A gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals

Abstract

The application discloses a gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals and belongs to the technical field of data processing. The method comprises the following steps: acquiring monitoring time series data in a continuous operation period of a gas turbine in real time, wherein the monitoring time series data comprises sampling values of multiple monitoring signals at continuous sampling moments; dividing the monitoring time series data into windows according to a preset window length and a sliding step, and obtaining the mean and covariance of time-varying cointegration vectors of each window; constructing a dynamic threshold range according to the covariance of a current window, the health reference parameters of cointegration coefficients corresponding to part of the monitoring signals and the health reference parameters of cointegration bias terms; triggering an anomaly mark when the cointegration bias term and at least one cointegration coefficient exceed the corresponding threshold; and outputting an alarm signal when the anomaly mark is triggered for a continuous preset number of windows. The application can track the time-varying evolution of the cointegration relationship under variable working conditions of the gas turbine, and early warning of sudden failures is realized.

Description

Technical Field

[0001] This invention belongs to the field of data processing technology, specifically relating to a gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals. Background Technology

[0002] During the operation of a gas turbine, real-time monitoring signals such as vibration, temperature, pressure, and speed collected by sensors constitute key indicators of the turbine's real-time operating status. Accurate anomaly detection of these monitoring signals is crucial for ensuring the safe operation of the gas turbine and enabling predictive maintenance, and is a key aspect of intelligent equipment operation and maintenance.

[0003] Cointegration analysis, as a method for handling non-stationary multivariate time series, has been widely applied in the field of industrial anomaly detection in recent years. It captures the long-term linear equilibrium relationship between multiple non-stationary time series through cointegration vectors and constructs stationary cointegration residuals as the core indicator for anomaly detection. Compared with traditional methods based on single-variable threshold judgments, cointegration analysis can more effectively reveal changes in the intrinsic dependencies between variables, thus exhibiting higher sensitivity to potential degradation in equipment performance. For example, patent CN117633474B discloses an online identification method for stuck drill bit status in mining rigs based on cointegration analysis, verifying the engineering practicality of this technology in industrial scenarios.

[0004] However, traditional cointegration analysis methods still have significant limitations when applied to gas turbine monitoring signals. First, classic cointegration procedures such as the Johansen test typically rely on historical data over long time spans to estimate the cointegration vector. However, gas turbines often lack sufficient accumulated operating data to establish stable cointegration relationships during initial commissioning or after major overhauls. Second, the variable operating conditions, frequent start-ups and shutdowns, and fuel switching of gas turbines cause the cointegration relationships between monitoring signals to drift over time. Traditional static cointegration models cannot capture the dynamic evolution of this time-varying equilibrium relationship, leading to high false negatives and false negatives under varying operating conditions. Furthermore, existing cointegration detection schemes generally only set fixed thresholds for residuals to trigger alarms, lacking descriptions of the confidence and probability of the detection results, making it difficult for maintenance personnel to assess the effectiveness of the cointegration relationship.

[0005] In summary, there is an urgent need for a gas turbine monitoring signal cointegration modeling and anomaly detection method that can track time-varying cointegration relationships with limited data and has the ability to express uncertainty, in order to make up for the shortcomings of existing technologies. Summary of the Invention

[0006] To address the problems in the prior art, this invention provides a gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals.

[0007] The technical solution of the present invention is as follows:

[0008] This invention discloses a gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals, comprising the following steps:

[0009] 1) Real-time acquisition of monitoring time-series data of the gas turbine to be detected during continuous operation, wherein the monitoring time-series data includes the sampled values ​​of various monitoring signals at continuous sampling times;

[0010] 2) Divide the monitoring time series data into windows according to the preset window length and sliding step size; within each window, construct a state space model describing the time-varying cointegration relationship between each monitoring signal, and perform Bayesian parameter estimation to obtain the mean and covariance of the time-varying cointegration vector corresponding to each window; and extract the estimated value of the cointegration bias term and the estimated value of the cointegration coefficient corresponding to some monitoring signals from the mean of the time-varying cointegration vector of each window.

[0011] 3) Based on the covariance of each window in step 2) and the health benchmark parameters of each cointegration coefficient and cointegration bias term, construct the dynamic threshold range of the cointegration coefficient and cointegration bias term under each window. When the estimated value of the cointegration bias term and at least one estimated value of the cointegration coefficient of the window in step 2) exceeds the corresponding dynamic threshold range, an anomaly flag is triggered; when anomaly flags are triggered for a preset number of consecutive windows, an alarm signal is output.

[0012] Further, in step 2), constructing the state-space model includes: designating one type of monitoring signal as the observation variable and designating the remaining monitoring signals as state variables; using the sequence of observation variables within each window as the output term of the observation equation, and forming an extended state variable matrix by combining the sequence of state variables within the window with a unit vector used to introduce the cointegration bias term; establishing the observation equation based on the extended state variable matrix and the time-varying cointegration vector, wherein the time-varying cointegration vector includes the cointegration bias term and the cointegration coefficients corresponding to each state variable; using a first-order random walk model to describe the evolution of the time-varying cointegration vector of adjacent windows, and establishing a state transition equation; the observation equation and the state transition equation form the state-space model.

[0013] Further, in step 3), the method for generating the health baseline parameters of each cointegration coefficient and cointegration bias term includes: acquiring the monitoring time series data of the gas turbine during its historical healthy operating period, dividing it into sliding windows, obtaining the mean of the time-varying cointegration vector of each window during the historical healthy operating period, extracting the cointegration coefficient and cointegration bias term from the mean of the time-varying cointegration vector of each window, obtaining the mean and variance of each cointegration coefficient and the mean and variance of the cointegration bias term in all windows during the historical healthy operating period, that is, obtaining the health baseline parameters of the cointegration coefficient and the health baseline parameters of the cointegration bias term.

[0014] Further, in step 3), constructing the dynamic threshold range of cointegration coefficients and cointegration bias terms under each window includes: extracting the estimated variances corresponding to the cointegration coefficients and cointegration bias terms from the time-varying cointegration vector covariance of each window in step 2), and then obtaining the upper limit and lower limit of the dynamic thresholds of the cointegration coefficients and cointegration bias terms under each window based on the benchmark mean, the benchmark variance, the estimated variance, and the preset confidence coefficient, thereby obtaining the dynamic threshold range of the cointegration coefficients and cointegration bias terms under each window.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0016] 1) This invention models the cointegration relationship as a first-order random walk process within the state-space model framework, allowing the cointegration coefficients to evolve dynamically with time and operating conditions, thus breaking through the assumption of constant parameters in traditional cointegration models. Simultaneously, by using a sliding window mechanism, the posterior information of the previous sliding time window is used as the prior information of the current sliding time window, realizing information transfer between sliding time windows and improving the stability of cointegration estimation under varying operating conditions.

[0017] 2) This invention employs a Bayesian parameter estimation framework to sample the posterior distribution of the time-varying cointegration vector within each sliding time window, and achieves joint estimation of the cointegration vector, the state transition process noise covariance matrix, and the observation noise variance through multiple iterations within the window. Simultaneously, the method outputs the posterior mean and posterior covariance of the time-varying cointegration vector, achieving complete quantification of the estimation uncertainty.

[0018] 3) This invention superimposes the health baseline variance and the posterior estimate variance of the current window during anomaly detection to construct an adaptive dynamic threshold. The threshold is adaptively widened when parameter estimation uncertainty is high within the sliding time window, and tightened when estimation is accurate within the sliding time window. This fully utilizes the covariance information from the Bayesian estimation output, improving the robustness of the alarm system. Attached Figure Description

[0019] Figure 1 This is an overall flowchart of the gas turbine anomaly detection method of the present invention;

[0020] Figure 2 This is a graph of the state variables of the gas turbine involved in the embodiments of the present invention;

[0021] Figure 3 This is a graph showing the output power of the gas turbine involved in the embodiments of the present invention;

[0022] Figure 4 This is a graph showing the estimation results of the cointegration coefficient of the gas turbine involved in the embodiments of the present invention;

[0023] Figure 5This is a graph showing the estimation results of the gas turbine cointegration bias term involved in the embodiments of the present invention. Detailed Implementation

[0024] The present invention will be further described and illustrated below with reference to specific embodiments. The embodiments described are merely examples of the content of this disclosure and do not limit the scope of the invention. The technical features of each embodiment in the present invention can be combined accordingly, provided that there is no mutual conflict.

[0025] To address the aforementioned problems in the prior art, this invention provides a gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals. Figure 1 This is an overall flowchart of the gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals according to the present invention. The method includes the following steps:

[0026] S1: Real-time acquisition of operational monitoring data of the gas turbine to be inspected for anomalies from the on-site industrial gas turbine monitoring system. This operational monitoring data includes various monitoring signals, such as combustion chamber internal pressure, exhaust temperature, turbine temperature, fuel flow rate, compressor outlet temperature, compressor outlet pressure, and gas turbine output power.

[0027] S2: A sliding time window state-space model is performed on the cointegration relationship of the gas turbine operation monitoring data. The gas turbine output power is designated as the observed variable, and the combustion chamber internal pressure, exhaust temperature, turbine temperature, fuel flow rate, compressor outlet temperature, and compressor outlet pressure are designated as state variables. For each sliding time window, a corresponding observation equation is constructed using the cointegration relationship between the observed variables and the state variables. In the observation equation, cointegration coefficients are set for each state variable, and a cointegration bias term is set to characterize the offset between the observed variable and the weighted combination of each state variable. The cointegration coefficients and the cointegration bias term together form a time-varying cointegration vector. The observation equation allows for observation noise, and the residual fluctuation of the observation equation is characterized by the observation noise variance. For adjacent sliding time windows, a state transition equation is established to describe the evolution of the time-varying cointegrated vector across different sliding time windows. This state transition equation indicates that the time-varying cointegrated vector of the current sliding time window is derived from the time-varying cointegrated vector of the previous sliding time window. The state transition equation allows for state transition noise, and the state transition noise covariance matrix characterizes the degree of fluctuation of the time-varying cointegrated vector between adjacent sliding time windows. Finally, a state-space model is obtained, formed by the observation equation and the state transition equation. This state-space model describes the process of the cointegration relationship between the observed variables and state variables changing with the sliding time window. The time-varying cointegrated vector, the state transition noise covariance matrix, and the observation noise variance are the model parameters to be estimated for the state-space model. Specifically, the time-varying cointegrated vector characterizes the cointegration relationship between the observed variables and each state variable; the state transition noise covariance matrix characterizes the uncertainty of this cointegration relationship changing between adjacent sliding time windows; and the observation noise variance characterizes the residual fluctuations in the observation equation that are not explained by the cointegration relationship.

[0028] Specifically, in step 2), the steps of constructing the observation equations and state transition equations to obtain the state-space model include:

[0029] Industrial gas turbine monitoring system at all times The seven monitoring signals collected from the combustion chamber (internal pressure), exhaust temperature, turbine temperature, fuel flow rate, compressor outlet temperature, compressor outlet pressure, and gas turbine output power constitute a vector. , All monitoring signals have the same sampling frequency and perfectly aligned timestamps. The gas turbine output power is selected. As observed variables, six monitoring signals—combustion chamber internal pressure, exhaust temperature, turbine temperature, fuel flow rate, compressor outlet temperature, and compressor outlet pressure—are used as state variables. To introduce a cointegration bias term into the cointegration relationship, a constant term of 1 is added to the six monitoring signals to form extended state variables. , Suppose that the state variable and the extended state variable have the following cointegration relationship:

[0030]

[0031] in, This represents the first six elements of the extended state variables, namely the state variable portion consisting of combustion chamber internal pressure, exhaust temperature, turbine temperature, fuel flow rate, compressor outlet temperature, and compressor outlet pressure. The first six elements in the time-varying cointegration vector represent the cointegration coefficients corresponding to the six monitoring signals, respectively. It is a time-varying cointegrated vector. , express At time 1, the cointegration coefficients of the six monitoring signals; express The cointegration bias term at time; for Stationary random observation noise at any given time.

[0032] Furthermore, assuming that the time-varying cointegration vector between the state variables and the extended state variables remains constant at each time point within a sliding time window of length L, let the th... The time index on the sliding time window is Then the time-varying cointegration vector at each moment of the sliding time window satisfies:

[0033]

[0034] in, , , They represent the first The time-varying cointegrated vectors at the first, second, and Lth times within a sliding time window. For the first A time-varying cointegrated vector over a sliding time window.

[0035] Therefore, the operational monitoring data of the gas turbine is in the first... The estimation of the time-varying cointegration vector at each moment in the sliding time window simplifies to... Make an estimate.

[0036] By using a first-order random walk model to describe the evolution of a time-varying cointegrated vector within different sliding time windows, the state transition equation of the time-varying cointegrated vector can be constructed:

[0037]

[0038] in, For the first Time-varying cointegrated vectors over a sliding time window; the sliding step size between two adjacent sliding time windows is L / 2; For the first Noise in the state transition process over a sliding time window; For the first The noise covariance matrix of the state transition process over a sliding time window , Represents the time-varying cointegration vector dimensionality The values ​​of are derived from the inverse Wishart distribution. obtained from sampling, , All are the first The hyperparameters of the inverse Wishart distribution corresponding to each sliding time window take values ​​that vary with... Let's estimate together.

[0039] No. The observation equation within each sliding time window is:

[0040]

[0041] in, For the first A sequence of observed variables over a sliding time window , , , They represent the first Within a sliding time window, the observed variables at the first, second, and Lth time points; For the first An extended sequence of state variables over a sliding time window , , , They represent the first The transpose of the extended state variables at the first, second, and Lth time points within a sliding time window; For the first Observation noise over a sliding time window; Represents a unit vector with L rows and 1 column; For the first The variance of the observation noise over a sliding time window takes values ​​from the inverse Gamma distribution. obtained from sampling, , All are the first The hyperparameters of the inverse Gamma distribution corresponding to each sliding time window take values ​​that vary with... Let's estimate together.

[0042] 3) Based on the state-space model constructed in step 2), perform posterior estimation of the model parameters to be estimated within each sliding time window.

[0043] Step 3) includes:

[0044] 3.1) Perform parameter estimation for each sliding time window sequentially according to the preset sliding time window order. For the Using a sliding time window, the posterior mean and posterior covariance of the time-varying cointegrated vector from the previous sliding time window are used as prior information for the current sliding time window. The noise covariance matrix of the state transition process and the observation noise variance within the current sliding time window are fixed, and the observed variable sequence within the current sliding time window is combined with this information. and extended state variable sequence The transition Markov chain Monte Carlo algorithm is used to collect a large number of sample points, from which the posterior distribution of the time-varying cointegrated vector of the current sliding window is fitted, and then the mean and covariance of the time-varying cointegrated vector within the current sliding time window are estimated.

[0045] 3.2) Based on the sample points collected in step 3.1), update the first... The hyperparameters of the inverse Wishart distribution and the inverse Gamma distribution corresponding to each sliding time window are obtained, thus yielding the noise covariance matrix of the state transition process. Distribution and observation noise variance The distribution of the noise covariance matrix during the state transition process is then determined. The noise covariance matrix of the state transition process is estimated by sampling from the distribution; the noise variance is obtained from the observed noise variance. The variance of the observation noise is estimated by sampling from the distribution.

[0046] 3.3) Using the mean and covariance of the time-varying cointegrated vector estimated in step 3.1), and the hyperparameters of the inverse Wishart distribution and the inverse Gamma distribution obtained in step 3.2), as the prior distributions of the parameters for the next sliding time window, repeat steps 3.1) to 3.2) until the preset number of rounds is reached. After completing the last round of updates, the mean, covariance, state transition noise covariance matrix, and observation noise variance estimated in the last round are used as the final estimates of the mean, covariance, state transition noise covariance matrix, and observation noise variance for that sliding time window, respectively.

[0047] In step 3), the estimation of the parameters of the state-space model to be estimated over the sliding time window includes two loop processes. In each outer loop, steps 3.1) and 3.2) are executed completely to obtain a complete set of estimates for the mean of the time-varying cointegrated vector, the covariance of the time-varying cointegrated vector, the noise covariance matrix of the state transition process, and the variance of the observation noise for each sliding time window. After the outer loop is executed completely multiple times and terminated, the final estimates of the mean of the time-varying cointegrated vector, the covariance of the time-varying cointegrated vector, the noise covariance matrix of the state transition process, and the variance of the observation noise for the sliding time window are obtained. The inner loop is the transition Markov chain Monte Carlo algorithm in step 3.1), corresponding to the process in Steps 1-4 below. In each outer loop, the inner loop needs to be executed completely multiple times. After the inner loop is executed completely multiple times and terminated, a complete set of estimates for the mean and covariance of the time-varying cointegrated vector in step 3.1) is obtained.

[0048] For ease of distinction, in the following embodiments, each complete outer loop is called a round, and each complete inner loop is called an iteration.

[0049] In step 3.1), the specific steps for obtaining the posterior value of the cointegrated vector using the transition Markov chain Monte Carlo algorithm are as follows:

[0050] 3.1.1) Determine the prior distribution of the time-varying cointegrated vector within the sliding time window.

[0051] For the first sliding time window, the prior distribution of the time-varying cointegrated vector in the first round of the sliding time window is obtained based on the values ​​of the variables within the sliding time window, and its expression is:

[0052]

[0053] in, This represents the initial value of the prior distribution of the time-varying cointegrated vector in the first round of the first sliding time window; Let represent the mean of the prior Gaussian distribution of the time-varying cointegrated vector. , This represents the extended state variable sequence within the first sliding time window. This represents the sequence of observed variables within the first sliding time window; Let represent the initial value of the covariance of the prior Gaussian distribution of the time-varying cointegrated vector. , A constant set by humans; This represents the noise covariance matrix of the state transition process in the first round within the first sliding time window. , , These are the inverse Wishart distributions corresponding to the first sliding time window. The initial hyperparameters are set manually.

[0054] For subsequent sliding time windows The prior distribution of the time-varying cointegrated vector in the first round of the sliding time window is expressed as:

[0055]

[0056] in, Indicates the first The prior distribution of time-varying cointegrated vectors in the first round over a sliding time window; , They are the first The mean and covariance of the time-varying cointegrated vector estimated over a sliding time window; Indicates the first The noise covariance matrix of the state transition process in the first round over a sliding time window. , , The first The inverse Wishart distribution corresponding to each sliding time window The initial hyperparameters are set as follows: , .

[0057] For the first sliding time window, on the sliding time window... Rounds The expression for the prior distribution of the time-varying cointegrated vector is:

[0058]

[0059] in, It is the first sliding time window. The noise covariance matrix of the state transition process in each round , , For the first sliding time window The inverse Wishart distribution estimated in each round Hyperparameters.

[0060] For the The sliding time window, on the sliding time window, the first Rounds The expression for the prior distribution of the time-varying cointegrated vector is:

[0061]

[0062] in, It is the first The sliding time window in the first The noise covariance matrix of the state transition process in each round , , For the first The sliding time window in the first The inverse Wishart distribution estimated in each round Hyperparameters.

[0063] 3.1.2) For each sliding time window, collect data from the prior distribution of the time-varying cointegration vector of that sliding time window determined in step 3.1.1). We use a sample and then perform multiple inner loop iterations to solve for the mean and covariance of the time-varying cointegrated vector.

[0064] For the first sliding time window and the second The method for solving the mean and covariance of the time-varying cointegrated vector in step 3.1.2) is completely the same for each sliding time window, and will not be distinguished in the following description.

[0065] In the During this iteration, the following steps are performed when solving for the mean and covariance of the time-varying cointegration vector:

[0066] Step 1: Calculation The weight of each sample in a set of samples, if the current iteration is in the first (outer loop) round of the sliding time window, is expressed as follows:

[0067]

[0068] in, This indicates that in the first (outer) cycle, the... In the nth iteration The weights of each sample; This indicates that in the first (outer) cycle, the... In the nth iteration One sample; Indicates the first The variance of observation noise in the first round over a sliding time window. , , For the first Inverse Gamma distribution over a sliding time window The initial hyperparameters are set manually; This indicates that in the first (outer) cycle, the... In the nth iteration Sample Observe the variable sequence within the corresponding sliding time window. Extended state variable sequence and observation noise variance The likelihood function under the given conditions ; , They represent the first The second iteration and the first Temperature parameters for the next iteration , , This represents the preset total number of iterations over the sliding time window.

[0069] If the current iteration is at the th iteration in the sliding time window One (outer cycle) round The expression for the sample weights is:

[0070]

[0071] in, Indicates the first In the (outer loop) round, the first In the nth iteration The weights of each sample; Indicates the first In the (outer loop) round, the first In the nth iteration One sample; It is the first The sliding time window is in the previous one The variance of observation noise over each round , , It is the first The sliding time window in the first The estimated values ​​for each round Hyperparameters of the distribution; Indicates the first In the first round, the In the nth iteration Sample Observe the variable sequence within the corresponding sliding time window. Extended state variable sequence and observation noise variance The likelihood function under the given conditions .

[0072] Step 2: Normalize the weights of each sample, that is:

[0073]

[0074] in, Indicates the first In the (outer loop) round, the first In the nth iteration The normalized weights of each sample.

[0075] The step size matrix in the update process is calculated based on the normalized weights:

[0076]

[0077] in, Indicates the first The step size matrix used to generate candidate samples in the next iteration; This is the scaling factor; Indicates the first In the (outer loop) round, the first The weighted mean of each sample in the next iteration. .

[0078] Step 3: Based on the weights after sample normalization For the present Each sample is weighted and sampled. During the resampling process, one sample is first weighted... The intervals are divided into the following order: The segments are, in order, of length 1. Next, from A random number is drawn from the interval. The interval in which the random number falls is used to determine the corresponding sample, and this determined sample is used as a resampled sample. The above process is repeated. Next, obtain with A set of resampled samples , ,in Indicates the first In the (outer loop) round, the first In the nth iteration Each sample is resampled. In this process, points with larger normalized weights are more likely to be sampled multiple times, while points with smaller normalized weights are more likely to be not sampled.

[0079] Step 4: For each sample obtained after resampling, use that sample as the mean and... Construct a Gaussian distribution for the variance, and then collect a candidate sample from the Gaussian distribution. And accept the candidate sample with a certain probability. Then use candidate samples Replace the original sample Conversely, retain the original sample. In each (outer loop) round, the probability of a candidate sample being accepted is:

[0080]

[0081] in, Indicates that in a given , and Under these conditions, the resampled samples The corresponding prior probability density function; Indicates that in a given , and Under the conditions, candidate samples The prior probability density function; Indicates the first In the first round, the In the nth iteration Each resampled sample Observe the variable sequence within the corresponding sliding time window. Extended state variable sequence and observation noise variance The likelihood function under the given conditions; Indicates the first In the first round, the In the nth iteration candidate samples Observe the variable sequence within the corresponding sliding time window. Extended state variable sequence and observation noise variance The likelihood functions are given under the premise that they are calculated as follows:

[0082]

[0083]

[0084]

[0085]

[0086] In the first round of the sliding time window, that is When the value is 1, , In subsequent rounds of the sliding time window, i.e. When the value is greater than 1, , .

[0087] Step 5: Repeat Steps 1-4 using the updated sample. After completing the above iterations, retain the last iteration (i.e., the nth iteration). In the next iteration Using a sample, the mean and covariance of the time-varying cointegration vector are calculated. Specifically:

[0088]

[0089]

[0090] in, , They represent the first The first sliding time window The mean and covariance of the time-varying cointegrated vector estimated in each round; Indicates the first The first sliding time window In each round, complete The result obtained after the nth iteration One sample.

[0091] In step 3.2), the specific steps for updating the noise covariance matrix of the state transition process are as follows:

[0092] 3.2.1): Using the steps in step 3.1) The first sliding time window The result obtained in the last iteration of each round Calculate the outer product sum for each sample:

[0093]

[0094] in, Indicates the first The first sliding time window The sum of the outer products calculated in each round.

[0095] 3.2.2): Update the noise covariance matrix of the state transition process. The corresponding inverse Wishart distribution Hyperparameters:

[0096]

[0097]

[0098] in, , They represent the first The first sliding time window Round and number Estimates of the scaling hyperparameters of the inverse Wishart distribution over rounds; , They represent the first The first sliding time window Round and number Estimates of the degrees of freedom hyperparameters of the inverse Wishart distribution at each round.

[0099] 3.2.3): Symmetric and regularize the updated scale parameters to ensure positive definiteness:

[0100]

[0101] in, This represents the scale hyperparameters obtained after symmetry and regularization processing; This represents the transpose of the scale hyperparameters obtained after symmetry and regularization. Represents the regularization coefficient. ; This represents a 7th-order identity matrix.

[0102] 3.2.4): Sample the noise covariance matrix of the state transition process according to the updated inverse Wishart distribution to obtain the updated (i.e., the actual) noise covariance matrix of the state transition process. :

[0103]

[0104] In this embodiment, the probability density expression of the inverse Wishart distribution is:

[0105]

[0106] in, Representation matrix traces; express The reverse.

[0107] In step 3.2), the specific steps for updating the observation noise variance are as follows:

[0108] 3.2.5): Utilizing step 3.1) The first sliding time window The result obtained in the last iteration of each round Calculate the sum of squared residuals for each sample:

[0109]

[0110] in, Indicates the first The first sliding time window The sum of squared residuals calculated in each round.

[0111] 3.2.6): Update the observation noise variance Corresponding inverse Gamma distribution Hyperparameters:

[0112]

[0113]

[0114] in, , They represent the first The first sliding time window Round and number Estimates of the shape hyperparameters of the inverse Gamma distribution over rounds; , They represent the first The first sliding time window Round and number Estimates of the scaling hyperparameters of the inverse Gamma distribution over rounds.

[0115] 3.2.7): Sample the observation noise variance according to the updated inverse Gamma distribution to obtain the updated (i.e., the actual) observation noise variance. :

[0116]

[0117] In this embodiment, the conditional probability density expression for the observation noise variance is:

[0118]

[0119] in, Represents the sum of squared residuals. Under the condition of [condition], the updated observation noise variance The conditional probability density.

[0120] Complete the first step by steps 3.1) and 3.2). After estimating the parameters of one outer loop cycle within a sliding time window, the result of this cycle is... , , and The noise covariance matrix of the state transition process in the next outer loop iteration is passed to the next iteration within the same sliding time window. and observation noise variance Construction of the prior distribution and calculation of the likelihood function.

[0121] Complete the first A sliding time window preset After the last outer loop, the mean of the time-varying cointegrated vector obtained in the last outer loop iteration is... Time-varying cointegrated vector covariance State transition process noise covariance matrix and observation noise variance As the first The final parameter estimation results for each sliding time window.

[0122] Among them, As the first Time-varying cointegration vectors of sliding time windows The estimated value, and and Pass to the The sliding time window is used to construct the first... The prior distribution of the time-varying cointegrated vector within the sliding time window; the first... The hyperparameters within each sliding time window are reset to their initial preset values, i.e. , , , This is to avoid the hyperparameters accumulating continuously between different sliding windows and affecting the stability of the estimation.

[0123] 4) Move from the current sliding time window to the next sliding time window according to the preset sliding step size, and execute step 3) in the next sliding time window to obtain the final estimation results of the time-varying cointegration vector mean, time-varying cointegration vector covariance, state transition process noise covariance matrix and observation noise variance corresponding to the next sliding time window.

[0124] 5) Repeat steps 3) and 4) until the parameter estimation for all sliding time windows is completed.

[0125] 6) In the offline phase, the operating monitoring data of the target gas turbine during known fault-free periods are used to perform parameter estimation through steps 1)-5) to obtain the mean of the time-varying cointegration vector corresponding to each sliding time window under healthy operating conditions; the cointegration coefficient and cointegration bias term are extracted from the mean of the time-varying cointegration vector, and the benchmark mean and benchmark variance of the cointegration coefficient and cointegration bias term are determined according to the cointegration coefficient and cointegration bias term of each sliding time window under healthy operating conditions.

[0126] 7) In the online phase, obtain the mean and covariance of the time-varying cointegration vector corresponding to the real-time operation monitoring data for which the sliding time window parameters have been estimated according to steps 1) to 5). Extract the estimated value of the cointegration coefficient and the estimated value of the cointegration bias term for the current sliding time window from the mean of the time-varying cointegration vector, and extract the corresponding estimated variance from the covariance of the time-varying cointegration vector. Construct a dynamic threshold range based on the benchmark mean, benchmark variance, and estimated variance. When the estimated value of the cointegration bias term exceeds the corresponding dynamic threshold range, and at least one estimated value of the cointegration coefficient exceeds the corresponding dynamic threshold range, trigger an anomaly flag.

[0127] 8) To reduce false alarms, a continuous sliding time window confirmation mechanism is adopted. When multiple consecutive sliding time windows trigger the anomaly flag, an alarm signal is output, along with the numerical values ​​of the monitoring data during the abnormal period and the estimated cointegration coefficients of the corresponding state variables.

[0128] In the offline phase of anomaly detection, all normal operating data are first collected during the period when the target gas turbine is known to be operating healthily. Parameter estimation is then performed according to steps 1) to 5) to obtain the mean of the time-varying cointegration vector for each sliding time window under healthy operating conditions.

[0129]

[0130] in, Indicates the first [unit / item] under healthy operating conditions The mean of the time-varying cointegrated vector of the nth sliding time window, which represents the nth time window under healthy operating conditions. Estimates of the time-varying cointegration vector for each sliding time window. , This represents the total number of sliding time windows constructed using operational monitoring data under healthy conditions; Indicates the first [unit / item] under healthy operating conditions The cointegration coefficients corresponding to the six state variables in a sliding time window; Indicates the first [unit / item] under healthy operating conditions Cointegration bias term in a sliding time window.

[0131] Next, the estimated value of the time-varying cointegration vector is used to obtain the benchmark mean and benchmark variance of the cointegration coefficient and cointegration bias term under healthy operating conditions:

[0132]

[0133]

[0134]

[0135]

[0136] in, , These represent the baseline mean and baseline variance of the cointegration bias term under healthy operating conditions, respectively. , These represent the first [unit / item] under healthy operating conditions. The benchmark mean and benchmark variance of each cointegration coefficient; Indicates the first [unit / item] under healthy operating conditions The first sliding time window corresponds to the first Each cointegration coefficient .

[0137] During online operation, for each newly acquired sliding time window Obtain the estimated value of the time-varying cointegration vector on the current sliding time window after executing steps 1) to 5). Covariance , where the covariance It is in matrix form. In this embodiment, the time-varying cointegration vector includes cointegration coefficients corresponding to six state variables and a cointegration bias term, therefore m=7, so the covariance of the time-varying cointegration vector is an m×m matrix. Then, the diagonal elements are extracted from the matrix covariance, where... The estimated variance of the cointegration bias term is, i.e., , For the first The estimated variance of each cointegration coefficient.

[0138] The variance mentioned above reflects the parameter estimation uncertainty within the current sliding time window due to limited data or noise levels. To account for this uncertainty and reduce false alarms, a dynamic threshold for anomaly detection is constructed by superimposing the baseline variance and the estimated variance of the sliding time window. For the cointegration bias term:

[0139]

[0140] in, Represents a sliding time window The upper limit for anomaly detection control of the cointegration bias term; Represents a sliding time window The lower limit for anomaly detection control of the cointegration bias term.

[0141] For each cointegration coefficient:

[0142]

[0143] in, Represents a sliding time window The first An upper limit for anomaly detection control of each cointegration coefficient; Represents a sliding time window The first The lower limit for anomaly detection control of each cointegration coefficient; This is the confidence coefficient, which is usually set to 3, but can also be adjusted between 2 and 4 depending on the false alarm tolerance in industrial scenarios.

[0144] When the uncertainty of parameter estimation is large, the threshold is automatically widened to reduce false alarms caused by data fluctuations or insufficient samples; when the estimation is accurate, the threshold is tightened to improve the sensitivity to real abnormal changes.

[0145] Within a sliding time window, when a cointegration bias term is detected to exceed a threshold range, and at least one cointegration coefficient term also exceeds the threshold range, an anomaly is considered to exist within the current sliding time window, triggering an anomaly flag. When continuous... When a sliding time window is marked as abnormal, a final alarm is triggered, outputting an alarm signal, as well as the numerical values ​​of the monitored operating data during the abnormal period and the estimated cointegration coefficients corresponding to the state variables.

[0146] The following is an embodiment of the present invention for early warning of gas turbine faults.

[0147] The data used in this embodiment comes from an in-service 25 MW gas turbine unit. During unit operation, various thermodynamic and operating parameters are continuously collected through multiple sensors deployed on key components such as the compressor, combustion chamber, and turbine. These parameters include: combustion chamber internal pressure, exhaust temperature, turbine temperature, fuel flow rate, compressor outlet temperature, compressor outlet pressure, and gas turbine output power. Figure 2 and Figure 3 As shown. The sampling time interval for all measuring points was 1 minute, with consistent sampling frequency and perfectly aligned timestamps. 33,120 sample points were collected for each variable, corresponding to 23 consecutive days of unit operation.

[0148] like Figure 2 and Figure 3 As shown, at the 2.6×10 4Near a sample point, the gas turbine unit experienced a sudden malfunction and urgently implemented load reduction operation. The data is presented in normalized form. As can be observed from the graph, at this point in time, the parameters at each measuring point and the gas turbine output power experienced a sharp drop without any obvious warning. Subsequent inspection confirmed that the malfunction was caused by a sudden crack on the compressor blade outlet side.

[0149] This invention is applied to the aforementioned gas turbine monitoring data to achieve early warning of sudden failures. During state-space modeling, the following will be used... Figure 2 The six monitoring signals are used as state variables in the state-space model. Figure 3 The output power of the gas turbine is used as the observation variable in the state-space model.

[0150] In the time-varying cointegration estimation process, a sliding window cointegration model is first performed on the first 10,000 sample points to obtain the baseline mean and variance of each cointegration parameter, as well as the baseline mean and variance of the cointegration bias term. Then, time-varying cointegration modeling is performed on the subsequent 23,120 samples, and a dynamic threshold is used to detect precursors of sudden faults. The hyperparameters of this algorithm are set as follows: sliding time window length of 200, sliding step size of 100, and covariance coefficient on the first sliding time window. Transition Markov chain Monte Carlo sampling points Number of iterations Priors for hyperparameters , , , Confidence coefficient .

[0151] Figure 4 and Figure 5 The invention demonstrates the cointegration modeling and anomaly detection results on gas turbine data, wherein cointegration coefficient 1 is the cointegration coefficient corresponding to the combustion chamber internal pressure, cointegration coefficient 2 is the cointegration coefficient corresponding to the exhaust temperature, cointegration coefficient 3 is the cointegration coefficient corresponding to the turbine temperature, cointegration coefficient 4 is the cointegration coefficient corresponding to the fuel flow rate, cointegration coefficient 5 is the cointegration coefficient corresponding to the compressor outlet temperature, and cointegration coefficient 6 is the cointegration coefficient corresponding to the compressor outlet pressure. Figure 4 and Figure 5 The red line in the diagram represents the dynamic threshold ranges of the cointegration coefficient and the cointegration bias term, respectively. In the 1.1×10... 4 Up to 1.2×10 4 Near a certain sample point, the cointegration coefficients 1 and 6 began to deviate continuously from the anomaly detection control range, indicating that the long-term equilibrium relationship between variables experienced significant drift due to changes in combustion chamber internal pressure and compressor outlet pressure. Meanwhile, Figure 5The cointegration bias term in the data also began to deviate continuously from the anomaly detection control range during the same period, with its value gradually increasing from near zero in the healthy state to about 6.

[0152] According to the alarm logic of the present invention, in the 1.1×10 4 Up to 1.2×10 4 The method triggers a final alarm near each sample point. Based on a 1-minute sampling interval for each sample point, the method can detect the precursors of sudden blade fracture failures approximately 9 days in advance, verifying the effectiveness and engineering practical value of the proposed method in early warning of sudden failures in gas turbines.

[0153] The above-described embodiments are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. Those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals, characterized in that, Includes the following steps: 1) Real-time acquisition of monitoring time-series data of the gas turbine to be detected during continuous operation, wherein the monitoring time-series data includes the sampled values ​​of various monitoring signals at continuous sampling time; wherein the various monitoring signals include gas turbine output power, combustion chamber internal pressure, exhaust temperature, turbine temperature, fuel flow rate, compressor outlet temperature and compressor outlet pressure; 2) Divide the monitoring time series data into windows according to the preset window length and sliding step size; within each window, construct a state space model describing the time-varying cointegration relationship between each monitoring signal, and perform Bayesian parameter estimation to obtain the mean and covariance of the time-varying cointegration vector corresponding to each window; Then, the estimated value of the cointegration bias term and the estimated value of the cointegration coefficient corresponding to some monitoring signals are extracted from the mean of the time-varying cointegration vector of each window. Constructing the state-space model includes: designating one type of monitoring signal as the observed variable and the remaining monitoring signals as state variables; using the sequence of observed variables within each window as the output term of the observation equation; forming an extended state variable matrix by combining the sequence of state variables within the window with a unit vector used to introduce the cointegration bias term; establishing the observation equation based on the extended state variable matrix and the time-varying cointegration vector, wherein the time-varying cointegration vector includes the cointegration bias term and the cointegration coefficients corresponding to each state variable; using a first-order random walk model to describe the evolution of the time-varying cointegration vectors of adjacent windows, and establishing a state transition equation; the observation equation and the state transition equation form the state-space model. Bayesian parameter estimation of the state-space model includes: a) For the current window, based on the mean and covariance of the time-varying cointegrated vector of the previous window, and the current value of the noise covariance matrix of the state transition process of the state transition equation in the current window, construct the prior distribution of the time-varying cointegrated vector of the current window, and collect multiple time-varying cointegrated vector samples. b) Combining the current value of the observation noise variance of the observation equation, the transition Markov chain Monte Carlo algorithm is used to update the current time-varying cointegrated vector sample, obtain the time-varying cointegrated vector sample set, and update the noise covariance matrix and observation noise variance of the state transition process. c) Repeat step b) until the preset number of rounds is reached, and obtain the mean and covariance of the time-varying cointegrated vector of the current window based on the time-varying cointegrated vector sample set; 3) Based on the covariance of each window in step 2) and the health benchmark parameters of each cointegration coefficient and cointegration bias term, construct the dynamic threshold range of the cointegration coefficient and cointegration bias term under each window. When the estimated value of the cointegration bias term and at least one estimated value of the cointegration coefficient of the window in step 2) exceeds the corresponding dynamic threshold range, an anomaly flag is triggered; when anomaly flags are triggered for a preset number of consecutive windows, an alarm signal is output.

2. The gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals according to claim 1, characterized in that, In step b), updating the current time-varying cointegrated vector sample using the transitional Markov chain Monte Carlo algorithm includes: The likelihood value of each current time-varying cointegrated vector sample is obtained based on the current value of the observation noise variance, the observation variable sequence of the current window, and the extended state variable matrix. The weight of the current time-varying cointegrated vector sample is determined based on the likelihood value. Then, based on the weight of the current time-varying cointegrated vector sample, resampling and candidate sample acceptance are performed to obtain the updated time-varying cointegrated vector sample, forming a time-varying cointegrated vector sample set.

3. The gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals according to claim 1, characterized in that, In step b), updating the noise covariance matrix of the state transition process includes: obtaining the outer product sum based on each time-varying cointegrated vector sample in the time-varying cointegrated vector sample set and the mean of the time-varying cointegrated vector in the previous window, and updating the noise covariance matrix of the state transition process based on the outer product sum.

4. The gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals according to claim 1, characterized in that, In step b), updating the observation noise variance includes: obtaining the residual sum of squares based on the observation variable sequence, the extended state variable matrix, and the time-varying cointegrated vector samples in the time-varying cointegrated vector sample set, and updating the observation noise variance based on the residual sum of squares.

5. The gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals according to claim 1, characterized in that, In step 3), the method for generating the health baseline parameters of each cointegration coefficient and cointegration bias term includes: acquiring the monitoring time series data of the gas turbine during its historical healthy operating period, dividing it into sliding windows, obtaining the mean of the time-varying cointegration vector of each window during the historical healthy operating period, extracting the cointegration coefficient and cointegration bias term from the mean of the time-varying cointegration vector of each window, obtaining the mean and variance of each cointegration coefficient and the mean and variance of the cointegration bias term in all windows during the historical healthy operating period, that is, obtaining the health baseline parameters of the cointegration coefficient and the health baseline parameters of the cointegration bias term.

6. The gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals according to claim 1, characterized in that, In step 3), constructing the dynamic threshold range of cointegration coefficients and cointegration bias terms under each window includes: extracting the estimated variances corresponding to the cointegration coefficients and cointegration bias terms from the time-varying cointegration vector covariance of each window in step 2), and then obtaining the upper limit and lower limit of the dynamic thresholds of the cointegration coefficients and cointegration bias terms under each window according to the health benchmark parameters, the estimated variances and the preset confidence coefficients, thereby obtaining the dynamic threshold range of the cointegration coefficients and cointegration bias terms under each window.

7. The gas turbine anomaly detection method based on time-varying cointegration modeling of monitoring signals according to claim 1, characterized in that, In step 3), while outputting the alarm signal, the monitoring time series data and time-varying cointegration vector corresponding to each window are also output.

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