Parameter sensitivity optimization method for aviation oil reformed fuel cell

Abstract

The application discloses a parameter sensitivity optimization method for aviation reforming fuel cells, defines a plurality of discrete typical working condition points in a flight envelope, and gives the reference value of a design parameter under each working condition point by an experience function; a central difference method is used for local sensitivity scanning, a parameter-efficiency-sensitivity curve is obtained, and high sensitivity, medium sensitivity, robustness and negative sensitivity parameters are divided; a SOBOL method is used for global sensitivity analysis, and the first-order main effect and interaction effect of each parameter are quantified; the local and global results are comprehensively considered to formulate a parameter optimization scheme under the working condition; the optimization results under each working condition are compared, the change rule of the parameter sensitivity with the working condition is identified, and global key parameters and parameters needing to be scheduled are extracted. The application realizes system thermal-electric-power collaborative optimization, significantly reduces the interaction coupling between parameters while improving the efficiency, and enhances the full profile availability and robustness.

Description

Technical Field

[0001] This invention belongs to the field of aviation fuel cell power system design and optimization technology, specifically relating to a parameter sensitivity optimization method for aviation fuel reforming fuel cells. Background Technology

[0002] The aviation fuel reforming-solid oxide fuel cell (SOFC) endothermic power generation system is an advanced energy system that converts aviation kerosene into hydrogen-rich gas through a steam reforming reaction, and then generates electricity efficiently through an SOFC stack. In actual flight, this system must adapt to a wide range of operating conditions (i.e., flight envelope) such as altitude, Mach number, and ambient temperature. Throughout the entire flight profile (takeoff, climb, cruise, maneuvering, landing, etc.), power demands vary drastically from tens to hundreds of kilowatts, with corresponding changes in heat dissipation requirements. This makes it difficult to determine the order of energy distribution among multiple media and sources, including heat, pressure, and chemical energy, within the system.

[0003] Currently, parameter studies for such systems mainly employ single-parameter perturbation methods or orthogonal experimental methods. Single-parameter perturbation methods can only assess the independent influence of parameters near local reference points, failing to detect the interactive coupling between parameters, and even less able to reflect the global behavior under the coupling of multiple physical processes. Orthogonal experimental methods have limited sampling points and analytical accuracy, making it difficult to reveal sensitivity patterns across operating conditions. Furthermore, existing methods typically analyze only a single rated operating condition, without systematically comparing the changing patterns of design parameter sensitivity under different operating conditions. This results in optimization schemes that are difficult to adapt to varying operating condition requirements and cannot solve design challenges across operating conditions and multiple constraints, such as "energy cascade utilization sequence" and "pressure release timing coordination."

[0004] Therefore, there is an urgent need for a closed-loop method that can perform stepwise sensitivity analysis, quantify the main effects and interaction effects of parameters for multiple discrete typical operating conditions, and extract optimization rules across operating conditions, so as to provide a condition-specific and quantifiable decision basis for the coordinated design of thermal-electrical-power systems under varying operating conditions. Summary of the Invention

[0005] To overcome the problems existing in the prior art, the purpose of this invention is to provide a parameter sensitivity optimization method for aviation fuel reforming fuel cells. This method is a multi-condition stepped parameter sensitivity analysis and optimization method for aviation fuel reforming-SOFC endothermic power generation systems. It can perform stepped sensitivity analysis for multiple discrete typical operating conditions, quantify the main effects and interaction effects of parameters, and extract closed-loop optimization rules across operating conditions. This provides a condition-specific and quantifiable decision basis for the coordinated design of thermal-electrical-power systems under varying operating conditions.

[0006] A parameter sensitivity optimization method for fuel cells in jet fuel reforming includes the following steps: Step S1: Model Establishment and Working Condition Definition Establish a numerical model of the system and determine the set of design parameters that affect system performance. And define multiple discrete typical operating points within the flight envelope. (Such as ground start-up, climb, cruise, maneuver, etc.). The baseline values ​​of each design parameter at each operating point are derived from previous experiments or empirical functions. The values ​​are provided to reflect the reasonable setting of design values ​​under different flight conditions.

[0007] Step S2: Local Sensitivity Analysis – Central Difference Method (Executed independently for each operating condition) For each typical operating point Perform the following operations independently: While keeping the remaining design parameters at their baseline values ​​for this operating condition, each design parameter is uniformly selected within its initial value range. sampling points ( The local sensitivity coefficient at each sampling point is calculated using the central difference formula. :

[0008] in For system efficiency, Take 1% to 2% of the design parameter range. Plot the "parameter value - system efficiency - local sensitivity" curve for each design parameter under this operating condition, and identify the positive and negative sensitive areas, the efficient operating range, and the critical point.

[0009] Step S3: Parameter classification based on local sensitivity (by working condition) At each typical operating point, the design parameters are classified according to the curve obtained in step S2: like If the value is less than 0 throughout the entire range, it is marked as a "negative sensitivity parameter"; like Marked as "highly sensitive parameter"; like Marked as "medium sensitivity parameter"; like Marked as "robust parameter".

[0010] Simultaneously record the efficient operating range (the area near the highest efficiency point) of each parameter under this working condition.

[0011] Step S4: Global Sensitivity Analysis – SOBOL Method (Executed independently for each operating condition) For each typical operating point The SOBOL method based on variance decomposition was used to quantify the main effects and interaction effects of each design parameter. Specifically, this included the following sub-steps: S4-1: Generate the Sobol sample matrix. Generate two Sobol sample matrices using the Sobol sequence. Independent sample matrix and The base sample size To eliminate the correlation between initial points, set a skip-before option. Each initial point, every One sample is taken from each point. The coordinates of each sample point are all in... Within the range. Then, and The normalized value in the formula is as follows The actual physical value range mapped to each design parameter.

[0012] S4-2: Construct the hybrid matrix. For each design parameter Construct a Mixing matrix , of which Columns taken from matrix The Columns, all other columns are taken from the matrix. The corresponding column. That is:

[0013] S4-3: Model Calculation. The matrix... , And each All sample points (total) Input a system model and calculate the corresponding system efficiency. Let the output vector be:

[0014] S4-4: Calculate the overall mean and overall variance:

[0015] S4-5: Calculate the first-order sensitivity index and the total effect index: ; ;

[0016] S4-6: Calculate the intensity of the interaction effect: . The larger the value, the stronger the coupling between this parameter and other parameters.

[0017] Step S5: Numerical estimation and error processing Based on the calculation results of step S4, numerical anomaly handling is performed: If Then set it to zero; if or Then increase the base sample size. Repeat step S4 until convergence.

[0018] Step S6: Optimization Decision Based on Working Conditions For each typical operating point Based on the results of steps S3 and S4, a parameter optimization scheme for this working condition is formulated: 1. For those marked as highly sensitive and globally first-order exponent under this operating condition The top 30% of design parameters will have their value range narrowed to the efficient operating range identified under this condition, with the narrowed range not exceeding 20% ​​of the original range. 2. For robust parameters, directly fix them at the value that is most economical to manufacture; 3. For negatively sensitive parameters, the reverse control strategy should be adopted within the optimized value range.

[0019] Step S7: Optimized closed-loop verification Using the optimized parameter range obtained in step S6 as input, repeat step S4 to obtain the optimized first-order exponent. and interaction effects By comparing with the original , Compare and verify the optimization effect.

[0020] Step S8: Comparison of results under multiple operating conditions and summary of patterns The results of parameter classification, optimization range, and interaction effects obtained under various typical operating conditions are compared and analyzed. 1. If a design parameter exhibits high sensitivity under multiple operating conditions and its first-order exponential increase is achieved after optimization, it is determined to be a global critical parameter. 2. If the sensitivity of a certain design parameter (such as the absolute value of local sensitivity or the magnitude of the first exponent) changes significantly with the operating conditions, it is determined that an operating condition scheduling strategy should be adopted in the subsequent continuous analysis of all operating conditions.

[0021] 3. Output the optimized parameter range, interaction effect quantification table, inverse control strategy, numerical error report, and multi-condition comparison conclusions for each operating point.

[0022] This invention first defines multiple discrete typical operating conditions within the flight envelope, with the baseline values ​​of design parameters for each operating condition given by an empirical function. Then, at each operating condition, the following steps are performed sequentially: a local sensitivity scan is conducted using the central difference method to obtain parameter-efficiency-sensitivity curves and classify parameters as highly sensitive, moderately sensitive, robust, and negatively sensitive; a global sensitivity analysis is performed using the SOBOL method to quantify the first-order main effects and interaction effects of each parameter; by combining local and global results, a parameter optimization scheme for that operating condition is formulated—a reverse control strategy that narrows the range of highly sensitive parameters, fixes robust parameters, and labels negatively sensitive parameters; finally, the optimization results for each operating condition are compared to identify the variation law of parameter sensitivity with operating conditions, and global key parameters and parameters requiring scheduling are extracted.

[0023] The beneficial effects of this invention are: This invention helps solve coupling problems in multi-medium, multi-source energy systems, such as improper distribution of high-temperature heat, insufficient chemical energy conversion, and premature pressure reduction of high-pressure working fluid, through a step-by-step closed-loop process of "discrete point selection under multiple operating conditions - local scanning under different operating conditions - global diagnosis under different operating conditions - unified optimization decision - cross-operating condition law extraction". It achieves coordinated optimization of system heat, electricity and power, significantly reduces the interaction coupling between parameters while improving efficiency, and enhances the availability and robustness of the whole profile.

[0024] This invention is applicable to the design of full flight envelope parameters for complex energy systems with variable operating conditions and multi-physics coupling. Attached Figure Description

[0025] Figure 1 This is a flowchart of a multi-condition stepped parameter sensitivity analysis and optimization method for aviation fuel reforming-SOFC endothermic power generation systems.

[0026] Figure 2 This is a schematic diagram of the "parameter value - system efficiency - local sensitivity" curve in local sensitivity analysis.

[0027] Figure 3 This is a schematic diagram of the "parameter value - system efficiency - local sensitivity (characteristic region)" curve in local sensitivity analysis.

[0028] Figure 4 This is a schematic diagram of an aviation fuel reforming-SOFC endothermic power generation system architecture. Detailed Implementation

[0029] The following is a specific example of the application of this invention in a certain type of fuel reforming-solid oxide fuel cell endothermic power generation system, as shown in Figure 4. Figure 4It is a high-efficiency hybrid power generation system integrating solid oxide fuel cells, gas turbines, and multi-stage waste heat recovery. With SOFC stack as the energy conversion core, air is first pressurized by the compressor and sent to the SOFC cathode. After being processed by the reformer, the fuel enters the anode and generates electricity through high-temperature electrochemical reaction. Unreacted exhaust gas is sent to the burner for supplementary combustion to drive the turbine to do work, realizing the hybrid cycle of fuel cell and gas turbine. The system follows the principle of energy cascade utilization, deeply recovering and utilizing high-temperature, medium-temperature and exhaust nozzle waste heat through four-stage heat exchangers. At the same time, CO2, N2, etc. in the exhaust gas are separated by separators, and the remaining water is returned to the reformer for reuse, realizing the self-circulation management of water. The system has the advantages of high power generation efficiency, full energy recovery, and environmental protection and low carbon emissions.

[0030] Figure 1 This is a flowchart illustrating a multi-condition stepped parameter sensitivity analysis and optimization method for aviation fuel reforming-SOFC endothermic power generation systems. The method includes the following steps: Step S1: Model Building and Parameter Definition A numerical model of a fuel reforming-SOFC endothermic power generation system is established, including the reforming reactor, SOFC stack, gas supply system, and thermal management module. The system net efficiency η is used as the performance index.

[0031] Determine 8 design parameters The initial value range and benchmark value are shown in Table 1.

[0032] Table 1 Initial range and baseline values ​​of design parameters

[0033] This example selects a typical operating condition (operating condition 1) for analysis.

[0034] Step S2: Calculate the local sensitivity coefficient (central difference method) S2.1 For each design parameter, N=100 sampling points are uniformly selected within its initial range.

[0035] S2.2 Taking the design point flow rate of turbine I (parameter 5) as an example, keep the other parameters as the baseline values ​​and run the model to calculate the efficiency η of each sampling point.

[0036] S2.3 Set the perturbation step size = 1.5% × parameter range. Calculate the local sensitivity coefficient for each sampling point using the formula:

[0037] S2.4 Plot the "parameter value - system efficiency - local sensitivity" curve. Taking parameter 5 as an example, as can be seen from Figures 2 and 3: due to... Figure 2 The sensitivity of most regions is 0, with abrupt changes only occurring in the range of 1.2-1.4. Therefore, the optimization range is selected within this region. Further sensitivity analysis of the feature regions is then performed, such as... Figure 3 Based on the sensitivity division, it was found that the absolute value of sensitivity changed from 7.58507 to 5.39397 near x=1.25. Therefore, x=1.25 was listed as the critical point between high sensitivity and medium-low sensitivity. In the high sensitivity optimization mode, 1.2 < x < 1.25 was selected, while in the medium-low sensitivity mode, it became 1.25-1.4.

[0038] Therefore, parameter 5 is inefficient in the range of 0 to 1.2, and its local sensitivity is approximately 0. At x=1.25, the absolute value of local sensitivity jumps, decreasing from 7.59% to 5.39%. The local sensitivity of the entire interval is negative.

[0039] The same calculations were performed on the other parameters to obtain the local sensitivity curves for each parameter.

[0040] Step S3: Select the optimization interval and classify parameters based on local sensitivity S3.1 Identify the efficient operating range: Based on the "parameter value - system efficiency" curve, identify the characteristic region. For parameter 5, this range is [1.2, 1.4].

[0041] S3.2 Determine the sensitivity threshold: Based on the local sensitivity curve, identify the location where the absolute value of sensitivity jumps or exceeds the threshold. For parameter 5, the absolute value of local sensitivity changes from 7.59% to 5.39% at x=1.25, therefore x=1.25 is taken as the dividing point between the high-sensitivity region and the medium-low-sensitivity region.

[0042] S3.3 Divide into high / medium / low sensitivity ranges: based on the following thresholds: ·like If the value is less than 0 throughout the entire range, it is marked as a "negative sensitivity parameter"; ·like Marked as "highly sensitive parameter"; ·like Marked as "medium sensitivity parameter"; ·like Marked as "robust parameter".

[0043] Therefore, the high sensitivity range of parameter 5 is 1.2 to 1.25, the medium-low sensitivity range is 1.25 to 1.4, and it is a negative sensitivity parameter.

[0044] S3.4 Repeat the above process for other parameters to obtain: • Parameter 1 (Design pressure ratio of compressor I): Negative sensitivity, high sensitivity region [4,6]; • Parameter 2 (Turbine I design pressure ratio): Positively sensitive, moderately sensitive region; • Parameter 3 (Turbine II design pressure ratio): Positively sensitive, high sensitivity region [4,6]; • Parameter 4 (Compressor I design point flow rate): Positively sensitive, high efficiency range [1.4, 1.6]; • Parameter 6 (Turbine II design point flow rate): Positively sensitive, high efficiency range [1.54, 1.6]; • Parameters 7 and 8: Abnormal (sensitivity > 100% or fluctuating), no interval is divided, set as control group.

[0045] S3.5 Output Optimization Interval Candidates: For each parameter, record two possible optimization intervals—high-sensitivity optimization mode (narrow range) and medium-low sensitivity optimization mode (slightly wider range).

[0046] Step S4: Global Sensitivity Analysis (SOBOL Method) S4-1 Settings = 2000, generate two 2000×8 Sobol matrices A and B, skip the first 10³ points, sample every 10² points, and map to the actual physical range.

[0047] S4-2 Construct a mixing matrix for each parameter i (The i-th column is B, and the rest are A).

[0048] S4-3 Run the model to calculate A, B, A total of 2000 × (2 + 8) = 20000 iterations are performed to obtain the output vector.

[0049] S4-4 Calculate the overall mean and overall variance:

[0050] S4-5 Calculate the first-order exponent according to formula (3) Total effect index :

[0051] S4-6 Calculating Interaction Effects The results before optimization (taking the low-to-medium sensitivity mode as an example) are shown in Table 2 of the report.

[0052] Table 2 Global Sensitivity Index Before Optimization

[0053] Step S5: Numerical estimation and error processing This embodiment uses When the value is 2000, no occurrence occurs. <0 or For anomalies such as >1, the calculation results are used directly. If anomalies occur, samples are added according to the rules until convergence.

[0054] Step S6: Optimization Decision Based on Working Conditions Combining the candidate optimization intervals obtained in step S3 and the first-order exponent rankings obtained in step S4, two optimization schemes are formulated: High-sensitivity optimization mode: Parameters 1, 2, 3: [4, 6]; Parameter 4: [1.4, 1.6]; Parameter 5: [1.2, 1.25]; Parameter 6: [1.54, 1.6]; Parameters 7 and 8 remain unchanged.

[0055] Medium-low sensitivity optimization mode: Parameters 1, 2, 3: [12, 14]; Parameter 4: [1.5, 2]; Parameter 5: [1.25, 1.4]; Parameter 6: [1.6, 2]; Parameters 7 and 8 remain unchanged.

[0056] Step S7: Optimized Global Sensitivity Verification Input the above optimization range and re-execute step S4 to obtain the optimized result. and The results (taking the low-to-medium sensitivity mode as an example) are shown in Table 3.

[0057] Table 3. Global Sensitivity Index and Changes After Optimization

[0058] Optimization effect assessment: The first-order exponential of key parameters is enhanced, the absolute value of the interaction effect decreases, and the system decoupling is successful.

[0059] Final output: 1. Parameter value range table for each optimization mode (Table 4).

[0060] 2. Quantification table of interaction effects between parameters (Table 3).

[0061] 3. Explanation of the reverse control strategy for negative sensitive parameter 5.

[0062] Table 4. Parameter range after optimization for low-sensitivity mode

[0063] Step S8: Multi-condition integrated analysis framework This method can be naturally extended to multiple discrete typical operating conditions. After independently executing steps S1 to S7 for each operating condition, a cross-operating condition comprehensive analysis is performed according to the following framework: Parameter classification consistency assessment: If a parameter is highly sensitive in ≥80% of the operating conditions and its first-order exponential value is enhanced after optimization, it is determined to be a global key parameter.

[0064] Interaction effect trend analysis: Observe the change of the absolute value of the average interaction effect with the working conditions.

[0065] Scheduling function generation: For operating condition-sensitive parameters, perform polynomial fitting or piecewise interpolation with the operating condition parameters as independent variables.

[0066] Output multi-condition reports: including a list of global key parameters, optimization ranges for each condition, scheduling functions, interaction effect trend charts, and efficiency improvement comparisons.

Claims

1. A parameter sensitivity optimization method for fuel cells used in jet fuel reforming, characterized in that, Includes the following steps: Step S1: Establish a numerical model of the system and determine the set of design parameters that affect system performance. And define multiple discrete typical operating points within the flight envelope. ( The baseline values ​​of each design parameter at each operating point are derived from previous experiments or empirical functions. The following values ​​are provided to reflect reasonable settings for design values ​​under different flight conditions; among them, The various design parameters that affect system performance, These are typical discrete operating conditions; Step S2: For each typical operating point The central difference method was used to perform local sensitivity analysis on the design parameters under this operating condition: keeping the remaining parameters as the baseline values ​​under this operating condition, a single parameter scan was performed on each design parameter within its value range to obtain the "parameter value-system efficiency-local sensitivity" curve under this operating condition, and the sensitivity characteristics of each design parameter under this operating condition were analyzed. Step S3: Based on the local sensitivity analysis results of Step S2, the design parameters are divided into high-sensitivity parameters, medium-sensitivity parameters, or robust parameters under each typical operating condition, and the preliminary optimization working range of each design parameter under that operating condition is determined. Step S4: For each typical operating point The SOBOL method was used to perform a global sensitivity analysis of the design parameters at this operating point, specifically including: S4-1: Generate two using a Sobol sequence Independent sample matrix and ,in Matrix elements are all in Within the interval, it is mapped to the actual physical value range of each design parameter, where The base sample size Indicates the total number of design parameters; S4-2: For each design parameter Construct a mixture matrix The first of the matrix Columns taken from matrix The Columns, the remaining columns are taken from the matrix. The corresponding column; S4-3: Transform the matrix , And each Input all sample points into the system model and calculate the corresponding system efficiency. Let the output vector be... , and ; S4-4: Calculate the overall mean Total variance ; S4-5: Calculate the first-order sensitivity index of each design parameter using the following formula. Total effect index : ； S4-6: Calculate the intensity of the interaction effect ; Step S5: Based on the calculation results of step S4, perform numerical estimation and error processing: If Then set it to zero; if or Then increase the base sample size. Repeat step S4 until convergence; Step S6: Combining the results of steps S3 and S4, formulate parameter optimization schemes for each typical operating point: for those marked as highly sensitive and globally first-order exponential under this operating condition... The top 30% of design parameters will have their value range narrowed to the efficient operating range under this condition, with the narrowed range not exceeding 20% ​​of the original range; for robust parameters, they will be fixed to the most economical manufacturing value; for negatively sensitive parameters, the reverse control strategy will be marked as required within the optimized value range. Step S7: Using the optimized parameter range obtained in step S6 as input, repeat step S4 to obtain the optimized first-order exponent. and interaction effects The optimization effect was verified by comparing it with the original result. Step S8: Compare the optimization schemes under various typical operating conditions, identify the pattern of design parameter sensitivity changes with operating conditions. If a certain design parameter is highly sensitive under multiple operating conditions and its first-order exponential increase is achieved after optimization, it is determined to be a global key parameter. If the sensitivity of a certain design parameter changes significantly with operating conditions, it is determined that an operating condition scheduling strategy should be adopted. Output the final optimization parameter value range, the quantitative results of the interaction effect between parameters, and control strategy suggestions for negatively sensitive parameters under each operating condition.

2. The parameter sensitivity optimization method for fuel cells in aviation fuel reforming according to claim 1, characterized in that, The specific method for local sensitivity analysis using the central difference method in step S2 is as follows: Under each selected operating condition, N sampling points are uniformly selected for each design parameter within its initial value range, where N≥50. The remaining design parameters are kept as baseline values ​​under that operating condition. At each sampling point... At this location, the local sensitivity coefficient is calculated using the following formula. : ； in For system efficiency, Take 1% to 2% of the range of this design parameter.

3. The parameter sensitivity optimization method for fuel cells in aviation fuel reforming according to claim 2, characterized in that, The parameter division criteria in step S3 are as follows: if If the value is less than 0 throughout the entire range, it is marked as a negatively sensitive parameter; if If it is, then it is marked as a highly sensitive parameter; if If it is, then it is marked as a moderately sensitive parameter; if If it is, then it is marked as a robust parameter.

4. The parameter sensitivity optimization method for fuel cells in aviation fuel reforming according to claim 1, characterized in that, In step S4-1, when generating the sample matrix using the Sobol sequence, the skip function is set before... Each initial point, every One sample is taken from each point to eliminate the correlation between the initial points.

5. The parameter sensitivity optimization method for fuel cells in aviation fuel reforming according to claim 1, characterized in that, In step S4 This includes: ground start-up, climb, cruise, and maneuver.

6. The parameter sensitivity optimization method for fuel cells in aviation fuel reforming according to claim 1, characterized in that, In step S5, =2000, not found <0 or If >1 is an anomaly, the calculation result is used directly; if an anomaly occurs, samples are added according to the rules until convergence.

7. The parameter sensitivity optimization method for fuel cells in aviation fuel reforming according to claim 1, characterized in that, In step S6, when comparing the optimization schemes under various typical working conditions, if a certain design parameter shows high sensitivity under multiple working conditions and the first-order exponential is enhanced after optimization, it is determined to be a global key parameter. If the sensitivity of a certain design parameter changes significantly with operating conditions, then it is determined that an operating condition scheduling strategy should be adopted.

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