A digital simulation debugging method and device for a flame detection system based on ultraviolet light signals

Abstract

The present application relates to a kind of flame detection system digital simulation debugging method and device based on ultraviolet light signal, to solve the closed-loop simulation debugging and system calibration problem of high fidelity ultraviolet electric signal under multiple working conditions.The core scheme is: based on standard industrial combustion test platform, deploy multi-view high fidelity ultraviolet sensor array, collect and multidimensional process original ultraviolet signal, extract time-frequency dynamic characteristics, with the help of improved local linear embedding and manifold trajectory evolution model, combined with kalman filter, realize the real-time fusion correction of model and actual deviation, finally generate the standardized simulation electric signal compensated by amplitude-frequency response, rising edge jitter and signal-to-noise characteristics, directly drive flame detection system through digital-analog conversion and impedance matching, realize full-condition closed-loop adaptive calibration.The method can efficiently reproduce real combustion situation, improve system debugging and accurate discrimination ability, applicable to hardware-in-the-loop simulation and online intelligent verification scene.

Description

Technical Field

[0001] This invention relates to the field of flame detection signal simulation and dynamic modeling technology, and in particular to a digital simulation debugging method and device for a flame detection system based on ultraviolet light signals. Background Technology

[0002] Currently, the testing and debugging of flame detection systems commonly employs ultraviolet signals generated by the physical combustion of real flames as the basic signal source, or simulates flame signals using simple electrical signal waveform generators / database playback. A widely used simulation method in this field focuses on one-dimensional time series signals. Through signal acquisition and simple statistical feature extraction, the ultraviolet signals under typical operating conditions are reproduced using a waveform library, and then output to the front end of the flame detection system for performance verification and fault tolerance testing. These methods are simple to implement, have low technical barriers, and can effectively cover typical operating conditions such as stable combustion, flameout, and deflagration, making them applicable to basic functions and fault response detection.

[0003] In recent years, industry trends have focused on improving the discrimination accuracy and adaptive debugging capabilities of flame detection systems under complex operating conditions. Related research has gradually introduced signal processing techniques such as spectral analysis, wavelet transform, and principal component analysis to extract and perform high-order modeling of the multi-scale dynamic features contained in flame ultraviolet signals, thereby improving the detail reproduction of simulation signals. Simultaneously, experimental schemes utilizing neural networks or deep learning for black-box fitting and playback of flame signals have emerged, aiming to expand the data coverage and expressiveness of simulations.

[0004] However, existing technologies generally suffer from the following prominent problems: First, in the simulation signal modeling stage, it relies heavily on offline waveform acquisition and playback, or uses global statistical features (such as mean, standard deviation, main frequency distribution, etc.) for parameterization. This results in the output signal severely lacking the ability to accurately reproduce the dynamic characteristics of real flame ultraviolet signals (such as rapid changes in millisecond-level flicker frequency, abrupt changes in amplitude, signal amplitude-frequency resonance, dynamic boundary transitions, non-stationary disturbances, etc.), leading to a significant increase in the probability of misjudgment by the flame detection system in highly dynamic scenarios.

[0005] Second, traditional one-dimensional time series modeling and simple Fourier frequency domain analysis can only capture the global coarse-grained energy distribution of flame signals. They lack accurate modeling of manifold relationships, random disturbance trajectories and complex transition processes between different operating conditions. They cannot realize the continuous trajectory simulation of combustion states from weak combustion to deflagration to flameout, and it is also difficult to express the intrinsic response mechanism of signals under parameter perturbations.

[0006] Third, although black-box algorithms such as neural networks can improve the ability to reproduce some complex patterns, the models lack physical interpretability, have limited response to parameter perturbations or system feedback, have low debugging efficiency, and lack model generalization and verifiability, making them difficult to apply to full-process closed-loop adaptive calibration for industrial scenarios.

[0007] Fourth, existing simulation systems almost entirely lack the ability to achieve online parameter adaptive correction based on feedback from the AD terminal of the flame detection system. They cannot utilize actual sampling deviation information to perform closed-loop optimization of the simulation signal, making it difficult to eliminate system-level errors and reducing the consistency and confidence of debugging and verification.

[0008] Fifth, the electrical signals output by existing simulation devices typically only consider basic amplitude matching and fail to effectively compensate for the amplitude-frequency response curve, rising edge dynamic jitter, and signal-to-noise attenuation characteristics of real ultraviolet sensors, making it difficult to achieve full current performance in terms of electronic characteristics compared to real operating conditions. Summary of the Invention

[0009] This application provides a digital simulation debugging method and apparatus for a flame detection system based on ultraviolet light signals, which aims to solve one of the problems or issues of the prior art mentioned in the background.

[0010] This application provides a digital simulation and debugging method for a flame detection system based on ultraviolet light signals, specifically including: S1: Deploy a high-fidelity ultraviolet sensor array on a standard industrial combustion test platform to simultaneously collect raw ultraviolet electrical signals under various operating conditions such as weak combustion, stable combustion, pulsating combustion, deflagration, and flameout transition, and set the sampling rate to no less than 10kHz to obtain a set of raw ultraviolet electrical signals containing millisecond-level flicker details.

[0011] S2: Perform sliding window framing on the original ultraviolet signal set, set the length of each frame to 256 points, and perform short-time Fourier transform operation to convert the time-domain signal into a time-frequency energy distribution spectrum set that characterizes the energy distribution pattern.

[0012] S3: Construct a high-dimensional time-frequency feature vector set based on the time-frequency energy distribution map set, and perform dimensionality reduction mapping while preserving local neighborhood relationships to generate a three-dimensional geometric manifold space that represents the topological structure of different combustion states.

[0013] S4: Establish a differentiable parameterized motion equation within the three-dimensional geometric manifold space, and introduce combustion stability coefficient, heat release fluctuation rate and oxidant disturbance intensity as control variables to drive trajectory evolution, so as to construct a manifold trajectory evolution model that can simulate the dynamic evolution path of flame.

[0014] S5: Read the actual response deviation data from the AD acquisition terminal of the flame detection system, input it into the online Kalman filter, and perform real-time fusion calculation with the prediction output of the manifold trajectory evolution model to generate a dynamic correction factor sequence for correcting the trajectory direction.

[0015] S6: The target trajectory points in the three-dimensional geometric manifold space are reverse mapped using the dynamic correction factor sequence. The mapping results are then processed using nonlinear interpolation and phase-preserving resampling techniques to reconstruct a high-fidelity simulated ultraviolet waveform data stream.

[0016] S7: Based on the simulated ultraviolet waveform data stream, electrical compensation parameters are superimposed according to the amplitude-frequency response characteristics, rising edge jitter characteristics, and signal-to-noise ratio attenuation law of the real ultraviolet sensor to generate a standardized simulated electrical signal equivalent to the output of the real sensor.

[0017] S8: The standardized simulated electrical signal is used as the excitation signal to replace the physical sensor and is directly output to the sampling input terminal of the flame detection system to complete the closed-loop simulation debugging and calibration process under all working conditions without the intervention of physical light source.

[0018] This invention also provides a digital simulation and debugging device for a flame detection system based on ultraviolet light signals, comprising: Signal acquisition module: Deploy a high-fidelity ultraviolet sensor array on a standard industrial combustion test platform to simultaneously acquire raw ultraviolet electrical signals under various operating conditions such as weak combustion, stable combustion, pulsating combustion, deflagration and flameout transition, and set the sampling rate to no less than 10kHz to obtain a set of raw ultraviolet electrical signals containing millisecond-level flicker details; Time-frequency spectrum construction module: Performs sliding window framing processing on the original ultraviolet signal set, sets the length of each frame to 256 points, and performs short-time Fourier transform operation to convert the time-domain signal into a time-frequency energy distribution spectrum set that characterizes the energy distribution law; Dimensionality reduction mapping module: Based on the time-frequency energy distribution map set, a high-dimensional time-frequency feature vector set is constructed, and dimension reduction mapping is performed while preserving local neighborhood relationships to generate a three-dimensional geometric manifold space representing the topological structure of different combustion states; Trajectory evolution modeling module: Differentiable parameterized motion equations are established in the three-dimensional geometric manifold space. Combustion stability coefficient, heat release fluctuation rate and oxidant disturbance intensity are introduced as control variables to drive trajectory evolution, so as to construct a manifold trajectory evolution model that can simulate the dynamic evolution path of flame. Fusion correction module: Reads the actual response deviation data of the AD acquisition terminal of the flame detection system, inputs it into the online Kalman filter and performs real-time fusion calculation with the prediction output of the manifold trajectory evolution model to generate a dynamic correction factor sequence for correcting the trajectory direction; Reconstruction module: The target trajectory points in the three-dimensional geometric manifold space are reverse mapped using the dynamic correction factor sequence. The mapping results are processed by nonlinear interpolation and phase-preserving resampling techniques to reconstruct a high-fidelity simulated ultraviolet waveform data stream. Compensation module: Based on the simulated ultraviolet waveform data stream, electrical compensation parameters are superimposed according to the amplitude-frequency response characteristics, rising edge jitter characteristics and signal-to-noise ratio attenuation law of the real ultraviolet sensor to generate a standardized simulated electrical signal equivalent to the output of the real sensor. Closed-loop debugging module: The standardized simulation electrical signal is used as the excitation signal to replace the physical sensor and is directly output to the sampling input terminal of the flame detection system to complete the closed-loop simulation debugging and calibration process under all working conditions without the intervention of physical light source.

[0019] This application provides a digital simulation debugging method and device for a flame detection system based on ultraviolet light signals, which has the following beneficial effects: (1) By introducing differential geometry and dynamic system theory to model the flame ultraviolet signal in manifold space, the traditional method relies on only one-dimensional time series analysis or spectrum statistics to overcome the problem of insufficient characterization ability, and effectively improves the intrinsic restoration accuracy of flame dynamic features. In this three-dimensional embedded space, different combustion states present trajectory distribution with clear topological semantics - the steady combustion state gathers in the central region, the flameout process is manifested as a manifold path shrinking towards the boundary, and strong pulsating combustion forms a closed ring structure, so that the evolution relationship between complex combustion conditions can be expressed geometrically, which significantly enhances the discrimination consistency and physical interpretability of the simulation signal in multimodal transition scenarios, and solves the technical problem of easy confusion between pulsating combustion and flameout misjudgment in the existing technology.

[0020] (2) Based on the manifold space, a differentiable parameterized motion equation is constructed, and online Kalman filtering is integrated to achieve closed-loop feedback correction, which breaks through the open-loop limitation of traditional simulation methods that cannot respond to the deviation of the actual system. By introducing a small number of control variables with clear physical meaning, such as combustion stability coefficient and heat release fluctuation rate, to drive trajectory evolution, and combined with real-time AD terminal feedback data to dynamically adjust the simulated path direction, the generated signal can adaptively match the behavioral characteristics of the real sensor output, which greatly improves the dynamic alignment between the digital simulation environment and the real flame detection system. At the same time, nonlinear interpolation and phase-preserving resampling technology are used to map the manifold points back to the original signal domain, and a hardware response compensation layer is superimposed to achieve a high degree of consistency with the real ultraviolet sensor output in key electrical dimensions such as amplitude frequency response, rising edge jitter, and signal-to-noise ratio attenuation, ensuring that the simulated signal has sufficient confidence and test validity when connected to downstream detection.

[0021] (3) The overall approach abandons the traditional path of relying on physical flame sources, pre-stored waveform libraries or deep neural network black box fitting, and constructs a signal generation mechanism that is completely based on geometric mechanism modeling, transparent in process and supports human intervention. It not only avoids the resource consumption caused by large-scale data annotation and model training, but also realizes the verifiability and traceability of the entire process from modeling, evolution to output. The mechanism supports full-condition coverage testing under conditions without real combustion, and is especially suitable for simulation debugging of high-risk and difficult-to-reproduce scenarios (such as deflagration mutation and multi-stage flameout chain reaction), which significantly reduces testing costs and safety risks. At the same time, the model is highly lightweight and can achieve real-time signal generation without a high-performance computing platform, and has good engineering deployment capabilities and system compatibility.

[0022] The above technical solutions jointly construct a flame signal simulation system that combines high fidelity, strong interpretability, and closed-loop adaptability. This fundamentally improves the technical capability of digital simulation in the dynamic reproduction of complex combustion, provides a stable, accurate, and controllable virtual testing environment for the research and development and verification of flame detection systems, and effectively promotes the paradigm shift of simulation debugging in the field of industrial safety monitoring from "experience-driven" to "mechanism-driven". Attached Figure Description

[0023] Figure 1 This is the main flowchart of a digital simulation and debugging method for a flame detection system based on ultraviolet light signals.

[0024] Figure 2 This is a sub-flowchart of a digital simulation debugging method for a flame detection system based on ultraviolet light signals.

[0025] Figure 3 This is another sub-flowchart of a digital simulation debugging method for a flame detection system based on ultraviolet light signals. Detailed Implementation

[0026] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0027] The following disclosure provides many different embodiments or examples for implementing different structures of the invention. To simplify the disclosure, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the invention. Furthermore, reference numerals and / or letters may be repeated in different examples; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed.

[0028] like Figure 1 As shown, this application provides a digital simulation and debugging method for a flame detection system based on ultraviolet light signals, specifically including: S1: Deploy a high-fidelity ultraviolet sensor array on a standard industrial combustion test platform to simultaneously collect raw ultraviolet electrical signals under various operating conditions such as weak combustion, stable combustion, pulsating combustion, deflagration, and flameout transition, and set the sampling rate to no less than 10kHz to obtain a set of raw ultraviolet electrical signals containing millisecond-level flicker details.

[0029] S2: Perform sliding window framing on the original ultraviolet signal set, set the length of each frame to 256 points, and perform short-time Fourier transform operation to convert the time-domain signal into a time-frequency energy distribution spectrum set that characterizes the energy distribution pattern.

[0030] S3: Construct a high-dimensional time-frequency feature vector set based on the time-frequency energy distribution map set, and perform dimensionality reduction mapping while preserving local neighborhood relationships to generate a three-dimensional geometric manifold space that represents the topological structure of different combustion states.

[0031] S4: Establish a differentiable parameterized motion equation within the three-dimensional geometric manifold space, and introduce combustion stability coefficient, heat release fluctuation rate and oxidant disturbance intensity as control variables to drive trajectory evolution, so as to construct a manifold trajectory evolution model that can simulate the dynamic evolution path of flame.

[0032] S5: Read the actual response deviation data from the AD acquisition terminal of the flame detection system, input it into the online Kalman filter, and perform real-time fusion calculation with the prediction output of the manifold trajectory evolution model to generate a dynamic correction factor sequence for correcting the trajectory direction.

[0033] S6: The target trajectory points in the three-dimensional geometric manifold space are reverse mapped using the dynamic correction factor sequence. The mapping results are then processed using nonlinear interpolation and phase-preserving resampling techniques to reconstruct a high-fidelity simulated ultraviolet waveform data stream.

[0034] S7: Based on the simulated ultraviolet waveform data stream, electrical compensation parameters are superimposed according to the amplitude-frequency response characteristics, rising edge jitter characteristics, and signal-to-noise ratio attenuation law of the real ultraviolet sensor to generate a standardized simulated electrical signal equivalent to the output of the real sensor.

[0035] S8: The standardized simulated electrical signal is used as the excitation signal to replace the physical sensor and is directly output to the sampling input terminal of the flame detection system to complete the closed-loop simulation debugging and calibration process under all working conditions without the intervention of physical light source.

[0036] This invention also provides a digital simulation and debugging device for a flame detection system based on ultraviolet light signals, comprising: Signal acquisition module: Deploy a high-fidelity ultraviolet sensor array on a standard industrial combustion test platform to simultaneously acquire raw ultraviolet electrical signals under various operating conditions such as weak combustion, stable combustion, pulsating combustion, deflagration and flameout transition, and set the sampling rate to no less than 10kHz to obtain a set of raw ultraviolet electrical signals containing millisecond-level flicker details; Time-frequency spectrum construction module: Performs sliding window framing processing on the original ultraviolet signal set, sets the length of each frame to 256 points, and performs short-time Fourier transform operation to convert the time-domain signal into a time-frequency energy distribution spectrum set that characterizes the energy distribution law; Dimensionality reduction mapping module: Based on the time-frequency energy distribution map set, a high-dimensional time-frequency feature vector set is constructed, and dimension reduction mapping is performed while preserving local neighborhood relationships to generate a three-dimensional geometric manifold space representing the topological structure of different combustion states; Trajectory evolution modeling module: Differentiable parameterized motion equations are established in the three-dimensional geometric manifold space. Combustion stability coefficient, heat release fluctuation rate and oxidant disturbance intensity are introduced as control variables to drive trajectory evolution, so as to construct a manifold trajectory evolution model that can simulate the dynamic evolution path of flame. Fusion correction module: Reads the actual response deviation data of the AD acquisition terminal of the flame detection system, inputs it into the online Kalman filter and performs real-time fusion calculation with the prediction output of the manifold trajectory evolution model to generate a dynamic correction factor sequence for correcting the trajectory direction; Reconstruction module: The target trajectory points in the three-dimensional geometric manifold space are reverse mapped using the dynamic correction factor sequence. The mapping results are processed by nonlinear interpolation and phase-preserving resampling techniques to reconstruct a high-fidelity simulated ultraviolet waveform data stream. Compensation module: Based on the simulated ultraviolet waveform data stream, electrical compensation parameters are superimposed according to the amplitude-frequency response characteristics, rising edge jitter characteristics and signal-to-noise ratio attenuation law of the real ultraviolet sensor to generate a standardized simulated electrical signal equivalent to the output of the real sensor. Closed-loop debugging module: The standardized simulation electrical signal is used as the excitation signal to replace the physical sensor and is directly output to the sampling input terminal of the flame detection system to complete the closed-loop simulation debugging and calibration process under all working conditions without the intervention of physical light source.

[0037] Step S1: Deploy a high-fidelity ultraviolet sensor array on a standard industrial combustion test platform to simultaneously collect raw ultraviolet electrical signals under various conditions, including weak combustion, stable combustion, pulsating combustion, deflagration, and flameout transition. Set the sampling rate to no less than 10kHz to obtain a set of raw ultraviolet electrical signals containing millisecond-level flicker details. Specifically, this includes: S1.1: Perform spatial topology analysis on the positions of the burner nozzle, flame stabilizer, and observation window of the standard industrial combustion test platform. Determine the layout coordinates of the high-fidelity ultraviolet sensor array based on the distribution law of the flame radiation field to generate a sensor layout scheme with multi-view coverage capability.

[0038] When performing spatial topology analysis on the burner nozzle, flame stabilizer, and observation window positions of a standard industrial combustion test platform, the platform's three-dimensional structural data is used as the initial input, including burner geometry, nozzle diffusion angle, flame stabilizer diameter, shape of the transparent area of ​​the observation window, and its relative coordinate position within the furnace. A three-dimensional radiation intensity model is constructed based on the flame radiation field distribution law. The ultraviolet radiation power density at each spatial point is calculated using the radiative transfer equation. The finite difference method is used to discretize the radiation field in the three-dimensional mesh of the furnace and form an ultraviolet radiation intensity distribution matrix. Local extremum analysis is performed on the radiation intensity matrix to determine the spatial range of the radiation intensity peak region and the low-intensity transition region. The minimum sensor redundancy deployment set is calculated according to the requirements of multi-view coverage capability. Using multi-objective optimization, the view coverage rate and signal strength attenuation rate are used as optimization objective functions to solve for the optimal deployment coordinates under the constraint of the adjustable range of the sensor mounting bracket. For each deployment coordinate, the shortest optical path distance and obstruction coefficient between the burner nozzle, flame stabilizer, and observation window are calculated. Deployment points with severe obstruction or high interference are eliminated, and the set of deployment points that meet the conditions for high-fidelity signal acquisition is retained. Through the above spatial topology analysis processing method, the three-dimensional structural data of the previous step is transformed into a sensor layout scheme with multi-view coverage capability, realizing the reasonable deployment and optimal positioning of the high-fidelity ultraviolet sensor array.

[0039] For example, on an industrial boiler test platform, the burner nozzle diameter is 40mm, the diffusion angle is 15°, the flame stabilizing plate diameter is 100mm, and the observation window diameter is 80mm, located 1.2m horizontally from the nozzle's central axis on the furnace sidewall. The transparent area is circular. A grid of 8000 spatial points with a 0.05m spacing is established within the three-dimensional furnace. The ultraviolet radiation power density is calculated using a radiative transfer model, with the power density unit being W / m². The peak region is concentrated at 0.4m from the nozzle outlet, reaching a power density of 12.5W / m². Peak points are located in the radiation intensity matrix, and coverage optimization is performed. The sensor coverage rate is set to 95%, and the signal strength attenuation threshold is set to 0.8. Multi-objective optimization yields eight candidate deployment coordinates. An occlusion coefficient is calculated for each candidate coordinate, and points with an occlusion coefficient exceeding 0.4 are discarded, ultimately retaining six deployment points located at different locations on the furnace top, sidewall, and bottom, achieving multi-view coverage. During the verification of the sensor layout scheme, the peak amplitude of the ultraviolet signal at each deployment point was significantly improved through experiments, and the signal acquisition consistency remained within the expected range, meeting the requirements for subsequent high-fidelity data acquisition.

[0040] S1.2: Install a broadband response ultraviolet photomultiplier tube assembly according to the sensor layout scheme, and configure fuel supply parameters for five typical operating conditions: weak combustion, stable combustion, pulsating combustion, deflagration and flameout transition, in order to construct a standard test scenario set that can reproduce the combustion state throughout the entire life cycle.

[0041] The input conditions are the high-fidelity ultraviolet sensor array layout coordinates and spatial topology data generated by step S1.1. The execution objects are the ultraviolet photomultiplier tube assembly with broadband spectral response characteristics and the fuel supply control system of the combustion test platform.

[0042] Using the layout coordinate data as an installation reference, the ultraviolet photomultiplier tube assembly corresponding to each sensor array coordinate point is positioned and fixed on the preset mounting bracket in the burner nozzle, flame stabilizer and observation window area. The mechanical adjustment mechanism ensures that the incident angle between the sensor optical axis and the center of the flame radiation field is consistent, so as to maximize the ultraviolet signal capture efficiency.

[0043] Based on the fuel supply parameter requirements of five typical operating conditions, the fuel supply control system is called to set the fuel mass flow rate, air ratio and nozzle pressure. The accuracy of the parameters is verified by using a mass flow meter and pressure sensor in a closed loop, and the set values ​​and fuel mixing ratio are synchronously written into the controller.

[0044] Fuel supply timing curves are defined for weak combustion, stable combustion, pulsating combustion, detonation and flameout transition conditions, and the flow rate values ​​at the curve nodes are used to calculate the heat release rate corresponding to the conditions using mathematical formulas.

[0045] The operating voltage and gain coefficient of the ultraviolet photomultiplier tube assembly are configured using the bias power supply module to ensure that its broadband response characteristics match the real ultraviolet radiation field under all operating conditions, and the dark current baseline is monitored in real time to determine the installation stability.

[0046] The combustion state monitoring module marks the combustion state of the test platform under different operating conditions, and binds the fuel supply parameters and sensor installation status as input conditions for the standard test scenario set, so as to realize the construction of scenarios that can reproduce the combustion state throughout the entire life cycle.

[0047] By mechanically installing, setting fuel parameters, and configuring the working status of photoelectric components, the deployment plan results of the previous step are transformed into a standard test scenario set with full operating condition coverage, thereby realizing the construction of the physical environment for original signal acquisition and the controllability of operating conditions.

[0048] S1.3: Utilize a high-precision synchronous trigger controller to perform timing alignment operations on each working condition within the standard test scenario set, locking the sampling clock frequency to a sampling rate of not less than 10kHz, in order to obtain the raw voltage signal stream with millisecond-level time resolution.

[0049] For each combustion condition in the standard test scenario set that has been constructed according to the sensor layout scheme, the multi-channel timing synchronization function of the high-precision synchronous trigger controller is invoked to input the acquisition channel trigger signal of each ultraviolet photomultiplier tube component to the synchronous control matrix module, ensuring that the sampling start time of all channels is consistent.

[0050] Frequency locking is performed on the clock source parameters within the synchronization control matrix to stably set the main clock source frequency to no less than 10000Hz. The phase-locked loop circuit is used to maintain the phase consistency and jitter suppression performance of the sampling clock, ensuring that the acquisition channels under each operating condition obtain a consistent millisecond-level time reference.

[0051] Based on the locked master clock source, synchronous delay compensation calculations are performed on the status signals of the fuel supply controller under each operating condition to achieve precise alignment between combustion event triggering and sampling window.

[0052] The trigger signal after delay compensation is divided into sampling periods by a high-precision synchronous trigger controller, and the number of sampling points per period is calculated as 10000 / f, ensuring that waveform data containing millisecond-level flicker details is captured in each period.

[0053] The time-synchronized ultraviolet voltage signal streams output from each operating condition acquisition channel are sent to the buffer array and additional timestamps and operating condition number metadata are added to form a raw voltage signal stream matrix with millisecond-level time resolution and operating condition identification.

[0054] By using the timing alignment and sampling frequency locking processing of the high-precision synchronous trigger controller, the standard test scenario set of the previous step is transformed into a raw voltage signal stream with millisecond-level time resolution and high consistency, thus significantly improving the timing synchronization accuracy of multi-condition ultraviolet signal acquisition.

[0055] S1.4: Bandpass filtering and baseline drift correction are applied to the original voltage signal stream to remove power frequency interference and dark current noise components, so as to extract a pure analog electrical signal sequence that characterizes the instantaneous change in the intensity of flame ultraviolet radiation.

[0056] S1.5: Perform multi-channel data fusion and encapsulation based on the pure analog electrical signal sequence, and perform structured storage according to the operating condition label and timestamp index to finally generate a set of original ultraviolet electrical signals containing complete dynamic feature information.

[0057] Step S2: Perform sliding window framing on the original ultraviolet signal set, setting each frame length to 256 points and performing short-time Fourier transform to convert the time-domain signal into a time-frequency energy distribution spectrum set characterizing the energy distribution pattern. Specifically, this includes: S2.1: Perform a Hamming window function loading operation on the original ultraviolet electrical signal set to generate a windowed signal sequence with the characteristic of suppressing spectral leakage, ensuring that the energy concentration of subsequent frequency domain analysis meets the requirements of high-fidelity modeling.

[0058] The original ultraviolet electrical signal set, which has been multi-channel fused and structured in step S1, is designated as the execution object of this sub-step. The sequences of each channel are sequentially input into the Hamming window loading processing unit for amplitude modulation before frequency domain analysis. The Hamming window coefficients are calculated point-by-point according to a preset window length, and point-by-point multiplication is used to multiply the coefficients by the corresponding sample values ​​to achieve window function superposition, reducing the spectral leakage effect caused by abrupt amplitude changes at both ends of the sequence. The formula for calculating the window coefficients is set as follows: Where n is the current sampling point number, N is the total number of points in the window, and π is the constant pi. The coefficients of each group of w(n) calculated by the above formula are multiplied by the amplitude of the corresponding original sequence sampling value to obtain the windowed signal matrix, ensuring that the amplitude center segment within each window is not weakened and the boundary segment transitions rapidly. The windowed signal matrix is ​​numerically normalized to adjust the amplitude of all signals within the window to a uniform dimension range, facilitating the quantitative analysis of energy concentration in subsequent short-time Fourier transforms. The normalized windowed signal matrix is ​​stored in the time-frequency analysis buffer and used as the direct input for the sliding window truncation process in S2.2. Through the Hamming window loading method described above, the original ultraviolet signal from step S1 is transformed into a windowed signal sequence with characteristics that suppress spectral leakage and whose energy concentration meets the requirements of high-fidelity modeling, achieving boundary optimization and signal stabilization before frequency domain analysis.

[0059] For example, a set of raw ultraviolet electrical signals with a sampling rate of 10000Hz is input into a Hamming window loading processing unit, with a window length of 256 points, n ranging from 0 to 255, and N being 256. For the 128th sampling point, w(128) = 0.54 is calculated according to the formula. 0.46 × cos(2 × π × 128 / 256) = 0.54 0.46 × cos(π) = 0.54 0.46 × ( 1) = 1.0 indicates that the window function is assigned full amplitude at the center position, resulting in the best spectral leakage suppression effect. The windowed signal matrix is ​​generated by calculating the coefficients of all sampling points sequentially and multiplying them by the corresponding original amplitudes. After normalization, the amplitude range is stabilized within ±1.0. In subsequent short-time Fourier transforms, the energy concentration of this signal sequence is significantly improved, the main lobe width is reduced, the side lobe amplitude suppression effect is enhanced, and signal noise interference is greatly reduced when capturing millisecond-level flicker details.

[0060] S2.2: Based on the windowed signal sequence, an overlapping sliding window mechanism is used for truncation processing. The window length is set to 256 points and the overlap rate is 50% to generate a discrete time frame sequence containing millisecond-level flickering details, thereby realizing localized segmentation of the continuous combustion process.

[0061] For the windowed signal sequence with the Hamming window function already loaded, time-domain truncation is performed based on the overlapping sliding window mechanism. First, the window length is set to 256 points to match the sampling span of the millisecond-level flicker signal. The starting position of each window is algebraically calculated according to the signal sampling rolling offset scheme. The initial window offset is equal to the set length multiplied by (1...). The window overlap rate is set to 0.5. The windowed signal sequence and the window step size vector are mapped according to the starting index to perform multi-segment segmentation, avoiding frame boundary distortion caused by signal abrupt changes. During the segmentation process, an index matrix is ​​generated for each window segment. The index matrix stores the global sequence number of each continuous sample in rows, ensuring time alignment consistency for subsequent frequency domain transformations. The generated index matrix is ​​applied to the windowed signal sequence to form a discrete-time frame set, and amplitude normalization is performed on each frame signal within the set. The normalized discrete-time frame set is labeled with operating condition tags and timestamp indices, forming a localized fragment dataset containing millisecond-level flicker details, ensuring controllable temporal segmentation of the continuous combustion process.

[0062] By employing the aforementioned methods of overlapping window truncation, index matrix formation, and amplitude normalization, the windowed signal sequence from the previous step is transformed into a discrete-time frame sequence with precise time boundaries and uniform amplitude dimensions. This enables localized segmentation of the continuous combustion process, providing stable and high-resolution input data for subsequent frequency domain conversion.

[0063] For example, a 20,000-point ultraviolet signal sequence was acquired on an industrial combustion test platform after being windowed using a Hamming window. The sampling rate was 10 kHz, the window length was set to 256 points, the overlap rate to 0.5, and the calculated window step vector was 128 points. The entire sequence was segmented to obtain approximately 155 overlapping window frames. The mean amplitude μ of each frame was calculated to be 0.245, and the standard deviation σ was calculated to be 0.086. After normalizing the nth sampled value within the frame using a formula, the amplitude range was obtained as follows: The standardized discrete frame signals range from 2.38 to 2.51. The frame sets are further tagged with operating conditions (e.g., steady combustion, flameout transition) and start timestamps, ultimately forming 155 localized data segments containing millisecond-level flicker details. Subsequent FFT processing verifies that the spectral details contained in each frame show a significant increase in energy concentration within the 0–2kHz range, indicating that this truncation method can effectively preserve the local characteristics of the dynamic combustion process and improve the accuracy of subsequent time-frequency analysis.

[0064] S2.3: Perform a fast Fourier transform operation on each frame of data in the discrete time frame sequence to convert the time-domain amplitude information into a set of complex frequency-domain coefficients, thereby obtaining spectral component data characterizing the instantaneous flame radiation intensity.

[0065] The input is a discrete-time frame sequence processed by Hamming window loading and overlapping sliding window truncation, with each frame containing a time-domain signal of ultraviolet radiation intensity at 256 sampling points. A Fast Fourier Transform (FFT) is applied to each frame to convert the time-domain amplitude sequence into a corresponding set of complex coefficients in the frequency domain. During FFT calculation, the input frame signal is treated as a real-valued sequence, and a radix-2 decomposition strategy is applied to reduce computational complexity. Simultaneously, phase information is preserved during the butterfly operation for subsequent joint amplitude and phase analysis. A complete spectrum is constructed using the real and imaginary parts of the complex coefficients, and the frequency domain coefficients are calculated using the following formula: Where x(n) is the time-domain signal value of the nth sampling point, N is the total number of sampling points, k is the frequency index, and j is the imaginary unit. The complex coefficients corresponding to each frequency index are stored as amplitude-phase pairs.

[0066] The amplitude-phase pairs are output as spectral component data of the instantaneous flame radiation intensity to provide complete frequency domain information for subsequent short-time power spectral density calculations. This processing method transforms the discrete-time frame sequence from the previous step into spectral component data containing energy and phase characteristics across the entire frequency band, achieving a high-precision mapping from the time domain to the frequency domain.

[0067] S2.4: Calculate the squared modulus of each frequency point based on the spectral component data and perform normalization processing to generate a short-time power spectral density matrix that characterizes the distribution density of ultraviolet light energy in the frequency domain per unit time, and quantify the spectral energy characteristics under different combustion conditions.

[0068] S2.5: The short-time power spectral density matrix is ​​stacked and recombined in time axis order to generate a time-frequency energy distribution map set with a time-frequency two-dimensional topology, completing the dimensional mapping from discrete frame data to continuous dynamic combustion feature map.

[0069] The short-time power spectral density matrix is ​​indexed and sorted sequentially along the time axis to ensure that the time stamps of adjacent frames are strictly incremented and consistent with the original sampling time sequence, so as to form a spectral matrix sequence with continuous temporal correlation.

[0070] The sorted spectrum matrix sequence is indexed and concatenated in the time dimension. The correspondence between frequency components and time frames is preserved in the two-dimensional plane through matrix concatenation operations, generating a preliminary time-frequency two-dimensional array set.

[0071] Column normalization is used to perform amplitude ratio unification processing on the frequency dimension of the initial two-dimensional array set to eliminate the influence of sampling amplitude differences between different frames on the energy distribution topology, thereby obtaining a unified energy scale for each frequency component in the entire time domain.

[0072] Time-axis interpolation resampling technology is applied to the normalized two-dimensional array set, and the target time resolution is set to the millisecond equivalent frequency of the original sampling, in order to repair the time dimension gaps introduced by window overlap rate and truncation length, and to ensure the continuity of the time-frequency spectrum.

[0073] The data set processed by interpolation and resampling is input into the topology mapping generator. The frequency component index is fixed by row-major storage, while the time series is stored in the column dimension. This makes the matrix form a strict two-dimensional topology mapping at the data structure level, resulting in a complete time-frequency two-dimensional topology energy distribution map set.

[0074] By stacking, recombining and interpolation normalization, the short-time power spectral density matrix result from the previous step is transformed into a two-dimensional topological map set with continuous time correlation and uniform amplitude scale, realizing a multi-dimensional mapping from discrete frame data to dynamic combustion feature maps.

[0075] like Figure 2 As shown, step S3 involves constructing a high-dimensional time-frequency feature vector set based on the time-frequency energy distribution map set, and performing dimensionality reduction mapping while preserving local neighborhood relationships to generate a three-dimensional geometric manifold space representing the topological structure of different combustion states. Specifically, this includes: S3.1: Obtain the two-dimensional matrix data of each frame in the time-frequency energy distribution map set, perform row-first flattening and normalization processing on the frequency component energy values ​​in the matrix to generate a high-dimensional time-frequency feature vector set representing the instantaneous combustion state of a single frame, ensuring that all operating condition data are in a unified numerical dimension space.

[0076] S3.2: Calculate the Euclidean distance metric between any two feature vectors based on the high-dimensional time-frequency feature vector set, and use K-nearest neighbor search to determine the local neighborhood point set of each target vector to generate a neighborhood index matrix containing local geometric constraints, providing data basis for maintaining the local topology in the future.

[0077] Distance metric calculations are performed on the high-dimensional time-frequency feature vector set after flattening and normalization. The Euclidean distance between each feature vector and all other feature vectors is calculated to form a global distance matrix. Based on the global distance matrix, a K-nearest neighbor search is used to determine the k nearest neighbors for each target feature vector. The value of k is preset based on the local continuity of combustion state features and manifold sampling density to ensure that the local correlation characteristics of combustion state evolution are preserved during dimensionality reduction. The neighborhood point indices of each target feature vector are sorted in ascending order of distance value and stored in a neighborhood index matrix. The rows of the neighborhood index matrix correspond to the target feature vector number, and the columns correspond to the global index position of the neighboring point in the feature set. For each group of neighboring points in the neighborhood index matrix, a local geometric constraint information set is further generated by combining the corresponding distance values, which serves as the input parameter for subsequently constructing the local reconstruction weight coefficient matrix.

[0078] Using the Euclidean distance formula Here, x and y represent the energy values ​​of any two eigenvectors at a certain frequency component, respectively. The summation of squares covers all dimensions of the eigenvectors, ensuring that the inter-point spacing data in the real geometric space is obtained. Through the above processing method, the high-dimensional time-frequency eigenvector set of the previous step is transformed into a neighborhood index matrix containing precise local geometric constraints, thus achieving complete preservation of the local topological structure during the dimensionality reduction mapping process.

[0079] S3.3: Construct a local reconstruction weight coefficient matrix based on the neighborhood index matrix, introduce a regularization term to optimize the least squares loss function to solve for the optimal reconstruction weights, and generate a weight allocation scheme that can accurately describe the local linear combination relationship in the high-dimensional space, ensuring the consistency of the local neighborhood topology before and after dimensionality reduction.

[0080] Perform matrix row traversal operation on the neighborhood index matrix obtained via S3.2, and construct an initialization template for the local reconstruction weight coefficient matrix for the local neighborhood point set of each target feature vector to ensure that each row corresponds to a unique reconstruction constraint relationship.

[0081] In each row of the initialization template, a least squares loss function is introduced to represent the target feature vector as an estimate of the linear combination of its neighborhood points. An error function is established and the local Euclidean distance metric is used as the initial value of the inner weights.

[0082] The above error function is embedded in a regularization term to avoid ill-conditioned weight matrix. The regularization term adopts the L2 norm squared form.

[0083] The error function and the regularization term are weighted and summed to obtain the optimization objective function. Partial derivative operations are performed on the objective function to establish a system of linear equations about the weight coefficients, ensuring the constraint that the sum of the weights of each neighborhood is 1 and avoiding global drift.

[0084] The above linear equations are solved using matrix decomposition methods (such as Cholesky decomposition or QR decomposition) to achieve accurate calculation of the optimal reconstruction weights. The results are then filled into the corresponding rows of the local reconstruction weight coefficient matrix to form a complete weight allocation scheme.

[0085] After completing the above chain derivation process, the neighborhood index matrix from the previous step is transformed into numerical weight allocation data that can be used for improved local linear embedding dimensionality reduction through the optimization solution process of the locally reconstructed weight coefficient matrix, thereby achieving geometric consistency of the local neighborhood topology before and after dimensionality reduction mapping.

[0086] S3.4: Construct a low-dimensional embedding cost function using the optimal reconstruction weight scheme, and solve the three-dimensional coordinate matrix using the gradient descent iterative method to minimize the global reconstruction error, thereby generating a three-dimensional geometric manifold space coordinate point set that represents the distribution law of all operating conditions such as weak combustion, stable combustion and flameout.

[0087] A low-dimensional embedding cost function is constructed by inputting the optimal reconstruction weight scheme. The local reconstruction error in the high-dimensional time-frequency feature vector set is used as the core calculation objective of the cost function to ensure that the neighborhood topology remains consistent during the dimensionality reduction process.

[0088] The cost function structure, which includes global and local error terms, is formed based on the weight allocation scheme. A three-dimensional embedded space coordinate matrix is ​​introduced as an optimization variable, and constraints are set to prevent coordinate drift and scale imbalance.

[0089] The partial derivatives of the cost function are explicitly solved for each three-dimensional coordinate component to obtain a sequence of gradient vectors, which serve as the direction for updating the coordinate matrix during gradient descent iterations.

[0090] By setting iteration step size and convergence threshold parameters, the gradient descent process can gradually reduce the global reconstruction error value while preserving the original high-dimensional space geometric relationship, so as to achieve the optimal mapping in the low-dimensional space.

[0091] Through continuous iterative accumulation, the corresponding embedded coordinate points under each working condition are obtained, forming the distribution law of weak combustion, stable combustion, and flameout states on the low-dimensional spatial topology, and constructing a three-dimensional geometric manifold space coordinate point set.

[0092] Through the gradient descent solution process, the high-dimensional local reconstruction weight data of the previous step is transformed into three-dimensional spatial mapping coordinates that meet the global optimal conditions, so as to realize the stable topological presentation of different combustion states on the visualized geometric manifold.

[0093] S3.5: Perform cluster density analysis and boundary curvature extraction operations on the coordinate point set of the three-dimensional geometric manifold space, identify the topological boundary features between the steady-burning central region and the flameout transition path, generate a state topology mapping map with clear physical semantics, and complete the final dimensionality reduction mapping from high-dimensional spectral data to low-dimensional manifold space.

[0094] A cluster distribution analysis model based on kernel density estimation is loaded onto the coordinate point set of the three-dimensional geometric manifold. The radial basis function is called to extract the probability density values ​​in the local space of each coordinate point, and a density threshold is set based on the global mean deviation to divide high-density cluster domains and sparse boundary domains. Spatial connectivity retrieval is performed on the high-density cluster domains to generate the central mass coordinate vector set of the steady-burning cluster domain. The principal axis direction and scale are calculated by constructing an ellipsoid fitting model through the covariance matrix. The curvature estimation operator is called to perform second-order derivative discretization on each trajectory curve in the sparse boundary domain. Based on the curvature threshold, the continuous curvature change sequence of the flameout transition path is identified, and the maximum curvature point and the monotonically changing curvature segment are extracted as topological boundary features. The curvature features of the central mass of the steady-burning cluster domain and the flameout path are spatially registered to construct a state boundary mapping framework with clear physical semantics. The spatial relationship map of the steady-burning central domain, the flameout path and other combustion state cluster domains is output in the form of a two-dimensional topological projection. By using cluster density analysis and boundary curvature extraction, the coordinate point set of the three-dimensional geometric manifold space in the previous step is transformed into a state topology mapping diagram with physical semantics, thus realizing a complete dimensionality reduction mapping from high-dimensional spectral data to low-dimensional manifold space.

[0095] like Figure 3 As shown, step S4 involves establishing differentiable parameterized equations of motion within the three-dimensional geometric manifold space, introducing combustion stability coefficient, heat release fluctuation rate, and oxidizer disturbance intensity as control variables to drive trajectory evolution, thereby constructing a manifold trajectory evolution model capable of simulating the dynamic evolution path of the flame. Specifically, this includes: S4.1: Based on the center point of the steady-burning cluster distribution and the curvature path of the extinguishing transition boundary in the three-dimensional geometric manifold space, extract the key geometric invariants that characterize the topological structure of the combustion state to generate a set of basic manifold metric parameters for defining the manifold space metric tensor.

[0096] Based on the center point of the steady-burning cluster distribution and the curvature path of the flameout transition boundary within a three-dimensional geometric manifold space, the spatial coordinate point set and state topology mapping map output by the previous dimensionality reduction mapping step are read to locate the geometric center of the steady-burning cluster distribution and extract the continuous curvature value sequence of the boundary curvature path as input reference coordinates. Three-dimensional Euclidean position calculation is performed on the center point of the steady-burning cluster, and the center coordinate vector is determined using a weighted centroid formula, where the weights are provided by the cluster density function to reflect the stability level of the combustion state. For the curvature path of the flameout transition boundary, the curvature value of each boundary point is calculated using a curvature formula, and the rate of change of curvature is used as an important geometric feature to distinguish the transition stages of the combustion state. A curvature-centroid distance joint index is used to combine the ratio of the rate of change of curvature to the center coordinate distance into a multi-dimensional geometric invariant set to eliminate the influence of spatial scale and shape differences under different operating conditions. The set of multidimensional geometric invariants is normalized to ensure that the values ​​of each invariant are on a uniform dimension. Then, the correlation between the invariants is analyzed through covariance matrix decomposition, and the geometric invariants with the highest contribution are selected as the basic manifold metric parameters. The coordinates of the steady-state combustion center are determined using centroid calculation. Boundary curvature path features are extracted using curvature calculation. A set of geometric invariant vectors is formed by combining the centroid coordinates and the rate of change of curvature, and then input into the metric tensor construction module to achieve the basic metric parameterization of the three-dimensional geometric manifold.

[0097] Through the above calculation and processing methods, the set of coordinate points in the three-dimensional manifold space in the previous step is transformed into a set of basic manifold metric parameters that characterize the topological features of the combustion state, thereby realizing a quantitative characterization of the manifold space and providing a spatial metric benchmark with clear physical semantics and numerical stability for the subsequent establishment of differentiable parameterized motion equations in the manifold space.

[0098] For example, on an industrial combustion test platform, the steady-burning cluster distribution consists of 120 coordinate points with an average cluster density weight of 2.5. The coordinates of the steady-burning center, calculated using the centroid formula, are (1.25, 0.98, 0.56). The curvature path of the flameout transition boundary contains 60 boundary points with an average curvature value of 1.8. The curvature change rate sequence shows an increasing trend in the experiment, and after normalization, the change rate range is [0.12, 0.88]. After screening the ratio of curvature change rate to centroid distance through covariance matrix decomposition, the three sets of geometric invariants with the highest contribution are (0.65, 0.72, 0.80), which are used as basic manifold metric parameters input into the subsequent manifold tangent space mapping matrix construction module. The verification results show that this parameter set can stably distinguish between weak combustion, steady combustion, and flameout states within the manifold space, improving the model's fitting accuracy for the transition trajectory and the consistency of its discrimination of combustion states.

[0099] S4.2: Construct a Riemannian manifold tangent space mapping matrix using the aforementioned basic manifold metric parameter set, and project the three physical control variables—combustion stability coefficient, heat release fluctuation rate, and oxidant disturbance intensity—to the tangent space basis to generate a manifold control vector sequence characterizing the multi-physics coupling effect.

[0100] Using the set of fundamental manifold metric parameters formed by the center point of the steady-state cluster distribution and the curvature path of the flameout transition boundary in the three-dimensional geometric manifold space as input conditions, a Riemannian manifold tangent space mapping matrix describing the geometric properties of the manifold space is constructed based on this parameter set. For the numerical sequence of combustion stability coefficients, a multidimensional coordinate projection operation based on the metric tensor is performed, decomposing the coefficients along the tangent space basis vector direction to obtain the first type of physical projection component reflecting the steady-state resonance characteristics. For the data sequence of heat release fluctuation rate, the orthogonalization feature of the tangent space basis is utilized to introduce mutual coupling coefficients between the basis during the projection process, thereby achieving directional constraints on high-frequency energy changes and generating the second type of physical projection component related to the energy release rhythm. For the real-time sampled value of oxidant disturbance intensity, a tangent space local nonlinear mapping function is used to jointly modulate its amplitude and direction to form the third type of physical projection component reflecting the effect of oxidant supply changes. The above three types of physical projection components are vector superimposed in the tangent space coordinate system to generate a manifold control vector sequence containing the combined effect of each physical control variable. This processing method transforms the basic manifold metric parameter set into multiphysics coupled control commands that can directly drive trajectory evolution, thereby achieving geometrically consistent mapping of control variables in the manifold space.

[0101] S4.3: Define the nonlinear velocity field function in the manifold space based on the manifold control vector sequence, and use Lie derivative operations to describe the instantaneous rate of action of the control variables on the manifold trajectory, so as to generate the manifold differential evolution equation characterizing the dynamic evolution trend of the flame.

[0102] Based on the combustion stability coefficient, heat release fluctuation rate, and oxidant disturbance intensity values ​​contained in the manifold control vector sequence, the metric tensor data corresponding to the three-dimensional geometric manifold space is called to construct the initial coefficient matrix of the nonlinear velocity field.

[0103] Each element of the manifold control vector sequence is projected onto the local tangent space basis of the three-dimensional manifold space to form a set of tangent space components containing directional and amplitude information.

[0104] In the set of tangent space components, the contribution weight of each component to the velocity field is calculated using the manifold metric tensor, and the distribution function of the velocity field vector is constructed according to the component direction.

[0105] The parameterized equation of the manifold trajectory curve is differentiated using Lie derivative operations to calculate the instantaneous rate of action of the control variables on the trajectory, forming a differential term characterizing the dynamic changes of the velocity field.

[0106] The velocity field distribution function and the differential term are matrix synthesized to obtain the nonlinear velocity field function expression in the manifold space. The coupling term between multiple physical control variables is explicitly introduced into this expression to fully characterize the velocity field characteristics of the flame state change.

[0107] The rate of action of the trajectory curve function is calculated using the following Lie derivative formula: in, For the velocity field vector, For trajectory curve functions, For manifold coordinate components, For the dimension of manifold space, Let be the component of the velocity field in the coordinate direction. This formula quantifies the rate of change of the instantaneous effect of the velocity field function on the trajectory curve.

[0108] Through the chain operation described above, the manifold control vector sequence obtained in the previous step is transformed into a nonlinear velocity field function containing coupled control terms, thereby realizing the construction of differential evolution equations for the dynamic evolution trend of the flame.

[0109] S4.4: Perform Runge-Kutta numerical integration iteration on the manifold differential evolution equation, and calculate the displacement increment of the trajectory point in the manifold space by combining the temporal variation law of the manifold control vector sequence, so as to generate a discrete manifold trajectory point set simulating the evolution of the entire working condition from weak combustion to deflagration.

[0110] In the process of solving the manifold differential evolution equation, a sequence of manifold control vectors, consisting of combustion stability coefficient, heat release fluctuation rate, and oxidant disturbance intensity, is injected as a time-dependent input into the integration drive port. Based on this time-dependent input, a coefficient matrix of a fourth-order Runge-Kutta iterator is constructed, corresponding to four stage slope estimation variables, K1 to K4, to quantify the instantaneous velocity field distribution of the current trajectory point in the three-dimensional manifold space. The initial slope K1 is calculated by calling the Riemannian manifold velocity field function, and the slope is offset and corrected using a half-step time evolution factor to obtain intermediate slopes K2 and K3; the terminal slope K4 is calculated based on the full-step time evolution factor, forming a multi-slope combination that can be used for high-precision integration. The Runge-Kutta weighted synthesis formula is used to synthesize the slopes according to weighted coefficients to calculate the displacement increment of the trajectory point within one integration step in the manifold space, ensuring the numerical stability and local curvature fidelity of the trajectory evolution. The aforementioned displacement increments are accumulated and iterated over time steps to form a discrete trajectory point sequence covering weak combustion, stable combustion, pulsating combustion, deflagration, and flameout transition, providing a precise spatial coordinate reference for subsequent smoothness constraint optimization. Through dynamic integral iteration, the manifold differential equation from the previous step is transformed into a discrete trajectory point set arranged in a time series, achieving numerical reconstruction of the evolution path under all operating conditions.

[0111] S4.5: Based on the discrete manifold trajectory point set, perform smoothness constraint optimization processing, use spline interpolation to eliminate high-frequency jitter noise generated by numerical integration and maintain the continuity of manifold curvature, so as to construct the final differentiable manifold trajectory evolution model and output it to the Kalman filter.

[0112] When performing smoothness constraint processing on a discrete manifold trajectory point set, the point set is used as the input object. Its coordinate sequence in the three-dimensional geometric manifold space is read, and a corresponding curvature continuity check matrix is ​​established. The curvature change rate data of each trajectory segment in the curvature continuity check matrix is ​​called, and high-frequency jitter regions are identified based on a preset continuity threshold. These regions are marked as target segments requiring interpolation optimization. For each marked segment, a spline interpolation basis function matrix is ​​constructed, and the coordinate values ​​of the discrete trajectory points and the curvature change rate are input as joint interpolation constraints to the spline interpolation solver to ensure the continuity of trajectory curvature and the smoothness of the physical state during interpolation. The continuous function form trajectory curve solved by the spline interpolation solver is used to replace the original discrete trajectory point set, generating a continuous manifold trajectory curve after removing high-frequency jitter from the numerical integration process. The continuous trajectory curve is combined with the manifold space metric tensor to form a differentiable trajectory evolution function. It is verified that the first and second derivatives do not exhibit abrupt changes across the entire operating range, thus satisfying the smoothness and differentiability requirements for input to the Kalman filter. Through spline interpolation smoothing and curvature continuity preservation, the discrete integration result from the previous step is transformed into continuously differentiable manifold trajectory data, achieving the expected technical effect of stable operation within the Kalman filter and accurate description of the flame's dynamic evolution path.

[0113] Step S5: Read the actual response deviation data from the AD acquisition terminal of the flame detection system, input it into the online Kalman filter, and perform real-time fusion calculation with the prediction output of the manifold trajectory evolution model to generate a dynamic correction factor sequence for correcting the trajectory direction. Specifically, this includes: The online Kalman filter is a recursive state estimator used to fuse the actual response deviation data from the AD acquisition end of a flame monitoring system with the predicted output of the manifold trajectory evolution model, generating a dynamic correction factor sequence in real time. This filter can process noisy observation data online, suppress measurement noise and model uncertainty, and achieve adaptive correction of the manifold trajectory under non-stationary combustion conditions (such as pulsating combustion and flameout transition).

[0114] The online Kalman filter consists of the following six core modules: State Prediction Module: This module uses the state estimate from the previous time step of the manifold trajectory evolution model to predict the prior state estimate and its covariance matrix for the current time step. Specifically, it takes the optimal estimate from the previous time step as input and, based on the locally linearized state transition matrix of the manifold trajectory evolution model, calculates one step backward to obtain the predicted state vector and predicted covariance matrix for the current time step. The output of this module will serve as the basis for subsequent residual and gain calculations.

[0115] Observation Input Module: This module receives the measured state observation dataset from the AD acquisition terminal of the flame monitoring system. The dataset contains the amplitude error vector and phase lag parameter at the current moment. This module performs format verification, timestamp alignment, and dimension normalization on the measured data to ensure comparison with the predicted state under the same benchmark.

[0116] The residual calculation module performs element-wise differencing between the measured observation vector and the predicted state vector to calculate the residual vector (i.e., innovation), and simultaneously calculates the residual covariance matrix. The residual reflects the instantaneous deviation between the current simulated trajectory and the actual combustion dynamics; the covariance matrix quantifies the uncertainty of this deviation, providing a statistical basis for subsequent gain adjustments.

[0117] Gain Calculation Module: This module dynamically calculates the optimal filter gain matrix based on the prediction covariance matrix and the observation noise covariance matrix. The magnitude of the gain determines the correction weight of the residuals to the state estimation: the gain decreases when the noise is high and increases when the model is uncertain. This module uses a numerically stable matrix inversion method to ensure the reliability of online calculations.

[0118] State Update Module: This module uses the gain matrix to weight and correct the residual vector, then adds the correction to the predicted state to obtain the optimal state estimate (posterior estimate) for the current time step. Simultaneously, it updates the covariance matrix of the state estimate to prepare for the prediction at the next time step. The state increment vector output by this module directly reflects the direction and magnitude of the manifold trajectory adjustment needed.

[0119] Output interface module: This module decomposes the increment generated by the state update into the combustion stability coefficient correction, heat release fluctuation rate correction and oxidant disturbance intensity correction, packages them into a dynamic correction factor sequence, and outputs it to step S6 for subsequent reverse mapping and waveform reconstruction.

[0120] Construction method: (a) Offline pre-training stage: Data preparation: Simultaneously collect the predicted state sequence of the manifold trajectory evolution model and the measured state sequence of the AD terminal of the flame monitoring system from various typical operating conditions of the standard industrial combustion test platform to form a paired training dataset.

[0121] Noise parameter calibration: The initial value of the process noise covariance matrix Q is determined by statistically analyzing the variance of the prediction error sequence; the initial value of the observation noise covariance matrix R is determined by performing variance analysis on the amplitude and phase data of repeated measurements at the AD acquisition end.

[0122] Initial state setting: The average state vector under stable combustion conditions is used as the initial state estimate. The square of the fluctuation range of the state variable during stable combustion is used as the diagonal element of the initial covariance matrix P0.

[0123] Offline verification: The filter is simulated in an open loop using the training dataset. Q and R are adjusted until the residual sequence exhibits zero-mean, white noise characteristics.

[0124] (II) Online Operation Phase: The following steps are executed sequentially for each sampling period: State prediction: Invoke the manifold trajectory evolution model and estimate the state based on the previous time step. and control input u k 1. Calculate the predicted state at the current moment. and predicted covariance .

[0125] Residual calculation: Read the measured observation vector z k Calculate the residual vector and residual covariance matrix ,in For the observation matrix, To observe the noise covariance matrix, This represents the measured observation vector.

[0126] Gain calculation: using the Kalman gain formula: State Update: Update the state estimate and its covariance: Output dynamic correction factor: extract state increment The corrections for combustion stability coefficient, heat release volatility, and oxidant disturbance intensity are encapsulated into a dynamic correction factor sequence.

[0127] By using an online Kalman filter structure, real-time estimation and adaptive compensation of the deviation between the simulated trajectory and the actual combustion dynamics are achieved, which significantly improves the realism of the simulated ultraviolet waveform under complex working conditions and the convergence speed of the system closed-loop debugging.

[0128] S5.1: Obtain the actual ultraviolet electrical signal sampling sequence fed back by the AD acquisition terminal of the flame detection system, and extract the amplitude error vector and phase lag parameter at the current moment to construct a measured state observation dataset containing the system response deviation characteristics.

[0129] S5.2: Based on the measured state observation dataset, call the predicted state vector output by the manifold trajectory evolution model, calculate the residual covariance matrix between the measured state and the predicted state, so as to quantify the degree of deviation between the current simulated trajectory and the actual combustion dynamics.

[0130] Based on the measured state observation dataset, the predicted state vector output by the manifold trajectory evolution model is invoked. A residual vector data structure is established for the amplitude and phase information at the same time point, and the measured and predicted states are precisely aligned according to time index to form a paired sequence. The amplitude and phase difference components within the paired sequence are centered to eliminate the interference of static bias on the statistical characteristics of the residuals. A two-dimensional residual matrix is ​​constructed from the centered difference components, where one dimension corresponds to the amplitude deviation and the other to the phase deviation, providing an input basis for covariance calculation. The covariance definition formula is used to perform matrix multiplication and normalization on the residual matrix, and the values ​​of each element of the residual covariance matrix are calculated. The diagonal elements of the covariance matrix are used as the variance quantification index of amplitude and phase errors, and the off-diagonal elements are used as the quantification index of the correlation between amplitude and phase errors, forming a numerical evaluation system characterizing the degree of deviation between the current simulated trajectory and the actual combustion dynamics. By using the above processing method, the result of the previous step is transformed into a residual covariance matrix that can be used for filter gain update, thereby realizing a quantitative assessment of the degree of deviation and providing an accurate error statistical basis for adaptive calibration.

[0131] For example, in a weak combustion condition test scenario, the measured state observation dataset consists of an amplitude error vector and a phase lag parameter, with the amplitude error range being [missing information]. From 0.2V to 0.15V, the phase lag is From 5° to 3°, the predicted state vector is generated by the manifold trajectory evolution model. 1000 samples are obtained through time index alignment, and after differencing and centering, a 1000×2 residual matrix is ​​formed. The covariance matrix is ​​calculated using the formula, with the sample size n being 1000, and the residual mean vector μ being 0.001V in the amplitude direction and 0.02° in the phase direction. The diagonal elements of the covariance matrix are 0.0045 and 0.35, representing the amplitude error variance and phase error variance, respectively, while the off-diagonal element is 0.012, representing the correlation between amplitude and phase errors. This output covariance matrix serves as the basis for weight adjustment in the subsequent filter gain update step, significantly improving the filter's ability to suppress abrupt changes and noise, thus greatly enhancing the matching degree between the simulated trajectory and the actual combustion process.

[0132] S5.3: Utilize the residual covariance matrix to perform online Kalman filter gain update, dynamically adjust the state estimation weight coefficients, and generate the optimal filter gain matrix that can suppress noise interference and track sudden operating conditions in real time.

[0133] For the input conditions comprised of the residual covariance matrix, during the gain matrix calculation of the online Kalman filter, the covariance matrix is ​​structurally paired with the uncertainty matrix of the predicted state to form an operational basis for dynamically adjusting the state estimation weight coefficients. Matrix inversion and matrix multiplication are performed on the prediction error covariance matrix and the measured observation error covariance matrix to construct the invertibility constraint of the gain calculation denominator. A numerically stable matrix decomposition method (such as Cholesky decomposition) is used to verify the positive definiteness of the prediction covariance matrix, ensuring that the matrix condition number remains within an acceptable range during time iteration. Based on the verified covariance matrix, the Kalman gain formula is solved. in To predict the state covariance matrix, For the observation matrix, To observe the noise covariance matrix, This is the transpose of the observation matrix. The gain matrix and the residual covariance matrix are then multiplied element-wise to generate an intermediate gain matrix that suppresses observation noise interference at the current time. The intermediate gain matrix is ​​then subjected to temporal smoothing to maintain its ability to continuously track trajectory changes under abrupt changes, while reducing the weight of irrelevant disturbances under stable conditions. Through a gain matrix update strategy, the residual covariance result from the previous step is transformed into an optimal filter gain matrix that suppresses noise interference in real time and has abrupt change tracking capability, achieving the technical effect of dynamically adjusting the state estimation weight coefficients.

[0134] For example, in the test of a mixed operating condition of stable combustion and abnormal pulsation in an industrial boiler, let the predicted state covariance matrix be... The diagonal elements are 0.002, and the observation noise covariance matrix... The diagonal elements are 0.0005, and the observation matrix is... This is the identity matrix. The Kalman gain is calculated using the above formula, firstly... The positive definiteness was verified by performing Cholesky decomposition. The inverse of the denominator matrix was obtained by matrix inversion, resulting in an inverse value of 2000. The numerator matrix was calculated to be 0.002, and multiplied by 2000 to obtain an initial gain matrix element value of 4.0. Combining the current amplitude distribution of the residual covariance matrix, exponential weighted smoothing was performed on the gain matrix with a smoothing factor of 0.85. The resulting filtered gain matrix maintained a gain level of 4.0 during the steady-state combustion phase and increased to 6.5 during the abnormal pulsation phase, achieving a significant tracking capability for sudden changes in operating conditions, and the amplitude of noise error in the output signal was significantly reduced.

[0135] S5.4: Based on the optimal filter gain matrix, perform a weighted correction operation on the residual covariance matrix, and fuse the amplitude error vector and phase lag parameter in the measured state observation dataset to calculate the state update increment vector representing the trajectory correction direction and amplitude.

[0136] Based on the optimal filter gain matrix, the residual covariance matrix is ​​subjected to matrix multiplication and weighting. The weight coefficients of the matrix elements are limited to the values ​​at the corresponding positions in the dynamic filter gain matrix to maintain the consistency of priority in the control variable response correction. The magnitude error vector data is read row by row from the weighted residual covariance matrix. The phase lag parameter is extracted in the column direction and normalized in real time to ensure the consistency of the dimensions of magnitude and phase for subsequent vector operations. The normalized magnitude error vector and the normalized phase lag parameter are concatenated column by column to form a joint state deviation vector sequence. The projection values ​​of each deviation component on the manifold space basis are calculated through vector inner product operations to obtain a preliminary coefficient set for the trajectory correction direction. The Euclidean norm is used to normalize the projection coefficient set to obtain a directional unit vector with consistent dimensions. The weighted average of the magnitude error vector and the phase lag parameter is superimposed on each component of this unit vector to calculate the scalar coefficient of the trajectory correction amplitude. The scalar multiplication operation is performed between the direction unit vector and the amplitude scalar coefficient to generate a state update increment vector representing the trajectory vector increment. Each component of this vector directly corresponds to the control variable correction command of the manifold trajectory evolution model. Through this processing method, the filter gain update result of the previous step is transformed into quantifiable trajectory correction direction and amplitude data, realizing dynamic trajectory adaptive adjustment.

[0137] S5.5: Iteratively update the control variable parameters of the manifold trajectory evolution model according to the state update increment vector, and generate a dynamic correction factor sequence including the combustion stability coefficient correction, heat release fluctuation rate correction and oxidant disturbance intensity correction, so as to complete the closed-loop adaptive calibration of the target trajectory direction in the manifold space.

[0138] In this sub-step, the state update increment vector is used as input and decomposed into correction instructions corresponding to amplitude and phase components, which are then applied to three physical control variables: combustion stability coefficient, heat release fluctuation rate, and oxidant disturbance intensity. A parameter update matrix is ​​constructed based on the current values ​​of the manifold control variables. Vector translation calculations are performed within the tangent space of the Riemannian manifold using a numerical iteration strategy to ensure that the control variables maintain curvature consistency and physical interpretability during the update process. The parameter update matrix is ​​scaled using an iteration step size adjustment rule, ensuring that the magnitude of the corrections across each variable dimension is proportionally distributed according to the eigenvalue distribution of the residual covariance matrix. A constrained optimization method is employed to introduce a physical stability criterion, performing tolerance checks on the updated control variables and eliminating abnormal correction components exceeding the stability threshold, resulting in a final control variable correction set filtered by physical constraints. The optimized set of control variable corrections is remapped back into the control vector sequence of the manifold trajectory evolution model to generate a dynamic correction factor sequence containing corrections for combustion stability coefficient, heat release fluctuation rate, and oxidizer disturbance intensity. This ensures that the target trajectory within the manifold space remains highly consistent with the actual combustion dynamics during closed-loop adaptive calibration. Through this process, the residual correction results from the previous step are transformed into dynamic correction factors that can directly drive the manifold trajectory evolution, achieving closed-loop adaptive calibration of the target trajectory within the three-dimensional geometric manifold space.

[0139] Step S6: The target trajectory points within the three-dimensional geometric manifold space are reverse-mapped using the dynamic correction factor sequence. The mapping results are then processed using nonlinear interpolation and phase-preserving resampling techniques to reconstruct a high-fidelity simulated ultraviolet waveform data stream. Specifically, this includes: S6.1: Obtain the dynamic correction factor sequence and the coordinates of the initial target trajectory points in the three-dimensional geometric manifold space, and perform vector offset operation on the coordinates of the initial target trajectory points based on the affine transformation matrix to generate a set of corrected manifold trajectory points containing real-time response deviation compensation information.

[0140] Obtain the dynamic correction factor sequence generated by step S5 and the coordinate matrix of the initial target trajectory points stored in the three-dimensional geometric manifold space. Perform parameter registration on the two in the same coordinate system to ensure that the deviation compensation amount and the manifold point position are in the same spatial reference benchmark.

[0141] An affine transformation matrix for coordinate adjustment is constructed, which contains four basic transformation components: rotation, scaling, translation, and shearing. Each control variable in the dynamic correction factor sequence is mapped to its corresponding transformation coefficient to form a complete affine transformation parameter set with physical control semantics.

[0142] The initial target trajectory point coordinate matrix is ​​vectorized, each trajectory point is decomposed into a single row vector containing three-dimensional coordinate components, and matrix multiplication is performed with the affine transformation matrix in index order to achieve spatial position offset driven by control variables.

[0143] The response deviation compensation value corresponding to the dynamic correction factor sequence is superimposed at the translation component of the matrix multiplication operation, so that each trajectory point contains real-time compensation information from the Kalman filter correction at its new coordinate position after transformation.

[0144] The set of trajectory point vectors that have undergone affine transformation and deviation superposition is reassembled into a set of trajectory points in a three-dimensional geometric manifold space. This set has already demonstrated the adaptive correction effect of the AD acquisition system response deviation in its spatial morphology.

[0145] By using the above-mentioned affine transformation and deviation superposition processing method, the dynamic correction factor sequence of the previous step is transformed into correction data that can be directly applied to the manifold space coordinates, thereby achieving high-precision compensation for the deviation of the target trajectory point in response to the real combustion state in three-dimensional space.

[0146] For example, in a simulation and debugging scenario of an industrial boiler burner, the initial target trajectory point coordinate matrix contains 500 three-dimensional coordinates, each coordinate component being in millimeters. The dynamic correction factor sequence includes a combustion stability coefficient correction of 0.02, a heat release fluctuation rate correction of 0.015, and an oxidant disturbance intensity correction of 0.01. The rotation component of the affine transformation matrix is ​​set to rotate 1.5 × 10⁻⁶ around the Z-axis. 3 Radius, scaling component is 1.002 times, translation components are 0.25 mm in the X direction and Y direction respectively. The distance is 0.18 mm in the Z direction and 0.12 mm in the Z direction, with a shear component of 0.001. After vectorizing the three-dimensional coordinate matrix, matrix multiplication is performed with the affine matrix mentioned above. The corresponding deviation compensation value is then superimposed at the translation component position to obtain the corrected trajectory point set. The maximum displacement change in the manifold space is 0.39 mm, and the curvature continuity does not change abruptly. It has been verified that after inversely mapping this set to the time-frequency characteristic space, the root mean square value of the deviation of the generated simulated ultraviolet waveform in the amplitude-frequency response is significantly reduced to 0.004, effectively improving the matching degree of the simulated signal to the dynamics of the real system.

[0147] S6.2: Read the modified manifold trajectory point set, and use the improved local linear embedding inverse mapping mechanism to perform manifold to feature space back projection processing on the modified manifold trajectory point set to reconstruct a high-dimensional time-frequency feature vector restoration set corresponding to the current combustion state.

[0148] The input condition is the set of corrected manifold trajectory points, which contains trajectory coordinate point data after being processed by a dynamic correction factor sequence and an affine transformation matrix. It has real-time response deviation compensation information and is represented in three-dimensional geometric manifold space coordinates.

[0149] Perform inverse mapping input preprocessing on the corrected manifold trajectory point set, group the trajectory coordinates according to the working condition label, and generate a group index to facilitate the preservation of local structure during the inverse mapping process.

[0150] Based on index grouping, the improved local linear embedding neighborhood weight matrix is ​​called to read the local neighborhood set and linear reconstruction weights corresponding to each trajectory point, ensuring local geometric consistency during high-dimensional feature space restoration.

[0151] In the inverse mapping operation, the three-dimensional coordinate matrix is ​​used as a low-dimensional input, and the corresponding high-dimensional time-frequency feature vector is recovered through the solution process. Specifically, the three-dimensional coordinate values ​​of each trajectory point are multiplied by matrix, and fused with their neighborhood weight coefficients in a linear combination relationship to output the estimated value of the original high-dimensional feature components.

[0152] For the output feature components, numerical restoration is performed based on the normalized scale of the time-frequency energy distribution. A linear proportional inverse transform is used to map the energy values ​​corresponding to the low-dimensional coordinates back to the original unit scale, ensuring the consistency of the restored features in terms of numerical dimensions.

[0153] The inverse mapping output is optimized secondaryly by correcting local error constraints. The high-dimensional feature vector is iteratively adjusted using a residual minimization method to minimize its distance metric from the original feature space. This error constraint enables accurate reconstruction of the high-dimensional time-frequency feature vector restoration set.

[0154] Through the above chain processing method, the corrected manifold trajectory point set is transformed into a high-dimensional time-frequency feature vector restoration set corresponding to the current combustion state, achieving the expected technical effect of local topology preservation and energy scale restoration in the inverse mapping process.

[0155] For example, in a test scenario where the combustion state is pulsating combustion and the corresponding corrected manifold trajectory point set contains 500 trajectory points, the three-dimensional coordinates of each trajectory point are divided into 5 groups according to the operating condition label. A K-nearest neighbor search with a neighborhood size of 8 is used to obtain the neighborhood set, and the size of the reconstructed weight coefficient matrix of the trajectory point is read as 8×3. In the inverse mapping operation, matrix multiplication is used to map the three-dimensional coordinates back to a 256-dimensional high-dimensional feature vector. The obtained feature components are restored to the original time-frequency energy scale by normalized scaling inverse transformation. The normalized values ​​ranging from 0 to 1 are mapped back to the actual radiation intensity values ​​from 0 to 120 μW / cm². In the error constraint optimization, the residual iteration step size is set to 0.001, and the number of iterations is 200. The mean square error between the final high-dimensional feature vector restoration set and the target feature components is significantly reduced. The high-dimensional time-frequency feature vector restoration set is highly consistent with the ultraviolet signal of the real pulsating combustion state in terms of time-frequency spectral morphology and energy distribution characteristics, providing accurate input for subsequent cubic spline interpolation to generate a smooth spectral surface.

[0156] S6.3: Based on the high-dimensional time-frequency feature vector restoration set, the discrete frequency domain energy distribution data is continuously fitted using the cubic spline nonlinear interpolation method to generate continuous time-frequency energy distribution surface data with smooth spectral transition characteristics.

[0157] Based on the high-dimensional time-frequency feature vector reconstruction set, the frequency domain energy distribution extraction module is invoked to perform a frequency index-based arrangement operation on the energy values ​​of discrete frequency points, forming an energy sequence that meets the interpolation calculation order requirements. The actual frequency difference between adjacent frequency points is obtained using a node spacing calculator and used as the input to the abscissa sequence of the spline interpolation parameter matrix, ensuring the accuracy of the fitting function under non-uniform frequency sampling conditions. A cubic spline coefficient solver is invoked to perform piecewise cubic polynomial coefficient calculations on the arranged energy sequence and corresponding frequency differences. Natural boundary conditions or smoothed second derivative conditions are set using a boundary condition constraint set, and the interpolation results of each frequency segment are concatenated into a continuous function surface dataset. A spectral smoothing optimizer is used to perform gradient continuity checks and high-frequency oscillation suppression processing on the surface data, eliminating peaks and fluctuations during the fitting process and ensuring a smooth surface transition. Through the above nonlinear cubic spline interpolation processing method, the high-dimensional time-frequency feature vector reconstruction set of the previous step is transformed into continuous time-frequency energy distribution surface data with smooth spectral transition characteristics, achieving continuity and high-fidelity preservation of time-frequency domain features.

[0158] For example, in an industrial boiler combustion commissioning scenario, a high-dimensional time-frequency feature vector reconstruction set is obtained after inverse mapping. Its frequency sampling points are 0.5 kHz, 1.3 kHz, 2.0 kHz, 3.5 kHz, and 5.0 kHz, with corresponding energy values ​​of 2.15, 3.02, 4.87, 3.45, and 2.10 (unit: mW), respectively. After processing with a frequency difference calculator, an adjacent frequency difference sequence {0.8, 0.7, 1.5, 1.5} kHz is obtained. A cubic spline coefficient solver is then called to calculate the coefficients for the energy data between each pair of adjacent frequency points. For example, the coefficient results for the first segment are a=2.15, b=1.0875, c=-0.425, and d=0.13125. An interpolation formula is applied to fit any target frequency f within the first segment. For example, at f = 0.9 kHz, the calculated energy value is approximately 2.234 mW, and the gradient change of the smooth surface at this frequency point is abrupt. A natural boundary condition mode is selected using a boundary condition constraint generator to ensure that the second derivative is zero at 0.5 kHz and 5.0 kHz. After concatenating the interpolation functions of all segments, a gradient continuity check is performed on the surface using a spectral smoothing optimizer, significantly reducing oscillations at high frequencies. Continuous time-frequency energy distribution surface data is output for the short-time inverse Fourier transform in step S6.4. The surface data maintains a smooth transition across the entire frequency domain, significantly improving the fidelity of the time-series signal synthesized from this surface under complex combustion conditions.

[0159] S6.4: Perform short-time inverse Fourier transform on the continuous time-frequency energy distribution surface data, and introduce the instantaneous phase information extracted by Hilbert-Huang transform as a constraint condition for phase-preserving resampling processing to synthesize a preliminary simulated ultraviolet time-series signal containing millisecond-level flashing details of real flames.

[0160] The continuous time-frequency energy distribution surface data, processed by cubic spline nonlinear interpolation, is acquired. The short-time Fourier inverse transform module is invoked to perform inverse transform calculations in each local time-frequency segment, converting the smooth spectral surface into corresponding time-domain signal components. The set of complex spectral coefficients generated during the inverse transform is input into an instantaneous phase analyzer. The signal is decomposed into several intrinsic mode functions (IMFs) using the Hilbert-Huang transform, and instantaneous phase information is extracted for each IMF. The extracted instantaneous phase sequence is loaded as a constraint into the resampling control module. During phase-preserving resampling, the sampling point positions are adjusted to maintain the phase continuity and temporal consistency of the original combustion dynamics. Energy-weighted synthesis is performed on the time-domain components of each IMF after phase-preserving resampling to calculate the total time-series signal. The synthesized total time-series signal sequence is checked for amplitude and phase consistency, and high-frequency distortion components caused by numerical interpolation are removed, generating a preliminary simulated ultraviolet time-series signal containing millisecond-level flicker details of a real flame. Through the aforementioned phase-constrained inverse transformation and resampling process, the time-frequency surface data from the previous step is transformed into a high-fidelity simulated ultraviolet waveform, thus achieving a complete reproduction of the dynamic characteristics of combustion.

[0161] For example, on an industrial combustion simulation platform equipped with a broadband response ultraviolet photomultiplier tube, for time-frequency energy distribution surface data under stable combustion conditions, the length of each frame of the inverse Fourier transform was set to 256 points, and the sampling interval was 0.1ms. The resulting complex spectral coefficients were decomposed into 5 IMF components by Hilbert-Huang transform. The instantaneous phase extraction resolution of the IMF was set to 0.05ms, and the original sampling rate was adjusted from 10kHz to 12kHz during phase-holding resampling to improve time accuracy. For each IMF component, an energy weight value was calculated. For example, the energy weight of the third IMF component at t=2.5ms was 0.82, corresponding to an instantaneous amplitude of 1.15V. Substituting this into the formula, the value of the synthesized signal at that moment was 0.943V. After synthesis at all time points, the initial simulated ultraviolet time-series signal showed a significantly improved match with the real flame signal on the amplitude-frequency response curve, and the complete reproduction of combustion dynamic details was achieved in subsequent hardware compensation layer verification.

[0162] S6.5: Obtain the preliminary simulated ultraviolet timing signal, and perform frame alignment and amplitude normalization verification processing on the preliminary simulated ultraviolet timing signal according to the preset sampling rate synchronization standard, so as to output the final high-fidelity simulated ultraviolet waveform data stream for subsequent hardware compensation layer to call.

[0163] Step S7: Based on the simulated ultraviolet waveform data stream, electrical compensation parameters are superimposed according to the amplitude-frequency response characteristics, rising edge jitter characteristics, and signal-to-noise ratio attenuation law of the real ultraviolet sensor to generate a standardized simulated electrical signal equivalent to the output of the real sensor. Specifically, this includes: S7.1: Obtain the amplitude-frequency response curve dataset of a real ultraviolet sensor under standard test conditions, and use the system identification method to perform pole and zero extraction processing on the amplitude-frequency response curve dataset to generate a set of digital filter transfer function coefficients characterizing the frequency selectivity of the sensor.

[0164] S7.2: Construct an infinite impulse response digital filter network based on the set of transfer function coefficients of the digital filter, input the high-fidelity analog ultraviolet waveform data stream into the infinite impulse response digital filter network to perform convolution operation, so as to generate a pre-compensated time sequence signal sequence after amplitude-frequency characteristic correction.

[0165] The digital filter transfer function coefficient set, generated by extracting poles and zeros from the amplitude-frequency response curve, is used as input to construct the filter network for the signal correction module within the hardware compensation layer. Based on the transfer function coefficient set, an infinite impulse response structure design method is invoked to generate the filter distribution matrix according to the time-domain stability constraints of the pole and zero sequences within the coefficient set. A high-fidelity analog ultraviolet waveform data stream is loaded onto the filter input, and the convolution result matrix between the data stream and the filter coefficient set is calculated sequentially by the convolution operation unit. A numerical integration accuracy control strategy is employed to eliminate the accumulated error caused by the finite word length during convolution and to maintain the phase continuity of the output waveform. The convolution result matrix is ​​then normalized to ensure consistency with the amplitude-frequency characteristics of the real sensor across the entire frequency band. Through these processing methods, the high-fidelity analog ultraviolet waveform data from the previous step is transformed into a pre-compensated time-series signal sequence with amplitude-frequency characteristic correction, achieving the expected technical effect of matching the signal frequency response with the real sensor.

[0166] For example, high-fidelity simulated ultraviolet waveform data streams under stable combustion conditions were collected on an industrial combustion test platform. The data stream sampling rate was set to 10000 Hz. The amplitude-frequency response curve was identified by the system, yielding a transfer function coefficient set with a pole sequence length of 5 and a zero sequence length of 4. Based on this coefficient set, an IIR filter network was constructed, with the filter order set to 5. The coefficient matrix was normalized to unity gain, and the convolution operation used floating-point precision. After the convolution operation, the output signal was normalized to ensure that its peak amplitude corresponds to the peak response of the real sensor under stable combustion conditions. The results showed that the output signal's agreement with the real sensor's amplitude-frequency curve was significantly improved across the entire frequency band. The pre-compensated timing signal had an amplitude error of less than 0.02 V in the 50 Hz to 5 kHz range, verifying the performance improvement effect of this step.

[0167] S7.3: Read the statistical distribution model of rising edge jitter of the real ultraviolet sensor under transient illumination, and use a Gaussian white noise generator combined with random process modulation to perform perturbation superposition processing on the jumping edges of the pre-compensated time sequence signal to generate a dynamic fluctuation signal stream containing the jitter characteristics of the real rising edge.

[0168] In the input conditions, the pre-compensated timing signal sequence is output by the amplitude-frequency characteristic correction process, which has the frequency selectivity of a real ultraviolet sensor, but has not yet introduced the rising edge jitter characteristics under transient illumination conditions.

[0169] Based on experimental observation data from real ultraviolet sensors under transient illumination conditions, a statistical distribution model of amplitude versus time offset along the jump is extracted, and this distribution model is used as a jitter feature parameter library for subsequent modulation.

[0170] Call the Gaussian white noise generator to generate a random perturbation sequence according to the standard deviation and mean parameters in the statistical distribution model, and ensure that the spectral characteristics of the random sequence meet the white noise assumption.

[0171] By using random process modulation, the transition edge indexes of the random disturbance sequence and the pre-compensated time sequence are matched point by point. Through dual-channel injection of amplitude modulation and phase modulation, the distribution matching of the disturbance data within the duration of the transition edge is achieved.

[0172] The modulation amount is calculated using the following formula: in, For the first The amplitude after modulation at each transition edge point Original amplitude value The standard deviation of jitter, This represents the Gaussian white noise perturbation.

[0173] Band-limited filtering is performed on the transition edges after amplitude and phase modulation to suppress high-frequency pseudo-components introduced by the modulation process and maintain the physical rationality of the signal waveform edges.

[0174] By superimposing Gaussian white noise and modulating random processes, the pre-compensated time-series signal sequence is transformed into a dynamic fluctuating signal stream containing real rising edge jitter characteristics, thereby realizing the realistic reproduction of the output characteristics of the real sensor in the transient response process of the analog signal.

[0175] For example, a high-fidelity ultraviolet sensor with a sampling rate of 10kHz was configured on a standard industrial combustion test platform. Under transient illumination conditions, the standard deviation of the rise-edge jitter was observed to be 0.15V, with a mean of 0V. The duration from the start of the rise-edge to the steady state in the pre-compensated timing signal sequence was set to 2ms. For each rise-edge point, a Gaussian white noise generator was used to output the disturbance amount, and the amplitude was modulated according to the formula. At the same time, random process modulation was used to map the disturbance sequence to the phase, maintaining the temporal consistency and amplitude correlation of the disturbance process. After band-limited filtering, the output dynamic fluctuation signal stream exhibited the same rising-edge random hysteresis characteristics and waveform fluctuation pattern as the real sensor output in experimental verification, significantly improving the transient realism of the simulation signal and the effectiveness of system debugging.

[0176] S7.4: Establish a background noise injection mapping table based on the signal-to-noise ratio attenuation law of the real ultraviolet sensor. Query the background noise injection mapping table according to the instantaneous amplitude of the dynamic fluctuation signal stream to obtain the corresponding noise power spectral density parameter. Use colored noise synthesis to superimpose the calculated background noise component onto the dynamic fluctuation signal stream to generate a noisy simulated electrical signal with real signal-to-noise ratio attenuation characteristics.

[0177] Instantaneous amplitude extraction is performed on the dynamic fluctuation signal stream after rising edge jitter processing to form an amplitude index sequence for noise power retrieval. A background noise injection mapping table is constructed based on the signal-to-noise ratio attenuation characteristics of a real ultraviolet sensor under different radiation intensities. The amplitude index sequence is used as the query key to match the corresponding noise power spectral density parameter set. A spectrum segmentation mapping operation is performed on the obtained noise power spectral density parameter set, associating each parameter with the corresponding frequency component of the dynamic fluctuation signal stream according to frequency bands. Colored noise synthesis is invoked to synthesize background noise signals with target power distribution characteristics in each frequency band according to the noise power spectral density parameter set. Phase consistency correction is performed on the noise signals in each frequency band to ensure coherence with the dynamic fluctuation signal stream. The phase-consistency-corrected background noise signals are accumulated to the corresponding frequency components of the dynamic fluctuation signal stream according to frequency bands, forming a noisy simulated electrical signal output set with realistic signal-to-noise ratio attenuation characteristics. Through the above-mentioned noise floor mapping retrieval, power spectral density binding, frequency band colored noise synthesis and phase consistency correction calculation, the dynamic fluctuation signal stream of the previous step is transformed into a noisy simulated electrical signal that is equivalent to the output of the real sensor in terms of amplitude frequency response, thereby achieving accurate replication of the real physical noise characteristics.

[0178] For example, signal-to-noise ratio curves of a real ultraviolet sensor under both weak and strong combustion conditions are acquired on an industrial combustion test bench. A noise floor injection mapping table is established with an amplitude range of 0.1V to 4.5V. The noise power spectral density parameter corresponding to each amplitude in the mapping table ranges from (1.0 × 10⁻⁶) / 4.5V. -6 Up to 2.5×10 -The signal strength (3 W / Hz) is divided into 64 frequency bands. The instantaneous amplitude of the dynamic fluctuating signal stream is located within a specific range, and the corresponding power spectral density parameters are obtained by searching a mapping table. During colored noise synthesis, a first-order autoregressive filter is used to construct the spectral shape, causing the noise to attenuate slowly in the low-frequency range and rapidly in the high-frequency range. The noise and original signal are synthesized using a frequency domain accumulation method, with phase consistency correction applied before accumulation to ensure a stable instantaneous phase difference between the noise and the signal. The synthesized noisy simulated electrical signal has a signal-to-noise ratio (SNR) of approximately 22.3 under weak combustion conditions and approximately 13.6 under strong combustion conditions, achieving a significant improvement in matching the noise behavior of real sensors.

[0179] S7.5: Perform range normalization and DC bias calibration operations on the noisy simulated electrical signal, and adjust the signal output level according to the input impedance matching requirements of the AD acquisition front end of the flame detection system, so as to finally generate a standardized simulated electrical signal equivalent to the output of the real sensor.

[0180] Step S8: The standardized simulated electrical signal is used as the excitation signal to replace the physical sensor and directly output to the sampling input terminal of the flame detection system, completing the full-condition closed-loop simulation debugging and calibration process without the intervention of a physical light source. Specifically, this includes: S8.1: Acquire the standardized simulated electrical signal data stream after processing by the hardware response compensation layer, and use the high-precision digital-to-analog conversion interface to perform a mapping transformation operation from discrete digital quantity to continuous analog quantity on the data stream to generate a continuous voltage or current analog waveform signal with the actual electrical characteristics of the sensor.

[0181] S8.2: Receive the continuous voltage or current analog waveform signal, and perform source impedance matching and high-frequency noise suppression processing on the signal through an impedance matching network and a low-pass filter circuit to output an impedance matching simulated electrical signal that is equivalent to the output characteristics of a real ultraviolet sensor.

[0182] S8.3: Import the impedance matching simulation electrical signal and inject it directly into the AD acquisition front-end input port of the flame detection system to replace the traditional physical ultraviolet sensor to perform analog sampling and digital quantization processing, so as to obtain the original digital sampling sequence reflecting the simulated flame state.

[0183] S8.4: Based on the original digital sampling sequence, the flame detection system performs real-time logical operations and threshold comparison analysis on the preset combustion state discrimination to generate system state judgment results including successful ignition, stable combustion, abnormal pulsation, or flameout fault.

[0184] S8.5: Read the system status judgment result and perform closed-loop consistency verification with the preset standard operating condition expected indicators. Based on the verification deviation, dynamically adjust the digital twin modeling parameters and iteratively optimize the simulation output strategy to complete the full-condition adaptive calibration and debugging verification process without the intervention of physical light source.

[0185] The system receives a dual-input dataset consisting of the system state determination result and the expected indicators of the preset standard operating condition. A closed-loop consistency verification module is then invoked to perform a precise quantitative comparison between the two, generating a multi-dimensional deviation vector containing amplitude, spectral, and phase differences. This multi-dimensional deviation vector is input into a deviation resolver based on time-frequency topology mapping. Component decomposition is performed according to the weight coefficients of each difference dimension to extract the control parameter deviation group that has the highest impact on combustion state determination. For the extracted control parameter deviation group, an online gradient update mechanism is used to adjust the combustion stability coefficient, heat release fluctuation rate, and oxidant disturbance intensity in the digital twin modeling parameter library, ensuring that the parameter adjustment is synchronized with the real-time trajectory evolution. The adjusted modeling parameters are re-injected into the simulation output strategy scheduler. Based on the principles of phase preservation and energy constraint, the signal synthesis path is iteratively optimized to ensure that the new simulation waveform approximates the expected values ​​of the standard operating condition in terms of amplitude-frequency response, rising edge jitter, and signal-to-noise ratio attenuation. Through the above closed-loop consistency verification and dynamic parameter adjustment, the system state determination result of the previous step is transformed into quantifiable deviation data and iteratively optimized modeling parameters, achieving full-condition adaptive calibration and debugging verification without the intervention of a physical light source.

[0186] For example, in the commissioning scenario of an industrial boiler combustion system, the expected performance indicators for standard operating conditions are set as follows: steady-state amplitude of 2.8V, main frequency of 120Hz, and phase delay not exceeding 3ms. The actual measured amplitude of the system state determination is 2.6V, main frequency of 118Hz, and phase delay of 4ms. The closed-loop consistency verification module calculates the amplitude deviation to be 2.8V. 2.6, frequency deviation is 120 118, phase deviation is 4 3. Generate the deviation vector [0.2, 2, 1]. The deviation resolver calculates the total weighted deviation of 0.2×0.5+2×0.3+1×0.2 after setting the weighting coefficients (amplitude 0.5, frequency 0.3, phase 0.2), resulting in 0.76. Based on this value, the combustion stability coefficient is adjusted from 0.85 to 0.89, the heat release fluctuation rate from 0.12 to 0.11, and the oxidant disturbance intensity from 0.05 to 0.045. After the optimized parameter set is applied in the simulation output strategy, the amplitude of the generated simulated ultraviolet waveform is increased to 2.79V, the main peak frequency is increased to 119.8Hz, and the phase delay is shortened to 3.05ms, which significantly improves the consistency between the simulation signal and the expected standard operating conditions, and realizes high-precision adaptive calibration under complex operating conditions.

[0187] This invention also provides a digital simulation and debugging device for a flame detection system based on ultraviolet light signals, comprising: Signal acquisition module: Deploy a high-fidelity ultraviolet sensor array on a standard industrial combustion test platform to simultaneously acquire raw ultraviolet electrical signals under various operating conditions such as weak combustion, stable combustion, pulsating combustion, deflagration and flameout transition, and set the sampling rate to no less than 10kHz to obtain a set of raw ultraviolet electrical signals containing millisecond-level flicker details; Time-frequency spectrum construction module: Performs sliding window framing processing on the original ultraviolet signal set, sets the length of each frame to 256 points, and performs short-time Fourier transform operation to convert the time-domain signal into a time-frequency energy distribution spectrum set that characterizes the energy distribution law; Dimensionality reduction mapping module: Based on the time-frequency energy distribution map set, a high-dimensional time-frequency feature vector set is constructed, and dimension reduction mapping is performed while preserving local neighborhood relationships to generate a three-dimensional geometric manifold space representing the topological structure of different combustion states; Trajectory evolution modeling module: Differentiable parameterized motion equations are established in the three-dimensional geometric manifold space. Combustion stability coefficient, heat release fluctuation rate and oxidant disturbance intensity are introduced as control variables to drive trajectory evolution, so as to construct a manifold trajectory evolution model that can simulate the dynamic evolution path of flame. Fusion correction module: Reads the actual response deviation data of the AD acquisition terminal of the flame detection system, inputs it into the online Kalman filter and performs real-time fusion calculation with the prediction output of the manifold trajectory evolution model to generate a dynamic correction factor sequence for correcting the trajectory direction; Reconstruction module: The target trajectory points in the three-dimensional geometric manifold space are reverse mapped using the dynamic correction factor sequence. The mapping results are processed by nonlinear interpolation and phase-preserving resampling techniques to reconstruct a high-fidelity simulated ultraviolet waveform data stream. Compensation module: Based on the simulated ultraviolet waveform data stream, electrical compensation parameters are superimposed according to the amplitude-frequency response characteristics, rising edge jitter characteristics and signal-to-noise ratio attenuation law of the real ultraviolet sensor to generate a standardized simulated electrical signal equivalent to the output of the real sensor. Closed-loop debugging module: The standardized simulation electrical signal is used as the excitation signal to replace the physical sensor and is directly output to the sampling input terminal of the flame detection system to complete the closed-loop simulation debugging and calibration process under all working conditions without the intervention of physical light source.

[0188] For those skilled in the art, various other corresponding changes and modifications can be made based on the technical solutions and concepts described above, and all such changes and modifications should fall within the protection scope of the claims of this invention.

[0189] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this application pertains. The terms “first,” “second,” “third,” and similar terms used in this patent application specification and claims do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms “an” or “a” and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms “comprising” or “including” and similar terms mean that the element or object preceding “comprising” or “including” encompasses the element or object listed following “comprising” or “including” and its equivalents, and do not exclude other elements or objects. The “multiple” mentioned in the embodiments of this application refers to two or more. A and / or B indicate three possibilities: A; B; and A and B.

[0190] The above description is merely an exemplary embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and such modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A digital simulation and debugging method for a flame detection system based on ultraviolet light signals, specifically including: S1: Collect raw ultraviolet electrical signals from a standard industrial combustion test platform to generate a raw ultraviolet electrical signal set; S2: Generate a time-frequency energy distribution spectrum set based on the original ultraviolet electrical signal set; S3: Construct a high-dimensional time-frequency feature vector set based on the time-frequency energy distribution map set, and perform dimensionality reduction mapping while preserving local neighborhood relationships to generate a three-dimensional geometric manifold space that characterizes the topological structure of different combustion states; S4: Constructing a manifold trajectory evolution model based on three-dimensional geometric manifold space; S5: Read the actual response deviation data of the AD acquisition terminal of the flame detection system, input it into the online Kalman filter and perform real-time fusion calculation with the prediction output of the manifold trajectory evolution model to generate a dynamic correction factor sequence for correcting the trajectory direction; S6: The target trajectory points in the three-dimensional geometric manifold space are reverse mapped using a dynamic correction factor sequence. The mapping results are then processed using nonlinear interpolation and phase-preserving resampling techniques to reconstruct a high-fidelity simulated ultraviolet waveform data stream. S7: Based on the simulated ultraviolet waveform data stream, electrical compensation parameters are superimposed according to the amplitude-frequency response characteristics, rising edge jitter characteristics and signal-to-noise ratio attenuation law of the real ultraviolet sensor to generate a standardized simulated electrical signal equivalent to the output of the real sensor. S8: The standardized simulated electrical signal is used as the excitation signal to replace the physical sensor and is directly output to the sampling input terminal of the flame detection system to complete the closed-loop simulation debugging and calibration process under all working conditions without the intervention of physical light source.

2. The digital simulation and debugging method for a flame detection system based on ultraviolet light signals according to claim 1, characterized in that, The process of acquiring raw ultraviolet electrical signals from a standard industrial combustion test platform to generate a raw ultraviolet electrical signal set involves deploying a high-fidelity ultraviolet sensor array on the platform to simultaneously acquire raw ultraviolet electrical signals under various conditions, including weak combustion, stable combustion, pulsating combustion, deflagration, and flameout transition. The sampling rate is set to no less than 10kHz to obtain a raw ultraviolet electrical signal set containing millisecond-level flicker details.

3. The digital simulation and debugging method for a flame detection system based on ultraviolet light signals according to claim 1, characterized in that, The process of generating a time-frequency energy distribution map set based on the original ultraviolet electrical signal set specifically involves performing sliding window framing processing on the original ultraviolet electrical signal set, setting the length of each frame to 256 points, and performing short-time Fourier transform operation to convert the time-domain signal into a time-frequency energy distribution map set that characterizes the energy distribution pattern.

4. The digital simulation and debugging method for a flame detection system based on ultraviolet light signals according to claim 1, characterized in that, The construction of the manifold trajectory evolution model based on the three-dimensional geometric manifold space specifically involves establishing differentiable parameterized motion equations within the three-dimensional geometric manifold space, and introducing combustion stability coefficient, heat release fluctuation rate, and oxidant disturbance intensity as control variables to drive trajectory evolution, thereby constructing a manifold trajectory evolution model capable of simulating the dynamic evolution path of flames.

5. The digital simulation and debugging method for a flame detection system based on ultraviolet light signals according to claim 1, characterized in that, The online Kalman filter includes a state prediction module, an observation input module, a residual calculation module, a gain calculation module, a state update module, and an output interface module.

6. The digital simulation and debugging method for a flame detection system based on ultraviolet light signals according to claim 1, characterized in that, S3 specifically includes: The two-dimensional matrix data of each frame in the time-frequency energy distribution map set is obtained, and the frequency component energy values ​​in the matrix are subjected to row-first flattening and normalization to generate a high-dimensional time-frequency feature vector set characterizing the instantaneous combustion state of a single frame. The Euclidean distance metric between any two feature vectors is calculated based on a high-dimensional time-frequency feature vector set, and the local neighborhood point set of each target vector is determined to generate a neighborhood index matrix containing local geometric constraints. A local reconstruction weight coefficient matrix is ​​constructed based on the neighborhood index matrix. A regularization term is introduced to optimize the least squares loss function to solve for the optimal reconstruction weights, generating a weight allocation scheme that can accurately describe the local linear combination relationship in high-dimensional space. A low-dimensional embedding cost function is constructed using the optimal reconstruction weight scheme. The three-dimensional coordinate matrix is ​​solved to minimize the global reconstruction error, generating a set of three-dimensional geometric manifold space coordinate points that characterize the distribution patterns of all operating conditions, such as weak combustion, stable combustion, and flameout. Cluster density analysis and boundary curvature extraction are performed on the coordinate point set of the three-dimensional geometric manifold space to identify the topological boundary features between the steady-burning central region and the flameout transition path, and generate a state topology mapping map with clear physical semantics, thus completing the final dimensionality reduction mapping from high-dimensional spectral data to low-dimensional manifold space.

7. The digital simulation and debugging method for a flame detection system based on ultraviolet light signals according to claim 1, characterized in that, S4 specifically includes: Based on the center point of the steady-burning cluster distribution and the curvature path of the flameout transition boundary in the three-dimensional geometric manifold space, key geometric invariants characterizing the topological structure of the combustion state are extracted to generate a set of basic manifold metric parameters for defining the manifold space metric tensor. Using the aforementioned set of basic manifold metric parameters, a Riemannian manifold tangent space mapping matrix is ​​constructed. The three physical control variables—combustion stability coefficient, heat release fluctuation rate, and oxidant disturbance intensity—are projected onto the tangent space basis to generate a manifold control vector sequence characterizing the multi-physics coupling effect. The nonlinear velocity field function in the manifold space is defined based on the manifold control vector sequence. Lie derivative operations are used to describe the instantaneous rate of action of the control variables on the manifold trajectory, so as to generate the manifold differential evolution equation characterizing the dynamic evolution trend of the flame. Generate discrete manifold trajectory point sets based on manifold differential evolution equations; The discrete manifold trajectory point set of the city is subjected to smoothness constraint optimization to eliminate high-frequency jitter noise generated by numerical integration and maintain the continuity of manifold curvature, so as to construct the final differentiable manifold trajectory evolution model and output it to the Kalman filter.

8. The digital simulation and debugging method for a flame detection system based on ultraviolet light signals according to claim 7, characterized in that, The process of generating a discrete manifold trajectory point set based on the manifold differential evolution equation specifically involves performing Runge-Kutta numerical integration iteration on the manifold differential evolution equation, and calculating the displacement increment of the trajectory points in the manifold space by combining the temporal variation law of the manifold control vector sequence, so as to generate a discrete manifold trajectory point set simulating the evolution of the entire working condition from weak combustion to deflagration.

9. The digital simulation and debugging method for a flame detection system based on ultraviolet light signals according to claim 1, characterized in that, S5 specifically includes: The actual ultraviolet electrical signal sampling sequence fed back by the AD acquisition terminal of the flame detection system is obtained, and the amplitude error vector and phase lag parameter at the current moment are extracted to construct a measured state observation dataset containing the system response deviation characteristics. Based on the measured state observation dataset, the predicted state vector output by the manifold trajectory evolution model is called to calculate the residual covariance matrix between the measured state and the predicted state, so as to quantify the degree of deviation between the current simulated trajectory and the actual combustion dynamics. Based on the residual covariance matrix, the state estimation weight coefficients are dynamically adjusted to generate the optimal filter gain matrix that can suppress noise interference and track sudden operating conditions in real time. Based on the optimal filter gain matrix, a weighted correction operation is performed on the residual covariance matrix. The amplitude error vector and phase lag parameter in the measured state observation dataset are fused together to calculate the state update increment vector representing the trajectory correction direction and amplitude. The control variable parameters of the manifold trajectory evolution model are iteratively updated according to the state update increment vector to generate a dynamic correction factor sequence including the combustion stability coefficient correction, the heat release fluctuation rate correction, and the oxidant disturbance intensity correction, so as to complete the closed-loop calibration of the target trajectory direction in the manifold space.

10. A digital simulation and debugging device for a flame detection system based on ultraviolet light signals, characterized in that, The device includes: Signal acquisition module: Deploy a high-fidelity ultraviolet sensor array on a standard industrial combustion test platform to simultaneously acquire raw ultraviolet electrical signals under various operating conditions such as weak combustion, stable combustion, pulsating combustion, deflagration and flameout transition, and set the sampling rate to no less than 10kHz to obtain a set of raw ultraviolet electrical signals containing millisecond-level flicker details; Time-frequency spectrum construction module: Performs sliding window framing processing on the original ultraviolet signal set, sets the length of each frame to 256 points, and performs short-time Fourier transform operation to convert the time-domain signal into a time-frequency energy distribution spectrum set that characterizes the energy distribution law; Dimensionality reduction mapping module: Based on the time-frequency energy distribution map set, a high-dimensional time-frequency feature vector set is constructed, and dimension reduction mapping is performed while preserving local neighborhood relationships to generate a three-dimensional geometric manifold space representing the topological structure of different combustion states; Trajectory evolution modeling module: Differentiable parameterized motion equations are established in the three-dimensional geometric manifold space. Combustion stability coefficient, heat release fluctuation rate and oxidant disturbance intensity are introduced as control variables to drive trajectory evolution, so as to construct a manifold trajectory evolution model that can simulate the dynamic evolution path of flame. Fusion correction module: Reads the actual response deviation data of the AD acquisition terminal of the flame detection system, inputs it into the online Kalman filter and performs real-time fusion calculation with the prediction output of the manifold trajectory evolution model to generate a dynamic correction factor sequence for correcting the trajectory direction; Reconstruction module: The target trajectory points in the three-dimensional geometric manifold space are reverse mapped using the dynamic correction factor sequence. The mapping results are processed by nonlinear interpolation and phase-preserving resampling techniques to reconstruct a high-fidelity simulated ultraviolet waveform data stream. Compensation module: Based on the simulated ultraviolet waveform data stream, electrical compensation parameters are superimposed according to the amplitude-frequency response characteristics, rising edge jitter characteristics and signal-to-noise ratio attenuation law of the real ultraviolet sensor to generate a standardized simulated electrical signal equivalent to the output of the real sensor. Closed-loop debugging module: The standardized simulation electrical signal is used as the excitation signal to replace the physical sensor and is directly output to the sampling input terminal of the flame detection system to complete the closed-loop simulation debugging and calibration process under all working conditions without the intervention of physical light source.

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