Boiler wall temperature measuring method based on PSO-BiLSTM

Abstract

The invention discloses a boiler wall temperature measuring method based on PSO-BiLSTM, and belongs to the field of boiler safety monitoring. According to the method, the pipe outer wall temperature and the air outlet temperature are collected, after preprocessing of moving average filtering, wavelet noise reduction and the like, a PSO algorithm is used for optimizing BiLSTM model hyper-parameters, a Fourier heat transfer equation and BiLSTM output inversion oxide skin thickness are fused, the inner wall temperature is corrected through nonlinear compensation, and incremental learning is carried out through ultrasonic thickness measurement data. According to the method, the wall temperature prediction precision is improved, the model adaptability is enhanced, the system cost and complexity are reduced, and an effective scheme is provided for boiler safety monitoring.

Description

Technical Field

[0001] This invention relates to the field of boiler safety monitoring technology, and in particular to a boiler wall temperature measurement method based on PSO-BiLSTM. Background Technology

[0002] In recent years, with the widespread application of supercritical (SC) and ultra-supercritical (USC) thermal power generating units, the problem of oxide scale accumulation in high-temperature boiler pipes has become increasingly prominent. Oxide scale (mainly composed of Fe3O4 and Cr2O3) gradually thickens and detaches under high-temperature steam conditions, not only leading to thinner pipe walls and increased thermal resistance, but also potentially clogging pipes or entering the turbine with steam, causing blade erosion and triggering serious safety accidents. Traditionally, boiler pipe oxide scale detection mainly relies on offline methods during shutdown maintenance, such as ultrasonic thickness measurement, magnetic detection, or X-ray imaging. However, these methods have significant drawbacks. For example, ultrasonic detection requires direct contact with the pipe surface and relies on the echo signal at the interface between the pipe wall and the oxide scale. However, the acoustic impedance difference between the oxide scale and the substrate is small, resulting in low signal resolution, and the sensor is easily damaged under high-temperature conditions, making online monitoring impossible. Another example is magnetic detection: it indirectly assesses oxide scale thickness by measuring changes in the external magnetic field of paramagnetic austenitic steel pipes, but its measurement stability is poor due to factors such as uneven magnetization of the pipe material and environmental electromagnetic interference.

[0003] Although foreign attempts have attempted to use PAC (Process Acoustic Detection) systems to assess oxide scale movement through vibration signals, the high-temperature, high-pressure steam environment places stringent demands on sensor tolerance, resulting in probe lifespans typically less than six months and limited installation locations (only monitoring straight pipe sections). A domestic power plant application case shows that the PAC system has a false alarm rate as high as 30%, limiting its practicality. Furthermore, while the support vector machine-based modeling method for predicting oxide scale accumulation in DC boiler pipes performs well in sample predictions, its performance is highly dependent on the selection of the penalty factor C and the kernel function parameter g. Traditional methods determine parameters through cross-validation or empirical formulas, lacking global optimization capabilities. Summary of the Invention

[0004] To address the above problems, this invention provides a boiler wall temperature measurement method based on PSO-BiLSTM, which aims to combine the advantages of particle swarm optimization algorithm and bidirectional long short-term memory network to significantly improve the efficiency of boiler safety monitoring.

[0005] The specific solution of the present invention is as follows: The boiler wall temperature measurement method based on PSO-BiLSTM includes the following steps: S1 collects the temperature of the outer wall of the superheated pipe of the DC boiler and the temperature of the outlet of the gas, and realizes real-time communication between the sensor and the edge computing terminal through the Modbus protocol. S2, preprocess the collected data, including moving average filtering, wavelet denoising and outlier processing, to obtain normalized data; S3, the Bidirectional Long Short-Term Memory (BiLSTM) network model is optimized and trained using the Particle Swarm Optimization (PSO) algorithm to minimize the mean square error; S4. Wall temperature is predicted based on oxide scale thickness inversion and nonlinear compensation of inner wall temperature.

[0006] Furthermore, S2 specifically includes: S21, Perform a moving average filter on the data to smooth out transient noise caused by pipe vibration or electromagnetic interference; S22 uses wavelet packet transform to perform multi-scale decomposition of the signal, extracting low-frequency effective cost and removing high-frequency noise; S23, outlier processing is performed based on the 3σ criterion, removing data points that deviate from the mean ± 3 times the standard deviation, short-term missing values ​​are filled by linear interpolation, and long-term missing values ​​trigger the sensor self-test program and record the fault log. S24, a segmented mapping strategy is used to normalize the data, mapping the outer wall temperature and the outlet temperature to the interval [-1, 1] respectively.

[0007] Preprocessing steps such as moving average filtering, wavelet denoising, and outlier handling effectively eliminate noise interference caused by factors such as pipeline vibration and electromagnetic interference, improving data reliability. Specifically, moving average filtering smooths instantaneous noise, wavelet packet transform removes high-frequency interference, the 3σ criterion and interpolation strategy ensure data integrity, and piecewise mapping normalization unifies the data scale, providing high-quality input for subsequent BiLSTM model training. This significantly reduces prediction bias caused by data noise and improves wall temperature prediction accuracy.

[0008] Furthermore, S22 specifically includes: S221, perform wavelet decomposition on the signal to obtain the coefficients of each layer; S222, perform soft thresholding on the detail coefficients of the 5th layer; S223 reconstructs the signal and removes high-frequency noise.

[0009] The soft thresholding of the level 5 detail coefficients in wavelet denoising accurately removes high-frequency noise components while preserving effective low-frequency features in the signal. This operation avoids the signal distortion caused by hard thresholding, achieving a balance between noise suppression and signal fidelity through a soft thresholding strategy of 0.5×σ. The reconstructed signal more accurately reflects temperature change trends, providing a more reliable data foundation for oxide scale thickness inversion, thereby improving the model's ability to capture temperature hysteresis effects.

[0010] Furthermore, the BiLSTM network structure includes an input layer, a bidirectional LSTM hidden layer, and a fully connected output layer: The input layer receives timing window data, which includes normalized sequences of pipe outer wall temperature and outlet temperature. The bidirectional LSTM hidden layer consists of two independent LSTM units, which extract temporal features from the forward and backward directions respectively. The information flow is dynamically adjusted through a gating mechanism to capture the temperature hysteresis effect caused by oxide thickening. The fully connected output layer maps the LSTM output to the oxide thickness and corrects the inner wall temperature.

[0011] The BiLSTM network employs a bidirectional LSTM hidden layer structure, simultaneously extracting temporal features through forward and backward LSTM units. This allows for a comprehensive capture of the time dependence and hysteresis effects of temperature changes during oxide scale thickening. A gate mechanism dynamically adjusts the information flow, effectively filtering redundant information and focusing on key temperature features. Fully connected layers map temporal features to oxide scale thickness and inner wall temperature, combining ReLU and linear activation functions to balance nonlinear modeling capability and numerical stability, enabling the model to accurately characterize the complex mapping relationship between oxide scale thickness and the temperature field.

[0012] Furthermore, S3 specifically includes: S31, initialize the population size, each particle encodes three parameters, including the number of hidden layer nodes, learning rate and dropout rate; S32, construct a BiLSTM model with each set of parameters, train it based on preprocessed temperature data, and calculate the mean square error (MSE) between the predicted and actual values ​​as the fitness. S33 iteratively updates the velocity and position of each particle until the iteration termination condition is met, and outputs the globally optimal parameters.

[0013] The PSO algorithm is used to globally optimize the hyperparameters of BiLSTM. By initializing the population size and iteratively updating particle positions and velocities, the optimal combination of hidden layer nodes, learning rate, and dropout rate can be quickly searched. This process uses mean squared error as the fitness function, avoiding the blindness of traditional empirical parameter tuning and effectively solving the problem of BiLSTM easily getting trapped in local optima. The optimized model exhibits significantly enhanced generalization ability, higher adaptability to temperature data under different operating conditions, and can maintain stable prediction accuracy over a long period.

[0014] Furthermore, S4 specifically includes: S41, Calculate the initial oxide scale thickness based on the Fourier heat transfer equation; S42, input the real-time data sequence into the PSO-BiLSTM model, output the predicted oxide scale thickness, and dynamically update the equivalent thermal conductivity; S43, when the predicted oxide scale thickness is greater than the preset threshold, a nonlinear compensation term is introduced, and the corrected inner wall temperature is calculated based on the nonlinear compensation term.

[0015] This invention integrates a physical model with a data-driven mechanism for oxide scale thickness inversion and inner wall temperature compensation. The initial thickness is calculated using the Fourier heat transfer equation, and combined with BiLSTM dynamic prediction and nonlinear compensation, it leverages the advantages of both theoretical derivation and data fitting. When the predicted thickness exceeds a threshold, the nonlinear compensation term quantifies the nonlinear impact of oxide scale thickening on wall temperature. The corrected predicted inner wall temperature more closely approximates actual operating conditions, effectively addressing the prediction bias caused by nonlinear heat transfer of oxide scale in traditional physical models.

[0016] Furthermore, S41 specifically uses the following formula to calculate the initial oxide scale thickness: ; ; in, Indicates the equivalent thermal conductivity; Indicates the initial oxide scale thickness; T inner Indicates the temperature of the inner wall of the pipe; T outer Indicates the temperature of the outer wall of the pipe; q represents heat flux density; Indicates the flow rate of the working fluid; c p Indicates the specific heat capacity of the working fluid; T outlet Indicates the outlet temperature; T inlet Indicates the inlet temperature; A represents the cross-sectional area of ​​the pipe.

[0017] Furthermore, the method also includes: measuring the oxide scale thickness using an ultrasonic thickness gauge and feeding the measured data back to the model for incremental learning.

[0018] Incremental learning is performed using measured data from an ultrasonic thickness gauge. Through periodic verification and a sliding window update mechanism, the model can adapt to dynamic changes in oxide scale thickness in real time. When the continuous prediction error exceeds the limit, automatic weight fine-tuning and training set updates are triggered, freezing some network parameters and reducing the learning rate. This avoids overfitting while ensuring long-term tracking of oxide scale growth trends. This mechanism reduces manual intervention costs, improves system adaptability, and continuously optimizes wall temperature prediction accuracy over time.

[0019] Compared with existing technologies, the advantages of this invention are: significantly improved accuracy, efficiency, and reliability in monitoring boiler superheater oxide scale thickness and wall temperature. By integrating a physical heat transfer model with a bidirectional long short-term memory network (BiLSTM) and dynamically adjusting network parameters using a particle swarm optimization (PSO) algorithm, the problems of traditional methods—reliance on multiple sensors, high hardware costs, and poor dynamic adaptability—are effectively solved. High-precision prediction can be achieved using only tube outer wall temperature and outlet temperature data, greatly simplifying the system architecture and reducing deployment and maintenance costs. The bidirectional time-series modeling capability of the BiLSTM network accurately captures temperature change patterns, while PSO global optimization avoids local optima, enhancing the model's adaptability to complex operating conditions such as oxide scale thickening. Nonlinear compensation mechanisms and dynamic threshold correction further eliminate heat transfer deviations, and a graded alarm system provides real-time warnings of over-limit risks, preventing tube rupture accidents. In addition, periodic ultrasonic calibration and incremental learning functions ensure long-term model stability, reducing the need for manual intervention. The overall solution balances safety and economy, is suitable for supercritical units, and provides reliable support for efficient boiler operation and lifespan management. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this drawing or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this drawing. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0021] Figure 1 This is a flowchart of the method of the present invention; Figure 2 The flowchart shows the optimization process for the PSO-BiLSTM model. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described and illustrated below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. All other embodiments obtained by those skilled in the art based on the embodiments provided by this invention without inventive effort are within the scope of protection of this invention.

[0023] like Figure 1 As shown, this invention provides a boiler wall temperature measurement method based on PSO-BiLSTM, including the following steps: S1 collects the temperature of the outer wall of the superheated pipe of the DC boiler and the temperature of the outlet, and realizes real-time communication between the sensor and the edge computing terminal through the Modbus protocol.

[0024] Specifically, sensors are used to detect the temperature of the outer wall of the superheated pipes of the DC boiler and the temperature of the outlet. The detected data is transmitted to the edge computing terminal via the Modbus / TCP protocol.

[0025] S2 preprocesses the collected data, including moving average filtering, wavelet denoising, and outlier handling, to obtain normalized data. Specifically, this includes the following: Applying a moving average filter to the data can effectively smooth out transient noise caused by pipeline vibration or electromagnetic interference.

[0026] Wavelet packet transform is used to perform multi-scale decomposition of the signal, extracting low-frequency effective cost and removing high-frequency noise, specifically including: The signal is decomposed into wavelet coefficients to obtain the coefficients of each layer; The detail coefficients of the 5th layer are subjected to soft thresholding, with threshold = 0.5 × σ, where σ is the noise standard deviation; Reconstruct the signal and remove high-frequency noise.

[0027] Outlier handling is performed based on the 3σ criterion, removing data points that deviate from the mean by ±3 standard deviations. Short-term missing values ​​are filled by linear interpolation, while long-term missing values ​​trigger the sensor self-test program and record the fault log.

[0028] A segmented mapping strategy is used for data normalization, mapping the outer wall temperature and the outlet temperature to the interval [-1, 1], respectively. The specific formula is as follows: ; Where x represents the raw data, including the temperature of the outer wall of the pipe and the temperature of the outlet; This represents the normalized data; This represents the minimum value in the original data; This represents the maximum value in the original data.

[0029] S3 optimizes the training of the Bidirectional Long Short-Term Memory (BiLSTM) network model using the Particle Swarm Optimization (PSO) algorithm to minimize the mean squared error.

[0030] The BiLSTM network architecture is designed as an input layer, a bidirectional LSTM hidden layer, and a fully connected output layer: The input layer receives timing window data with a length of 10 seconds, including the normalized outer wall temperature T of the tube. outer and outlet temperature T outlet sequence.

[0031] The bidirectional LSTM layer consists of two independent LSTM units, which extract temporal features from the forward and backward directions respectively. Each layer has 64 hidden nodes. The information flow is dynamically adjusted through forget gate, input gate and output gate mechanisms to capture the temperature hysteresis effect caused by oxide thickening.

[0032] The fully connected layer maps the LSTM output to the oxide thickness δ and the corrected inner wall temperature T. inner_final The hidden layer activation function is ReLU, and the output layer activation function is a linear function, balancing nonlinear modeling and numerical stability.

[0033] To optimize model hyperparameters, the Particle Swarm Optimization (PSO) algorithm is introduced for global search, such as... Figure 2 As shown. The PSO initial population size is 50, and each particle encodes three parameters, including the number of hidden layer nodes, learning rate, and dropout rate. The inertia weight is linearly reduced from the initial value of 0.9 to 0.4, the acceleration factor is set to c1=c2=2.0, and the fitness function uses mean squared error (MSE), calculated as follows: ; Where n represents the number of samples; Indicates the model's predicted value; Represents the actual label value; MSE stands for Mean Square Error.

[0034] The velocity and position of each particle are iteratively updated until the iteration termination condition is met, and the globally optimal parameters are output.

[0035] Specifically, during the iteration process, the particle determines its optimal position P based on its individual position. best and the global optimal position g best Update position and velocity using the following formula: ; ; in, For the updated speed; The updated position; Current speed; Current position; w represents the inertia weight; c1 and c2 are acceleration factors; r1 and r2 are random numbers in the interval [0, 1].

[0036] Convergence criterion: The process terminates when the MSE change rate is less than 1% after 100 iterations or 10 consecutive iterations, and the optimal parameters are output.

[0037] S4. Wall temperature is predicted based on oxide scale thickness inversion and nonlinear compensation of inner wall temperature.

[0038] S41, the initial oxide scale thickness is calculated based on the Fourier heat transfer equation, and the specific formula is as follows: ; ; in, Indicates the equivalent thermal conductivity; Indicates the initial oxide scale thickness; T inner Indicates the temperature of the inner wall of the pipe; T outer Indicates the temperature of the outer wall of the pipe; q represents heat flux density; Indicates the flow rate of the working fluid; c p Indicates the specific heat capacity of the working fluid; T outlet Indicates the outlet temperature; T inlet Indicates the inlet temperature; A represents the cross-sectional area of ​​the pipe.

[0039] S42, input the real-time data sequence into the PSO-BiLSTM model, and output the predicted oxide scale thickness δ. pred And dynamically update the equivalent thermal conductivity λ oxide .

[0040] Model prediction: The real-time pipe outer wall temperature sequence and outlet temperature sequence, preprocessed by moving average filtering and wavelet denoising, are input into the trained PSO-BiLSTM model. The model utilizes its bidirectional temporal feature extraction capability to output the predicted oxide scale thickness δ at the current moment. pred .

[0041] Equivalent thermal conductivity inversion: Equivalent thermal conductivity of oxide scale It is not fixed; it varies with the composition, structure, and thickness of the oxide scale. Traditional methods treat it as a constant, leading to accumulated errors. This invention, based on Fourier's heat transfer law, utilizes a PSO-BiLSTM model to predict δ in real time, providing a more accurate value. pred Dynamic inversion The calculation formula is as follows: .

[0042] Parameter closed-loop correction: update the parameters obtained from the inversion in this period. The initial oxide scale thickness is stored and used for calculation in the next computation cycle. This constitutes a closed-loop correction system of "data-driven prediction, physical parameter update, and physical model correction". In this way, the model can adaptively capture the changes in thermal conductivity during oxide scale growth, ensuring that the physical model part based on the Fourier equation always maintains high accuracy, thus complementing the BiLSTM data model.

[0043] S43, When the predicted oxide scale thickness is greater than a preset threshold, a nonlinear compensation term is introduced. : ; in, This is a preset threshold for the thickness of the oxide layer; k is the compensation coefficient.

[0044] The corrected inner wall temperature is calculated based on this nonlinear compensation term: .

[0045] The oxide scale thickness is measured every 24 hours using an ultrasonic thickness gauge (Olympus 38DL), and the measured data is fed back to the model for incremental learning. If the prediction error exceeds 5% for 5 consecutive times, the weight update process is automatically triggered: the parameters of the first two layers of BiLSTM are frozen, only the fully connected layer is fine-tuned, the learning rate is reduced to 10% of the initial value, and the training set uses a sliding window to retain the latest 200 sets of samples to ensure that the model adapts to changes in working conditions.

[0046] To facilitate understanding, a specific example is used below to illustrate part of the calculation process. Assume the collected data for the superheated pipes of a once-through boiler are as follows: working fluid flow rate is 0.5 kg / s, pipe cross-sectional area A = 0.01 m². 2 The specific heat capacity of the working fluid is 4.18 kJ / (kg·℃), the outlet temperature is 400℃, and the inlet temperature is 350℃.

[0047] According to Fourier's heat transfer equation, the formula for calculating heat flux density is: ; Substituting the data: q = 0.5 × 4.18 × (400 - 350) / 0.01 = 10450 kW / m 2 .

[0048] Assuming an equivalent thermal conductivity of 1.5 kW / (m·℃), an inner wall temperature of 500℃, and an outer wall temperature of 450℃, the formula for calculating the initial oxide scale thickness is as follows: ; Substituting the data, the initial oxide scale thickness is calculated to be: 1.5×(500-450) / 10450=7.2mm.

[0049] Before the initial deployment of the model, normal operating data of the boiler under typical load range (e.g., 50%~100% rated load) for at least one month was collected. Statistical analysis was performed on the collected data of pipe outer wall temperature and outlet temperature, and the minimum statistical value was taken as x. min Set the temperature to 480℃, and record the maximum value as x. max Let 520℃ be the initial normalized scale, and the current measured temperature of the pipe's outer wall be 500℃. ; X norm =2×[(500-480) / (520-480)]-1=0; After normalization, the temperature of the outer wall of the tube is 0.

[0050] The preprocessed data is input into the PSO-BiLSTM model, and the predicted oxide scale thickness is 8 mm. With a preset threshold of 7.5 mm, a nonlinear compensation term ΔT is introduced: ; Corrected inner wall temperature T inner-final The calculation formula is: T inner-final= T inner +ΔT=500+0.025=500.025.

[0051] This example demonstrates the complete process from data acquisition, preprocessing, physical model calculation to model prediction and compensation. In practical applications, parameters need to be dynamically adjusted based on real-time data.

[0052] It should be noted that the present invention is not limited to the above-described embodiments. The above embodiments are merely examples, and any embodiments that have the same structure and perform the same effects as the technical concept within the scope of the present invention are included within the scope of the present invention. Furthermore, various modifications that can be conceived by those skilled in the art to the embodiments, and other ways of constructing by combining some of the constituent elements of the embodiments, without departing from the spirit of the present invention, are also included within the scope of the present invention.

Claims

1. A method for boiler wall temperature measurement based on PSO-BiLSTM, characterized in that, The method comprises the following steps: S1, collecting the outer wall temperature of the superheater pipe of the once-through boiler and the outlet temperature, and realizing real-time communication between the sensor and the edge computing terminal through the Modbus protocol; S2, preprocessing the collected data, including sliding average filtering, wavelet denoising and outlier processing, to obtain normalized data; S3, optimizing and training the bidirectional long short-term memory network (BiLSTM) model through the particle swarm optimization (PSO) algorithm to minimize the mean square error; S4, predicting the wall temperature according to the oxide scale thickness inversion and the nonlinear compensation of the inner wall temperature. 2.The PSO-BiLSTM based boiler wall temperature measurement method of claim 1, wherein, The S2 specifically comprises: S21, performing sliding average filtering on the data to smooth the transient noise caused by pipe vibration or electromagnetic interference; S22, performing multi-scale decomposition on the signal by using wavelet packet transform, extracting low-frequency effective cost and eliminating high-frequency noise; S23, performing outlier processing based on the 3σ criterion, eliminating data points deviating from the mean value by ±3 times the standard deviation, filling short-time missing values by linear interpolation, and triggering the sensor self-checking program and recording fault logs for long-time missing; S24, normalizing the data by using the piecewise mapping strategy, and mapping the outer wall temperature and the outlet temperature to the interval [-1, 1]. 3.The PSO-BiLSTM based boiler wall temperature measurement method of claim 1, wherein, The S22 specifically comprises: S221, performing wavelet decomposition on the signal to obtain the coefficients of each layer; S222, performing soft threshold processing on the 5th layer detail coefficients; S223, reconstructing the signal to remove high-frequency noise. 4.The PSO-BiLSTM based boiler wall temperature measurement method of claim 1, wherein, The BiLSTM network structure comprises an input layer, a bidirectional LSTM hidden layer and a fully connected output layer: The input layer receives the time window data, including the normalized outer wall temperature and outlet temperature sequence; The bidirectional LSTM hidden layer is composed of two independent LSTM units, which extract time sequence features from the forward and backward directions respectively, dynamically adjust the information flow through the gate mechanism, and capture the temperature lag effect caused by the thickening of the oxide scale; The fully connected output layer maps the LSTM output to the oxide scale thickness and the corrected inner wall temperature. 5.The PSO-BiLSTM based boiler wall temperature measurement method of claim 1, wherein, The S3 specifically comprises: S31, initializing the population size, and encoding three parameters for each particle, including the number of hidden layer nodes, the learning rate and the dropout rate; S32, constructing the BiLSTM model with each set of parameters, training based on the preprocessed temperature data, and calculating the mean square error (MSE) between the predicted value and the actual value as the fitness; S33, iteratively updating the speed and position of each particle until the iteration termination condition is met, and outputting the global optimal parameters. 6.The PSO-BiLSTM based boiler wall temperature measurement method of claim 1, wherein, The S4 specifically comprises: S41, calculating the initial oxide scale thickness based on the Fourier heat equation; S42, inputting the real-time data sequence into the PSO-BiLSTM model to output the predicted oxide scale thickness, and dynamically updating the equivalent thermal conductivity; S43, when the predicted oxide scale thickness is greater than a preset threshold, introducing a nonlinear compensation term, and calculating the corrected inner wall temperature based on the nonlinear compensation term.

7. The PSO-BiLSTM based boiler wall temperature measurement method of claim 1, wherein, The S41 specifically calculates the initial oxide scale thickness by using the following formula: ； ； wherein represents the equivalent thermal conductivity; represents the initial scale thickness; T inner represents the temperature of the inner wall of the pipe; T outer T represents the temperature of the outer wall of the pipe; q represents the heat flux density; Indicates the flow rate of the working fluid; c p Cp represents the specific heat capacity of the working fluid; T outlet Indicates the outlet temperature; T inlet represents the inlet temperature; A represents the pipe cross-sectional area.

8. The PSO-BiLSTM based boiler wall temperature measurement method of claim 1, wherein, The method further comprises: measuring the oxide scale thickness by using an ultrasonic thickness gauge, and feeding the measured data back to the model for incremental learning.

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