System contribution rate calculation method based on principal component regression analysis

Abstract

The invention relates to the technical field of equipment system evaluation, in particular to a system contribution rate calculation method based on principal component regression analysis, which can solve the problems that the existing capability index cannot effectively reflect the influence degree of the capability index on the system effect and lacks the actual application value to a certain extent. The method comprises the following steps: designing task scenarios and extracting capability indexes; forming a plurality of scenario simulation samples through the designed task scenario, performing simulation operation on all the simulation samples for multiple times by using a simulation platform, and evaluating the system efficiency corresponding to each simulation sample; establishing an incidence matrix of system efficiency and capability indexes by using data output by simulation evaluation; calculating the principal components of the capability indexes by using a principal component analysis method, and eliminating the correlation influence between the capability indexes; the correlation degree of the capability indexes and the system efficiency is calculated through a multiple regression analysis method, and in a multiple regression model, the coefficient of each capability index is the system contribution rate of the capability index.

Description

Technical Field

[0001] The present application relates to the technical field of equipment system evaluation, and in particular to a method for calculating system contribution rate based on principal component regression analysis. Background Art

[0002] With the development of science and technology, weapons and equipment are also moving towards a systematized direction. The system contribution rate is used to describe the degree of influence of a certain capability indicator on the system effectiveness. Research on the system contribution rate can realize the demonstration and planning of the key technologies of the system, provide important methodological support for training and model development, and promote the supporting development of key technologies of the system. The calculation method of the system contribution rate is the key issue of the system contribution rate research, so it is of great significance to carry out research on the calculation method of the system contribution rate.

[0003] At present, the calculation method of system contribution rate is mainly based on analytical model calculation, such as grey target theory, ANP method, etc. To calculate the contribution rate based on the analytical model, it is necessary to build a correlation model between capability indicators and system effectiveness based on expert experience, which leads to problems such as large influence of subjective factors and large randomness of calculation results.

[0004] However, the contribution rate of capability indicators to system effectiveness varies depending on the task background, equipment system, and task process. The contribution rate obtained through analytical methods is only a static measurement of the capability indicators to the system's unique capabilities. It cannot effectively reflect the impact of capability indicators on system effects and lacks practical application value. Summary of the invention

[0005] In order to solve the problem that the contribution rate of capability indicators to system effectiveness varies due to the influence of task background, equipment system, and task process, the contribution rate obtained by analytical method is only a static measurement of the capability indicator to the system's unique capability, which cannot effectively reflect the degree of influence of the capability indicator on the system effect and lacks practical application value. This application provides a system contribution rate calculation method based on principal component regression analysis.

[0006] The embodiment of the present application is implemented as follows:

[0007] In a first aspect, the present application provides a method for calculating system contribution rate based on principal component regression analysis, comprising:

[0008] Design task scenarios and extract capability indicators based on the capability indicator requirements for system contribution rate calculation and specific task background;

[0009] A plurality of simulation samples are formed by the designed task assumptions, and a simulation platform is used to perform multiple simulation runs on all the simulation samples to evaluate the system performance corresponding to each simulation sample;

[0010] Using the data output by the simulation evaluation, a correlation matrix between the system effectiveness and the capability index is established;

[0011] The principal component analysis method is used to calculate the principal components of the capability indicators and eliminate the correlation effects between the capability indicators;

[0012] The multiple regression analysis method is used to calculate the correlation between the capability index and the system effectiveness. In the multiple regression model, the coefficient of each capability index is the system contribution rate of this capability index.

[0013] In a possible implementation, combining the capability indicator requirements of system contribution rate calculation with the specific task background, designing task assumptions and extracting capability indicators further includes:

[0014] Deploy entities, plan processes, build equipment models, and build behavior models;

[0015] Extracting capability indicators that need to be calculated based on the constructed equipment model and behavior model;

[0016] An experiment is designed for the capability index, including the design of the number of experimental levels of the capability index and the selection of experimental sample points.

[0017] In one possible implementation, the data generated by system simulation can be used to establish a correlation matrix between capability indicators and system effectiveness. The calculation of the system contribution rate is to find out the degree of influence of the capability indicators on the system effectiveness. Regression analysis is to study the degree of interdependence between multiple variables, which corresponds to the calculation of the system contribution rate, that is, to study the degree of interdependence between capability indicators and system effectiveness.

[0018] In a possible implementation, for the regression method of calculating the system contribution rate, the system effectiveness is set as the dependent variable Y, and the capability index is set as the independent variable X.

[0019] In a possible implementation, when the capability indicator X of the experimental design has only one variable, its calculation model can be regarded as a univariate linear regression model, and the formula is as follows:

[0020] Y = a + bx + ε;

[0021] Among them, b is the regression coefficient, which is the contribution rate of the capability indicator x to the system performance that we need to solve. The parameter b can be estimated through the simulation experiment sample data.

[0022] In a possible implementation, when the capability index X of the experimental design is multiple variables, its calculation model can be regarded as a multiple linear regression model, and the formula is as follows:

[0023] Y=a+b1x1+b2x2+L+b px p +ε;

[0024] Where X=(x1,x2,…x p ) are p experimental design capability indicators, b1, b2, … b p is the corresponding system contribution rate value.

[0025] In a possible implementation, the least square method is used to solve the capability indicator contribution rate parameter b in the two formulas. Before the regression analysis and parameter estimation, the sample data of the capability indicator needs to be dimensionally processed using a standardized method.

[0026] In one possible implementation, for the experimental data of n hypothetical samples, x ij (i=1,2,…,n;j=1,2,…,p) represents the i-th sample of the j-th index,

[0027] definition:

[0028] The standardized transformation of the original data is:

[0029]

[0030] In one possible implementation, in the calculation of the system contribution rate, when multiple capability indicators are selected for experimental design, the contribution rate of each capability indicator to the system performance may influence and correlate with each other, that is, the contribution rate of one capability indicator to the system performance will be affected by the level of another indicator, and there is a potential correlation between the indicators. In the linear regression model, when the capability indicators are collinear, the least squares method is used to estimate the result, and the mean error is large, resulting in unstable parameter estimation.

[0031] Principal component regression is to use the principal components of the original independent variables to replace the original independent variables for regression analysis. It not only retains most of the information of the original indicators, but also has the advantage that the principal components are independent of each other. Therefore, after replacing the original indicators with the principal components, the regression equation of the principal components and the target variables is established using the least squares method. The calculated regression coefficient can overcome the disadvantage of "unstable estimation".

[0032] In a possible implementation, the steps for calculating the system contribution rate based on principal component regression analysis are as follows:

[0033] Standardize changes in independent variables;

[0034] Calculate the correlation coefficient matrix;

[0035] Calculate the eigenvalues ​​and corresponding eigenvectors of the correlation matrix;

[0036] Calculate the principal component contribution rate and select the appropriate principal component;

[0037] Calculate principal component variables;

[0038] Perform regression analysis on principal components;

[0039] Solve the system contribution rate.

[0040] The technical solution provided by this application can at least achieve the following beneficial effects:

[0041] The system contribution rate calculation method based on principal component regression analysis provided in the present application can not only eliminate the influence of subjective factors in the analytical model construction process based on the principal component regression analysis method, but also can be based on a strict mathematical theoretical model: principal component analysis and multivariate regression analysis. On the basis of eliminating the correlation influence between capability indicators, the contribution rate of capability indicators to system performance can be quantitatively calculated. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, a brief introduction will be given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0043] Figure 1 It is a flow chart of a method for calculating system contribution rate based on principal component regression analysis, shown in an exemplary embodiment of the present application;

[0044] Figure 2 It is a specific flow chart of a method for calculating a system contribution rate shown in an exemplary embodiment of the present application;

[0045] Figure 3 It is a flowchart of the steps of calculating the system contribution rate based on principal component regression analysis shown in an exemplary embodiment of the present application. DETAILED DESCRIPTION

[0046] In order to make the purpose, implementation mode and advantages of the present application clearer, the exemplary implementation mode of the present application will be clearly and completely described below in conjunction with the drawings in the exemplary embodiments of the present application. Obviously, the described exemplary embodiments are only part of the embodiments of the present application, not all of the embodiments. It should be understood that the specific embodiments described here are only used to explain the present application and are not used to limit the present application.

[0047] It should be noted that the brief description of terms in this application is only for the convenience of understanding the embodiments described below, and is not intended to limit the embodiments of this application. Unless otherwise specified, these terms should be understood according to their common and usual meanings.

[0048] The terms "first", "second", "third", etc. in the specification and claims of this application and the above drawings are used to distinguish similar or similar objects or entities, and do not necessarily mean to limit a specific order or sequence, unless otherwise noted. It should be understood that the terms used in this way can be interchangeable under appropriate circumstances.

[0049] The terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover but not exclude inclusion, for example, a product or device comprising a list of components is not necessarily limited to all the components expressly listed but may include other components not expressly listed or inherent to such product or device.

[0050] Before explaining the system contribution rate calculation method based on principal component regression analysis provided in the embodiment of the present application, the application scenario and implementation environment of the embodiment of the present application are first introduced.

[0051] With the development of science and technology, weapons and equipment are also moving towards a systematized direction. The system contribution rate is used to describe the degree of influence of a certain capability indicator on the system effectiveness. Research on the system contribution rate can realize the demonstration and planning of the key technologies of the system, provide important methodological support for training and model development, and promote the supporting development of key technologies of the system. The calculation method of the system contribution rate is the key issue of the system contribution rate research, so it is of great significance to carry out research on the calculation method of the system contribution rate.

[0052] At present, the calculation method of system contribution rate is mainly based on analytical model calculation, such as grey target theory, ANP method, etc. To calculate the contribution rate based on the analytical model, it is necessary to build a correlation model between capability indicators and system effectiveness based on expert experience, which leads to problems such as large influence of subjective factors and large randomness of calculation results. At the same time, the contribution rate of capability indicators to system effectiveness varies depending on the task background, equipment system, and task process. The contribution rate obtained by analytical methods is only a static measurement of the capability indicators to the system's unique capabilities, which cannot effectively reflect the degree of influence of capability indicators on system effects and lacks practical application value.

[0053] There is a problem of subjective factors affecting the calculation of system contribution rate: the previous system contribution rate calculation method based on analytical models needs to build a correlation model between capability indicators and system effectiveness based on expert experience, which leads to problems such as large influence of subjective factors and large randomness of calculation results.

[0054] There is also the problem of interaction between capability indicators in the calculation of system contribution rate: in the calculation of system contribution rate, when multiple capability indicators are involved, the contribution rate of each capability indicator to the system performance may have mutual influence and correlation, resulting in large errors in the calculation of system contribution rate.

[0055] Based on this, the present application provides a method for calculating the system contribution rate based on principal component regression analysis. First, a system contribution rate calculation process based on principal component regression analysis is given; then, a correlation matrix between capability indicators and system effectiveness is established based on simulation data, and the system contribution rate is solved by regression analysis; in response to the correlation problem of capability indicators, a method for calculating the system contribution rate based on principal component regression is designed, and the principal components of the capability indicators are used instead of the capability indicators for regression analysis, which not only retains most of the information of the original capability indicators, but also has the advantage that the principal components are independent of each other.

[0056] Next, the technical solution of the present application and how the technical solution of the present application solves the above-mentioned technical problems will be described in detail through embodiments and in combination with the accompanying drawings. The embodiments may be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. Obviously, the described embodiments are part of the embodiments of the present application, not all of them.

[0057] Figure 1 It is a flowchart of a method for calculating system contribution rate based on principal component regression analysis, shown in an exemplary embodiment of the present application.

[0058] In an exemplary embodiment, Figure 1 As shown, a method for calculating the system contribution rate based on principal component regression analysis is provided, and the method may include the following steps:

[0059] Step 100: Design task scenarios and extract capability indicators based on the capability indicator requirements for system contribution rate calculation and specific task context.

[0060] Step 200: A plurality of simulation samples of the assumptions are formed by the designed task assumptions, and a simulation platform is used to perform multiple simulation runs on all the simulation samples to evaluate the system performance corresponding to each simulation sample.

[0061] Step 300: Using the data output by the simulation evaluation, establish a correlation matrix between the system performance and the capability index.

[0062] Step 400: Calculate the principal components of the capability indicators using the principal component analysis method to eliminate the correlation effects between the capability indicators.

[0063] Step 500: Calculate the correlation between the capability index and the system performance using a multiple regression analysis method. In the multiple regression model, the coefficient of each capability index is the system contribution rate of the capability index.

[0064] Figure 2 It is a specific flow chart of a method for calculating system contribution rate shown in an exemplary embodiment of the present application.

[0065] In one possible implementation, Figure 2 As shown, the specific implementation steps of the calculation method are as follows:

[0066] First, based on the capability indicator requirements of system contribution rate calculation and the specific task background, typical task scenarios are designed, including entity deployment, process planning, equipment model and behavior model construction.

[0067] Then, the capability indicators that need to be calculated are extracted from the constructed equipment model and behavior model, and experimental design is performed on the indicators, including the design of the capability indicator experimental level number and the selection of experimental sample points;

[0068] Through the task assumptions of the experimental design, multiple simulation samples are formed. The simulation platform is used to perform multiple simulation runs on all simulation samples to evaluate the system performance corresponding to each simulation sample.

[0069] Using the data output from the simulation evaluation, a correlation matrix of system effectiveness (dependent variable) and capability indicators (independent variables) is established;

[0070] The principal component analysis method is used to calculate the principal components of the capability indicators and eliminate the correlation effects between the capability indicators;

[0071] The multiple regression analysis method is used to calculate the correlation between the capability index and the system effectiveness. In the multiple regression model, the coefficient of each capability index is the system contribution rate of this capability index.

[0072] Figure 3 It is a flowchart of the steps of calculating the system contribution rate based on principal component regression analysis shown in an exemplary embodiment of the present application.

[0073] In a possible implementation, some embodiments of the present application can establish a correlation matrix between capability indicators and system performance through data generated by system simulation, and the calculation of system contribution rate is to solve the degree of influence of capability indicators on system performance. Regression analysis is a quantitative statistical analysis method to study the degree of mutual dependence between multiple variables. Corresponding to the calculation of system contribution rate, it is to study the degree of mutual dependence between capability indicators and system performance. For the regression method of calculating system contribution rate, system performance is regarded as dependent variable Y, and capability indicator is regarded as independent variable X. When the capability indicator X of the experimental design has only one variable, its calculation model can be regarded as a univariate linear regression model, such as Formula 1.

[0074] Y=a+bx+ε (1)

[0075] Where b is the regression coefficient, that is, the contribution rate of the capability indicator x to the system performance that we need to solve. The parameter b can be estimated through the simulation experiment sample data.

[0076] When the capability indicator x of the experimental design is multiple variables, its calculation model can be regarded as a multiple linear regression model, as shown in Formula 2.

[0077] Y=a+b1x1+b2x2+L+b p x p +ε (2)

[0078] where X=(x1,x2,…x p ) are p experimental design capability indicators, b1, b2, … b p is the corresponding system contribution rate value.

[0079] The least squares method can be used to solve the capability index contribution rate parameter b in formula 1 and formula 2. Before the regression analysis and parameter estimation, the sample data of the capability index needs to be dimensionless. Here, the standardized method is used. For the experimental data of n hypothetical samples, x ij (i=1,2,…,n;j=1,2,…,p) represents the i-th sample of the j-th index, defined as: The standardized transformation of the original data is:

[0080]

[0081] In the calculation of system contribution rate, when multiple capability indicators are selected for experimental design, the contribution rate of each capability indicator to system performance may affect and correlate with each other. That is, the contribution rate of one capability indicator to system performance will be affected by the level of another indicator, and there is a potential correlation between the indicators. In the linear regression model, when the capability indicators are collinear, the least squares method is used to estimate the result, and the mean error is large, resulting in unstable parameter estimation.

[0082] Principal component regression is to use the principal components of the original independent variables to replace the original independent variables for regression analysis. It not only retains most of the information of the original indicators, but also has the advantage that the principal components are independent of each other. Therefore, after replacing the original indicators with the principal components, the regression equation of the principal components and the target variables is established using the least squares method. The calculated regression coefficient can overcome the disadvantage of "unstable estimation".

[0083] like Figure 3 As shown, the specific calculation steps include:

[0084] (1) Standardize the independent variables

[0085] Formula 3 is used for standardization transformation, and the standardized data matrix is ​​as follows:

[0086]

[0087] (2) Calculate the correlation coefficient matrix

[0088]

[0089] in:

[0090]

[0091] (3) Calculate the eigenvalues ​​and corresponding eigenvectors of the correlation matrix

[0092]

[0093] where (λ1,λ2,…,λ p ) is the eigenvalue of R, (a 11 ,a 12 ,…,a 1p ),…,(a p1 ,a p2 ,…,a pp ) is its corresponding eigenvector.

[0094] (4) Calculate the principal component contribution rate and select the appropriate principal component

[0095] The contribution rate of the i-th principal component is expressed as To express the cumulative contribution rate of the current m principal components: When a certain value is reached (usually 70%-85% is used as the criterion), the first m principal components are taken.

[0096] (5) Calculate the principal component variables

[0097] Z i =a i1 X1+a i2 X2+…a iP X p ,(i=1,2,…,p) (8)

[0098] (6) Regression analysis of principal components

[0099] The regression model is:

[0100] y t =a+b1Z t1 +b2Z t2 +…b m Z tm +ε t ,(t=1,2,…,n) (9)

[0101] The least squares estimation of the model is performed so that The error is minimized, thus estimating the parameters b1, b2, …b p .

[0102] (7) Solving the system contribution rate

[0103] Substituting formula 8 into formula 9, we can get the system performance y and capability indicators x1, x2, …x p The linear regression model is:

[0104] Y=c0+c1x1+c2x2+…+c p x p +ε (10)

[0105] where c1, c2, … c p for x1,x2,…x p The corresponding system contribution rate value.

[0106] It can be seen that the present application has the following improvements compared with the prior art:

[0107] (1) System contribution rate calculation method based on multivariate regression analysis

[0108] Based on the system simulation data, a correlation matrix of system effectiveness (dependent variable) and capability index (independent variable) is constructed, and the correlation degree between capability index and system effectiveness is calculated using a multiple regression analysis model. In the multiple regression model, the coefficient of each capability index is the system contribution rate of this index.

[0109] (2) Method for eliminating the interaction effects of capability indicators based on principal component analysis

[0110] First, the capability index (independent variable) X is standardized using formula (4), and the correlation coefficient after the standardized transformation is calculated using formula (5). The eigenvalue and eigenvector of the correlation coefficient are calculated using formula (7). Based on the eigenvalue and eigenvector, the principal component Z without interactive influence is calculated using formula (8). The new independent variable Z is used to perform regression analysis on the system effectiveness (dependent variable) Y, which can eliminate the interactive influence between the capability indicators.

[0111] It should be understood that, although the various steps in the flowcharts involved in the above-mentioned embodiments are displayed in sequence according to the instructions, these steps are not necessarily executed in sequence according to the order of the instructions. Unless there is a clear explanation in this article, the execution of these steps is not strictly limited in order, and these steps can be executed in other orders. Moreover, at least a portion of the steps in the flowcharts involved in the above-mentioned embodiments may include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a portion of the steps or stages in other steps.

[0112] The technical features of the above embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0113] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A method for calculating system contribution rate based on principal component regression analysis, characterized in that: include: Design task scenarios and extract capability indicators based on the capability indicator requirements for system contribution rate calculation and specific task background; A plurality of simulation samples are formed by the designed task assumptions, and a simulation platform is used to perform multiple simulation runs on all the simulation samples to evaluate the system performance corresponding to each simulation sample; Using the data output by the simulation evaluation, a correlation matrix between the system effectiveness and the capability index is established; The principal component analysis method is used to calculate the principal components of the capability indicators and eliminate the correlation effects between the capability indicators; The multiple regression analysis method is used to calculate the correlation between the capability index and the system effectiveness. In the multiple regression model, the coefficient of each capability index is the system contribution rate of this capability index.

2. The method for calculating the system contribution rate based on principal component regression analysis according to claim 1, characterized in that: The step of combining the capability indicator requirements of the system contribution rate calculation with the specific task background, designing task assumptions and extracting capability indicators further includes: Deploy entities, plan processes, build equipment models, and build behavior models; Extracting capability indicators that need to be calculated based on the constructed equipment model and behavior model; An experiment is designed for the capability index, including the design of the number of experimental levels of the capability index and the selection of experimental sample points.

3. The method for calculating the system contribution rate based on principal component regression analysis according to claim 1, characterized in that: The data generated by system simulation can be used to establish a correlation matrix between capability indicators and system effectiveness. The calculation of system contribution rate is to find out the influence of capability indicators on system effectiveness. Regression analysis is to study the degree of interdependence between multiple variables, which corresponds to the calculation of system contribution rate, that is, to study the degree of interdependence between capability indicators and system effectiveness.

4. The method for calculating the system contribution rate based on principal component regression analysis according to claim 3, characterized in that: In the regression method for calculating the system contribution rate, the system effectiveness is set as the dependent variable Y, and the capability index is set as the independent variable X.

5. The method for calculating the system contribution rate based on principal component regression analysis according to claim 4, characterized in that: When the capability index X of the experimental design has only one variable, its calculation model can be regarded as a univariate linear regression model, and the formula is as follows: Y=a+bx+ε; Among them, b is the regression coefficient, which is the contribution rate of the capability indicator x to the system performance that we need to solve. The parameter b can be estimated through the simulation experiment sample data.

6. The method for calculating the system contribution rate based on principal component regression analysis according to claim 5, characterized in that: When the capability index X of the experimental design is multiple variables, its calculation model can be regarded as a multiple linear regression model, and the formula is as follows: Y=a+b1x1+b2x2+L+b p x p +e; Where X=(x1,x2,…x p ) are p experimental design capability indicators, b1, b2, … b p is the corresponding system contribution rate value.

7. The method for calculating the system contribution rate based on principal component regression analysis according to claim 6, characterized in that: The least square method is used to solve the capability index contribution rate parameter b in the two formulas. Before estimating the parameters through regression analysis, the sample data of the capability index needs to be dimensionally processed using a standardized method.

8. The method for calculating the system contribution rate based on principal component regression analysis according to claim 7, characterized in that: For the experimental data of n hypothetical samples, x ij (i=1,2,…,n;j=1,2,…,p) represents the i-th sample of the j-th index, definition: The standardized transformation of the original data is:

9. The method for calculating the system contribution rate based on principal component regression analysis according to claim 8, characterized in that: In the calculation of system contribution rate, when multiple capability indicators are selected for experimental design, the contribution rate of each capability indicator to system performance may influence and correlate with each other, that is, the contribution rate of one capability indicator to system performance will be affected by the level of another indicator, and there is a potential correlation between the indicators. In the linear regression model, when there is collinearity in the capability indicators, the least squares method is used to estimate the results, and the mean error is large, resulting in unstable parameter estimation. Principal component regression is to use the principal components of the original independent variables to replace the original independent variables for regression analysis. It not only retains most of the information of the original indicators, but also has the advantage that the principal components are independent of each other. Therefore, after replacing the original indicators with the principal components, the regression equation of the principal components and the target variables is established using the least squares method. The calculated regression coefficient can overcome the disadvantage of "unstable estimation".

10. The method for calculating the system contribution rate based on principal component regression analysis according to claim 8, characterized in that: The steps for calculating the system contribution rate based on principal component regression analysis are as follows: Standardize changes in independent variables; Calculate the correlation coefficient matrix; Calculate the eigenvalues ​​and corresponding eigenvectors of the correlation matrix; Calculate the principal component contribution rate and select the appropriate principal component; Calculate principal component variables; Perform regression analysis on principal components; Solve the system contribution rate.

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