A multi-element parallel system parameter sensitivity evaluation method and related device

Abstract

This invention discloses a multivariate parallel system parameter sensitivity assessment method and related apparatus, belonging to the field of complex system parameter sensitivity analysis technology. The method includes: determining the sensitivity analysis object, including the response variable and at least one explanatory variable affecting the response variable; collecting operational data and performing preprocessing and standardization; using correlation coefficient method, mutual information method, principal component regression method, stepwise regression method, and random forest method in parallel to calculate the sensitivity index of each explanatory variable; normalizing the indices obtained by each method; and weighting and fusing the data according to system characteristics and method applicability to obtain a comprehensive sensitivity assessment result. This invention, by integrating the advantages of multiple linear and nonlinear sensitivity analysis methods and combining them with an adaptive weighted fusion mechanism, overcomes the limitations of single methods and achieves robust, comprehensive, and engineering-interpretable parameter sensitivity assessment in complex engineering systems.

Description

Technical Field

[0001] This invention belongs to the field of parameter sensitivity analysis technology for complex systems, and relates to a multi-parallel system parameter sensitivity assessment method and related apparatus. Background Technology

[0002] As modern industrial and information systems grow in scale and complexity, the interactions and dependencies between internal variables become exceptionally intricate. Accurately identifying the sensitivity of system outputs or key performance indicators to their internal parameters or input variables has become a crucial step in system optimization design, reliability analysis, fault diagnosis, and operational control. Sensitivity analysis aims to quantify the degree to which the uncertainty of input variables affects system output, thereby identifying key influencing factors and guiding resource allocation and decision-making.

[0003] In the field of industrial pipelines, key performance indicators such as pipeline pressure, flow rate, and temperature are affected by multiple internal parameters, including upstream valve opening, pump operating status, and downstream load changes. Accurately identifying the sensitivity of these parameters to system output (such as pipeline pressure) has become a crucial step in pipeline system optimization design, operation control, leak detection, fault diagnosis, and reliability analysis. However, single sensitivity analysis methods often have limitations for the acquired data. Linear methods are sensitive to linear relationships and computationally simple, but cannot effectively characterize complex nonlinear dependencies. Information theory-based methods can capture both linear and nonlinear relationships, but their results are significantly affected by the discretization method and require a large sample size. Model-based methods have the ability to handle nonlinearity and interactions; stepwise regression can automatically select variables but may get stuck in local optima, while random forests are robust but have relatively weak model interpretability, and their "black box" nature sometimes makes them unsuitable for scenarios requiring high clarity of mechanisms. Traditional global variance methods are theoretically sound, but require extensive model calls or sampling, resulting in a heavy computational burden and making them difficult to apply directly to complex systems based on historical operating data, lacking explicit physical models, or with high simulation costs. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a multi-parallel system parameter sensitivity evaluation method and related device to solve the problem that the single sensitivity analysis method in the prior art has application limitations and is difficult to adapt to engineering scenarios with complex industrial systems, multivariate coupling, significant nonlinearity, and complex data conditions.

[0005] To achieve the above objectives, the present invention employs the following technical solution: A multi-parallel system parameter sensitivity evaluation method includes: S1, Obtain the sensitivity analysis object from the target engineering system, the sensitivity analysis object including the response variable and at least one explanatory variable that affects the response variable; S2, collect the operational data of the response variable and the explanatory variable, and perform preprocessing and standardization on the operational data; S3, multiple sensitivity analysis methods are used in parallel to calculate the sensitivity index of each explanatory variable relative to the response variable; the multiple sensitivity analysis methods include correlation coefficient method, mutual information method, principal component regression method, stepwise regression method and random forest method; S4, normalize the sensitivity indices obtained by each method respectively; S5. Based on system characteristics and method applicability, a weighted fusion is performed to obtain the comprehensive sensitivity evaluation result of the response variable.

[0006] A further improvement of the present invention is that: Preferably, in S2, the preprocessing includes data alignment, time series checking, elimination of duplicate points, removal of bad points, and interpolation to complete missing values.

[0007] Preferably, in S2, the correlation coefficient method uses the Pearson correlation coefficient to measure the degree of linear correlation between the explanatory variable and the response variable, and the sensitivity index is the absolute value of the Pearson correlation coefficient.

[0008] Preferably, in S2, the mutual information method measures the statistical dependence between the explanatory variable and the response variable based on information entropy and joint entropy, and the sensitivity index is the mutual information value.

[0009] Preferably, in S2, the principal component regression method first performs principal component decomposition on the explanatory variables to obtain the principal component score matrix and loading matrix, establishes a regression model in the orthogonal principal component space to obtain regression coefficients, and then maps the regression coefficients back to the original variable space. The sensitivity index is the absolute value of the mapped regression coefficients.

[0010] Preferably, in S2, the stepwise regression method introduces variables by performing an F-test using the forward selection criterion and removes variables by performing an F-test using the backward elimination criterion. After multiple iterations of screening, significant influencing variables are obtained, and the sensitivity index is the absolute value of the standardized regression coefficient.

[0011] Preferably, in S2, the random forest method constructs a decision tree ensemble based on Bootstrap aggregation and random subspace methods, and evaluates the feature contribution through permutation importance. The sensitivity index is the permutation importance calculated based on out-of-bag error.

[0012] Preferably, in S1, the response variables are pressure, temperature, flow rate, vibration power, and vibration accuracy during system operation, and the explanatory variables are valve opening, pump operating frequency, or heater power.

[0013] Preferably, in S5, the weighted fusion based on system characteristics and method applicability considers factors such as system physical characteristics and variable relationships, data completeness and quality, and the degree of multicollinearity among variables when allocating weights.

[0014] A multi-parallel system parameter sensitivity evaluation device, comprising: The analysis object module obtains sensitivity analysis objects from the target engineering system. The sensitivity analysis objects include response variables and at least one explanatory variable that affects the response variables. The data processing module collects the operational data of the response variable and the explanatory variable, and performs preprocessing and standardization on the operational data; The sensitivity index module employs multiple sensitivity analysis methods in parallel to calculate the sensitivity index of each explanatory variable relative to the response variable; these multiple sensitivity analysis methods include correlation coefficient method, mutual information method, principal component regression method, stepwise regression method, and random forest method. The normalization module normalizes the sensitivity indices obtained by each method. The sensitivity assessment module performs weighted fusion based on system characteristics and method applicability to obtain a comprehensive sensitivity assessment result for the response variable.

[0015] Compared with the prior art, the present invention has the following beneficial effects: This invention discloses a multivariate parallel system parameter sensitivity assessment method, which is a multivariate parallel system parameter sensitivity comprehensive analysis algorithm, including the following steps: 1) For the target system, clarify the specific object of sensitivity analysis; 2) Collect operational data of response variables and explanatory variables, and preprocess the data; 3) Use five sensitivity analysis algorithms in parallel (correlation coefficient, mutual information, principal component regression, stepwise regression, and random forest) to calculate the sensitivity index of each explanatory variable relative to the response variable; 4) Normalize the sensitivity indices obtained by each method to map them to a unified scaling range; 5) Perform weighted fusion according to system characteristics and method applicability to obtain the comprehensive sensitivity assessment result. This invention is particularly suitable for complex systems with strong component coupling and significant nonlinear characteristics, and can provide comprehensive monitoring and diagnosis for the operation monitoring, fault diagnosis, and maintenance decision-making of key equipment. The system sensitivity analysis algorithm of this invention, based on multiple analysis methods, can effectively integrate the advantages of multiple analysis methods, overcome the limitations of a single method, and adapt to the characteristics and data conditions of different systems through a reasonable normalization and weighted fusion mechanism, thereby providing more robust, comprehensive, and engineering-practical sensitivity analysis results. This invention also has the following advantages: (1) The sensitivity analysis method described in this invention integrates five methods—correlation coefficient analysis, mutual information analysis, principal component regression, stepwise regression, and random forest—for parallel analysis. This design retains the computational efficiency and clear interpretability of linear methods (correlation coefficient and principal component regression) while fully capturing the complex nonlinear relationships and interaction effects between system variables through mutual information and random forest methods. This complementary multi-method architecture ensures that a comprehensive and reliable sensitivity assessment can be obtained for complex systems, whether linearly dominant, nonlinearly significant, or both coexisting.

[0016] (2) This invention introduces a fusion mechanism that dynamically assigns weights based on the characteristics of the target subsystem, data quality, and the reliability of each method. Unlike simple equal-weighted averaging or method stacking, this invention assigns appropriate weights to different analysis methods by analyzing data completeness, noise level, collinearity, and the nonlinear characteristics of the system itself, and then performs weighted fusion.

[0017] (3) While pursuing comprehensive analysis, this invention also takes into account the practicality of engineering applications. By retaining linear model components and providing clear intermediate results, the interpretability of the overall analysis process is enhanced. From data preprocessing, multi-method parallel computing, normalization to weighted fusion, the entire process is highly automated, which can save a lot of time and cost in analysis. Attached Figure Description

[0018] Figure 1 Here is a flowchart of the overall process for system sensitivity analysis. Figure 2 This is a schematic diagram of a specific application system architecture applicable to the present invention; Figure 3 A comparison chart of sensitivity indicators for various valves is provided for specific applications. Figure 4 A comprehensive sensitivity rating chart for each valve is provided for specific applications. Detailed Implementation

[0019] Hereinafter, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first," "second," "third," or "fourth" may explicitly or implicitly include one or more of that feature.

[0020] The method provided in this application can be applied to mobile phones, tablets, wearable devices, in-vehicle devices, augmented reality (AR) / virtual reality (VR) devices, laptops, and ultra-mobile personal computers. In this application, the specific type of terminal device is not limited to terminal devices such as mobile personal computers (UMPCs), netbooks, and personal digital assistants (PDAs).

[0021] It should be noted that the terms "first," "second," etc., used in the specification and drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0022] See Figure 1This is a schematic diagram of the overall process of the system sensitivity analysis method described in this invention. The method is based on key variables that are measurable, adjustable, or recordable during system operation, and first determines the object of sensitivity analysis. Specifically, the system state variables whose changing patterns need to be evaluated are determined as response variables, and the control variables, structural parameters, or operating parameters that may affect the response variable are determined as explanatory variables. The first aspect of this invention discloses a multivariate parallel system parameter sensitivity assessment method, including the following steps: Step 1: For the target system, identify the specific objects of the sensitivity analysis.

[0023] The sensitivity analysis algorithm described in this invention requires a clear definition of the target system to be analyzed. Based on mechanistic knowledge, operational experience, or structural analysis, it identifies all specific objects that may affect the response variable. In this process, along the material flow, energy flow, and control signal flow, it identifies key objects and parameters located upstream, downstream, or in the control loop of the response variable. Based on experience and mechanistic knowledge, it selects observable and operable explanatory variables from the specific objects.

[0024] It should be noted that the systems in this invention are engineering systems, including but not limited to: fluid transport systems (such as pipeline networks and pumping station systems), energy and power systems (such as generator sets and gas turbines), manufacturing and assembly systems (such as CNC machine tools and robotic production lines), transportation systems (such as high-speed rail traction and automobile suspension), and environmental and building systems (such as HVAC and structural health monitoring). Within each system, there are multiple structures, devices, or components that are mechanically or electrically connected to each other; these are collectively referred to as specific objects in this invention. Based on experience and mechanistic knowledge, explanatory variables that can influence the response variables are selected from these specific objects.

[0025] In these systems, the response variables are key performance indicators such as pressure, temperature, flow rate, vibration power, and vibration accuracy during the operation of a specific object, while the explanatory variables are controllable or adjustable parameters that affect the above response variables. In acquiring the response and explanatory variables, selection is based on mechanistic relationships, prioritizing variables with direct physical interactions with the response variables, and also on observability. Explanatory variables should have readily available data sources, obtainable through sensors, control systems, experimental records, or simulation platforms. For variables that cannot be directly measured, substitute variables can be used, such as valve opening degree, valve position feedback, or actuator commands to characterize the valve's regulation state.

[0026] For example, if pipeline pressure is used as the response variable, the main explanatory variables affecting its change are the flow rate entering the pipeline and the flow rate leaving the pipeline. Therefore, the opening degree of the upstream valve and the downstream valve are both candidate explanatory variables.

[0027] In a specific example, the explanatory variables are adjustable or observable physical parameters such as valve opening, pump operating frequency, and heater power; the response variables are key performance indicators such as pipeline pressure, system temperature, and flow rate.

[0028] As a preferred approach, explanatory variables should be selected that can be adjusted, controlled, or used for engineering decision-making. The purpose of sensitivity analysis is usually not only to explain the influence relationship, but also to provide a basis for subsequent control optimization, fault diagnosis, and emergency response. Therefore, operable variables have more engineering value.

[0029] Step 2: Collect operational data for response and explanatory variables, preprocess the data, and standardize the variable dimensions and numerical ranges as needed.

[0030] The response and explanatory variables of the specific objects identified in the sensitivity analysis in step 1 are collected or calculated, and the collected parameters are preprocessed. The specific preprocessing process includes data alignment, time series checking, elimination of duplicate points, removal of bad points, and linear interpolation to complete missing values.

[0031] Specifically, data alignment involves aligning data sequences from different sources or with different timestamps based on a unified time reference or key identifier to ensure that the data have a consistent correspondence in the time dimension. In any implementation, the sampling interval of the unified time reference is 1 second to 10 minutes, preferably 1 minute.

[0032] Specifically, time series inspection verifies the time order, sampling interval, and timestamp consistency of the data, identifies and records problems such as out-of-order data, abnormal intervals, or duplicate timestamps in the time series; if out-of-order timestamps are detected, the data is reordered according to the chronological order.

[0033] Specifically, the process of eliminating duplicates involves detecting and removing data records that are completely duplicated or have duplicate key features due to data acquisition or transmission, in order to avoid duplicate data interfering with the analysis results.

[0034] Specifically, removing bad pixels involves identifying and removing data points that clearly do not conform to physical laws, exceed reasonable numerical ranges, or have serious acquisition errors, and filtering them using a threshold judgment method.

[0035] For example, the threshold judgment method is as follows: if a data point exceeds ±3 times the standard deviation of its physical quantity's reasonable range, it is judged as a bad point and discarded. The reasonable range is set by those skilled in the art based on engineering experience. For example, the normal operating range of pipeline pressure is 0.1MPa-10MPa. If it exceeds this range, the collected data is judged as a bad point.

[0036] Specifically, missing value handling involves using linear interpolation to fill in any missing values ​​in the data. In a time series, if data is missing at a certain point in time, linear calculations are performed using the values ​​of the nearest valid data points before and after it to estimate a reasonable value for that point, thus ensuring the continuity of the data series.

[0037] It should be noted that if more than 5 consecutive data points are missing, a data quality alarm should be issued, prompting a priority check of the communication status of the data acquisition equipment.

[0038] Step 3: Five sensitivity analysis methods are used in parallel to calculate the sensitivity index of each explanatory variable relative to the response variable. The five sensitivity analysis methods include correlation coefficient, mutual information, principal component regression, stepwise regression, and random forest.

[0039] Specifically, step 3 involves parallel analysis using multiple methods, simultaneously performing correlation coefficient analysis, mutual information discretization and calculation, establishing a principal component spatial regression model and conducting principal component regression analysis, building a stepwise regression model with forward selection criteria to complete the analysis, and constructing a random forest prediction system using random permutation of eigenvalues ​​to complete sensitivity analysis. The specific process for each analysis method is as follows: 31) Correlation coefficient sensitivity analysis: This method measures the degree of linear correlation between explanatory variables and response variables in a target system. Specifically, the Pearson correlation coefficient is used to measure the degree of linear correlation between explanatory variable X and response variable Y. The formula for calculating its sensitivity assessment index is as follows: (1) Where n is the number of observed samples, For the i-th observation of the explanatory variable X, The sample mean of the explanatory variable X, For the i-th observation of the response variable Y, The sample mean of the response variable Y; The corresponding original sensitivity index is the absolute value of the correlation coefficient. The specific sensitivity assessment index for the target object is as follows: (2) The above The larger the index value, the stronger the linear sensitivity of the explanatory variable to the response variable.

[0040] 32) Mutual information sensitivity analysis: Based on information theory, the information entropy I(X), I(Y) and joint entropy I(X:Y) of the explanatory variable and the response variable are defined respectively to measure the statistical dependence between two random variables. It can capture linear and nonlinear relationships. The analysis results are affected by the discrete method.

[0041] The analysis process involves dividing discrete intervals using histograms based on sampling time for calculation. The core formula is: (3) For continuous variables, the calculation is performed after discretization using a histogram: (4) in, I ( X , Y ) is the explanatory variable X and response variables Y Mutual information between them P XY ( i , j The joint probability that a sample falls into both the i-th interval of X and the j-th interval of Y. , The number of intervals after discrete values ​​of variables X and Y; P X ( i The probability that a sample falls into the i-th interval of X simultaneously; The probability that a sample falls into the j-th interval of Y.

[0042] The mutual information sensitivity index for a specific object is: (5) S MI Used to describe how the response variable is affected by the explanatory variables.

[0043] Among them, joint entropy I≥0, I=0 indicates that the two variables are independent, and the larger the value, the higher the sensitivity of the response variable and the explanatory variable.

[0044] 33) Main Regression Sensitivity Analysis Principal component regression analysis aims to address the problem of multicollinearity among explanatory variables. When explanatory variables are highly correlated, the coefficient estimates of the standard regression model become unstable and difficult to interpret. This process first transforms the original variables into a set of mutually orthogonal principal components using principal component analysis. A regression model is then built in a decorrelated low-dimensional space. The regression relationship is then mapped back to the original variable space, and finally, the sensitivity of each original variable is assessed. This process eliminates multicollinearity among explanatory variables through principal component analysis. After standardizing the explanatory variables, principal component decomposition yields the score matrix T and loading matrix P of the principal components. After building a regression model in the orthogonal principal component space, regression coefficients are obtained. These coefficients are then transformed back to the original variable space, and the sensitivity of the variables is assessed through analysis of the regression coefficients. The specific process is as follows: a) Principal component decomposition of the standardized explanatory variables is performed using the following formula (6).

[0045] (6) Where T is the score matrix and P is the load matrix.

[0046] b) Using the principal component score T of each explanatory variable as the independent variable and the standardized response variable Y as the dependent variable, perform principal component regression using the following formula: (7) in, The regression coefficient vector in the principal component space The residual can be obtained through least binary component analysis. The estimated value.

[0047] In this process, the principal component regression relationship between each explanatory variable and each response variable is calculated to obtain the corresponding value.

[0048] c) Map the regression coefficients θ in the principal component space back to the original variable space to obtain the regression coefficients of the corresponding original explanatory variables. Complete the coefficient conversion and obtain the evaluation coefficients: (8) The main regression sensitivity indicators are as follows: (9) The corresponding original sensitivity index is the absolute value of the regression coefficient. This method can effectively handle multicollinearity and reduce the dimensionality of high-dimensional data. The larger the index value, the stronger the sensitivity.

[0049] 34) Stepwise regression sensitivity analysis: Through an iterative process of forward selection and backward elimination of variables, explanatory variables that have a significant impact on the response variable are automatically selected. First, an F-test is performed using the forward selection criterion: the sum of squared errors of the simplified model is calculated. The squared error of the complete model and the degrees of freedom of the simplified model. And the degrees of freedom of the complete model In the following formula, the numerator represents the increment of the mean squared regression, and the denominator is the mean squared error. The contribution of the newly added explanatory variables to the model is obtained by calculating the F-test. It should be noted that the newly added explanatory variables here refer to the explanatory variables added in the actual calculation process relative to the previous addition.

[0050] (10) When introducing a variable, the following criteria are used to determine whether the variable enters the model through forward selection: if the calculated F-value is greater than the entry threshold... If so, this variable is introduced into the regression model; typically, the F-critical value distribution corresponding to p=0.05 is used as the critical value.

[0051] (11) When removing variables, if the F-value corresponding to the variable in the model is less than the removal threshold... Variables whose contribution to the model is no longer significant are removed based on the following criteria: The critical value for eliminating variables is typically represented by the F-critical value distribution with p=0.10: (12) After multiple iterations, the explanatory variables that had the most significant impact on the model were selected, and the original regression coefficients were calculated. β The standard deviation σ of the explanatory variable X and the response variable Y Y and σ X The sensitivity coefficients are then obtained as follows: (13) The final stepwise regression sensitivity index is: (14) 35) Random forest sensitivity analysis is based on bootstrap aggregation and random subspace methods to construct decision tree ensembles, and evaluates feature contribution through permutation importance. For each tree, n samples are randomly drawn from the original data with replacement using bootstrap sampling. The resulting random forest model is trained. For each tree from i=1 to Ntrees, each node randomly selects K features and searches for the optimal split point among these K features until the stopping condition is met. The Gini index is introduced to measure the impurity of decision tree nodes. (15) Where t represents a node in the decision tree; i represents the class number; p(i|t) represents the probability or proportion of samples in node t belonging to class i; ∑ represents the summation over all classes in node t; and Gini(t) represents the Gini impurity of node t. Gini is an index of the impurity of a decision tree node; the smaller the exponent, the higher the node purity. Node splitting is performed according to the following criteria, selecting the feature and split point that maximizes ΔGini: (16) The importance assessment of random forests based on permutations is performed as follows: (17) Among them, Importance jN represents the importance of the j-th feature; j represents the feature number, corresponding to a specific explanatory variable in the sensitivity analysis; trees The total number of decision trees in the random forest is represented; t represents the t-th decision tree; Let be the out-of-bag error of the t-th tree. Let be the out-of-bag error after random permutation of the j-th feature.

[0052] The sensitivity metrics for random forests are as follows: (18) The larger the index value, the greater the influence of the feature on the model's prediction, and the stronger the sensitivity. This method can capture complex nonlinear relationships, automatically handle feature interactions, and achieve self-performance evaluation through out-of-bag error, but it is not sensitive to data distribution and outliers.

[0053] Step 4: Normalize the sensitivity indices obtained by each method to map them to a unified scaling range.

[0054] After performing the aforementioned sensitivity analyses, sensitivity indices from the correlation coefficient method, mutual information method, principal component regression method, stepwise regression method, and random forest method will be obtained respectively. In order to achieve comprehensive comparison, weighted integration, or ranking and screening of the analysis results of each method under a unified scale, it is necessary to normalize the various sensitivity indices and map them to a preset common numerical range [0,1].

[0055] Step 5: Perform weighted fusion based on system characteristics and method applicability to obtain the comprehensive sensitivity assessment result.

[0056] After normalizing the indices for each sensitivity analysis method, and considering the physical characteristics of the target subsystem, the completeness and quality of data acquisition, as well as the reliability and applicability of each analysis method, appropriate weights are assigned to each method. A weighted ensemble is then used to obtain the comprehensive sensitivity index. The calculation formula is as follows:

[0057] In the above process, the following three aspects are considered when allocating weights.

[0058] (1) System physical characteristics and variable relationships: If the relationship between variables is mainly linear, increase the weight of correlation coefficient and stepwise regression; if there is a significant nonlinear relationship, increase the weight of mutual information and random forest.

[0059] (2) Data completeness and quality: When the data quality is high and the noise is low, linear methods are more reliable; when the data is noisy or missing, robust ensemble methods (such as random forests) are more reliable.

[0060] (3) Multicollinearity among variables: When the explanatory variables are highly correlated, increase the weight of principal component regression to eliminate the interference of multicollinearity on the stability of regression coefficients.

[0061] A second aspect of the present invention discloses a multi-parallel system parameter sensitivity evaluation device, comprising: The analysis object module obtains sensitivity analysis objects from the target engineering system. The sensitivity analysis objects include response variables and at least one explanatory variable that affects the response variables. The data processing module collects the operational data of the response variable and the explanatory variable, and performs preprocessing and standardization on the operational data; The sensitivity index module employs multiple sensitivity analysis methods in parallel to calculate the sensitivity index of each explanatory variable relative to the response variable; these multiple sensitivity analysis methods include correlation coefficient method, mutual information method, principal component regression method, stepwise regression method, and random forest method. The normalization module normalizes the sensitivity indices obtained by each method. The sensitivity assessment module performs weighted fusion based on system characteristics and method applicability to obtain a comprehensive sensitivity assessment result for the response variable.

[0062] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0063] Example Figure 2 This is a schematic diagram of a specific application system architecture for an embodiment. The system includes an intermediate pipeline (serving as the target pipeline for pressure measurement) and valves 1 and 2 located upstream of the pipeline, and valves 3 and 4 located downstream. The upstream valves (valve 1 and valve 2) control the flow rate of the medium entering the pipeline, while the downstream valves (valve 3 and valve 4) control the flow rate of the medium exiting the pipeline. Since the pipeline pressure is determined by the dynamic balance of the inflow and outflow, changes in the opening degree of valves 1 to 4 directly affect the intermediate pipeline pressure, a key system state parameter. Based on this physical system structure and operating mechanism, this embodiment selects the valve opening degrees of valves 1, 2, 3, and 4 as explanatory variables for sensitivity analysis, and uses the intermediate pipeline pressure as the system response variable, thus forming a sensitivity analysis object set with clear engineering significance.

[0064] In this embodiment, the response variable is the intermediate pipeline pressure, and the explanatory variables are the valve openings of valves 1, 2, 3, and 4.

[0065] After identifying the analysis objects, raw data for the response variables and explanatory variables are collected during the same operational process. Since data collected from engineering sites often suffers from issues such as inconsistent sampling frequencies, timestamp offsets, local missing data, anomalous jumps, duplicate records, and measurement noise, preprocessing of the raw data is necessary before sensitivity analysis. This preprocessing includes, but is not limited to: time alignment of data for different variables, checking the continuity of the time series, removing duplicate sampling points, eliminating obviously abnormal data points, interpolating and imputing missing data, and standardizing the units and ranges of variables as needed. After preprocessing, a standardized dataset is obtained that meets the requirements of subsequent sensitivity analysis.

[0066] Subsequently, the standardized dataset was input into multiple sensitivity analysis modules, and multi-method sensitivity calculations were performed in parallel. These sensitivity analysis modules included correlation coefficient analysis, mutual information analysis, principal component regression analysis, stepwise regression analysis, and random forest analysis. The correlation coefficient analysis module measures the linear correlation between explanatory and response variables; the mutual information analysis module measures the statistical dependency between explanatory and response variables, reflecting nonlinear effects; the principal component regression analysis module, when there is correlation or multicollinearity among explanatory variables, transforms the original variables into mutually orthogonal principal components before performing regression analysis, thereby extracting the comprehensive contribution of each explanatory variable to the response variable; the stepwise regression analysis module screens the main influencing variables based on variable significance and model explanatory power; and the random forest analysis module characterizes the nonlinear contribution of explanatory variables to the response variable through ensemble learning and outputs variable importance indices.

[0067] Each sensitivity analysis module outputs the original sensitivity indices for its corresponding method. Because the indices obtained by different methods differ in form, numerical scale, and physical meaning—for example, correlation coefficients can be positive or negative, mutual information is non-negative, regression coefficients are affected by the variable's dimensions, and random forest importance is usually a relative contribution value—it is necessary to perform a unified normalization process on the calculation results of each method. After normalization, the sensitivity indices of each explanatory variable under different analysis methods are mapped to a unified scaling range, making the results obtained by different methods comparable.

[0068] After normalization, weights are further assigned to different sensitivity analysis methods based on system characteristics, data quality, variable coupling, and the applicability of each analysis method to the current data scenario. For example, when variables are primarily linearly related and data quality is high, the weights of correlation coefficient analysis and stepwise regression analysis can be increased; when there are significant nonlinear relationships between variables, the weights of mutual information analysis and random forest analysis can be increased; and when there is multicollinearity among explanatory variables, the weight of principal component regression analysis can be increased. By weighted ensemble of the normalized sensitivity results of each method, a comprehensive sensitivity score of each explanatory variable relative to the response variable is obtained. The explanatory variables are then ranked according to the comprehensive score to identify key influencing factors in the system.

[0069] Figure 3 and Figure 4 Simulation analysis results of the present invention in specific applications are presented. Figure 3This method is used to compare the sensitivity indices of valves 1, 2, 3, and 4 under different sensitivity analysis methods. It can be used to observe the consistency and differences in the influence of valve opening degree on intermediate pipeline pressure under different analysis methods. As shown in the figure, the sensitivity assessment trends of the five methods—correlation coefficient, mutual information, principal component regression, stepwise regression, and random forest—for the opening degrees of valves 1, 2, 3, and 4 are basically consistent, with the overall ranking being: valve 2 opening degree > valve 3 opening degree > valve 1 opening degree > valve 4 opening degree. This indicates that the evaluation results of each method have good stability and consistency. Specifically, for the correlation coefficient method, valve 2 opening > valve 3 opening > valve 1 opening > valve 4 opening; for mutual information, valve 3 opening > valve 2 opening > valve 1 opening > valve 4 opening; for principal component analysis, valve 2 opening > valve 3 opening > valve 1 opening > valve 4 opening; for stepwise regression, valve 2 opening > valve 3 opening > valve 1 opening > valve 4 opening; for random forest, valve 4 opening > valve 1 opening > valve 2 opening > valve 3 opening; for comprehensive scoring, valve 2 opening > valve 3 opening > valve 1 opening > valve 4 opening. Among them, the correlation coefficient and principal component regression index are generally stable, reliably reflecting the linear association and anti-collinearity characteristics between variables, and maintaining stable output even in multicollinearity scenarios. The mutual information and random forest indices are significantly higher than those of linear methods, effectively capturing the nonlinear dependence and variable interaction between valve opening and pipeline pressure, making up for the analytical shortcomings of pure linear methods. The stepwise regression index has the highest value and the most obvious discrimination, which can automatically strengthen the key variables with statistical significance for the response variable, further highlighting the core influence of valves 2 and 3. The differences in the indices of the same valve under different methods reflect the complementary characteristics of each algorithm in terms of linear / nonlinearity, anti-collinearity, feature selection, and robustness. The differences in the indices of different valves under the same method objectively reflect the actual influence intensity of each valve on the intermediate pipeline pressure. Overall results show that the multivariate parallel sensitivity analysis architecture adopted in this invention can comprehensively, stably, and reliably identify key influencing parameters in complex systems, providing solid data support for subsequent normalization and weighted fusion.

[0070] Figure 4 This is used to display the comprehensive sensitivity score results of each valve after normalization and weighted integration. It can be used to intuitively determine the overall impact of each valve on the intermediate pipeline pressure, and based on this, to identify key valves for priority monitoring, modeling, or control. Figure 4 As can be seen from the data, valve 2 has the greatest impact on the pressure of the intermediate pipeline and is the core control valve, which needs to be monitored and modeled in a key manner. Valve 3 is a key downstream throttling valve with a sensitivity close to that of valve 2, and is a secondary key parameter. The impact of valves 1 and 4 is relatively weak and can be used as routine monitoring objects.

[0071] Through the above process, this invention comprehensively utilizes the advantages of linear analysis, nonlinear analysis, dimensionality reduction regression analysis, variable screening analysis, and ensemble learning analysis, avoiding the limitations of single sensitivity analysis methods in complex systems. This method is particularly suitable for complex engineering systems with a large number of variables, correlations among explanatory variables, noisy or missing data, and nonlinear system responses, improving the stability, reliability, and engineering interpretability of sensitivity analysis results. The system sensitivity analysis algorithm based on multiple analysis methods described in this invention integrates multiple sensitivity analysis methods for parallel analysis, adaptively adjusting the weights of each method. It is particularly suitable for high-dimensional complex systems with numerous variables, multicollinearity, and noisy or missing data, offering good engineering practicality and high interpretability.

[0072] In summary, the system sensitivity analysis algorithm proposed in this invention has high comprehensive capabilities and practicality, can significantly reduce the time cost of sensitivity analysis, and can be applied to various sensitivity analysis fields.

[0073] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0074] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0075] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0076] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-parallel system parameter sensitivity evaluation method, characterized in that, include: S1, Obtain the sensitivity analysis object from the target engineering system, the sensitivity analysis object including the response variable and at least one explanatory variable that affects the response variable; S2, collect the operational data of the response variable and the explanatory variable, and perform preprocessing and standardization on the operational data; S3, multiple sensitivity analysis methods are used in parallel to calculate the sensitivity index of each explanatory variable relative to the response variable; the multiple sensitivity analysis methods include correlation coefficient method, mutual information method, principal component regression method, stepwise regression method and random forest method; S4, normalize the sensitivity indices obtained by each method respectively; S5. Based on system characteristics and method applicability, a weighted fusion is performed to obtain the comprehensive sensitivity evaluation result of the response variable.

2. The method for evaluating the sensitivity of system parameters in a multi-parallel system according to claim 1, characterized in that, In S2, the preprocessing includes data alignment, time series checking, elimination of duplicate points, removal of bad points, and interpolation to complete missing values.

3. The method for evaluating the sensitivity of system parameters in a multi-parallel system according to claim 1, characterized in that, In S3, the correlation coefficient method uses the Pearson correlation coefficient to measure the degree of linear correlation between the explanatory variable and the response variable, and the sensitivity index is the absolute value of the Pearson correlation coefficient.

4. The method for evaluating the sensitivity of system parameters in a multi-parallel system according to claim 1, characterized in that, In S3, the mutual information method measures the statistical dependence between explanatory and response variables based on information entropy and joint entropy, and the sensitivity index is the mutual information value.

5. The method for evaluating the sensitivity of system parameters in a multi-parallel system according to claim 1, characterized in that, In S3, the principal component regression method first performs principal component decomposition on the explanatory variables to obtain the principal component score matrix and loading matrix, establishes a regression model in the orthogonal principal component space to obtain regression coefficients, and then maps the regression coefficients back to the original variable space. The sensitivity index is the absolute value of the regression coefficients after mapping.

6. The method for evaluating the sensitivity of system parameters in a multi-parallel system according to claim 1, characterized in that, In S3, the stepwise regression method introduces variables by performing an F-test using the forward selection criterion and removes variables by performing an F-test using the backward elimination criterion. After multiple iterations of screening, significant influencing variables are obtained. The sensitivity index is the absolute value of the standardized regression coefficient.

7. The method for evaluating the sensitivity of system parameters in a multi-parallel system according to claim 1, characterized in that, In S3, the random forest method constructs a decision tree ensemble based on Bootstrap aggregation and random subspace methods, and evaluates the feature contribution through permutation importance. The sensitivity index is the permutation importance calculated based on out-of-bag error.

8. The method for evaluating the sensitivity of system parameters in a multi-parallel system according to claim 1, characterized in that, In S3, the response variables are pressure, temperature, flow rate, vibration power, and vibration accuracy during system operation, and the explanatory variables are valve opening, pump operating frequency, or heater power.

9. The method for evaluating the sensitivity of system parameters in a multi-parallel system according to claim 1, characterized in that, In S5, the weighted fusion based on system characteristics and method applicability considers factors such as system physical characteristics and variable relationships, data completeness and quality, and the degree of multicollinearity among variables when allocating weights.

10. A multi-parallel system parameter sensitivity evaluation device, characterized in that, include: The analysis object module obtains sensitivity analysis objects from the target engineering system. The sensitivity analysis objects include response variables and at least one explanatory variable that affects the response variables. The data processing module collects the operational data of the response variable and the explanatory variable, and performs preprocessing and standardization on the operational data; The sensitivity index module employs multiple sensitivity analysis methods in parallel to calculate the sensitivity index of each explanatory variable relative to the response variable; these multiple sensitivity analysis methods include correlation coefficient method, mutual information method, principal component regression method, stepwise regression method, and random forest method. The normalization module normalizes the sensitivity indices obtained by each method. The sensitivity assessment module performs weighted fusion based on system characteristics and method applicability to obtain a comprehensive sensitivity assessment result for the response variable.

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