Cloud-edge collaborative mathematical experiment virtual-real synchronization system and method thereof

Abstract

The invention discloses a virtual-real synchronization system and a virtual-real synchronization method for a mathematical experiment based on cloud-edge collaboration, relates to the technical field of cloud-edge collaboration, and realizes dynamic correction of an experiment result by collecting physical experiment data at a terminal and combining a theoretical probability model. When the experimental sample size is insufficient or the experimental deviation is too large, the system can generate an adjustment factor based on the network and edge computing state, and request compensation data from the cloud. And the cloud end generates high-correlation preprocessed data by using a historical data set and combining compressed sampling processing, so that delay caused by large-scale data transmission is avoided. And then, the terminal performs weighted fusion on the physical experiment data and the compensation data according to the fusion weight to obtain a more accurate and stable mixed experiment result, and the result is visually displayed by a probability distribution curve. According to the invention, the authenticity of the experiment and the statistical reliability are considered, and the data transmission efficiency and the processing real-time performance are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of cloud-edge collaboration, in particular to a mathematical experiment virtual-real synchronization system and method based on cloud-edge collaboration. BACKGROUND

[0002] With the development of education informatization and intelligent computing, mathematical experiments are gradually evolving from traditional physical experiments to a combination of virtual and real methods. By collecting experimental data on terminal devices and analyzing virtual calculation results, not only can the intuitiveness and interactivity of the experiment be enhanced, but also the sample size of the experiment can be expanded to some extent, thereby improving the reliability of the statistical results. Under the promotion of new computing modes such as cloud computing and edge computing, the virtual-real synchronization method of mathematical experiments has gradually become an important application direction in teaching and scientific research.

[0003] However, in the existing virtual-real synchronization process of mathematical experiments, there are still some problems: when the sample size of physical experiments is small or the experimental frequency deviates greatly from the theoretical probability, the statistical reliability of the experimental results is insufficient, and usually the cloud compensation data is used to improve the reliability of the experimental results; but since the compensation data is usually large in scale, the transmission and processing efficiency is limited, which makes it difficult to integrate with the physical experimental data in time, thereby affecting the real-time and accuracy of the experimental results. SUMMARY

[0004] In view of the deficiencies in the prior art, the present application provides a mathematical experiment virtual-real synchronization system and method based on cloud-edge collaboration.

[0005] In order to achieve the above-mentioned purpose, the technical scheme of the present application is as follows:

[0006] In a first aspect, the present application discloses a mathematical experiment virtual-real synchronization method based on cloud-edge collaboration, comprising the following steps:

[0007] Obtaining physical experiment data collected by a terminal device; the physical experiment data includes an experiment type identifier, an experiment sample size, and a number of event occurrences, and a corresponding theoretical probability value is obtained according to the experiment type identifier;

[0008] Calculating an event frequency based on the physical experiment data, and calculating a confidence interval based on the theoretical probability value and the experiment sample size;

[0009] Judging whether the event frequency exceeds the confidence interval and whether the experiment sample size is lower than a preset sample size threshold;

[0010] If the judgment result is yes, generating an adjustment factor based on the current network bandwidth and the edge computing load rate, and sending a compensation data request containing the experiment type identifier and the adjustment factor to the cloud;

[0011] acquire a preprocessed data set returned by the cloud, the preprocessed data set being obtained by the cloud sampling and compressing a historical compensation data set according to a compression ratio determined according to an adjustment factor, and the historical compensation data set being obtained according to an experiment type identifier matching;

[0012] calculate a fusion weight based on the physical experiment data, perform weighted fusion on the physical experiment data and the preprocessed data set according to the fusion weight, and obtain mixed experiment data;

[0013] generate a probability distribution curve based on the mixed experiment data and send the probability distribution curve to a terminal device for display.

[0014] In a second aspect, the present application discloses a cloud-edge collaborative mathematical experiment virtual-real synchronization system, comprising:

[0015] a data acquisition module configured to acquire physical experiment data collected by a terminal device, wherein the physical experiment data comprises an experiment type identifier, an experiment sample size, and an event occurrence frequency, and a corresponding theoretical probability value is acquired according to the experiment type identifier;

[0016] an edge computing processing module configured to calculate an event frequency based on the physical experiment data, and calculate a confidence interval based on the theoretical probability value and the experiment sample size;

[0017] a judgment processing module configured to judge whether the event frequency is beyond the confidence interval and whether the experiment sample size is lower than a preset sample size threshold;

[0018] a judgment response module configured to, when the judgment results are both yes, generate an adjustment factor based on a current network bandwidth and an edge computing load state, and send a compensation data request containing the experiment type identifier and the adjustment factor to the cloud;

[0019] a preprocessed data set acquisition module configured to acquire a preprocessed data set returned by the cloud, wherein the preprocessed data set is obtained by the cloud performing the following operations:

[0020] matching a historical compensation data set according to an experiment type identifier, and determining a compression ratio according to the adjustment factor;

[0021] sampling and compressing the historical compensation data set according to the compression ratio, and taking the compressed data set as the preprocessed data set;

[0022] a data fusion module configured to calculate a fusion weight based on the physical experiment data, perform weighted fusion on the physical experiment data and the preprocessed data set according to the fusion weight, and obtain mixed experiment data;

[0023] a distribution curve generation module configured to generate a probability distribution curve based on the mixed experiment data and send the probability distribution curve to a terminal device for display.

[0024] Compared with the prior art, the present application has the following beneficial effects:

[0025] 1. By combining network bandwidth and edge computing load to generate an adjustment factor, the compensation data request is no longer fixed, but can be dynamically adjusted according to real-time resource conditions, thereby optimizing data transmission efficiency and resource utilization;

[0026] 2. By matching historical compensation data and performing compression sampling according to the adjustment factor, transmission of redundant data is avoided, the data volume is significantly reduced, and the relevance and timeliness of the compensation data are improved;

[0027] 3. The problem of large scale of cloud compensation data and difficulty in timely fusion in the existing mathematical experiment virtual-real synchronization method is effectively solved, and the comprehensive improvement of real-time performance, accuracy and resource optimization utilization is realized. BRIEF DESCRIPTION OF DRAWINGS

[0028] The disclosure of the present application will be described with reference to the accompanying drawings. It should be understood that the drawings are for illustrative purposes only and are not intended to limit the scope of protection of the present application, and in the drawings, the same reference numerals are used to refer to the same parts. Among them:

[0029] Figure 1 is a flow chart of the method of the present application;

[0030] Figure 2 is a data flow chart of the present application;

[0031] Figure 3 is a specific strategy diagram of sampling compression of the present application;

[0032] Figure 4 is a system architecture diagram of the present application. DETAILED DESCRIPTION

[0033] It is easy to understand that according to the technical scheme of the present application, those skilled in the art can propose a plurality of structure modes and implementation modes which can be replaced with each other without changing the essential spirit of the present application. Therefore, the following specific embodiments and drawings are only exemplary descriptions of the technical scheme of the present application, and should not be regarded as the whole or as a limitation or restriction on the technical scheme of the present application.

[0034] In the existing virtual-real synchronous process of mathematical experiments, when the sample size of real experiments is insufficient or the event frequency deviates significantly from the theoretical probability, the system needs to rely on cloud compensation data to improve the statistical reliability. However, the cloud historical data set is large in size, and its transmission process is restricted by network bandwidth fluctuations and edge computing node load state, making it difficult to dynamically adapt the data compression and transmission efficiency to real-time environmental changes. At the same time, when the matching degree of the event distribution characteristics of the historical data set and the current experimental scene is insufficient, direct data fusion may cause statistical bias accumulation, thereby reducing the effectiveness of the mixed experimental data.

[0035] For example, in a probability and statistics experiment based on an edge computing node deployment, when the sample size of the coin toss experiment collected by the terminal device is only 60% of the preset threshold and the measured frequency of the positive side exceeds the confidence interval, the edge node needs to request historical compensation data from the cloud. At this time, if the network bandwidth decreases to 75% of the baseline value and the edge computing load rate reaches 80%, the traditional fixed compression ratio transmission mechanism will cause the historical data set transmission delay to exceed the real-time requirement threshold. At the same time, there is an abnormal distribution section of 10 consecutive positive events in the cloud historical data set, and if event sequence feature recognition and differential processing are not performed in the compression process, direct fusion will distort the event distribution law of the mixed experimental data.

[0036] If the above problems are not solved, the dynamic resource coordination capability of the experimental system will not meet the real-time requirements of virtual-real data fusion, resulting in a lag in the generation of probability distribution curves relative to the teaching demonstration rhythm. Improper handling of abnormal event sections during data compression will disrupt the visual presentation of statistical laws, causing mixed experimental data to deviate from the theoretical probability model and reducing the reliability of statistical inference conclusions in the experimental teaching process. The continuous execution of inefficient data compression and transmission tasks by the edge computing node under high load conditions will also exacerbate the fragmentation of computing resources and affect the response stability of the system to concurrent experimental requests.

[0037] In the face of the above problems, the present application first addresses the constraints of network bandwidth fluctuations and edge computing load on data transmission efficiency. The traditional fixed compression mechanism cannot adapt to real-time environmental changes, so the present application considers introducing dynamic adjustment factors for network bandwidth and load rate to generate an adaptive compression ratio by quantitatively evaluating the current transmission environment. At the same time, to eliminate the distribution differences between historical data and the current experimental scene, the present application analyzes the volatility characteristics and concentration indicators of event sequences and establishes a compression ratio correction mechanism based on event distribution characteristics to ensure that statistical laws are preserved during compression of key sections. Further, the present application finds that simply increasing the amount of compensation data can cause sample weight imbalance, so a dynamic fusion weight based on the experimental sample size threshold is designed to achieve statistical balance of virtual-real data through weighted fusion.

[0038] To this end, as Figure 1As shown, the present application proposes a cloud-edge collaborative mathematical experiment virtual-real synchronization method, including the following steps:

[0039] Obtaining physical experiment data collected by a terminal device; the physical experiment data includes an experiment type identifier, an experiment sample size, and an event occurrence frequency, and a corresponding theoretical probability value is obtained according to the experiment type identifier; the physical experiment data refers to the data generated in the actual experiment collected by the terminal device, and the experiment type identifier, the experiment sample size, and the event occurrence frequency can be obtained by using a sensor or a manual input method, and the experiment type identifier is used to match the corresponding theoretical probability value database.

[0040] Calculating an event frequency based on the physical experiment data, and calculating a confidence interval based on the theoretical probability value and the experiment sample size; the confidence interval refers to a statistical range calculated based on the theoretical probability value and the experiment sample size, and can be realized by using a standard normal distribution quantile combined with a probability variance formula, and is used to judge whether the experiment frequency deviates from the theoretical expectation.

[0041] Judging whether the event frequency exceeds the confidence interval and whether the experiment sample size is lower than a preset sample size threshold; the preset sample size threshold refers to a pre-set minimum effective sample size standard, and can be set according to statistical significance requirements, and is used to judge whether the current experiment data size is insufficient.

[0042] If the judgment results are all yes, generating an adjustment factor based on the current network bandwidth and the edge computing load rate, and sending a compensation data request containing the experiment type identifier and the adjustment factor to the cloud; the adjustment factor refers to an adjustment coefficient dynamically generated according to the real-time network bandwidth and the edge computing load, and can be realized by calculating a bandwidth reference ratio and a load rate, and is used to control the data compression ratio of the cloud to balance the transmission efficiency and the data quality.

[0043] Obtaining a pre-processing data set returned by the cloud, the pre-processing data set being obtained by sampling and compressing a historical compensation data set by the cloud according to a compression ratio, the compression ratio being determined according to the adjustment factor, and the historical compensation data set being obtained by matching according to the experiment type identifier; the pre-processing data set refers to a data set obtained by sampling and compressing the historical compensation data by the cloud, and can be realized by using a combination of key segment interval sampling and ordinary segment random sampling, and is used to reduce the transmission amount on the premise of ensuring the data distribution characteristics.

[0044] Calculating a fusion weight based on the physical experiment data, and performing weighted fusion on the physical experiment data and the pre-processing data set according to the fusion weight to obtain mixed experiment data; the fusion weight refers to the weighting ratio of the physical experiment data and the pre-processing data set in the mixing, and can be dynamically calculated by using the ratio of the experiment sample size and the preset threshold, and is used to optimize the statistical reliability of the mixed data.

[0045] Generate a probability distribution curve based on the mixed experimental data and send it to the terminal device for display. The probability distribution curve refers to the visualization result of the event occurrence probability generated based on the mixed experimental data. It can be realized by using a histogram or kernel density estimation method, which is used to visually display the experimental statistical results.

[0046] The core innovation of the present application is to dynamically adjust the virtual-real data fusion process through cloud-edge collaborative mechanism. When detecting insufficient experimental samples or statistical bias, the historical data is intelligently compressed based on network status and the mixing weight is optimized, which not only ensures the effective transmission of compensation data but also improves the statistical reliability of the mixed results. The scheme solves the problem of low transmission efficiency of compensation data in traditional virtual-real synchronization, which leads to poor real-time performance. At the same time, through the weighted fusion mechanism, the credibility of small sample experiments is enhanced.

[0047] As shown in Figure 2 , it is a data flowchart of the present application; as a preferred embodiment, the scheme of the present application is implemented as follows:

[0048] In a probability statistical experiment, the terminal device collected 100 coin toss experiment data, of which 52 were heads up and 48 were tails up. The experiment type identifier is "coin_toss" and the theoretical probability value is 0.5.

[0049] First, calculate the event frequency as 52 / 100=0.52, and the confidence interval as [0.415, 0.585]. Since the event frequency is outside the confidence interval and the experimental sample size 100 is lower than the preset sample size threshold 500, the compensation data request is triggered.

[0050] Assume that the current network bandwidth is 80Mbps, the baseline bandwidth is 100Mbps, and the edge computing load rate is 60%. The adjustment factor is calculated as 0.32. Send a compensation data request to the cloud containing the "coin_toss" identifier and the adjustment factor 0.32.

[0051] The cloud determines the compression ratio as 0.4 according to the adjustment factor 0.32, samples and compresses the historical compensation data set, and returns a preprocessed data set containing 400 experiment data, of which the number of heads is 203 and the number of tails is 197.

[0052] Calculate the fusion weight as 0.2. Weighted fusion of real experiment data and preprocessed data set:

[0053] The mixed number of heads is: 52x0.2+203x0.8=172.8;

[0054] The mixed number of tails is: 48x0.2+197x0.8=167.2.

[0055] Based on the mixed experimental data, the probability distribution curve is generated, and the positive probability is about 0.508, which is closer to the theoretical probability 0.5.

[0056] Through the above scheme, the virtual and real synchronization of mathematical experiment in cloud edge cooperation is realized. By dynamically adjusting the data compression ratio, the network bandwidth and the change of computing load are adapted, and the data transmission efficiency is improved. The weighted fusion method is adopted, and the weights of the physical experiment data and the cloud compensation data are balanced, and the statistical reliability of the mixed experimental data is improved. The generated probability distribution curve more accurately reflects the theoretical probability model, and enhances the intuitiveness and reliability of the mathematical experiment. This method overcomes the limitations of the traditional fixed compression mechanism, improves the real-time and accuracy of the virtual and real data fusion, and provides more effective technical support for mathematical experiment teaching.

[0057] The application further proposes an acquisition process of the compression ratio, which includes:

[0058] The event distribution characteristic analysis is performed on the historical compensation data set to extract the event type concentration index and the event sequence fluctuation coefficient.

[0059] The dynamic adjustment factor is corrected based on the event type concentration index to generate a basic compression ratio.

[0060] The basic compression ratio is dynamically compensated according to the event sequence fluctuation coefficient to obtain a final compression ratio.

[0061] The event distribution characteristic analysis quantifies the distribution concentration degree of different types of events in the data set by calculating the event type concentration index.

[0062] Event type concentration index is used to measure whether the data set is dominated by one or several event types. The higher the concentration, the more likely the data redundancy is, and the more space can be compressed.

[0063] For example:

[0064] The occurrence frequency of all event types (such as "heads" and "tails" in coin tossing) in the statistical historical compensation data set is counted.

[0065] The event type with the highest occurrence frequency is found, and its frequency is recorded as .

[0066] The total number of events in the historical compensation data set is counted .

[0067] Then is taken as the event type concentration index .

[0068] Event type concentration index is a value between 0 and 1. The larger the value (closer to 1), the more uneven the data distribution, the more concentrated.

[0069] The event sequence fluctuation coefficient is used to quantify whether there is an abnormally long continuous same event segment in the event sequence. Such a "long continuous segment" is often an anomaly or key phenomenon that needs to be focused on in a probability experiment and should be protected during compression.

[0070] For example:

[0071] Event sequence scanning is performed on the historical compensation data set to identify the maximum length segment of continuous same events , The number of events in the maximum length segment (for example, "positive" appears 10 times in a row);

[0072] Calculate the average continuous length of events in the entire sequence This can be estimated by dividing the total number of events by the number of event type change points.

[0073] Take as the event sequence fluctuation coefficient. The larger the value, the more "abnormal" the continuous segment in the sequence (i.e., a continuous segment far exceeding the average length), and a large value means that the sequence has a fluctuation characteristic that needs to be protected.

[0074] The generation of the basic compression ratio uses a sigmoid function to convert the event type concentration index into a weight, and a weighting calculation is performed in combination with an adjustment factor.

[0075] The dynamic compensation process protectsively adjusts the basic compression ratio according to whether the event sequence fluctuation coefficient exceeds a threshold value, and reduces the compression ratio of the key segment when the fluctuation coefficient is high.

[0076] Through the above technical solutions, the application realizes intelligent compression of historical compensation data sets. By introducing event distribution feature analysis, the characteristics of the data set can be more accurately grasped, and a more reasonable compression ratio can be generated. This method not only guarantees the representativeness of the compressed data, but also improves the efficiency of data transmission and processing, effectively solving the problem of low transmission and processing efficiency caused by the large size of compensation data in the prior art.

[0077] The application further proposes that the calculation process of the basic compression ratio is as follows:

[0078] Based on the adjustment factor The base compression ratio base is set to :

[0079] , wherein is a preset compression reference coefficient;

[0080] According to the event type concentration index Calculate concentration weight

[0081] , wherein , are preset sigmoid function parameters;

[0082] Calculate the basic compression ratio through the weighting formula

[0083] .

[0084] , wherein the compression reference coefficient is used to determine the initial compression base according to the adjustment factor , which is used to fine-tune the body compression strategy, and its value is pre-set by the staff according to the historical data size, ensuring that the initial compression base matches the current network resource state; the sigmoid function parameters , control the curve shape of the concentration weight , the slope , and the threshold , which functions to make rapidly approach 1 when the threshold is exceeded , and otherwise approach 0, so that the weight presents a nonlinear response to the change in the event type concentration index , and its value is configured by the staff according to historical experience values.

[0085] When the data concentration is high, i.e. is large, at this time tends to 1, , indicating that the data redundancy is high at this time, and a more aggressive compression is adopted.

[0086] When the data concentration is low, i.e. is small, at this time tends to 0, , indicating that the data distribution is uniform at this time, and the original compression ratio is maintained without aggressive processing.

[0087] The weighting formula dynamically combines the adjustment factor and the concentration weight to balance the comprehensive influence of event type concentration and network bandwidth, edge computing load.

[0088] For example, when is 0.8, is 1.2,​​ The calculation is 0.96.

[0089] Set 5, 0.5. Assuming 0.7, then The calculation result is about 0.73.

[0090] The basic compression ratio is calculated by the weighted formula:

[0091] .

[0092] Through the above technical solution, the application realizes adaptive basic compression ratio calculation based on adjustment factor and event type concentration. This method considers dynamic factors such as network bandwidth, computing load, and the characteristics of the data set itself, thereby ensuring data representation while improving compression efficiency. This adaptive calculation method can dynamically adjust the compression strength according to the actual situation, avoiding data distortion or low transmission efficiency caused by fixed compression ratio.

[0093] The application further proposes a calculation process of the final compression ratio, including:

[0094] Event sequence scanning is performed on the historical compensation data set to identify the maximum length segment of consecutive identical events;

[0095] Determine whether the event sequence fluctuation coefficient exceeds the preset fluctuation threshold;

[0096] If the result is yes, calculate the protection weight of consecutive identical events :

[0097] , wherein is the number of events in the maximum length segment, is the total number of events in the historical compensation data set;

[0098] Based on the protection weight of the same event Generate the final compression ratio :

[0099] ;

[0100] If the result is no, obtain the final compression ratio based on the basic compression ratio :

[0101] .

[0102] ​From the time dimension of the data, the most significant non-random, abnormal fluctuation pattern is located. In probability statistics, a long continuous same event (such as 10 consecutive heads) is a small probability event, and such "abnormalities" are often the objects that need to be observed and analyzed in mathematical experiments, so they can be retained when data compression.

[0103] Event sequence scanning is realized by traversing the time series data of the historical compensation data set, setting a temporary counter and a variable to record the current continuous event type and its length. Each event is checked in turn: if the next event is the same as the current event type, the counter is incremented by 1; if not, the counter is reset and the new event type is recorded. In the entire traversal process, the maximum continuous segment length encountered is compared and updated constantly, and its value is assigned to , , which represents the number of events contained in the longest continuous same event segment in the data set.

[0104] For example, in the coin toss sequence

positive, positive, positive, negative, positive, positive, positive, positive

[0105] The setting of the preset fluctuation threshold is to determine whether the fluctuation of the historical compensation data set is large enough to decide whether it is necessary to start the protective compensation mechanism; the preset fluctuation threshold is an empirical value, and its value is determined according to the event sequence fluctuation coefficient, for example, it can be set to 1.0. This means that when the maximum continuous segment length deviates from the average length by 100%, it is considered to be an abnormal significant fluctuation.

[0106] The calculation of the protection weight uses the ratio of the maximum continuous segment length to the total number of events, which can quantify the proportion of the most critical abnormal segment in the entire data set. The larger the value (closer to 1), the higher the importance of this abnormal segment in the global, and the stronger protection it needs to be given.

[0107] For example, , , then , which means that this long continuous segment accounts for 15% of the entire data volume.

[0108] When the event sequence fluctuation coefficient exceeds the preset fluctuation threshold, the final compression ratio calculation formula is:

[0109] ;

[0110] The formula uses a segmented weighting method, which essentially divides the entire data set into "normal part" and "key segment part that needs protection" for differential compression, and then takes the weighted sum.

[0111] : represents the compression performed on the non-critical segment part (occupying total data amount) . This part of data is processed according to the planned basic compression ratio

[0112] : represents the compression performed on the critical segment part (occupying total data amount)

[0113] The final obtained is the sum of the above two parts, which is the weighted average of the compression ratios of the above two parts. The final effect is:

[0114] In order to obtain effective protection for the critical segment, the overall compression ratio is slightly reduced, i.e. .

[0115] When the event sequence fluctuation coefficient does not exceed the preset fluctuation threshold, the final compression ratio calculation formula is:

[0116] .

[0117] At this time, it indicates that the event sequence fluctuation coefficient is within the acceptable normal range, indicating that no special sequence pattern is found that needs special protection. Therefore, the basic compression ratio determined by the network state and data concentration can be directly used without additional compensation.

[0118] For example, for a historical compensation data set containing 100 events, the maximum length of the continuous same event identified by scanning is 10 events.

[0119] At this time, the event sequence fluctuation coefficient is 0.6, which exceeds the set preset fluctuation threshold of 0.5, so the protection weight is 10 / 100=0.1.

[0120] The obtained is 0.8, so the final compression ratio is:

[0121] .

[0122] Through the above technical solution, this application can dynamically adjust the compression ratio according to the fluctuation of the event sequence, improving compression efficiency while ensuring data representativeness. For event sequences with large fluctuations, introducing a protection weight for consecutive identical events can effectively preserve key event information and avoid data distortion caused by over-compression. For event sequences with small fluctuations, directly using the basic compression ratio simplifies the calculation process and improves processing speed. This adaptive compression method can achieve a balance in different types of experimental data, ensuring both the quality of the compressed data and improving the efficiency of data transmission and processing.

[0123] like Figure 3 The diagram shown illustrates the specific sampling compression strategy in this application. This application further proposes sampling compression of the historical compensation dataset according to a compression ratio, including:

[0124] The event sequences in the historical compensation dataset are divided into key segments and ordinary segments. Segments with consecutive identical events having a length greater than 3 are designated as key segments, while the remaining events are designated as ordinary segments.

[0125] Based on the final compression ratio Calculate the compression ratios for critical sections and ordinary sections separately;

[0126] Based on the compression ratio of the key sections, the key sections are sampled at equal intervals.

[0127] Based on the compression ratio of the ordinary segment, random sampling is applied to the ordinary segment.

[0128] By comparing adjacent events during the traversal of the historical compensation dataset, all segments consisting of consecutive identical events are identified, and the starting index and length of each segment are recorded. Key segments and ordinary segments are divided according to the length of consecutive identical events. Consecutive identical events with a length greater than 3 are low-probability events (e.g., the probability of getting heads four times in a row is 6.25%), and have higher observation and analysis value. They are "anomalies" or "patterns" that need to be focused on in mathematical experiments. This method can efficiently separate "notable patterns" from "random noise or ordinary fluctuations".

[0129] Key segments are sampled at equal intervals to preserve the continuity of the event sequence.

[0130] For example:

[0131] For a length of The key sections, based on the compression ratio of the key sections. The number of events that need to be retained is calculated as follows: .

[0132] Then, with For step size, fixed interval sampling is performed within the segment.

[0133] Equal interval sampling can maximize the preservation of the continuity and trend of the original sequence. A consecutive 5 positive event segment may retain the 1st, 3rd, and 5th events after equal interval sampling, still presenting the pattern of "consecutive positive appearance", which is more mathematically valuable than random sampling which may only retain the middle two isolated points.

[0134] Random sampling is used in ordinary segments to reduce data redundancy.

[0135] For example:

[0136] All events in the ordinary segment are regarded as a set, and the number of events to be retained is calculated according to the compression ratio of the ordinary segment . Then, a random number generator is used to extract events from the set unbiasedly.

[0137] Random sampling is simple, efficient, and suitable for scattered data without obvious patterns. It can ensure that the sampling result represents the distribution of the original ordinary segment in a statistical sense, while maximizing the compression target.

[0138] Through the above technical solutions, the application realizes efficient data compression while ensuring data representation. Equal interval sampling of key segments ensures the preservation of important data features, while random sampling of ordinary segments maintains the overall distribution characteristics of the data. This differentiated sampling strategy not only reduces the burden of data transmission and processing, but also maintains the statistical properties of the data, thereby improving the efficiency and accuracy of virtual-real synchronization experiments. In addition, through special processing of consecutive identical events, this method can better capture important patterns and trends in the data, further enhancing the reliability of the experimental results.

[0139] The application further proposes to calculate the compression ratio of the key segment and the ordinary segment based on the final compression ratio . The process of calculating the compression ratio of the key segment and the ordinary segment respectively is as follows:

[0140] Based on the number and average length of the key segment, the key segment coverage is calculated .

[0141] ;

[0142] Wherein, N is the number of key segments, L is the average number of events in the key segment, T is the total number of events in the historical compensation data set;

[0143] Based on the key segment coverage , the key event compression coefficient is generated respectively , common event compression coefficient :

[0144] ;

[0145] ;

[0146] key event compression coefficient , common event compression coefficient respectively calculate the compression ratio of key segment and common segment:

[0147] The compression ratio of key segment is:

[0148] ;

[0149] The compression ratio of common segment is:

[0150] .

[0151] The key segment coverage is calculated by the product of the number of key segments, the average event quantity and the total number of events, which is used to quantify the relative scale and influence of key segments in the entire historical data set, and to accurately measure the "portion" of data that needs to be specially protected.

[0152] Key segment coverage The calculation formula is ; the numerator represents the total quantity of events contained in the key segment, and the denominator is the sum of the number of events in the historical compensation data set; thus, The actual physical meaning of means that 25% of the events in the entire data set belong to those longer continuous patterns that need to be protected.

[0153] Linearly map the key segment coverage key event compression coefficient , common event compression coefficient , which is used to adjust the compression strength of key segment and common segment.

[0154] When , there is no key segment; at this time , This set of values as the benchmark defines the initial resource tilt allocation strategy, that is, even without key segments, the compression of common segments ( ) is more aggressive than the overall level by default, thus reserving protection space for potential key data that may exist.

[0155] With the increase of the key segment coverage, the key segment compression coefficient becomes smaller, which directly reduces the compression ratio of the key segment, and achieves stronger protection. On the contrary,

[0156] With the increase of the key segment coverage, the key segment compression coefficient becomes smaller, which directly reduces the compression ratio of the key segment, and achieves stronger protection. With the increase of the key segment coverage, the key segment compression coefficient becomes smaller, which directly reduces the compression ratio of the key segment, and achieves stronger protection.

[0157] The key segment coverage The coefficient of the linear mapping is 0.3, reflecting the sensitivity of the entire change; and , The average value is 1, which means that the compression resources are in a "trade-off" relationship between the key segment and the ordinary segment, and the overall consistency with the is maintained.

[0158] Based on the product of , respectively, the compression ratio of the key segment and the ordinary segment is calculated. For example: when

[0159] , , At this time, the overall data needs to be compressed by 40%.

[0160] Based on the above parameters, the calculation process is as follows:

[0161] ;

[0162] ;

[0163] The key segment compresses 55.6% of the data.

[0164] 6;

[0165] ;

[0166] The ordinary segment compresses 24.4% of the data.

[0167] ​By the technical solution, the application realizes the differential compression of the key segment and the ordinary segment. The key segment has higher information density due to containing continuous same events, and thus a lower compression ratio is adopted to retain more information. On the contrary, the information density of the ordinary segment is lower, and a higher compression ratio can be adopted. The differential compression strategy can guarantee the representativeness of the compressed data and improve the data transmission and processing efficiency. Meanwhile, by introducing the key segment coverage As a regulation parameter, the compression ratio can be dynamically adjusted according to the actual data characteristics, further improving the adaptability and flexibility of the compression strategy.

[0168] The application further proposes a calculation process of the confidence interval as follows:

[0169] Obtain a theoretical probability value , an experimental sample size .

[0170] The lower limit value of the confidence interval is denoted as , and the calculation formula is as follows: .

[0171] The upper limit value of the confidence interval is denoted as , and the calculation formula is as follows: .

[0172] Wherein, is the standard normal distribution quantile corresponding to the preset confidence level.

[0173] The confidence interval is a scientific fault tolerance range of the event frequency, which can be understood as that when the event frequency is in the confidence interval, it can be considered as normal random fluctuation, rather than significant deviation that needs to be corrected. The confidence interval can be expressed as , and the mathematical basis is the central limit theorem and normal distribution property in probability theory.

[0174] The theoretical probability value represents the ideal probability of the event occurrence, which is the theoretical target that the physical experiment data tends to approach. For example, the of the coin tossing experiment is 0.5, and the probability of the occurrence of a certain point of the die is 1 / 6.

[0175] The experimental sample size represents the scale of the physical data. The larger the sample size is, the narrower the confidence interval is, and the stricter the judgment standard is.

[0176] is the quantile of the standard normal distribution, which is a constant corresponding to a preset confidence level. The confidence level is a probability value set in advance, indicating the reliability requirement for the judgment result, and is usually set to 95% or 99%. The value corresponding to the 95% confidence level is about 1.96, and the value corresponding to the 99% confidence level is about 2.58. The larger the value, the wider the confidence interval, the larger the tolerance range, and the more conservative the judgment. The larger the value, the wider the confidence interval, the larger the tolerance range, and the more conservative the judgment.

[0177] represents the variance of the theoretical probability. When the value is 0.5, the maximum value is 0.25, which means that the natural volatility of the data is the largest at this time, so the confidence interval is also the widest, which is completely consistent with the mathematical principle.

[0178] is the standard error, which is an index to measure the size of sampling error. is located in the denominator position, which is a key technical feature: The larger the value, the smaller the standard error, and the narrower the confidence interval, reflecting the statistical law that "the larger the sample size, the more accurate the estimation".

[0179] For example: taking a specific coin tossing experiment as an example to illustrate the calculation process:

[0180] The theoretical probability value is 0.5, the sample size is 50, and the preset 95% confidence level ( ) is set.

[0181] Calculate the standard error:

[0182] ;

[0183] Calculate the confidence interval:

[0184] ;

[0185] ;

[0186] The confidence interval is: .

[0187] Suppose that in 50 events, there are 30 heads, then

[0188] The event frequency . The judgment is true, then it is considered that the deviation is within the normal fluctuation range, and the compensation mechanism is not triggered.

[0189] If there are only 28 heads, then ​, also in the interval, the compensation mechanism is not triggered.

[0190] If there are only 15 positive faces, then , a significant deviation is judged, and the compensation mechanism is triggered.

[0191] Through the above technical scheme, the confidence interval of the experimental result can be accurately calculated, and the reliability of the experimental data is provided. By setting a reasonable confidence level, the accuracy and sensitivity of statistical inference can be effectively balanced. Further, the method can be applied to different types of probability experiments, and has wide application value. Since the calculation process is simple and intuitive, it is easy to implement on edge devices, thereby improving the efficiency of data processing.

[0192] The application further proposes a generation process of the adjustment factor as follows:

[0193] Obtain the current network bandwidth , edge computing load rate ;

[0194] Based on the current network bandwidth , edge computing load rate , a dynamic adjustment factor is calculated :

[0195] , wherein is a preset reference bandwidth.

[0196] The generation process of the dynamic adjustment factor contains two input parameters: the current network bandwidth obtained by real-time monitoring of the network transmission link, and the edge computing load rate collected through the edge node resource monitoring interface. The preset reference bandwidth is preset according to a typical network environment, and is used for normalizing the bandwidth parameter. The function limits the bandwidth ratio to less than 1 to avoid excessive amplification of the adjustment factor in a high bandwidth scenario. The edge computing load rate is represented by a value from 0 to 1, and when the load rate rises, the term causes the adjustment factor to decrease linearly, reducing the amount of compensation data requests.

[0197] When the network bandwidth is lower than the reference bandwidth, the ratio is less than 1, and the adjustment factor decreases with the decrease of the bandwidth. When the edge computing load rate rises, the term decreases, further reducing the value. The adjustment factor directly affects the compression ratio of the historical compensation data set by the cloud, The smaller the value, the higher the compression ratio used by the cloud, reducing the amount of data transmitted.

[0198] For example, when For 50Mbps, At 100Mbps, If at this time ,but Cloud-based A higher compression ratio is generated, compressing historical datasets to a corresponding ratio, significantly reducing transmission latency. This dynamic adjustment mechanism automatically balances data compensation needs with transmission processing efficiency when network bandwidth fluctuates or edge node load changes, ensuring that the generation process of mixed experimental data meets real-time requirements.

[0199] Through the above technical solution, this application can dynamically adjust the request intensity of cloud compensation data according to network transmission capacity and the real-time load status of edge computing nodes, avoiding overload transmission when network bandwidth is limited or edge computing resources are scarce, and ensuring efficient transmission of compensation data and stable operation of edge nodes. This adjustment mechanism effectively balances the contradiction between data transmission efficiency and system processing capacity by quantifying the coupling relationship between network and computing resources, thereby improving the reliability and real-time performance of the virtual-real experimental data fusion process.

[0200] This application further proposes a method for obtaining mixed experimental data as follows:

[0201] Obtain the experimental sample size and the preset sample size threshold;

[0202] The ratio of the experimental sample size to a preset sample size threshold is used as the fusion weight. ;

[0203] Process physical experimental data and preprocessed datasets separately according to event type;

[0204] For the same event type, the fusion weight is applied. The number of events and the number of events in the preprocessed dataset are linearly weighted and fused.

[0205] The number of occurrences of all event types is aggregated to form mixed experimental data.

[0206] Among them, the fusion weight The generation process is achieved by quantizing the experimental sample size to a preset threshold, and the upper limit of the weight is automatically limited when the sample size reaches the threshold.

[0207] The experimental sample size is denoted as The preset sample size threshold is denoted as Then the fusion weight for: .

[0208] For example, if a coin is tossed 50 times, 100 times, This means that the physical data accounts for 50% of the weight in the fusion, and the compensation data accounts for 50% of the weight. This respects the physical data and greatly corrects it with historical data.

[0209] Based on the fusion weight The purpose of linear weighted fusion is to allocate the weight to each specific event to generate the final mixed occurrence number.

[0210] According to the event type, it is the key to ensure the correctness of the algorithm. Each possible event type (such as "heads" and "tails" of a coin, "1 point" to "6 point" of a die) must be calculated independently.

[0211] For a specific event type, the formula for calculating the mixed occurrence number is:

[0212] ;

[0213] Where the physical occurrence number is the occurrence number of the event type counted from the physical experiment data this time; the compensation occurrence number is the occurrence number of the event type counted from the preprocessed compensation data set; is the weight of the compensation data, which is the fusion weight This is a trade-off to ensure that the sum is 1. Specific embodiments

[0215] Take the coin toss experiment as an example:

[0216] Physical data: toss 50 times, the result is {"heads": 28, "tails": 22}.

[0217] Compensation data: after preprocessing, it is {"heads": 23, "tails": 27}.

[0218] Calculate the fusion weight: , Then .

[0219] Linearly weighted fusion by event type:

[0220] The mixed number of heads is: .

[0221] The mixed number of tails is: .

[0222] The combined experimental data are summarized as follows: {"Front": 25.5, "Negative": 24.5}; here, only the meaning of the data is considered, so the number of times is also expressed in decimal places to ensure the integrity of the data.

[0223] Results: The actual data showed more heads (28 / 50=0.56), while the compensated data showed more tails (27 / 50=0.54). The fused result (25.5 / 50=0.51) is closer to the theoretical probability of 0.5, and also includes information from this experiment.

[0224] Through the above technical solution, this application effectively addresses the problem of low statistical reliability caused by insufficient sample size in physical experiments. By dynamically calculating the fusion weights, the original characteristics of the physical experimental data are preserved, while cloud-based compensation data supplements the sample size, thereby improving the rationality of the mixed data distribution. Simultaneously, the event-type-based grouping mechanism avoids data interference between different event types, ensuring the accuracy of the weighted fusion process, and ultimately significantly improving the reliability of statistical analysis while guaranteeing the real-time nature of experimental results.

[0225] like Figure 4 The diagram shown is a system architecture diagram of this application. This application further proposes a cloud-edge collaborative mathematical experiment virtual-real synchronization system, including a data acquisition module, an edge computing processing module, a judgment processing module, a judgment response module, a preprocessing dataset acquisition module, a data fusion module, and a distribution curve generation module.

[0226] The data acquisition module receives physical experimental parameters uploaded by terminal devices through a standardized data interface. The experiment type identifier triggers a query operation in the theoretical probability database, realizing the association and matching between theoretical values ​​and experimental data.

[0227] The edge computing processing module has a built-in confidence interval calculation unit that generates a confidence interval range based on theoretical probability values ​​and sample size, and generates real-time frequency data through the event frequency calculation unit.

[0228] The judgment and processing module integrates dual-condition judgment logic, which compares the event frequency with the confidence interval boundary value and performs difference calculation between the experimental sample size and the preset threshold.

[0229] The response determination module includes a network status monitoring unit, which collects bandwidth and edge computing load rate in real time, outputs adjustment factors through a dynamic factor generation algorithm, and encapsulates the factor and the experiment type identifier into a compensation request data packet.

[0230] The preprocessing dataset acquisition module establishes a compressed data transmission channel with the cloud to receive historical datasets after event sequence analysis and compression ratio adjustment.

[0231] The data fusion module adopts a weight dynamic allocation mechanism, generates a fusion weight according to a ratio of an experimental sample quantity to a threshold value, and performs weighted calculation on physical data and preprocessed data.

[0232] The distribution curve generation module is built-in with a probability distribution model, generates a curve image based on mixed data, and transmits the curve image to a terminal device through a display interface.

[0233] Through the above technical solution, the application effectively solves the problem of insufficient real-time caused by low transmission efficiency of cloud compensation data, reduces network bandwidth occupation through dynamic adjustment factor and hierarchical compression mechanism, realizes data collaborative optimization of edge side and cloud, and at the same time, adopts an adaptive fusion strategy based on a sample quantity threshold, corrects statistical deviation by using cloud historical data on the premise of ensuring the dominance of physical experiment data, and significantly improves the confidence of mixed experiment results. The modular design of the system makes the network resource scheduling, calculation task allocation and data fusion processing form a closed loop, and the stable virtual-physical data synchronization performance can be maintained when the edge computing load fluctuates.

[0234] The technical scope of the present application is not limited to the content in the above description, and those skilled in the art can make various modifications and changes to the above embodiments without departing from the technical idea of the present application, and these modifications and changes should all belong to the protection scope of the present application.

Claims

1. A cloud-edge collaborative mathematical experiment virtual-real synchronization method, characterized by: The method comprises the following steps: Obtaining physical experiment data collected by a terminal device; the physical experiment data comprises an experiment type identifier, an experiment sample size, and an event occurrence frequency, and a corresponding theoretical probability value is obtained according to the experiment type identifier; Calculating an event frequency based on the physical experiment data, and calculating a confidence interval based on the theoretical probability value and the experiment sample size; Determining whether the event frequency exceeds the confidence interval and whether the experiment sample size is lower than a preset sample size threshold; If the determination result is yes, generating an adjustment factor based on a current network bandwidth and an edge computing load rate, and sending a compensation data request comprising the experiment type identifier and the adjustment factor to a cloud; Obtaining a preprocessed data set returned by the cloud, wherein the preprocessed data set is obtained by sampling and compressing a historical compensation data set according to a compression ratio by the cloud, the compression ratio is determined according to the adjustment factor, and the historical compensation data set is obtained by matching according to the experiment type identifier; Calculating a fusion weight based on the physical experiment data, and performing weighted fusion on the physical experiment data and the preprocessed data set according to the fusion weight to obtain mixed experiment data; Generating a probability distribution curve based on the mixed experiment data and sending the probability distribution curve to the terminal device for display.

2. The cloud-edge collaborative mathematical experiment virtual-real synchronization method according to claim 1, characterized in that: The obtaining process of the compression ratio comprises: Performing event distribution feature analysis on the historical compensation data set to extract an event type concentration index and an event sequence fluctuation coefficient; Correcting a dynamic adjustment factor based on the event type concentration index to generate a basic compression ratio; Performing dynamic compensation on the basic compression ratio according to the event sequence fluctuation coefficient to obtain a final compression ratio.

3. The cloud-edge collaborative mathematical experiment virtual-real synchronization method according to claim 2, characterized in that: The calculation process of the basic compression ratio is as follows: Based on the adjustment factor Setting a base compression ratio base is: wherein is a preset compression reference coefficient; According to the event type concentration index Computing concentration weights : wherein, , are both preset sigmoid function parameters; Calculating the base compression ratio by a weighting formula : 。 4. The cloud-edge collaborative mathematical experiment virtual-real synchronization method according to claim 2, characterized in that: The calculation process of the final compression ratio comprises: Performing event sequence scanning on the historical compensation data set to identify the maximum length of continuous same events; Determining whether the event sequence fluctuation coefficient exceeds a preset fluctuation threshold; If the result of the judgment is yes, the protection weight of the continuous same event is calculated : wherein, is the number of events in the largest length segment, is the total number of events of the historical compensation dataset; Protection weights based on same event Generating final compression ratio : ； If the result of the judgment is No, the final compression ratio is obtained based on the base compression ratio :​ 。 5. The cloud-edge collaboration mathematical experiment virtual-real synchronization method according to claim 1, characterized in that: The sampling and compressing of the historical compensation data set according to the compression ratio comprises: Dividing the event sequence in the historical compensation data set into key segments and ordinary segments, wherein a segment with a continuous same event length greater than 3 is a key segment, and the rest of the events are ordinary segments; based on the final compression ratio the compression ratio of the key segment and the normal segment is calculated respectively; Performing equal interval sampling on the key segments based on the compression ratio of the key segments; Performing random sampling on the ordinary segments based on the compression ratio of the ordinary segments.

6. The cloud-edge collaboration mathematical experiment virtual-real synchronization method according to claim 5, characterized in that: based on the final compression ratio The process of calculating the compression ratio of the key segment and the normal segment respectively is as follows: Based on the number of key segments and the average length, the key segment coverage is calculated : ； wherein, is the number of key segments, is the average event quantity in the key segments, is the total event number of the historical compensation dataset; Based on key segment coverage Generating key event compression coefficients respectively : ordinary event compression coefficients ； ； Key event compression coefficient Normal event compression coefficient Calculate the compression ratio of key segment and normal segment respectively: The compression ratio of the key segments is: ； The compression ratio of the ordinary segments is: 。 7. The cloud-hetnet mathematical experiment virtual-real synchronization method according to claim 1, characterized in that: The calculation process of the confidence interval is: Acquiring theoretical probability value , experimental sample size ; The lower limit value of the confidence interval is denoted as The calculation formula is: ; The upper limit value of the confidence interval is denoted as The calculation formula is: ; wherein is the pre-set signal level corresponding to the standard normal distribution quantile.

8. The cloud-edge collaboration mathematical experiment virtual-real synchronization method according to claim 1, characterized in that: The generation process of the adjustment factor is: acquiring current network bandwidth , edge computing load rate ; based on current network bandwidth , edge computing load rate computing dynamic adjustment factor : wherein, is a predetermined reference bandwidth.

9. The cloud-edge collaboration mathematical experiment virtual-real synchronization method according to claim 1, characterized in that: The acquisition method of the mixed experiment data is: Obtaining the experiment sample size and the preset sample size threshold; The ratio of the experimental sample quantity to the preset sample quantity threshold is taken as a fusion weight ; Processing the physical experiment data and the preprocessed data set according to the event type respectively; For the same event type according to the fusion weight Linearly weighted fusion is performed on the number of occurrences of events and the number of occurrences in the preprocessed data set; Summarizing the mixed occurrence frequency of all event types to form the mixed experiment data.

10. A cloud-edge collaborative mathematical experiment virtual-real synchronous system, characterized in that: Comprise: A data acquisition module is configured to obtain physical experiment data collected by a terminal device; the physical experiment data comprises an experiment type identifier, an experiment sample size, and an event occurrence frequency, and a corresponding theoretical probability value is obtained according to the experiment type identifier; An edge computing processing module is configured to calculate an event frequency based on the physical experiment data, and calculate a confidence interval based on the theoretical probability value and the experiment sample size; A determination processing module is configured to determine whether the event frequency exceeds the confidence interval and whether the experiment sample size is lower than a preset sample size threshold; A judgment response module is configured to, when the judgment results are all yes, generate an adjustment factor based on the current network bandwidth and the edge computing load state, and send a compensation data request containing the experimental type identifier and the adjustment factor to the cloud; A preprocessed data set acquisition module is configured to acquire a preprocessed data set returned by the cloud, wherein the preprocessed data set is obtained by sampling and compressing a historical compensation data set by the cloud according to a compression ratio, the compression ratio is determined according to the adjustment factor, and the historical compensation data set is obtained by matching according to the experimental type identifier; A data fusion module is configured to calculate a fusion weight based on the physical experiment data, and perform weighted fusion on the physical experiment data and the preprocessed data set according to the fusion weight to obtain mixed experiment data; A distribution curve generation module is configured to generate a probability distribution curve based on the mixed experiment data and send the probability distribution curve to a terminal device for display.

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