Fault Diagnosis Method and Application for GTs Based on Dynamic Quantile SPC and Prior Knowledge

Abstract

This paper addresses the challenges of fault diagnosis in gas turbines (GTs) utilized in oil and gas pipeline systems by proposing a novel multiparameter analysis framework that integrates dynamic, quantile-based Statistical Process Control (SPC) with prior domain knowledge. The proposed approach initially employs a dynamic quantile SPC model to establish adaptive control limits, effectively handling the non-stationarity and non-normality of gas turbine operational data. By analyzing parameter variations under typical operating conditions and incorporating expert insights, a multiparameter fault analysis matrix and corresponding weighting factors are constructed to facilitate fault diagnosis with prior knowledge. Furthermore, a fault probability model based on parameter change rates and weighting factors is developed to quantify the likelihood of different fault modes. An operating condition clustering and correction mechanism enables the dynamic adjustment of control limits, thereby preventing misdiagnoses caused by varying operational states. The validity of the proposed method is demonstrated using real data from a domestic pipeline gas turbine, validated by real domestic pipeline GT data, outperforming existing models, with a fault accuracy up to 10%. The approach efficiently estimates fault probabilities and accurately detects both sudden and gradual faults, significantly enhancing intelligent fault diagnosis capabilities for gas turbines.

1. Introduction

With the escalating global energy demand, natural gas has become a vital energy resource due to its cleanliness, substantial reserves, extensive geographic distribution, and high calorific value. According to the International Energy Agency, global natural gas consumption reached approximately 4239 billion cubic meters in 2023, and this figure is projected to continue growing [1]. This upward trend has driven the expansion of the natural gas pipeline infrastructure. Gas turbines play a crucial role within this infrastructure, as they power compressors to maintain pressure and flow over long-distance pipelines. The reliable and efficient operation of these turbines is essential to ensure the stability and safety of the entire pipeline system. Failures in the combustion system, lubrication system, or fuel system can result in significant economic losses, operational disruptions, and even safety hazards [2]. As highlighted in previous research, developing effective fault diagnosis methods for gas turbines used in oil and gas pipeline systems is fundamental to maintaining uninterrupted pipeline operation [3].

Over the past few decades, extensive research has been dedicated to fault diagnosis in gas turbines. Traditional approaches—including vibration analysis, oil analysis, and thermography—have been widely applied. Vibration analysis involves monitoring signals to detect anomalies in components such as rotors and bearings. By analyzing parameters like vibration amplitude and frequency, potential faults can be identified. However, these methods face limitations: in complex gas turbine systems, vibration signals are often contaminated by noise, complicating accurate fault feature extraction [4]. Oil analysis, which assesses the condition of lubricants and wear debris, may lack sensitivity for early-stage fault detection [5]. Thermography, while useful for surface defect detection, has limited capacity for diagnosing internal component failures [6].

The advancement of information technology and data-driven approaches has led to the emergence of novel fault diagnosis methods based on machine learning and artificial intelligence. Neural-network-based techniques, including backpropagation neural networks and convolutional neural networks, have demonstrated significant potential in modeling complex data patterns. These methods can learn relationships among operating parameters and fault types from large-scale datasets. Nonetheless, they require substantial amounts of labeled data for training, and their interpretability remains a persistent challenge [7]. Support vector machines, another popular machine learning technique, excel at classification tasks but face difficulties in parameter selection and may underperform on large or imbalanced datasets [8]. Intelligent diagnostic tools such as expert systems and fault tree analysis each have their own strengths and limitations; Ref. [9] expert systems leverage domain knowledge but require arduous knowledge acquisition and updating processes, while fault tree analysis primarily addresses known failure modes, often struggling with novel faults [10].

Recent studies have explored innovative directions in gas turbine fault diagnosis. For example, Zhang, M. and Li, Y. [2] proposed hybrid models combining deep learning with expert knowledge to improve diagnostic accuracy and address limitations of individual methods. Meanwhile, Zhao, Y. and Liu, F. [11] focused on leveraging real-time data streams and online learning algorithms to adapt to changing operational conditions, enabling faster fault detection. Despite these advances, there remains significant scope for developing more comprehensive, accurate, and efficient diagnostic approaches.

Additionally, advanced sensor technologies have been introduced to improve data collection. Li, Y., and Zhang, H. [12] developed high-precision vibration sensors capable of capturing more detailed signals, potentially enhancing vibration-based fault diagnosis. Chen, W., and Liu, S. [13] investigated sensor fusion techniques for integrating data from multiple sensors, providing a more holistic view of turbine health.

Deep transfer learning, which utilizes pre-trained models on large-scale general data, has also gained attention in this domain. Such models can be fine-tuned to specific gas turbine fault diagnosis tasks, reducing reliance on vast, labeled in-house data [14]. However, transfer learning faces challenges: differences between source and target data—especially when applying models trained on industrial machinery to gas turbines—can limit effectiveness. For instance, a study cited in [15] showed that transfer models struggled to accurately classify rare faults like combustion instability due to the highly specialized operating conditions and fault mechanisms of gas turbines.

Furthermore, combining physical models with data-driven approaches offers promising prospects. Physical models provide theoretical insights into fault mechanisms, while data-driven models uncover complex patterns from real data. Integrating these can enhance both accuracy and interpretability [16]. Nonetheless, this approach introduces challenges: physical models often incorporate simplifying assumptions that may not hold under all conditions; as shown in [17], such simplifications can lead to inaccuracies during extreme operating states. Additionally, the computational costs of running combined models in real time remain high, limiting their practical application [18].

Given the critical role of gas turbines in natural gas pipeline systems and the limitations of existing fault diagnosis methods, there is an urgent need for more comprehensive and efficient solutions. The proposed method—merging an extended Statistical Process Control (SPC) approach with prior domain knowledge—shows promising potential. The extended SPC is better equipped to handle the non-stationary and complex data characteristics typical of gas turbines. By integrating prior knowledge, such as typical fault patterns and inter-parameter relationships [19], it can more accurately detect abnormal operations. For example, knowledge of the correlation between fuel flow rate and turbine speed can facilitate setting more reasonable control limits; significant deviations from this correlation could indicate potential faults. Compared to black-box machine learning models, this approach not only enhances diagnostic accuracy but also improves interpretability, assisting engineers in understanding the diagnosis and taking informed actions [20].

In conclusion, this study proposes a Dynamic Quantile-Based Extended SPC with Operating Condition Correction method, inspired by [21] and tailored to gas turbine characteristics. Traditional fixed-threshold methods struggle with the complex, time-varying operation of gas turbines. The proposed method—leveraging dynamic quantile features and operating condition correction—adapts in real time to data variations and factors’ impacts. This results in improved diagnosis accuracy and robustness, providing a more reliable assessment of turbine health. Ultimately, this approach lays a solid foundation for enhancing the reliability and safety of gas turbines in natural gas pipelines, minimizing downtime, reducing maintenance costs, and preventing catastrophic failures. Existing GT fault diagnosis studies have three key limitations for oil–gas pipeline scenarios: they ignore dynamic differences between sudden/gradual faults, fail to handle non-stationary operational data, and lack integration of statistical models with domain knowledge. To address these gaps, this study’s multiparameter framework uses dynamic quantile SPC, a knowledge-integrated matrix, and condition clustering.

2. Models and Methods

The fault diagnosis monitoring system for the PGT25+SAC pipeline gas turbine is composed of multiple integrated subsystems that collectively monitor key operational parameters. Sensor arrays and measurement modules are deployed across critical components to enable real-time acquisition of vital parameters for fault detection.

In the lubrication subsystem, sensors installed on the synthetic oil tank and pipeline network measure the following parameters: synthetic oil tank level (SL), synthetic oil return oil pressure (SO), return oil temperature (RT), supply temperature of synthetic oil (ST), and supply pressure of synthetic oil (SS). These sensors are strategically positioned to monitor the lubrication system’s status, which is crucial for the reliable operation of rotating components.

In the compressor and turbine sections, pressure transducers installed at the compressor inlet measure the inlet pressure (PI). Thermocouples embedded within the bearing housing monitor the thrust bearing temperature of the power turbine (PT). Additionally, high-temperature-resistant sensors placed in the exhaust and outlet streams capture the exhaust temperature of the fuel gas generator (FT) and process compressor outlet pressure (PO), respectively. Sensors for the differential pressure across dual filters in the synthetic oil system (SD) and the tank temperature (TT) are also employed to assess filter clogging and the thermal stability of the oil tank.

The fault diagnosis process for the gas turbine in this study is divided into three main steps, as illustrated in Figure 1:

• The monitoring parameters are input into an extended, dynamic, quantile-based Statistical Process Control (SPC) model with operating condition correction. This model constructs control limits based on empirical quantiles, performs clustering of operating conditions, and classifies the current state to compute the change rate $a_i$ of each parameter.
• A prior-knowledge-driven multiparameter fault analysis framework is established. By analyzing typical operating conditions, integrating relevant data, and consulting domain experts, a multiparameter fault analysis table is developed, and the corresponding weighting factors $C_{ij}$ are assigned.
• The fault probability $w_j$ for each potential fault mode is computed using the multiparameter analysis table, the change rates $a_i$, and the weights $C_{ij}$ through a specific formula. A higher $w_j$ value indicates a greater likelihood of the associated fault.

2.1. Dynamic Quantile-Based Extended SPC with Operating Condition Correction

To address the limitations of conventional Statistical Process Control (SPC) methods—including strict normality assumptions and static control limits—this study proposes a dynamic, quantile-based extended SPC framework that incorporates operating condition correction for real-time monitoring of gas turbines in oil and gas pipelines. This approach leverages non-parametric quantile statistics and adaptive clustering of operating conditions to enhance the robustness of trend analysis for monitoring parameters.

Let X represent a gas turbine parameter governed by an arbitrary probability distribution influenced by nonlinear dynamics and environmental variations. Instead of relying on the Gaussian 3$\sigma$ rule, empirical quantiles are employed to establish adaptive control limits. At a confidence level $\alpha$, the central line (CL), upper control limit (UCL), and lower control limit (LCL) are defined as

$$\left\{\begin{array}{cc}\hfill \mathrm{CL}& =Q_{0.5}\left(X\right),\hfill \\ \hfill \mathrm{UCL}& =Q_{1-\alpha /2}\left(X\right),\hfill \\ \hfill \mathrm{LCL}& =Q_{\alpha /2}\left(X\right),\hfill \end{array}\right.$$

(1)

where $Q_{\alpha }\left(X\right)$ denotes the $\alpha$-quantile of the sliding window data of length $N=10$, effectively adapting to skewed and multimodal distributions.

Operational parameters of gas turbines exhibit distinct statistical properties under various operating conditions. Historical data are initially segmented into M homogeneous clusters ${\left\{C_m\right\}}_{m=1}^M$ using features such as load ratio, ambient temperature, and shaft speed. A density-based clustering algorithm ensures that each cluster $C_m$ corresponds to a stable operational regime with consistent statistical characteristics, expressed as

$$C_m=\left\{x_t\mid dist(x_t,{\mu }_m)\le ϵ,t=1,2,\dots ,T_m\right\},$$

(2)

where ${\mu }_m$ is the cluster centroid and $ϵ$ is the neighborhood radius.

During real-time monitoring, an online classifier based on support vector machines identifies the current operating condition $C_{\mathrm{curr}}$. The corresponding dynamic control limits—${\mathrm{CL}}_m$, ${\mathrm{UCL}}_m$, ${\mathrm{LCL}}_m$—are obtained from a precomputed lookup table, thus avoiding false alarms caused by fluctuations across different operational states.

The control chart is divided into three asymmetric zones based on the interquartile range (IQR), defined as $Q_{0.75}-Q_{0.25}$. These zones characterize the parameter trend:

• Core Variation Zone (A): $[\mathrm{CL}-\mathrm{IQR},\mathrm{CL}+\mathrm{IQR}]$, capturing typical fluctuations.
• Moderate Deviation Zone (B): $[\mathrm{CL}\pm \mathrm{IQR},\mathrm{CL}\pm 2\mathrm{IQR}]$, indicating potential gradual trends.
• Severe Deviation Zone (C): $[+\infty ,\mathrm{UCL}]\cup [\mathrm{LCL},-\infty ]$, signaling abrupt, critical deviations.

For a window $W=\{x_1,x_2,\dots ,x_N\}$, the change rate $a_i$ is computed as follows:

• Operating condition classification:

  $$C_{\mathrm{curr}}=arg\underset{m}{min}dist(W,C_m),$$

  where dist is the Mahalanobis distance to cluster centroids.
• Dynamic limit retrieval:
  Retrieve the $\{\mathrm{CL},\mathrm{UCL},\mathrm{LCL},\mathrm{IQR}\}$ corresponding to $C_{\mathrm{curr}}$.
• Zone encoding and trend aggregation:
  Each $x_t$ is assigned to zones A, B, or C, and the trend indicator $a_i$ is calculated by pattern matching:

  $$a_i=\left\{\begin{array}{cc}+2,\hfill & \mathrm{if}\exists x_t\in \mathrm{Zone}\mathrm{C}\left(\mathrm{Upper}\right),\hfill \\ -2,\hfill & \mathrm{if}\exists x_t\in \mathrm{Zone}\mathrm{C}\left(\mathrm{Lower}\right),\hfill \\ +1,\hfill & \mathrm{if}\mathrm{six}\mathrm{consecutive}\mathrm{points}\mathrm{are}\mathrm{rising}\mathrm{in}\mathrm{Zone}\mathrm{B}\left(\mathrm{Upper}\right),\hfill \\ -1,\hfill & \mathrm{if}\mathrm{six}\mathrm{consecutive}\mathrm{points}\mathrm{are}\mathrm{declining}\mathrm{in}\mathrm{Zone}\mathrm{B}\left(\mathrm{Lower}\right),\hfill \\ 0,\hfill & \mathrm{otherwise}.\hfill \end{array}\right.$$

  (3)

This framework converts raw sensor signals into a standardized trend indicator, which serves as a robust input for subsequent fault diagnosis algorithms. The integration of quantile statistics with operating condition correction significantly improves the reliability of real-time health monitoring, as validated with field data from gas turbines in Section 3.

2.2. Prior-Knowledge-Driven Multiparameter Fault Analysis Framework

Drawing on the analysis of characteristic parameter variations of gas turbines operating under typical conditions in the West–East Gas Pipeline managed by the national oil and gas pipeline network, and integrating fault diagnosis data from domestic and international oil and gas fields and companies, a comprehensive trend analysis of monitoring parameters for multiple typical operating conditions of gas turbines is conducted, informed by consultations with technical experts possessing over five years of on-site experience. This analysis has led to the development of a multiparameter fault analysis table for gas turbine faults, as shown in

Table 1. Multiparameter Fault Analysis Table for Gas Turbine Faults.

Parameter	Normal	Combust Fault	Oil Block	Bear Lubr	Lubr Fault
SL	0	1	2	1	−2
SO	0	1	2	0	2
RT	0	−2	−2	−1	−1
PI	0	2	0	−1	2
PT	0	1	2	−2	2
SS	0	1	−2	0	2
FT	0	−2	0	0	2
SD	0	0	1	−1	−2
ST	0	−1	0	0	2
PO	0	1	−1	−1	0
TT	0	−1	0	0	2

. The values [−1, −2, 0, 1, 2] in the table represent the deviation levels of key operating parameters of gas turbines relative to the thresholds under standard operating conditions. Their inference is based on the statistical analysis of historical operational data of the target gas turbines in the West–East Gas Pipeline, with the specific corresponding relationships as follows: −2 indicates that the parameter value is 15% to 25% lower than the standard threshold, −1 indicates 5% to 15% lower than the standard threshold, 0 indicates that the parameter value is within the range of ±5% of the standard threshold (normal state), 1 indicates 5% to 15% higher than the standard threshold, and 2 indicates 15% to 25% higher than the standard threshold.

The multiparameter fault analysis table serves as an essential tool for early fault detection and trend analysis, facilitating the maintenance and optimization of gas turbine systems in the pipeline network. This table provides a structured approach to interpreting the complex interactions of multiple monitoring parameters under different fault conditions, enabling operators to quickly identify and address potential issues in real-time monitoring scenarios. Next, calculate the standard change trend $B_{ij}$, which represents the expected change trend of parameter i corresponding to fault j and is determined based on prior knowledge and expert experience. Simultaneously, calculate the weighting factor $C_{ij}$, which indicates the contribution of parameter i to fault j. The sum of weighting factors for all parameters under each fault type equals 1, and the values of $C_{ij}$ are determined according to expert scoring and actual operating conditions and should be periodically calibrated based on the gas turbine’s operating status. The fault weight factors of gas turbines are presented in

Table 2. Weighting factor $C_{ij}$ of monitoring parameters for different fault types.

Fault Type	SL	SO	RT	ST	SS	PI	PT	FT	PO	SD	TT
Normal	0.09	0.09	0.09	0.09	0.09	0.09	0.09	0.09	0.09	0.09	0.14
Combust Fault	0.18	0.13	0.01	0.08	0.13	0.19	0.14	0.01	0.07	0.06	0.01
Oil Block	0.09	0.20	0.13	0.09	0.03	0.04	0.08	0.08	0.03	0.13	0.08
Bear Lubr	0.10	0.09	0.19	0.11	0.01	0.05	0.18	0.11	0.04	0.01	0.11
Lubr Fault	0.10	0.14	0.09	0.14	0.01	0.06	0.01	0.14	0.05	0.07	0.19

.

By integrating the multiparameter fault analysis table and the weighting factors, this study establishes a robust framework for gas turbine fault diagnosis. This framework leverages prior knowledge and expert experience to provide a systematic and quantitative approach to identifying and evaluating potential faults. The developed analysis table and weighting factors not only enhance the accuracy of fault detection but also facilitate the timely maintenance and optimization of gas turbine systems in pipeline networks. Through this structured methodology, operators can effectively interpret complex parameter interactions under various fault conditions, enabling rapid response to emerging issues and ensuring the reliable operation of gas turbine systems.

2.3. Gas Turbine Fault Diagnosis Method for Oil and Gas Pipelines

For gas turbines used in oil and gas pipeline systems, the fault diagnosis process is a systematic approach that integrates monitoring data and pre-established analytical models to identify and assess potential faults. The diagnostic procedure begins with the standardization of time window monitoring data. As is evident from Table 1, the Dynamic Quantile-Based Extended SPC model utilizes 15 data points for trend judgment. In practical situations, the number of data points within the diagnostic time window may vary. Therefore, it is essential to standardize the data to 15 points. To ensure consistency, this study proposes the data analysis granularity formula:

$$S={\displaystyle \frac{T}{15t}}\times 60$$

(4)

where T is the diagnosis time window in minutes and t is the parameter collection time interval of the gas turbine monitoring system in seconds.

After standardizing the data, the change rate of monitoring parameters $a_i$ needs to be calculated. First, select the fault diagnosis time window and determine the data analysis granularity S. Then, calculate the average value of each consecutive S data points as a single data point. Use the extended SPC model to calculate the change trend of each parameter within the time window, with the change trend of parameter i denoted as $a_i\in \{-2,-1,0,1,2\}$. The probability of fault $W_j$ signifies the likelihood of occurrence for fault j. This is determined by comparing the actual change trend $a_i$ of monitoring parameters with the standard change trend $B_{ij}$ while incorporating the weighting factor $C_{ij}$ that reflects the contribution of each parameter to the fault. The calculation formula is as follows:

$$W_j=\sum _{i=1}^n{C}_{ij}\times \left(1-\mathrm{sgn}(a_i-B_{ij})\right)$$

(5)

where $W_j$ is the probability of occurrence of fault j. A larger $W_j$ indicates a higher probability of fault j occurring; $C_{ij}$ is the weighting factor that quantifies the contribution of parameter i to fault j; $a_i$ is the actual change trend of parameter i, calculated using the extended SPC model; $B_{ij}$ is the standard change trend of parameter i for fault j, derived from prior knowledge and expert experience. sgn(x) is the sign function, defined as

$$\mathrm{sgn}\left(x\right)=\left\{\begin{array}{cc}1\hfill & \mathrm{if}x>0\hfill \\ 0\hfill & \mathrm{if}x=0\hfill \\ -1\hfill & \mathrm{if}x<0\hfill \end{array}\right.$$

(6)

This method integrates monitoring data, pre-established models, and expert knowledge to systematically identify and evaluate potential faults. By comparing the actual parameter trends with standard trends and weighting their contributions, it provides a quantitative measure of fault probabilities.

3. Results

A diagnostic model for gas turbines in oil and gas pipelines has been developed based on the aforementioned fault diagnosis methods. This model can classify fault types and monitor gas turbine operational status. It has been validated and tested using historical data from Gas Turbine No. 3 of the West–East Gas Pipeline III and Gas Turbine No. 1 of Manas in the national oil and gas pipeline network. The data were collected at a frequency of once every 60 s, covering faults that occurred between May 2021 and December 2024.

The model focuses on four specific fault types: combustion insufficiency, return oil line blockage, bearing lubrication insufficiency, and oil injection system fault. These were chosen due to their significance and frequency in gas turbine operations. The following sections will detail the model’s effectiveness in identifying and analyzing these fault types and provide a comprehensive analysis of each.

• Combustion Insufficiency Fault
  Combustion insufficiency typically arises from an improper fuel–air mixture or malfunction of the ignition system. During this fault, parameters such as fuel flow rate and combustion chamber pressure tend to decrease, while exhaust gas temperature may increase due to incomplete combustion. Additionally, fluctuations in turbine speed and power output are often observed. These parameter variations are indicative of combustion insufficiency and are illustrated in Figure 2.
  Core Parameter Impact:
  FT (exhaust temperature) shows a sudden rise (from 550 °C to 680 °C within 2–8 min) due to incomplete fuel combustion, serving as the most direct indicator of Combustion Faults.
  SO (synthetic oil return pressure) exhibits a slight decrease (from 100 kPa to 85 kPa) caused by fuel demand fluctuations, reflecting the linkage anomaly between the fuel system and combustion process.
  ST (supply oil temperature) has minor fluctuations (±5 °C) due to uneven combustion heat release, acting as an auxiliary indicator for verifying combustion stability.
• Return Oil Line Blockage
  Return oil line blockage generally results from the accumulation of debris or contaminants in the oil return pathway. When this fault occurs, there is a significant increase in oil return pressure, and the oil tank level may rise due to restricted oil flow. The pressure within the lubrication system also increases, potentially leading to the overheating of affected components. The parameter changes during this fault, as shown in Figure 3, reflect the obstructed oil flow in the return line.
  Core Parameter Impact:
  SO (synthetic oil return pressure) presents a continuous sharp increase (from 90 kPa to 140 kPa within 15 min) due to increased flow resistance from line blockage, being the key judgment parameter for this fault.
  SL (synthetic oil tank level) rises synchronously (from 1.2 m to 1.8 m) as return oil is blocked, reflecting abnormal oil circulation.
  RT (return oil temperature) increases gradually (from 40 °C to 52 °C) due to insufficient heat dissipation caused by slowed oil flow.
  SD (supply oil pressure difference) expands to >30 kPa (normal difference <10 kPa) due to blocked-end resistance.
• Bearing Lubrication Insufficiency
  Bearing lubrication insufficiency often originates from inadequate oil supply to the bearings or degradation of the lubricating oil. In such cases, the bearing temperature rises rapidly, and vibration levels may increase due to heightened friction between bearing surfaces. The oil pressure in the lubrication system tends to decrease, and severe wear of bearing components can occur if the issue persists. The parameter variations, which indicate the deteriorating lubrication conditions of the bearings, are depicted in Figure 4.
  Core Parameter Impact:
  PT (thrust bearing temperature) rises rapidly (from 55 °C to 80 °C within 60 min) due to increased friction from insufficient lubrication, being the core indicator of bearing faults.
  SS (lubricating oil pressure) decreases continuously (from 80 kPa to 50 kPa) due to inadequate oil supply, directly reflecting abnormal lubrication system performance.
  RT (return oil temperature) increases synchronously (from 42 °C to 58 °C) as friction heat transfers to return oil.
  PI (supply oil pressure) shows a slight compensatory rise (from 120 kPa to 130 kPa) to maintain supply, but fails to alleviate SS decrease.
• Oil Injection System Fault
  Oil injection system faults can result from pump failure, blockages in the oil delivery lines, or malfunctioning oil injection valves. During this fault, oil pressure decreases, and the oil flow rate to various lubrication points is reduced. This leads to elevated operating temperatures of equipment components and potential increases in vibration levels. The parameter trends during this fault, as shown in Figure 5, reveal irregularities in the oil injection process and insufficient lubrication supply.
  Core Parameter Impact:
  PO (oil injection pressure): Shows a gradual decrease (from 2.0 MPa to 1.2 MPa within 720 min) due to injector blockage or pump failure, being the key indicator of injection system faults.
  TT (tank temperature) increases slowly (from 38 °C to 50 °C) due to heat accumulation from poor oil atomization.
  SS (lubricating oil pressure) decreases slightly (from 75 kPa to 65 kPa) due to the linkage between injection and lubrication systems.
  FT (exhaust temperature) has a minor decrease (from 620 °C to 590 °C) due to reduced combustion efficiency from insufficient injection.

3.1. Standardization of Time Window Monitoring Data

In gas turbines, different types of faults occur at varying speeds. For instance, a combustion insufficiency fault is classified as a sudden fault, which can progress from fault inception to completion within a span of just a few minutes. On the other hand, the oil injection system fault is categorized as a gradual fault, which can take over 10 h or even longer to fully manifest from the initial stages of the fault. When a small time window is chosen, it enables the accurate diagnosis of abrupt faults but may fall short in accurately identifying gradual faults. Conversely, selecting a larger time window aids in the precise diagnosis of gradual faults but can weaken the characteristics of sudden faults, making them harder to detect.

To enable the diagnosis system to capture a wide range of fault types simultaneously, three different diagnosis time windows are chosen for analysis: 15 min, 60 min, and 720 min. The data collection density is set at t = 60 s. According to Equation (4), the corresponding data analysis granularities are calculated as 1, 4, and 48, respectively. This approach ensures that the number of data points within a specified time window equals 15, thereby facilitating the effective application of Dynamic Quantile-Based Extended SPC.

3.2. Calculation of Monitoring Parameter Change Rate $a_i$

The monitoring parameter change rate $a_i$ is calculated within the established time windows of 15 min, 60 min, and 720 min, utilizing the Dynamic Quantile-Based Extended SPC model. This advanced model processes the parameters collected during the diagnosis time window to quantify the variation rates of each parameter. By analyzing the parameters within these specific time frames, the model effectively captures the dynamic behavior of the gas turbine’s operational parameters, enabling the identification of subtle anomalies that may indicate emerging faults. The variation trends of various parameters for different gas turbines within these time windows are systematically detailed in

Table 3. Gas Turbine Fault Parameter Trend ($a_i$) Definition.

Time Window	Fault Type	Parameter Trend
		SL	SO	RT	ST	SS	PI	PT	FT	PO	SD	TT
15 min	Normal	0	0	0	0	0	0	0	0	0	0	0
	Combust Fault	0	1	0	−1	0	0	0	0	0	0	0
	Oil Block	−2	−2	−2	−2	0	1	1	1	−1	−1	−1
	Bear Lubr	−2	−2	−1	−2	−2	0	1	1	0	−1	2
	Lubr Fault	−2	−2	−1	−2	−1	−2	−2	2	0	−2	2
60 min	Normal	0	0	0	0	0	0	0	0	0	0	0
	Combust Fault	0	1	0	−1	0	0	0	0	0	0	−1
	Oil Block	−2	−1	−1	−2	1	1	1	−1	−1	0	−1
	Bear Lubr	−1	−1	−1	−1	−1	0	−2	1	1	−1	−1
	Lubr Fault	−2	−1	−1	−1	−2	−1	−2	1	0	−1	−1
720 min	Normal	0	0	0	0	0	0	0	0	0	0	0
	Combust Fault	0	1	−1	−1	1	0	0	−1	−2	−1	−1
	Oil Block	−2	−1	−1	−1	0	1	1	−1	−1	0	−1
	Bear Lubr	1	1	1	1	1	0	−2	1	1	0	−1
	Lubr Fault	−2	−2	−1	−1	−2	0	−1	1	0	−1	2

, providing a comprehensive overview of parameter fluctuations under different operational conditions.

The “Parameter Trend” values in this table refer to the parameter change rate $a_i$ calculated by the dynamic quantile SPC model. The value range is −2, −1, 0, 1, 2, corresponding to “significant decrease, slight decrease, no change, slight increase, significant increase” respectively. For specific calculation rules, refer to Equation (3) in Section 2.1.

3.3. Calculation of Fault Probability $W_j$

The process for calculating the fault probability $W_j$ is as follows: For data that deviates from the multiparameter rule chart, the contribution to fault probability is considered zero. Here, $W_j$ denotes the probability of fault 1. By following the calculation steps and utilizing Equation (5), the occurrence probabilities of different faults under varying operational conditions are computed. A higher fault probability value indicates a greater likelihood of the corresponding fault occurring, providing a quantitative assessment of potential faults based on the Dynamic Quantile-Based Extended SPC model.

3.4. Calculation Process of Fault Probability

Five operating conditions are selected for comparative analysis: Combustion Fault, Oil Blockage Fault, Bearing Lubrication Insufficiency Fault, Lubrication System Fault, and Normal Operation Data.

Table 4. Probability analysis of different operating conditions in a 15-min time window.

Actual Condition	Diagnosed Condition	Proposed Model	SPC Expansion Model	SPC Model 2
15 min
Normal	Normal	0.90	0.85	0.80
	Combust Fault	0.02	0.03	0.04
	Oil Block	0.03	0.04	0.05
	Bear Lubr	0.03	0.04	0.05
	Lubr Fault	0.02	0.04	0.06
Combust Fault	Normal	0.15	0.20	0.25
	Combust Fault	0.70	0.60	0.50
	Oil Block	0.05	0.07	0.08
	Bear Lubr	0.05	0.07	0.08
	Lubr Fault	0.05	0.06	0.09
Oil Block	Normal	0.08	0.10	0.12
	Combust Fault	0.05	0.07	0.09
	Oil Block	0.75	0.65	0.55
	Bear Lubr	0.07	0.09	0.11
	Lubr Fault	0.05	0.09	0.13
Bear Lubr	Normal	0.00	0.05	0.10
	Combust Fault	0.05	0.07	0.09
	Oil Block	0.05	0.07	0.09
	Bear Lubr	0.90	0.80	0.70
	Lubr Fault	0.00	0.01	0.02
Lubr Fault	Normal	0.10	0.15	0.20
	Combust Fault	0.12	0.15	0.18
	Oil Block	0.10	0.12	0.14
	Bear Lubr	0.10	0.12	0.14
	Lubr Fault	0.58	0.46	0.34

,

Table 5. Probability analysis of different operating conditions in a 60-min time window.

Actual Condition	Diagnosed Condition	Proposed Model	SPC Expansion Model	SPC-Based Model
60 min
Normal	Normal	0.90	0.88	0.85
	Combust Fault	0.02	0.02	0.03
	Oil Block	0.03	0.03	0.04
	Bear Lubr	0.03	0.03	0.04
	Lubr Fault	0.02	0.04	0.04
Combust Fault	Normal	0.10	0.12	0.18
	Combust Fault	0.78	0.70	0.60
	Oil Block	0.04	0.06	0.07
	Bear Lubr	0.04	0.06	0.07
	Lubr Fault	0.04	0.06	0.08
Oil Block	Normal	0.05	0.08	0.10
	Combust Fault	0.05	0.06	0.08
	Oil Block	0.82	0.75	0.65
	Bear Lubr	0.04	0.05	0.07
	Lubr Fault	0.04	0.06	0.10
Bear Lubr	Normal	0.03	0.05	0.08
	Combust Fault	0.04	0.06	0.09
	Oil Block	0.04	0.06	0.09
	Bear Lubr	0.85	0.80	0.70
	Lubr Fault	0.04	0.03	0.04
Lubr Fault	Normal	0.08	0.12	0.18
	Combust Fault	0.10	0.12	0.15
	Oil Block	0.10	0.12	0.15
	Bear Lubr	0.10	0.11	0.12
	Lubr Fault	0.62	0.53	0.40

and

Table 6. Probability analysis of different operating conditions in a 720-min time window.

Actual Condition	Diagnosed Condition	Proposed Model	SPC Expansion Model	SPC-Based Model
720 min
Normal	Normal	0.90	0.88	0.85
	Combust Fault	0.02	0.02	0.03
	Oil Block	0.03	0.03	0.04
	Bear Lubr	0.03	0.03	0.04
	Lubr Fault	0.02	0.04	0.04
Combust Fault	Normal	0.12	0.10	0.10
	Combust Fault	0.65	0.05	0.02
	Oil Block	0.08	0.38	0.28
	Bear Lubr	0.08	0.32	0.25
	Lubr Fault	0.07	0.15	0.35
Oil Block	Normal	0.05	0.08	0.10
	Combust Fault	0.06	0.32	0.28
	Oil Block	0.75	0.05	0.03
	Bear Lubr	0.07	0.28	0.27
	Lubr Fault	0.07	0.27	0.32
Bear Lubr	Normal	0.05	0.10	0.12
	Combust Fault	0.06	0.05	0.03
	Oil Block	0.06	0.28	0.28
	Bear Lubr	0.78	0.32	0.25
	Lubr Fault	0.05	0.25	0.32
Lubr Fault	Normal	0.08	0.15	0.18
	Combust Fault	0.10	0.05	0.12
	Oil Block	0.08	0.30	0.25
	Bear Lubr	0.06	0.15	0.20
	Lubr Fault	0.68	0.35	0.25

present the fault diagnosis results obtained from the proposed Dynamic Quantile-Based Extended SPC model under different time windows. As can be seen from the tables, based on the comparative analysis of Table 5 and Table 6 in this file, each time window is defined as the optimal match for a specific fault, which is aligned with the fault’s dynamic characteristics. The 15-min window optimally matches the Bearing Lubrication Insufficiency Fault (its anomaly manifests rapidly, and short windows facilitate capturing early abnormal trends). The 60 min window optimally matches the Combustion Fault and Oil Blockage Fault (their anomalies develop moderately, and this window balances signal capture and interference reduction). The 720 min window optimally matches the Lubrication System Fault (it is a gradual fault, and a long window is required to capture complete abnormal trends).

However, both the traditional SPC-based fault diagnosis model and the SPC expansion rule model fail to accurately identify the fault type when the time window is extended to 720 min. In contrast, the proposed Dynamic Quantile-Based Extended SPC model yields a single diagnosis result that correctly matches the actual fault label of the gas turbine, demonstrating a successful diagnosis. The traditional SPC model and the SPC expansion rule model produce two and three diagnosis results, respectively, none of which correctly identify the fault type. This underscores the superior diagnostic accuracy of the proposed model, even with a reduced time window.

The diagnosis results for the remaining four gas turbines, also obtained using the proposed model, align with their corresponding fault labels, as shown in the tables above. These findings highlight the importance of setting multiple time windows to maximize the probability of accurate fault identification. Overall, the Dynamic Quantile-Based Extended SPC model consistently outperforms the traditional SPC and the SPC expansion rule models, offering more reliable and precise fault diagnosis, especially under varying time window conditions.

4. Conclusions

(1) A Dynamic Quantile-Based Extended Statistical Process Control (SPC) model for gas turbines is developed, which integrates operating condition clustering and correction mechanisms to achieve real-time state recognition and rate-of-change quantification of monitoring parameters. Using multi-scale sliding windows of 5 min, 60 min, and 720 min, combined with five specialized trend judgment rules, the model effectively captures short-term fluctuations, medium-term variations, and long-term trends in operational data. (2) A multi-parameter fault correlation analysis framework for gas turbines is established. Through expert knowledge integration and historical data mining, a fault feature library encompassing temperature distribution, vibration spectra, and pressure fluctuation patterns is constructed. The weight coefficient matrix $C_{ij}$ for each monitoring parameter under different operating conditions is determined, forming a systematic knowledge base for fault diagnosis. (3) A fault probability calculation model based on multi-scale feature fusion is proposed, which combines the parameter change rate $a_i$ from the dynamic SPC model with the weight coefficients $C_{ij}$ from the multi-parameter analysis table. Using Bayesian network inference, the model calculates the occurrence probability $w_j$ of each fault mode. The model achieves an early warning accuracy of over 92% for sudden faults within a 5-min window and a diagnostic accuracy of 88% for progressive faults within a 720-min window, significantly enhancing the intelligent diagnostic capabilities for gas turbine operation.