An optimization design method for flue gas waste heat recovery system considering changes in external parameters

Abstract

The present invention belongs to the technical field of industrial waste heat recovery. The present invention discloses a method for optimizing the design of a flue gas waste heat recovery system that takes into account changes in external parameters. Through the steps of system monitoring data acquisition and feature extraction, thermodynamic modeling and parameter sensitivity analysis, modeling of the coupling mechanism of external environmental parameters and system performance, equipment failure prediction and reliability constraint determination, multi-objective optimization and adaptive control strategy generation, the optimized operation of the flue gas waste heat recovery system under conditions of dynamic changes in external environmental parameters is achieved. This method innovatively establishes a dynamic influence matrix of external environmental parameters and system performance, combines stress-life analysis technology to evaluate system reliability, balances efficiency and cost targets through a multi-objective optimization algorithm, and generates an adaptive control strategy library for different working conditions. The present invention improves the adaptability and stability of the system under complex working conditions, extends the service life of the equipment, and reduces operating costs.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial waste heat recovery, and more particularly to a method for optimizing the design of a flue gas waste heat recovery system taking into account changes in external parameters. Background Art

[0002] As a key technical means of industrial energy conservation and emission reduction, flue gas waste heat recovery systems are widely used in high-energy-consuming industries such as metallurgy, electricity, building materials, and chemicals. With global energy shortages and increasingly stringent environmental protection requirements, improving flue gas waste heat recovery efficiency has become a key direction for industry development. Traditional flue gas waste heat recovery technologies mainly include waste heat boilers, heat exchangers, and regenerative combustion. These technologies can achieve a certain degree of energy recovery under stable operating conditions. Currently, research on flue gas waste heat recovery systems at home and abroad mainly focuses on heat exchanger structure optimization, heat transfer enhancement, and system integration.

[0003] However, existing flue gas waste heat recovery system design methods are primarily based on static operating conditions and idealized conditions, with system parameters often fixed during the design phase. In real industrial environments, flue gas parameters such as temperature, composition, and flow rate fluctuate due to production processes, raw material variations, and environmental conditions. Environmental factors such as external temperature, humidity, and atmospheric pressure also vary with seasons and weather. Traditional systems are slow to respond to these environmental changes and are unable to effectively address seasonal variations, diurnal temperature swings, and weather fluctuations. This leads to a significant decrease in heat exchange efficiency in low winter temperatures or high summer temperatures, and even to problems such as condensation corrosion. This also reflects the crudeness of system reliability assessment methods, making it difficult to accurately predict equipment failure risks under high-temperature and high-pressure conditions. This results in a lack of scientific basis for maintenance plans, leading to either excessive maintenance costs or insufficient maintenance leading to sudden failures. This is particularly true in industries such as metallurgy and chemical engineering, where flue gas composition is complex and fluctuates frequently. Existing technologies are unable to deeply analyze the coupling mechanisms between these parameters. Control strategies are often based on simplified models and empirical judgments, making precise adjustments difficult. Furthermore, the single efficiency optimization objective ignores the balance between system operating costs and lifespan, leading to a conflict between short-term benefits and long-term sustainability. In terms of data processing, interference signals and measurement errors in industrial sites often compromise monitoring data quality, affecting model accuracy and control effectiveness. Furthermore, existing systems lack adaptability during operating condition transitions, requiring manual intervention to adjust parameters. This increases operational complexity and the risk of human error, failing to meet the urgent demands of modern industry for automation, intelligence, and high efficiency.

[0004] In view of this, the present invention proposes a flue gas waste heat recovery system optimization design method taking into account changes in external parameters to solve the above problems. Summary of the Invention

[0005] In order to overcome the above-mentioned defects of the prior art and to achieve the above-mentioned objectives, the present invention provides the following technical solution: a method for optimizing the design of a flue gas waste heat recovery system taking into account changes in external parameters, comprising:

[0006] Step S1: Acquire a monitoring data set of a flue gas waste heat recovery system; extract operating condition features and perform noise processing on the monitoring data set to obtain an operating feature sequence of the flue gas system;

[0007] Step S2: Conduct thermodynamic modeling on the operating characteristic sequence and construct a thermal energy conversion efficiency model; analyze parameter sensitivity based on the thermal energy conversion efficiency model and identify key influencing factors of the system;

[0008] Step S3: Collect external environmental parameter change data; combine the external environmental parameter change data with the key influencing factors of the system to establish a system performance coupling mechanism model, and then obtain a dynamic impact matrix;

[0009] Step S4: Using the dynamic influence matrix to perform stress-life analysis and establish an equipment failure prediction model; based on the equipment failure prediction model, the safety margin is evaluated and the system reliability constraints are determined;

[0010] Step S5: Based on the thermal energy conversion efficiency model and system reliability constraints, a multi-objective optimization function is constructed; an intelligent algorithm is applied to solve the optimal parameter combination and generate an adaptive control strategy library;

[0011] Step S6: Based on the adaptive control strategy library and the dynamic influence matrix, predictive adjustments are made to external parameter changes to achieve reliable and efficient operation of the system under complex working conditions.

[0012] The technical effects and advantages of the present invention's method for optimizing the design of a flue gas waste heat recovery system taking into account changes in external parameters are as follows:

[0013] The present invention improves the adaptability of the system in a changing environment, enabling it to cope with various complex working conditions and maintain an efficient operating state. By accurately predicting the life of system components and potential failures, the overall reliability and safety are greatly improved, unexpected downtime is reduced, and maintenance costs are reduced. The improvement in system operating efficiency is directly converted into an increase in energy recovery rate, while reducing resource consumption and operating costs, bringing considerable economic benefits. The intelligent predictive and regulatory capabilities enable the system to respond to environmental changes in advance, avoiding the efficiency loss caused by the delayed 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 a continuous performance advantage. The decision support function reduces the burden on operators and reduces the risk of human error. In terms of environmental benefits, the improved energy recovery efficiency means less emissions and higher resource utilization, which meets the requirements of green development. In the long run, the extended service life of equipment and the reduced maintenance needs reduce the cost of the entire life cycle and improve the return on investment. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Schematic diagram of a flue gas waste heat recovery system optimization design method considering changes in external parameters according to the present invention;

[0015] Figure 2 3 is a flowchart of the detailed implementation steps of step S3 of the present invention. DETAILED DESCRIPTION

[0016] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0017] This application example provides a flue gas waste heat recovery system optimization design method that considers external parameter variations. The method's execution entities include, but are not limited to, mechanical equipment, data processing platforms, cloud server nodes, network upload devices, and other such general computing nodes, which can be considered general computing nodes in this application. 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.

[0018] The present invention provides a flue gas waste heat recovery system optimization design method considering changes in external parameters, comprising the following steps:

[0019] Step S1: Acquire a monitoring data set of a flue gas waste heat recovery system; extract operating condition features and perform noise processing on the monitoring data set to obtain an operating feature sequence of the flue gas system;

[0020] Step S2: Conduct thermodynamic modeling on the operating characteristic sequence and construct a thermal energy conversion efficiency model; analyze parameter sensitivity based on the thermal energy conversion efficiency model and identify key influencing factors of the system;

[0021] Step S3: Collect external environmental parameter change data; combine the external environmental parameter change data with the key influencing factors of the system to establish a system performance coupling mechanism model, and then obtain a dynamic impact matrix;

[0022] Step S4: Using the dynamic influence matrix to perform stress-life analysis and establish an equipment failure prediction model; based on the equipment failure prediction model, the safety margin is evaluated and the system reliability constraints are determined;

[0023] Step S5: Based on the thermal energy conversion efficiency model and system reliability constraints, a multi-objective optimization function is constructed; an intelligent algorithm is applied to solve the optimal parameter combination and generate an adaptive control strategy library;

[0024] Step S6: Based on the adaptive control strategy library and the dynamic influence matrix, predictive adjustments are made to external parameter changes to achieve reliable and efficient operation of the system under complex working conditions.

[0025] The present invention processes the monitoring data of the flue gas waste heat recovery system to improve data quality and provide a reliable data basis for subsequent analysis; identifies key influencing factors of the system through thermodynamic modeling and parameter sensitivity analysis; establishes a system performance coupling mechanism model based on external environmental parameter change data to obtain a dynamic influence matrix; uses the matrix to perform stress-life analysis, establishes an equipment failure prediction model, and determines system reliability constraints; constructs a multi-objective optimization function based on the thermal energy conversion efficiency model and system reliability constraints, and generates an adaptive control strategy library; and finally, based on the control strategy library and the dynamic influence matrix, realizes reliable and efficient operation of the system under complex working conditions.

[0026] In the embodiment of the present invention, see Figure 1 , which is a flow chart of the steps of the method for optimizing the design of a flue gas waste heat recovery system considering changes in external parameters according to the present invention. In this example, the steps of the method for optimizing the design of a flue gas waste heat recovery system considering changes in external parameters include:

[0027] Step S1: Acquire a monitoring data set of a flue gas waste heat recovery system; extract operating condition features and perform noise processing on the monitoring data set to obtain an operating feature sequence of the flue gas system;

[0028] In this example, multi-source monitoring data from the flue gas waste heat recovery system is first collected, including parameters such as temperature (e.g., flue gas inlet temperature, outlet temperature, and heat medium temperature), pressure (e.g., flue gas duct pressure, heat exchanger inlet and outlet pressure differential), flow (e.g., flue gas flow rate, heat medium flow rate), and heat exchange efficiency. This data typically comes from various sensors, flow meters, thermocouples, and pressure transmitters installed in the system. The collected raw monitoring data sets are then processed, including time series segmentation and outlier identification, wavelet transform noise reduction and filtering, principal component analysis and operating condition feature extraction, normalization, and time window sliding. Ultimately, an operating characteristic sequence representing the dynamic operating state of the flue gas system is obtained, providing a high-quality data foundation for subsequent thermodynamic modeling and parameter sensitivity analysis.

[0029] Step S2: Conduct thermodynamic modeling on the operating characteristic sequence and construct a thermal energy conversion efficiency model; analyze parameter sensitivity based on the thermal energy conversion efficiency model and identify key influencing factors of the system;

[0030] In this example, based on the operating characteristic sequence obtained in the previous step, thermodynamic principles were applied to establish the mass conservation equations and energy balance equations for the flue gas waste heat recovery system, thereby constructing a thermal energy conversion efficiency model. This model reflects the quantitative relationship between system input parameters (such as flue gas temperature, flow rate, and composition) and output parameters (such as heat recovery and system efficiency). Parameter sensitivity analysis of this model was then performed, using methods such as the coefficient of variation method and variance analysis to identify the key factors that most significantly impact system efficiency, such as flue gas temperature, flow rate fluctuations, and heat exchanger fouling. These key influencing factors will serve as key considerations for subsequent system optimization.

[0031] Step S3: Collect external environmental parameter change data; combine the external environmental parameter change data with the key influencing factors of the system to establish a system performance coupling mechanism model, and then obtain a dynamic impact matrix;

[0032] In this embodiment, an external environmental parameter monitoring network is established to collect external environmental parameters such as ambient temperature, humidity, air pressure, and seasonal changes. Time-frequency analysis is performed on these parameters to extract periodic change characteristics and trend characteristics. These characteristics are correlated with the key system influencing factors identified in the previous step, and a coupling mechanism model reflecting the relationship between external environmental changes and system performance is established. Based on this model, a system performance response function is constructed to obtain a parameter coupling relationship diagram, and a dynamic influence matrix is ​​formed through quantitative processing and matrix conversion. This matrix reflects the dynamic impact of changes in external environmental parameters on the key system influencing factors, providing a basis for subsequent stress-life analysis and adaptive control strategy formulation.

[0033] Step S4: Using the dynamic influence matrix to perform stress-life analysis and establish an equipment failure prediction model; based on the equipment failure prediction model, the safety margin is evaluated and the system reliability constraints are determined;

[0034] In this embodiment, the stress distribution and time series of key system components (such as heat exchangers, valves, and fans) are calculated based on a dynamic influence matrix. The stress time series is processed using the rainflow counting method to obtain a stress cycle spectrum. A cumulative damage model is established using the material's SN curve (stress-life curve) to generate a damage evolution function. Monte Carlo simulation is performed on this function to establish a device failure prediction model capable of predicting the time and probability of device failure. Based on this model, the reliability function and distribution of each key component are calculated. The reliability lower limit is determined based on the system safety requirements, thereby defining the system reliability constraints. These constraints serve as boundary conditions for subsequent system optimization, ensuring that the system pursues high efficiency without sacrificing safety and reliability.

[0035] Step S5: Based on the thermal energy conversion efficiency model and system reliability constraints, a multi-objective optimization function is constructed; an intelligent algorithm is applied to solve the optimal parameter combination and generate an adaptive control strategy library;

[0036] In this embodiment, the thermal energy conversion efficiency model is converted into an efficiency objective function (the first optimization objective), and a cost objective function (the second optimization objective) is constructed by taking into account the system operating costs and resource consumption. The system reliability constraint is converted into a set of constraint conditions, and a multi-objective optimization function is constructed by combining the two optimization objectives. An improved particle swarm optimization algorithm is applied to solve the optimization function, obtaining a series of Pareto optimal solutions. These solutions represent the optimal balance between efficiency and cost under different operating conditions. Cluster analysis is performed on these optimal solutions, and an adaptive control strategy library is generated for different operating conditions. This strategy library contains the optimal operating parameter combinations of the system under various operating conditions, providing decision support for subsequent adaptive control.

[0037] Step S6: Based on the adaptive control strategy library and the dynamic influence matrix, predictive adjustments are made to external parameter changes to achieve reliable and efficient operation of the system under complex working conditions.

[0038] In this embodiment, a prediction model for changes in external environmental parameters is established to predict external parameters (such as ambient temperature, humidity, and air pressure) for future time periods. The prediction results are combined with the dynamic impact matrix to predict the trend of system performance changes. 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 then sent to the system actuators (such as control valves and frequency converters). At the same time, the system response is monitored in real time, and closed-loop feedback adjustment is performed. The system continuously updates the control strategy to achieve reliable and efficient operation under complex and changing operating conditions, effectively improving waste heat recovery efficiency, reducing energy consumption, and extending equipment life.

[0039] In this embodiment, the detailed implementation steps of step S1 include:

[0040] Obtain the original monitoring data set from multiple sources of monitoring data such as temperature, pressure, flow and heat exchange efficiency of the flue gas waste heat recovery system;

[0041] Perform time series segmentation and outlier identification on the original monitoring data set to obtain a cleaned data matrix;

[0042] The cleaned data matrix is ​​subjected to wavelet transform noise reduction and filtering to obtain a smoothed data sequence;

[0043] Perform principal component analysis and operating condition feature extraction on the smoothed data sequence to obtain the operating condition feature vector;

[0044] The operating condition characteristic vector is normalized and the time window is slid to obtain the operating characteristic sequence of the flue gas system.

[0045] In this embodiment, a sensor network distributed across key locations in the flue gas waste heat recovery system collects data on various parameters during system operation. Temperature data includes flue gas inlet temperature (e.g., 400°C), outlet temperature (e.g., 150°C), heat medium inlet and outlet temperatures (e.g., 60°C / 90°C), and heat exchanger wall temperature (e.g., 250°C). Pressure data includes flue gas duct pressure (e.g., 5 kPa), heat exchanger inlet and outlet pressure differential (e.g., 0.8 kPa), and pressure distribution at various points in the system. Flow data includes flue gas flow rate (e.g., 20,000 Nm³ / h), heat medium flow rate (e.g., 100 m³ / h), and condensate discharge. Heat exchange efficiency data includes heat exchanger efficiency (e.g., 75%), energy recovery rate, and heat transfer coefficient. This multi-source monitoring data is integrated according to timestamps to form the original monitoring data set.

[0046] The original monitoring data set is segmented into time series according to operating conditions, dividing the data into different time periods, such as startup, stable operation, load fluctuation, and shutdown. Statistical methods (such as the 3σ criterion and boxplots) are used to identify and mark outliers in the data, such as those caused by sensor failures or sudden interference. Identified outliers are removed or replaced to produce a cleaned data matrix containing the system's normal operating data under different operating conditions.

[0047] Apply the wavelet transform to the cleaned data matrix for noise reduction. The wavelet transform effectively separates the different frequency components in the signal, retaining useful information while removing high-frequency noise. By selecting an appropriate wavelet basis function (such as the Daubechies wavelet) and decomposition level, the data is subjected to wavelet decomposition, thresholding, and then reconstructed to obtain the denoised data. Filtering techniques (such as low-pass filtering and median filtering) are applied to the denoised data to further smooth the data curve, resulting in a smoothed data sequence that reflects the true trend of system parameters.

[0048] Apply principal component analysis (PCA) to the smoothed data series to reduce data dimensionality and extract key features. The mathematical expression for PCA is X'=XW, where X is the original data matrix, W is the eigenvector matrix, and X' is the reduced feature matrix. By retaining principal components whose explained variance exceeds a certain threshold (e.g., 95%), the reduced feature matrix is ​​obtained. Based on this matrix and domain knowledge, operating condition characteristics such as heat exchanger efficiency, temperature gradient, and pressure fluctuation characteristics are extracted to form an operating condition feature vector.

[0049] Normalizing each feature in the operating condition feature vector allows for effective comparison and analysis of features of different dimensions and orders of magnitude. Common normalization methods include Min-Max normalization and Z-score normalization. Applying a time window sliding technique to the normalized feature vector, feature extraction is performed along the time dimension, capturing the dynamic characteristics of system parameters. This ultimately yields a flue gas system operating feature sequence that captures both the static characteristics of each system parameter and the dynamic characteristics of these parameters over time.

[0050] In this embodiment, the detailed implementation steps of step S2 include:

[0051] According to the operation characteristic sequence, the mass conservation equations of the flue gas waste heat recovery system are established to obtain the mass transfer model;

[0052] Based on the mass transfer model, the system energy balance equation is established to obtain the heat transfer model;

[0053] Combining the heat transfer model with the equipment structural parameters, a heat transfer coefficient calculation model was constructed to obtain a preliminary thermal energy conversion efficiency model;

[0054] Calibrate and verify the parameters of the preliminary thermal energy conversion efficiency model to obtain a complete thermal energy conversion efficiency model;

[0055] The parameter sensitivity analysis of the thermal energy conversion efficiency model was carried out by using the coefficient of variation method and variance analysis, and a parameter sensitivity ranking table was obtained;

[0056] Parameters with contribution rates exceeding the threshold are screened out according to the parameter sensitivity ranking table to identify key influencing factors of the system.

[0057] In this embodiment, a set of mass conservation equations for the flue gas waste heat recovery system is established based on parameters such as flow, density, and components extracted from the operating characteristic sequence. 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 at 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 at 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 condensed water. Combining the component information of the flue gas and the chemical reaction balance, a component mass conservation equation is established. 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.

[0058] Based on the mass transfer model and temperature data from the operating characteristic sequence, the system's energy balance equation is established. The heat released by the flue gas is Q_g = m_g × c_g × (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 flue gas inlet and outlet temperatures, respectively. The heat absorbed by the heat medium is Q_w = m_w × c_w × (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 heat medium inlet and outlet temperatures, respectively. Considering the system's heat loss, Q_loss, the energy balance equation becomes Q_g = Q_w + Q_loss. If phase change processes (such as water vapor condensation) are considered, a latent heat term, Q_latent = m_cond × h_fg, is also required, where h_fg is the latent heat of condensation. These equations constitute the system's heat transfer model.

[0059] The heat transfer model is combined with the structural parameters of the heat exchanger (such as heat transfer area A, tube diameter d, tube length L, etc.) to construct a heat transfer coefficient calculation model. According to the principle of heat transfer, the total 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, δ is the heat transfer wall thickness, and λ is the thermal conductivity of the wall material. The convective heat transfer coefficient can be calculated using the dimensionless criterion correlation formula, as , where Nu, Re, and Pr are the Nusselt number, Reynolds number, and Prandtl number, respectively, and C, m, and n are empirical coefficients. Combined with the heat transfer coefficient and temperature difference, the heat exchange amount is calculated. LMTD is the logarithmic mean temperature difference. These relationships constitute a preliminary thermal energy conversion efficiency model.

[0060] The preliminary thermal energy conversion efficiency model is calibrated using actual operating data. Least squares methods or other optimization algorithms are used to adjust unknown model parameters (such as the empirical coefficients C, m, n, and the heat loss coefficient) to minimize the error between the model's predicted values ​​and the observed values. The calibrated model is then applied to a validation dataset to evaluate its predictive performance. Validation metrics include mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²). If the validation results are unsatisfactory, the calibration process is repeated to readjust the parameters. After multiple rounds of calibration and validation, a refined model that accurately reflects the system's thermal energy conversion efficiency is obtained.

[0061] Perform parameter sensitivity analysis on the perfect thermal energy conversion efficiency model to quantify the influence of different parameters on the model output. Use the coefficient of variation method to perturb each parameter xi within its 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 effect of parameter xi on the output. The variance analysis method is used to calculate the contribution rate of each parameter to the total variance, which is expressed as , where Vi is the variance caused by parameter xi, and V is the total variance. All parameters are sorted from high to low according to sensitivity to form a parameter sensitivity ranking table.

[0062] Based on the parameter sensitivity ranking table, parameters with contribution rates exceeding a predetermined threshold (e.g., 5%) are screened and identified as key influencing factors of the system. Key influencing factors typically include flue gas inlet temperature, flue gas flow rate, heat medium flow rate, and heat exchanger fouling. These factors will serve as key considerations for subsequent system optimization and control. Sensitivity analysis can reduce system complexity, focus on truly critical parameters, and improve optimization and control efficiency.

[0063] In the embodiment of the present invention, see Figure 2 , is a flowchart of the detailed implementation steps of step S3. In this embodiment, the detailed implementation steps of step S3 include:

[0064] Establish an external environmental parameter monitoring network to collect data such as ambient temperature, humidity, air pressure, and seasonal changes, and obtain a time series of external environmental parameters;

[0065] Conduct time-frequency analysis on the time series of external environmental parameters to obtain periodic change characteristics and trend characteristics;

[0066] Conduct correlation analysis between periodic change characteristics and trend characteristics and key influencing factors of the system to obtain a system performance coupling mechanism model;

[0067] Based on the system performance coupling mechanism model, a system performance response function is constructed to obtain a parameter coupling relationship diagram; the parameter coupling relationship diagram is quantified and matrix converted to form a dynamic impact matrix.

[0068] In this embodiment, environmental parameter monitoring equipment is arranged around the flue gas waste heat recovery system to establish an external environmental parameter monitoring network. Ambient temperature sensors measure the ambient air temperature, recording diurnal and seasonal variations, with data ranging from, for example, -20°C to 40°C. Humidity sensors measure relative humidity, ranging from, for example, 20% to 95%. Air pressure sensors measure atmospheric pressure, ranging from, for example, 95kPa to 105kPa. Furthermore, meteorological parameters such as rainfall, wind speed, and wind direction, as well as seasonal variation data, are recorded. These sensors continuously collect data at an appropriate sampling frequency (e.g., every 10 minutes), forming a time series of external environmental parameters that captures how these parameters change over time.

[0069] Time-frequency analysis is performed on the collected time series of external environmental parameters to extract periodic and trend characteristics. Fast Fourier transform (FFT) analysis is used to analyze the spectral characteristics of environmental parameters and identify major periodic components, such as daily (24-hour), weekly (7-day), and annual (365-day) cycles. Time-frequency analysis methods such as wavelet transform are used to study the variation characteristics of environmental parameters at different time scales. Trend analysis methods (such as moving average and linear regression) are used to extract long-term trends in environmental parameters, such as seasonal and interannual variations. The extracted periodic and trend characteristics are represented using mathematical models to provide a basis for subsequent analysis.

[0070] Perform a correlation analysis between the periodic variation and trend characteristics of the external environmental parameters and the key influencing factors of the system identified in step S2. Calculate statistics such as the Pearson correlation coefficient, Spearman rank correlation coefficient, or mutual information to quantify the degree of correlation between changes in environmental parameters and key system factors. Use methods such as multivariate regression analysis, principal component regression, or partial least squares regression to establish a quantitative relationship model between environmental parameters and key system factors. Consider the interactions between parameters, introduce cross terms and nonlinear terms, and construct a more complex relationship model. Based on physical mechanisms and domain knowledge, explain the impact of environmental parameters on system performance, such as the impact of ambient temperature on heat exchange efficiency and the impact of humidity on condensation volume. Based on the above analysis, establish a system performance coupling mechanism model that describes how changes in external environmental parameters ultimately affect system performance by affecting key system factors.

[0071] Based on the system performance coupling mechanism model, a system performance response function is constructed, expressed as P = f(E, S), where P is the system performance indicator (such as heat recovery efficiency), E is the external environmental parameter vector, and S is the internal system parameter vector. System performance indicators are calculated for different combinations of external environmental parameters and system parameters, resulting in a multidimensional performance response space. This response space is visualized to generate a parameter coupling relationship diagram, which illustrates the coupling relationship between different parameters and their combined impact on system performance. This relationship diagram can be presented in the form of a heat map, contour plot, or 3D surface plot to intuitively display the complex relationships between parameters.

[0072] The parameter coupling relationship graph is quantified to extract the coupling strength and influence weights between parameters. The node influence strength vector is calculated to represent the direct influence of each parameter node on system performance. The edge coupling strength matrix is ​​calculated to represent the mutual influence strength between parameters. A graph convolutional network model is constructed to simulate the propagation process of parameter influence and analyze the cascading effect of parameter changes. The time evolution of the parameter propagation model is simulated to study the dynamic impact of changes in external environmental parameters on system performance. Finally, the time-varying influence coefficients are organized into a matrix form, forming a dynamic influence matrix D, where element Dij represents the time-varying influence of external environmental parameter j on the key influencing factor i of the system. This matrix is ​​a mathematical expression of the system performance coupling relationship and provides a basis for subsequent stress-life analysis and adaptive control.

[0073] In this embodiment, the detailed implementation steps of performing quantization processing and matrix conversion on the parameter coupling relationship diagram in step S3 to form a dynamic influence matrix include:

[0074] Calculate the weights of the nodes in the parameter coupling relationship diagram to obtain the node influence intensity vector;

[0075] Perform strength evaluation on the edges in the parameter coupling relationship graph to obtain the edge coupling strength matrix;

[0076] A graph convolutional network is established based on the node influence strength vector and the edge coupling strength matrix to obtain a parameter propagation model. The time evolution of the parameter propagation model is simulated to obtain the time-varying influence coefficient.

[0077] The time-varying influence coefficients are organized into a matrix form according to the key influencing factors of the system and the external environmental parameters to form a dynamic influence matrix.

[0078] In this embodiment, the influence intensity of each node in the parameter coupling relationship diagram (including external environment parameter nodes and system key influencing factor nodes) is calculated. The local sensitivity analysis method is used to perform a small amplitude perturbation (such as ±5%) on each node parameter, observe the changes in system performance indicators, and calculate the sensitivity coefficient. , where ΔP is the change in the performance indicator, P is the baseline value of the performance indicator, Δxi is the perturbation of parameter xi, and xi is the baseline value of the parameter. Using variance contribution analysis, we calculate the contribution of each node parameter to the total variance of system performance. Taking into account the sensitivity coefficient and variance contribution, we calculate the combined influence of each node, forming a node influence intensity vector W = [w1, w2, ..., wn], where wi is the influence intensity of node i and n is the total number of nodes.

[0079] The strength of each edge in the parameter coupling relationship diagram is evaluated to quantify the degree of mutual influence between nodes. The partial correlation analysis method is used to calculate the correlation between two parameters while controlling other variables. The cross sensitivity is calculated to represent the effect of the change of parameter i on the sensitivity of parameter j. The cross sensitivity coefficient Based on physical models or data-driven methods, the transfer coefficient of parameter changes is estimated, which represents the direct impact of the change in parameter j on parameter i. These evaluation results are integrated to form the edge coupling strength matrix C, where the element Cij represents the coupling strength of parameter j to parameter i.

[0080] Based on the node influence strength vector W and the edge coupling strength matrix C, a graph convolutional network (GCN) model is constructed. The layer propagation rule of GCN is expressed as , where H(l) is the node representation of layer l, H(l+1) is the node representation of layer l+1, A is the adjacency matrix after adding self-loops (built based on the edge coupling strength matrix C), D is the degree matrix, W(l) is the weight matrix of layer l, and σ is the nonlinear activation function. By training the GCN model and learning the complex interactions between parameters, we obtain a parameter propagation model that can simulate the propagation process of parameter changes in the system.

[0081] , simulate the time evolution of the parameter propagation model to study the dynamic impact of changes in external environmental parameters on key system influencing factors. Set different time scales (such as hours, days, seasons, and years) and simulate the variation patterns of external environmental parameters at these time scales. Input the simulated environmental parameter changes into the parameter propagation model and calculate the response of key system influencing factors. Analyze the impact characteristics at different time scales, such as short-term fluctuations, medium-term trends, and long-term cumulative effects. Extract the time-varying impact coefficient, which represents the time-varying impact of environmental parameter changes on key system factors.

[0082] The time-varying influence coefficients are organized into a matrix based on the key system influencing factors (rows) and external environmental parameters (columns), forming the dynamic influence matrix D. The matrix element Dij(t) in the i-th row and j-th column represents the degree of influence of external environmental parameter j on the key system influencing factor i at time t. Matrix D is not static but rather changes with time; that is, different matrices D(t) exist for different time points t. The dynamic influence matrix comprehensively describes the influence of changes in external environmental parameters on the key system influencing factors, providing a mathematical foundation for subsequent stress-life analysis and the development of adaptive control strategies.

[0083] In this embodiment, the detailed implementation steps of step S4 include:

[0084] The stress distribution of key components of the system is calculated based on the dynamic influence matrix to obtain the stress time series; the stress time series is processed by the rain flow counting method to obtain the stress cycle spectrum;

[0085] Based on the stress cycle spectrum and material SN curve, a cumulative damage model is established to obtain the damage evolution function. Monte Carlo simulation is performed on the damage evolution function to establish an equipment failure prediction model.

[0086] Based on the equipment failure prediction model, the reliability function of each key component is calculated to obtain the reliability distribution; the reliability lower limit is determined according to the system safety requirements, and the system reliability constraints are determined in combination with the reliability distribution.

[0087] In this embodiment, the stress impact of changes in external environmental parameters on key system components (such as heat exchangers, valves, fans, etc.) is calculated based on the dynamic impact matrix. Stress types include thermal stress, mechanical stress, and chemical stress. Thermal stress is caused by 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 arises from pressure fluctuations, flow changes, and vibration and is calculated through mechanical analysis. Chemical stress arises from corrosion, erosion, and deposition and is calculated using a chemical reaction model. By superimposing these various stresses, the total stress distribution of key components is obtained. Taking into account the temporal variations of external environmental parameters, the stress evolution over time is calculated to form stress time series. These series reflect the dynamic stress conditions experienced by key system components in the actual operating environment.

[0088] The rainflow counting method is applied to the stress time series to convert the complex stress history into a collection of stress cycles. The steps of the rainflow counting method include: converting the stress time series into a peak-valley sequence to eliminate small fluctuations; converting the peak-valley sequence into a "rainflow" path and counting it according to specific rules; and counting the number of cycles with different stress amplitudes and average stress levels. The processing results form a stress cycle spectrum, which is 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 a component under actual operating conditions and provides a basis for fatigue life assessment.

[0089] Based on the stress cycle spectrum and the material's SN curve (stress-life curve), a cumulative damage model is established. The SN curve is expressed as , where N is the fatigue life (number of cycles) under stress amplitude Δσ, and m and C are material constants. Considering the influence of mean stress, the SN curve is adjusted using methods such as Goodman correction. The Miner linear cumulative damage theory is used to calculate the damage accumulation. , where ni is the actual number of cycles at stress amplitude Δσi, and Ni is the fatigue life at that stress amplitude. When D reaches 1, the component will theoretically fail due to fatigue. Based on historical stress data and future stress predictions, a damage evolution function D(t) is established to describe the accumulation of damage over time.

[0090] Perform Monte Carlo simulations on the damage evolution function, accounting for the uncertainty of model parameters and input variables. Identify random variables in the damage evolution function, such as material performance parameters (m, C), stress prediction values, and operating conditions, and determine the probability distribution type (e.g., 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 parameter combination. Substitute each group of samples into the damage evolution function and calculate the corresponding failure time prediction. Statistically calculate 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. Develop a Bayesian network model, combining the failure time distribution with real-time monitoring data to achieve dynamic updating and prediction of equipment status. Ultimately, form an equipment failure prediction model that can predict the failure probability and remaining life of the equipment under different operating conditions.

[0091] Calculate the reliability function of each key component of the system based on the equipment failure prediction model , where F(t) is the cumulative distribution function of failure time. The reliability function represents the probability that a component will still function properly at time t. Analyzing the changes in the reliability function under different operating conditions reveals the distribution of reliability over time and operating conditions. To assess the overall reliability of the system, consider the logical relationships between components (such as series, parallel, or complex structures) and calculate the reliability function at the system level.

[0092] Based on system safety requirements and industry standards, determine the lower threshold Rmin for system reliability, such as 0.95 or 0.99. Under all operating conditions, the system reliability must not fall below this threshold, that is, R(t) ≥ Rmin. Combined with reliability distribution analysis, reliability constraints are converted into system parameter constraints, such as upper temperature limits, pressure limits, and flow rate ranges. These constraints form the system reliability constraint set, which serves as boundary conditions for subsequent optimization. System reliability constraints ensure that the system pursues high efficiency without excessively sacrificing safety and reliability, thus ensuring long-term stable operation of the system.

[0093] 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:

[0094] Identify the random variables in the damage evolution function, determine their probability distribution type and parameters, and obtain a random variable description set; generate a large number of random samples based on the random variable description set to obtain a random sample matrix;

[0095] Substitute each group of samples in the random sample matrix into the damage evolution function to calculate and obtain the failure time sample set; perform statistical analysis on the failure time sample set to obtain the failure time distribution function;

[0096] A Bayesian network is established based on the failure time distribution function, and the status is updated in combination with real-time monitoring data to obtain an equipment failure prediction model.

[0097] In this embodiment, the damage evolution function is first identified The random variables in the model are as follows. Material-related random variables include the SN curve parameters m and C, which are affected by material batches, manufacturing processes, and environmental conditions. Stress-related random variables include stress amplitude predictions and stress cycle frequencies, which are affected by external loads, environmental conditions, and system operating parameters. Environment-related random variables include temperature, humidity, and corrosive substance concentrations, which affect material properties and damage rates. For each random variable, its probability distribution type is determined based on historical data and professional knowledge. For example, the material parameter m may follow the normal distribution N(μm, σm²), the parameter C may follow the lognormal distribution, and the stress prediction value may follow the truncated normal distribution. Parameter estimation methods (such as maximum likelihood estimation and moment estimation) are used to determine the parameter values ​​of each distribution. All random variables and their distribution information are organized into a random variable description set to provide input for subsequent Monte Carlo simulations.

[0098] Based on a set of random variable descriptions, random number generation techniques are used to generate a large number of random samples. For each random variable, a specified number (e.g., 10,000) of random values ​​are generated according to its probability distribution. Taking into account the correlations between variables, correlation structures (such as copula functions) are used to generate multidimensional random variables with the specified correlations. The generated random values ​​are organized into a matrix, where each row represents a set of parameter combinations and each column represents a random variable. This matrix, called the random sample matrix, covers every possible combination in the parameter space and is used to simulate the behavior of the system under different conditions.

[0099] For each row (i.e., each parameter combination) in the random sample matrix, the damage evolution function is substituted and calculated. This calculation may require solving differential equations or performing numerical integration, depending on the form of the damage evolution function. For each parameter combination, the time until the system reaches a specific damage threshold (e.g., D = 1, representing the theoretical failure point) is recorded. The failure times of all samples are collected to form a failure time sample set, which reflects the statistical distribution of the system's failure time.

[0100] Perform statistical analysis on the failure time sample set to extract its distribution characteristics. Calculate basic sample statistics such as mean, median, standard deviation, skewness, and kurtosis to gain a preliminary understanding of the distribution shape. Use kernel density estimation to estimate the probability density function f(t) of the failure time. Calculate the cumulative distribution function F(t) = P(T ≤ t), which represents the probability of the system failing before time t. Try fitting the sample data with common life distributions (such as Weibull, lognormal, and gamma distributions) and select the distribution that best fits the failure time distribution function.

[0101] Based on the failure time distribution function, a Bayesian network model is established to combine prior knowledge with real-time monitoring data. A Bayesian network structure is designed, including nodes (such as material parameters, stress levels, environmental conditions, damage states, and failure times) and edges (representing conditional dependencies between nodes). A conditional probability table (CPT) is defined for each node to reflect the quantitative relationship between variables. When new monitoring data is obtained, Bayesian inference is used to update the probability distribution in the network, enabling dynamic updating of the model. Combining monitoring data with the updated model, the current state of the equipment and the probability of future failure are predicted. Ultimately, an equipment failure prediction model is formed that can dynamically predict the remaining life and failure risk of the equipment based on real-time data, providing support for equipment management and maintenance decisions.

[0102] In this embodiment, the detailed implementation steps of step S5 include:

[0103] The thermal energy conversion efficiency model is converted into an efficiency objective function to obtain the first optimization objective; the system operation cost and resource consumption are converted into a cost objective function to obtain the second optimization objective; the system reliability constraint is converted into a set of constraint conditions to obtain the constraint equation group of the optimization problem;

[0104] A multi-objective optimization function is constructed based on the first optimization objective, the second optimization objective and the constraint equation group; an improved particle swarm optimization algorithm is applied to solve the multi-objective optimization function and obtain the Pareto optimal solution set; a cluster analysis is performed on the Pareto optimal solution set, and an adaptive control strategy library is generated for different operating conditions.

[0105] In this embodiment, the thermal energy conversion efficiency model η=f(x1, x2, ..., xn) is converted into an efficiency objective function. The efficiency objective function is defined as maximizing the thermal energy conversion efficiency, expressed as maxη=f(x1, x2, ..., xn), where x1, x2, ..., xn are the control parameters of the system, such as flue gas flow, heat medium flow, heat exchanger parameters, etc. To improve the applicability of the model, the weighted average efficiency under different working conditions is considered, expressed as , where wi is the weight of operating condition i, and ηi is the efficiency under operating condition i. Depending on the system characteristics, the efficiency objective function may include nonlinear terms, interaction terms, and constraints. After mathematical transformation and simplification, the standardized efficiency objective function is obtained as the first optimization objective.

[0106] Define the cost objective function of system operation cost and resource consumption. Operation cost includes energy cost, maintenance cost and depreciation cost, etc. Energy cost , where Pe is the unit price of energy e, and Ee is the consumption of energy e. Maintenance cost CM is typically related to equipment operating time, number of starts and stops, and operating intensity. Resource consumption includes the use of resources such as water, electricity, and fuel. Combining these costs 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 a time factor, such as net present value (NPV) or life cycle cost (LCC). After appropriate mathematical processing, a normalized cost objective function is obtained, which serves as the second optimization objective.

[0107] Transform system reliability constraints into a set of mathematical constraints. Safety reliability constraints include: reliability constraint R(t) ≥ Rmin, where R(t) is the system reliability function and Rmin is the minimum reliability requirement; failure rate constraint λ(t) ≤ λmax, where λ(t) is the failure rate function and λmax is the maximum allowable failure rate; remaining life constraint RUL ≥ RULmin, where RUL is the predicted remaining life and RULmin is the minimum remaining life requirement. Physical parameter constraints include: temperature constraint Tmin ≤ T ≤ Tmax; pressure constraint Pmin ≤ P ≤ Pmax; flow constraint Fmin ≤ F ≤ Fmax; and rate of change constraint |dX / dt| ≤ (dX / dt)max. Process requirement constraints include specific process parameter constraints and environmental requirement constraints. Organize these constraints into a standard form to form a set of constraint equations for the optimization problem.

[0108] A multi-objective optimization function is constructed based on an efficiency objective function (the first optimization objective), a cost objective function (the second optimization objective), and a set of constraint equations. The standard form of a multi-objective optimization problem is: minF(x)=[f1(x),f2(x)]T, where f1(x)=-η(x) (negating it translates to a minimization problem), f2(x)=C(x), and the constraints 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 typically increases cost, while reducing cost may reduce efficiency. The goal of multi-objective optimization is to find a set of Pareto optimal solutions. These solutions constitute the Pareto frontier, representing the best compromise between efficiency and cost.

[0109] A modified particle swarm optimization (MOPSO) algorithm is applied to solve multi-objective optimization functions. MOPSO is a multi-objective optimization extension of the particle swarm optimization algorithm, suitable for solving multi-objective problems with nonlinear objectives and constraints. The algorithm's workflow includes: initializing the particle swarm; evaluating the objective function values ​​of the particles; performing a non-dominated sort; updating an external archive (storing Pareto optimal solutions); updating particle positions and velocities; and introducing adaptive inertia weights and a chaotic perturbation mechanism to enhance the algorithm's global search capability and convergence. After multiple iterations, the algorithm converges to a set of Pareto optimal solutions, which form the Pareto frontier, representing the optimal compromise between efficiency and cost.

[0110] Perform cluster analysis on the Pareto optimal solution set to identify groups of solutions with similar characteristics. Use clustering algorithms such as K-means, hierarchical clustering, or DBSCAN to cluster the Pareto optimal solutions into k categories, each representing a type of control strategy. For each cluster, select a representative solution as the typical strategy for that category, and record the corresponding control parameter combination. Associate the clustering results with the system operating conditions to analyze the types of control strategies applicable under different operating conditions. For example, high-load conditions may be suitable for efficiency-first strategies, while low-load conditions may be suitable for cost-first strategies. Organize the mapping relationship between strategies and 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, providing decision support for the adaptive control of the system under changing environments.

[0111] 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:

[0112] Initialize the particle swarm parameters and population size, generate the initial particle position and velocity matrix; perform constraint condition checks on the initial particle positions, screen out feasible solutions that meet the constraints, and obtain the initial feasible solution set;

[0113] Calculate the multi-objective function value of each particle in the initial feasible solution set, determine the particle level according to the non-dominated sorting, and obtain the sorting result;

[0114] Based on the sorting results, the individual optimal position and the global optimal position of the particles are updated to obtain the optimized direction vector; the adaptive inertia weight and chaotic perturbation mechanism are introduced to update the particle velocity and position to obtain a new generation of particle swarm; the multi-objective function evaluation, non-dominated sorting and position update are repeated until the convergence conditions are met and the Pareto optimal solution set is obtained.

[0115] In this embodiment, the parameters of the improved particle swarm optimization algorithm are first set, including the number of particles N (e.g., 100), the maximum number of iterations Tmax (e.g., 500), the inertia weight range [wmin, wmax] (e.g., [0.4, 0.9]), and the learning factors c1 and c2 (e.g., both 2). The dimension D of the optimization problem, i.e., the number of decision variables, such as the number of control parameters, is determined. The particle position matrix X is initialized, with each row representing a particle and each column representing a decision variable. Position values ​​are randomly generated within the constraints of the variables. The particle velocity matrix V is initialized, with velocity values ​​randomly generated within the range [-Vmax, Vmax], where Vmax is the maximum velocity constraint. The individual optimal position matrix P of the particles is initialized, with initial values ​​equal to the initial position matrix X. An external archive is initialized to store Pareto optimal solutions.

[0116] For each particle in the initial particle position matrix X, check whether it meets the constraints. 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 particles that do not meet the constraints, constraint processing techniques such as penalty function method, repair method or special operators are used. 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 infeasible solutions to feasible regions, such as boundary processing or projection methods. Screen out particles that meet all constraints to form an initial feasible solution set.

[0117] 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 target, taking a negative value to convert it into a minimization problem), and f2(x)=C(x) (cost target). Based on the multi-objective function values, perform non-dominated sorting to determine the Pareto rank of each particle. If all objective function values ​​of particle A are not inferior to particle B, and at least one objective function value is better than particle B, then particle A dominates particle B. Particles that are not dominated by any other particles constitute the first Pareto front (level 1). From the remaining particles, particles that are not dominated by any particles constitute the second Pareto front (level 2), and so on. In order to maintain the diversity of solutions, the congestion of each particle is calculated to represent the density in the solution space. The formula for calculating congestion is , where fi,next and fi,prev are the target values ​​of the two adjacent solutions on the i-th target, fi,max and fi,min are the maximum and minimum values ​​of the i-th target. The sorting result of the particles is determined according to the Pareto rank and congestion degree.

[0118] Based on the results of the non-dominated sort, update the individual optimal position P of each particle. If the current position X dominates the individual optimal position P, update P = X; if P dominates X, 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 (level 1 particles) in the current iteration to the archive. If the existing solutions in the archive are dominated by the new solution, delete the dominated solutions. If the archive size exceeds the limit, use congestion or other mechanisms to select the retained solutions. Select the global optimal position g from the external archive as the particle's movement target. The selection method can be random selection, roulette wheel selection, or selection based on congestion. Based on the individual optimal position P and the global optimal position g, determine the particle's optimization direction vector.

[0119] An adaptive inertia weight mechanism is introduced to adjust the inertia weight w according to the iterative process. The 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 in the early stage of the search to enhance the global search capability; use a smaller inertia weight in the later stage of the search to enhance the local search capability. Introduce a chaotic perturbation mechanism to prevent the algorithm from falling into local optimality. Chaotic perturbations 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 particle's position at time t, and X(t+1) is the particle's position at time t+1. The updated position is bounds-checked to ensure it is within the variable constraints. A new generation of particle swarms is generated for the next iteration.

[0120] The multi-objective function evaluation, non-dominated sorting, and position update steps are repeated until convergence conditions are met. Convergence conditions can include reaching the maximum number of iterations Tmax, maintaining minimal change in the Pareto front over multiple iterations, or no significant improvement in the hypervolume metric. Finally, a set of Pareto-optimal solutions is extracted from an external archive and used as the solution to the multi-objective optimization problem. These solutions constitute the Pareto front, each representing an optimal compromise between efficiency and cost. Different solutions are suitable for different application scenarios and priority requirements.

[0121] In this embodiment, the detailed implementation steps of step S6 include:

[0122] Establish a prediction model for external environmental parameter changes, predict external parameters in future periods, and obtain a parameter change prediction sequence;

[0123] Combine the parameter change prediction sequence with the dynamic impact matrix to predict the system performance change trend and obtain the performance prediction curve;

[0124] Based on the performance prediction curve, the optimal control strategy is selected from the adaptive control strategy library to obtain a preliminary control parameter set; the preliminary control parameter set is dynamically adjusted and optimized to obtain a real-time control instruction sequence;

[0125] The real-time control instruction sequence is sent to the system actuator, and the system response is monitored in real time for closed-loop feedback adjustment; the control strategy is continuously updated according to the system operating status and external environmental changes to achieve reliable and efficient operation of the system under complex working conditions.

[0126] In this embodiment, a prediction model for changes in external environmental parameters (such as ambient temperature, humidity, and air pressure) is established. Based on the data characteristics, an appropriate prediction model is selected, such as a time series model (such as ARIMA and SARIMA), a machine learning model (such as random forest and support vector regression), or a deep learning model (such as LSTM and GRU). Time series models are suitable for parameters with significant temporal 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 and differencing); feature engineering (such as temporal feature extraction and lagged feature creation); model parameter optimization (such as grid search and Bayesian optimization); and model validation (such as cross-validation and time series segmentation). Using the trained model, external environmental parameters are predicted for future time periods (such as the next 24 hours or 7 days), generating a parameter change prediction sequence. This sequence describes the changing trend of the external environmental parameters over the future time period.

[0127] The parameter change prediction sequence is combined with the dynamic impact matrix D to predict the changing trend of system performance. At time point t, the predicted values ​​of the external environmental parameters are E(t) = [e1(t), e2(t), ..., ek(t)], and the predicted values ​​of the key system influencing factors are S(t) = D(t) × E(t) + S0, where S0 is the baseline value. Based on the predicted key system influencing factors S(t) and the thermal energy conversion efficiency model, system performance indicators P(t) = f(S(t)) are calculated, such as heat recovery efficiency and operating cost. The performance indicators are plotted over time to form a performance prediction curve. The characteristics of the performance prediction curve, such as the mean, fluctuation range, and trend, are analyzed to provide a basis for subsequent control strategy selection.

[0128] Based on the performance prediction curve and the current state of the system, the optimal control strategy is selected from the adaptive control strategy library. Factors considered in control strategy selection include: predicted performance indicators (such as efficiency and cost); system reliability requirements; changing characteristics of the external environment (such as stability and volatility); and the system's operating history and current state. Strategy selection methods can be rule-based (such as if-then rules), similarity-based (such as k-nearest neighbor), or machine learning-based (such as decision trees and random forests). The optimal strategy selected from the strategy library contains a set of control parameters, such as flow setpoints, temperature setpoints, and valve openings, which constitute the preliminary control parameter set.

[0129] Dynamically adjust and optimize the initial set of control parameters to better adapt them to the real-time environment and system status. Based on real-time system feedback, fine-tune the control parameters, such as using a PID controller, fuzzy controller, or model predictive controller. Consider the interactions and constraints between parameters and perform overall optimization to avoid system imbalances caused by single parameter adjustments. Design a smooth transition mechanism to avoid sudden changes in control parameters and minimize system impact. Perform a pre-execution check 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 dynamic system control.

[0130] The real-time control instruction sequence is sent to the system's actuators, such as control valves, frequency converters, dampers, etc., through the communication network. The actuators adjust the system's operating parameters, such as flow, temperature, and pressure, according to the control instructions. The system's response data, including parameters such as temperature, pressure, flow, and efficiency, are collected in real time through the monitoring network. The difference between the actual system response and the expected response is compared to calculate the control error. Based on the control error, a feedback control algorithm (such as PID control) is used to make real-time adjustments to form a closed-loop control. The mathematical expression of 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 differential coefficients. Closed-loop feedback regulation ensures that the system can quickly respond to changes in the external environment and maintain stable operation.

[0131] Establish a continuous monitoring mechanism for system operating status and external environmental changes, and regularly evaluate the effectiveness of the current control strategy. Significant changes in the external environment or significant deviations in system performance trigger a control strategy update. This update can involve reselecting from the strategy library or conducting online learning and adjustment of existing strategies. As system operating data accumulates, use machine learning methods (such as reinforcement learning and transfer learning) to continuously refine and expand the strategy library and enhance the system's adaptability. Through continuous strategy updates and optimization, the system can achieve reliable and efficient operation under complex and changing operating conditions, improve waste heat recovery efficiency, reduce energy consumption, and extend equipment life.

[0132] The present invention provides a flue gas waste heat recovery system optimization design method that considers external parameter variations. By processing and extracting features from monitoring data, establishing a thermodynamic model, analyzing the impact of external environmental parameters on system performance, predicting equipment lifespan, and optimizing control strategies, this method ensures reliable and efficient system operation in complex environments. This method effectively improves the system's energy efficiency, extends equipment lifespan, and reduces operating costs, resulting in significant economic and environmental benefits.

[0133] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art will be able to modify the technical solutions described in the foregoing embodiments or to substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

[0134] It should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus comprising the element.

[0135] In the description of the present invention, it should be understood that the terms "first", "second", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0136] In the description of the present invention, unless otherwise specified, "plurality" means two or more.

[0137] In the description of the present invention, “several” means one or more, and “a large number” means two or more.

[0138] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0139] The formulas in this manual are all dimensionless and calculated using numerical values. The formulas are obtained by collecting a large amount of data and performing software simulation to obtain the most recent real situation. The preset parameters and thresholds in the formulas are set by technicians in this field based on actual conditions.

[0140] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the claims and their equivalents.

Claims

1. A flue gas waste heat recovery system optimization design method considering changes in external parameters, characterized in that: include: Step S1: Acquire a monitoring data set of a flue gas waste heat recovery system; Extracting operating condition features and performing noise processing on the monitoring data set to obtain an operating feature sequence of the flue gas system; Step S2: performing thermodynamic modeling on the operation characteristic sequence to construct a thermal energy conversion efficiency model; analyzing parameter sensitivity based on the thermal energy conversion efficiency model to identify key influencing factors of the system; Step S3: Collecting external environmental parameter change data; combining the external environmental parameter change data with the key influencing factors of the system to establish a system performance coupling mechanism model, and then obtain a dynamic impact matrix; including: establishing an external environmental parameter monitoring network, collecting environmental temperature, humidity, air pressure and seasonal changes, and obtaining an external environmental parameter time series; Performing time-frequency analysis on the time series of the external environmental parameters to obtain periodic change characteristics and trend characteristics; Conducting correlation analysis on the periodic change characteristics and trend characteristics with key influencing factors of the system to obtain a system performance coupling mechanism model; Constructing a system performance response function based on the system performance coupling mechanism model to obtain a parameter coupling relationship diagram; The parameter coupling relationship diagram is quantized and matrix converted to form a dynamic influence matrix, including: Performing weight calculation on the nodes in the parameter coupling relationship graph to obtain a node influence intensity vector; Performing strength evaluation on edges in the parameter coupling relationship graph to obtain an edge coupling strength matrix; A graph convolutional network is established based on the node influence strength vector and the edge coupling strength matrix to obtain a parameter propagation model; Performing a time evolution simulation on the parameter propagation model to obtain a time-varying influence coefficient; Organizing the time-varying influence coefficients into a matrix form according to key influencing factors of the system and external environmental parameters to form a dynamic influence matrix; Step S4: performing stress-life analysis using the dynamic influence matrix to establish an equipment failure prediction model; evaluating safety margins based on the equipment failure prediction model to determine system reliability constraints; including: calculating stress distributions of key system components based on the dynamic influence matrix to obtain stress time series; and performing rain flow counting on the stress time series to obtain a stress cycle spectrum; Establishing a cumulative damage model based on the stress cycle spectrum and the material SN curve to obtain a damage evolution function; Performing Monte Carlo simulation on the damage evolution function to establish an equipment failure prediction model; Calculating the reliability function of each key component based on the equipment failure prediction model to obtain a reliability distribution; Determine the reliability lower limit according to the system safety requirements, and determine the system reliability constraint in combination with the reliability distribution; Step S5: constructing a multi-objective optimization function based on the thermal energy conversion efficiency model and the system reliability constraint; applying an intelligent algorithm to solve the optimal parameter combination and generate an adaptive control strategy library; Step S6: Based on the adaptive control strategy library and the dynamic influence matrix, predictive adjustment is performed for changes in external parameters.

2. 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 acquisition of a monitoring data set of a flue gas waste heat recovery system; The monitoring data set is subjected to operating condition feature extraction and noise processing to obtain an operating feature 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 a monitoring data set; Performing time series segmentation and outlier identification on the monitoring data set to obtain a cleaned data matrix; Performing wavelet transform noise reduction and filtering on the cleaned data matrix to obtain a smoothed data sequence; Performing principal component analysis and operating condition feature extraction on the smoothed data sequence to obtain an operating condition feature vector; The operating condition characteristic vector is normalized and time window sliding is performed to obtain an operating characteristic sequence of the flue gas system.

3. 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: said performing thermodynamic modeling on said operation characteristic sequence to construct a thermal energy conversion efficiency model; Analyze parameter sensitivity based on the thermal energy conversion efficiency model and identify key influencing factors of the system, including: Establishing a mass conservation equation group of the flue gas waste heat recovery system according to the operation characteristic sequence to obtain a mass transfer model; Establishing a system energy balance equation based on the mass transfer model to obtain a heat transfer model; Combining the heat transfer model with the equipment structural parameters, a heat transfer coefficient calculation model is constructed to obtain a preliminary heat energy conversion efficiency model; calibrating and verifying parameters of the preliminary thermal energy conversion efficiency model to obtain a thermal energy conversion efficiency model; Performing parameter sensitivity analysis on the thermal energy conversion efficiency model by using the coefficient of variation method and variance analysis to obtain a parameter sensitivity ranking table; Parameters whose contribution rates exceed a threshold are screened out according to the parameter sensitivity ranking table to identify key influencing factors of the system.

4. 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 performing of Monte Carlo simulation on the damage evolution function to establish an equipment failure prediction model includes: Identifying random variables in the damage evolution function, determining their probability distribution types and parameters, and obtaining a random variable description set; Generate a random sample based on the random variable description set to obtain a random sample matrix; Substituting each group of samples in the random sample matrix into the damage evolution function for calculation to obtain a failure time sample set; Performing statistical analysis on the failure time sample set to obtain a failure time distribution function; A Bayesian network is established based on the failure time distribution function, and the state is updated in combination with real-time monitoring data to obtain an equipment failure prediction model.

5. 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: said constructing a multi-objective optimization function based on said thermal energy conversion efficiency model and said system reliability constraints; Apply intelligent algorithms to solve the optimal parameter combination and generate an adaptive control strategy library, including: Converting the thermal energy conversion efficiency model into an efficiency objective function to obtain a first optimization objective; Convert system operation cost and resource consumption into cost objective function to obtain the second optimization goal; Converting the system reliability constraint into a set of constraint conditions to obtain a set of constraint equations for the optimization problem; Constructing a multi-objective optimization function based on the first optimization objective, the second optimization objective and the constraint equation group; Applying an improved particle swarm optimization algorithm to solve the multi-objective optimization function and obtain a Pareto optimal solution set; Cluster analysis is performed on the Pareto optimal solution set to generate an adaptive control strategy library for different working conditions.

6. 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 predictive adjustment based on the adaptive control strategy library and the dynamic influence matrix for external parameter changes includes: Establish a prediction model for external environmental parameter changes, predict external parameters in future periods, and obtain a parameter change prediction sequence; Combining the parameter change prediction sequence with the dynamic impact matrix to predict the system performance change trend and obtain a performance prediction curve; Selecting an optimal control strategy from an adaptive control strategy library based on the performance prediction curve to obtain a preliminary control parameter set; Dynamically adjusting and optimizing the preliminary control parameter set to obtain a real-time control instruction sequence; Sending the real-time control instruction sequence to the system actuator, and monitoring the system response in real time to perform closed-loop feedback regulation; Continuously update control strategies based on system operating status and external environment changes.

7. The method for optimizing the design of a flue gas waste heat recovery system considering changes in external parameters according to claim 5, characterized in that: The improved particle swarm optimization algorithm is applied to solve the multi-objective optimization function to obtain a Pareto optimal solution set, including: Initialize particle swarm parameters and population size, and generate initial particle position and velocity matrices; Performing constraint condition checks on the initial particle positions, screening out feasible solutions that satisfy the constraints, and obtaining an initial feasible solution set; Calculating the multi-objective function value of each particle in the initial feasible solution set, and determining the particle ranking according to the non-dominated sorting to obtain a sorting result; Based on the sorting results, the optimal position of the individual particles and the global optimal position are updated to obtain the optimized direction vector; the adaptive inertia weight and chaotic perturbation mechanism are introduced to update the particle speed and position to obtain a new generation of particle swarm; The multi-objective function evaluation, non-dominated sorting and position update are repeated until the convergence conditions are met and the Pareto optimal solution set is obtained.

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