Flue gas waste heat recovery system optimization design method considering external parameter change

Abstract

The invention belongs to the technical field of industrial waste heat recovery, and discloses a flue gas waste heat recovery system optimization design method considering external parameter changes. The method comprises the steps of system monitoring data acquisition and feature extraction, thermodynamic modeling and parameter sensitivity analysis, external environment parameter and system performance coupling mechanism modeling, equipment failure prediction and reliability constraint determination, multi-objective optimization and self-adaptive control strategy generation and the like. Optimized operation of the flue gas waste heat recovery system under the condition of dynamic change of external environment parameters is achieved. According to the method, a dynamic influence matrix of external environment parameters and system performance is initiatively established, the reliability of the system is evaluated in combination with a stress-life analysis technology, efficiency and cost targets are balanced through a multi-target optimization algorithm, and a self-adaptive control strategy library for different working conditions is generated. The adaptability and stability of the system under complex working conditions are improved, the service life of equipment is prolonged, and the operation cost is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial waste heat recovery, and more specifically, to an optimized design method for a flue gas waste heat recovery system considering external parameter changes. Background Art

[0002] As an important technical means for industrial energy conservation and emission reduction, the flue gas waste heat recovery system is widely used in high-energy-consuming industries such as metallurgy, electric power, building materials, and chemical engineering. With the global energy shortage and increasingly strict environmental protection requirements, improving the flue gas waste heat recovery efficiency has become the key development direction of the industry. Traditional flue gas waste heat recovery technologies mainly include forms such as waste heat boilers, heat exchangers, and regenerative combustion. These technologies can achieve a certain degree of energy recovery under stable operating conditions. At present, the research on flue gas waste heat recovery systems at home and abroad mainly focuses on aspects such as the optimization of heat exchanger structures, heat transfer enhancement, and system integration.

[0003] However, the existing design methods for flue gas waste heat recovery systems are mainly based on static operating conditions and ideal conditions, and system parameters often remain fixed during the design stage. In the actual industrial environment, parameters such as flue gas temperature, composition, and flow rate fluctuate due to production processes, raw material changes, and environmental conditions. Environmental factors such as external air temperature, humidity, and atmospheric pressure also change with seasons and weather. Traditional systems are insensitive to external environmental changes and cannot effectively respond to environmental factors such as seasonal alternation, day-night temperature difference, and weather fluctuations, resulting in a significant decrease in heat exchange efficiency in low-temperature winter or high-temperature summer environments, and even problems such as condensation corrosion. At the same time, it reflects that the reliability assessment method of the system is rough, and it is difficult to accurately predict the equipment failure risk under high-temperature and high-pressure conditions, resulting in a lack of scientific basis for maintenance plans, either excessive maintenance increases costs, or insufficient maintenance leads to sudden failures. Especially in industries such as metallurgy and chemical engineering, the flue gas composition is complex and fluctuates frequently. Existing technologies cannot deeply analyze the coupling mechanism between parameters, and control strategies are often based on simplified models and empirical judgments, making it difficult to achieve precise regulation. In addition, the single efficiency optimization goal ignores the balance between system operation costs and lifespan, resulting in a contradiction between short-term benefits and long-term sustainability. In terms of data processing, interference signals and measurement errors in industrial sites often make the quality of monitoring data worrying, affecting model accuracy and control effects. In addition, the existing system has poor adaptability during the process of operating condition conversion and requires manual intervention to adjust parameters, increasing operation complexity and the risk of human errors, and cannot meet the urgent needs of modern industry for automation, intelligence, and high efficiency.

[0004] In view of this, the present invention proposes an optimized design method for a flue gas waste heat recovery system considering external parameter changes to solve the above problems. Summary of the Invention

[0005] To overcome the above-mentioned defects of the prior art and to achieve the above object, the present invention provides the following technical solution: An optimization design method for a flue gas waste heat recovery system considering external parameter changes, comprising: Step S1: Obtain the monitoring data set of the flue gas waste heat recovery system; extract the operating characteristics and process the noise of the monitoring data set to obtain the operating characteristic sequence of the flue gas system; Step S2: Perform thermodynamic modeling on the operating characteristic sequence to construct a thermal energy conversion efficiency model; analyze the parameter sensitivity based on the thermal energy conversion efficiency model to identify the key influencing factors of the system; Step S3: Collect the data of external environmental parameter changes; combine the data of external environmental parameter changes with the key influencing factors of the system to establish a system performance coupling mechanism model, and then obtain a dynamic influence matrix; Step S4: Use the dynamic influence matrix to perform stress-life analysis to establish an equipment failure prediction model; evaluate the safety margin based on the equipment failure prediction model to determine the system reliability constraint; Step S5: Based on the thermal energy conversion efficiency model and the system reliability constraint, construct a multi-objective optimization function; apply an intelligent algorithm to solve the optimal parameter combination to generate an adaptive control strategy library; Step S6: Based on the adaptive control strategy library and the dynamic influence matrix, perform predictive adjustment for external parameter changes to achieve reliable and efficient operation of the system under complex working conditions.

[0006] Technical effects and advantages of the optimization design method for a flue gas waste heat recovery system considering external parameter changes according to the present invention: The present invention improves the adaptability of the system in a variable environment, enabling it to cope with various complex working conditions and maintain an efficient operating state. By accurately predicting the life and potential failures of system components, the overall reliability and safety are greatly improved, the unexpected downtime is reduced, and the maintenance cost is lowered. The improvement of the system operation efficiency is directly translated into an increase in the energy recovery rate, while reducing resource consumption and operation cost, bringing considerable economic benefits. The intelligent predictive adjustment ability enables the system to respond to environmental changes in advance, avoiding the efficiency loss caused by the lag response of traditional systems. In addition, the system operates stably and efficiently throughout the year, is not significantly affected by seasonal climate changes, and maintains continuous performance advantages. The decision support function reduces the burden on operators and lowers the risk of human errors. In terms of environmental protection benefits, the improved energy recovery efficiency means less emissions and higher resource utilization rate, meeting the requirements of green development. In the long run, the extension of the equipment service life and the reduction of maintenance requirements reduce the total life cycle cost and improve the return on investment. Description of the Drawings

[0007] Figure 1Schematic diagram of an optimization design method for a flue gas waste heat recovery system considering external parameter changes according to the present invention; Figure 2 Schematic diagram of the detailed implementation steps of step S3 of the present invention. Detailed implementation manners

[0008] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0009] The application example provides an optimization design method for a flue gas waste heat recovery system considering external parameter changes. The execution subjects of the method include but are not limited to: general computing nodes such as mechanical equipment, data processing platforms, cloud server nodes, and network upload devices. The data processing platform includes but is not limited to at least one of an industrial process monitoring system, an energy management system, and an equipment health monitoring system.

[0010] The present invention provides an optimization design method for a flue gas waste heat recovery system considering external parameter changes, including the following steps: Step S1: Obtain the monitoring data set of the flue gas waste heat recovery system; extract the operating characteristics and process the noise of the monitoring data set to obtain the operating characteristic sequence of the flue gas system; Step S2: Perform thermodynamic modeling on the operating characteristic sequence to construct a thermal energy conversion efficiency model; analyze the parameter sensitivity based on the thermal energy conversion efficiency model to identify the key influencing factors of the system; Step S3: Collect the data of external environmental parameter changes; combine the data of external environmental parameter changes with the key influencing factors of the system to establish a system performance coupling mechanism model, and then obtain a dynamic influence matrix; Step S4: Use the dynamic influence matrix to perform stress-life analysis to establish an equipment failure prediction model; evaluate the safety margin based on the equipment failure prediction model to determine the system reliability constraint; Step S5: Based on the thermal energy conversion efficiency model and the system reliability constraint, construct a multi-objective optimization function; apply an intelligent algorithm to solve the optimal parameter combination to generate an adaptive control strategy library; Step S6: Based on the adaptive control strategy library and the dynamic influence matrix, perform predictive adjustment for external parameter changes to achieve reliable and efficient operation of the system under complex working conditions.

[0011] By processing the monitoring data of the flue gas waste heat recovery system, the present invention improves the data quality and provides a reliable data basis for subsequent analysis. By means of thermodynamic modeling and parameter sensitivity analysis, the key influencing factors of the system are identified. Combining the data of external environmental parameter changes, a system performance coupling mechanism model is established to obtain a dynamic influence matrix. Using this matrix for stress-life analysis, an equipment failure prediction model is established to determine the system reliability constraint. Based on the heat energy conversion efficiency model and the system reliability constraint, a multi-objective optimization function is constructed to generate an adaptive control strategy library. Finally, based on the control strategy library and the dynamic influence matrix, the reliable and efficient operation of the system under complex working conditions is realized.

[0012] In the embodiment of the present invention, refer to Figure 1 , which is a schematic diagram of the step flow of the optimization design method for the flue gas waste heat recovery system considering external parameter changes. In this example, the steps of the optimization design method for the flue gas waste heat recovery system considering external parameter changes include: Step S1: Obtain the monitoring data set of the flue gas waste heat recovery system; extract the working condition characteristics and process the noise of the monitoring data set to obtain the operation characteristic sequence of the flue gas system; In this embodiment, first collect the multi-source monitoring data of the flue gas waste heat recovery system, including parameters such as temperature (such as flue gas inlet temperature, outlet temperature, heat medium temperature, etc.), pressure (such as flue gas pipeline pressure, pressure difference at the inlet and outlet of the heat exchanger, etc.), flow rate (such as flue gas flow rate, heat medium flow rate, etc.) and heat exchange efficiency. These data usually come from various sensors, flow meters, thermocouples and pressure transmitters installed in the system. Process the collected original monitoring data set, including time series segmentation and outlier identification, wavelet transform noise reduction and filtering processing, principal component analysis and working condition characteristic extraction, normalization processing and time window sliding, etc., and finally obtain the operation characteristic sequence representing the dynamic operation state of the flue gas system, providing a high-quality data basis for subsequent thermodynamic modeling and parameter sensitivity analysis.

[0013] Step S2: Conduct thermodynamic modeling on the operation characteristic sequence to construct a heat energy conversion efficiency model; analyze the parameter sensitivity based on the heat energy conversion efficiency model to identify the key influencing factors of the system; In this embodiment, based on the operation characteristic sequence obtained in the previous step, use the thermodynamic principle to establish the mass conservation equation set and energy balance equation of the flue gas waste heat recovery system, and construct a heat energy conversion efficiency model. This model reflects the quantitative relationship between the input parameters (such as flue gas temperature, flow rate, composition, etc.) and output parameters (such as heat energy recovery amount, system efficiency, etc.) of the system. Then, conduct parameter sensitivity analysis on this model, and through methods such as the coefficient of variation method and variance analysis, identify the key factors that have the most significant impact on the system efficiency, such as flue gas temperature, flow rate fluctuation, fouling degree of the heat exchanger, etc. These key influencing factors will be the key considerations for subsequent system optimization.

[0014] Step S3: Collect data on changes in external environmental parameters; combine the data on changes in external environmental parameters with the key influencing factors of the system to establish a system performance coupling mechanism model, and then obtain a dynamic influence matrix; In this embodiment, an external environmental parameter monitoring network is established to collect external environmental parameters such as environmental temperature, humidity, air pressure, and seasonal changes. Time-frequency analysis is performed on these parameters to extract periodic change characteristics and trend characteristics. Correlation analysis is performed on these characteristics and the key influencing factors of the system identified in the previous step to establish a coupling mechanism model reflecting the relationship between external environmental changes and system performance. Based on this model, a system performance response function is constructed to obtain a parameter coupling relationship diagram, and through quantization processing and matrix transformation, a dynamic influence matrix is formed. This matrix reflects the dynamic influence degree of changes in external environmental parameters on the key influencing factors of the system, providing a basis for subsequent stress-life analysis and the formulation of adaptive control strategies.

[0015] Step S4: Use the dynamic influence matrix for stress-life analysis to establish an equipment failure prediction model; evaluate the safety margin based on the equipment failure prediction model to determine the system reliability constraint; In this embodiment, based on the dynamic influence matrix, the stress distribution and time series of key system components (such as heat exchangers, valves, fans, etc.) are calculated. The rain flow counting method is used to process the stress time series to obtain a stress cycle spectrum. A cumulative damage model is established in combination with the material S-N curve (stress-life curve) to obtain a damage evolution function. Monte Carlo simulation is performed on this function to establish an equipment failure prediction model that can predict the equipment failure time and probability. Based on this model, the reliability functions and distributions of each key component are calculated, and the lower limit of reliability is determined in combination with the system safety requirements, thereby determining the system reliability constraint. These constraints will serve as the boundary conditions for subsequent system optimization to ensure that the system does not sacrifice safety and reliability while pursuing high efficiency.

[0016] Step S5: Based on the thermal energy conversion efficiency model and the system reliability constraint, construct a multi-objective optimization function; apply an intelligent algorithm to solve for the optimal parameter combination to generate an adaptive control strategy library; In this embodiment, the thermal energy conversion efficiency model is transformed into an efficiency objective function (the first optimization objective), and at the same time, considering the system operation cost and resource consumption, a cost objective function (the second optimization objective) is constructed. The system reliability constraints are transformed into a set of constraint conditions, and a multi-objective optimization function is constructed by combining the two optimization objectives. The improved particle swarm optimization algorithm is applied to solve this optimization function, obtaining a series of Pareto optimal solutions, which represent the optimal balance points between efficiency and cost under different working conditions. Cluster analysis is performed on these optimal solutions, and an adaptive control strategy library is generated for different working conditions. This strategy library contains the optimal operation parameter combinations of the system under various working conditions, providing decision-making support for subsequent adaptive control.

[0017] Step S6: Based on the adaptive control strategy library and the dynamic influence matrix, perform predictive adjustment for external parameter changes to achieve reliable and efficient operation of the system under complex working conditions.

[0018] In this embodiment, a prediction model for external environmental parameter changes is established to predict external parameters (such as environmental temperature, humidity, air pressure, etc.) in the future time period. The prediction results are combined with the dynamic influence matrix to predict the change trend of system performance. Based on the prediction results, the optimal control strategy is selected from the adaptive control strategy library to obtain a preliminary set of control parameters. These parameters are dynamically adjusted and optimized to generate a real-time control instruction sequence, which is sent to the system actuators (such as control valves, frequency converters, etc.). At the same time, the system response is monitored in real time for closed-loop feedback regulation. The system continuously updates the control strategy to achieve reliable and efficient operation under complex and variable working conditions, effectively improving the waste heat recovery efficiency, reducing energy consumption, and extending the equipment life.

[0019] In this embodiment, the detailed implementation steps of step S1 include: Obtain the original monitoring data set for multi-source monitoring data such as the temperature, pressure, flow rate, and heat exchange efficiency of the flue gas waste heat recovery system; Perform time series segmentation and outlier identification on the original monitoring data set to obtain a cleaned data matrix; Perform wavelet transform denoising and filtering on the cleaned data matrix to obtain a smoothed data sequence; Perform principal component analysis and working condition feature extraction on the smoothed data sequence to obtain a working condition feature vector; Perform normalization processing and time window sliding on the working condition feature vector to obtain the operation feature sequence of the flue gas system.

[0020] In this embodiment, through the sensor network distributed at key parts of the flue gas waste heat recovery system, various parameter data during the operation of the system are collected. The temperature data include the flue gas inlet temperature (such as 400°C), the outlet temperature (such as 150°C), the heat medium inlet and outlet temperatures (such as 60°C / 90°C), the heat exchanger wall temperature (such as 250°C), etc. The pressure data include the flue gas pipeline pressure (such as 5 kPa), the pressure difference between the inlet and outlet of the heat exchanger (such as 0.8 kPa), the pressure distribution at each point of the system, etc. The flow data include the flue gas flow rate (such as 20,000 Nm³ / h), the heat medium flow rate (such as 100 m³ / h), the condensate discharge amount, etc. The heat exchange efficiency data include the heat exchanger efficiency (such as 75%), the energy recovery rate, the heat transfer coefficient, etc. These multi-source monitoring data are integrated according to the time stamp to form the original monitoring data set.

[0021] The original monitoring data set is segmented in time series according to the operating conditions, and the data is divided into different time periods such as the startup stage, the stable operation stage, the load fluctuation stage, the shutdown stage, etc. Statistical methods (such as the 3σ criterion, the box plot method, etc.) are used to identify and mark the outliers in the data, such as the data anomalies caused by sensor failures, sudden interferences, etc. The identified outliers are removed or replaced to obtain the cleaned data matrix, which contains the normal operation data of the system under different operating conditions.

[0022] The wavelet transform method is applied to the cleaned data matrix for noise reduction processing. The wavelet transform can effectively separate different frequency components in the signal, remove high-frequency noise while retaining useful information. An appropriate wavelet basis function (such as the Daubechies wavelet) and decomposition level are selected to perform wavelet decomposition on the data, and then threshold processing and reconstruction are carried out to obtain the denoised data. Filtering techniques (such as low-pass filtering, median filtering, etc.) are applied to the denoised data to further smooth the data curve, and a smoothed data sequence is obtained, which reflects the true change trend of the system parameters.

[0023] The principal component analysis (PCA) method is applied to the smoothed data sequence to reduce the data dimension and extract the main features. The mathematical expression of PCA is X' = XW, where X is the original data matrix, W is the eigenvector matrix, and X' is the feature matrix after dimension reduction. By retaining the principal components with the proportion of explained variance greater than a certain threshold (such as 95%), the feature matrix after dimension reduction is obtained. Based on this matrix and domain knowledge, operating condition features such as heat exchanger efficiency, temperature gradient, pressure fluctuation characteristics, etc. are extracted to form the operating condition feature vector.

[0024] Normalize each feature in the operating condition feature vector so that features with different dimensions and magnitudes can be effectively compared and analyzed. Common normalization methods include Min-Max normalization, Z-score standardization, etc. Apply the time window sliding technique to the normalized feature vector to extract features in the time dimension and capture the dynamic change characteristics of system parameters. Finally, obtain the operation feature sequence of the flue gas system, which contains both the static features of system parameters and reflects the dynamic characteristics of parameter changes over time.

[0025] In this embodiment, the detailed implementation steps of step S2 include: Establish a mass conservation equation set of the flue gas waste heat recovery system based on the operation feature sequence to obtain a mass transfer model; Based on the mass transfer model, establish a system energy balance equation to obtain a heat transfer model; Combine the heat transfer model with the equipment structure parameters to construct a heat transfer coefficient calculation model to obtain a preliminary thermal energy conversion efficiency model; Calibrate and verify the parameters of the preliminary thermal energy conversion efficiency model to obtain a complete thermal energy conversion efficiency model; Conduct parameter sensitivity analysis on the thermal energy conversion efficiency model through the coefficient of variation method and variance analysis to obtain a parameter sensitivity ranking table; According to the parameter sensitivity ranking table, screen out the parameters with a contribution rate exceeding the threshold to identify the key influencing factors of the system.

[0026] In this embodiment, based on parameters such as flow rate, density, and components extracted from the operation feature sequence, establish a mass conservation equation set of the flue gas waste heat recovery system. For the flue gas side, the mass conservation equation is m_g_in = m_g_out, where m_g_in and m_g_out are the mass flow rates of the flue gas inlet and outlet, respectively. For the heat medium side, the mass conservation equation is m_w_in = m_w_out, where m_w_in and m_w_out are the mass flow rates of the heat medium inlet and outlet, respectively. If the generation of condensed water is considered, the equation is modified to m_g_in = m_g_out + m_cond, where m_cond is the mass flow rate of the condensed water. Combine the component information of the flue gas and chemical reaction equilibrium to establish a component mass conservation equation. For example, for a certain component i, m_i_in = m_i_out + m_i_reacted, where m_i_reacted is the mass of component i participating in the reaction. These equations together constitute the mass transfer model of the system.

[0027] Based on the mass transfer model and the temperature data in the operating characteristic sequence, establish the energy balance equation of the system. The heat released by the flue gas \(Q_g = m_g\times c_g\times(T_{g\_in}-T_{g\_out})\), where \(c_g\) is the specific heat capacity of the flue gas, and \(T_{g\_in}\) and \(T_{g\_out}\) are the inlet and outlet temperatures of the flue gas respectively. The heat absorbed by the heat medium \(Q_w = m_w\times c_w\times(T_{w\_out}-T_{w\_in})\), where \(c_w\) is the specific heat capacity of the heat medium, and \(T_{w\_in}\) and \(T_{w\_out}\) are the inlet and outlet temperatures of the heat medium respectively. Considering the heat loss \(Q_{loss}\) of the system, the energy balance equation is \(Q_g = Q_w+Q_{loss}\). If the phase change process (such as water vapor condensation) is considered, the latent heat term \(Q_{latent}=m_{cond}\times h_{fg}\) needs to be added, where \(h_{fg}\) is the latent heat of condensation. These equations constitute the heat transfer model of the system.

[0028] Combine the heat transfer model with the structural parameters of the heat exchanger (such as heat transfer area \(A\), pipe diameter \(d\), pipe length \(L\), etc.) to construct a heat transfer coefficient calculation model. According to the heat transfer principle, the overall heat transfer coefficient \(U\) can be expressed as , where \(h_g\) and \(h_w\) are the convective heat transfer coefficients on the flue gas side and the heat medium side respectively, \(\delta\) is the thickness of the heat transfer wall, and \(\lambda\) is the thermal conductivity of the wall material. The convective heat transfer coefficient can be calculated through dimensionless criterion correlation equations, such as , where \(Nu\), \(Re\), and \(Pr\) are the Nusselt number, Reynolds number, and Prandtl number respectively, and \(C\), \(m\), and \(n\) are empirical coefficients. Combine the heat transfer coefficient and the temperature difference to calculate the heat exchange amount , where \(LMTD\) is the logarithmic mean temperature difference. The thermal energy conversion efficiency of the system . These relationships constitute a preliminary thermal energy conversion efficiency model.

[0029] Use the actual operating data to calibrate the parameters of the preliminary thermal energy conversion efficiency model. Adopt the least squares method or other optimization algorithms to adjust the unknown parameters in the model (such as empirical coefficients \(C\), \(m\), \(n\), heat loss coefficient, etc.) to minimize the error between the model prediction value and the actual observation value. The calibrated model is applied to the validation dataset to evaluate the prediction performance of the model. The validation indicators include the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (\(R^2\)), etc. If the validation result is not satisfactory, return to the calibration step to readjust the parameters. After multiple rounds of calibration and validation, a perfect model that accurately reflects the thermal energy conversion efficiency of the system is obtained.

[0030] Conduct a parameter sensitivity analysis on the perfect thermal energy conversion efficiency model to quantify the influence degree of different parameters on the model output. Adopt the coefficient of variation method to perturb each parameter \(x_i\) within its variation range and calculate the output coefficient of variation , where σi is the output standard deviation caused by the perturbation of parameter xi, and μi is the corresponding output mean. The larger the CVi value, the more significant the influence of parameter xi on the output. Using the analysis of variance method, calculate the contribution rate of each parameter to the total variance, expressed as , where Vi is the variance caused by parameter xi and V is the total variance. Sort all parameters from high to low according to sensitivity to form a parameter sensitivity ranking table.

[0031] According to the parameter sensitivity ranking table, select the parameters whose contribution rate exceeds a predetermined threshold (such as 5%). These parameters are identified as the key influencing factors of the system. The key influencing factors usually include flue gas inlet temperature, flue gas flow rate, heat medium flow rate, fouling degree of the heat exchanger, etc. These factors will be the key considerations for subsequent system optimization and control. Through sensitivity analysis, the system complexity can be reduced, focusing on the truly important parameters and improving the efficiency of optimization and control.

[0032] In the embodiment of the present invention, refer to Figure 2 , which is a schematic diagram of the detailed implementation steps of step S3. In this embodiment, the detailed implementation steps of step S3 include: Establish an external environmental parameter monitoring network, collect data such as environmental temperature, humidity, air pressure, and seasonal changes, and obtain the external environmental parameter time series; Conduct time-frequency analysis on the external environmental parameter time series to obtain periodic change characteristics and trend characteristics; Conduct correlation analysis on the periodic change characteristics and trend characteristics with the key influencing factors of the system to obtain the system performance coupling mechanism model; Based on the system performance coupling mechanism model, construct a system performance response function to obtain a parameter coupling relationship diagram; conduct quantitative processing and matrix conversion on the parameter coupling relationship diagram to form a dynamic influence matrix.

[0033] In this embodiment, environmental parameter monitoring devices are arranged around the flue gas waste heat recovery system to construct an external environmental parameter monitoring network. The environmental temperature sensor measures the surrounding air temperature, records the daily and seasonal changes, and the data range is, for example, -20°C to 40°C. The humidity sensor measures the relative humidity, with a range of, for example, 20% to 95%. The air pressure sensor measures the atmospheric pressure, with a range of, for example, 95 kPa to 105 kPa. In addition, meteorological parameters such as rainfall, wind speed, and wind direction, as well as seasonal change data, are also recorded. These sensors continuously collect data at an appropriate sampling frequency (such as once every 10 minutes) to form an external environmental parameter time series, which contains the changes of environmental parameters over time.

[0034] Perform time-frequency analysis on the time series of the collected external environmental parameters to extract the periodic and trend features therein. Use the fast Fourier transform (FFT) to analyze the spectral characteristics of the environmental parameters and identify the main periodic components, such as the daily cycle (24 hours), weekly cycle (7 days), and annual cycle (365 days), etc. Use time-frequency analysis methods such as wavelet transform to study the variation characteristics of the environmental parameters at different time scales. Adopt trend analysis methods (such as moving average, linear regression, etc.) to extract the long-term trends of the environmental parameters, such as seasonal change trends and inter-annual change trends. Represent the extracted periodic change features and trend features with a mathematical model to provide a basis for subsequent analysis.

[0035] Conduct a correlation analysis on the periodic change features and trend features of the external environmental parameters and the key influencing factors of the system identified in step S2. Calculate statistical quantities such as Pearson correlation coefficient, Spearman rank correlation coefficient, or mutual information to quantify the degree of correlation between the environmental parameter changes and the key factors of the system. Use methods such as multiple regression analysis, principal component regression, or partial least squares regression to establish a quantitative relationship model between the environmental parameters and the key factors of the system. Consider the interaction between parameters, introduce cross terms and non-linear terms to construct a more complex relationship model. Based on physical mechanisms and domain knowledge, explain the influence mechanism of environmental parameters on system performance, such as the influence of environmental temperature on heat transfer efficiency, the influence of humidity on the condensation amount, etc. Based on the above analysis, establish a system performance coupling mechanism model, which describes how the changes in external environmental parameters ultimately affect system performance by influencing the key factors of the system.

[0036] Based on the system performance coupling mechanism model, construct a system performance response function, expressed as P = f(E, S), where P is the system performance index (such as heat energy recovery efficiency), E is the external environmental parameter vector, and S is the system internal parameter vector. For different combinations of external environmental parameters and system parameters, calculate the system performance index to obtain a multi-dimensional performance response space. Visualize the response space to generate a parameter coupling relationship diagram, which shows the coupling relationship between different parameters and the comprehensive impact on system performance. The relationship diagram can be in the form of a heat map, contour map, or 3D surface map, etc., to intuitively display the complex relationship between parameters.

[0037] Quantify the parameter coupling relationship diagram, and extract the coupling strength and influence weight between parameters. Calculate the node influence strength vector, which represents the direct influence degree of each parameter node on the system performance. Calculate the edge coupling strength matrix, which represents the mutual influence strength between parameters. Construct a graph convolutional network model to simulate the propagation process of parameter influence and analyze the cascade effect of parameter changes. Conduct a time-evolution simulation on the parameter propagation model to study the dynamic influence process of external environmental parameter changes on the system performance. Finally, organize the time-varying influence coefficients into a matrix form to form the dynamic influence matrix D, where the element Dij represents the time-varying influence degree of the external environmental parameter j on the key influence factor i of the system. This matrix is the mathematical expression of the coupling relationship of the system performance and provides a basis for subsequent stress-life analysis and adaptive control.

[0038] In this embodiment, the detailed implementation steps of quantifying the parameter coupling relationship diagram and performing matrix conversion in step S3 to form the dynamic influence matrix include: Calculate the weights of the nodes in the parameter coupling relationship diagram to obtain the node influence strength vector; Evaluate the strength of the edges in the parameter coupling relationship diagram to obtain the edge coupling strength matrix; Establish a graph convolutional network based on the node influence strength vector and the edge coupling strength matrix to obtain the parameter propagation model; conduct a time-evolution simulation on the parameter propagation model to obtain the time-varying influence coefficients; Organize the time-varying influence coefficients into a matrix form according to the key influence factors of the system and the external environmental parameters to form the dynamic influence matrix.

[0039] In this embodiment, calculate the influence strength of each node (including the external environmental parameter node and the key influence factor node of the system) in the parameter coupling relationship diagram. Adopt the local sensitivity analysis method to slightly perturb each node parameter (such as ±5%) and observe the change of the system performance index, and calculate the sensitivity coefficient , where ΔP is the change amount of the performance index, P is the reference value of the performance index, Δxi is the perturbation amount of the parameter xi, and xi is the reference value of the parameter. Adopt the variance contribution analysis method to calculate the contribution ratio of each node parameter to the total variance of the system performance. Considering the sensitivity coefficient and the variance contribution comprehensively, calculate the comprehensive influence strength of the node to form the node influence strength vector W = [w1, w2,..., wn], where wi is the influence strength of node i and n is the total number of nodes.

[0040] Evaluate the strength of each edge in the parameter coupling relationship diagram to quantify the mutual influence degree between nodes. Adopt the partial correlation analysis method to calculate the correlation between two parameters under the condition of controlling other variables. Calculate the cross-sensitivity, which represents the influence of the change of parameter i on the sensitivity of parameter j, and the cross-sensitivity coefficient Based on physical models or data-driven methods, estimate the transfer coefficients of parameter changes, which represent the direct influence degree of the change in parameter j on parameter i. Integrate these evaluation results to form the edge coupling strength matrix C, where the element Cij represents the coupling strength of parameter j on parameter i.

[0041] Based on the node influence strength vector W and the edge coupling strength matrix C, construct a graph convolutional network (GCN) model. The layer propagation rule of GCN is expressed as , where H(l) is the node representation of the l-th layer, H(l + 1) is the node representation of the (l + 1)-th layer, A is the adjacency matrix after adding self-loops (constructed based on the edge coupling strength matrix C), D is the degree matrix, W(l) is the weight matrix of the l-th layer, and σ is the non-linear activation function. By training the GCN model, learn the complex interaction relationships between parameters to obtain a parameter propagation model, which can simulate the propagation process of parameter changes in the system.

[0042] , conduct time evolution simulation on the parameter propagation model to study the dynamic influence process of external environmental parameter changes on the key influencing factors of the system. Set different time scales (such as hours, days, seasons, years), and simulate the change patterns of external environmental parameters on these time scales. Input the simulated environmental parameter changes into the parameter propagation model, and calculate the response process of the key influencing factors of the system. Analyze the influence characteristics on different time scales, such as short-term fluctuations, medium-term trends, and long-term cumulative effects, etc. Extract the time-varying influence coefficients, which represent the time-varying influence degree of environmental parameter changes on the key factors of the system.

[0043] Organize the time-varying influence coefficients into a matrix form according to the key influencing factors of the system (rows) and external environmental parameters (columns) to form the dynamic influence matrix D. The element Dij(t) in the i-th row and j-th column of the matrix represents the influence degree of the external environmental parameter j on the key influencing factor i of the system at time t. The matrix D is not static but changes with time, that is, for different time points t, there are different matrices D(t). The dynamic influence matrix comprehensively describes the influence law of external environmental parameter changes on the key influencing factors of the system, providing a mathematical basis for subsequent stress-life analysis and the formulation of adaptive control strategies.

[0044] In this embodiment, the detailed implementation steps of step S4 include: Calculate the stress distribution of the key components of the system based on the dynamic influence matrix to obtain the stress time series; perform rainflow counting method processing on the stress time series to obtain the stress cycle spectrum; Based on the stress cycle spectrum and the material S-N curve, establish a cumulative damage model to obtain the damage evolution function; conduct Monte Carlo simulation on the damage evolution function to establish an equipment failure prediction model; Calculate the reliability functions of each key component based on the equipment failure prediction model to obtain the reliability distribution; determine the lower limit of reliability according to the system safety requirements, and determine the system reliability constraint in combination with the reliability distribution.

[0045] In this embodiment, based on the dynamic influence matrix, calculate the stress influence of the change of external environmental parameters on the key components of the system (such as heat exchangers, valves, fans, etc.). The stress types include thermal stress, mechanical stress, chemical stress, etc. Thermal stress results from temperature gradients and temperature fluctuations, and the calculation formula is , where E is the elastic modulus, α is the coefficient of thermal expansion, and ΔT is the temperature difference. Mechanical stress results from pressure fluctuations, flow rate changes, vibration, etc., and is calculated through mechanical analysis. Chemical stress results from corrosion, erosion, deposition, etc., and is calculated through chemical reaction models. Superimpose various stresses to obtain the total stress distribution of the key components. Considering the time variation of external environmental parameters, calculate the change process of stress over time to form a stress time series. These series reflect the dynamic stress conditions borne by the key components of the system in the actual operating environment.

[0046] Apply the rainflow counting method to the stress time series to convert the complex stress history into a set of stress cycles. The steps of the rainflow counting method include: converting the stress time series into a peak-valley series to eliminate minor fluctuations; converting the peak-valley series into a "rainflow" path and counting according to specific rules; counting the number of cycles at different stress amplitudes and mean stress levels. The processing result forms a stress cycle spectrum, expressed as , where n is the number of cycles, Δσ is the stress amplitude, and σm is the mean stress level. The stress cycle spectrum comprehensively describes the stress cycles experienced by the component under actual working conditions and provides a basis for fatigue life assessment.

[0047] Based on the stress cycle spectrum and the S-N curve (stress-life curve) of the material, establish a cumulative damage model. The S-N curve is expressed as , where N is the fatigue life (number of cycles) at the stress amplitude Δσ, and m and C are material constants. Considering the influence of the mean stress, use methods such as Goodman correction to adjust the S-N curve. Adopt Miner's linear cumulative damage theory to calculate the cumulative damage amount , where ni is the actual number of cycles at the stress amplitude Δσi, and Ni is the fatigue life at this stress amplitude. When D reaches 1, the component will theoretically undergo fatigue failure. Based on historical stress data and future stress predictions, establish a damage evolution function D(t) to describe the cumulative process of damage over time.

[0048] Perform Monte Carlo simulation on the damage evolution function, considering the uncertainties of model parameters and input variables. Identify the random variables in the damage evolution function, such as material property parameters (m, C), stress prediction values, operating conditions, etc., and determine the probability distribution types (such as normal distribution, Weibull distribution, etc.) and parameters of these variables. Generate a large number of random samples, with each group of samples representing a possible combination of parameters. Substitute each group of samples into the damage evolution function for calculation to obtain the corresponding predicted failure time. Statistically analyze the failure time distribution of all samples to obtain the probability density function f(t) and cumulative distribution function F(t) of the failure time. Establish a Bayesian network model, combine the failure time distribution with real-time monitoring data to achieve dynamic update and prediction of the equipment status. Finally, form an equipment failure prediction model that can predict the failure probability and remaining life of the equipment under different operating conditions.

[0049] Based on the equipment failure prediction model, calculate the reliability function of each key component of the system , where F(t) is the cumulative distribution function of the failure time. The reliability function represents the probability that the component can still operate normally at time t. Analyze the change of the reliability function under different operating conditions to obtain the distribution law of reliability over time and operating conditions. Evaluate the overall reliability of the system, considering the logical relationship between components (such as series, parallel or complex structure), and calculate the reliability function at the system level.

[0050] According to the safety requirements of the system and industry standards, determine the lower threshold Rmin of the system reliability, such as 0.95 or 0.99. Under any operating conditions, the reliability of the system shall not be lower than this threshold, that is, R(t) ≥ Rmin. Combining the reliability distribution analysis, transform the reliability constraint into the constraint conditions of system parameters, such as upper temperature limit, pressure limit, flow range, etc. These constraint conditions form the system reliability constraint set, which serves as the boundary conditions for subsequent optimization. The system reliability constraint ensures that while the system pursues high efficiency, it will not overly sacrifice safety and reliability, guaranteeing the long-term stable operation of the system.

[0051] In this embodiment, the detailed implementation steps of performing Monte Carlo simulation on the damage evolution function in step S4 and establishing the equipment failure prediction model include: Identify the random variables in the damage evolution function, determine their probability distribution types and parameters to obtain the random variable description set; generate a large number of random samples based on the random variable description set to obtain the random sample matrix; Substitute each group of samples in the random sample matrix into the damage evolution function for calculation to obtain the failure time sample set; perform statistical analysis on the failure time sample set to obtain the failure time distribution function; Based on the failure time distribution function, establish a Bayesian network, and perform status update by combining real-time monitoring data to obtain the equipment failure prediction model.

[0052] In this embodiment, the random variables in the damage evolution function are first identified. Material-related random variables include the S-N curve parameters m and C, which are affected by material batches, manufacturing processes, and environmental conditions. Stress-related random variables include the predicted stress amplitude and stress cycle frequency, which are affected by external loads, environmental conditions, and system operating parameters. Environment-related random variables include temperature, humidity, and corrosive substance concentration, etc., which affect material properties and damage rates. For each random variable, based on historical data and professional knowledge, determine its probability distribution type. For example, the material parameter m may follow a normal distribution N(μm, σm²), the parameter C may follow a lognormal distribution, and the stress prediction value may follow a truncated normal distribution. Use parameter estimation methods (such as maximum likelihood estimation, moment estimation, etc.) to determine the parameter values of each distribution. Organize all random variables and their distribution information into a random variable description set, providing input for subsequent Monte Carlo simulations.

[0053] Based on the random variable description set, use random number generation techniques to generate a large number of random samples. For each random variable, generate a specified number (such as 10,000) of random values according to its probability distribution. Considering the correlation between variables, use a correlation structure (such as a Copula function) to generate multi-dimensional random variables with specified correlations. Organize the generated random values into a matrix form, where each row represents a set of parameter combinations and each column represents a random variable. This matrix is called a random sample matrix, which covers various possible combinations of the parameter space and is used to simulate the behavior of the system under different conditions.

[0054] For each row (i.e., each set of parameter combinations) in the random sample matrix, substitute it into the damage evolution function for calculation. The calculation process may require solving differential equations or performing numerical integration, depending on the form of the damage evolution function. For each set of parameters, record the time when the system reaches a specific damage threshold (such as D = 1, representing the theoretical failure point). Collect the failure times of all samples to form a failure time sample set, which reflects the statistical distribution of the system failure time.

[0055] Conduct a statistical analysis on the failure time sample set to extract its distribution characteristics. Calculate the basic statistics of the samples, such as mean, median, standard deviation, skewness, and kurtosis, etc., to preliminarily understand the shape of the distribution. Use the kernel density estimation method to estimate the probability density function f(t) of the failure time. Calculate the cumulative distribution function F(t)=P(T≤t), representing the probability that the system fails before time t. Try to fit the sample data with common lifetime distributions (such as Weibull distribution, lognormal distribution, gamma distribution, etc.), and select the distribution with the best fitting effect as the failure time distribution function.

[0056] Based on the failure time distribution function, a Bayesian network model is established, which combines prior knowledge with real-time monitoring data. Design the Bayesian network structure, including nodes (such as material parameters, stress levels, environmental conditions, damage states, failure times, etc.) and edges (representing the conditional dependence relationships between nodes). Define the conditional probability table (CPT) of the nodes, which reflects the quantitative relationships between variables. When new monitoring data is obtained, use Bayesian inference to update the probability distribution in the network, realizing the dynamic update of the model. Combine the monitoring data and the updated model to predict the current state and future failure probability of the equipment. Finally, an equipment failure prediction model is formed, which can dynamically predict the remaining life and failure risk of the equipment according to real-time data, providing support for equipment management and maintenance decisions.

[0057] In this embodiment, the detailed implementation steps of step S5 include: Convert the thermal energy conversion efficiency model into an efficiency objective function to obtain the first optimization objective; convert the system operation cost and resource consumption into a cost objective function to obtain the second optimization objective; convert the system reliability constraints into a set of constraint conditions to obtain the constraint equations of the optimization problem; Construct a multi-objective optimization function based on the first optimization objective, the second optimization objective, and the constraint equations; apply an improved particle swarm optimization algorithm to solve the multi-objective optimization function to obtain the Pareto optimal solution set; perform clustering analysis on the Pareto optimal solution set to generate an adaptive control strategy library for different working conditions.

[0058] In this embodiment, the thermal energy conversion efficiency model η = f(x1, x2,..., xn) is converted into an efficiency objective function. Define the efficiency objective function as maximizing the thermal energy conversion efficiency, expressed as max η = f(x1, x2,..., xn), where x1, x2,..., xn are the control parameters of the system, such as flue gas flow rate, heat medium flow rate, heat exchanger parameters, etc. To improve the applicability of the model, consider the weighted average efficiency under different working conditions, expressed as , where wi is the weight of working condition i, and ηi is the efficiency under working condition i. According to the system characteristics, the efficiency objective function may include non-linear terms, interaction terms, and constraint conditions. After mathematical transformation and simplification, a normalized efficiency objective function is obtained as the first optimization objective.

[0059] Define the cost objective function of the system operation cost and resource consumption. The operation cost includes energy cost, maintenance cost, depreciation cost, etc. The energy cost , where Pe is the unit price of energy e and Ee is the consumption of energy e. The maintenance cost CM is usually related to the equipment operation time, start-stop times, and operation intensity. Resource consumption includes the usage amounts of resources such as water, electricity, and fuel. Combining these cost and consumption items, the cost objective function is defined as minC = CE + CM + CD +..., where CD is the equipment depreciation cost. The cost objective function may include time factors such as the net present value NPV or the life cycle cost LCC. Through appropriate mathematical processing, a normalized cost objective function is obtained as the second optimization objective.

[0060] Convert the system reliability constraints into a set of constraint conditions in mathematical form. The safety and reliability constraints include: the reliability constraint R(t) ≥ Rmin, where R(t) is the system reliability function and Rmin is the minimum reliability requirement; the failure rate constraint λ(t) ≤ λmax, where λ(t) is the failure rate function and λmax is the maximum allowable failure rate; the remaining useful life constraint RUL ≥ RULmin, where RUL is the predicted remaining useful life and RULmin is the minimum remaining useful life requirement. The physical parameter constraints include: the temperature constraint Tmin ≤ T ≤ Tmax; the pressure constraint Pmin ≤ P ≤ Pmax; the flow rate constraint Fmin ≤ F ≤ Fmax; the rate of change constraint |dX / dt| ≤ (dX / dt)max. The process requirement constraints include specific process parameter constraints and environmental requirement constraints. Organize these constraint conditions into a standard form to form the constraint equation set of the optimization problem.

[0061] Based on the efficiency objective function (the first optimization objective), the cost objective function (the second optimization objective), and the constraint equation set, construct a multi-objective optimization function. The standard form of the multi-objective optimization problem is: minF(x) = [f1(x), f2(x)]T, where f1(x) = -η(x) (take the negative value to convert it into a minimization problem), f2(x) = C(x), subject to the constraint conditions gi(x) ≤ 0, i = 1, 2,..., m and hj(x) = 0, j = 1, 2,..., p. This is an optimization problem with conflicting objectives. Improving efficiency usually increases costs, and reducing costs may reduce efficiency. The purpose of multi-objective optimization is to find a set of Pareto optimal solutions, which form the Pareto front and represent the best compromise between efficiency and cost.

[0062] Solve the multi-objective optimization function using the improved particle swarm optimization algorithm (MOPSO). MOPSO is a multi-objective optimization extension based on the particle swarm optimization algorithm and is suitable for solving multi-objective problems with non-linear objectives and constraints. The algorithm process includes: initializing the particle swarm; evaluating the objective function values of the particles; performing non-dominated sorting; updating the external archive (storing Pareto optimal solutions); updating the particle positions and velocities; introducing an adaptive inertia weight and chaotic perturbation mechanism to enhance the global search ability and convergence of the algorithm. After multiple iterations, the algorithm converges to a set of Pareto optimal solutions, which form the Pareto front, representing the optimal trade-off between efficiency and cost.

[0063] Perform clustering analysis on the Pareto optimal solution set to identify solution groups with similar characteristics. Use clustering algorithms such as K-means, hierarchical clustering, or DBSCAN to cluster the Pareto optimal solutions into k classes, where each class represents a type of control strategy. For each cluster, select a representative solution as the typical strategy for that class and record the corresponding control parameter combination. Associate the clustering results with the system operating conditions and analyze the types of control strategies applicable under different operating conditions. For example, a high-load operating condition may be suitable for an efficiency-first strategy, while a low-load operating condition may be suitable for a cost-first strategy. Organize the mapping relationship between the strategies and the operating conditions into strategy selection rules to form an adaptive control strategy library. This strategy library contains the optimal control parameter combinations for different operating conditions and provides decision support for the adaptive control of the system in a changing environment.

[0064] In this embodiment, the detailed implementation steps of applying the improved particle swarm optimization algorithm to solve the multi-objective optimization function in step S5 to obtain the Pareto optimal solution set include: Initialize the particle swarm parameters and population size, and generate the initial particle position and velocity matrices; perform constraint condition checks on the initial particle positions, filter out the feasible solutions that meet the constraints, and obtain the initial feasible solution set; Calculate the multi-objective function values of each particle in the initial feasible solution set, and determine the particle ranks according to non-dominated sorting to obtain the sorting result; Update the particle individual optimal positions and global optimal positions based on the sorting result to obtain the optimization direction vectors; introduce an adaptive inertia weight and chaotic perturbation mechanism to update the particle velocities and positions to obtain a new generation of particle swarms; repeat the execution of multi-objective function evaluation, non-dominated sorting, and position update until the convergence condition is met to obtain the Pareto optimal solution set.

[0065] In this embodiment, first, set the parameters of the improved particle swarm optimization algorithm, including the number of particles N (such as 100), the maximum number of iterations Tmax (such as 500), the range of inertia weight [wmin, wmax] (such as [0.4, 0.9]), the learning factors c1 and c2 (such as both are 2), etc. Determine the dimension D of the optimization problem, that is, the number of decision variables, such as the number of control parameters. Initialize the position matrix X of the particles, where each row represents a particle and each column represents a decision variable, and the position values are randomly generated within the constraint range of the variables. Initialize the velocity matrix V of the particles, and the velocity values are randomly generated within the range of [-Vmax, Vmax], where Vmax is the maximum velocity limit. Initialize the individual optimal position matrix P of the particles, and the initial value is equal to the initial position matrix X. Initialize the external archive for storing Pareto optimal solutions.

[0066] For each particle in the initial particle position matrix X, check whether it satisfies the constraint conditions. For the equality constraint hj(x) = 0, check |hj(x)| ≤ ε, where ε is a small allowable error. For the inequality constraint gi(x) ≤ 0, directly check whether gi(x) is less than or equal to 0. For the particles that do not satisfy the constraints, use constraint handling techniques, such as the penalty function method, the repair method, or special operators, etc. The penalty function method adds the degree of constraint violation to the objective function, such as f'(x) = f(x) + Σ(ri·max{0, gi(x)}²), where ri is the penalty coefficient. The repair method maps the infeasible solution to the feasible region, such as boundary handling or projection methods. Select the particles that satisfy all the constraints to form the initial feasible solution set.

[0067] For each particle in the initial feasible solution set, calculate its multi-objective function value F(x) = [f1(x), f2(x)]T, where f1(x) = -η(x) (efficiency objective, taking the negative value to convert it into a minimization problem), f2(x) = C(x) (cost objective). Based on the multi-objective function values, perform non-dominated sorting to determine the Pareto rank of each particle. If all the objective function values of particle A are not worse than those of particle B, and at least one objective function value is better than that of particle B, then particle A dominates particle B. The particles that are not dominated by any other particles form the first Pareto front (rank 1). From the remaining particles, the particles that are not dominated by any particles form the second Pareto front (rank 2), and so on. To maintain the diversity of the solutions, calculate the crowding degree of each particle, which represents the density in the solution space. The formula for calculating the crowding degree is , where fi, next and fi, prev are the objective values of two adjacent solutions on the i-th objective, and fi, max and fi, min are the maximum and minimum values of the i-th objective. According to the Pareto rank and the crowding degree, determine the sorting result of the particles.

[0068] Based on the result of non-dominated sorting, update the personal best position P of each particle. If the current position X dominates the personal best position P, then update P = X; if P dominates X, then keep P unchanged; if X and P do not dominate each other, randomly select one as the new P. Update the external archive, and add the non-dominated solutions (particles of rank 1) in the current iteration to the archive. If the existing solutions in the archive are dominated by the new solutions, delete the dominated solutions. If the archive size exceeds the limit, use crowding degree or other mechanisms to select the solutions to be retained. Select the global best position g from the external archive as the moving target of the particle. The selection method can be random selection, roulette wheel selection, or selection based on crowding degree, etc. Based on the personal best position P and the global best position g, determine the optimization direction vector of the particle.

[0069] Introduce an adaptive inertia weight mechanism to adjust the inertia weight w according to the iterative process. A commonly used adaptive strategy is linear decrease, , where t is the current iteration number and Tmax is the maximum iteration number. Use a larger inertia weight at the initial stage of the search to enhance the global search ability; use a smaller inertia weight at the later stage of the search to enhance the local search ability. Introduce a chaotic perturbation mechanism to avoid the algorithm falling into a local optimum. Chaotic perturbation can be generated using chaotic systems such as Logistic mapping, Tent mapping, or Chebyshev mapping. Update the velocity and position of the particle. The velocity update formula is: , where r1 and r2 are random numbers between [0, 1], V(t + 1) is the velocity of the particle at time t + 1, and V(t) is the velocity of the particle at time t; the position update formula is , X(t) is the position of the particle at time t, and X(t + 1) is the position of the particle at time t + 1. Perform boundary checking on the updated position to ensure it is within the variable constraint range. Generate a new generation of particle swarm for the next round of iteration.

[0070] Repeat the above steps of multi-objective function evaluation, non-dominated sorting, and position update until the convergence condition is met. The convergence condition can be reaching the maximum iteration number Tmax, or the Pareto front changing very little in consecutive rounds of iteration, or the Hypervolume index no longer increasing significantly, etc. Finally, extract the Pareto optimal solution set from the external archive as the solution to the multi-objective optimization problem. These solutions form the Pareto front, and each solution represents an optimal trade-off between efficiency and cost. Different solutions are suitable for different application scenarios and priority requirements.

[0071] In this embodiment, the detailed implementation steps of step S6 include: Establish a prediction model for external environment parameter changes, predict the external parameters in the future time period, and obtain a parameter change prediction sequence; Combine the parameter change prediction sequence with the dynamic influence matrix to predict the change trend of the system performance and obtain the performance prediction curve; Select the optimal control strategy from the adaptive control strategy library based on the performance prediction curve to obtain the preliminary control parameter set; dynamically adjust and optimize the preliminary control parameter set to obtain the real-time control instruction sequence; Send the real-time control instruction sequence to the system actuator, and monitor the system response in real time for closed-loop feedback regulation; continuously update the control strategy according to the system operating state and external environment changes to achieve reliable and efficient operation of the system under complex working conditions.

[0072] In this embodiment, a prediction model for changes in external environment parameters (such as environmental temperature, humidity, air pressure, etc.) is established. According to the data characteristics, a suitable prediction model is selected, such as time series models (ARIMA, SARIMA, etc.), machine learning models (random forest, support vector regression, etc.) or deep learning models (LSTM, GRU, etc.). Time series models are suitable for parameters with obvious time correlation, such as the ARIMA(p, d, q) model, where p is the autoregressive order, d is the differencing order, and q is the moving average order. Machine learning and deep learning models are suitable for parameters with complex nonlinear relationships. The model training process includes: data preprocessing (such as normalization, differencing, etc.); feature engineering (such as time feature extraction, lag feature creation, etc.); model parameter optimization (such as grid search, Bayesian optimization, etc.); model verification (such as cross-validation, time series segmentation, etc.). Use the trained model to predict the external environment parameters for future time periods (such as the next 24 hours, 7 days, etc.) to obtain the parameter change prediction sequence. This sequence describes the change trend of the external environment parameters in the future time period.

[0073] Combine the parameter change prediction sequence with the dynamic influence matrix D to predict the change trend of the system performance. For time point t, the predicted value of the external environment parameter is E(t)=[e1(t), e2(t),..., ek(t)], and the predicted value of the key influencing factors of the system is S(t)=D(t)×E(t)+S0, where S0 is the reference value. Based on the predicted key influencing factors S(t) of the system and the thermal energy conversion efficiency model, calculate the system performance index P(t)=f(S(t)), such as the thermal energy recovery efficiency, operating cost, etc. Plot the change curve of the performance index over time to form the performance prediction curve. Analyze the characteristics of the performance prediction curve, such as the mean, fluctuation range, trend, etc., to provide a basis for subsequent control strategy selection.

[0074] Based on the performance prediction curve and the current state of the system, select the optimal control strategy from the adaptive control strategy library. The considerations for control strategy selection include: predicted performance metrics (such as efficiency, cost, etc.); the reliability requirements of the system; the change characteristics of the external environment (such as stability, volatility, etc.); the operating history and current state of the system. The method of strategy selection can be rule-based methods (such as IF-THEN rules), similarity-based methods (such as k-nearest neighbors), or machine learning-based methods (such as decision trees, random forests, etc.). The optimal strategy selected from the strategy library contains a set of control parameters, such as flow setpoint, temperature setpoint, valve opening, etc., and these parameters form the preliminary control parameter set.

[0075] Dynamically adjust and optimize the preliminary control parameter set to make it more adaptable to the real-time environment and system state. Based on the real-time feedback of the system, fine-tune the control parameters, such as using PID controllers, fuzzy controllers, or model predictive controllers, etc. Consider the mutual influence and constraint conditions among the parameters for overall optimization to avoid system imbalance caused by single parameter adjustment. Design a smooth transition mechanism to avoid sudden changes in control parameters and reduce the impact on the system. Conduct pre-execution checks on the adjusted control parameters to ensure compliance with safety constraints and operating specifications. Organize the optimized control parameters in chronological order to form a real-time control instruction sequence for the dynamic control of the system.

[0076] Send the real-time control instruction sequence to the actuators of the system, such as control valves, frequency converters, dampers, etc., through the communication network. The actuators adjust the operating parameters of the system, such as flow rate, temperature, pressure, etc., according to the control instructions. Real-time collect the response data of the system through the monitoring network, including parameters such as temperature, pressure, flow rate, efficiency, etc. Compare the difference between the actual response and the expected response of the system and calculate the control error. Based on the control error, use a feedback control algorithm (such as PID control) for real-time adjustment to form a closed-loop control. The mathematical expression of the feedback control is , where u(t) is the control output, e(t) is the control error, and Kp, Ki, and Kd are the proportional, integral, and derivative coefficients. The closed-loop feedback regulation ensures that the system can quickly respond to changes in the external environment and maintain stable operation.

[0077] Establish a continuous monitoring mechanism for the system operation status and external environment changes, and regularly evaluate the effectiveness of the current control strategy. When significant changes occur in the external environment or obvious deviations appear in the system performance, trigger the update of the control strategy. The update method can be to re-select from the strategy library or to perform online learning and adjustment on the existing strategy. With the accumulation of system operation data, use machine learning methods (such as reinforcement learning, transfer learning, etc.) to continuously improve and expand the strategy library and enhance the system's adaptability. Through the continuous update and optimization of the strategy, achieve the reliable and efficient operation of the system under complex and variable working conditions, improve the waste heat recovery efficiency, reduce energy consumption, and extend the equipment life.

[0078] The optimized design method for the flue gas waste heat recovery system considering external parameter changes provided by the present invention, through processing and feature extraction of the monitoring data, establishing a thermodynamic model, analyzing the influence of external environment parameters on the system performance, predicting the equipment life, and optimizing the control strategy, realizes the reliable and efficient operation of the system under complex environments. This method effectively improves the energy utilization efficiency of the system, extends the equipment life, and reduces the operation cost, having significant economic and environmental benefits.

[0079] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, it is still possible to modify the technical solutions recorded in the foregoing embodiments or perform equivalent replacements on some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0080] It should be noted that in this article, the term "including", "comprising" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without further limitations, an element defined by the statement "including one..." does not exclude the existence of additional identical elements in the process, method, article or device including the said element.

[0081] In the description of the present invention, it should be understood that the terms "first", "second", etc. are only used for distinguishing descriptions and cannot be understood as indicating or implying relative importance.

[0082] In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0083] In the description of the present invention, the meaning of "several" is one or more, and the meaning of "a large number" is two or more.

[0084] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0085] For the formulas in this specification, the dimensional quantities are removed and only the numerical values are calculated. The formula is obtained by collecting a large amount of data and performing software simulation to get a formula that is closest to the actual situation. The preset parameters and threshold selection in the formula are set by those skilled in the art according to the actual situation.

[0086] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the claims and their equivalents.

Claims

1. An optimization design method for a flue gas waste heat recovery system considering external parameter changes, characterized in that, Including: Step S1: Obtain the monitoring data set of the flue gas waste heat recovery system; Extract the operating characteristics and process noise from the monitoring data set to obtain the operating characteristic sequence of the flue gas system; Step S2: Perform thermodynamic modeling on the operating characteristic sequence to construct a thermal energy conversion efficiency model; analyze the parameter sensitivity based on the thermal energy conversion efficiency model to identify the key influencing factors of the system; Step S3: Collect the data of external environmental parameter changes; combine the data of external environmental parameter changes with the key influencing factors of the system to establish a system performance coupling mechanism model, and then obtain a dynamic influence matrix; Step S4: Use the dynamic influence matrix to perform stress-life analysis to establish an equipment failure prediction model; evaluate the safety margin based on the equipment failure prediction model to determine the system reliability constraint; Step S5: Based on the thermal energy conversion efficiency model and the system reliability constraint, construct a multi-objective optimization function; apply an intelligent algorithm to solve the optimal parameter combination to generate an adaptive control strategy library; Step S6: Based on the adaptive control strategy library and the dynamic influence matrix, perform predictive adjustment for external parameter changes.

2. The optimization design method of the flue gas waste heat recovery system considering external parameter changes according to claim 1, characterized in that, The obtaining of the monitoring data set of the flue gas waste heat recovery system; Extract the operating characteristics and process noise from the monitoring data set to obtain the operating characteristic sequence of the flue gas system, including: Collect the temperature, pressure, flow rate and heat exchange efficiency of the flue gas waste heat recovery system to obtain the monitoring data set; Perform time series segmentation and outlier identification on the monitoring data set to obtain the cleaned data matrix; Perform wavelet transform denoising and filtering on the cleaned data matrix to obtain a smooth data sequence; Perform principal component analysis and operating characteristic extraction on the smooth data sequence to obtain the operating characteristic vector; Perform normalization processing and time window sliding on the operating characteristic vector to obtain the operating characteristic sequence of the flue gas system.

3. The optimization design method of the flue gas waste heat recovery system considering external parameter changes according to claim 1, characterized in that, The performing of thermodynamic modeling on the operating characteristic sequence to construct a thermal energy conversion efficiency model; Analyze the parameter sensitivity based on the thermal energy conversion efficiency model to identify the key influencing factors of the system, including: Establish a mass conservation equation set of the flue gas waste heat recovery system according to the operating characteristic sequence to obtain a mass transfer model; Based on the mass transfer model, establish a system energy balance equation to obtain a heat transfer model; Combine the heat transfer model with the equipment structure parameters to construct a heat transfer coefficient calculation model to obtain a preliminary thermal energy conversion efficiency model; Perform parameter calibration and verification on the preliminary thermal energy conversion efficiency model to obtain the thermal energy conversion efficiency model; Perform parameter sensitivity analysis on the thermal energy conversion efficiency model by the coefficient of variation method and variance analysis to obtain a parameter sensitivity ranking table; According to the parameter sensitivity ranking table, screen out the parameters with a contribution rate exceeding the threshold to identify the key influencing factors of the system.

4. The optimization design method of the flue gas waste heat recovery system considering the change of external parameters according to claim 1, wherein, The collecting of the data of external environmental parameter changes; combining the data of external environmental parameter changes with the key influencing factors of the system to establish a system performance coupling mechanism model, and then obtaining a dynamic influence matrix, including: Establish an external environmental parameter monitoring network, collect the environmental temperature, humidity, air pressure and seasonal changes to obtain the external environmental parameter time series; Perform time-frequency analysis on the time series of the external environmental parameters to obtain periodic change characteristics and trend characteristics; Conduct correlation analysis on the periodic change characteristics and trend characteristics with the key influencing factors of the system to obtain a system performance coupling mechanism model; Construct a system performance response function based on the system performance coupling mechanism model to obtain a parameter coupling relationship diagram; Perform quantization processing and matrix transformation on the parameter coupling relationship diagram to form a dynamic influence matrix.

5. The optimization design method of the flue gas waste heat recovery system considering the change of external parameters according to claim 4, characterized in that, The performing quantization processing and matrix transformation on the parameter coupling relationship diagram to form a dynamic influence matrix includes: Calculate the weights of the nodes in the parameter coupling relationship diagram to obtain a node influence intensity vector; Evaluate the intensity of the edges in the parameter coupling relationship diagram to obtain an edge coupling intensity matrix; Establish a graph convolutional network based on the node influence intensity vector and the edge coupling intensity matrix to obtain a parameter propagation model; Perform time evolution simulation on the parameter propagation model to obtain time-varying influence coefficients; Organize the time-varying influence coefficients into a matrix form according to the key influencing factors of the system and the external environmental parameters to form a dynamic influence matrix.

6. The optimization design method for the flue gas waste heat recovery system considering the change of external parameters according to claim 1, characterized in that Use the dynamic influence matrix to perform stress-life analysis and establish an equipment failure prediction model; Evaluate the safety margin based on the equipment failure prediction model and determine the system reliability constraints, including: Calculate the stress distribution of the key components of the system based on the dynamic influence matrix to obtain a stress time series; Perform rainflow counting method processing on the stress time series to obtain a stress cycle spectrum; Establish a cumulative damage model based on the stress cycle spectrum and the material S-N curve to obtain a damage evolution function; Perform Monte Carlo simulation on the damage evolution function to establish an equipment failure prediction model; Calculate the reliability function of each key component based on the equipment failure prediction model to obtain a reliability distribution; Determine the lower limit of reliability according to the system safety requirements and combine the reliability distribution to determine the system reliability constraints.

7. The method for optimizing the design of a flue gas waste heat recovery system considering external parameter changes according to claim 6, characterized in that, The performing Monte Carlo simulation on the damage evolution function to establish an equipment failure prediction model includes: Identify the random variables in the damage evolution function, determine their probability distribution types and parameters to obtain a random variable description set; Generate random samples based on the random variable description set to obtain a random sample matrix; Substitute each group of samples in the random sample matrix into the damage evolution function for calculation to obtain a failure time sample set; Perform statistical analysis on the failure time sample set to obtain a failure time distribution function; Establish a Bayesian network based on the failure time distribution function and perform state update in combination with real-time monitoring data to obtain an equipment failure prediction model.

8. The optimized design method for a flue gas waste heat recovery system considering external parameter changes according to claim 1, characterized in that, Based on the thermal energy conversion efficiency model and the system reliability constraints, construct a multi-objective optimization function; Apply intelligent algorithms to solve the optimal parameter combination and generate an adaptive control strategy library, including: Convert the thermal energy conversion efficiency model into an efficiency objective function to obtain a first optimization objective; Convert the system operation cost and resource consumption into a cost objective function to obtain a second optimization objective; Convert the system reliability constraints into a set of constraint conditions to obtain a constraint equation system for the optimization problem; Construct a multi-objective optimization function based on the first optimization objective, the second optimization objective, and the constraint equations; Apply an improved particle swarm optimization algorithm to solve the multi-objective optimization function to obtain a Pareto optimal solution set; Perform clustering analysis on the Pareto optimal solution set to generate an adaptive control strategy library for different working conditions.

9. The method for optimizing the design of a flue gas waste heat recovery system considering changes in external parameters according to claim 1, characterized in that, The prediction and adjustment for external parameter changes based on the adaptive control strategy library and the dynamic influence matrix includes: Establish a prediction model for external environmental parameter changes to predict external parameters in future time periods and obtain a parameter change prediction sequence; Combine the parameter change prediction sequence with the dynamic influence matrix to predict the change trend of system performance and obtain a performance prediction curve; Select the optimal control strategy from the adaptive control strategy library based on the performance prediction curve to obtain a preliminary control parameter set; Dynamically adjust and optimize the preliminary control parameter set to obtain a real-time control instruction sequence; Send the real-time control instruction sequence to the system actuator, and monitor the system response in real time for closed-loop feedback regulation; Continuously update the control strategy according to the system operating state and external environment changes.

10. The method for optimizing the design of a flue gas waste heat recovery system considering external parameter changes according to claim 8, wherein The application of the improved particle swarm optimization algorithm to solve the multi-objective optimization function to obtain a Pareto optimal solution set includes: Initialize the particle swarm parameters and population size to generate an initial particle position and velocity matrix; Check the constraint conditions for the initial particle positions, screen out the feasible solutions that meet the constraints to obtain an initial feasible solution set; Calculate the multi-objective function values of each particle in the initial feasible solution set, and determine the particle ranks according to non-dominated sorting to obtain a sorting result; Update the individual optimal position and global optimal position of the particles based on the sorting result to obtain an optimization direction vector; introduce an adaptive inertia weight and a chaos perturbation mechanism to update the particle velocities and positions to obtain a new generation of particle swarm; Repeat the execution of multi-objective function evaluation, non-dominated sorting, and position update until the convergence condition is met to obtain a Pareto optimal solution set.

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