Water turbine governor fault modeling and parameter optimization method based on iterative learning control

Abstract

The invention discloses a water turbine governor fault modeling and parameter optimization method based on iterative learning control. The method comprises the following steps: S1, system dynamics modeling; s2, iterative learning parameter updating, wherein a water turbine governor fault diagnosis method based on iterative learning control realizes progressive identification of fault features through periodically correcting model parameters; s3, fault feature extraction: calculating a residual signal of an actual output and a model predicted value, performing time-frequency analysis on the residual signal by adopting improved Morlet wavelet transform, and extracting an energy entropy feature and a time domain statistical feature; s4, fault diagnosis and dynamic optimization: based on the extracted fault features, fault detection and classification are realized through a three-level linkage decision mechanism, a dynamic adjustment strategy is introduced to carry out online optimization on a diagnosis rule base, and fault modeling and parameter optimization closed loop are completed; according to the method, the problem of modeling misalignment of a traditional method under a nonlinear working condition is effectively solved.

Description

Technical Field

[0001] This invention relates to the field of hydro turbine governor technology, and in particular to a method for fault modeling and parameter optimization of hydro turbine governors based on iterative learning control. Background Technology

[0002] As a core control device in hydropower systems, the turbine governor's dynamic characteristics directly affect grid frequency stability and unit regulation quality. With the increasing proportion of renewable energy, governors need to maintain control accuracy over a wider operating range, placing higher demands on the real-time performance and reliability of fault diagnosis. Traditional mechanistic model-based methods suffer from modeling errors under nonlinear conditions, while data-driven methods are limited by a scarcity of fault samples. Both fall short of meeting the demands of modern power systems for fault self-healing capabilities.

[0003] Current fault diagnosis faces three key challenges: First, the hydraulic-mechanical coupling characteristics of speed governors result in a strongly nonlinear relationship between fault parameters and output response; second, the fault data available in the field is mostly fragmented data under single operating conditions, making it difficult to support supervised learning requirements; and third, existing methods are insufficiently adaptable to time-varying operating conditions. For example, a case study of the Yunnan power grid shows that conventional methods have a false alarm rate as high as 34% during load abrupt changes. These limitations essentially stem from the lack of iterative optimization mechanisms in the fault modeling process.

[0004] Current fault diagnosis technologies for hydro turbine governors suffer from several key shortcomings: First, mechanistic model-based methods heavily rely on the assumption of system linearity, making it difficult to accurately describe the nonlinear characteristics during actual operation. Second, data-driven methods face the challenge of small sample sizes; statistics from the National Energy Administration in 2023 show that actual fault samples account for only 0.3%-1.2% of normal operation data, resulting in insufficient generalization ability of the diagnostic model.

[0005] More seriously, existing methods generally have poor adaptability to time-varying operating conditions. The 2021 Fujian Power Grid accident analysis report pointed out that 63% of malfunctions stemmed from the failure to promptly correct model mismatch caused by water hammer effects. Regarding real-time performance, methods such as deep belief networks suffer from excessive computational costs, with a single diagnosis taking over 200ms and consuming 83.7MB of memory, making it difficult to meet the needs of embedded deployments in the field. The combined fault case at the Baihetan Hydropower Station in 2023 further exposed the limitations of traditional methods—when hydraulic servo jamming and sensor drift occurred simultaneously, the system incorrectly identified it as a simple PID parameter problem, reflecting the current technology's severe inadequacy in identifying coupled faults.

[0006] These shortcomings can be summarized in three aspects: first, the contradiction between static modeling and dynamic systems; second, the imbalance between sample scarcity and model complexity; and third, the disconnect between offline learning modes and online application requirements. Of particular note is the fact that monitoring data from a pumped-storage power station shows that under frequency fluctuation conditions, the variance of parameter estimation by a traditional Kalman filter increases by 4.6 times. This parameter drift directly leads to a higher false alarm rate in fault warnings. These limitations severely restrict the development of intelligent operation and maintenance of turbine speed control systems, necessitating the establishment of new adaptive diagnostic methods with online learning capabilities. Summary of the Invention

[0007] The purpose of this invention is to overcome the above-mentioned shortcomings and provide a fault modeling and parameter optimization method for turbine governors based on iterative learning control, which improves the modeling accuracy of nonlinear operating conditions. The fault modeling method for turbine governors based on iterative learning control effectively solves the modeling inaccuracy problem of traditional methods under nonlinear operating conditions through a dynamic correction mechanism.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for fault modeling and parameter optimization of a hydro turbine governor based on iterative learning control, comprising the following steps: S1. System dynamics modeling: Establish a state space model of the turbine governor that includes fault parameters, take the guide vane opening and guide vane speed as state variables, couple water hammer effect, viscous friction and fault disturbance terms to construct system dynamic equations, and use parameterization method to characterize mechanical jamming, hydraulic leakage and sensor drift faults as key parameter offsets. S2. Iterative learning parameter update: The fault diagnosis method for turbine governors based on iterative learning control achieves progressive identification of fault characteristics by periodically correcting model parameters; S3. Fault Feature Extraction: Calculate the residual signal between the actual output and the model prediction value, and use the improved Morlet wavelet transform to perform time-frequency analysis on the residual signal to extract energy entropy features and time-domain statistical features. S4. Fault Diagnosis and Dynamic Optimization: Based on the extracted fault features, fault detection and classification are achieved through a three-level linkage decision-making mechanism. A dynamic adjustment strategy is introduced to optimize the diagnostic rule base online, completing the closed loop of fault modeling and parameter optimization.

[0009] Preferably, in S1, the system dynamic equation is: ; Where J is the moment of inertia. Let B be the equivalent stiffness due to water hammer effect, B be the coefficient of viscous friction, u be the control input, and f be the stiffness. d This is a comprehensive disturbance term that includes mechanical jamming and hydraulic leakage faults. y represents the rotation angle of the water turbine. , For the turbine speed, This is the angular acceleration of the water turbine.

[0010] Preferably, the equivalent stiffness due to water hammer effect The coefficient of viscous friction B is expressed as follows: ;in, This is the initial value of the equivalent stiffness. This is the disturbance value; This is the initial value of the viscous friction coefficient. This represents the disturbance value.

[0011] Preferably, the comprehensive disturbance term is modeled as follows:

[0012] in Let d(t) be the amplitude of the chalcogenide force, and d(t) be the unknown disturbance.

[0013] Preferably, S2 specifically comprises: S2.1 Construct a dynamic learning mechanism, whose iterative update law can be expressed as: ; in This is the controller parameter vector for the k-th iteration; Let be the learning gain matrix for the k-th iteration; This is the sensitivity matrix; This is the output error vector for the k-th iteration; S2.2 The sensitivity matrix is ​​calculated using the numerical difference method: ; Among them, y i It is the i-th output of the system; It is the first k The parameter estimates at the next iteration; It is the first one to be optimized. j One parameter; δ is the perturbation step size; S2.3 The learning gain matrix Γk is adaptively adjusted according to the Lyapunov stability condition: ; Where η and β are adjustment coefficients to ensure the convergence of the algorithm; S2.4. A dual-time-scale update strategy is adopted, with different update frequencies set for fast-changing parameters and slow-changing parameters. Fast-changing parameters are updated in every iteration, while slow-changing parameters are updated once after every N iterations. S2.5 After each iteration, the parameter estimates are constrained within the physically feasible region by the projection operator: ; Guarantee stiffness parameters ∈[0.8 1.2 The coefficient of friction B ≥ 0.

[0014] Preferably, step S2 further includes the following step: S2.6 To improve anti-interference capability, a Butterworth low-pass filter is introduced into the error channel: ; in This is the original output error vector for the k-th iteration; For the first k The filtered error vector of the next iteration; This is the transfer function of the Butterworth low-pass filter; The coefficients in the denominator of the transfer function; These are the numerator coefficients of the transfer function.

[0015] Preferably, the formula for calculating the residual signal between the actual output and the model prediction in step S3 is as follows: ; in This is the residual signal; To calculate the actual output; These are the model's predicted values.

[0016] Preferably, the formula for time-frequency analysis of the residual signal using the improved Morlet wavelet transform in step S3 is as follows: ; Where a is the scale parameter and b is the translation parameter. W ( a , b ) are wavelet coefficients, This is the residual signal.

[0017] Preferably, the extraction of energy entropy features and time-domain statistical features in S3 includes: Energy entropy characteristics: ; Where E is the value of energy entropy; N is the total number of frequency bands; Pi is the energy probability of the i-th frequency band; Time-domain statistical characteristics: ; Where μ is the sample mean of the residual signal; σ is the sample standard deviation; and e(k) is the discrete-time value.

[0018] Preferably, in S4, the three-level linkage decision-making mechanism includes: the primary detection layer uses a sliding time window (L=1s) to calculate the transient energy index and trigger an abnormal alarm; the intermediate diagnosis layer constructs a TSK-type fuzzy system and classifies fault modes through S-type membership functions; the advanced analysis layer uses matrix singular value decomposition technology to separate coupled faults under the constraint of condition number threshold cond(J)<100.

[0019] Preferably, in step S4, the dynamic adjustment strategy includes: updating the feature baseline value using the exponentially weighted moving average (EWMA) method; and optimizing the rule weights of the diagnostic rule base online using the fault feature vector as the state input through the Q-learning algorithm.

[0020] The beneficial effects of this invention are as follows: This invention achieves significant breakthroughs in nonlinear condition modeling, few-sample learning, and time-varying adaptability. Traditional methods suffer from modeling errors exceeding 28% under strongly nonlinear conditions, while this invention controls the error to within 5% through a dynamic compensation mechanism. Addressing the issue of scarce fault samples, traditional data-driven methods require a large amount of labeled data, while this invention achieves over 90% accuracy with only a small number of samples. Regarding time-varying condition adaptability, traditional methods suffer from severe parameter drift and slow response, while this invention significantly improves dynamic performance through an intelligent update mechanism. These improvements enable a qualitative leap in the accuracy, real-time performance, and reliability of turbine governor fault diagnosis, providing an innovative solution for equipment health management in complex industrial scenarios. Furthermore, it improves the accuracy of nonlinear condition modeling; the turbine governor fault modeling method based on iterative learning control effectively solves the modeling inaccuracy problem of traditional methods under nonlinear conditions through a dynamic correction mechanism. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating a fault modeling and parameter optimization method for a hydro turbine governor based on iterative learning control. Figure 2 This is a schematic diagram of fault feature extraction and diagnosis. Detailed Implementation

[0022] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0023] Example 1: An iterative learning-based fault model method for hydro-turbine governors achieves high-precision fault diagnosis through a dynamic parameter correction mechanism. This method first establishes a state-space model containing fault parameters, coupling key parameters such as guide vane opening and speed with fault characteristics (e.g., jamming force, stiffness changes). During the iteration process, the system collects real-time operating data such as guide vane position and oil pressure, compares it with the model's predicted values, calculates parameter corrections using a sensitivity matrix, and introduces adaptive learning gain and robust filtering to ensure convergence.

[0024] This method employs a dual-timescale update strategy, setting different update cycles for rapidly changing parameters (such as sensor gain) and slowly changing parameters (such as mechanical wear). By constructing a parameter feasible region projection operator, it ensures that all estimated values ​​meet physical constraints, such as controlling stiffness parameter fluctuations within ±20% of the nominal value and maintaining the non-negative characteristic of the friction coefficient. To improve engineering applicability, the system also integrates a safety monitoring module, which automatically triggers a protection mechanism when excessive jamming force or abnormal parameters are detected. The specific construction process is as follows: 1. System dynamics modeling The turbine governor is a typical nonlinear electromechanical-hydraulic coupled system, and its dynamic characteristics can be described by state-space equations. Let the guide vane opening be the state variable x1, and the guide vane velocity be x2, then the system dynamic equations are:

[0025] Where J is the moment of inertia. denoted as the equivalent stiffness due to water hammer effect, B as the viscous friction coefficient, u as the control input, and fe as the comprehensive disturbance term including faults such as mechanical jamming and hydraulic leakage.

[0026] Fault modeling employs a parametric approach, representing system anomalies as deviations in key parameters. Faults related to stiffness parameters and friction coefficients can be expressed as:

[0027] The nonlinear clamping force is modeled as follows:

[0028] in Let d(t) be the amplitude of the chalcogenide force, and d(t) be the unknown disturbance.

[0029] This modeling faces three main challenges: first, the strong nonlinear coupling between the water hammer effect and mechanical motion leads to significant errors in traditional linearization methods; second, the coupling effect between faults makes it difficult to identify individual faults; and third, high real-time requirements necessitate the algorithm to complete calculations within a 10ms control cycle. To address these issues, an iterative learning framework is adopted, dynamically correcting model parameters by repeatedly running data, while a hierarchical modeling strategy is introduced to separate fast-changing and slow-changing fault characteristics.

[0030] 2. Iterative learning The turbine governor fault diagnosis method based on iterative learning control achieves progressive identification of fault features by periodically correcting model parameters. The core of this method lies in constructing a dynamic learning mechanism, whose iterative update law can be expressed as:

[0031] in This is the controller parameter vector for the k-th iteration; Let be the learning gain matrix for the k-th iteration; This is the sensitivity matrix; The output error vector is the result of the k-th iteration; the sensitivity matrix is ​​calculated using the numerical difference method.

[0032] This method employs a dual-timescale update strategy, setting different update frequencies for rapidly changing parameters (such as sensor gain) and slowly changing parameters (such as mechanical wear). This differentiated processing of rapidly changing parameters (5ms update) and slowly changing parameters (10min update) reduces the fault detection delay from 5 minutes to 40 seconds and lowers the parameter drift variance by 83%, perfectly solving the performance degradation problem of traditional methods under dynamic conditions such as power grid frequency fluctuations. Through the dual-timescale parameter update mechanism and forgetting factor design, this method significantly improves its adaptability under time-varying conditions. (Learning gain matrix) Adaptive adjustment based on Lyapunov stability conditions:

[0033] Here, η and β are adjustment coefficients to ensure the convergence of the algorithm. After each iteration, the parameter estimates are constrained within the physically feasible region by the projection operator:

[0034] Guarantee stiffness parameters ∈[0.8 1.2 Physical constraints such as friction coefficient B≥0. This is the initial reference value for the equivalent stiffness due to the water hammer effect.

[0035] To improve anti-interference capability, a Butterworth low-pass filter is introduced into the error channel:

[0036] This filter effectively suppresses the effects of high-frequency noise, with the cutoff frequency set to 1 / 5 of the system bandwidth. Through no more than 20 iterations, the parameter estimation error can be converged to within 5%, meeting the requirements of engineering applications.

[0037] 3. Fault Feature Extraction Feature extraction based on residual signal analysis employs a multi-scale method. First, the residual between the actual output and the model prediction is calculated:

[0038] Time-frequency analysis using an improved Morlet wavelet transform:

[0039] Where 'a' is the scale parameter and 'b' is the translation parameter. Feature extraction includes: Energy entropy characteristics:

[0040] Time-domain statistical characteristics:

[0041] 4. Fault Diagnosis Rules The core of the turbine governor fault diagnosis system lies in the construction of an intelligent analysis system that deeply integrates feature extraction, hierarchical decision-making, and dynamic optimization. The system first comprehensively analyzes the operating status using multi-physical quantity feature tomography, and then constructs a fault feature basis using an adaptive wavelet packet decomposition method to achieve fine-grained mining of signal features in the time-frequency domain. This method automatically selects the optimal basis function from 16 sub-frequency bands by designing a cost function containing an energy term and a sparse penalty term (λ=0.1), and calculates the spectral kurtosis index of each frequency band to quantify the signal's impact characteristics. Simultaneously, the system also establishes a dynamic Jacobian matrix to analyze parameter sensitivity and calculates the parameter observability index, providing multi-dimensional feature support for subsequent diagnosis.

[0042] Based on feature analysis, the system employs a three-level linkage decision-making mechanism to achieve accurate fault identification. The primary detection layer uses a sliding time window (L=1s) to calculate transient energy indices, immediately triggering an alarm when abnormal energy fluctuations, excessive stiffness parameters, or excessive jamming forces are detected. The intermediate diagnostic layer constructs a TSK-type fuzzy system, using S-shaped membership functions and regular antecedent activation strength calculations to achieve accurate classification of complex fault modes. The advanced analytical layer utilizes matrix singular value decomposition (SVD) technology to effectively separate coupled faults while ensuring numerical stability (condition number threshold cond(J) < 100). This hierarchical processing mechanism, progressing from shallow to deep, ensures both real-time detection and accurate diagnosis.

[0043] To ensure continuous optimization of the diagnostic system, a closed-loop dynamic adjustment strategy was designed. By introducing the Exponentially Weighted Moving Average (EWMA) method to update feature benchmark values ​​in real time, the system can adapt to changes in the operating environment. Simultaneously, a Q-learning algorithm is used to optimize the rule base online, using fault feature vectors as state input and continuously adjusting rule weights through a reinforcement learning mechanism. Actual operational data shows that this diagnostic system has achieved significant results in a hydropower station on the Lancang River, not only increasing the single fault detection rate to 95.2% and the composite fault identification rate to 88.7%, but also completing the entire analysis process within 23ms, fully meeting the real-time requirements of the field control system. This technical approach, integrating advanced signal processing, fuzzy inference, and machine learning, provides a reliable solution for the intelligent operation and maintenance of hydropower units.

[0044] The embodiments of the present invention have the following advantages: 1. An iterative learning control-based method was designed to achieve accurate modeling through a dynamic correction mechanism, addressing the modeling inaccuracies caused by the strong nonlinear characteristics of the turbine governor. This method employs an error feedback compensation strategy to identify nonlinear parameters such as hydraulic dead zones and friction hysteresis online. Under conditions where the guide vane opening is >70%, the model error of the traditional method is reduced to within 5% (28.7%). By constructing a nonlinear state equation containing quadratic and cross terms, the model fidelity under complex conditions such as large opening and rapidly changing loads is significantly improved.

[0045] 2. A scheme integrating virtual sample generation and incremental learning is proposed to solve the industry problem of scarce fault samples. Synthetic fault samples are generated by superimposing parameter perturbations on normal data, and the feature space is expanded by combining sliding window technology, which improves the effective data utilization rate by 10 times. A classification accuracy of over 90% can be achieved with only 7 sets of actual fault data.

[0046] 3. A dual-timescale update mechanism and a dynamic forgetting factor are proposed to effectively address time-varying operating conditions such as power grid frequency fluctuations. Through optimized algorithm design, the timeliness of fault detection is significantly improved, greatly reducing the detection delay of traditional methods, while effectively suppressing fluctuations in parameter estimation. Under dynamic conditions such as rapid load changes, the system maintains a high fault identification accuracy, demonstrating excellent robustness and adaptability. This improvement enables the method to better cope with various complex operating conditions in power system operation.

[0047] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for modeling and parameter optimization of a water turbine governor failure based on iterative learning control, characterized in that, The method comprises the following steps: S1, system dynamics modeling: a state space model of a hydraulic turbine governor containing fault parameters is established, the guide vane opening and the guide vane movement speed are taken as state variables, a system dynamics equation is constructed by coupling water hammer effect, viscous friction and fault disturbance term, and a parameterization method is used to characterize mechanical jamming, hydraulic leakage and sensor drift fault as key parameter deviation; S2, iterative learning parameter updating: a fault diagnosis method of the hydraulic turbine governor based on iterative learning control realizes gradual identification of fault characteristics by periodically correcting model parameters; S3, fault feature extraction: a residual signal of actual output and model prediction value is calculated, an improved Morlet wavelet transform is used for time-frequency analysis of the residual signal, and energy entropy features and time domain statistical features are extracted; S4, fault diagnosis and dynamic optimization: based on the extracted fault features, fault detection and classification are realized through a three-stage linkage decision mechanism, a dynamic adjustment strategy is introduced to optimize the diagnosis rule base online, and a fault modeling and parameter optimization closed loop is completed.

2. The method of claim 1, wherein the method is characterized by, In S1, the system dynamics equation is: ； where J is the moment of inertia, B is the viscous friction coefficient, u is the control input, f d is the comprehensive disturbance term containing mechanical jamming, hydraulic leakage failure, , y is the rotation angle of the water turbine, , is the rotation speed of the water turbine, is the angular acceleration of the water turbine.

3. The method of claim 2, wherein the method further comprises: Water hammer effect equivalent stiffness and the viscous friction coefficient B are respectively expressed as: ; wherein, is an initial value of the equivalent stiffness, is a perturbation value; is an initial value of the viscous friction coefficient, is a perturbation value.

4. The method of claim 2, wherein the method further comprises: The comprehensive disturbance term is modeled as: wherein is the stick force amplitude, d(t) is the unknown disturbance.

5. The method of claim 1, wherein the method further comprises: S2 specifically is: S2.1, a dynamic learning mechanism is constructed, and the iterative updating law can be expressed as: ； wherein is the controller parameter vector for the kth iteration; is the learning gain matrix for the kth iteration; is the sensitivity matrix; is the output error vector for the kth iteration; S2.2, the sensitivity matrix is calculated by the numerical difference method: ； Among them, y i It is the i-th output of the system; It is the first k The parameter estimates at the next iteration; It is the first one to be optimized. j One parameter; δ is the perturbation step size; S2.3, the learning gain matrix Γk is adaptively adjusted according to the Lyapunov stability condition: ； Where η and β are adjustment coefficients to ensure the convergence of the algorithm; S2.4, a double-time-scale updating strategy is adopted, different updating frequencies are set for fast-varying parameters and slow-varying parameters, and the fast-varying parameters are updated every iteration; the slow-varying parameters are updated once every N iterations; S2.5, after each iteration, the parameter estimation value is constrained in the physical feasible region by a projection operator: ； Guaranteeing stiffness parameters ∈ [0.8 , 1.2 ], friction coefficient B ≥ 0.

6. The method of claim 5, wherein the method further comprises: S2 also includes the following steps: S2.6, to improve the anti-interference ability, a Butterworth low-pass filter is introduced in the error channel: ； wherein is the original output error vector for the kth iteration; is the filtered error vector for the kth iteration; k is the filtered error vector for the kth iteration; is the transfer function of a Butterworth low-pass filter; is the denominator coefficient of the transfer function; is the numerator coefficient of the transfer function.

7. The method according to claim 1, wherein, In S3, the formula for calculating the residual signal of actual output and model prediction value is: ； wherein is the residual signal; is the calculated actual output; is the model predicted value.

8. The method according to claim 1, wherein, In S3, the formula for time-frequency analysis of the residual signal by the improved Morlet wavelet transform is: ； where a is a scale parameter and b is a translation parameter, W a b are wavelet coefficients, is a residual signal.​​ 9.The water turbine governor fault modeling and parameter optimization method based on iterative learning control according to claim 1, wherein, In S3, the energy entropy features and time domain statistical features include: Energy entropy features: ； Where E is the value of energy entropy; N is the total number of frequency bands; Pi is the energy probability of the i th frequency band; Time domain statistical features: ； Where μ is the sample mean of the residual signal; σ is the sample standard deviation; e(k) is the discrete time value.

10. The method of claim 1, wherein the method further comprises: In S4, the three-stage linkage decision mechanism includes: the primary detection layer calculates the transient energy index using a sliding time window (L=1s) to trigger an abnormal alarm; the intermediate diagnosis layer constructs a TSK type fuzzy system to realize fault mode classification through an S-shaped membership function; the advanced analysis layer uses matrix singular value decomposition technology to separate the coupled faults under the constraint of a condition number threshold cond(J)<100.

11. The method of claim 1, wherein the method further comprises: In S4, the dynamic adjustment strategy includes: updating the feature reference value by using the exponential weighted moving average (EWMA) method; using the Q-learning algorithm to input the fault feature vector as the state to optimize the rule weight of the diagnosis rule base online.

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