The thermoacoustic behavior of a combustion system can be determined numerically via acoustic tools such as Helmholtz solvers or network models coupled with a model for the flame dynamic response. Within such a framework, the flame response to flow perturbations can be described by a Finite Impulse Response (FIR) model, which can be derived from LES time series via system identification. However, the estimated FIR model will inevitably contain uncertainties due to e.g., the statistical nature of the identification process, low signal-to-noise ratio or finite length of time series. Thus, a necessary step towards reliable thermoacoustic stability analysis is to quantify the impact of uncertainties in FIR model on the growth rate of thermoacoustic modes. There are two practical considerations involved in this topic. First, how to efficiently propagate uncertainties from the FIR model to the modal growth rate of the system, considering it is a high dimensional uncertainty quantification (UQ) problem? Second, since longer CFD simulation time generally leads to less uncertain FIR model identification, how to determine the length of the CFD simulation required to obtain satisfactory confidence? To address the two issues, a dimensional reduction UQ methodology called “Active Subspace approach” is employed in the present study. For the first question, Active Subspace approach is applied to exploit a low-dimensional approximation of the original system, which allows accelerated UQ analysis. Good agreement with Monte Carlo analysis demonstrates the accuracy of the method. For the second question, a procedure based on Active Subspace approach is proposed, which can serve as an indicator for terminating CFD simulation. The effectiveness of the procedure is verified in the paper.

This study assesses and compares two alternative approaches to determine the acoustic scattering matrix of a pre-mixed turbulent swirl combustor: 1) The acoustic scattering matrix coefficients are obtained directly from a compressible Large Eddy Simulation (LES). Specifically, the incoming and outgoing characteristic waves f and g extracted from the LES are used to determine the respective transmission and reflection coefficients via System Identification techniques. 2) The flame transfer function (FTF) is identified from LES time series data of upstream velocity and heat release rate. The transfer matrix of the reactive combustor is then derived by combining the FTF with the Rankine-Hugoniot relations across a compact heat source and a transfer matrix of the cold combustor, which is deduced from a linear network model. Linear algebraic transformation of the transfer matrix consequently yields the combustor scattering matrix. A cross-comparison study that includes comprehensive experimental data shows that both approaches successfully predict the scattering matrix of the reactive turbulent swirl combustor.

This paper studies the behavior of Industrial Gas Turbines (IGTs) based on time-series measurements with low sampling rates. The aim is to find the most suitable set of statistical/time-domain features derived from the measurements, which can represent the characteristic behavior of the IGTs, or alternatively, which can discriminate between different engines or different states of an engine. For this end, a scheme of optimal feature selection process is proposed in the paper. For cross-fleet analysis, signals from a group of inter-duct thermocouples on IGT engines are studied. A feature matrix is formulated at each sliding time step, by calculating the statistical features of the sensor group, after the time-domain features of the individual sensor measurements are calculated. Feature matrix values from different engines are then clustered, and a modified Davies–Bouldin index is introduced to measure the quality of the clusters. Finally, grid search is run to find the optimal set of the features, which form the clusters with the most similarity, or otherwise, the most discrepancy across the IGT engines. The window size effect is also investigated. To demonstrate that the optimal feature selection process is also useful for fault diagnosis of IGTs, the proposed scheme is then applied on a group of different measurements on an IGT, i.e. from burner tip thermocouples, in a fault diagnostic scenario, which is subsequently validated using a k-nearest neighbor classification algorithm. The case studies have demonstrated that, ultimately, the developed techniques can be broadly applied to other groups of measurements for both cross-fleet analysis and fault diagnosis of IGTs.

Maintenance costs are a substantial contributor to airline operating costs. In this context, understanding, analyzing, and predicting engine performance deterioration is crucial. While diagnostic methods for analyzing the current module and overall engine condition are established in state-of-the-art engine condition monitoring (ECM) systems, deterioration modeling and prognosis are still fields of research. The identification of the contribution of deterioration mechanisms, such as fouling, erosion, and abrasion, to the in-service deterioration poses a key challenge in this area. This paper focuses on a top-down approach for the high pressure compressor (HPC) module. The selected approach is to quantify the contribution of individual deterioration mechanisms to the overall HPC efficiency deterioration based on in-flight measurements. This is accomplished by first using the in-flight measurements to analyze the HPC efficiency loss. Then, the resulting time series of the analyzed HPC efficiency loss are preprocessed. Finally, models of the deterioration mechanisms are fitted to the preprocessed time series. The deterioration models are chosen based on literature references to the respective deterioration mechanisms. As multiple influencing factors affect the deterioration mechanisms, a fleet analysis is conducted to select the model inputs. The fitting process involves a parametric nonlinear regression problem. The outcome is an estimation of the evolution of the deterioration mechanisms over time. This methodology is used to evaluate all available in-service engines of the same type and fleet and to define a fleet model. In the final step, benefits and limitations of the fleet model are investigated.

It is necessary to quantitatively resolve the flow field generated in compressors at various operating conditions including the surge. In this study, fast-responding pressure-sensitive-paint (PSP) and temperature-sensitive-paint (TSP) was applied to measurement of steady and unsteady pressure and temperature fields in a turbocharger compressor. The surface pressure of a compressor impeller and the diffuser downstream of the impeller was measured under the rotating speed of 133,000 rpm with various mass flow rate of the inlet. Blue LED strobes were used as the excitation light source for PSP/TSP. The luminescence from PSP/TSP were captured by a high-speed camera. These instruments were controlled using the signal synchronized with a fixed rotation angle of the impeller, which was detected using a gap sensor installed near the impeller. The pressure was calculated from the time-series of the PSP signal. The output of PSP/TSP was compared with the signal from semiconductor pressure transducers and the thermal image taken by an infrared camera. For the analysis of the diffuser, the power spectra of the pressure field were obtained using the fast Fourier transform of the time-series data of the pressure fluctuation. The pressure field on the impeller was successfully obtained with the aid of adequate temperature compensation by TSP. It was confirmed that the time-averaged pressure on the impeller blades increased as the inlet mass flow rate was decreased. Large-amplitude points were distributed on the extension line of the impeller blades in the diffuser when the surge occurs.

This paper addresses the challenge of forecasting the future values of gas turbine measureable quantities. The final aim is the simulation of “virtual sensors” capable of producing statistically coherent measurements aimed at replacing anomalous observations discarded from the time series. Among the different available approaches, the Bayesian Forecasting Method (BFM) adopted in this paper uses the information held by a pool of observations as knowledge base to forecast the values at a future state. The BFM algorithm is applied in this paper to Siemens field data to assess its prediction capability, by considering two different approaches, i.e. single-step prediction (SSP) and multi-step prediction (MSP). While SSP predicts the next observation by using true data as base of knowledge, MSP uses previously predicted data as base of knowledge to perform the prediction of future time steps. The results show that BFM single-step average prediction error can be very low, when filtered field data are analyzed. On the contrary, the average prediction error achieved in case of BFM multi-step prediction is remarkably higher. To overcome this issue, the BFM single-step prediction scheme is also applied to clusters of time-wise averaged data. In this manner, an acceptable average prediction error can be achieved by considering clusters composed of 60 observations.

Statistical parametric methodologies are widely employed in the analysis of time series of gas turbine sensor readings. These methodologies identify outliers as a consequence of excessive deviation from a statistically-based model, derived from available observations. Among parametric techniques, the k-σ methodology demonstrates its effectiveness in the analysis of stationary time series. Furthermore, the simplicity and the clarity of this approach justify its direct application to industry. On the other hand, the k-σ methodology usually proves to be unable to adapt to dynamic time series, since it identifies observations in a transient as outliers. As this limitation is caused by the nature of the methodology itself, two improved approaches are considered in this paper in addition to the standard k-σ methodology. The two proposed methodologies maintain the same rejection rule of the standard k-σ methodology, but differ in the portions of the time series from which statistical parameters (mean and standard deviation) are inferred. The first approach performs statistical inference by considering all observations prior to the current one, which are assumed reliable, plus a forward window containing a specified number of future observations. The second approach proposed in this paper is based on a moving window scheme. Simulated data are used to tune the parameters of the proposed improved methodologies and to prove their effectiveness in adapting to dynamic time series. The moving window approach is found to be the best on simulated data in terms of True Positive Rate ( TPR ), False Negative Rate ( FNR ) and False Positive Rate ( FPR ). Therefore, the performance of the moving window approach is further assessed towards both different simulated scenarios and field data taken on a gas turbine.

The reliability of gas turbine health state monitoring and forecasting depends on the quality of sensor measurements directly taken from the unit. Outlier detection techniques have acquired a major importance, as they are capable of removing anomalous measurements and improve data quality. To this purpose, statistical parametric methodologies are widely employed thanks to the limited knowledge of the specific unit required to perform the analysis. The backward and forward moving window (BFMW) k-σ methodology proved its effectiveness in a previous study performed by the authors, to also manage dynamic time series, i.e. during a transient. However, the estimators used by the k-σ methodology are usually characterized by low statistical robustness and resistance. This paper aims at evaluating the benefits of implementing robust statistical estimators for the BFMW framework. Three different approaches are considered in this paper. The first methodology, k-MAD, replaces mean and standard deviation of the k-σ methodology with median and mean absolute deviation (MAD), respectively. The second methodology, σ-MAD, is a novel hybrid scheme combining the k-σ and the k-MAD methodologies for the backward and the forward windows, respectively. Finally, the bi-weight methodology implements bi-weight mean and bi-weight standard deviation as location and dispersion estimators. First, the parameters of these methodologies are tuned and the respective performance is compared by means of simulated data. Different scenarios are considered to evaluate statistical efficiency, robustness and resistance. Subsequently, the performance of these methodologies is further investigated by injecting outliers in field data sets taken on selected Siemens gas turbines. Results prove that all the investigated methodologies are suitable for outlier identification. Advantages and drawbacks of each methodology allow the identification of different scenarios in which their application can be most effective.

Centrifugal compressor is a piece of key equipment for factories. Among the components of centrifugal compressor, impeller is a pivotal part as it is used to transform kinetic energy to pressure energy. But it usually leads to blade crack or failure as irregular aerodynamic load effect on the blade. Therefore, early crack feature extraction and pattern recognition is important to prevent it from failure. Although time series analysis for monitored signal can be used on feature extraction, incipient weak feature extraction method should be investigated. In this research, pressure pulsation sensors arranged in close vicinity to crack area are used to monitor the blade crack and feature extraction. As there are different kinds of flow interference, the pressure pulsation signal for centrifugal compressor is full of nonlinear characteristics. Therefore, how to obtain the weak information from monitored signal is investigated. Although FFT and envelope analysis have been widely used for rotating equipment, they are not suitable for the determination of incipient crack of a blade as the signal modulation and noise interference. In this research, stochastic resonance is used for the pressure pulsation signal. The results show that it is an effective tool to blade incipient crack classification on centrifugal compressor.

The present work aims at investigating a new methodology developed at Ansaldo Energia, for the transient finite element modelling of the whole engine with an axisymmetric approach. The strong coupling and non linearity in the heat transfer process during transient thermal analyses are handled by a partly coupled scheme. The 2D axisymmetric finite element model includes a dedicated thermal fluid network where fluid-metal temperatures are computed. In the overall procedure the selected finite element solver is a customized version of CalculiX ® , while mass flow rates and pressure distributions in each thermal fluid network element are provided by external fluid network solvers in terms of customized time series. This paper represents a first insight about a fully integrated WEM (Whole Engine Modelling) procedure currently under development. Geometrical changes during operation, lead to different fluid properties affecting heat transfer coefficients too. These modified conditions in their turn impact the material temperature and displacements. The future implementation steps will be oriented on the adoption of a customized version of the native CalculiX ® fluid network solver with the aim of developing a fully integrated procedure able to take into account the interaction between the secondary air system and the modifications in the clearances and gaps due to the thermal and mechanical loads. In this paper, a detailed description of the procedure will be reported with comprehensive discussions about some fundamental modelling aspects. Preliminary results, related to the first application of the new methodology to the transient thermal modelling of a simplified test case representative of real engine geometries, will be presented.

Anomaly detection in sensor time series is a crucial aspect for raw data cleaning in gas turbine industry. In addition to efficiency, a successful methodology for industrial applications should be also characterized by ease of implementation and operation. To this purpose, a comprehensive and straightforward approach for Detection, Classification and Integrated Diagnostics of Gas Turbine Sensors (named DCIDS) is proposed in this paper. The tool consists of two main algorithms, i.e. the Anomaly Detection Algorithm (ADA) and the Anomaly Classification Algorithm (ACA). The ADA identifies anomalies according to three different levels of filtering based on gross physics threshold application, inter-sensor statistical analysis (sensor voting) and single-sensor statistical analysis. Anomalies in the time series are identified by the ADA, together with their characteristics, which are analyzed by the ACA to perform their classification. Fault classes discriminate among anomalies according to their time correlation, magnitude and number of sensors in which an anomaly is contemporarily identified. Results of anomaly identification and classification can subsequently be used for sensor diagnostic purposes. The performance of the tool is assessed in this paper by analyzing two temperature time series with redundant sensors taken on a Siemens gas turbine in operation. The results show that the DICDS is able to identify and classify different types of anomalies. In particular, in the first dataset, two severely incoherent sensors are identified and their anomalies are correctly classified. In the second dataset, the DCIDS tool proves to be capable of identifying and classifying clustered spikes of different magnitudes.

For the evaluation and improvement of fan noise reduction notions and the verification of broadband sound power measurement in flow ducts, special interest was given to the analysis of the broadband noise fields in duct. Two axial sensor arrays were wall-flush mounted upstream of a single-stage axial fan in the circular duct section of the fan inlet, staggered by 180° in the circumferential direction. During the tests, the rotating drum was rotated by step of 6 degrees to give a total 840 measurement points. There are two static reference microphones mounted upstream of rotating measurement section. Time-series of 12 seconds duration were recorded at each of the 30 azimuthal positions of the rotating duct in order to allow for a statistically accurate cross-correlation data analysis. This method is able to discriminate the sound waves propagating in upstream and downstream directions. Special attention was given to the blade passing frequencies of the axial fan. Rotor-stator interaction mode dominates the incident sound field, while modes with low azimuthal order play an important role in the reflected sound field. The reflected broadband sound power is almost 10dB lower than the transmitted sound field in a broad-frequency range. On the whole, this method behaves robustly in decomposition of broadband noise in flow duct and delivers physically meaningful broadband mode amplitudes.

This paper documents the set-up and validation of nonlinear autoregressive exogenous (NARX) models of a heavy-duty single-shaft gas turbine. The considered gas turbine is a General Electric PG 9351FA located in Italy. The data used for model training are time series data sets of several different maneuvers taken experimentally during the start-up procedure and refer to cold, warm and hot start-up. The trained NARX models are used to predict other experimental data sets and comparisons are made among the outputs of the models and the corresponding measured data. Therefore, this paper addresses the challenge of setting up robust and reliable NARX models, by means of a sound selection of training data sets and a sensitivity analysis on the number of neurons. Moreover, a new performance function for the training process is defined to weigh more the most rapid transients. The final aim of this paper is the set-up of a powerful, easy-to-build and very accurate simulation tool which can be used for both control logic tuning and gas turbine diagnostics, characterized by good generalization capability.

Centrifugal compressor is a piece of key equipment for factories. Among the components of a centrifugal compressor, impeller is a pivotal part as it is used to transform kinetic energy to pressure energy. The blades are exposed to centrifugal forces, gas pressure, and the friction force which usually lead to cracks. Therefore, early crack feature extraction and pattern recognition are important to prevent it from failure. Although time series analysis for monitored signals can be used on feature extraction, it is not enough. So the incipient weak feature extraction method should be investigated. In this research, pressure pulsation sensors arranged close to crack area are used to monitor the blade crack signal and extract the feature information. As the different kinds of interference of flow, the pressure pulsation signals for a centrifugal compressor are full of nonlinear characteristics. Therefore, how to obtain the weak information from monitored signals effectively should be investigated. A method on blade crack classification is present by continuous wavelet transform (CWT) and envelope spectrum in this research. Simulation signal analysis and experimental investigation on blade crack classification are carried out to verify the effectiveness of this method. The results show that it is an effective tool for blade incipient crack classification for a centrifugal compressor.

In steam turbine plants, the last stages of the low pressure (LP) turbines can deliver up to 20% of the overall power of the plant. It poses lots of challenges to designers especially when the last stages are operated under low volume flow conditions. In the current paper, numerical simulations are conducted to investigate the flow features in a LP steam turbine. In steady calculations, flows under six different mass flow rates are simulated. Performances and flow patterns in last stage rotor (LSR) in low mass flow rates are highlighted. Since the last stage is modeled as a full blade annulus, flow patterns and blade force in circumferential distribution are examined. Results show that under low mass flow rate conditions, vortices occur in the last stage and the diffuser. The LSR acts like a compressor. The periodical distributions of pressure in LSR passages are broken. High amplitude aerodynamic force fluctuations are found on LSR blades in low mass flow cases. By conducting unsteady simulations, the time series of aerodynamic force are demonstrated to have the similar trend and magnitude of that in steady spatial sequence. The mechanism for aerodynamic force excitation is discussed in the current paper. Unsteady pressure fluctuation in tip section of LSR at low mass flow rates seems to have a significant correlation with the aerodynamic force fluctuation level rise.

The results of stereo Particle-Image-Velocimetry measurements are presented in this paper to gain further insight into the wake of a finite width Gurney flap. It is attached to an FX 63-137 airfoil which is known for a very good performance at low Reynolds numbers and is therefore used for small wind turbines and is most appropriate for tests in the low speed wind tunnel presented in this study. The Gurney flaps are a promising concept for load control on wind turbines but can have adverse side effects, e.g. shedding of additional vortices. The investigation focuses on frequencies and velocity distributions in the wake as well as on the structure of the induced tip vortices. Phase averaged velocity fields are derived of a Proper-Orthogonal-Decomposition based on the stereo PIV measurements. Additional hot-wire measurements were conducted to analyze the fluctuations downstream of the finite width Gurney flaps. Experiments indicate a general tip vortex structure that is independent from flap length but altered by the periodic shedding downstream of the flap. The influence of Gurney flaps on a small wind turbine is investigated by simulating a small 40 kW turbine in Q-Blade. They can serve as power control without the need of an active pitch system and the starting performance is additionally improved. The application of Gurney flaps imply tonal frequencies in the wake of the blade. Simulation results are used to estimate the resulting frequencies. However, the solution of Gurney flaps is a good candidate for large scale wind turbine implementation as well. A FAST simulation of the NREL 5MW turbine is used to generate realistic time series of the lift. The estimations of control capabilities predict a reduction in the standard deviation of the lift of up to 65%. Therefore finite width Gurney flaps are promising to extend the lifetime of future wind turbines.

Separated shear layer behaviors under the conditions without and with elevated inlet freestream turbulence intensity ( FSTI =2.5%) are investigated by using large eddy simulations (LES) in this paper. The study is performed on a low-Re high-lift LP turbine blade (T106D-EIZ) at Reynolds number ( Re ) of 60,154 (based on the chord and outflow velocity) and isentropic exit Mach number of 0.402. A number of detection points are set along the dividing streamlines and long time series of data are gathered. The time-mean flow and the transient vortex structures are discussed, which indicated the FSTI can suppress the open separation and thus improve the aeroperformance. Power spectra and wavelet analysis are applied to axial velocity and pressure signals of the detection points. The results show that although the vortices pairing are missed, the subharmonic of the roll-up frequency is still observable under the elevated FSTI condition. It is also found that both of the locations and power of the vortices roll-up, as well as vortices pairing, vary with time in large scales and these phenomena are weakened under the elevated FSTI condition.

In this study, we employ a method based on Bayesian statistics to determine the rate of acoustic decay from dynamic pressure measurements inside a combustor. It is common, that lean premixed flames tend to drive thermoacoustic instabilities at specific eigenfrequencies. Hence, the dissipation of acoustic energy inside the combustor, its absorption at the boundaries and its transfer over the in- and outlets must always exceed the acoustic excitation from the flame to avoid pulsations. Quantitative measures for the level of stability are of high technical relevance. In that context the occurring eigenfrequencies and their damping rates are important indicators for the stability margin of gas turbine combustors. A modular swirl burner is investigated in an atmospheric single burner test rig under lean premixed conditions. For the experimental determination of the damping rates, a siren is used to externally excite resonant frequencies of the combustion system. After interrupting the forcing abruptly, time series of the decaying signals are recorded by dynamic pressure sensors inside the combustion chamber. For the analysis of this data, an algorithm based on a Bayesian network approach, which uses a Gibbs Sampler is employed. Probability distributions of frequencies and decay rates are obtained with the Markov-Chain Monte-Carlo (MCMC) method. For the investigated configuration, the influence of the acoustic boundary conditions and the preheat temperature on eigenmodes and damping rates is evaluated. Finally, the results are compared to a network model of the test rig. With that approach, the Open-Loop Gain (OLG) is evaluated for the frequency range of interest. Eigenfrequencies as well as their corresponding damping rates are obtained from Nyquist analysis.

This paper presents a new technique for precursor identification in high speed compressors. The technique is a pseudo-correlation integral method referred to as the correlation method. To provide a basis for comparison, the traveling wave energy technique, which has been used extensively to study pre-stall data, is also briefly presented and applied. The correlation method has a potential advantage over the traveling wave energy method because it uses a single sensor for detection. It also requires no predisposition about the expected behavior of the data to detect “changes” in the behavior of the compressor. Both methods are used in this study to identify stall procursive events in the pressure fluctuations measured from circumferential pressure transducers located at the front face of the compressor rig. The correlation method successfully identified stall formation or changes in the compressor dynamics from data captured from four different configurations of a NASA Lewis single stage high speed compressor while it was transitioned from stable operation into stall. This paper includes an exposition on the use of nonlinear methods to identify stall precursors, a description of the methodologies used for the study, information on the NASA high speed compressor rig and experimental data acquisition, and results from the four compressor configurations. The experimental results indicate that the correlation method provides ample warning of the onset of rotating stall at high speed, in some tests on the order of 2000 rotor revolutions. Complementary features of the correlation method and the traveling wave energy method are discussed, and suggestions for future developments are made.

This paper presents a methodology of sensor diagnosis which appears to be particularly suitable also for application in the field of small/medium power size industrial gas turbines. The methodology is based on the Analytical Redundancy technique and uses ARX (Auto Regressive with eXternal input) MISO (Multi-Input/Single-Output) linear dynamic models obtained from time series data of the gas turbine operating condition. The linear models allow the on-line calculation of some measurable parameter starting from the values of other measured parameters. The comparison between computed and measured values of the same parameters allows setting-up a vector of residuals which, if compared with the columns of the fault matrix, permits the identification of a possible sensor fault. The initial applications of the methodology to a single-shaft industrial gas turbine show an unambiguous and certain detection and isolation of fault in sensors used both in the measurement only and in feedback by the machine control system.