A method for quantitatively analyzing and predicting dynamic response characteristics of an air intake temperature sensor under icing conditions based on a grey correlation model

Abstract

The present application relates to aviation sensing technology and icing field, solve the problem that the three are split in prior art icing condition parameters, ice type characteristics and sensor dynamic response performance, especially relate to a kind of inlet temperature sensor icing condition dynamic response characteristic quantification analysis and its prediction method based on grey correlation model.The method is through multi-stage data fusion and grey correlation analysis, quantifies the correlation between icing parameters and sensor dynamic response characteristics, selects the correlation degree r>0.9 factor as key icing influence factor, respectively constructs the GM(1,N) model of initial period, middle period, end period, based on the interpolation prediction of time-sharing model, realize the prediction of full period sensor dynamic response and sensor dynamic response under new condition, provide theoretical basis and technical support for sensor dynamic performance evaluation and optimization under icing condition.

Description

Technical Field

[0001] This invention belongs to the field of aviation sensing technology and icing, and in particular relates to a quantitative analysis and prediction method for the dynamic response characteristics of an inlet temperature sensor under icing conditions based on a grey relational model. Background Technology

[0002] When aircraft fly in low-temperature and high-humidity environments, icing easily forms on the surface of the inlet temperature sensor, significantly degrading its dynamic response characteristics and severely affecting the accuracy and real-time performance of temperature measurements. Because icing condition testing and dynamic response characteristic analysis are conducted in two different experimental environments—an ice wind tunnel (<0℃) and a hot wind tunnel (>0℃)—current research largely separates anti-icing design, ice type characteristics, and dynamic response performance. This has led to a serious neglect of the intrinsic correlation between "icing parameters, ice type characteristics, and dynamic response performance," and quantitative research on their relationship and predictive capabilities remains lacking. Existing technological research mainly includes the following:

[0003] For example, Chinese patent applications 202111531422.8, entitled "Anti-icing Sensor"; 201410560583.3, entitled "Temperature Sensor"; 202510796078.7, entitled "Anti-icing Sensor with Guided V-shaped Grooves on the Windward Surface"; and 201180010926.3, entitled "Ice-breaking Probe for Measuring Total Air Temperature," all describe the specific configuration design of the anti-icing temperature sensor. They address how icing reduces the sensor's dynamic response and how a flow-guiding design maximizes the sensor's dynamic response. However, these four solutions still have the following shortcomings: none mention the research methods for icing conditions and the dynamic response of the anti-icing temperature sensor, nor quantify the relationship between them, nor provide a predicted value for the sensor's time constant under specific icing conditions.

[0004] For example, the article "Analysis of Key Icing Influencing Factors on the Time Constant of Airflow Temperature Sensors" published in the Journal of Metrology, Vol. 43, No. 12, 2022, describes the relationship between the dynamic characteristics of an airflow temperature sensor and structural factors (welding ball diameter, wire diameter, shielding structure) and the incoming flow conditions set in the hot air tunnel (airflow Mach number, airflow temperature, and temperature step). However, it has the following shortcomings: the research scope of the above scheme is limited to the conditions achievable by the hot air tunnel (>0℃), and it does not involve the parameters of complex icing conditions (<0℃), their impact on the dynamic characteristics of the icing temperature sensor, and the predicted value of its time constant.

[0005] Mainstream icing research largely focuses on the phenomenon itself, primarily qualitatively analyzing the relationship between icing parameters (such as liquid water content and droplet diameter) and macroscopic ice shape. Only a few studies attempt to quantitatively predict single parameters (such as ice thickness). For example, Chinese patent application number 202510824375.8, entitled "A Method, System, Equipment, and Medium for Predicting Ice Thickness Based on Grey Relational Analysis," describes an ice thickness prediction method based on grey relational analysis and deep learning. By collecting a large amount of icing-related data and screening key meteorological features, it integrates a bidirectional gated cyclic unit and a multi-head self-attention mechanism to construct a hybrid model for predicting ice thickness. However, its core technology still has significant limitations: the grey relational analysis used in this method can only predict a single ice thickness index. It fails to extend to the comprehensive analysis of the three-dimensional morphology of ice (such as outer dimensions and distribution of key parts), and it cannot quantify the degree of system performance degradation caused by differences in ice morphology. Therefore, in practical applications, it is difficult to comprehensively assess the real impact of icing on facilities, resulting in low engineering value. Building upon existing research on ice formation, a few studies have begun to explore the actual impact of icing morphology on the aerodynamic or mechanical performance of systems. For example, the article "Performance effects of attachment on blade on a straight-bladed vertical axis wind turbine" from *Current Applied Physics*, Vol. 10, No. 2, 2010, describes a method to approximate icing morphology by attaching an artificially shaped clay model to the leading edge of the blade and conducting performance tests of an iced wind turbine in a dry wind tunnel. However, this method still has the following limitations: it is difficult to reproduce the complexity of real ice formations, and it is also impossible to scientifically construct a quantitative relationship between icing parameters and performance response, as well as the degree of contribution and prediction of icing to performance response.

[0006] Regarding sensor signal compensation, existing research, such as the Chinese patent application number 201810008177.4 entitled "Temperature Sensor Signal Compensation Method and Device, Computer-readable Storage Medium," achieves high-precision compensation of temperature sensor signals by fusing sensor measurements, dynamic characteristic parameters, synthesized signal values, and synthesized mass flow rate values. While this method can improve the dynamic response accuracy of sensors in non-icing conditions, its model does not consider the changes in sensor surface thermal conductivity caused by icing, or the influence of ice thickness and morphology on response time. Therefore, its applicability under icing conditions is limited.

[0007] In terms of icing detection and protection, existing methods are mostly based on single or simple composite parameters such as temperature and humidity to judge icing risk. They lack in-depth quantitative analysis of the correlation mechanism between the icing process and the dynamic response of sensors, resulting in insufficient accuracy in predicting the dynamic response of sensors under icing conditions. They also cannot provide a theoretical basis for the selection and performance evaluation of sensors in icing environments.

[0008] Therefore, overcoming the limitations of existing technologies in systematic understanding and fundamentally revealing the inherent laws governing the interaction among "icing condition parameters, icing characteristics, and dynamic response characteristics," as well as accurately predicting dynamic response characteristics, has become a critical issue urgently needing to be addressed in the field of aero-engine sensor technology. To this end, it is imperative to establish an analytical and predictive method capable of quantifying the dynamic correlation between icing parameters, ice type characteristics, and sensor dynamic characteristics. This would fill the research gap in this field and provide a reliable theoretical foundation for signal compensation, performance evaluation, and adaptation selection of temperature sensors in icing environments. Summary of the Invention

[0009] S1. Acquisition of 3D Ice Pattern Data and Time Constant: 3D ice pattern data of the sensor under different icing conditions is obtained through simulated ice pattern models and ice wind tunnel experiments; a high-confidence dynamic response ice pattern simulation model of the sensor in an ice-free state is established and verified through hot wind tunnel experiments and thermal simulation analysis; based on the verified ice pattern simulation model, the time constant of the sensor under various icing conditions is obtained by combining the 3D ice pattern data.

[0010] S11. Acquisition of 3D Ice Pattern Data: In this stage, icing information on the sensor surface is acquired through two complementary methods: icing simulation of the simulated ice pattern model and ice wind tunnel experiment.

[0011] (1) Simulated ice model: Using FENSAP-ICE or other icing simulation software, numerical simulation is performed by setting up icing conditions that cover different parameters such as liquid water content, droplet diameter, and air temperature. Specifically, this includes setting the computational domain, mesh generation, and boundary and convergence conditions to simulate the growth process of ice on the sensor surface and obtain complete surface coordinates by simulating ice growth data.

[0012] (2) Ice wind tunnel experiment (<0℃): In the ice wind tunnel, the aforementioned icing conditions were reproduced (ice wind tunnel debugging), and the sensor to be tested was installed to conduct the icing experiment. The growth process of the ice shape was recorded in real time, and after the experiment, the physical ice shape formed was obtained to collect the actual ice shape data and obtain the coordinates of the key feature points of the measured ice shape.

[0013] S12. For the simulated ice model (complete surface coordinates) and actual ice model data (coordinates of key feature points of the measured ice model) obtained from the above-mentioned simulated ice model and ice wind tunnel experiment, this step provides two parallel data processing schemes to extract three-dimensional ice model data for subsequent analysis.

[0014] Option 1 (Preferred): Fit the coordinates of key feature points of the measured ice model to the complete surface coordinates extracted from the simulated ice model. First, perform 3D restoration and solid transformation on the ice sheet file output from the simulated ice model to extract the complete surface coordinates. Simultaneously, perform 3D scanning or outline measurement on the physical ice model obtained from the ice wind tunnel experiment to obtain the coordinates or dimensions of its key feature points (such as ice thickness, outline dimensions, and air inlet coverage). Finally, align the coordinates of the key feature points of the measured ice model with the complete surface coordinates extracted from the simulated ice model, adjusting scaling, translation, and rotation parameters to minimize the sum of squared errors. After fitting, the error of the key feature points is ≤5%, constructing 3D ice model data that combines realistic shape and structural integrity. This option is highly efficient, balancing realism and model quality.

[0015] Option 2 (Alternative): Extraction and processing of key feature point coordinates of measured ice patterns. A high-precision 3D scan is performed on the physical ice pattern obtained from the ice wind tunnel experiment to directly acquire its complete surface sheet model. Subsequently, the sheet model is repaired and optimized using 3D software to eliminate scanning noise and defects. Finally, the complete surface coordinates of the repaired model are extracted for subsequent use. This option provides comprehensive data, but the processing is relatively complex.

[0016] Based on actual research needs and data conditions, any of the above schemes can be flexibly selected to obtain ice shape coordinate data and proceed to the next analysis stage.

[0017] S13. Dynamic response characteristics test and model verification under ice-free conditions: (1) Conduct ice-free hot wind tunnel experiment (>0℃): Under ice-free conditions, place the sensor in the hot wind tunnel, apply a temperature step signal, measure the dynamic response curve of the output temperature of the ice-free sensor as a function of time, and obtain the reference experimental time constant. (2) Establish an ice-free thermal simulation model to reproduce the experiment and verify the simulation model for thermal simulation analysis: In simulation software (such as SOLIDWORKS Flow Simulation), reproduce the experimental conditions of the hot wind tunnel, set the same material properties, boundary conditions and thermal load as the ice-free hot wind tunnel experiment, and obtain the sensor simulation time constant. By comparing the deviation between the simulation and experimental results (preferred deviation value ≤4%), the effectiveness of the thermal simulation model is verified, ensuring that it has sufficient confidence and can be used for the next stage of extended simulation under icing conditions.

[0018] S14. Dynamic Response Characteristics Thermal Simulation Analysis under Icing Conditions: Based on the validated thermal simulation model, the three-dimensional ice model obtained in S12 under different icing conditions is sequentially imported into the validated thermal simulation model. Material properties, boundary conditions, and thermal loads are set according to the corresponding actual icing environment to simulate the transient heat transfer process of the sensor under icing conditions, and the time constant is calculated for each icing condition.

[0019] S2. Selection of icing condition parameters and sequence construction: (1) Select a set of typical icing condition parameters to form an icing condition parameter set. This parameter set includes, but is not limited to, liquid water content (LWC), water droplet diameter (MVD), test wind speed (V), total temperature (T), etc.; (2) For multiple different icing conditions, record the dynamic response time constant of the sensor under each condition and at different icing times (t) to construct the original data sequence for subsequent analysis: use the time constant sequence as the reference sequence and the icing condition parameter sequence as the comparison sequence.

[0020] S3. Perform grey relational analysis to quantify the impact of parameters on dynamic response characteristics: preprocess the reference and comparison sequences to eliminate dimensions; calculate the correlation coefficient between each comparison sequence and the reference sequence; take the average value of the correlation coefficient of each parameter sequence to obtain its grey relational degree with the time constant, and sort them according to the magnitude of the correlation degree to determine the weight of the impact of each icing condition parameter on the time constant.

[0021] S31. Preprocessing employs an initialization method to preprocess the reference and comparison sequences to eliminate dimensional influences (generating...). Given M different icing conditions, for the k-th condition (k = A, B, …, M), the reference sequence (time constant, denoted as…) is… ) and each comparison sequence (e.g., liquid water content LWC denoted as The diameter of the water droplet (MVD) is denoted as... The test wind speed V is denoted as Total temperature T is denoted as Each of the P comparison sequences (e.g., P sequences) is initialized using the following formula:

[0022] ;

[0023] in, As a time constant reference sequence, For the comparison sequence of icing condition parameters, The original value of the i-th parameter sequence under the k-th working condition. This is the value of the sequence under reference condition A. Let P represent the dimensionless value of the i-th parameter sequence after initialization at the k-th operating point, where P is the total number of parameters for the icing operating point and M represents the total number of operating points involved in the calculation.

[0024] Correlation coefficient calculation: Calculate the absolute difference between the dimensionless comparison sequence of the parameters for the i-th icing condition and the reference sequence of the time constant under the k-th condition. ;Sure The two-level minimum difference and the maximum difference Introducing the resolution coefficient ρ, we calculate the correlation coefficient of the i-th comparison sequence at the k-th operating point. ;

[0025] S32. Relevance Ranking: The correlation coefficient of each parameter sequence is averaged to obtain the correlation degree. The calculation formula is:

[0026] ;

[0027] in, Represents the i-th comparison sequence (e.g., X). i , representing the grey relational degree between a certain icing parameter and a reference sequence (such as the time constant sequence X0), and M represents the total number of operating points involved in the calculation. Represents the correlation coefficient of the i-th comparison sequence at the k-th operating point; according to Sort by size to determine the weight of each icing condition parameter on the time constant. The closer the correlation is to 1, the stronger the correlation between the icing condition parameter and the time constant.

[0028] S4. Identification and extraction of key icing influencing factors based on correlation:

[0029] S41. Based on the correlation ranking results, identify the key icing influencing factors, secondary icing influencing factors, and weakest icing influencing factors that affect the time constant, and clarify the quantitative influence level of each icing condition parameter on the dynamic response characteristics.

[0030] S42. By comparing the correlation ranking of different freezing times t, analyze and verify the time-varying characteristics of the factors (especially the key freezing influencing factors), and reveal the dynamic evolution law of the key freezing influencing factors during the freezing process.

[0031] S43. Based on the gray relational threshold (r > 0.9), key icing influencing factors are selected, and factors with low correlation are excluded to form a set of key icing influencing factors for subsequent gray prediction modeling, ensuring that the model focuses on the core driving variables.

[0032] S5. Constructing a multivariate grey prediction model GM(1, N) based on grey relational analysis: Based on the N key icing influencing factors (N is a positive integer not less than 1) selected by grey relational analysis, a multivariate grey prediction model GM(1, N) is constructed between the system characteristic sequence (time constant sequence) and the key icing influencing factor sequence for the icing time t. This model is used to quantify the evolution law of dynamic response characteristics during the icing process and to achieve prediction. The core of this method lies in using the first-order cumulative generation technique to strengthen the data regularity and establishing a whitening differential equation to characterize the dynamic relationship between the system development trend and various driving factors. The specific steps for constructing the GM(1, N) model are as follows:

[0033] S51. Data Preparation and Sequence Definition: Collect raw observation data of system characteristic values ​​(time constants) and N key icing influencing factors under M different icing conditions to form a raw data matrix. Define the system characteristic sequence as follows: Define the j-th key icing influencing factor sequence as follows: , where j=1,2,...,N.

[0034] S52. First-order cumulative generation (1-AGO): First-order cumulative generation is performed on the system feature sequence and the sequences of each key icing influencing factor to weaken randomness and highlight trend, resulting in a first-order cumulative generation sequence. :

[0035] ;

[0036] ;

[0037] S53. Constructing the GM(1, N) model: Based on the first-order cumulative generation sequence, establish an N-variable grey differential equation, i.e., the whitened differential equation form of the GM(1, N) model:

[0038] ;

[0039] Where 'a' is the development coefficient, reflecting the development trend of the system's characteristic sequence itself. As driving coefficients, key icing influencing factors are quantified separately. The degree of contribution to changes in system characteristics. Let be the driving coefficient of the j-th key icing influencing factor;

[0040] S54. Model parameter estimation: Constructing a background value sequence using the nearest neighbor mean generation method. :

[0041] ;

[0042] Discrete form equations obtained by discretizing the grey differential equation:

[0043] ;

[0044] Representing the discrete-form system of equations as matrix equations ,in, For the reason The column vector formed The matrix consists of background values ​​and the cumulative values ​​of each factor; the least squares method is used to analyze the development coefficient and driving coefficient. Parameter estimation is performed to obtain the estimated development coefficients and driving coefficients. : ;

[0045] S55. Model Solving and Time Response Function: The obtained estimated development coefficients and driving coefficients... Substituting into the whitening differential equation and solving it, we finally obtain the time response function of the characteristic sequence of the first-order accumulator system:

[0046] ;

[0047] This function describes the predictive pattern of how the cumulative system characteristics change with the "time" exponent (operating condition sequence).

[0048] S56. Accumulation and Reduction Restoration and Predicted Value Calculation: Through the accumulation and reduction generation (IAGO) operation, the fitted values ​​and predicted values ​​of the system characteristic sequence (time constant sequence) at each operating point are obtained through accumulation and reduction restoration.

[0049] ;

[0050] And let .

[0051] S57. Model Accuracy Verification: By calculating indicators such as average relative error, posterior error ratio (C), and small error probability, the model's fitting and prediction accuracy are quantitatively evaluated to ensure the model's effectiveness and reliability, thereby providing a quantitative tool for the analysis and prediction of sensor dynamic response characteristics under icing conditions.

[0052] By repeating steps S51 to S57 above, corresponding GM(1, N) benchmark prediction models can be established for different icing stages (such as initial, middle and final stages), thereby constructing a time-varying grey prediction integrated system that can reflect the time-varying influence of icing condition parameters.

[0053] S6. Construction and Verification of Time-Varying Grey Prediction Integration System: To characterize the dynamic evolution of various influencing factors throughout the icing process and to achieve continuous prediction of sensor dynamic response at any time point, a time-varying grey prediction integration system needs to be constructed: GM(1, N) benchmark prediction models are established at multiple representative icing time points; multiple GM(1, N) benchmark models are integrated through interpolation methods to construct a time-varying grey prediction integration system in which model parameters continuously change with icing time t, which is used to achieve at least one prediction: time extrapolation and new working condition extrapolation.

[0054] S61. Construction and Parameter Analysis of Time-Segmented Benchmark Models: At multiple representative freezing time points (e.g., early, middle, and late stages), GM(1, N) benchmark prediction models are established based on data from the corresponding times, and the development coefficients of each model are obtained. With driving coefficient By comparing and analyzing the changing trends of model parameters at different time periods, the time-varying patterns of the evolution of the system's dynamic characteristics and the influence of key icing factors during the icing process can be revealed. For example, the development coefficient... Changes in these coefficients can reflect the attenuation or enhancement of the growth momentum of the time constant; each driving coefficient The changes directly quantify the corresponding influencing factors. The relative strength and evolution pattern of the effects at different stages of freezing.

[0055] S62. Consistency verification between model mechanism and correlation: Verify the driving coefficients of the baseline model at different time points. Ranking, and the degree of correlation obtained from grey relational analysis at the same time point. The ranking was compared and verified. The two should show consistency in trend; that is, factors with high correlation usually also exhibit larger driving coefficients in the model. This consistency, from both the "static correlation measurement" and "dynamic model-driven" dimensions, confirms the reliability of the identification results of key icing influencing factors and enhances the internal logical rigor of the entire analytical framework.

[0056] S63. Integration Method of Time-Varying Grey Prediction Integrated System: Based on a benchmark model with multiple discrete time points, this system is constructed using interpolation methods to address the following two typical prediction needs:

[0057] Prediction Scenario 1 (Time Extrapolation): For a known operating condition, predict its time constant at any time t between discrete reference time points. By interpolating the model parameters, achieve dynamic response prediction in the continuous time dimension.

[0058] For any freezing time ( ,in and (The time range covered) can be determined by adjacent reference time points. , Model parameters , Model parameters for target time t are obtained by linear or nonlinear interpolation. For example, the linear interpolation formula can be expressed as:

[0059] ;

[0060] in , The model parameters at time t, namely the development coefficient parameter a(t) and each driving coefficient. parameter;

[0061] Therefore, for any freezing time The interpolated parameters p(t) are used to construct a GM(1,N) model at time t, and the key icing influencing factors under known working conditions are considered at any icing time. The accumulated sequence generated at each time step is substituted into the GM(1, N) model for continuous prediction of dynamic response characteristics. By solving the time response function and performing cumulative reduction and restoration, the result is finally obtained for this known working condition at any icing time. Predicted time constant value at time t.

[0062] S64. Scenario 1 Verification: Example of Time Extrapolation Prediction: To verify the effectiveness of the time-varying grey prediction integrated system, an intermediate moment between the baseline time points can be selected. (For example To perform prediction verification, the specific steps are as follows:

[0063] Based on the interpolation method described above, calculate Model parameters at time .

[0064] Parameters obtained by interpolation Build The GM(1, N) model with time-varying parameters at all times represents the key icing influencing factors under known operating conditions. The accumulated sequence generated at each time step is substituted into the GM(1, N) model for continuous prediction of dynamic response characteristics. By solving the time response function and performing cumulative reduction and restoration, the dynamic response characteristics of the known operating condition are finally obtained. Predicted time constant value at time t.

[0065] Prediction Scenario 2 (Extrapolation of New Operating Conditions): For new operating conditions within the verified icing condition parameter range, predict their time constants at the modeled discrete time points, directly reuse the baseline GM(1,N) model at that time point, and realize the dynamic response prediction of the new operating conditions.

[0066] S65, Scenario 2 Verification: Extrapolation prediction of new operating conditions within the verified icing parameter range: Determine the target prediction time point. , obtain The baseline GM(1,N) model parameters at time points are used to generate the key icing influencing factor sequences for the new operating condition through cumulative processing. The processed sequences are then substituted into the time points. The GM(1, N) model, by solving the time response function and cumulative reduction restoration, that is, by interpolating to calculate the predicted value of the instantaneous time constant, finally obtains the value of the new working condition. Predicted time constant value at time t.

[0067] The quantitative analysis and prediction model established by the method of this invention has an effective applicability range based on the icing parameter range verified by the embodiments.

[0068] By employing the above technical solution, this invention provides a quantitative analysis and prediction method for the dynamic response characteristics of an intake air temperature sensor under icing conditions based on a grey relational model. Compared with existing technologies, it has at least the following beneficial effects:

[0069] By employing the above technical solution, the present invention has at least the following beneficial effects compared to the prior art:

[0070] 1. A systematic and quantifiable research paradigm has been constructed, solving the problem of fragmented key mechanisms. This invention innovatively proposes a multi-stage integrated research framework of "icing simulation / experiment - ice pattern extraction - thermal simulation / experiment - correlation analysis - dynamic prediction". This framework, for the first time, organically links and cross-verifies the icing characteristic test of the ice wind tunnel (<0℃), the dynamic response test of the hot wind tunnel (>0℃), and numerical simulation. It fundamentally opens up the data flow and correlation path between "icing condition parameters → three-dimensional ice pattern characteristics → sensor dynamic response characteristics (time constant)", overcoming the limitation of isolated research of the three in the prior art, and realizing closed-loop analysis and quantitative characterization of the entire chain of icing's impact on sensor dynamic response characteristics.

[0071] 2. This invention represents a leap from qualitative experience to quantitative principles, accurately identifying and quantifying key icing influencing factors and their time-varying patterns. For the first time, this invention systematically applies a grey relational model to the quantitative analysis of product performance in the field of icing engineering, rigorously quantifying the correlation between sensor time constants and multiple icing parameters (such as LWC, MVD, V, and T). This method not only scientifically identifies key icing influencing factors affecting dynamic response (e.g., the highest correlation with liquid water content LWC in the example), secondary icing influencing factors, and weak icing influencing factors, accurately ranking the contribution of each parameter; but also reveals the dynamic evolution of the influence of key icing influencing factors (e.g., wind speed V has the most significant impact in the medium term) by comparing the correlation at different icing time scales. This breaks through the long-standing reliance on qualitative descriptions and engineering experience in this field, providing a clear quantitative map for understanding the mechanism of icing degradation.

[0072] 3. A high-precision time-varying dynamic prediction model was established, enabling proactive early warning of dynamic response attenuation under icing conditions. Based on key icing influencing factors identified through grey relational analysis, this invention further constructed a multivariate grey prediction model GM(1, N) and a time-varying grey prediction integrated system. This system can not only accurately fit and predict the time constant within known operating conditions, but also continuously predict the sensor's dynamic response at any icing moment through parameter interpolation, and extrapolate and predict new operating conditions that have not been experienced but are within the verified icing parameter range. This provides accurate dynamic characteristic parameter inputs for real-time evaluation of sensor performance under icing conditions, attenuation early warning, and signal compensation systems, significantly improving the reliability of temperature measurement and the safety of the control system in icing environments.

[0073] 4. It provides direct engineering optimization guidance, transforming theoretical analysis into clear sensor anti-icing design criteria. The quantitative analysis conclusions of this invention have clear engineering orientation. The analysis shows that liquid water content (LWC) is a key factor affecting icing, which directly and quantitatively guides the design direction of the sensor's anti-icing structure: that is, the focus should be on optimizing the sensor's windward surface structure to reduce the effective retention of local LWC, significantly improving the sensor's inherent robustness in icing environments. Attached Figure Description

[0074] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0075] Figure 1 This is a schematic diagram of the method flow proposed in this invention;

[0076] Figure 2 This is a multi-stage research framework diagram for the present invention;

[0077] Figure 3 The figure shows the fitted ice pattern at 0 min, 1 min, 5 min, and 10 min under working condition B of the present invention and its influence on the airflow at the temperature measuring end of the sensor.

[0078] Figure 4 This is a diagram illustrating the effect of icing time on the sensor time constant in an embodiment of the present invention.

[0079] Figure 5 This is a schematic diagram comparing the predicted and actual values ​​of the time constant in operating condition B in this embodiment of the invention.

[0080] Figure 6 This is a schematic diagram comparing the predicted and calculated time constants for the new operating condition F in an embodiment of the present invention. Detailed Implementation

[0081] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The embodiments of the present invention are illustrated below through specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0082] Please refer to Figures 1 to 6 A specific implementation method of this embodiment is given:

[0083] S1. Acquisition of 3D Ice Pattern Data and Time Constant: 3D ice pattern data of the sensor under different icing conditions is obtained through simulated ice pattern models and ice wind tunnel experiments; a high-confidence dynamic response ice pattern simulation model of the sensor in an ice-free state is established and verified through hot wind tunnel experiments and thermal simulation analysis; based on the verified ice pattern simulation model, the time constant of the sensor under various icing conditions is obtained by combining the 3D ice pattern data; The multi-stage research framework constructed includes, for example... Figure 2 As shown, extract the ice type data, such as... Figure 3 As shown:

[0084] S11. Acquisition of 3D Ice Pattern Data: In this stage, icing information on the sensor surface is acquired through two complementary methods: numerical simulation of the simulated ice pattern model and ice wind tunnel experiments.

[0085] (1) Simulated ice model: Using FENSAP-ICE software, different freezing conditions parameters (as shown in Table 1) were set for numerical simulation: covering freezing conditions with different liquid water content, droplet diameter, air temperature and other parameters. Specifically, the computational domain was set, the mesh was generated, and the boundary and convergence conditions were set to simulate the growth process of ice on the sensor surface and to obtain complete surface coordinates by simulating ice growth.

[0086] (2) Ice wind tunnel experiment (<0℃): In the ice wind tunnel, the aforementioned icing conditions were reproduced (ice wind tunnel debugging), and the sensor to be tested was installed to conduct the icing experiment. The growth process of the ice shape was recorded in real time, and after the experiment, the physical ice shape formed was obtained to collect the actual ice shape data and obtain the coordinates of the key feature points of the measured ice shape.

[0087] S12. For the simulated ice model data (complete surface coordinates) and actual ice model data (coordinates of key feature points of the measured ice model) obtained from the above simulated ice model and ice wind tunnel experiment respectively, this step provides two parallel data processing schemes to extract three-dimensional ice model data for subsequent analysis.

[0088] Preferably, the key feature point coordinates of the measured ice shape are fitted with the complete surface coordinates extracted from the simulated ice shape model. First, the ice shape sheet file output from the simulated ice shape model is 3D repaired and solidified using UG software to extract the complete surface coordinates. Simultaneously, the physical ice shape obtained from the ice wind tunnel experiment is 3D scanned or its outline measured to obtain the coordinates or dimensions of its key feature points (including ice shape, ice thickness, and the coverage area of ​​specific sensor air inlets). Finally, the key feature point coordinates of the measured ice shape are aligned with the complete surface coordinates extracted from the simulated ice shape model. Scaling, translation, and rotation parameters are adjusted to minimize the sum of squared errors. After fitting, the error of the key feature points is ≤5%, constructing 3D ice shape data that combines realistic shape and structural integrity. This scheme is highly efficient, balancing realism and model quality. Example B shows the fitted ice shapes at 0 min, 1 min, 5 min, and 10 min as follows: Figure 3 As shown.

[0089] S13. Dynamic response characteristics test and model verification under ice-free conditions: (1) Conduct ice-free hot wind tunnel experiment (>0℃): Under ice-free conditions, place the sensor in the hot wind tunnel, apply a temperature step signal, measure the dynamic response curve of the output temperature of the ice-free sensor as a function of time, and obtain the reference experimental time constant. (2) Establish an ice-free thermal simulation model to reproduce the experiment and verify the simulation model for thermal simulation analysis: In the simulation software SOLIDWORKS Flow Simulation, reproduce the experimental conditions of the hot wind tunnel, set the same material properties, boundary conditions and thermal load as the ice-free hot wind tunnel experiment, and obtain the sensor simulation time constant. By comparing the deviation between the simulation and experimental results (3.6%), the deviation is controllable, to verify the effectiveness of the thermal simulation model and ensure that it has sufficient confidence and can be used for the next stage of extended simulation under icing conditions.

[0090] S14. Dynamic Response Characteristics Thermal Simulation Analysis under Icing Conditions: For the 15 typical ice types listed in Table 1, their corresponding 3D models were sequentially imported into the thermal simulation software. Based on the actual icing environment, appropriate material properties, boundary conditions, and thermal loads were set to simulate the transient heat transfer process of the sensor under different icing conditions, and the time constant for each condition was calculated.

[0091] Table 1. Parameters for Icing Conditions

[0092]

[0093] S2. Select icing condition parameters and construct the sequence. The influence of icing time on the sensor time constant is shown in the figure below. Figure 4 As shown: (1) Select a set of typical icing conditions parameters, including liquid water content (LWC), water droplet diameter (MVD), test wind speed (V), total temperature (T), etc.; (2) For multiple different icing conditions, record the dynamic response time constant of the sensor under each condition and at different icing times (t), so as to construct the original data sequence for subsequent analysis: the time constant sequence is used as the reference sequence, and the sequence of parameters for each icing condition is used as the comparison sequence, as shown in Table 2; (3) Figure 4 The curve's trend and characteristics are described below: Figure 4The curves showing the variation of sensor time constant with icing time (0 min, 1 min, 5 min, 10 min) under five typical icing conditions (AE) are presented. Overall, the time constant of all conditions shows a monotonically increasing trend with increasing icing time, indicating that the accumulation of ice continuously degrades the dynamic response speed of the sensor. All curves exhibit a common characteristic of rapid growth in the initial stage (1-5 min) and a gradual slowdown in the later stage (5-10 min), indicating that the impact of ice accumulation on dynamic characteristics is particularly significant in the early stages of icing. The ranking and spacing of the curves visually reflect the differences in the strength of the influence of different combinations of icing parameters on the time constant, providing a data foundation for subsequent grey relational analysis.

[0094] Table 2. Effect of Icing Time on Sensor Time Constant

[0095]

[0096] S3. Perform grey relational analysis to quantify the impact of parameters on dynamic response characteristics (taking 10 min as an example):

[0097] S31. Preprocess the reference and comparison sequences to eliminate dimensional effects (generate...) The formula is:

[0098] ;

[0099] Where X0 is the time constant reference sequence, X1 (LWC), X2 (MVD), X3 (V), and X4 (T) are comparison sequences, and the preprocessing results of the working condition parameters with the 10-minute time constant as the reference sequence are shown in Table 3; This is the processed dimensionless comparison sequence value.

[0100] Table 3. Preprocessing results of operating condition parameters with the time constant of the 10-minute icing time as the reference sequence.

[0101]

[0102] S32. Correlation Coefficient Calculation: Calculate the absolute difference between the dimensionless comparison sequence of parameters for each icing condition and the reference sequence of time constants under each condition. , ;Sure The two-level minimum difference and the maximum difference Table 4 The results of the absolute difference of the working parameters with a 10-minute time constant as the reference sequence are shown in Table 4.

[0103] Table 4. Results of absolute differences in operating parameters for the 10-minute icing time using the reference sequence.

[0104]

[0105] S33, Introducing the resolution coefficient Calculate the correlation coefficient of each comparison sequence at each operating point (generating) Table 5 That is, the correlation coefficient sequence of the corresponding parameters), the formula is: The correlation coefficient results of the working condition parameters with the 10-minute time constant as the reference sequence are shown in Table 5.

[0106] Table 5. Results of correlation coefficients for operating parameters with the time constant of the 10-minute icing time as the reference sequence.

[0107]

[0108] S34. Relevance Ranking: Take the average of the correlation coefficients for each parameter sequence to obtain the correlation degree. ), The time constants for the 1-minute icing time are the correlation results and ranking of the working condition parameters of the reference sequence: r1(LWC) = 0.933, r3(V) = 0.923, r2(MVD) = 0.918, r4(T) = 0.662; the time constants for the 5-minute icing time are the correlation results and ranking of the working condition parameters of the reference sequence: r3(V) = 0.933, r1(LWC) = 0.929, r2(MVD) = 0.919, r4(T) = 0.661; the time constants for the 10-minute icing time are the correlation results and ranking of the working condition parameters of the reference sequence: r1(LWC) = 0.938, r2(MVD) = 0.938, r3(V) = 0.921, r4(T) = 0.651. The closer the correlation is to 1, the stronger the correlation between the icing condition parameter and the time constant.

[0109] S4. Key factor identification and extraction based on correlation:

[0110] S41. Based on the correlation ranking results, identify the key icing influencing factors (highest correlation and stable), secondary icing influencing factors (medium correlation), and weakest icing influencing factors (lowest correlation) that affect the time constant, and clarify the quantitative influence level of each icing condition on the dynamic response characteristics.

[0111] S42. By comparing the correlation ranking of different freezing times t, analyze and verify the time-varying characteristics of the factors (especially the key freezing influencing factors), and reveal the dynamic evolution law of the key freezing influencing factors during the freezing process.

[0112] S43. Based on the gray relational degree threshold (r > 0.9), LWC, MVD, and V are selected as key icing influencing factors, and factors with low correlation are excluded to form a set of key icing influencing factors for subsequent gray prediction modeling, ensuring that the model focuses on the core driving variables.

[0113] From a numerical perspective, the following conclusions can be drawn: (1) Key icing influencing factors: Liquid water content (LWC) has the highest correlation (0.929-0.938), which is the core factor affecting the time constant. The larger the LWC, the faster the icing rate, the more severe the flow channel blockage, and the larger the time constant. The high correlation of the key icing influencing factor LWC indicates that to reduce the degradation of the time constant, it is necessary to focus on reducing the impact and accumulation of local liquid water. This directly guides and quantifies the design of the "anti-icing sensor with a V-shaped groove for guiding flow on the windward side" as described in application number 202510796078.7: by guiding and diverting water through the V-shaped groove, the liquid film is dispersed and accelerated, thereby reducing the local residence of effective LWC and suppressing icing from the source. (2) Secondary icing influencing factors: Wind speed (V) has the second highest correlation (0.921-0.933), and the influence is most obvious in the medium term (5 min). The higher the wind speed, the higher the energy of water droplet impact, the faster the icing rate, and the larger the time constant. (3) Weaker icing influencing factors: The correlation of water droplet diameter (MVD) increases with time (0.918-0.938), indicating that MVD has a time-varying cumulative effect on the time constant. When the difference in ice shape increases with time, it indirectly prolongs the heat transfer path, resulting in a continuous increase in the time constant. (4) Minimal icing influencing factors: The correlation of total temperature (T) is always the lowest (0.651-0.662). This is because the distribution of icing area is dominated by the sensor structure. Total temperature can only indirectly affect the ice shape by influencing the freezing rate, thus affecting the time constant.

[0114] S5. Constructing a multivariate grey prediction model GM(1, N) based on grey relational analysis: Based on the selected key icing influencing factors LWC, MVD, and V, GM(1,3) models are constructed for the initial, middle, and final time periods, respectively. This section uses a 10-minute icing time as an example to elaborate on the construction process of the GM(1,3) prediction model. The modeling method is exactly the same for 1-minute and 5-minute time points.

[0115] S51. Start data preparation and sequence definition. The original data matrix is ​​shown in Table 6.

[0116] Table 6. Original data matrix under the 10-minute freezing time condition.

[0117]

[0118] Define sequence:

[0119] System characteristic sequence: X0⁽ 0 = [20.85, 26.50, 29.60, 24.05, 26.00]

[0120] Key icing influencing factor sequence: X1⁽ 0 ⁾ = [0.8, 1.0, 2.0, 0.5, 1.0] (LWC)

[0121] Key icing influencing factor sequence: X2⁽ 0 ⁾ = [25, 25, 25, 20, 20] (MVD)

[0122] Key icing influencing factor sequence: X3⁽ 0 ⁾ = [32, 48, 48, 66, 66] (V)

[0123] S52, First-order cumulative generation (1-AGO):

[0124] First-order cumulative generation operations were performed on the system characteristic sequence and the sequences of each key icing influencing factor to weaken randomness and highlight trend, resulting in first-order cumulative generation sequences. :

[0125] i=0,1,2,3; k=A,B,C,D,E;

[0126] The calculation yielded:

[0127] = [20.85, 47.35, 76.95, 101.00, 127.00]

[0128] = [0.8, 1.8, 3.8, 4.3, 5.3]

[0129] = [25, 50, 75, 95, 115]

[0130] = [32, 80, 128, 194, 260];

[0131] S53. Construct the GM(1,3) model. Based on the first-order cumulative generation sequence, establish an N-variable grey differential equation, i.e., the whitened differential equation form of the GM(1, N) model:

[0132] ;

[0133] Where a is the development coefficient, and b1, b2, b3 are the driving coefficients.

[0134] S54. Model parameter estimation:

[0135] Background value sequence generated using the nearest neighbor mean generation method :

[0136] ;

[0137] The calculation yielded: ;

[0138] Discrete form equations obtained by discretizing the grey differential equation:

[0139] ;

[0140] Representing the discrete-form system of equations as matrix equations ,in, For the reason The column vector formed It is a matrix composed of background values ​​and the cumulative values ​​of each factor. :

[0141] ;

[0142] ;

[0143] S55, Parameter Estimation:

[0144] The least squares method was used to analyze the development coefficient and driving coefficient. Parameter estimation is performed to obtain the estimated development coefficients and driving coefficients. :

[0145] ;

[0146] The result, calculated and rounded to four decimal places, is as follows:

[0147] ;

[0148] S56. Time Response Function:

[0149] Substitute the estimated evolution coefficients and driving coefficients into the whitening differential equation and solve:

[0150] ;

[0151] Solving the differential equation yields the time response function:

[0152] ;

[0153] in, .

[0154] S57. Accuracy Verification and Subtraction Recovery:

[0155] The predicted value is obtained by cumulative subtraction and restoration:

[0156] ;

[0157] The prediction results are compared below:

[0158]

[0159] Model accuracy metrics:

[0160] Mean relative error: ε avg = 2.09%

[0161] Posterior error ratio: C = S2 / S1 = 0.32 (first-order precision)

[0162] Small error probability: P = 0.92 (first-level precision)

[0163] Based on this method, baseline prediction models for 1 minute and 5 minutes can be constructed respectively.

[0164] S6. Construction and Verification of Time-Varying Grey Prediction Integrated System

[0165] S61. Construction and Parameter Analysis of Time-Divided Benchmark Model

[0166] The model parameters at the three time points were summarized and analyzed:

[0167]

[0168] S62. Consistency verification between model mechanism and correlation degree

[0169] Review of the results of grey relational analysis:

[0170] The time constant of the 1-minute freezing time is the correlation result of the working condition parameters of the reference sequence and their sorting from largest to smallest: r1(LWC) = 0.933, r3(V) = 0.923, r2(MVD) = 0.918;

[0171] The time constant of the 5-minute freezing time is the correlation result of the working condition parameters of the reference sequence and their sorting from largest to smallest: r3(V) = 0.933, r1(LWC) = 0.929, r2(MVD) = 0.919;

[0172] The time constant of the 10-minute freezing time is the correlation result of the working condition parameters of the reference sequence and their sorting from largest to smallest: r1(LWC) = 0.938, r2(MVD) = 0.938, r3(V) = 0.921.

[0173] The correspondence between model driving coefficients and correlation ranking:

[0174] 1. 1 minute: b1(4.8261) > b3(0.1035) > b2(0.0528), consistent with r1 (LWC) > r3 (V) > r2 (MVD).

[0175] 2. 5 minutes: b3(0.2516) > b1(3.2154) > b2(0.0821), consistent with r3(V) > r1(LWC) > r2(MVD).

[0176] 3. 10 minutes: b1(5.0124) > b2(0.1217) > b3(0.1839), which is basically consistent with r1(LWC) ≈ r2(MVD)>r3(V) (Note: In the actual correlation, r1(LWC) and r2(MVD) are almost equal, and b1 is significantly greater than b2 in the model, indicating that LWC still has a slight advantage in the long term).

[0177] S63, Time-varying Grey Prediction Integrated System:

[0178] A baseline GM(1,3) model, established based on three discrete physical time points (1 min, 5 min, and 10 min), is integrated into a time-varying grey prediction ensemble system with continuously variable parameters through parameter interpolation. This system aims to address the following two typical prediction needs:

[0179] Prediction Scenario 1 (Time Extrapolation): For a known working condition (i.e., the working condition AE used for modeling), when it is necessary to predict its time constant for any physical time t (e.g., 3.5 min) between the modeling time points, this time-varying gray prediction integrated system is used.

[0180] Implementation method: Obtain the model parameters a(t) and other parameters at time t through interpolation. Construct the GM(1,3) model for that moment, and then substitute the parameters of that working condition into it for prediction.

[0181] Prediction Scenario 2 (New Operating Condition Extrapolation): For a new operating condition within the verified icing parameter range, when it is necessary to predict its value at a certain modeled physical time point... When the time constant is 10 min (e.g.), the baseline GM(1,3) model corresponding to that time moment is used directly for prediction.

[0182] The core of the time-varying grey prediction integrated system lies in constructing a continuous interpolation function for model parameters as a function of physical time t. For any physical time t (1 ≤ t ≤ 10 min), its model parameters p(t) (representing a(t), b1(t), b2(t), b3(t)) can be obtained by linear interpolation of the parameters of adjacent reference points:

[0183] 1. When 1 ≤ t ≤ 5 min: p(t) = p(1min) + (t-1) / 4 × [p(5min) - p(1min)]

[0184] 2. When 5 ≤ t ≤ 10 min: p(t) = p(5 min) + (t - 5) / 5 × [p(10 min) - p(5 min)]

[0185] S64, Scenario 1 Verification: Example of Time Extrapolation Prediction, predicting parameters at t = 3.5 min. Assume we need to predict the time constant of condition B (LWC=1.0, MVD=25, V=48) at 3.5 minutes:

[0186] S641. Calculate the interpolation parameters:

[0187] a(3.5) = -0.1523 + (3.5-1) / 4 × [-0.0487 - (-0.1523)] = -0.0985

[0188] b1(3.5) = 4.8261 + 2.5 / 4 × [3.2154 - 4.8261] = 3.8192

[0189] b2(3.5) = 0.0528 + 2.5 / 4 × [0.0821 - 0.0528] = 0.0711

[0190] b3(3.5) = 0.1035 + 2.5 / 4 × [0.2516 - 0.1035] = 0.1961

[0191] S642, Construct the GM(1,3) model at 3.5 minutes:

[0192] ;

[0193] S643. Substitute the accumulated value of the factor sequence for operating condition B, solve for the time response function, and predict the time constant. ;

[0194] According to the appendix Figure 5As shown, the model prediction value (approximately 19.84) at t=3.5 min is compared with the time constant curve of working condition B plotted based on actual data. The two are in good agreement, and the prediction deviation is within the allowable range, further verifying the effectiveness and accuracy of the model in predicting intermediate times.

[0195] S65, Scenario 2 Verification: For the example of extrapolating the new operating condition within the verified icing parameter range, the time constant prediction of the new operating condition F (LWC=2.0, MVD=25, V=66) at 10 minutes will be strictly based on the constructed and verified 10-minute GM(1,3) baseline model. The parameters of this model are:

[0196] a = -0.0258

[0197] b1 = 5.0124 (LWC driving coefficient)

[0198] b2 = 0.1217 (MVD driving coefficient)

[0199] b3 = 0.1839 (V driving coefficient)

[0200] The time response function is:

[0201] ;

[0202] S651. Define a new operating condition F sequence, whose original parameter sequence is:

[0203] X1⁽ 0 ⁾ = [2.0, 2.0, 2.0, 2.0, 2.0] (LWC)

[0204] X2⁽ 0 ⁾ = [25, 25, 25, 25, 25] (MVD)

[0205] X3⁽ 0 ⁾ = [66, 66, 66, 66, 66] (V)

[0206] S652. Calculate the first-order cumulative generation (1-AGO) sequence.

[0207] At k=10min (corresponding to the k=5th point in the sequence; if the intervals are 1, 5, and 10 minutes, this is the endpoint), the cumulative effect of each factor is its original value multiplied by time. For the 5 data point structure used in the modeling, the cumulative value up to the 5th point is calculated as follows:

[0208] X1⁽¹⁾(5) = 2.0 × 10 = 20 (cumulative LWC)

[0209] X2⁽¹⁾(5) = 25 × 10 = 250 (Cumulative MVD)

[0210] X3⁽¹⁾(5) = 66 × 10 = 660 (cumulative V)

[0211] S653. Solve for the time response function (calculate the predicted cumulative time constant).

[0212] First, calculate the key term Σ(bᵢ / a)Xᵢ⁽¹⁾ (5) in the model:

[0213] 1. (b1 / a) ×

[0214] 2. (b2 / a) ×

[0215] 3. (b3 / a) ×

[0216] 4. Sum: Σ(bᵢ / a)Xᵢ⁽¹⁾(5) = -3885.6 + (-1179.45) + (-4704.41) = -9769.46

[0217] Assume the initial accumulated value X0⁽¹⁾(1) = 20.85 (referencing the initial value of working condition A, as an order of magnitude anchor). Then:

[0218] ;

[0219] Where e is the natural constant (approximately 2.71828).

[0220] S654, Cumulative Subtraction and Restoration (Calculating the Predicted Instantaneous Time Constant)

[0221] To obtain the instantaneous value at the 10th minute (k=5), a predicted cumulative value at k=4 is needed. This is calculated using the same formula. (For a timeframe of 7.5 minutes, interpolation is required to calculate the cumulative factor value at that point; the process will not be detailed here.)

[0222] To directly provide the final prediction result, we use model simulation to complete the above recursive calculation. The final result is:

[0223] Prediction results: For the new operating condition F (LWC=2.0, MVD=25, V=66), the model predicted value of the sensor time constant is approximately 30.8 after 10 minutes of icing.

[0224] like Figure 6 As shown, the predicted value is in good agreement with the result (30.45) obtained by conducting a 10-minute icing test and simulating ice pattern extraction based on the same working conditions (LWC=2.0, MVD=25, V=66, T=-5) and simulating the time constant under icing conditions according to the steps described in the patent. The relative deviation is about 1.15%, which meets the engineering accuracy requirements and further verifies the applicability and predictive reliability of the model to the new working conditions.

[0225] The prediction model established in the embodiments of this invention has an effective applicability primarily based on the designed series of icing test conditions (see Table 1). Specifically, this model has been experimentally verified within the following parameter ranges and exhibits high prediction confidence:

[0226] Liquid water content (LWC): 0.5 ~ 2.0 g / m³

[0227] Average volumetric diameter (MVD) of water droplets: 20 ~ 25 μm

[0228] Incoming air velocity (V): 32 ~ 66 m / s

[0229] Freezing time (t): 1 ~ 10 min

[0230] Total temperature (T): Covers the typical freezing temperature range (e.g., -20℃ ~ -2℃)

[0231] Compared with existing technologies, the embodiments provided by this invention solve the core problem of the fragmented relationship between "icing condition parameters, ice type characteristics, and dynamic response characteristics" in existing technologies. By constructing a multi-stage integrated research framework and introducing a grey relational model for quantitative analysis, this invention systematically reveals for the first time the degree of influence and dynamic evolution law of key icing parameters on the dynamic response characteristics of sensors, and further establishes a high-precision time-varying prediction model. This provides a direct theoretical basis and key technical tools for the quantitative evaluation of sensor performance under icing conditions, attenuation early warning, and optimization of anti-icing structures, breaking through the long-standing predicament of relying on qualitative analysis and empirical judgment in this field, and has important theoretical value and engineering guiding significance.

[0232] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

[0233] It should be noted that this application describes various aspects of embodiments within the scope of the appended claims. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure or function described herein is merely illustrative. Based on this invention, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth in this application can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth in this application.

[0234] It should also be noted that the illustrations provided in the above embodiments are only schematic representations of the basic concept of the present invention. The illustrations only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0235] Furthermore, specific details have been provided in the above description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

Claims

1. A method for quantitatively analyzing and predicting the dynamic response characteristics of an air intake temperature sensor under icing conditions based on a grey correlation model, characterized in that, The method comprises the following steps: S1, three-dimensional ice shape data and time constant acquisition: obtain three-dimensional ice shape data of the sensor under different icing conditions through simulation ice shape model and icing wind tunnel experiment; establish and verify a high-confidence dynamic response ice shape simulation model of the sensor under the non-icing state through hot wind tunnel experiment and hot simulation analysis; based on the verified ice shape simulation model, obtain the time constant of the sensor under each icing condition in combination with the three-dimensional ice shape data; S2, icing condition parameter and sequence construction: select multiple icing condition parameter sets including liquid water content, water droplet diameter, test wind speed and total temperature; record the time constant of the dynamic response of the sensor under each icing condition and different icing time t for multiple different icing conditions, and construct an original data sequence, wherein the time constant sequence is taken as a reference sequence, and each icing condition parameter sequence is taken as a comparison sequence; S3, implement grey correlation analysis, pre-process the reference sequence and the comparison sequence to eliminate the dimension; calculate the correlation coefficients of each comparison sequence and the reference sequence; take the average of the correlation coefficients of each parameter sequence to obtain the grey correlation degree of the time constant, and sort the correlation degrees according to the size to determine the weight of the influence of each icing condition parameter on the time constant; S4, key icing influencing factor identification and extraction based on the correlation degree: identify the key icing influencing factor and the secondary icing influencing factor according to the correlation degree sorting result; analyze the time-varying characteristics of the key influencing factor by comparing the correlation degree sorting results under different icing time t; filter out the key influencing factor according to the preset correlation degree threshold; S5, construct a multivariate grey prediction model GM(1, N) based on grey correlation analysis: for icing time t, construct a multivariate grey prediction model GM(1, N) between the system characteristic sequence and the key icing influencing factor sequence by using the N key icing influencing factors filtered out, wherein N is a positive integer not less than 1, and the system characteristic sequence is the time constant sequence, to quantify the dynamic response characteristics in the icing process; S6, construct a time-varying grey prediction integrated system: establish a GM(1, N) benchmark prediction model at multiple representative icing time points; integrate multiple GM(1, N) benchmark models by using an interpolation method to construct a time-varying grey prediction integrated system with continuously changing model parameters with icing time t, which is used to realize at least one of time extrapolation and new condition extrapolation prediction.

2. The method according to claim 1, wherein the method is characterized by: In step S1, the acquisition of three-dimensional ice shape data specifically comprises: performing three-dimensional repair and entity conversion on the ice shape slice file output by the simulation ice shape model to extract complete surface coordinates; performing three-dimensional scanning or contour measurement on the physical ice shape obtained through the icing wind tunnel experiment to obtain key feature point coordinates including ice thickness and contour size; align the key feature point coordinates of the measured ice shape with the complete surface coordinates extracted from the simulation ice shape model, adjust the scaling, translation and rotation parameters to minimize the sum of squared errors, and fit the key feature point error to be less than or equal to 5%, to construct three-dimensional ice shape data with real shape and complete structure.

3. The method according to claim 1, wherein the method is characterized by: In step S1, the hot wind tunnel experiment and hot simulation analysis specifically comprise: Developing ice-free hot-wind tunnel experiment: placing ice-free sensor in hot-wind tunnel, applying temperature step signal, measuring the dynamic response curve of the output temperature of the ice-free sensor over time and obtaining the reference experimental time constant; Establishing ice-free thermal simulation model for reproducing the experiment and verifying the simulation model: using simulation software to reproduce the hot-wind tunnel experiment conditions, setting the same material properties, boundary conditions and thermal loads as the ice-free hot-wind tunnel experiment, and obtaining the simulation time constant; Comparing the measured and simulated results to verify the effectiveness of the simulation model, the relative deviation of the simulation and experimental results is ≤4%, which verifies that the simulation model is effective.

4. The method according to claim 1, wherein the method is characterized by: In step S3, the initial value method is used for initial value processing of the reference sequence and the comparison sequence to eliminate the dimensional difference, and the specific formula is: ； wherein, is a time constant reference sequence, is a frozen condition parameter comparison sequence, is the original value of the i-th parameter sequence under the k-th condition, is the value of the sequence under the reference condition A, represents the dimensionless value of the i-th parameter sequence under the k-th condition point after the initial value processing, P is the total number of frozen condition parameters, and M represents the total number of condition points participating in the calculation.

5. The method according to claim 4, wherein the method is characterized by: In step S3, the correlation coefficient is calculated according to the formula: ； wherein, is the absolute difference between the comparison sequence of dimensionless i-th icing operating condition parameter and the reference sequence of time constant in the k-th operating condition: , and are the minimum and maximum values, respectively, of all with ρ being the resolution factor.

6. The method according to claim 5, wherein the method is characterized by: In step S3, the calculation formula of the grey correlation degree is as follows: ； wherein, represents the grey correlation degree between the i th comparison sequence and the reference sequence, M represents the total number of working condition points participating in the calculation, represents the correlation coefficient of the i th comparison sequence at the k th working condition point.

7. The method according to claim 1, wherein the method is characterized by: In step S4, the preset correlation degree threshold is 0.9, and the parameters with a correlation degree greater than 0.9 are screened as key icing influencing factors.

8. The method according to claim 1, wherein the method is characterized by: In step S5, the GM(1, N) model is constructed, which specifically includes the following steps: Data preparation and sequence definition: Collect the original observation data of time constant as the system eigenvalue and N key icing influencing factors under M different icing conditions, form the original data matrix, define the system eigenvalue sequence as , and define the jth key icing influencing factor sequence as , where j = 1, 2,..., N; First-order accumulated generation 1-AGO: first-order accumulated generation operation is respectively performed on the system characteristic sequence and each key icing influencing factor sequence to obtain a first-order accumulated generation sequence : ； ； Constructing the GM(1, N) model: based on the first-order accumulation generation sequence, establishing the N-variable gray differential equation, i.e. the whitening differential equation form of the GM(1, N) model: ； wherein a is a development coefficient reflecting the development trend of the system characteristic sequence itself, is a driving coefficient, respectively quantifying the key icing influencing factors the contribution degree to the system characteristic change, is a driving coefficient of the jth key icing influencing factor; Model parameter estimation: The background value sequence is constructed by the method of close-to-mean generation : ； The discrete form of the grey differential equation obtained by discretizing it can be expressed as a matrix equation. ,in, For the reason The column vector formed It is a matrix composed of background values ​​and the cumulative values ​​of each factor. Given the parameter vector to be estimated, the least squares method is used to estimate the development coefficient and driving coefficient. The estimated development coefficient and driving coefficient are obtained. ; Model solving and time response function: substituting the estimated development coefficient and driving coefficient into the whitening differential equation and solving, finally obtaining the time response function of the first-order accumulation system characteristic sequence; Cumulative reduction and prediction value calculation: through the cumulative reduction IAGO operation, the fitting value and the prediction value of the time constant at each working condition point are obtained by cumulative reduction. 9.The method of claim 1, wherein the method further comprises: determining a dynamic response characteristic of the intake temperature sensor in the icing condition based on the gray relational model. In step S6, the time extrapolation is for known working conditions, to predict the time constant at any time t between discrete reference time points. Through model parameter interpolation, dynamic response prediction in continuous time dimension is realized, and the prediction steps specifically include: by linear interpolation of the model parameters at the adjacent reference time points , , , , : ； wherein , represent the model parameters at time t, i.e. the development coefficient parameter a(t) and the individual drive coefficients parameters; For any icing time, the GM(1, N) model at time t is constructed by using the interpolated parameter p(t), and the cumulative generation sequence of each key icing influencing factor at any icing time t under the known working condition is substituted into the GM(1, N) model for continuous prediction of dynamic response characteristics. Through solving the time response function and cumulative reduction, the time constant prediction value of the known working condition at any icing time t is finally obtained.

10. The method according to claim 9, wherein the method is characterized by: In step S6, the new working condition extrapolation is for a new working condition within the parameter interval of the verified icing working condition, to predict the time constant at the discrete time points of the built model. The reference GM(1, N) model of the time point is directly reused to realize dynamic response prediction of the new working condition, and the prediction steps specifically include: Determining a prediction target time point , obtaining the reference GM(1, N) model parameters at the time point, performing accumulation generation processing on the key icing influencing factor sequence of the new working condition, substituting the processed sequence into the GM(1, N) model at the time point , obtaining the time constant prediction value of the new working condition at the time point by solving the time response function and performing accumulation reduction, and finally obtaining the time constant prediction value of the new working condition at the time point.

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