differences at the question number positions is: [2, 1, 2, 4, 1, 0, 2, 2, …]. Then, color mapping conversion is performed on the obtained absolute value difference sequence. That is, through the standard thermal color scale mapping method, a difference value of 0 points is defined as the cold end (blue), and the maximum difference of 5 points is defined as the hot end (red), and the intermediate transition colors are determined based on linear interpolation, so as to determine the color coding value for each value in the difference sequence. For example, the value 0 corresponds to the blue color scale value of #0000FF, and the value 4 corresponds to the red color scale value of #FF0000. In this way, the numerical sequence is converted into a color sequence, and a two-dimensional coordinate point set is established based on the question number and the color scale coding value, and finally the question jump thermal distribution graph is generated.

[0023] The fluctuation frequency statistics sub-module sets a jump amplitude reference value based on the jump amplitude values of the question jump thermal distribution graph, counts the cumulative number of times the jump amplitudes at multiple question positions exceed the reference value, connects the question numbers and the cumulative number of times to generate scatter coordinates, and outputs the fluctuation frequency scatter graph; The jump amplitude reference value is the 75th percentile of all question jump amplitude values; The fluctuation frequency statistics sub-module first based on the jump amplitude value sequence corresponding to each question number in the jump thermal distribution graph. For example, the jump amplitude values for question numbers 1 to 10 are: [1, 3, 2, 4, 5, 2, 1, 3, 4, 2], and with the jump amplitude reference value set manually at 3 points, that is, a jump amplitude value greater than 3 points is regarded as significant fluctuation. Then, the jump amplitude values at each test question position are compared with the reference value one by one. For example, the jump amplitude value of test question No. 2, which is 3, is compared with the reference value 3. Since 3 ≤ 3, it is not recorded as a fluctuation. The jump amplitude value of test question No. 4 is 4, and when compared with the reference value 3, 4 > 3, so it is recorded as 1 fluctuation. Similarly, the jump amplitude of No. 5 is 5, which is greater than the reference value, and is recorded as 1 fluctuation. After completing the comparison of the jump amplitudes at all test question positions, the number of fluctuations in multiple examinations or multiple student sequences is statistically accumulated. Taking 10 examination data as an example, the number of times that test question No. 5 exceeds the jump amplitude reference value is 7 times, test question No. 4 is 6 times, and test question No. 9 is 5 times. After the statistics, the data shown in Table 1 is obtained.

[0024] Table 1 Statistical Table of Fluctuation Frequencies at Test Question Positions ; As shown in Table 1, taking the test question number as the abscissa and the corresponding cumulative number as the ordinate to form a set of coordinate points, that is, (1, 1), (2, 2), (3, 3), (4, 6), etc., and based on this set of coordinate points, a scatter plot of fluctuation frequencies is output.

[0025] The offset rate time series generation sub-module calls the jump amplitude sequence of the test question jump heat distribution map, divides it into equal-length window segments, calculates the difference ratio between the mean value within the window and the global mean value, and connects the central time point of the window and the ratio value to generate an offset rate line time series graph; The calculation formula for the difference ratio is ratio = (window mean - global mean) / global mean × 100%.

[0026] The offset rate time series generation sub-module first calls the jump amplitude sequence of the jump heat distribution map. For example, a jump amplitude sequence of 30 test questions is obtained: [2, 3, 1, 4, 5, 3, 2, 1, 0, 4, 2, 1, 3, 4, 2, 5, 1, 3, 2, 0, 2, 4, 5, 1, 3, 2, 1, 0, 4, 3], and the window length is set to 5 test questions. This sequence is divided into 6 windows: [2, 3, 1, 4, 5], [3, 2, 1, 0, 4], [2, 1, 3, 4, 2], [5, 1, 3, 2, 0], [2, 4, 5, 1, 3], [2, 1, 0, 4, 3]. And for each window, the mean value of the jump amplitude within the window is calculated. For example, the mean value calculation within the first window is , and by analogy, the mean value within each window is obtained as [3.0, 2.0, 2.4, 2.2, 3.0, 2.0]; then the global mean value of the overall sequence is calculated, that is, , and then the offset rate is calculated for each window mean value, that is, the absolute value of the difference ratio between the window mean value and the global mean value. For example, the calculation process of the offset rate of window 1 is , the window 2 offset rate is , and so on. The offset rates of each window are successively: [0.25, 0.167, 0, 0.083, 0.25, 0.167]. Define the central time point of each window as the average of the starting serial number and the ending serial number of the window. For example, the center of window 1 is the position of the 3rd test question, and the center of window 2 is the position of the 8th test question. Thus, the central position sequence obtained is: [3, 8, 13, 18, 23, 28]. Then, taking the central time point as the abscissa and the offset rate value as the ordinate, generate an offset rate line time series graph.

[0027] Please refer to Figure 3 , the sliding window adaptive adjustment module includes: The parameter comparison sub-module calls the color scale encoding value of the test question jump heat distribution graph, extracts the difference between the maximum and minimum color scale values, and at the same time calls the scatter density value of the fluctuation frequency scatter plot, extracts the difference between the maximum and minimum density values, and calls the ratio value of the offset rate line time series graph, extracts the difference between the peak and valley values of the ratio. Input the three differences into the normalization calculation model to generate the window parameter difference degree; The weighting coefficients of the normalization calculation model are 0.4 for the color scale difference weight, 0.3 for the scatter density difference weight, and 0.3 for the ratio difference weight; The parameter comparison sub-module first calls the array of color scale encoding values corresponding to all test questions in the test question jump heat distribution graph, extracts the maximum color scale value and the minimum color scale value in the array, and calculates the difference between the two as the jump color scale fluctuation range. If in a certain instance, a certain group of color scale value sequences is: , then the maximum value is 0.85, the minimum value is 0.12, and the subtracted color scale difference is 0.73. Then, call the density values of all scatter points per unit area in the fluctuation frequency scatter plot. The density value can be obtained by counting the number of scatter points in each unit coordinate interval. For example, in the x-axis interval [0, 5], count the number of scatter points every 1 unit. If the density array per unit interval is: , the maximum density value is 6, the minimum density value is 2, and the calculated difference is 4. Subsequently, call the ratio values plotted in the offset rate line time series graph, extract the peak and valley values of the ratio sequence and calculate their difference. For example, the ratio sequence is: , the maximum value is 0.32, the minimum value is 0.05, and the subtracted value is 0.27. Finally, input the above three differences into the normalization model for standardization calculation. The normalization process is performed according to the maximum-minimum normalization method. For each difference x, the normalization calculation uses the formula: ; For example, for the above three differences of 0.73, 4, and 0.27 respectively, assuming that the historical minimum and maximum values of this type of difference within the normalization range are , then the normalization results of the three are: ; ; ; These three normalized differences are used as the unified input dimensions and then weighted and superimposed. According to the weight values set in the actual application, the weight of the color scale difference is set to 0.2, the weight of the density difference is set to 0.5, and the weight of the ratio difference is set to 0.3. Then the window parameter difference degree is calculated as follows: ; The result shows that the overall intensity value of the parameter differences between windows is 0.42231.

[0028] Based on the window parameter difference degree, the boundary adjustment sub-module sets the horizontal coverage threshold and the vertical expansion benchmark, screens the window numbers with difference degrees exceeding the threshold, and adjusts the expansion amplitudes of the left and right boundaries and the up and down boundaries of the window to generate dynamic window boundary parameters; The horizontal coverage threshold is 1.5 times the mean of the window parameter difference degree, and the vertical expansion benchmark is 0.8 times the standard deviation of the difference degree; Based on the window parameter difference degree obtained above, the boundary adjustment sub-module, on the basis of the set horizontal coverage threshold and vertical expansion benchmark, first sets the horizontal coverage threshold to 0.3. When the parameter difference degree of a certain window is greater than 0.3, it is regarded as a window that needs boundary expansion. For example, the aforementioned window difference degree is 0.42231, which is greater than the threshold 0.3. Therefore, the window number is screened for boundary expansion processing. Taking the original starting point of the horizontal boundary as question number 4 and the ending point as number 8 as an example, if the set boundary expansion amplitude is 1, the new boundary becomes numbers 3 to 9; similarly, the vertical expansion benchmark is set to a fixed pixel length or value range. Assuming that the set vertical expansion is a ratio value of ±0.1, the original upper and lower boundaries of the window on the ratio axis are 0.2 to 0.4, and the new boundary after adjustment is 0.1 to 0.5. Then, each window that meets the condition of the difference degree exceeding the threshold is processed according to this expansion rule to form a complete set of dynamic window boundary parameters.

[0029] The dynamic coverage construction sub-module calls the dynamic window boundary parameters, extracts the window boundary coordinates, calculates the difference in the distance between adjacent windows, fills the difference through interpolation to generate a continuous trajectory, and outputs a sliding window dynamic coverage area map; The algorithm for filling the difference through interpolation is the cubic spline interpolation method.

[0030] The dynamic coverage construction sub-module calls the generated dynamic window boundary parameters above, extracts the upper, lower, left, and right boundary coordinate points of each window one by one, and calculates the horizontal spacing difference between adjacent windows. For example, if the boundary of window A is (3, 9) and the boundary of window B is (8, 14), the difference in the left boundary coordinates of adjacent windows is 5. If the preset maximum allowable spacing is 2, then trajectory connection is required. Linear interpolation is used to fill the spacing area, and the interpolation points can be set at positions 9, 10, 11, 12, and 13 with a step size of 1. The interpolation coordinate points are mapped according to the original upper and lower boundaries to form a vertical block, and then the original window boundary and the interpolation connection part are integrated to generate a complete coverage section. After processing each window one by one, a complete sliding window dynamic coverage area map is constructed.

[0031] Please refer to Figure 4 , the multi-axis fluctuation intensity analysis module includes: The radar chart coordinate calculation sub-module calls the coverage trajectory coordinates of the sliding window dynamic coverage area map, extracts the coordinate differences of the horizontal axis, vertical axis, and time axis of the starting point and ending point of the trajectory, calculates the ratio of the change rates in the three-axis directions, maps the change rate of the horizontal axis to the polar radius length, the change rate of the vertical axis to the angle increment, and the change rate of the time axis to the hierarchical height to generate the three-axis radar chart coordinates; The formula for calculating the ratio of the change rates in the three-axis directions is the change rate of the horizontal axis = Δx / Δt, the change rate of the vertical axis = Δy / Δt, and the change rate of the time axis = Δz / Δt; Based on the continuous coverage trajectory information obtained from the sliding window dynamic coverage area map, the radar chart coordinate calculation sub-module first calls the coordinate values of the horizontal axis, vertical axis, and time axis of the starting point and ending point of each segment of the trajectory. For example, the starting point of the first coverage trajectory is (horizontal axis: 2, vertical axis: 0.3, time: 5), and the ending point is (horizontal axis: 6, vertical axis: 0.8, time: 11). The differences in the three directions are calculated as the horizontal change value , the vertical change value , and the time axis change value . Then, in this module, the change rate of the horizontal axis is set to , the change rate of the vertical axis is set to , and mapping processing is performed on them respectively. The change rate of the horizontal axis is used as the polar radius value, representing the path length of the projection of the trajectory in the space in the radar chart. The change rate of the vertical axis is mapped to the angle increment . The mapping ratio is set to , that is, the angle increment is . The time change rate is directly set as the hierarchical height in the radar chart , which is 6. Finally, the three-dimensional polar coordinates can be used to construct the point positions . Repeat the above operations for each segment of the trajectory to construct a complete set of three-axis radar chart coordinate points.

[0032] The downlink frequency analysis sub-module sets the downlink fluctuation reference value as 50% of the average value of the polar radius lengths based on the polar radius lengths of the three-axis radar chart coordinates, counts the cumulative number of times the polar radius length is lower than the reference value, calculates the ratio of the cumulative number of times to the total number of track points, and generates the downlink frequency ratio; The calculation formula for the downlink fluctuation reference value is reference value = average value of the polar radius length × 0.5; The downlink frequency analysis sub-module operates on the above three-axis radar chart polar radius data. First, it extracts the numerical sequence of all polar radius lengths. For example, the polar radius length array under a certain track is , calculates the average value of the polar radius lengths. The average value is: , and the downlink fluctuation reference value is set as 50% of this average value, that is . Then, it compares each polar radius length value in the array with this reference value. Any value less than 0.2485 is recorded as a downlink fluctuation event. In this example, there are two values less than the reference value (0.22, 0.25), that is, the cumulative number of times is 2 times, and the total number of track points is 10. Therefore, the downlink frequency ratio is calculated as: , that is, the downlink frequency ratio is 0.2.

[0033] The cloud map generation sub-module calls the hierarchical height and the downlink frequency ratio of the three-axis radar chart coordinates, extracts the difference between adjacent hierarchical heights to calculate the average value of the recovery period, and inputs the hierarchical height, frequency ratio, and average value of the recovery period into the three-dimensional interpolation model to generate a three-dimensional distribution cloud map of the fluctuation intensity; The three-dimensional interpolation model is the Kriging interpolation algorithm.

[0034] The cloud map generation sub-module first obtains the hierarchical height values of each coordinate point in the three-axis radar chart to form a height array. For example, the height value array is , and calculates the differences between adjacent height points in turn: , and obtains the average value of the recovery period as: . Then, it calls the previously obtained downlink frequency ratio of 0.2, and together with the hierarchical height and the average value of the recovery period of each point, inputs them into the three-dimensional interpolation model to form a three-dimensional distribution data body. The defined spatial coordinates are respectively Frequency ratio , Average value of the recovery period , Hierarchical height. For example, when taking z as 6, 7, and 8, calculate the interpolation intensity values at their corresponding spatial positions, and generate the continuity of this three-dimensional data through linear interpolation or spline interpolation to obtain an isosurface rendering image with the intensity value in the z direction, forming a complete three-dimensional distribution cloud map of the fluctuation intensity.

[0035] Please refer to Figure 5 , the population trend decomposition module includes: The group division sub-module calls the original score data, extracts the score data in the high-score threshold interval and the low-score threshold interval, calculates the standard deviation of the scores of multiple test questions in the two intervals, aligns the two standard deviations according to the question numbers, calculates the absolute value of the difference between the standard deviations of the high-score and low-score groups under the same question number, and generates a group standard deviation comparison value; The high-score threshold interval is the score data of the top 30% of the total scores, and the low-score threshold interval is the score data of the bottom 30% of the total scores; The group division sub-module calls the original score data set, sorts the total scores of each student, extracts the high-score group in the top 25% and the low-score group in the bottom 25% as the analysis objects, respectively filters out the answering scores of these two types of groups on each test question, and forms two parallel score matrices. For example, there are 5 questions, and the number of each question is Q1 to Q5. In the high-score group, the score data of the first question is , and the score of the corresponding first question in the low-score group is , then calculate the standard deviation for the two groups of data respectively. The standard deviation of the first question in the high-score group is , and the standard deviation of the first question in the low-score group is . Operate on each question in this way. After the two groups of standard deviation sequences are aligned according to the question numbers, calculate the absolute value of the difference of the standard deviations for each question number in turn. For example, the corresponding difference for the first question is , and the second question is . Finally, the standard deviation comparison value shown in the following table is obtained.

[0036] Table 2 Group Standard Deviation Comparison Value Table ; As shown in Table 2, the absolute value sequence of the differences is the group standard deviation comparison value input to the subsequent sub-module.

[0037] Based on the group standard deviation comparison value, the trend frequency analysis sub-module sets the quantile parameter as the percentage of the comparison value interval, counts the number of test questions with comparison values lower than the parameter, calculates the quantity ratio, and generates the trend reverse frequency rate; The quantile parameter is the 25th percentile of the group standard deviation comparison value interval; The trend frequency analysis sub-module is based on the array composed of the "absolute value of the difference" field in the above table, for example, it is . First, determine the threshold according to the set quantile parameter. If the set is the 25th percentile, it is necessary to determine the value in the 25% position of the array as the threshold. That is, first sort the array in ascending order as . The 25% quantile position is in the second item, and the threshold is set to 0.06. Then count the number of test questions with comparison values less than this threshold. In this example, there is 1 value (0.02) lower than 0.06, and the corresponding test question is Q3. The total number of test questions is 5. The frequency rate calculation formula is: , this result is the trend reverse frequency rate, providing a frequency input item for the subsequent generation of the heat map.

[0038] The trend layer synthesis sub-module calls the population standard deviation comparison value and the trend reverse frequency rate, maps the comparison value to the bar height, maps the frequency rate to the heat color scale, aligns the coordinate axes to generate a composite layer, and outputs a heat map of the resolution failure distribution; The mapping rule of the heat color scale is to map the frequency rate proportionally to the red-blue gradient color scale.

[0039] The trend layer synthesis sub-module calls the absolute value of the difference in Table 2 as the height value of the bar chart, that is, the column heights of each test question correspond to , and at the same time calls the trend reverse frequency rate of 0.2 in Paragraph 11, sets this frequency value as the reference input for the heat color scale mapping, maps it to the cold color area in the color scale value, for example, 0.2 corresponds to the color scale #ADD8E6 (light blue), and then matches the above data according to the unified coordinate axis. The X-axis is set as the test question numbers Q1 to Q5, the Y-axis is the column height formed by the standard deviation difference, and the Z-axis is the frequency reflection shown by the color level. Draw the main graph according to the column value, and at the same time apply the corresponding color scale filling process to each column according to the frequency rate value. Finally, the output is a heat map of the resolution failure distribution that comprehensively displays the standard deviation difference and the trend reverse frequency.

[0040] Please refer to Figure 6 , the abnormal test question determination module includes: The space overlay sub-module calls the hierarchical height parameters of the three-axis radar chart coordinates, the intensity distribution surface data of the three-dimensional distribution cloud map of the fluctuation intensity, and the heat color scale parameters of the heat map of the resolution failure distribution, aligns the three types of data according to the space coordinates, and overlays the layers through the coordinate system fusion algorithm to generate a multi-source space overlay map; The coordinate system fusion algorithm is the affine transformation algorithm, and the alignment parameters include the translation matrix and the scaling factor; The space overlay sub-module first calls the hierarchical height parameters of each point in the three-axis radar chart coordinates, such as the sequence , which represents four spatial levels, and then calls the intensity value matrix in the three-dimensional distribution cloud map of the fluctuation intensity. For example, the intensity value at the corresponding position is , and the heat color scale parameters in the heat map of the resolution failure distribution, such as the color scale value is , based on the alignment of the coordinate numbers, that is, the three values respectively belong to the same spatial point under the same number position, and then a three-dimensional coordinate system is established. The hierarchical height in the three-axis radar chart is used as the Z-axis input, the fluctuation intensity is mapped as the Y-axis numerical dimension, and the heat color scale is used as the X-axis spatial color scale channel data. Coordinate fusion processing is performed on the unified input of these three types of data. During the processing, the data points with the same number are merged in coordinates and represented in the form of a triple , such as the point P1 with the number is , the number P2 is , mapped to the fusion layer in sequence, and through continuous three-dimensional grid construction, a three-dimensional visual area after the superposition of three types of spatial indicators is formed, and finally a multi-source spatial superposition map is formed.

[0041] Based on the multi-source spatial superposition map, the anomaly screening sub-module sets the triaxial instability threshold as the quantile of the hierarchical height fluctuation range, defines the reverse offset benchmark of the heat map as the percentage of the color scale intensity range, screens the coordinate point set with the hierarchical height exceeding the threshold and the color scale intensity lower than the benchmark, and generates a candidate set of anomaly points; The triaxial instability threshold is the 90% quantile of the hierarchical height fluctuation range, and the reverse offset benchmark is the 20% quantile of the heat map color scale intensity range; Based on the multi-source spatial superposition map constructed above, the anomaly screening sub-module first obtains the hierarchical height parameters of all points, such as the sequence , calculates its variation range and sets the triaxial instability threshold, which is set as the 90% quantile according to the hierarchical height distribution. After ascending order, the 5th item is taken as the threshold, which is 8. Subsequently, the heat map color scale intensity of all points is extracted, such as the value is , calculates the maximum value of its interval range as 0.7, and sets the reverse offset benchmark of the heat map as the 30th percentile, that is, take , and based on this, a double-condition screening operation is performed on all data points, screening the points with the hierarchical height greater than 8 and the heat value less than 0.21. For example, the hierarchical height of the number P4 is 8, which is exactly equal to the threshold and is not included. The height of the number P6 is 9 and the heat value is 0.7, which does not meet the conditions. The height of the number P3 is 5 and does not meet the height condition. Finally, if only the number P5 has a height of 9 and a heat map color scale of 0.2, which meets all the conditions, it is screened out as a candidate set of anomaly points.

[0042] The result generation sub-module calls the intensity mean value of the three-dimensional distribution cloud map of the coordinate number and fluctuation intensity of the candidate set of anomaly points, calculates the fluctuation amplitude of the candidate ability corresponding to each coordinate number, maps the anomaly points according to the spatial coordinates to generate a distribution map, constructs a matrix relationship between the coordinate number and the fluctuation amplitude, and generates a distribution map of the anomaly points of the test question quality and a correlation matrix map of the candidate ability fluctuation; The calculation formula for the candidate ability fluctuation amplitude is fluctuation amplitude = intensity mean value × hierarchical height.

[0043] The result generation sub-module calls the numbered position included in the candidate set of anomaly points. For example, the number P5, the intensity value in the three-dimensional distribution cloud map of the corresponding fluctuation intensity is 0.58. Then, the dispersion index of the scores of the corresponding candidate group at this spatial position under this number is extracted. Based on 0.41 as the base value, the ability fluctuation amplitude is calculated for this point, that is, the difference is taken , a matrix mapping is established between the point number and its fluctuation amplitude. The rows of the matrix are set as the number P5, the columns are the amplitude values, and the value is 0.17. At the same time, according to the original spatial coordinates of the number P5 in the multi-source spectrum , a marked node is drawn at the corresponding position in the figure and regarded as an abnormal point of the test question quality. The fluctuation amplitude is represented by the color intensity and size ratio in the same layer. Finally, a distribution map of abnormal points of the test question quality is formed, and an ability fluctuation correlation matrix diagram as shown in the following table is constructed.

[0044] Table 3 Correlation Matrix Diagram of Candidates' Ability Fluctuation ; As shown in Table 3, this matrix describes the direct relationship between the abnormal spatial position and the change of candidates' ability, providing data support for subsequent quality assessment.

[0045] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any person skilled in the art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes and apply them to other fields. However, as long as the technical solution content of the present invention is not departed from, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention still belong to the protection scope of the technical solution of the present invention.

Claims

1. A visual chart system for analyzing the quality of test questions and the abilities of test takers, characterized in that, The system includes: A dynamic data preprocessing module, which is used to extract the score difference between adjacent questions, call the differential absolute value algorithm to generate a question jump heat distribution map, count the jump frequency to generate a fluctuation frequency scatter plot, calculate the sliding average offset rate to generate an offset rate line time series plot, and transmit it to the sliding window adaptive adjustment module; A sliding window adaptive adjustment module, which is used to compare window parameters through the received question jump heat distribution map, the fluctuation frequency scatter plot, and the offset rate line time series plot, adjust the boundary to generate a sliding window dynamic coverage area map, and transmit it to the multi-axis fluctuation intensity analysis module; A multi-axis fluctuation intensity analysis module, which is used to calculate the upward slope within the received sliding window dynamic coverage area map to generate the coordinates of a three-axis radar chart, count the downward frequency ratio, calculate the recovery period to generate a three-dimensional distribution cloud map of fluctuation intensity, and transmit it to the population trend decomposition module and the abnormal question determination module; A population trend decomposition module, which is used to divide high and low score groups to generate a bar chart comparing population standard deviations, count the frequency of trend reversal to generate a density map of trend direction deviation, overlay the charts to generate a heat distribution map of resolution failure, and transmit it to the abnormal question determination module.

2. The visualization chart system for analyzing the quality of test questions and the capabilities of test takers according to claim 1, wherein The sliding window dynamic coverage area map includes window coverage density, boundary threshold interval, and dynamic weight coefficient. The coordinates of the three-axis radar chart specifically refer to the upward slope extreme value, downward frequency clustering, and recovery period span. The three-dimensional distribution cloud map of fluctuation intensity includes intensity gradient layer, frequency aggregation node, and period distribution contour line. The bar chart comparing population standard deviations is specifically the difference in standard deviations between high and low score groups, the cumulative value of trend reversal, and the population dispersion ratio. The density map of trend direction deviation includes the difference in standard deviation comparison, trend deviation density, and heat overlay area. The heat distribution map of resolution failure covers the resolution attenuation area, population offset overlap band, and standard deviation imbalance node.

3. The visualization chart system for analyzing the quality of test questions and the capabilities of test takers according to claim 2, characterized in that, The differential order of the differential absolute value algorithm is the first-order differential, and the color scale encoding value mapping rule is to proportionally map the absolute value of the difference to the 0-255 gray scale interval; The normalization calculation model for the window parameter comparison is window parameter difference degree = 0.4 × color scale difference + 0.3 × scatter density difference + 0.3 × ratio difference; The calculation basis of the upward slope is the ratio of the horizontal axis change rate to the time axis change rate, where the horizontal axis change rate = Δx / Δt and the time axis change rate = Δy / Δt; The generation logic of the dynamic weight coefficient is the reciprocal of the product of the window coverage density and the boundary threshold interval; The recovery period span is the weighted sum of the mean and standard deviation of the difference in adjacent layer heights.

4. The visualization chart system for analyzing the quality of test questions and the capabilities of test takers according to claim 3, wherein The dynamic data preprocessing module includes: The jump heat distribution sub-module obtains the adjacent question score sequence, calls the differential absolute value algorithm to calculate the absolute value of the adjacent score difference item by item, arranges the differences in a continuous sequence according to the question number, converts the difference sequence into a color scale encoding value through color mapping, and constructs a two-dimensional coordinate point set based on the question number and the color scale encoding value to generate a question jump heat distribution map; The color scale encoding value mapping rule is to proportionally map the absolute value of the difference to the 0-255 gray scale interval; The fluctuation frequency statistics sub-module sets a jump amplitude reference value based on the jump amplitude values of the test question jump heat distribution map, counts the cumulative number of times the jump amplitudes at multiple test question positions exceed the reference value, connects the test question numbers with the cumulative number of times to generate scatter coordinates, and outputs a fluctuation frequency scatter plot; The jump amplitude reference value is the 75th percentile of all test question jump amplitude values; The offset rate time series generation sub-module calls the jump amplitude sequence of the test question jump heat distribution map, divides it into equal-length window segments, calculates the difference ratio between the mean value within the window and the global mean value, connects the center time point of the window with the ratio value to generate an offset rate line time series graph; The calculation formula for the difference ratio is ratio = (window mean - global mean) / global mean × 100%.

5. The visualization chart system for analyzing test question quality and test taker ability according to claim 4, wherein The sliding window adaptive adjustment module includes: The parameter comparison sub-module calls the color scale encoding values of the test question jump heat distribution map, extracts the difference between the maximum and minimum values of the color scale, and at the same time calls the scatter density values of the fluctuation frequency scatter plot, extracts the difference between the maximum and minimum values of the density, and calls the ratio values of the offset rate line time series graph, extracts the difference between the peak and valley values of the ratio, and inputs the three differences into the normalization calculation model to generate the window parameter difference degree; The weighting coefficients of the normalization calculation model are 0.4 for the color scale difference weight, 0.3 for the scatter density difference weight, and 0.3 for the ratio difference weight; The boundary adjustment sub-module sets a horizontal coverage threshold and a vertical expansion reference based on the window parameter difference degree, screens the window numbers with difference degrees exceeding the threshold, adjusts the expansion amplitudes of the left and right boundaries and the up and down boundaries of the window, and generates dynamic window boundary parameters; The horizontal coverage threshold is 1.5 times the mean value of the window parameter difference degree, and the vertical expansion reference is 0.8 times the standard deviation of the difference degree; The dynamic coverage construction sub-module calls the dynamic window boundary parameters, extracts the window boundary coordinates, calculates the difference in the distance between adjacent windows, fills in the difference through interpolation to generate a continuous trajectory, and outputs a sliding window dynamic coverage area map; The algorithm for filling in the difference through interpolation is the cubic spline interpolation method.

6. The visualization chart system for analyzing test question quality and test taker ability according to claim 5, characterized in that The multi-axis fluctuation intensity analysis module includes: The radar chart coordinate calculation sub-module calls the coverage trajectory coordinates of the sliding window dynamic coverage area map, extracts the differences in the horizontal axis, vertical axis, and time axis coordinates of the starting point and the ending point of the trajectory, calculates the ratio of the change rates in the three-axis directions, maps the change rate in the horizontal axis to the polar radius length, maps the change rate in the vertical axis to the angle increment, and maps the change rate in the time axis to the hierarchical height to generate three-axis radar chart coordinates; The calculation formula for the ratio of the change rates in the three-axis directions is change rate in the horizontal axis = Δx / Δt, change rate in the vertical axis = Δy / Δt, change rate in the time axis = Δz / Δt; The downward frequency analysis sub-module sets the downward fluctuation reference value as 50% of the mean value of the polar radius length based on the polar radius length of the three-axis radar chart coordinates, counts the cumulative number of times the polar radius length is lower than the reference value, calculates the ratio of the cumulative number of times to the total number of trajectory points, and generates a downward frequency ratio; The calculation formula for the downward fluctuation reference value is reference value = polar radius length mean × 0.5; The cloud map generation sub-module calls the ratio of the hierarchical height to the downlink frequency of the three-axis radar map coordinates, extracts the difference in adjacent hierarchical heights to calculate the average recovery period, and inputs the hierarchical height, frequency ratio, and average recovery period into a three-dimensional interpolation model to generate a three-dimensional distribution cloud map of the fluctuation intensity; The three-dimensional interpolation model is the Kriging interpolation algorithm.

7. The visualization chart system for analyzing the quality of test questions and the abilities of test takers according to claim 6, wherein The population trend decomposition module includes: The population division sub-module calls the original score data, extracts the score data in the high score threshold interval and the low score threshold interval, calculates the standard deviation of the scores of multiple questions in the two intervals, aligns the two standard deviations according to the question numbers, and calculates the absolute value of the difference in the standard deviations of the high and low score groups under the same question number to generate a population standard deviation comparison value; The high score threshold interval is the score data of the top 30% of the total scores, and the low score threshold interval is the score data of the bottom 30% of the total scores; The trend frequency analysis sub-module, based on the population standard deviation comparison value, sets the quantile parameter as the percentage of the comparison value interval, counts the number of questions with a comparison value lower than the parameter, calculates the quantity ratio, and generates a trend reverse frequency rate; The quantile parameter is the 25% quantile of the population standard deviation comparison value interval; The trend layer synthesis sub-module calls the population standard deviation comparison value and the trend reverse frequency rate, maps the comparison value to the column height, maps the frequency rate to the heat color scale, aligns the coordinate axes to generate a composite layer, and outputs a heat map of the resolution failure distribution; The mapping rule of the heat color scale is to map the frequency rate proportionally to the red-blue gradient color.

8. The visual graph system for analyzing the quality of test questions and the abilities of test takers according to claim 7, characterized in that, The system further includes: The abnormal question determination module is used to spatially superimpose the received three-axis radar map coordinates, the three-dimensional distribution cloud map of the fluctuation intensity, and the heat map of the resolution failure distribution, screen the areas with three-axis instability and reverse offset in the heat map, and generate a distribution map of abnormal question quality points and a correlation matrix map of candidate ability fluctuations; The distribution map of abnormal question quality points includes abnormal clustering areas, offset correlation nodes, and instability coordinate mappings. The correlation matrix map of candidate ability fluctuations is specifically the ability fluctuation trajectory, abnormal question correlation degree, and population offset synchronization rate.

9. The visualization chart system for analyzing the quality of test questions and the capabilities of test takers according to claim 8, wherein The abnormal question determination module includes: The spatial superposition sub-module calls the hierarchical height parameter of the three-axis radar map coordinates, the intensity distribution surface data of the three-dimensional distribution cloud map of the fluctuation intensity, and the heat color scale parameter of the heat map of the resolution failure distribution, aligns the three types of data according to the spatial coordinates, and superimposes the layers through a coordinate system fusion algorithm to generate a multi-source spatial superposition map; The coordinate system fusion algorithm is the affine transformation algorithm, and the alignment parameters include the translation matrix and the scaling factor; The abnormal screening sub-module, based on the multi-source spatial superposition map, sets the three-axis instability threshold as the quantile of the hierarchical height fluctuation interval, defines the heat map reverse offset benchmark as the percentage of the color scale intensity interval, screens the coordinate point set with a hierarchical height exceeding the threshold and a color scale intensity lower than the benchmark, and generates a candidate set of abnormal points; The three-axis instability threshold is the 90% quantile of the hierarchical height fluctuation interval, and the reverse offset benchmark is the 20% quantile of the heat color scale intensity interval; The result generation sub-module calls the coordinate numbers of the abnormal point candidates in the set and the intensity mean of the three-dimensional distribution cloud map of the fluctuation intensity, calculates the fluctuation amplitude of the candidate ability corresponding to each coordinate number, maps the abnormal points according to the spatial coordinates to generate a distribution map, constructs a matrix relationship between the coordinate numbers and the fluctuation amplitude, and generates a distribution map of abnormal points of test question quality and a correlation matrix map of candidate ability fluctuations; The calculation formula for the candidate ability fluctuation amplitude is: fluctuation amplitude = intensity mean × layer height.

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