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Statistically enhanced classification of centrifugal compressor operating condition
Abstract
Centrifugal compressors are prone to aerodynamic instabilities, which are different flow structures detrimental to compressor efficiency and safety of operation. It has been shown that instabilities can be identified using a feature space approach, using processed historic data to define classes of operating conditions. A challenge lies in shaping the boundaries to ensure proper classification of new data, especially in the region of transition between instabilities. In this study, Gaussian process classification (GPC) is used as a classification enhancement for a centrifugal compressor instabilities detection system. GPC provides a probabilistic output that allows for investigating the probability distribution of each class and build flexible and adaptable boundaries between the classes. The performance of GPC is compared with another threshold approach from the literature. The results show that in the studied case, GPC is more accurate and provides higher flexibility in the transition zone but it can be prone to errors further away from the class boundaries
Based on entropy characteristics, some complex nonlinear dynamics of the dynamic pressure at the outlet of a centrifugal compressor are analyzed, as the centrifugal compressor operates in a stable and unstable state. First, the 800-kW centrifugal compressor is tested to gather the time sequence of dynamic pressure at the outlet by controlling the opening of the anti-surge valve at the outlet, and both the stable and unstable states are tested. Then, multi-scale fuzzy entropy and an improved method are introduced to analyze the gathered time sequence of dynamic pressure. Furthermore, the decomposed signals of dynamic pressure are obtained using ensemble empirical mode decomposition (EEMD), and are decomposed into six intrinsic mode functions and one residual signal, and the intrinsic mode functions with large correlation coefficients in the frequency domain are used to calculate the improved multi-scale fuzzy entropy (IMFE). Finally, the statistical reliability of the method is studied by modifying the original data. After analysis of the relationships between the dynamic pressure and entropy characteristics, some important intrinsic dynamics are captured. The entropy becomes the largest in the stable state, but decreases rapidly with the deepening of the unstable state, and it becomes the smallest in the surge. Compared with multi-scale fuzzy entropy, the curve of the improved method is smoother and could show the change of entropy exactly under different scale factors. For the decomposed signals, the unstable state is captured clearly for higher order intrinsic mode functions and residual signals, while the unstable state is not apparent for lower order intrinsic mode functions. In conclusion, it can be observed that the proposed method can be used to accurately identify the unstable states of a centrifugal compressor in real-time fault diagnosis.
This work presents an introduction to feature-based time-series analysis. The time series as a data type is first described, along with an overview of the interdisciplinary time-series analysis literature. I then summarize the range of feature-based representations for time series that have been developed to aid interpretable insights into time-series structure. Particular emphasis is given to emerging research that facilitates wide comparison of feature-based representations that allow us to understand the properties of a time-series dataset that make it suited to a particular feature-based representation or analysis algorithm. The future of time-series analysis is likely to embrace approaches that exploit machine learning methods to partially automate human learning to aid understanding of the complex dynamical patterns in the time series we measure from the world.
Scikit-learn is a Python module integrating a wide range of state-of-the-art
machine learning algorithms for medium-scale supervised and unsupervised
problems. This package focuses on bringing machine learning to non-specialists
using a general-purpose high-level language. Emphasis is put on ease of use,
performance, documentation, and API consistency. It has minimal dependencies
and is distributed under the simplified BSD license, encouraging its use in
both academic and commercial settings. Source code, binaries, and documentation
can be downloaded from http://scikit-learn.sourceforge.net.
Detection of aerodynamic instabilities in compressors is of great importance for machine safety and efficiency. It is a challenge due to their highly non-stationary and non-linear character. In this study, a method of instability detection in centrifugal compressor employing empirical mode decomposition (EMD) is proposed. The method has proven to work well in isolating and highlighting features of instabilities from highly non-stationary, non-linear and noisy pressure signals. Two Instability Detection Features (IDFs) based on energy of selected intrinsic mode functions (IMFs) were defined for detection of inlet recirculation (IDF-IR) and surge (IDF-S). Two level classification is offered by the proposed method. The first allows to differentiate stable and unstable working conditions. The second distinguishes between two types of flow instability: local - inlet recirculation and global - surge. The proposed method was evaluated using short, high-frequency pressure signals collected for known operating conditions. Accuracy of inlet recirculation detection reached 100%, while detection of surge was 99% accurate. The EMD-based instabilities detection method has a traceable connection with the physics of the flow, thus it is fully explainable and should perform similarly well for different machines and measurement systems if appropriate IMFs are employed.
Aerodynamic instabilities in centrifugal compressors are dangerous phenomena affecting machine efficiency and in severe cases leading to failure of the compressing system. Quick and robust instability detection during compressor operation is a challenge of utmost importance from an economical and safety point of view. Rapid indication of instabilities can be obtained using a pressure signal from the compressor. Detection of aerodynamic instabilities using pressure signal results in specific challenges, as the signal is often highly contaminated with noise, which can influence the performance of detection methods. The aim of this study is to investigate and compare the performance of two non-linear signal processing methods—Empirical Mode Decomposition (EMD) and Singular Spectrum Analysis (SSA)—for aerodynamic instability detection. Two instabilities of different character, local—inlet recirculation and global—surge, are considered. The comparison focuses on the robustness, sensitivity and pace of detection—crucial parameters for a successful detection method. It is shown that both EMD and SSA perform similarly for the analysed machine, despite different underlying principles of the methods. Both EMD and SSA have great potential for instabilities detection, but tuning of their parameters is important for robust detection.
Centrifugal compressor machinery is subject to a potentially damaging phenomenon called surge at low mass flow rates. This effect may be preceded by a phenomena known as inlet recirculation — a flow reversal upstream of the impeller. A methodology to isolate inlet recirculation as a characteristic feature for monitoring of centrifugal compressor instability is presented in this study. The methodology is based on a nonparametric time series analysis technique called as singular spectrum analysis (SSA). SSA decomposes a signal into a number of Reconstructive Components (RCs), from which data trends and oscillatory components may be extracted. The frequency spectra of each RC and their relative contributions to the reconstruction of the original signal were examined and comparisons were made with spectral maps in existing literature. Individual and independent RCs were chosen to construct a compressor’s instability monitoring system. Additionally, the performance of SSA was determined by the Window length parameter. The effect of modification of this parameter was also studied, and the various viable choices of component for the basis of inlet recirculation diagnosis were considered. The methodology was implemented in pressure dynamical signals measured in an experimental centrifugal compressor rig. High frequency pressure measurements were taken at a number of flow conditions and locations within the compressor. The results demonstrated the potential of a methodology based on SSA to identify and extract oscillatory components with information about the local effect of inlet recirculation and eventually successfully monitor centrifugal compressor’s instability.
The aim of this article is to present the application of empirical mode decomposition (EMD) for centrifugal blower flow instabilities detection. The analysis of pressure signal features extracted by EMD technique provides indicators of flow phenomena, which could be used for creating an efficient data-based controller. Quasi-dynamic pressure signals from industrial-size blower are used as an input data for EMD algorithms. An energy-based approach to intrinsic mode functions (IMF) is applied, showing the possibility of condition monitoring and instabilities detection, distinctly displaying surge conditions and inlet recirculation. Different intrinsic mode functions (IMFs) are used to detect different instabilities. EMD also presents some potential in detection of optimal operation conditions for impeller, providing additional benefit for a control system. The possibilities of EMD analysis applied to centrifugal blowers and compressors will be further investigated. INTRODUCTION Aerodynamic instabilities detection and avoidance in compressors has been a topic of interest for numerous researchers for over 75 years (Day 2015). Surge and stall are major phenomena influencing compressor performance and posing a threat to machine operation. Surge presents itself by low frequency fluid oscillations at characteristic system frequency, which is often close to the Helmholtz frequency. The structure vibration it induces are dangerous to the machine operation and can cause its destruction (Fink et al. 2008; Liskiewicz and Horodko 2015) Surge detection in centrifugal compressors is often based on previously created compressor map and locating machine operating position on it in continuous manner. The surge line
Design and Analysis of Centrifugal Compressors is a comprehensive overview of the theoretical fluid dynamic models describing the flow in centrifugal compressors and the modern techniques for the design of more efficient centrifugal compressors. The author — a noted expert in the field, with over 40 years of experience — evaluates relevant numerical and analytical prediction models for centrifugal compressors with special attention to their accuracy and limitations. Relevant knowledge from the last century is linked with new insights obtained from modern CFD. Emphasis is to link the flow structure, performance and stability to the geometry of the different compressor components.
Design and Analysis of Centrifugal Compressors is an accessible resource that combines theory with experimental data and previous research with recent developments in computational design and optimization. This important resource
• Covers the basic information concerning fluid dynamics that are specific for centrifugal compressors and clarifies the differences with axial compressors
• Provides an overview of performance prediction models previously developed in combination with extra results from research conducted by the author
• Describes helpful numerical and analytical models for the flow in the different components in relation to flow stability, operating range and performance
• Includes the fundamental information for the aerodynamic design of more efficient centrifugal compressors
• Explains the use of computational fluid dynamics (CFD) for the design and analysis of centrifugal compressors
Written for engineers, researchers and designers in industry as well as for academics specializing in the field, Design and Analysis of Centrifugal Compressors offers an up to date overview of the information needed for the design of more effective centrifugal compressors.
Recent studies showed that a prompt detection of the stall inception, connected with a specific model to predict its associated aerodynamic force, could provide room for an extension of the left margin of the operating curve of high-pressure centrifugal compressors. In industrial machines working in the field, however, robust procedures to detect and identify the phenomenon are still missing, i.e., the operating curve is almost ever cut preliminarily by the manufacturer by a proper safety margin; moreover, no agreement is found in the literature about a well-defined threshold to define the onset of the stall. In particular, in some cases, the intensity of the arising subsynchronous frequency is compared to the revolution frequency, while in many other ones it is compared to the blade passage frequency. A large experience in experimental stall analyses collected by the authors revealed that in some cases unexpected spikes could make this direct comparison not reliable for a robust automatic detection. To this end, a new criterion was developed based on an integral analysis of the area subtended to the entire subsynchronous spectrum of the dynamic pressure signal of probes positioned just outside the impeller exit. A dimensionless parameter was then defined to account for the spectrum area increase in proximity to stall inception. This new parameter enabled the definition of a reference threshold to highlight the arising of stall conditions, whose validity and increased robustness was here verified based on a set of experimental analyses of different types of full-stage test cases of industrial centrifugal compressors at the test rig.
Deficient performances of turbocharger compressors inside turbo-charged engines limit the behaviour of the drive train. This problem has shifted the design space for compressors towards their performance at part-speed and low-flow conditions. The most dominant feature of these flow conditions is inlet recirculation. It causes a large portion of flow to be expelled through the rotor inlet, creating a blockage ring on the casing. While on the one hand, inlet recirculation is the main loss-source at low-speed and low-flow within centrifugal compressors, on the other hand, it also keeps the compressors functioning because it reduces incidence. This thesis aimed towards increasing the understanding of inlet recirculation, with the scope on improving the part-speed, low-flow performance of automotive turbocharger compressors. The phenomenon was investigated regarding its key features, the conditions at which it occurs and its impact on performance. Furthermore, a reduced order model was derived and the influence of the tip gap size as a design parameter was analysed. The research was carried out on an automotive turbocharger compressor which was investigated experimentally and numerically. Inlet recirculation is a phenomenon which takes place in the tip region of the rotor, extending far downstream and far upstream of the leading edge. The flow within the recirculation bubble features a strong positive swirl component, affecting the work input into the machine. The phenomenon is non-periodic in a time-averaged sense. An investigation of the rotor flow-field regarding inlet recirculation, carried out for the first time, revealed that the starting point of inlet recirculation is located far inside the rotor passage. An analysis based on mass, momentum and energy allowed the derivation of a low-order model to account for inlet recirculation in preliminary design. In the compressor map, inlet recirculation was present over 40% of the map width at low speeds. It maintained its presence with increasing rotor speed beyond the point where the inlet flow became transonic. The losses in the inlet recirculation zone were shown to be up to 35% of the total compressor loss at low speed. A loss analysis showed that inlet recirculation was the main loss source at low-flow conditions. The tip clearance study showed that the size and intensity of inlet recirculation was independent of the tip gap size. Efficiency gains due to reduced tip leakage were marginalised by the presence of inlet recirculation but the rotor maintained enhanced pressure rise capabilities for reduced tip gap sizes.
The Hilbert-Huang Transform (HHT) represents a desperate attempt to break the suffocating hold on the field of data analysis by the twin assumptions of linearity and stationarity. Unlike spectrograms, wavelet analysis, or the Wigner-Ville Distribution, HHT is truly a time-frequency analysis, but it does not require an a priori functional basis and, therefore, the convolution computation of frequency. The method provides a magnifying glass to examine the data, and also offers a different view of data from nonlinear processes, with the results no longer shackled by spurious harmonics — the artifacts of imposing a linearity property on a nonlinear system or of limiting by the uncertainty principle, and a consequence of Fourier transform pairs in data analysis. This is the first HHT book containing papers covering a wide variety of interests. The chapters are divided into mathematical aspects and applications, with the applications further grouped into geophysics, structural safety and visualization.
An experimental study is performed to characterize the behavior of a high-speed centrifugal compressor as it approaches instability. To achieve this, data at the inlet and exit of the centrifugal compressor are analyzed. Three inducer bleed conditions are examined. Data analysis indicates that the disturbance was a 9-lobed stall pattern occurring in or near the diffuser and suggests that the phenomena is different than that typically referred to as impeller stall. The component pressure characteristics show a reduction in diffuser performance corresponding to the rise in the spatial mode magnitude, with minimal effect on the impeller. It is suggested that the rotating stall condition that was observed in this compressor may play a similar role to that observed when rotating stall initiates surge in multistage axial compressor.
There are a number of surge control schemes in current use for centrifugal compressors employed in natural gas transmission systems. Basically, these schemes consist of a set of detection devices that either anticipate surge or detect it at its inception, and a set of control devices that act to prevent surge from occurring. A patent search was conducted in an attempt to assess the level and direction of technology development over the last 20 years and to define the focus for future R&D activities. In addition, the paper presents the current state of technology in three areas: surge control, surge detection, and surge suppression. Patent data obtained from on-line databases showed that most of the emphasis has been on surge control rather than on detection and control and that the current trend in surge control will likely continue toward incremental improvement of a basic or conventional surge control strategy. Various surge suppression techniques can be grouped in two categories: (i) those that are focused on better compressor interior design, and (ii) others that attempt to suppress surge by external and operational means.
Flow instability evolution in high pressure ratio centrifugal compressor with vaned diffuser
- X He
- X Zheng
X. He and X. Zheng, "Flow instability evolution in high pressure ratio centrifugal compressor with
vaned diffuser," Experimental Thermal and Fluid Science, vol. 98, pp. 719-730, 2018.
The kernel cookbook: Advice on covariance functions
- D Duvenaud
D. Duvenaud, "The kernel cookbook: Advice on covariance functions," URL https://www. cs. toronto.
edu/˜duvenaud/cookbook, 2014.