System and method for forewarning onset of impending sequence of oscillatory instabilities in target device

Abstract

The present invention discloses a system (100) and method for forewarning oscillatory instabilities in a target device (102). The system (100) comprises a data acquiring unit (104) comprising a sensor unit (202) in close proximity to the target device (102) to collect target device data from the target device (102). The system (100) comprises a forewarning unit (106) communicatively coupled to the data acquiring unit (104). The forewarning unit (106) receives and pre-processes the target device data and analyse the pre-processed target device data to derive a natural visibility graph measure (NVGM) and trigger an alert in case the NVGM falls below a predefined threshold value for identifying an onset of an impending sequence of bifurcations leading to oscillatory instabilities.

Description

System and method for forewarning onset of impending sequence of oscillatory instabilities in target device

[0001] The field of invention generally relates to all practical systems that are susceptible to different sequences of bifurcation to oscillatory instabilities. More specifically, it relates to a system and method for forewarning such instabilities in practical systems across various domains.

[0002] The study and management of oscillatory instabilities is a critical area in applications spanning a wide range of practical systems, including gas turbine engines, rocket engines, afterburners, industrial burners, wind turbine blades, bridges, skyscrapers, propellers, compressors, and other structures interacting with dynamic flows. Over the past few decades, understanding of these instabilities has grown significantly, driven by need to enhance system reliability, safety, and performance in industries such as aerospace, energy, and infrastructure. Such instabilities often emerge from low-amplitude aperiodic oscillations and can transition through various bifurcation sequences, resulting in large-amplitude oscillations that pose significant risks.

[0003] Currently, existing systems do not succeed in comprehensively addressing full spectrum of bifurcation sequences leading to oscillatory instabilities. Many conventional approaches focus primarily on detecting the onset of primary bifurcations. While these systems provide valuable insights into initial transitions to oscillatory states, they often lack the capability to anticipate subsequent transitions, such as secondary bifurcations, which can escalate into high-amplitude oscillations with severe consequences.

[0004] Other existing systems have tried to address this problem but fall short in several ways. Firstly, these systems are driven by increasing complexity of modern engineering systems and are incapable of fully addressing dynamic progression of oscillatory instabilities beyond initial detection. Additionally, a further drawback lies in their reliance on static sensitivity coefficients and fixed thresholds, which are tailored to specific operational conditions or instability types. In practice, the increasing complexity of modern systems introduces variability in instability patterns, and these systems fail to adapt to, consequently missing critical warning signs of impending engine shutdowns and making them unreliable across diverse applications.

[0005] Thus, in light of the above discussion, it is implied that there is need for a system and method for forewarning oscillatory instabilities in various target devices, which is reliable and does not suffer from the problems discussed above.Object of Invention

[0006] The principal object of this invention is to provide a system and method to forewarn oscillatory instabilities across the different spectrum of bifurcation sequences in practical systems. This ensures enhanced reliability and safety by enabling timely intervention to prevent catastrophic failures, such as engine shutdowns or structural damage, thereby optimizing system’s performance across diverse applications.

[0007] A further object of the invention is to provide a system and method for adapting to dynamic progression of instabilities with improved sensitivity to variability in oscillation patterns. This facilitates robust component-level monitoring, allowing individual elements such as turbine blades, compressors, or structural support to maintain operational integrity under complex and evolving conditions, reducing wear and extending service life.

[0008] Another object of the invention is to offer an actionable forewarning mechanism that empowers users, such as engineers and operators, with real-time insights regarding impending instabilities. This enhances user decision-making efficiency, minimizes operational downtime, and reduces the risk of human error by providing reliable warning across diverse practical scenarios.

[0009] This invention is illustrated in the accompanying drawings, throughout which, like reference letters indicate corresponding parts in the various figures.

[0010] The embodiments herein will be better understood from the following description with reference to the drawings, in which:Fig. 1

[0011] illustrates a system for forewarning oscillatory instabilities, in accordance with an embodiment;Fig. 2

[0012] 2 illustrates a block diagram of the system, depicting a detailed view of its internal architecture, in accordance with an embodiment;Fig. 3A

[0013] illustrates an operational method for forewarning oscillatory instabilities in the target device, in accordance with an embodiment;Fig. 3B

[0014] illustrates the operational method for forewarning oscillatory instabilities in the target device, in accordance with an embodiment;Fig. 4A

[0015] illustrates a graph depicting a sample time series of a sine wave, in accordance with an embodiment;Fig. 4B

[0016] illustrates a graph depicting an amplitude spectrum Af plotted against frequency, in accordance with an embodiment;Fig. 4C

[0017] illustrates the visibility graph constructed from the amplitude spectrum Af, in accordance with an embodiment;Fig. 5

[0018] illustrates a graph depicting a first stage of the forewarning process for determining an impending primary bifurcation in the target device, in accordance with an embodiment; andFig. 6

[0019] [Fig. illustrates a graph depicting a second stage of the forewarning process for determining an impending secondary bifurcation in the target device, in accordance with an embodiment.Statement of Invention

[0020] The present invention discloses a system for forewarning an onset of an impending sequence of bifurcation leading to oscillatory instabilities in a target device. The system comprises a data acquiring unit comprising a sensor unit in close proximity to collect target device data from the target device. A forewarning unit is operably connected to the data acquiring unit. The forewarning unit receives and pre-processes the target device data and analyze the pre-processed target device data to derive a natural visibility graph measure (NVGM) and trigger an alert if the NVGM falls below a predefined threshold value for forewarning the onset of the impending sequence of bifurcation leading to oscillatory instabilities.

[0021] The present invention discloses a method for forewarning an onset of an impending sequence of bifurcation leading to oscillatory instabilities in a target device. The method comprising, collecting target device data from the target device, by a sensor unit of a data acquiring unit, receiving and pre-processing the target device data and analyze the pre-processed target device data to derive a natural visibility graph measure (NVGM) and trigger an alert if the NVGM falls below a predefined threshold value for forewarning the onset of the impending sequence of bifurcation leading to oscillatory instabilities, by a forewarning unit

[0022] The embodiments herein and the various features and advantageous details thereof are explained more fully with reference to the non-limiting embodiments that are illustrated in the accompanying drawings and / or detailed in the following description. Descriptions of well-known components and processing techniques are omitted so as to not unnecessarily obscure the embodiments herein. The examples used herein are intended merely to facilitate an understanding of ways in which the embodiments herein may be practiced and to further enable those of skill in the art to practice the embodiments herein. Accordingly, the examples should not be construed as limiting the scope of the embodiments herein.

[0023] The present invention discloses a system and method for forewarning and alerting users of an impending sequence of bifurcation leading to oscillatory instabilities in devices by analysing real-time data to reveal critical transitions. The approach of the current invention leverages a unique graph-based metric to provide early alerts, enabling early and effective prevention of system disruptions across various applications in engineering fields.

[0024] illustrates a system 100 for forewarning oscillatory instabilities, comprising at least one target device 102, at least one data acquiring unit 104, at least one forewarning unit 106 and at least one output unit 108.

[0025] In an embodiment, the target device 102 comprises a system prone to oscillatory instabilities driven by dynamic interactions, such as combustion processes or aeroacoustics effects.

[0026] The target device 102 comprises at least one of engines, motors, gas turbine engines, rocket motors, afterburners, industrial burners, wind turbine blades, bridges, skyscrapers, propellers, compressors, or other structures exposed to turbulent flows and oscillations.

[0027] The target device 102 may be any active system or device where dynamics interactions can transition from low-amplitude aperiodic behaviour to high-amplitude limit cycle oscillations (LCO) through primary and secondary bifurcations.

[0028] The primary bifurcation refers to an initial critical transition where the target device 102 shifts from a stable, low-amplitude state to a high-amplitude oscillatory state. Primary bifurcations can be predicted easily based on data as they are based on a direct pattern / progression / sequence of a system’s behaviour.

[0029] The secondary bifurcation occurs subsequent to the primary bifurcation, leading to more complex oscillatory behaviours in the target device 102. Secondary bifurcations cannot be detected easily as they occur randomly and do not follow any pattern or sequence in the system’s behaviour.

[0030] In an embodiment, the data acquiring unit 104 is in close proximity to the target device 102 and functions as a sensory interface of the system 100. The data acquiring unit 104 captures target device data in real-time from the target device 102.

[0031] In an embodiment, the data acquiring unit 104 may comprise any device which monitors and records data of a target device 102, such as at least one of embedded systems with microcontrollers, Field-Programmable Gate Array (FPGAs), oscilloscopes with data logging features, Modular Data Acquisition (MDQ) systems and sound and vibration measurement instruments.

[0032] In an embodiment, the forewarning unit 106 is an analytical core of the system 100. The forewarning unit 106 is communicatively connected to the data acquiring unit 104, and is configured to pre-process the received target device data and further analyse the pre-processed target device data to forewarn one or more sequences of bifurcation leading to oscillatory instabilities. The forewarning unit 106 utilizes a multi-step methodology to derive a natural visibility graph measure (NVGM) and trigger an alert in case the NVGM falls below a predefined threshold value. to identify a sequence of bifurcation sequences, comprising primary and secondary bifurcations, which lead to oscillatory instabilities. Further, the forewarning unit 106 communicates the trigger to the output unit 108.

[0033] In an embodiment, the output unit 108 is coupled to the forewarning unit 106. The output unit 108 receives the trigger and generates one or more alert in case an alert is triggered by the forewarning unit 106 when the NVGM falls below the predefined threshold value, indicating at least one impending oscillatory bifurcation in the target device 102.

[0034] illustrates a block diagram 200 of the system 100, depicting a detailed view of its internal architecture, in accordance with an embodiment.

[0035] In an embodiment, the data acquiring unit 104 comprises a sensor unit 202 in close proximity to the target device 102 to collect target device data from the target device 102 and measure physical variables that reflect the dynamic behavior of the system 100, such as acoustic pressure fluctuations. The sensor unit 202 is in proximity such that it is able to collect data from the target device 102. The sensor unit 202 may be placed near or directly attached to the target device 102 to effectively capture the required target device data (e.g., acoustic signals) without interference or significant signal loss.

[0036] The sensor unit 202 may comprise at least one of a pressure sensor, a piezoelectric sensor, a piezoresistive sensor, and a microphone. The sensor unit 202 continuously monitors the target device 102, collecting time-series target device data that encapsulates a current operational state of the target device 102. The sensor unit 202 communicates the acquired target device data to the forewarning unit 106 for further processing. In an embodiment, the sensor unit 202 may be attached to or remotely monitoring the target device 102.

[0037] In an embodiment, the forewarning unit 106 comprises a signal conditioning module 204, a data acquisition device 206, a frequency domain converter 208, a sensitivity parameter input module 210, a spectral data module 212, a memory module 214, an NVGM module 216, and a warning generating module 218.

[0038] In an embodiment, the signal conditioning module 204 receives the time series target device data from the sensor unit 202 and processes it to enhance quality and compatibility for digital analysis. The signal conditioning module 204 performs amplification, filtering, and noise reduction to eliminate environmental interference or electrical noise, ensuring the time-series target device data accurately represents the dynamics of the target device 102.

[0039] In an embodiment, the data acquisition device 206 aggregates the conditioned target device data into a structured time-series data, denoted as x(N), which is suitable for further analysis, and communicates the same to the frequency domain converter 208.

[0040] In an embodiment, the frequency domain converter 208 receives the structured time-series data x(N) from the data acquisition device 206. The frequency domain converter 208 applies a Fast Fourier Transform (FFT) with a Hanning window to convert the time series data into a frequency spectrum, denoted as X(K), where K is a frequency index.

[0041] X(K) is a complex-valued array, with each element comprising a real part (Re(X(K)) and an imaginary part (Imag(X(K)).

[0042] The FFT transformation presents the frequency components of the target device data, such as dominant peaks or nodes that may indicate an onset of oscillatory behavior.

[0043] In an embodiment, the sensitivity parameter input module 210 is operably connected to the frequency domain converter 208 and enables selection of a sensitivity parameter q value. The sensitivity parameter input module 210 helps to adjust sensitivity of a spectral analysis, to select one of different bifurcation stages such as a primary bifurcation and a secondary bifurcation.

[0044] In an embodiment, the sensitivity parameter q value may be set manually by an operator or automatically by the forewarning unit 106 based on predefined conditions, offering flexibility to adapt to the dynamics of the target device 102.

[0045] In an embodiment, the sensitivity parameter q value is set to a value of “2” to forewarn a primary bifurcation in the target device 102.

[0046] In an embodiment, the sensitivity parameter q value is set to a value of “1” to forewarn a secondary bifurcation in the target device 102.

[0047] In embodiment, the spectral data module 212 receives the frequency spectrum X(K) from the frequency domain converter 208 and the sensitivity parameter q value from the sensitivity parameter input module 210, and generates a spectral representation defined by an equation provided below:

[0048] Spectrum(K) = |X(K)|q

[0049] In an embodiment, in case the sensitivity parameter q value is 2, the spectral data module 212 generates a power spectrum, highlighting energy contribution of each frequency which is particularly sensitive to a rapid rise of a dominant peak as the target device 102 nears the primary bifurcation. The power spectrum is defined by an equation provided below.

[0050] Power (K) = |X(K)|2

[0051] In an embodiment, in case the sensitivity parameter q value is 1, the spectral data module 212 generates an amplitude spectrum, providing a linear measure of oscillation magnitude. This aids in tracking the gradual increase in magnitude of a dominant frequency relative to other frequency components, facilitating detection of the secondary bifurcations. The amplitude spectrum is defined by an equation provided below.

[0052] Amplitude(K) = |X(K)|1

[0053] In an embodiment, the memory module 214 stores one or more parameters required for consistent operation, such as sensitivity parameter values (q=2 and q=1) and a predefined threshold value.

[0054] In an embodiment, the predefined threshold value for the NVGM is determined based on one or more factors specific to the target device 102. The one or more factors comprises at least one of operating conditions, target device type (thermofluidic system like combustors), one or more risk factors (e.g., potential for catastrophic failure), and the performance factors, balancing operational efficiency and threshold sensitivity.

[0055] In an embodiment, the predefined threshold value is set higher, in case the system 100 is configured to provide an early warning of an impending oscillatory instability. A higher threshold value enables the system 100 to detect the NVGM crossing the threshold at an earlier point in time, facilitating earlier intervention to mitigate the risk of bifurcation transitions.

[0056] In an embodiment, the predefined threshold value is set lower in case the system 100 is configured to issue a late warning of an impending oscillatory instability. A lower threshold delays the detection of the NVGM crossing the threshold, allowing the system 100 to issue an alert at a later point in time, which may be suitable for scenarios where delayed intervention is acceptable.

[0057] In an embodiment, the predefined threshold value is configured as 0.1 for detecting the primary bifurcation and / or the secondary bifurcation.

[0058] In an embodiment, the NVGM module 216 constructs a visibility graph from the spectral representation, defined by:

[0059] Spectrum(K) = |X(K)|q

[0060] where “q” is the sensitivity parameter value.

[0061] The NVGM module 216 obtains the spectral representation from the spectral data module 212 and treats each frequency K in the Spectrum (K) as a node in the visibility graph.

[0062] In the visibility graph, two nodes corresponding to respective frequencies are connected by an edge if a straight line can be drawn between them without being obstructed by any intermediate node. The NVGM module 216 further selects the frequency with highest value is selected as a peak node in the visibility graph.

[0063] In embodiment, the NVGM module 216 utilizes the visibility graph to compute the NVGM. The NVGM module 216 determines a value “m” as a ratio of degree of the peak node to its maximum possible degree in the visibility graph, wherein the degree represents a plurality of connections from the peak node to other nodes. The value “m” is represented as provided below.

[0064] m = (degree of the peak node) / (maximum possible degree for the peak node excluding the peak node connection to itself).

[0065] In an embodiment, the NVGM module 216 computes the NVGM by an equation provided below.

[0066] NVGM = 1 - m.

[0067] In an embodiment, an NVGM ≈ 1 indicates a fewer connections and low visibility, indicating a chaotic state with a broad frequency distribution.

[0068] In an embodiment, an NVGM ≈ 0 indicates many connections and high visibility, indicating an oscillatory state with the dominant frequency or the peak node.

[0069] In an embodiment, the choice of the sensitivity parameter q value influences overall structure of the visibility graph. When q=2, the prominence of the peak node increases, reducing the NVGM and enabling early detection of an impending primary bifurcation.

[0070] In an embodiment, when q=1, the visibility graph reflects a more balanced frequency distribution, allowing the NVGM to decrease gradually and providing a reliable forewarning of an impending secondary bifurcation.

[0071] In an embodiment, the NVGM module 216 calculates the NVGM with q=2 from the power spectrum, and if the NVGM falls below the predefined threshold of 0.1, the warning generating module 218 triggers a first alert for an impending primary bifurcation. Thereafter, the forewarning unit 106 may update the sensitivity parameter q value to 1.

[0072] In an embodiment, the NVGM module 216 calculates the NVGM with q=1 from the amplitude spectrum, and if the NVGM falls below the predefined threshold of 0.1, the warning generating module 218 triggers a second alert for an impending secondary bifurcation.

[0073] In an embodiment, the NVGM module 216 may calculate the NVGM for both primary and secondary bifurcations, based on only one of the power spectrum or the amplitude spectrum.

[0074] In an embodiment, one or more of the first alert and the second alert may be communicated by the warning generating module 218 to the output unit 108. The output unit 108 generates the first alert in case the forewarning unit triggers the first alert and the second alert in case the forewarning unit 106 triggers the second alert.

[0075] The warning generating module 218 may prioritize the second alert over the first alert, as the second alert addresses more critical secondary bifurcations that could lead to catastrophic events to the target device 102. For instance, the first alert may comprise one or two warnings for the impending primary bifurcation, and the second alert may comprise of multiple urgent warnings for the impending secondary bifurcation.

[0076] In an embodiment, the warning generating module 218 communicates at least one of two warnings (in the form of electronic signals) corresponding to the onset of said impending oscillatory instabilities (primary bifurcations and secondary bifurcations) in the target device 102 to the output unit 108.

[0077] In an embodiment, the output unit 108 receives the at least one of two warnings or electronic signals corresponding to the onset of said impending oscillatory instabilities in the target device 102, from the warning generator module 218.

[0078] In an embodiment, the output unit 108 receives the corresponding electronic signal or warning from the warning generating module 218 thereby facilitating the selection of appropriate control or prevention actions to mitigate or prevent oscillatory instabilities in the target device 102.

[0079] In an embodiment, the output unit 108 comprises at least one of the electronic signal or warning corresponding to the onset of said impending oscillatory instabilities in the target device 102, an alert display module 220, and a speaker, to enable the output unit 108 to select control and prevention actions to mitigate oscillatory instabilities in the target device 102 and generate at least one of a visual or auditory representation of the warnings.

[0080] In an embodiment, the the electronic signal enables the output unit 108 to facilitate selection of appropriate control or prevention actions to mitigate or prevent oscillatory instabilities in the target device 102.

[0081] The alert display module 220 displays the one or more alerts such as warning messages on operator or operator’s screen, such as “primary bifurcation detected” or “secondary bifurcation detected”, along with at least one relevant value of NVGM or a time of detection.

[0082] In an embodiment, the alert display module 220 may activate an alarm or buzzer to draw immediate attention to critical warnings for the target device 102, requiring rapid operator intervention.

[0083] In an embodiment, the alert display module 220 may send notifications to a device of the operator, ensuring alerts are received even if the operator is not physically present at the alert display module 220.

[0084] In an embodiment, the output unit 108 comprises a speaker to emit one or more audio alerts to notify the operator of the impending primary bifurcation or secondary bifurcation in the target device 102.

[0085] In an embodiment, the speaker may emit audio alerts in the form of pre-recorded voice messages, such as “primary bifurcation detected” or “secondary bifurcation detected” to indicate the type of instability detected in the target device 102.

[0086] Figures 3A-3B illustrate an operational method 300 for forewarning oscillatory instabilities in a target device 102, in accordance with an embodiment. The method 300 begins with acquiring time series target device data from the target device 102 using a sensor unit 202 of a data acquiring unit 102, as depicted at step 302. Subsequently, the method 300 discloses conditioning and digitizing the time series target device data using a signal conditioning module 204 of the data acquiring unit 104, as depicted at step 304. A data acquisition device 206 of the data acquiring unit 104 further processes the target device data to obtain structured time-series data. Thereafter, the method 300 discloses transforming the time-series data into a frequency domain using a frequency domain converter 208, as depicted at step 306. Thereafter, the method 300 discloses receiving a sensitivity parameter q value from an operator of the target device 102 using a sensitivity parameter input module 210, as depicted at step 308. Thereafter, the method 300 discloses generating a spectrum based on the sensitivity parameter q value, by a spectral data module 212, as depicted at step 310. In case, the sensitivity parameter q value is received as 2, a power spectrum is generated for primary bifurcation detection, and in case, the sensitivity parameter q value is received as 1, an amplitude spectrum is generated for secondary bifurcation detection, by the spectral data module 212. Thereafter, the method 300 discloses constructing a visibility graph from the generated spectrum and computing a NVGM using a NVGM module 216, as depicted at step 312. The NVGM module 216 computes a value “m” from the visibility gram to compute the NVGM as 1-m. Thereafter, the method 300 discloses comparing the NVGM value with a predefined threshold value of 0.1, as depicted at step 314. Thereafter, the method 300 discloses determining if the NVGM falls below the predefined threshold value, as depicted at step 316. Thereafter, the method 300 discloses triggering an alert by a warning generating module 218 if the NVGM falls below the predefined threshold value, as depicted at step 318. In case the NVGM is determined to be higher than the predefined threshold, the method 300 is prompted to repeat execution of the step 302 of collecting time series target device data, as depicted at step 320.

[0087] Figures 4A, 4B and 4C illustrate visual representations of key steps in the method 300 implemented by the system 100 for forewarning oscillatory instabilities in a target device 102, in accordance in an embodiment.

[0088] illustrates a graph 402 depicting a sample time series of a 160 Hz sine wave, plotted as amplitude versus time (in seconds, ranging from 0 to 1 second), in accordance with an embodiment. The 160 Hz sine wave serves as an example of time-series data x(N), comprising of N discrete data points, such as acoustic pressure fluctuations derived from the target device 102. The x-axis represents time t in seconds, and the y-axis represents an amplitude of the sine wave, ranging from -2 to 2. The sine wave exhibits a periodic oscillatory pattern at 160 Hz, providing a simplified representation of the oscillatory signal obtained from the target device 102 to be further processed by the system 100.

[0089] illustrates a graph 404 depicting an amplitude spectrum Af plotted against frequency in Hz, ranging from 0 to 500 Hz, in accordance with an embodiment. The x-axis represents frequency in Hz, and the y-axis represents the amplitude Af ranging from 0 to 500. A prominent peak is observed at 160 Hz, corresponding to a dominant frequency (peak node) of the sine wave depicted inThe amplitude spectrum Afis derived by applying a Fast Fourier Transform (FFT) to the time-series data by converting it from the time domain x(N) to the frequency domain (X(K)). The amplitude spectrum is a specific case of the generalized spectrum defined by the equation,

[0090] Spectrum(K) = |X(K)|q

[0091] where the sensitivity parameter q = 1. Likewise, forq= 2, a power spectrum is generated using the same equation of generalized spectrum.

[0092] illustrates the visibility graph 406 constructed from the amplitude spectrum depicted in, derived withq=1 by the equation,

[0093] Amplitude(K) = |X(K)|1

[0094] The x-axis represents frequency in Hz, ranging from 0 to 500 Hz, and the y-axis represents the amplitude Af, matching the scale ofEach frequency in the amplitude spectrum is treated as a node. A dot 408 is marked as the peak node at 160 Hz which is the frequency with the highest spectral value which is used as a reference for further analysis. A plurality of lines extends from the peak node to other nodes that satisfy the visibility condition, indicating connections in the visibility graph. The visibility condition enables a straight line to be drawn from the top of one node to the top of another node without being obstructed by intermediate nodes. This visibility graph is used to compute the NVGM to quantify the state of the target device 102. The value “m” is calculated as a ratio of degree of the peak node to its maximum possible degree, excluding its connection to itself. The NVGM is then calculated as NVGM = 1 – m. The NVGM close to 0 indicates an oscillatory state of the target device 102, while the NVGM close to 1 indicates a chaotic state of the target device 102.

[0095] illustrates a graph 500 depicting a first stage of the forewarning process for detecting an impending primary bifurcation in the target device 102, in accordance with an embodiment.

[0096] On the left y-axis ranging from 0 to 1500 Pa, root mean square (RMS) values of the acoustic pressure fluctuations, representing the amplitude of oscillations in the target device 102 are plotted. On the right y-axis, the NVGM, computed with the sensitivity parameter q value = 2 is plotted, ranging from 0 to 0.7. The x-axis represents a control parameter (CP), ranging from 0.89 to 1.05 comprising ranges for both primary bifurcation 504 and secondary bifurcation 506. The predefined threshold value of 0.1 at 508 is represented as a horizontal dashed line, indicating a level for triggering early warnings. An early warning point 502 is the point where the NVGM at q=2 begins a noticeable decrease at the predefined threshold value of 0.1, providing an early warning of the impending primary bifurcation.

[0097] illustrates a graph 600 depicting a second stage of the forewarning process for detecting an impending secondary bifurcation in the target device 102, in accordance with an embodiment.

[0098] On the left y-axis ranging from 0 to 1500 Pa, root mean square (RMS) values of the acoustic pressure fluctuations, representing the amplitude of oscillations in the target device 102 are plotted. On the right y-axis, the NVGM values computed with the sensitivity parameter q value = 1 are plotted, ranging from 0 to 1. The x-axis represents the control parameter CP, ranging from approximately 0.89 to 1.05, comprising ranges for both primary bifurcation 604 (CP = 1.00) and secondary bifurcation 606 (CP ≈ 1.03). The predefined threshold value of 0.1 at 608 is represented as a horizontal dashed line indicates the level for triggering early warnings. An early warning point 602 is the point where the NVGM at q=1 begins a noticeable decrease at the predefined threshold value of 0.1, providing an early warning of the impending secondary bifurcation.

[0099] The advantages of the current invention include the early detection and forewarning of oscillatory instabilities in the target device 102, enabling the prevention of catastrophic system disruptions. By leveraging the natural visibility graph measure NVGM with real-time data analysis, the system 100 identifies critical transition patterns, such as primary and secondary bifurcations, well before they lead to high-amplitude oscillations. This graph-based approach, demonstrated using sensitivity parameters q=2 and q=1, ensures that operators can intervene in a timely manner, mitigating risks in dynamic systems.

[0100] An additional advantage is that the current invention offers adaptability to a wide range of practical devices, enhancing its utility across diverse engineering applications. The methodology opted by the current invention, which employs the NVGM to quantify the state of the target device 102, can be used to detect thermoacoustic, aeroacoustics, or aeroelastic instabilities in devices such as gas turbine engines, rocket motors, wind turbine blades, bridges, and skyscrapers. This flexibility, combined with the ability to adjust the sensitivity parameter q for different bifurcation stages, ensures that the system 100 provides reliable forewarning regardless of the specific dynamics or operating conditions of the target device 102.

[0101] Applications of the current invention include the monitoring and forewarning of oscillatory instabilities in a variety of engineering systems prone to dynamic transitions, such as gas turbine engines, rocket motors, afterburners, industrial burners, wind turbine blades, bridges, skyscrapers, propellers, and compressors. Additionally, the current invention can be utilized in the area of design and development of device to get real-time early warnings for sequence of bifurcations leading to oscillatory instabilities in various systems such as thermofluidic systems, aeroacoustics systems, aeroelastic systems, climate systems, biological systems, electronic systems, infrastructural systems etc. The current invention is capable to enhance safety and performance across multiple industries.

[0102] The foregoing description of the specific embodiments will so fully reveal the general nature of the embodiments herein that others can, by applying current knowledge, readily modify and / or adapt for various applications such specific embodiments without departing from the generic concept, and, therefore, such adaptations and modifications should and are intended to be comprehended within the meaning and range of equivalents of the disclosed embodiments. It is to be understood that the phraseology or terminology employed herein is for the purpose of description and not of limitation. Therefore, while the embodiments herein have been described in terms of preferred embodiments, those skilled in the art will recognize that the embodiments herein can be practiced with modification within the scope of the embodiments as described here.

Claims

A system (100) for forewarning an onset of an impending sequence of oscillatory instabilities in a target device (102), comprising:a data acquiring unit (104) comprising a sensor unit (202) in close proximity to the target device (102) to collect target device data from the target device (102); anda forewarning unit (106) communicatively coupled to the data acquiring unit (104), wherein the forewarning unit (106) receives and pre-processes the target device data and analyses the pre-processed target device data to derive a natural visibility graph measure (NVGM) and trigger at least one alert in case the NVGM falls below a predefined threshold value, for forewarning the onset of the impending sequence of bifurcations leading to oscillatory instabilities.The system (100) as claimed in claim 1, wherein the forewarning unit (106) comprises:a frequency domain converter (208) to apply a fast Fourier transform (FFT) to the pre-processed target device data to obtain a frequency spectrum;a sensitivity parameter input module (210) to receive and record a sensitivity parameter (q) value; anda spectral data module (212) to generate a spectral representation of the target device data based on the frequency spectrum and the recorded sensitivity parameter (q) value.The system (100) as claimed in claim 2, wherein the spectral data module (212) is configured to:generate at least one of an amplitude spectrum and a power spectrum from the spectral representation based on the received sensitivity parameter (q) value,wherein the sensitivity parameter (q) value comprises a first value of 2 to detect a primary bifurcation, and wherein the sensitivity parameter (q) value comprises a second value of 1 to detect a secondary bifurcation.The system (100) as claimed in claim 2, wherein the forewarning unit (106) comprises an NVGM module (216) to:generate a visibility graph by selecting a peak node from the spectral representation comprising highest spectral value and connecting a plurality of nodes, each representing a frequency in the spectral representation, wherein the plurality of nodes is connected based on a visibility condition that enables a straight line to be formed between the plurality of nodes; andcompute the NVGM based on the visibility graph to quantify at least one state of the target device (102).The system (100) as claimed in claim 4, wherein the NVGM module (216) is configured to calculate the NVGM by:selecting the peak node from the plurality of nodes in the visibility graph based on its degree, wherein the degree represents a plurality of connections from the peak node to other nodes;computing a value “m” representing a ratio of degree of the peak node to a maximum possible degree of the peak node in the visibility graph, excluding a connection to itself; andcalculating the NVGM as one minus the value “m”.The system (100) as claimed in claim 5, wherein the forewarning unit (106) comprises a warning generating module (218) to:determine whether the NVGM falls below the predefined threshold value in case the sensitivity parameter (q) value comprises a first value of 2;trigger at least one first alert using the warning generating module (218) to forewarn at least one primary bifurcation in the target device (102); determine whether the NVGM falls below the predefined threshold value, in case the sensitivity parameter (q) value comprises a second value of 1;trigger at least one second alert using the warning generating module (218) to forewarn at least one secondary bifurcation in the target device (102); andcommunicate at least one electronic signal indicating the onset of said impending oscillatory instabilities in the target device (102) to an output unit (108).The system (100) as claimed in claim 1, wherein the sensor unit (202) is used for measuring acoustic pressure fluctuations in the target device (102), and wherein the sensor unit (202) comprises at least one of a pressure sensor, a piezoelectric sensor, a piezoresistive sensor, and a microphone.The system (100) as claimed in claim 6, wherein the output unit (108) receives and processes the one electronic signal from the warning generating module (218) and generate the alert comprising at least one visual alert and at least one audio alert, wherein the output unit (108) utilizes the electronic signal to enable selection of control or prevention actions for preventing the oscillatory instabilities in the target device (102), and wherein the output unit (108) comprises:an alert display module (220) to display the visual alert; anda speaker to emit the audio alert.The system as claimed in claim 1, wherein the forewarning unit (106) comprises:a signal conditioning module (204) to receive the target device data from the sensor unit (202) and perform signal conditioning on it to enhance quality and compatibility for digital analysis to generate conditioned target device data; anda data acquisition device (206) to receive and convert the conditioned target device data from the signal conditioning module (204) to generate pre-processed target device data comprising time-series data.A method (300) for forewarning an onset of an impending sequence of oscillatory instabilities in a target device (102), comprising:collecting target device data from the target device (102), by a sensor unit (202) of a data acquiring unit (104); andreceiving and pre-processing the target device data and analyzing the pre-processed target device data to derive a natural visibility graph measure (NVGM) and triggering an alert in case the NVGM falls below a predefined threshold value for forewarning the onset of the impending sequence of bifurcations leading to oscillatory instabilities, by a forewarning unit (106).The method (300) as claimed in claim 10, wherein pre-processing the target device data comprises:receiving the target device data from the sensor unit (202) and conditioning it to enhance quality and compatibility for digital analysis and generating conditioned target device data, by a signal conditioning module (204); andreceiving the conditioned target device data from the signal conditioning module (204) and converting the conditioned target device data to generate pre-processed target device data comprising time-series data, by a data acquisition device (206).The method as claimed in claim 10 comprising, utilizing the sensor unit (202) for measuring acoustic pressure fluctuations in the target device (102), wherein the sensor unit (202) comprises at least one of a pressure sensor, a piezoelectric sensor, a piezoresistive sensor, and a microphone.The method (300) as claimed in claim 10, wherein processing the target device data comprises:applying a fast Fourier transform (FFT) to the pre-processed target device data to obtain a frequency spectrum of the target device data, by a frequency domain converter (208) of the forewarning unit (106);receiving and recording a sensitivity parameter (q) value, by a sensitivity parameter input module (210) of the forewarning unit (106); andgenerating a spectral representation based on the frequency spectrum and the recorded sensitivity parameter (q) value, by a spectral data module (212) of the forewarning unit (106).The method (300) as claimed in claim 13, wherein generating the spectral representation by the spectral data module (212) comprises:generating at least one of an amplitude spectrum, and a power spectrum from the spectral representation based on the sensitivity parameter (q) value, wherein the sensitivity parameter (q) value comprises a first value of 2 to detect a primary bifurcation, and wherein the sensitivity parameter (q) value comprises a second value of 1 to detect a secondary bifurcation.The method (300) as claimed in claim 14, comprising:generating a visibility graph, by a NVGM module (216) by selecting a peak node from the spectral representation comprising highest spectral value and connecting a plurality of nodes, each representing a frequency in the spectral representation, wherein the plurality of nodes is connected based on a visibility condition enabling a straight line to be formed between the plurality of nodes, wherein the peak node is used as a reference for further processing; andcomputing the NVGM based on the visibility graph to quantify at least one state of the target device.The method (300) as claimed in claim 15, wherein computing the NVGM comprises:selecting the peak node from the plurality of nodes in the visibility graph based on its degree, by the NVGM module (216), wherein the degree represents a plurality of connections from the peak node to other nodes;computing a value “m” representing a ratio of a degree of the peak node to its maximum possible degree in the visibility graph, excluding a connection to itself, by the NVGM module (216), ; andcalculating the NVGM as one minus the value “m”, by the NVGM module (216).The method (300) as claimed in claim 16 comprising, using a warning generating module (218) of the forewarning unit (106) for:determining whether the NVGM falls below the predefined threshold value in case the sensitivity parameter (q) value comprises the first value of 2; and triggering at least one first alert to forewarn at least one primary bifurcation in the target device (102);determining whether the NVGM falls below the predefined threshold value in case the sensitivity parameter (q) value comprises the second value of 1; triggering at least one second alert to forewarn the secondary bifurcation in the target device (102); andcommunicating at least one electronic signal indicating the onset of said impending oscillatory instabilities in the target device (102) to an output unit (108).The method as claimed in claim 17 comprising:receiving and processing the one electronic signal from the warning generating module (218);generating the alert by an output unit (108), wherein the alert comprises at least one , visual alert and at least one audio alert;wherein the output unit (108) utilizing the electronic signal for selecting control or prevention actions for preventing oscillatory instabilities in the target device (102);displaying the visual alert by an alert display module (220) of the output unit (108); andemitting the audio alert by a speaker of the output unit (108).

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