Communication equipment fault early warning method based on Apriori algorithm and ARIMA model

Abstract

The invention discloses a communication equipment fault early warning method based on an Apriori algorithm and an ARIMA model, and belongs to the technical field of communication equipment fault early warning. According to the method, association rules are mined based on an Apriori algorithm, and index combinations and association relationships are found out; performing time sequence prediction on the key performance indexes based on an ARIMA model; and combining the predicted value with an association rule, and performing fault early warning by setting an early warning threshold value and an early warning rule. The method combines the advantages of two algorithms, can comprehensively and accurately analyze data, improves the early warning accuracy and timeliness, and is of great significance to the stable operation of a communication network.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of communication equipment fault early warning, and specifically relates to a communication equipment fault early warning method based on an Apriori algorithm and an ARIMA model. The present application combines the Apriori algorithm and the ARIMA model, fully utilizes the advantages of association rule mining and time series prediction, can more comprehensively and accurately analyze the operation data of communication equipment, and improves the accuracy and timeliness of fault early warning. BACKGROUND

[0002] With the rapid development of communication technology, the scale and complexity of communication equipment are increasing, and communication equipment failure may cause serious communication interruption and business loss. Traditional fault early warning methods often rely on manual experience and simple threshold judgment, and have problems such as low accuracy and poor timeliness, which are difficult to meet the requirements of modern communication networks for high reliability and stability. Therefore, a more effective communication equipment fault early warning method is needed to discover potential fault hidden dangers in advance and improve the operation efficiency and service quality of communication networks. SUMMARY

[0003] The problem to be solved by the present application is how to more timely and effectively early warn the faults of communication equipment in a network environment with increasing scale and complexity of communication equipment. To solve the above problem, the association rules mined by the Apriori algorithm can help operation and maintenance personnel better understand the relationship between various indicators of communication equipment, and provide strong basis for fault diagnosis and troubleshooting. The key performance indicators of communication equipment are effectively predicted by the ARIMA model to discover potential fault trends in advance, so that operation and maintenance personnel can take measures in advance to reduce the probability and impact of faults.

[0004] The technical scheme adopted by the present application is:

[0005] A communication equipment fault early warning method based on an Apriori algorithm and an ARIMA model, comprising the following steps:

[0006] Step 1, collecting various operation data of communication equipment, including device performance indicators, alarm information and log data, and preprocessing the collected data;

[0007] Step 2, dividing the preprocessed data into multiple transactions according to time sequence, each transaction containing various performance indicator data at the same time point, using the Apriori algorithm to mine the transaction data set, and mining the frequent item set and association rules in the communication equipment operation data;

[0008] Step 3, select the key performance indicators of the communication equipment to build an ARIMA model, train the ARIMA model using historical data, and predict the key performance indicators in a future set period based on the trained ARIMA model;

[0009] Step 4, combine the key performance indicator prediction value predicted by the ARIMA model with the association rules mined based on the Apriori algorithm, and issue a fault warning message when the warning condition is met.

[0010] Further, step 2 specifically includes the following steps:

[0011] Step 201, convert the preprocessed data into a transaction data set format suitable for Apriori algorithm processing, which contains multiple transactions divided in chronological order, each transaction representing a collection of performance indicators at a certain time point;

[0012] Step 202, set the minimum support threshold and the minimum confidence threshold;

[0013] Step 203, traverse all transactions at time points, extract each performance indicator in each transaction, and calculate the total number of all performance indicators extracted after traversing all transactions; after removing duplicates from all transactions at time points, multiple subsets containing only one performance indicator are generated, all subsets form a candidate 1-item set, then the total number of occurrences of each subset in the traversal of all transactions is counted, and the support of each subset is obtained by calculating the ratio of the number of occurrences of each subset to the total number of all performance indicators, finally, the calculated support is compared with the minimum support threshold, the subset greater than the minimum support threshold is included in the frequent 1-item set, and is recorded as the subset less than the minimum support threshold is discarded;

[0014] Step 204, for the generated frequent k-item set , when the first k-1 elements of two subsets are the same, connect the two subsets to generate a new subset, get a candidate (k+1)-item set , when the candidate (k+1)-item set is not empty, execute step 205, otherwise execute step 206; wherein k is initially 1;

[0015] Step 205, count the number of occurrences of each subset in the candidate (k+1)-item set in the traversal of all transactions, and calculate the ratio of the number of occurrences of each subset to the total number of all performance indicators to obtain the support of each subset, compare the calculated support with the minimum support threshold, and the subset greater than the minimum support threshold is included in the frequent (k+1)-item set Subsets with support less than the minimum support threshold are discarded; then k = k + 1, return to step 204, and terminate the iteration when the candidate (k + 1)-item set is empty.

[0016] Step 206, for frequent k-itemsets Generate all non-empty proper subsets of the association rules and construct candidate association rules; the form of the association rules is as follows: Where X is the antecedent, Y is the consequent, and X and Y are non-empty proper subsets of frequent k-itemsets, and , Association rules indicate that when X occurs, Y is also likely to occur.

[0017] Step 207: Calculate the confidence score for each candidate association rule. The confidence score of an association rule is the ratio of the support of the co-occurrence of the antecedent and consequent to the support of the antecedent. Then, filter the rules according to the minimum confidence score threshold. Rules with a confidence score exceeding the minimum confidence score threshold are marked as strong association rules. Then, merge multiple subsets of consequents Y with the same antecedent X in the filtered strong association rules to form association rules with more elements in the consequent.

[0018] Step 208: Calculate the confidence score for each association rule obtained after merging, filter according to the minimum confidence score threshold, and mark the rules with confidence scores exceeding the minimum confidence score threshold as strong association rules to obtain the integrated strong association rules;

[0019] Step 209: Use the Apriori algorithm to mine frequent itemsets and association rules in the communication equipment operation data, find the combination of indicators that simultaneously have support exceeding the minimum support threshold and the association relationships between them; screen and evaluate the mined association rules, and retain the rules with confidence greater than the minimum confidence threshold and those with practical significance.

[0020] Furthermore, step 3 specifically includes the following steps:

[0021] Step 301: Construct an ARIMA model for the key performance indicators of the communication equipment, including signal strength and data transmission rate;

[0022] Step 302: Use the augmented Dickey-Fuller test (ADF) to test the stationarity of the time series data of the key performance indicators; for the time series... ,in It is a white noise sequence, if Then the data is judged to be stable, if If the data is non-stationary, then the stationarity test is repeated after one difference operation. Finally, the time series data reaches a stationary state after d difference operations. The number of difference operations d when the stationary state is reached is taken as the difference order of the ARIMA model.

[0023] Step 303, calculate the autocorrelation function (ACF) to determine the lag order q: for time series Where n is the number of sequence samples, and the covariance of the sequence at lag k is... The variances of the sequence at time t and time tk are respectively and Autocorrelation coefficient of sequence with lag order k ; Starting with k=1, calculate the autocorrelation coefficient of the time series with lag order k. Then, increment the value of k by 1 and recalculate the autocorrelation coefficient of the sequence with lag k, until the autocorrelation coefficient is reached. At this point, the value of k is the moving average order q of the ARIMA model; the moving average order q indicates that the model considers the error values ​​of the past q times, which is used to correct the prediction bias caused by short-term random fluctuations.

[0024] Step 304, calculate the partial autocorrelation function PACF to determine the lag order p: for time series The regression model with lag order k is Partial autocorrelation function The regression coefficients of the k-th lag term in this model ; Calculate the regression coefficients of the time series with lag order k starting from k=1. When the regression coefficient Then, increment the k value by 1 and recalculate the autocorrelation coefficient of the sequence with lag k, until the regression coefficient is obtained. At this point, the value of k is the autoregressive order p of the ARIMA model; the autoregressive order p means that the model relies on its own values ​​at the past p time points to predict the current value;

[0025] Step 305: Use historical data to train and fit the ARIMA model to obtain a trained ARIMA model;

[0026] Step 306: Use the trained ARIMA model to predict the future values ​​of key performance indicators of the communication equipment.

[0027] Furthermore, step 4 specifically includes the following steps:

[0028] Step 401: Combine the key performance indicators predicted by the ARIMA model with the association rules mined based on the Apriori algorithm;

[0029] Step 402: Based on the association rules and the predicted values ​​of key performance indicators, set the fault warning threshold and warning rules; when the warning conditions are met, issue a fault warning message.

[0030] The advantages of this invention compared to the prior art are:

[0031] 1. This invention combines the Apriori algorithm with the ARIMA model, making full use of the advantages of association rule mining and time series prediction, which can more comprehensively and accurately analyze the operating data of communication equipment and improve the accuracy and timeliness of fault early warning.

[0032] 2. The association rules mined by the Apriori algorithm can help maintenance personnel better understand the relationships between various indicators of communication equipment, providing a strong basis for fault diagnosis and troubleshooting.

[0033] 3. The ARIMA model can effectively predict the key performance indicators of communication equipment, identify potential failure trends in advance, and enable maintenance personnel to take measures in advance to reduce the probability and impact of failures.

[0034] 4. This method has strong versatility and scalability, and can be applied to fault early warning of communication equipment of different types and scales, providing a reliable guarantee for the stable operation of communication networks. Attached Figure Description

[0035] Figure 1 This is a flowchart of the communication equipment fault early warning method of the present invention.

[0036] Figure 2 This is a flowchart of the Apriori mining algorithm of the present invention.

[0037] Figure 3 This is a flowchart of the ARIMA modeling and prediction process of the present invention. Detailed Implementation

[0038] The technical solution of the present invention will be described in detail below with reference to specific examples:

[0039] A method for early warning of communication equipment faults based on the Apriori algorithm and ARIMA model, such as Figure 1 As shown, it includes the following steps:

[0040] Step 1: Collect various operational data of the communication equipment, including equipment performance indicators, alarm information and log data, and preprocess the collected data.

[0041] Taking a certain communication station as an example, the base station's monitoring system collects performance data such as CPU utilization, memory usage, signal strength, and bit error rate of the equipment, as well as alarm information and log information generated by the equipment, with a collection cycle of 15 minutes.

[0042] Use data cleaning tools to remove obviously erroneous and duplicate data records from the collected data, such as deleting data with negative CPU usage or exceeding 100%;

[0043] The Min-Max normalization method is used to map the performance index data to the [0,1] interval for subsequent analysis and processing.

[0044] Step 2: Divide the preprocessed data into multiple transactions according to time order. Each transaction contains various performance index data at the same point in time. Use the Apriori algorithm to mine the transaction dataset to find frequent itemsets and association rules in the communication equipment operation data.

[0045] Step 2 specifically includes the following steps:

[0046] Step 201: Convert the preprocessed data into a transaction dataset format suitable for the Apriori algorithm. The transaction dataset contains multiple transactions divided in chronological order, and each transaction represents a set of performance metrics at a certain point in time.

[0047] Step 202: Set the minimum support threshold to 0.2, meaning that if the probability of a certain performance indicator data appearing at each time point is greater than 20%, it is determined to be a frequent itemset. Set the minimum confidence threshold to 0.8, meaning that when a certain performance indicator data shows a certain trend, the probability that another performance indicator shows a certain trend is greater than 80%. Use the Apriori algorithm to mine the transaction dataset.

[0048] Step 203: Iterate through all transactions at all time points, extracting each performance metric contained in each transaction, and calculate the total number of times all performance metrics extracted after iterating through all transactions. After deduplicating transactions at all time points, multiple subsets containing only one performance metric are generated. All subsets form candidate 1-itemsets, such as {high CPU utilization}, {high memory usage}, etc. Then, count the total number of times each subset appears during the iteration through all transactions, and obtain the support of each subset by calculating the ratio of the number of occurrences of each subset to the total number of occurrences of all performance metrics. Finally, compare the calculated support with the minimum support threshold. Subsets with a support greater than the minimum support threshold are classified as frequent 1-itemsets, denoted as... Subsets with support less than the minimum support threshold are discarded. For example, if the probability of {high CPU utilization} in all transactions exceeds the minimum support threshold of 0.2, it is determined to be a frequent itemset.

[0049] Step 204, for the generated frequent k-itemsets If two subsets have the same first k-1 elements, they are concatenated to form a new subset, resulting in a candidate (k+1)-itemset. , If the set is not empty, proceed to step 205; if the set is empty, proceed to step 206; where the initial value of k is 1.

[0050] Step 205: Count the number of times each subset in the candidate (k+1)-itemset appears during the traversal of all transactions, and calculate the ratio of the number of occurrences of each subset to the total number of occurrences of all performance metrics to obtain the support of each subset. Compare the calculated support with the minimum support threshold; subsets with support values ​​greater than the minimum support threshold are classified into frequent (k+1)-itemsets. Subsets with support less than the minimum support threshold are discarded; then k = k + 1, return to step 204, and terminate the iteration when the candidate (k + 1)-item set is empty.

[0051] Further iterations merge frequent itemsets pairwise to obtain candidate 2-itemsets such as {high CPU utilization, high memory usage}. Repeat the steps of calculating support and filtering based on the minimum support threshold. The iteration process terminates when the candidate itemsets are empty after multiple iterations. After multiple iterations, frequent itemsets such as {high CPU utilization, high memory usage, low signal strength} and {high CPU utilization, low signal strength, high bit error rate} are obtained.

[0052] Step 206, for frequent k-itemsets Generate all non-empty proper subsets of the association rules and construct candidate association rules; the form of the association rules is as follows: Where X is the antecedent, Y is the consequent, and X and Y are non-empty proper subsets of frequent k-itemsets, and , Association rules indicate that when X occurs, Y is also likely to occur.

[0053] For each frequent itemset, recursively generate all non-empty subsets, such as {high CPU utilization, low signal strength, high bit error rate}, recursively generating subsets like {high CPU utilization, low signal strength}, {low signal strength, high bit error rate}, and {high CPU utilization, high bit error rate}. Calculate the confidence score for each candidate subset and filter it according to the minimum confidence threshold to obtain strong association rules, such as "if CPU utilization is high, then the confidence score for high memory usage is 0.85".

[0054] Step 207: Calculate the confidence score for each candidate association rule. The confidence score of an association rule is the ratio of the support of the co-occurrence of the antecedent and consequent to the support of the antecedent. Then, filter the rules according to the minimum confidence score threshold. Rules with a confidence score exceeding the minimum confidence score threshold are marked as strong association rules. Then, merge multiple subsets of consequents Y with the same antecedent X in the filtered strong association rules to form association rules with the consequent containing more elements.

[0055] Step 208: Calculate the confidence score for each association rule obtained after merging, filter according to the minimum confidence score threshold, and mark the rules with confidence scores exceeding the minimum confidence score threshold as strong association rules to obtain the integrated strong association rules.

[0056] Step 209: Use the Apriori algorithm to mine frequent itemsets and association rules in the communication equipment operation data, find the combination of indicators that simultaneously have support exceeding the minimum support threshold and the association relationship between them; manually evaluate the mined association rules, remove some rules that do not conform to the actual situation or have no practical significance, and retain the rules that are closely related to communication equipment failures.

[0057] Step 3: Select key performance indicators of communication equipment to build an ARIMA model, and train the ARIMA model using historical data. Based on the trained ARIMA model, predict key performance indicators for a future time period.

[0058] Step 3 specifically includes the following steps:

[0059] Step 301: Construct an ARIMA model for the key performance indicators of the communication equipment, including signal strength and data transmission rate;

[0060] In this embodiment, signal strength is selected as the key performance indicator for ARIMA modeling.

[0061] Step 302: Use the augmented Dickey-Fuller test (ADF) to test the stationarity of the time series data of the key performance indicators; for the time series... ,in It is a white noise sequence, if Then the data is judged to be stable, if If the data is non-stationary, then the stationarity test is repeated after one difference operation. Finally, the time series data reaches a stationary state after d difference operations. The number of difference operations d when the stationary state is reached is taken as the difference order of the ARIMA model.

[0062] In this embodiment, after repeated testing following first-order difference calculation, it was found that the data had reached a stationary state, thus determining the difference order d = 1.

[0063] Step 303, calculate the autocorrelation function (ACF) to determine the lag order q: for time series Where n is the number of sequence samples, and the covariance of the sequence at lag k is... The variances of the sequence at time t and time tk are respectively and Autocorrelation coefficient of sequence with lag order k ; Starting with k=1, calculate the autocorrelation coefficient of the time series with lag order k. Then, increment the value of k by 1 and recalculate the autocorrelation coefficient of the sequence with lag k, until the autocorrelation coefficient is reached. At this point, the value of k is the moving average order q of the ARIMA model; the moving average order q indicates that the model considers the error values ​​of the past q times, which is used to correct the prediction bias caused by short-term random fluctuations.

[0064] In this embodiment, after calculating the differenced data, when the lag order is 2, the partial autocorrelation function PACF(k) is approximately equal to 0, and the moving average order q=2 is determined.

[0065] Step 304, calculate the partial autocorrelation function PACF to determine the lag order p: for time series The regression model with lag order k is Partial autocorrelation function The regression coefficients of the k-th lag term in this model ; Calculate the regression coefficients of the time series with lag order k starting from k=1. When the regression coefficient Then, increment the k value by 1 and recalculate the autocorrelation coefficient of the sequence with lag k, until the regression coefficient is obtained. At this point, the value of k is the autoregressive order p of the ARIMA model; the autoregressive order p means that the model relies on its own values ​​at the past p time points to predict the current value; in this embodiment, p=2 is determined.

[0066] Based on the above calculations, the parameters of the ARIMA model are determined to be p=2, d=1, and q=1.

[0067] Step 305: Use the signal strength data from the past month to train and fit the ARIMA(2,1,1) model, and estimate the model parameters by least squares to obtain the optimal ARIMA model.

[0068] Step 306: Use the trained ARIMA model to predict the signal strength for the next 24 hours to obtain a sequence of predicted values.

[0069] Step 4: Combine the predicted values ​​of key performance indicators obtained by the ARIMA model with the association rules mined based on the Apriori algorithm, and issue a fault warning message when the warning conditions are met.

[0070] Step 4 specifically includes the following steps:

[0071] Step 401: Combine the key performance indicators predicted by the ARIMA model with the association rules mined based on the Apriori algorithm;

[0072] Step 402: Based on the association rules and the predicted values ​​of key performance indicators, set the fault warning threshold and warning rules; when the warning conditions are met, issue a fault warning message.

[0073] When the signal strength predicted by the ARIMA model meets the above warning conditions, the system immediately issues a fault warning message to remind maintenance personnel to check and maintain the communication base station in a timely manner.

[0074] As can be seen from the above specific examples, the communication equipment fault early warning method based on the Apriori algorithm and ARIMA model of the present invention can effectively realize the early warning of communication equipment faults and has good application prospects.

Claims

1. A method for early warning of communication equipment faults based on the Apriori algorithm and the ARIMA model, characterized in that, Includes the following steps: Step 1: Collect various operational data of the communication equipment, including equipment performance indicators, alarm information and log data, and preprocess the collected data; Step 2: Divide the preprocessed data into multiple transactions according to time order. Each transaction contains various performance index data at the same point in time. Use the Apriori algorithm to mine the transaction dataset to find frequent itemsets and association rules in the communication equipment operation data. Step 3: Select key performance indicators of communication equipment to build an ARIMA model, and use historical data to train the ARIMA model. Based on the trained ARIMA model, predict key performance indicators for a future set time period. Step 4: Combine the predicted values ​​of key performance indicators obtained by the ARIMA model with the association rules mined based on the Apriori algorithm, and issue a fault warning message when the warning conditions are met.

2. The communication equipment fault early warning method based on the Apriori algorithm and ARIMA model according to claim 1, characterized in that, Step 2 specifically includes the following steps: Step 201: Convert the preprocessed data into a transaction dataset format suitable for the Apriori algorithm. The transaction dataset contains multiple transactions divided in chronological order, and each transaction represents a set of performance metrics at a certain point in time. Step 202: Set the minimum support threshold and the minimum confidence threshold; Step 203: Traverse all transactions at all time points, extract each performance metric contained in each transaction, and calculate the total number of times all performance metrics extracted after traversing all transactions. After deduplicating transactions at all time points, multiple subsets containing only one performance metric are generated. All subsets form candidate 1-itemsets. Then, count the total number of times each subset appears during the traversal of all transactions, and obtain the support of each subset by calculating the ratio of the number of occurrences of each subset to the total number of occurrences of all performance metrics. Finally, compare the calculated support with the minimum support threshold. Subsets with a support greater than the minimum support threshold are classified as frequent 1-itemsets, denoted as... Subsets with support less than the minimum support threshold are discarded. Step 204, for the generated frequent k-itemsets If two subsets have the same first k-1 elements, they are concatenated to form a new subset, resulting in a candidate (k+1)-itemset. , If the set is not empty, proceed to step 205; if the set is empty, proceed to step 206; where the initial value of k is 1. Step 205: Count the number of times each subset in the candidate (k+1)-itemset appears during the traversal of all transactions, and calculate the ratio of the number of occurrences of each subset to the total number of occurrences of all performance metrics to obtain the support of each subset. Compare the calculated support with the minimum support threshold; subsets with support values ​​greater than the minimum support threshold are classified into frequent (k+1)-itemsets. Subsets with support less than the minimum support threshold are discarded; then k = k + 1, return to step 204, and terminate the iteration when the candidate (k + 1)-item set is empty. Step 206, for frequent k-itemsets Generate all non-empty proper subsets of the association rules and construct candidate association rules; the form of the association rules is as follows: Where X is the antecedent, Y is the consequent, and X and Y are non-empty proper subsets of frequent k-itemsets, and , Association rules indicate that when X occurs, Y is also likely to occur. Step 207: Calculate the confidence score for each candidate association rule. The confidence score of an association rule is the ratio of the support of the co-occurrence of the antecedent and consequent to the support of the antecedent alone. Then, filter the rules according to the minimum confidence score threshold. Rules with a confidence score exceeding the minimum confidence score threshold are marked as strong association rules. Then, merge multiple subsets of consequents Y with the same antecedent X in the filtered strong association rules to form association rules with a consequent containing more elements. Step 208: Calculate the confidence score for each association rule obtained after merging, filter according to the minimum confidence score threshold, and mark the rules with confidence scores exceeding the minimum confidence score threshold as strong association rules to obtain the integrated strong association rules; Step 209: Use the Apriori algorithm to mine frequent itemsets and association rules in the communication equipment operation data, find the combination of indicators that simultaneously have support exceeding the minimum support threshold and the association relationships between them; screen and evaluate the mined association rules, and retain the rules with confidence greater than the minimum confidence threshold and those with practical significance.

3. The communication equipment fault early warning method based on the Apriori algorithm and ARIMA model according to claim 1, characterized in that, Step 3 specifically includes the following steps: Step 301: Construct an ARIMA model for the key performance indicators of the communication equipment, including signal strength and data transmission rate; Step 302: Use the augmented Dickey-Fuller test (ADF) to test the stationarity of the time series data of the key performance indicators; for the time series... ,in It is a white noise sequence, if Then the data is judged to be stable, if If the data is non-stationary, then the stationarity test is repeated after one difference operation. Finally, the time series data reaches a stationary state after d difference operations. The number of difference operations d when the stationary state is reached is taken as the difference order of the ARIMA model. Step 303, calculate the autocorrelation function (ACF) to determine the lag order q: for time series Where n is the number of sequence samples, and the covariance of the sequence at lag k is... The variances of the sequence at time t and time tk are respectively and Autocorrelation coefficient of sequence with lag order k ; Starting with k=1, calculate the autocorrelation coefficient of the time series with lag order k. Then, increment the k value by 1 and recalculate the autocorrelation coefficient of the sequence with lag k, until the autocorrelation coefficient is reached. At this point, the value of k is the moving average order q of the ARIMA model; the moving average order q indicates that the model considers the error values ​​of the past q times, which is used to correct the prediction bias caused by short-term random fluctuations. Step 304, calculate the partial autocorrelation function PACF to determine the lag order p: for time series The regression model with lag order k is Partial autocorrelation function The regression coefficients of the k-th lag term in this model ; Calculate the regression coefficients of the time series with lag order k starting from k=1. When the regression coefficient Then, increment the k value by 1 and recalculate the autocorrelation coefficient of the sequence with lag k, until the regression coefficient is obtained. At this point, the value of k is the autoregressive order p of the ARIMA model; the autoregressive order p means that the model relies on its own values ​​at the past p time points to predict the current value; Step 305: Use historical data to train and fit the ARIMA model to obtain a trained ARIMA model; Step 306: Use the trained ARIMA model to predict the future values ​​of key performance indicators of the communication equipment.

4. The communication equipment fault early warning method based on the Apriori algorithm and ARIMA model according to claim 1, characterized in that, Step 4 specifically includes the following steps: Step 401: Combine the key performance indicators predicted by the ARIMA model with the association rules mined based on the Apriori algorithm; Step 402: Based on the association rules and the predicted values ​​of key performance indicators, set the fault warning threshold and warning rules; when the warning conditions are met, issue a fault warning message.

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