Dynamic process monitoring method for drift spectrum analysis
By using point cloud matching and Gaussian process regression algorithms, the problems of high hardware cost and difficulty in demodulating drift spectrum of fiber optic sensors in dynamic process monitoring are solved, realizing low-cost and efficient dynamic process monitoring and visualization.
Patent Information
- Application Number
- CN202511464589.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-14
- Publication Date
- 2026-03-03
AI Technical Summary
Existing fiber optic sensors have high hardware costs in dynamic process monitoring, traditional spectral demodulation methods are difficult to handle drift spectra, machine learning methods require a large amount of training data and are costly, and existing systems are difficult to deploy in resource-constrained environments.
Point cloud matching technology is used to expand spectral data, and Gaussian process regression algorithm is used for spectral fitting. Savitzky-Golay filtering and Beer-Lambert law are used for data preprocessing to achieve effective demodulation of drift spectra.
It significantly reduces the need for training data, enables low-cost and efficient dynamic process monitoring and visualization, and has a simple system structure suitable for on-site deployment.
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Figure CN121598098A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of fiber optic sensor spectral analysis and demodulation, and specifically relates to a dynamic process monitoring method for drift spectral analysis. Background Technology
[0002] Dynamic process monitoring has significant application value in fields such as industrial production, medical and health care, and environmental monitoring. Fiber optic sensors demonstrate unique competitiveness in these applications requiring dynamic process monitoring due to their unique advantages, including resistance to electromagnetic interference, distributed measurement capabilities, real-time operation, online capability, low cost, and ease of integration.
[0003] In the field of dynamic monitoring, a common approach is to use laser pulses combined with optical feedback mechanisms to enhance the sensitivity of fiber optic sensors and optical microcavities to changes in external parameters. This method leverages the narrow linewidth of lasers and employs multi-frequency modulation strategies to effectively expand the measurement range and improve signal acquisition rates. Furthermore, continuous process monitoring can be achieved through real-time detection of optical power fluctuations. While these methods offer advantages in data acquisition speed, laser-based measurement systems typically come with high implementation costs. Frequency modulation requires components such as electro-optic modulators, complicating the system structure; narrowband spectral filters limit the dynamic response performance during frequency scanning; and detection methods relying on optical power changes are limited by low signal-to-noise ratios, making further improvements in measurement accuracy difficult. Therefore, it is necessary to develop more novel monitoring and demodulation technologies to broaden the technical framework for dynamic process monitoring.
[0004] In fiber optic sensing systems, traditional spectral demodulation techniques are typically based on steady-state spectral assumptions, achieving parametric inversion by tracking wavelength shifts or intensity changes in interference valleys. However, in real-world dynamic monitoring scenarios, environmental disturbances, device performance degradation, or changes in operating conditions often lead to overall or localized spectrum drift, reducing the applicability of traditional steady-state demodulation methods. While such drifts cause changes in signal morphology, they often contain crucial information closely related to process dynamics. Therefore, effective analysis of drift spectra becomes a core issue for achieving high-reliability dynamic monitoring. Recent research has utilized machine learning methods to improve demodulation immunity, but these methods rely on large amounts of high-quality labeled samples for model training, facing constraints such as high data acquisition costs and long training cycles in practice. Furthermore, existing technologies lack a systematic mathematical framework for modeling drift spectra, making it difficult to achieve quantitative analysis under drift conditions and high-fidelity reconstruction of dynamic processes. Therefore, effectively expanding spectral datasets under both steady-state and drift scenarios under limited labeling conditions has become a critical technical challenge that urgently needs to be overcome in this field.
[0005] Point clouds are a multidimensional structured data form containing rich spatiotemporal attribute information. Point cloud registration technology, by calculating spatial transformation parameters, can align point clouds acquired from different perspectives or time points to a unified coordinate system, and has been widely used in 3D reconstruction, building monitoring, and medical imaging. Similarly, in spectral sensing, the morphology of interference fringes is easily altered by disturbances in the monitoring environment. If spectral data is considered as a type of point cloud, point cloud registration methods can be used to effectively expand steady-state spectral datasets, thus providing a more sufficient and reliable data foundation for spectral analysis with drift. Point cloud registration is a nonparametric fitting method that can model high-dimensional data structures based on kernel functions, thus exhibiting excellent nonlinear fitting performance. Even with expanded datasets, achieving accurate demodulation of drifted spectra remains a key challenge. Compared to other common intelligent algorithms such as multilayer perceptrons, recurrent neural networks, and support vector machines, Gaussian process regression has the ability to output probability distributions, and its inference results are statistically interpretable. This characteristic makes Gaussian process regression a significant advantage in spectral demodulation tasks that emphasize physical interpretability.
[0006] Currently, technologies for dynamic measurement using optical principles include: using laser pulses. The narrow linewidth of laser pulses allows for modulation of multiple frequencies within a fixed wavelength range, ensuring good spatial resolution and measurement range; quasi-distributed sensors built using light source spectrometers based on narrowband emission filters; and real-time monitoring technologies based on optical power measurement. While these methods offer advantages in data acquisition speed, laser-based measurement systems typically come with high implementation costs. Frequency modulation requires components such as electro-optic modulators, complicating the system structure; narrowband spectral filters limit the dynamic response performance during frequency scanning; and detection methods relying on changes in optical power are limited by low signal-to-noise ratios, making it difficult to further improve measurement accuracy. Therefore, it is necessary to develop more novel monitoring and demodulation technologies to broaden the technological framework for dynamic process monitoring.
[0007] Some researchers have used machine learning demodulation to implement an interferometric fiber optic sensor that achieves high dynamic range and high sensitivity curvature measurement. Others have developed a fiber optic sensor for dynamically measuring the dynamic deformation of armor, analyzing the output signal through high-speed imaging. Still others have used deep learning to address the problem of insufficient recognition accuracy caused by drift, but this only identifies whether the sensor state is abnormal, without analyzing the drift phenomenon itself.
[0008] The above research has the following main shortcomings: laser-based monitoring methods are generally costly, with high laser prices and maintenance costs, resulting in excessively high monitoring system costs; frequency modulation requires optical modulators, increasing system complexity and cost, and the use of narrowband filters limits the dynamic response capability during frequency scanning, while optical power measurement-based methods are susceptible to noise, leading to limited measurement accuracy; traditional demodulation methods rely on steady-state spectral assumptions and cannot effectively handle drift spectra that occur during dynamic processes; machine learning methods require a large amount of training data, resulting in high data acquisition costs and long time cycles, and lack in-depth exploration of drift spectral structures and visualization analysis capabilities for dynamic processes; existing systems are typically hardware-complex and costly, making them difficult to deploy in resource-constrained environments. Summary of the Invention
[0009] Purpose of the invention: This invention addresses the problems of high system hardware cost of fiber optic sensors in dynamic detection applications and the difficulty of traditional spectral demodulation methods in analyzing drift spectra. It proposes a dynamic process monitoring method for drift spectral analysis, which takes the spectrum as the main variable of interest, overcomes the problems of dependence on steady-state conditions and large data requirements in existing technologies, and achieves low-cost and high-efficiency dynamic spectral analysis and visualization.
[0010] Technical solution: The present invention provides a dynamic process monitoring method for drift spectral analysis, comprising the following steps:
[0011] (1) Acquire raw spectral data of the dynamic process through fiber optic sensors and perform data preprocessing;
[0012] (2) The preprocessed spectral data is augmented based on point cloud matching;
[0013] (3) Divide the preprocessed spectral data into multiple segments according to the preset number of data points;
[0014] (4) Dynamic fitting of spectral data is achieved based on Gaussian process regression algorithm to obtain a well-fitted GPR model;
[0015] (5) Perform spectral reconstruction on the spectra at different temperatures.
[0016] Furthermore, the implementation process of step (1) is as follows:
[0017] The raw spectral data is processed based on the Savitzky-Golay filtering algorithm. For one-dimensional spectral data, the filtering calculation is expressed as follows:
[0018] (1)
[0019] in, It is the output value after filtering the j-th data point. It is the (j+h)th original data point, and k is the half-width of the filter window. These are the convolution coefficients. ;
[0020] Compensation for optical path length is performed based on Beer-Lambert's law:
[0021] (2)
[0022] in, Absorbance The molar absorptivity is 1. It is the concentration of the analyte. It is the optical path length. The incident light intensity Intensity of transmitted light;
[0023] Compensated absorbance The calculation formula is:
[0024] (3)
[0025] in, This is the absorbance measurement value. For optical path reference length, It is the actual optical path length measured.
[0026] Furthermore, the implementation process of step (2) is as follows:
[0027] (21) Obtain historical data: Obtain I available historical data of the spectrum at different temperatures, and the wavelength of each historical data can be discretized into J values; then describe each of the I spectral data into a two-column matrix. ;
[0028] (22) Determine the transfer characteristics of spectral data: transfer the spectral data with the highest temperature. Spectral data with minimum temperature Perform similarity assessments and identify transition characteristics between the two sets of data;
[0029] (23) Assembling critical spectral data: Based on the transfer matrix and translation matrix obtained in step (22), the critical spectral data can be spliced together. and One set of data is transferred to another set of data, thereby merging the maximum and minimum temperature spectral data to obtain the dynamic range of the overall temperature spectral data.
[0030] Furthermore, the implementation process of step (22) is as follows:
[0031] Point cloud matching is used to obtain the similarity mapping matrix R and the translation difference matrix T between the two sets of data. The point cloud matching algorithm is specifically as follows: finding a mapping matrix R and a difference T that minimizes the distance between the two sets of data.
[0032] (4)
[0033] The above formula can be transformed into the following process:
[0034] (5)
[0035] Where t represents the translation value in matrix T corresponding to that sample; and Representing the i-th and Data, and Then they represent respectively and The mean of the data; then, the partial derivatives of R and t in equation (4) are obtained to solve for the corresponding rotation and translation matrices.
[0036] Furthermore, the implementation process of step (23) is as follows:
[0037] (231) Data transfer: Based on the R and T matrices, and using the following formula, the data can be transferred. To data Transfer:
[0038] (6)
[0039] in, The data after the transfer;
[0040] (232) Finding similar data segments and combination points: and The overlapping data portions are integrated, and then the discarded data is augmented; the specific implementation process is as follows:
[0041] S1: Prepare the data, and denote the spectrum with the lowest temperature as X. low The spectrum with the highest temperature is X. high , The sliding window length is len, the sliding step size is s, the spectral length is L, and the initial error min error is set to infinity.
[0042] S2: i is the starting position of the sliding window, with i=0 as the starting marker and i=L-len as the ending marker;
[0043] S3: Traverse X with step size s. lowFor each possible starting position i of the sliding window, extract the sliding window segment S. low =X low [i, i+ len], after completing the above steps, i=i+s;
[0044] S4: j is the starting position of the sliding window, with j=0 as the starting marker and j=L-len as the ending marker;
[0045] S5: Traverse X with step size s. high For each possible sliding window start position j, for each j, extract the sliding window segment S. high =X high [j, j+ len];
[0046] S6: Compare sub-segments S based on step (22) low and S high The similarity is used to obtain the fitting error E;
[0047] S7: If E is less than min error, update min error = E and record the starting position Pos of the similar segment in the lowest temperature spectrum. low = i, the starting position Pos of the similar segment in the highest temperature spectrum. high =j, after completing the above steps, j = j + s;
[0048] S8: After completing all i and j iterations, output the final result Pos. low Pos high and fitting error E;
[0049] The data is obtained based on steps S1 to S8. and The spectral wavelength should be labeled 0-Pos low and Pos high -Combination augmentation is performed at the End, resulting in a matrix with a sample size of Pos. low + End- Pos high Where End represents the measured spectral length, this combined data is defined as .
[0050] Furthermore, the lengths of the multiple sub-segments in step (3) are equal.
[0051] Furthermore, the implementation process of step (4) is as follows:
[0052] The Gaussian Process Regression (GPR) algorithm is used as the basic model to achieve dynamic fitting of spectral data; the GPR model is as follows:
[0053] (7)
[0054] in, and These are the output and input of the GPR model, respectively. This indicates a mean of 0. Gaussian noise of variance;
[0055] The output of GPR is the mean and variance of the Gaussian distribution corresponding to the output sample. This is a Gaussian process, which is represented as:
[0056] (8)
[0057] in, This represents the mean of the Gaussian process, while This represents the covariance of the Gaussian process. In This represents another set of inputs;
[0058] The differences between different inputs are represented by covariance, which is calculated using a Gaussian kernel function; now, if we consider a training set... The input is The output is According to the principle of marginal distribution, when a new input is given... Then, a new output needs to be predicted. This is equivalent to calculating a given value in a joint distribution. The marginal conditional distributions are shown below, including the joint distribution and the corresponding kernel function:
[0059] (9)
[0060] in, Represents a unit diagonal matrix. and Represents the hyperparameters of the kernel function; Indicated by and Composed of samples , The kernel function matrix is constructed as input, and the parameters of the kernel function are estimated based on the maximum likelihood principle; assuming that the hyperparameters of the kernel function are known, the corresponding... The predicted distribution is calculated using the following formula:
[0061] (10)
[0062] in, Features corresponding to wavelengths in the data are used as input features, while features corresponding to spectral intensities are used as output features.
[0063] Furthermore, the implementation process of step (5) is as follows:
[0064] (51) The conversion ratio between the wavelength range of the corresponding spectrum and temperature is calculated according to the following formula:
[0065] (11)
[0066] in, This indicates the temperature at which the spectrum to be restored is located. This represents the lower bound of the spectral temperature considered during modeling. This represents the upper bound of the spectral temperature considered during modeling. This represents the minimum wavelength of the spectrum at the critical temperature. This represents the maximum wavelength of the spectrum at the upper limit of the spectral temperature, while This represents the initial value of the spectral wavelength corresponding to this temperature;
[0067] (52) Based on the initial wavelength value obtained by conversion, the wavelength can be input into the fitted GPR model to obtain the spectral intensity value at the corresponding wavelength.
[0068] (53) Process visualization: Combine the reconstructed parameters in chronological order to generate dynamic process change curves or three-dimensional maps to achieve process visualization.
[0069] Compared with existing technologies, the present invention has the following advantages: the present invention overcomes the dependence on steady-state spectra and can directly process drift spectra; through segmentation and matching strategies, it significantly reduces the requirement for training data; it achieves high-precision reconstruction and visualization of dynamic processes; the system structure is simple, requires no complex hardware support, and is suitable for field deployment. Attached Figure Description
[0070] Figure 1 This is a flowchart of the spectral data augmentation process proposed in this invention;
[0071] Figure 2 This is a diagram showing the comparison of similar segments in spectral data;
[0072] Figure 3 This is a schematic diagram showing how spectral data can be combined into a full spectrum and samples can be moved using a sliding window.
[0073] Figure 4 This is a comparison chart of the combined spectral data results of the method of the present invention;
[0074] Figure 5 This invention presents a flowchart of the spectral analysis process using the Gaussian process regression model.
[0075] Figure 6 This represents the recovery result of the heating phase in cycle 1;
[0076] Figure 7 A three-dimensional view of the heating phase of cycle 1;
[0077] Figure 8 This is a spectrum after the cooling process in cycle 2 has been broken down. Detailed Implementation
[0078] The invention will now be further described with reference to the accompanying drawings.
[0079] This invention proposes a dynamic process monitoring method for drift spectral analysis, comprising the following steps:
[0080] Step 1: Data Acquisition and Preprocessing: Acquire spectral data of the dynamic process through fiber optic sensors, and perform noise filtering and baseline correction.
[0081] A fiber optic sensor was fabricated based on monitoring requirements, and connected to a light source and spectrometer to construct a complete spectral acquisition system. By adjusting the state of the environment under test, dynamic spectral data was continuously acquired during the monitoring process using the spectrometer. To verify the effectiveness of the method, a tapered fiber optic sensor was fabricated, and a temperature measurement system was built for data acquisition. The experimental dataset covered a temperature range of 26.645 ℃ to 27.989 ℃, including 21 sets of intermediate temperature spectra that could be used for algorithm verification.
[0082] Having obtained expanded steady-state spectral samples through point cloud matching, the GPR model was used for spectral intensity prediction. For the experiment, two cyclical changes with different drift amplitudes ("isothermal-heating-cooling-isothermal") were created. In cycle 1, the temperature started at 26.724 ℃, gradually increasing to 27.294 ℃ in steps of 0.03 ℃, and then gradually decreasing back to 26.724 ℃ in steps of 0.03 ℃, with an overall temperature change of 0.57 ℃ within the cycle. In cycle 2, the temperature started at 26.724 ℃, gradually increasing to 27.864 ℃ in steps of 0.06 ℃, and then gradually decreasing back to 26.724 ℃ in steps of 0.06 ℃, with an overall temperature change of 1.14 ℃ within the cycle. All stable phase spectral temperatures were maintained at 26.724 °C, providing a baseline for subsequent analysis to better observe and analyze spectral changes with temperature. Matching error represents the degree of similarity between the actual and predicted spectra. Typically, in this invention, when the matching error is less than 0.01, the Ri of the two spectra is considered to be... 2 The value is higher than 0.7. Therefore, it is considered that the two spectra are similar when the matching error is less than 0.01.
[0083] The Savitzky-Golay filtering algorithm is used to process the original spectral data: This algorithm performs local polynomial least squares fitting on each data point and its neighboring points, which can effectively eliminate high-frequency noise, preserve the key features of the spectral data, and make subsequent analysis more reliable.
[0084] For one-dimensional spectral data, the filtering calculation can be expressed as:
[0085] (1)
[0086] in, It is the output value after filtering the j-th data point. It is the (j+h)th original data point, and k is the half-width of the filter window. These are the convolution coefficients. .
[0087] Optical path compensation is performed based on Beer-Lambert's law: Beer-Lambert's law describes the absorption characteristics of light propagating in a medium. By accurately calculating and compensating for optical path-related parameters, interference caused by changes in the optical path can be eliminated, ensuring that spectral data accurately reflects changes in the monitored parameters. Whether compensation is needed depends on the measurement requirements. Compensation is necessary when the optical path itself is a variable and high absolute accuracy is required, and the system's optical path is significantly unstable. When the optical path is fixed and stable, and the measurement only concerns the relative trend of change, processing efficiency can be improved, and no compensation is needed.
[0088] The Beer-Lambert law is expressed as follows:
[0089] (2)
[0090] in, Absorbance The molar absorptivity is 1. It is the concentration of the analyte. It is the optical path length. The incident light intensity The intensity of transmitted light.
[0091] Compensated absorbance The calculation formula is:
[0092] (3)
[0093] in, This is the absorbance measurement value. For optical path reference length, It is the actual optical path length measured.
[0094] Since the optical path of the measuring sensor is fixed and stable in this embodiment, the measurement only needs to consider the relative trend of temperature change, and no compensation is required.
[0095] Step 2: Spectral data augmentation based on point cloud matching, such as... Figure 1 As shown, the specific steps include:
[0096] (2.1) Obtaining historical data: 23 available historical data points for the spectrum at different temperatures were obtained. The wavelength of each historical data point can be discretized into 901 values. Subsequently, each of the 23 spectral data points was described as a two-column matrix. .
[0097] (2.2) Determine the spectral data transfer characteristics: the spectral data with the highest temperature of 27.989 ℃ Spectral data with the lowest temperature of 26.645 °C Perform similarity assessments and identify transition characteristics between the two sets of data, such as... Figure 2 As shown. Specifically, a point cloud matching algorithm is used to obtain the similarity mapping matrix R and the translation difference matrix T between the two sets of data. The point cloud matching algorithm is specifically described in the following formula, that is, to find a mapping matrix R and a difference T that minimizes the distance between the two sets of data.
[0098] (4)
[0099] The above formula can be transformed into the following process:
[0100] (5)
[0101] Where t represents the translation value in matrix T corresponding to that sample; and Representing the i-th and The data, and and Then they represent respectively and The mean of the data is then obtained. The corresponding rotation and translation matrices can then be solved by taking the partial derivatives of R and t in Equation 3.
[0102] (2.3) Assembling critical spectral data: Based on the transfer matrix and translation matrix obtained in step (2.2), the critical spectral data can be spliced together. and One set of data is transferred to another set of data, thereby merging the maximum and minimum temperature spectral data to obtain the dynamic range of the overall temperature spectral data, such as... Figure 3 As shown. Towards Taking data transfer as an example, the specific implementation involves the following steps:
[0103] (2.3.1) Data Transfer: Based on the R and T matrices, and using the following formula, the data can be transferred. To data Transfer:
[0104] (6)
[0105] in, This is the data after the transfer.
[0106] (2.3.2) Finding similar segments and combination points in the data: Due to the spectral data after transfer and There will be some overlap in the data between the two bands, so the data cannot be simply amplified together. This step aims to find the optimal combination point between the two data segments, that is... and The overlapping data is integrated, and then the discarded data is augmented.
[0107] The specific steps of the algorithm are as follows:
[0108] Step 1: Prepare the data, and denote the spectrum with the lowest temperature as X. low The spectrum with the highest temperature is X. high , The sliding window length is len, the sliding step size is s, the spectral length is L, and the initial error min error is set to infinity.
[0109] Step 2: i is the starting position of the sliding window. With i=0 as the starting mark and i=L-len as the ending mark, repeat the following process.
[0110] Step 3: Iterate through X with a step size s. low For each possible starting position i of the sliding window, extract the sliding window segment S. low = X low [i, i+ len], after completing the above steps, i=i+s.
[0111] Step 4: j is the starting position of the sliding window. With j=0 as the starting mark and j=L-len as the ending mark, repeat the following process.
[0112] Step 5: Iterate through X with a step size s. high For each possible sliding window start position j, for each j, extract the sliding window segment S. high = X high [j, j+ len].
[0113] Step 6: Based on (2.2) comparison sub-segment Slow and S high The similarity is used to obtain the fitting error E.
[0114] Step 7: If E is less than min error, update min error = E and record the starting position Pos of the similar segment in the lowest temperature spectrum. low = i, the starting position Pos of the similar segment in the highest temperature spectrum. high =j, after completing the above steps, j = j + s.
[0115] Step 8: After completing all i and j iterations, output the final result Pos. low Pos high And the fitting error E.
[0116] The data can be obtained by following the steps described above. and The spectral wavelength should be labeled 0-Pos low and Pos high -Combination augmentation is performed at the End, resulting in a matrix with a sample size of Pos. low + End- Pos high Where End represents the measured spectral length, this combined data is defined as .
[0117] The spectra at 26.645 °C and 27.989 °C were set as low-temperature and high-temperature reference standards, respectively. The matching algorithm proposed in this invention was used to generate continuously distributed full-spectrum data within this temperature range. To evaluate the consistency of the full spectrum with the steady-state spectral extension, the spectra at three temperature points (27.787 °C, 27.389 °C, and 26.818 °C) were selected as the true reference values and compared with the spectra predicted by the algorithm at the corresponding temperatures. Calculations show that the coefficient of determination R between the three and the measured spectra is consistent. 2 The values were 0.958, 0.929, and 0.844, respectively, indicating that the generated spectra had high fitting accuracy. Figure 4 The spectrum at 27.787 ℃ is compared with the spectrum obtained from the expanded dataset.
[0118] Step 3: Drift spectrum segmentation: The acquired drift spectrum is divided into multiple segments according to the time series, and each segment represents a state within a short period of time.
[0119] The acquired spectral data was divided into multiple segments of equal length, using a pre-defined number of data points as the step size. When the number of points in each segment is small enough, the sensor can be considered to be in a stable state within each segment's spectrum. The experiment used a step size of 20 for the spectrum, meaning each segment consisted of 20 data points.
[0120] Step 4: Fitting the dynamic characteristics of spectral data based on Gaussian process regression.
[0121] By inputting the overall change data of the spectral data of the highest and lowest temperatures obtained in step 2 into the statistical model, the dynamic characteristics of the spectrum can be fitted. This invention considers using the Gaussian process regression (GPR) algorithm as the basic model support to achieve dynamic fitting of the spectral data. Figure 5 This is a flowchart for spectral analysis using a Gaussian process regression model. The GPR model is as follows:
[0122] (7)
[0123] in, and These are the model's output and input, respectively. This indicates a mean of 0. Gaussian noise with variance.
[0124] The output of GPR is the mean and variance of the Gaussian distribution corresponding to the relevant output samples, as shown in equation (7). This is a Gaussian process (GP), which can be represented as:
[0125] (8)
[0126] in, This represents the mean of the Gaussian process, while This represents the covariance of the Gaussian process. In This indicates another set of inputs.
[0127] Using the Gaussian process regression algorithm, the differences between different inputs can be represented by covariance. In this invention, a Gaussian kernel function will be used to calculate the covariance. Now, considering a training set... The input is The output is Therefore, according to the principle of marginal distribution, when given a new input... Then, a new output needs to be predicted. This is equivalent to calculating a given value in a joint distribution. The marginal conditional distributions are shown below, including the joint distribution and the corresponding kernel function:
[0128] (9)
[0129] in, Represents a unit diagonal matrix. and This represents the hyperparameters of the kernel function. Indicated by and Composed of samples , The parameters of the kernel function, constructed as input, can be estimated based on the maximum likelihood principle. Therefore, we can now assume that the hyperparameters of the kernel function are known, and correspondingly... The predicted distribution can be calculated using the following formula:
[0130] (10)
[0131] in, Features corresponding to wavelengths in the data are used as input features, while features corresponding to spectral intensities are used as output features.
[0132] Step 5: Perform spectral reconstruction on the spectra at different temperatures.
[0133] (5.1) Conversion of initial wavelength values for spectral data: The characteristics of spectral data shift linearly with temperature changes. Therefore, the conversion ratio between the wavelength range of the spectrum and temperature can be calculated using the following formula:
[0134] (11)
[0135] in, This indicates the temperature at which the spectrum to be restored is located. Specifically, it was 26.645℃. Specifically, it was 27.989℃. Specifically, it is 1520nm. Specifically, it is 1610nm, and This represents the initial value of the spectral wavelength corresponding to this temperature.
[0136] (5.2) Spectral characteristic prediction: Based on the initial wavelength value obtained by conversion, the wavelength is input into the GPR model fitted in step 4 to obtain the spectral intensity value at the corresponding wavelength.
[0137] Figure 6 , Figure 7 These are the spectral graphs and three-dimensional visualizations of the heating process within cycle 1, respectively. The data units for the curves in the graphs are in °C. Figure 6 It can be seen that the multiple temperature changes within cycle 1 were accurately identified, and the spectral shift pattern is correct. From Figure 7The shift in the position of the right-hand trough is visually apparent; as the scanning time increases, the spectrum undergoes a redshift (i.e., a rightward shift). In cycle 1 of the drift spectrum, with a step size of 20 and a matching accuracy of 0.002 ℃, the fluctuation range of the restored result is 0.001 ℃, the matching accuracy is 100%, and the matching error is less than 0.003. This demonstrates that the algorithm accurately identifies the drift occurring within cycle 1.
[0138] Figure 8 This is the spectrum after the cooling process in cycle 2 is broken down. The curves in the graph correspond to data units in °C. In cycle 2, the drift spectrum was reconstructed with a step size of 20 and an accuracy of 0.002 °C. The fluctuation range is consistent with that determined in cycle 1, with a matching accuracy of 100% and a matching error of less than 0.003. This indicates that the algorithm accurately identifies drift phenomena occurring in cycle 2 with larger temperature changes compared to cycle 1.
[0139] Experimental results show that the method of the present invention can still achieve high-precision temperature reconstruction under the condition of a small number of labeled samples, with a matching accuracy of 100%, a matching error of less than 0.003, and a recognition accuracy greater than the mean absolute error of less than 0.002°C.
[0140] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A dynamic process monitoring method for drift spectral analysis, characterized in that, Includes the following steps: (1) Acquire raw spectral data of the dynamic process through fiber optic sensors and perform data preprocessing; (2) The preprocessed spectral data is augmented based on point cloud matching; (3) Divide the preprocessed spectral data into multiple segments according to the preset number of data points; (4) Dynamic fitting of spectral data is achieved based on Gaussian process regression algorithm to obtain a well-fitted GPR model; (5) Perform spectral reconstruction on the spectra at different temperatures.
2. The dynamic process monitoring method for drift spectral analysis according to claim 1, characterized in that, The implementation process of step (1) is as follows: The raw spectral data is processed based on the Savitzky-Golay filtering algorithm. For one-dimensional spectral data, the filtering calculation is expressed as follows: (1) in, It is the output value after filtering the j-th data point. It is the (j+h)th original data point, and k is the half-width of the filter window. These are the convolution coefficients. ; Compensation for optical path length is performed based on Beer-Lambert's law: (2) in, Absorbance The molar absorptivity is 1. It is the concentration of the analyte. It is the optical path length. The incident light intensity Intensity of transmitted light; Compensated absorbance The calculation formula is: (3) in, This is the absorbance measurement value. For optical path reference length, It is the actual optical path length measured.
3. The dynamic process monitoring method for drift spectral analysis according to claim 1, characterized in that, The implementation process of step (2) is as follows: (21) Obtain historical data: Obtain I available historical data of the spectrum at different temperatures, and the wavelength of each historical data can be discretized into J values; then describe each of the I spectral data into a two-column matrix. ; (22) Determine the transfer characteristics of spectral data: transfer the spectral data with the highest temperature. Spectral data with minimum temperature Perform similarity assessments and identify transition characteristics between the two sets of data; (23) Assembling critical spectral data: Based on the transfer matrix and translation matrix obtained in step (22), the critical spectral data can be spliced together. and One set of data is transferred to another set of data, thereby merging the maximum and minimum temperature spectral data to obtain the dynamic range of the overall temperature spectral data.
4. The dynamic process monitoring method for drift spectral analysis according to claim 3, characterized in that, The implementation process of step (22) is as follows: Point cloud matching is used to obtain the similarity mapping matrix R and the translation difference matrix T between the two sets of data. The point cloud matching algorithm is specifically as follows: finding a mapping matrix R and a difference T that minimizes the distance between the two sets of data. (4) The above formula can be transformed into the following process: (5) Where t represents the translation value in matrix T corresponding to that sample; and Representing the i-th and Data, and Then they represent and The mean of the data; then, the partial derivatives of R and t in equation (4) are obtained to solve for the corresponding rotation and translation matrices.
5. A dynamic process monitoring method for drift spectral analysis according to claim 3, characterized in that, The implementation process of step (23) is as follows: (231) Data transfer: Based on the R and T matrices, and using the following formula, the data can be transferred. To data Transfer: (6) in, The data after the transfer; (232) Finding similar data segments and combination points: and The overlapping data portions are integrated, and then the discarded data is augmented; the specific implementation process is as follows: S1: Prepare the data, and denote the spectrum with the lowest temperature as X. low The spectrum with the highest temperature is X. high The sliding window length is len, the sliding step size is s, the spectral length is L, and the initial error min error is set to infinity. S2: i is the starting position of the sliding window, with i=0 as the starting marker and i=L-len as the ending marker; S3: Traverse X with step size s. low For each possible starting position i of the sliding window, extract the sliding window segment S. low = X low [i, i+ len], after completing the above steps, i=i+s; S4: j is the starting position of the sliding window, with j=0 as the starting marker and j=L-len as the ending marker; S5: Traverse X with step size s. high For each possible starting position j of the sliding window, extract the sliding window segment S. high =X high [j, j+ len]; S6: Compare sub-segments S based on step (22) low and S high The similarity is used to obtain the fitting error E; S7: If E is less than min error, update min error = E and record the starting position Pos of the similar segment in the lowest temperature spectrum. low = i, the starting position Pos of the similar segment in the highest temperature spectrum. high =j, after completing the above steps, j = j + s; S8: After completing all i and j iterations, output the final result Pos. low Pos high and fitting error E; The data is obtained based on steps S1 to S8. and The spectral wavelength should be labeled 0-Pos low and Pos high -Combination augmentation is performed at the End, resulting in a matrix with a sample size of Pos. low + End- Pos high Where End represents the measured spectral length, this combined data is defined as .
6. The dynamic process monitoring method for drift spectral analysis according to claim 1, characterized in that, The lengths of the multiple sub-segments in step (3) are equal.
7. The dynamic process monitoring method for drift spectral analysis according to claim 1, characterized in that, The implementation process of step (4) is as follows: The Gaussian Process Regression (GPR) algorithm is used as the basic model to achieve dynamic fitting of spectral data; the GPR model is as follows: (7) in, and These are the output and input of the GPR model, respectively. This indicates a mean of 0. Gaussian noise of variance; The output of GPR is the mean and variance of the Gaussian distribution corresponding to the output sample. This is a Gaussian process, which is represented as: (8) in, This represents the mean of the Gaussian process, while This represents the covariance of the Gaussian process. In This represents another set of inputs; The differences between different inputs are represented by covariance, which is calculated using a Gaussian kernel function; now, if we consider a training set... The input is The output is According to the principle of marginal distribution, when a new input is given... Then, a new output needs to be predicted. This is equivalent to calculating a given value in a joint distribution. The marginal conditional distributions are shown below, including the joint distribution and the corresponding kernel function: (9) in, Represents a unit diagonal matrix. and Represents the hyperparameters of the kernel function; Indicates and Composed of samples , The kernel function matrix is constructed as input, and the parameters of the kernel function are estimated based on the maximum likelihood principle; assuming that the hyperparameters of the kernel function are known, the corresponding... The predicted distribution is calculated using the following formula: (10) in, Features corresponding to wavelengths in the data are used as input features, while features corresponding to spectral intensities are used as output features.
8. The dynamic process monitoring method for drift spectral analysis according to claim 1, characterized in that, The implementation process of step (5) is as follows: (51) The conversion ratio between the wavelength range of the corresponding spectrum and temperature is calculated according to the following formula: (11) in, This indicates the temperature at which the spectrum to be restored is located. This represents the lower bound of the spectral temperature considered during modeling. This represents the upper bound of the spectral temperature considered during modeling. This represents the minimum wavelength of the spectrum at the critical temperature. This represents the maximum wavelength of the spectrum at the upper limit of the spectral temperature, while This represents the initial value of the spectral wavelength corresponding to this temperature; (52) Based on the initial wavelength value obtained by conversion, the wavelength can be input into the fitted GPR model to obtain the spectral intensity value at the corresponding wavelength. (53) Process visualization: Combine the reconstructed parameters in chronological order to generate dynamic process change curves or three-dimensional maps to achieve process visualization.