FADS system atmospheric parameter algorithm simulation evaluation method, evaluation system and storage medium

Abstract

This invention provides a method, system, and storage medium for simulating and evaluating atmospheric parameters in a FADS system. The method utilizes status words to determine the correctness of pressure measurement data at each pressure measurement point, sets faulty pressure measurement points and removes their corresponding pressure measurement data, obtains new pressure measurement data by configuring a state matrix, and obtains atmospheric parameter calculation values ​​under different conditions by selectively adding error terms and selectively using filters to process the data. By comparing the error between the calculation values ​​and theoretical values, the parameters of the algorithm model are adjusted to obtain atmospheric parameter calculation values ​​with acceptable errors. Finally, the algorithm model is evaluated based on these calculation values. This invention addresses the technical problems in existing technologies where the impact of algorithm error introduction and faulty pressure measurement point isolation on the accuracy of atmospheric parameter calculation is not readily assessable.

Description

Technical Field

[0001] This invention relates to the field of flight atmospheric parameter measurement and flight control technology, and in particular to a simulation evaluation method, evaluation system and storage medium for atmospheric parameter algorithms of FADS system. Background Technology

[0002] The FADS (Flying Atmosphere Control System) utilizes an array of pressure sensors embedded in the aircraft's surface to detect surface pressure and employs specific algorithms to calculate atmospheric parameters such as static pressure, total pressure, Mach number, angle of attack, sideslip angle, and pressure altitude during flight. Compared to traditional pitot tube methods for measuring atmospheric data, FADS offers advantages such as a wider applicable Mach number range and a broader angle of attack range. The accuracy of the FADS algorithm directly impacts flight control quality; however, currently, there are no effective methods for evaluating algorithm accuracy. Summary of the Invention

[0003] This invention provides a simulation evaluation method, evaluation system and storage medium for atmospheric parameters of a FADS system, which can solve the technical problems in the prior art that cannot evaluate the impact of algorithm error introduction and isolation of fault pressure measurement points on the accuracy of atmospheric parameter calculation.

[0004] According to one aspect of the present invention, a method for simulating and evaluating atmospheric parameters of a FADS system is provided, the method comprising:

[0005] S1: Read the pressure data of each pressure measuring point of the FADS system from the memory for a single time or a continuous period of time. Determine the correctness of the pressure measurement data of each pressure measuring point through the status word. If there is incorrect pressure measurement data, proceed to S2. If all are correct, proceed to S3.

[0006] S2, determine the pressure measurement point corresponding to the incorrect pressure measurement data as the faulty pressure measurement point, load the fault model of the faulty pressure measurement point, and remove the pressure measurement data of the faulty pressure measurement point;

[0007] S3, sort the correct pressure measurement data according to the pressure measurement point number, and configure the state matrix for the sorted pressure measurement data to obtain the pressure measurement data after troubleshooting;

[0008] S4, Load the FADS system atmospheric parameter algorithm model and import the various parameters in the FADS system atmospheric parameter algorithm model;

[0009] S5, determine whether to add an error term. If yes, go to S6; otherwise, go to S7.

[0010] S6, add an error term to the pressure measurement data after troubleshooting to obtain pressure measurement data containing the error term;

[0011] S7, determine whether to use a filter. If yes, go to S8; otherwise, go to S9.

[0012] S8. The pressure measurement data after troubleshooting obtained in S3 or the pressure measurement data containing error terms obtained in S6 are filtered to obtain filtered pressure measurement data.

[0013] S9, based on the algorithm model loaded in S4 and the imported parameters, uses the pressure measurement data after troubleshooting obtained in S3, the pressure measurement data with error terms obtained in S6, or the filtered pressure measurement data obtained in S8 to calculate the calculated values ​​of atmospheric parameters.

[0014] S10: Calculate the difference between the calculated atmospheric parameters and the theoretical atmospheric parameters as the solution error of the algorithm model. Determine whether the solution error meets the design requirements. If not, adjust the parameters in the algorithm model and go to S5. If yes, go to S11.

[0015] S11, end the simulation and evaluate the algorithm model based on the solution results.

[0016] Furthermore, the atmospheric parameter algorithm models for the FADS system include: the FADS algorithm without stagnant points, the three-point FADS algorithm, the neural network algorithm, and the neural network algorithm based on the aerodynamic model.

[0017] Furthermore, the error terms include pressure sensor noise value, average pressure measurement error, and pressure measuring hole position error.

[0018] Furthermore, atmospheric parameters include static pressure, total pressure, Mach number, angle of attack, sideslip angle, and pressure altitude.

[0019] Furthermore, the method also includes: after S2 and before S3, selecting all or part of the pressure measurement points from the non-faulty pressure measurement points, and using the pressure measurement data corresponding to the selected pressure measurement points as the pressure measurement data sorted in S3.

[0020] According to another aspect of the present invention, an FADS system atmospheric parameter algorithm simulation evaluation system is provided. The evaluation system includes a fault judgment and processing module, an algorithm module, an error module, a filtering module, an error calculation module, and an evaluation module.

[0021] The fault diagnosis and processing module is used to read the pressure data of each pressure measurement point of the FADS system from the memory for a single time or a continuous period of time, determine the correctness of the pressure measurement data of each pressure measurement point through the status word, identify the pressure measurement point corresponding to the incorrect pressure measurement data as the fault pressure measurement point, load the fault model of the fault pressure measurement point, and remove the pressure measurement data of the fault pressure measurement point. The correct pressure measurement data is sorted according to the pressure measurement point number, and a status matrix is ​​configured for the sorted pressure measurement data to obtain the pressure measurement data after the fault is eliminated.

[0022] The algorithm module is used to load the FADS system atmospheric parameter algorithm model and import the various parameters in the FADS system atmospheric parameter algorithm model;

[0023] The error module is used to determine whether to add an error term. When it is determined that an error term should be added, the error term is added to the pressure measurement data after troubleshooting to obtain pressure measurement data containing the error term.

[0024] The filtering module is used to determine whether to use a filter, and when it is determined to use a filter, the filter is used to filter the pressure measurement data after troubleshooting or the pressure measurement data containing error terms to obtain the filtered pressure measurement data.

[0025] The algorithm module is also used to calculate atmospheric parameters based on the loaded algorithm model and imported parameters, using pressure measurement data after troubleshooting, pressure measurement data with error terms, or filtered pressure measurement data.

[0026] The error calculation module is used to calculate the difference between the calculated value of the atmospheric parameters and the theoretical value of the atmospheric parameters as the calculation error of the algorithm model, and to determine whether the calculation error meets the design requirements.

[0027] The algorithm module is also used to adjust the parameters in the algorithm model when the solution error does not meet the design requirements;

[0028] The evaluation module is used to output evaluation results when the solution error meets the design requirements.

[0029] According to another aspect of the present invention, a computer-readable storage medium storing a computer program is provided, wherein the computer program, when executed by a processor, implements the steps of the method described above.

[0030] This invention provides a simulation evaluation method, evaluation system, and storage medium for atmospheric parameter algorithms in a FADS system. The method utilizes status words to determine the correctness of pressure measurement data at each pressure measurement point, sets faulty pressure measurement points and removes their corresponding pressure measurement data, obtains new pressure measurement data by configuring the state matrix, and obtains atmospheric parameter calculation values ​​under different conditions by selectively adding error terms and selectively using filters to process the data. By comparing the error between the calculation values ​​and theoretical values, the parameters of the algorithm model are adjusted to obtain atmospheric parameter calculation values ​​with acceptable errors. Finally, the algorithm model is evaluated based on these calculation values. This method supports research on the impact of the number of pressure measurement points on measurement accuracy, thereby supporting FADS algorithm optimization research; it can meet the fault tolerance requirements for various error terms and fault types in the FADS system algorithm, which is an important step in FADS algorithm verification; and it can use a pressure sequence over a continuous time period for calculation, recalculating measurement data in actual applications to verify the reliability of the FADS algorithm. Attached Figure Description

[0031] The accompanying drawings, which form part of this specification, are provided to further illustrate embodiments of the invention and, together with the textual description, explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0032] Figure 1 A flowchart illustrating the FADS system atmospheric parameter algorithm simulation evaluation method provided according to a specific embodiment of the present invention is shown. Detailed Implementation

[0033] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. 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.

[0034] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0035] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0036] like Figure 1 As shown in the figure, a simulation and evaluation method for atmospheric parameters of a FADS system is provided according to a specific embodiment of the present invention. The method includes:

[0037] S1: Read the pressure data of each pressure measuring point of the FADS system from the memory for a single time or a continuous period of time. Determine the correctness of the pressure measurement data of each pressure measuring point through the status word. If there is incorrect pressure measurement data, proceed to S2. If all are correct, proceed to S3.

[0038] S2, determine the pressure measurement point corresponding to the incorrect pressure measurement data as the faulty pressure measurement point, load the faulty pressure measurement point's faulty pressure measurement point, and remove the pressure measurement data of the faulty pressure measurement point, that is, set the faulty pressure measurement point and then remove the corresponding pressure measurement data.

[0039] S3, sort the correct pressure measurement data according to the pressure measurement point number, and configure the state matrix for the sorted pressure measurement data to obtain the pressure measurement data after troubleshooting;

[0040] S4, load the FADS system atmospheric parameter algorithm model, including the non-stagnant FADS algorithm, the three-point FADS algorithm, the neural network algorithm, and the neural network algorithm based on the aerodynamic model, and import the various parameters in the FADS system atmospheric parameter algorithm model, that is, the values ​​of various variables in the algorithm model;

[0041] S5, determine whether to add an error term. If yes, go to S6; otherwise, go to S7.

[0042] S6, add an error term to the pressure measurement data after troubleshooting to obtain pressure measurement data containing the error term;

[0043] S7, determine whether to use a filter. If yes, go to S8; otherwise, go to S9.

[0044] S8. The pressure measurement data after troubleshooting obtained in S3 or the pressure measurement data containing error terms obtained in S6 are filtered to obtain filtered pressure measurement data.

[0045] S9, based on the algorithm model loaded in S4 and the imported parameters, uses the pressure measurement data after troubleshooting obtained in S3, the pressure measurement data with error terms obtained in S6, or the filtered pressure measurement data obtained in S8 to calculate the calculated values ​​of atmospheric parameters.

[0046] S10: Calculate the difference between the calculated atmospheric parameters and the theoretical atmospheric parameters as the solution error of the algorithm model. Determine whether the solution error meets the design requirements. If not, adjust the parameters in the algorithm model and go to S5. If yes, go to S11.

[0047] S11, end the simulation and evaluate the algorithm model based on the solution results.

[0048] This method, employing this configuration approach, provides a simulation evaluation method for atmospheric parameters in a FADS system. It utilizes status words to determine the correctness of pressure measurement data at each pressure measurement point, sets faulty pressure measurement points and removes their corresponding pressure measurement data, obtains new pressure measurement data by configuring the state matrix, and generates atmospheric parameter calculations under different conditions by selectively adding error terms and selectively using filters to process the data. By comparing the error between the calculated values ​​and theoretical values, the parameters of the algorithm model are adjusted to obtain atmospheric parameter calculations with acceptable error. Finally, the algorithm model is evaluated based on these calculations. This method supports research on the impact of the number of pressure measurement points on measurement accuracy, thereby supporting FADS algorithm optimization research. It can satisfy the fault tolerance capability testing of various error terms and fault types in the FADS system algorithm, which is an important step in FADS algorithm verification. It can use a pressure sequence over a continuous time period for calculation, recalculating measurement data in actual applications to verify the reliability of the FADS algorithm. Compared with existing technologies, the technical solution of this invention can solve the technical problems of existing technologies that cannot evaluate the impact of algorithm error introduction and faulty pressure measurement point isolation on the accuracy of atmospheric parameter calculation.

[0049] This invention takes the classic nine-point FADS system as an example. Based on the pressure measurement point number, it arranges the fault-free pressure points and, in conjunction with a state matrix, obtains new pressure data, namely, pressure measurement data excluding faulty pressure measurement points. The expression is as follows:

[0050]

[0051] In the above formula, [P] represents the pressure measurement data of the faulty pressure measurement point, P1, P2, P3, ..., P9 represent the original pressure measurement data of each pressure measurement point, and S1, S2, S3, ..., S9 represent the working status of each pressure measurement point, with "1" for normal and "0" for abnormal.

[0052] Furthermore, in this embodiment of the invention, the method further includes: after S2 and before S3, selecting all or part of the pressure measurement points from the non-faulty pressure measurement points, and using the pressure measurement data corresponding to the selected pressure measurement points as the pressure measurement data sorted in S3. That is, based on determining the correctness of the pressure at the measurement points, the number of pressure points used is adjusted to find the optimal solution.

[0053] Furthermore, in this embodiment of the invention, whether to add error terms and whether to use filters for data processing is determined according to specific circumstances. Error terms include the noise values ​​of one or more pressure sensors, the average pressure measurement error of one or more pressure channels, and the position error of the pressure measuring orifice. The noise value is normally distributed noise, and its standard deviation can be externally set, with setting rules including structural processing errors, pressure measurement accuracy indicators, and other design parameters. The filters include an average filter model and a low-pass filter model. Filter parameters can be manually set or imported from pre-set IIR filter parameters. The main purpose of setting filters in this invention is to address the verification requirements of the impact of filter parameter settings on the system algorithm. When filter parameters are set improperly, excessively slow pressure changes will affect the dynamics of the final atmospheric parameter calculation. Therefore, the principle for adjusting filter parameters is to both meet the dynamic requirements of atmospheric parameters and reduce the error of external noise on the final measurement.

[0054] Furthermore, in this embodiment of the invention, the calculated atmospheric parameters include static pressure, total pressure, Mach number, angle of attack, sideslip angle, and pressure altitude during the aircraft's flight. Verification data (such as theoretical simulation data, real experimental data, etc.) is imported, and pressure data from various pressure measurement points for a single or continuous period are read. Atmospheric parameters are calculated according to the above steps and pre-set parameters. The parameters in the algorithm model are adjusted until the calculated atmospheric parameters meet the error requirements compared to the theoretical input data. The calculated flight atmospheric parameters are saved locally. Historical calculation results can be selected for data comparison, and the calculation error is obtained by comparing it with theoretical values. The algorithm's tolerance to various error terms and fault types is then compared.

[0055] According to another aspect of the present invention, an FADS system atmospheric parameter algorithm simulation evaluation system is provided. The evaluation system includes a fault judgment and processing module, an algorithm module, an error module, a filtering module, an error calculation module, and an evaluation module.

[0056] The fault diagnosis and processing module is used to read the pressure data of each pressure measurement point of the FADS system from the memory for a single time or a continuous period of time, determine the correctness of the pressure measurement data of each pressure measurement point through the status word, identify the pressure measurement point corresponding to the incorrect pressure measurement data as the fault pressure measurement point, load the fault model of the fault pressure measurement point, and remove the pressure measurement data of the fault pressure measurement point. The correct pressure measurement data is sorted according to the pressure measurement point number, and a status matrix is ​​configured for the sorted pressure measurement data to obtain the pressure measurement data after the fault is eliminated.

[0057] The algorithm module is used to load the FADS system atmospheric parameter algorithm model and import the various parameters in the FADS system atmospheric parameter algorithm model;

[0058] The error module is used to determine whether to add an error term. When it is determined that an error term should be added, the error term is added to the pressure measurement data after troubleshooting to obtain pressure measurement data containing the error term.

[0059] The filtering module is used to determine whether to use a filter, and when it is determined to use a filter, the filter is used to filter the pressure measurement data after troubleshooting or the pressure measurement data containing error terms to obtain the filtered pressure measurement data.

[0060] The algorithm module is also used to calculate atmospheric parameters based on the loaded algorithm model and imported parameters, using pressure measurement data after troubleshooting, pressure measurement data with error terms, or filtered pressure measurement data.

[0061] The error calculation module is used to calculate the difference between the calculated value of the atmospheric parameters and the theoretical value of the atmospheric parameters as the calculation error of the algorithm model, and to determine whether the calculation error meets the design requirements.

[0062] The algorithm module is also used to adjust the parameters in the algorithm model when the solution error does not meet the design requirements;

[0063] The evaluation module is used to output evaluation results when the solution error meets the design requirements.

[0064] According to another aspect of the present invention, a computer-readable storage medium storing a computer program is provided, wherein the computer program, when executed by a processor, implements the steps of the method described above.

[0065] In summary, this invention provides a simulation evaluation method, evaluation system, and storage medium for atmospheric parameter algorithms in a FADS system. This method utilizes status words to determine the correctness of pressure measurement data at each pressure measurement point, sets faulty pressure measurement points and removes their corresponding pressure measurement data, obtains new pressure measurement data by configuring the state matrix, and obtains atmospheric parameter calculation values ​​under different conditions by selectively adding error terms and selectively using filters to process the data. By comparing the error between the calculation values ​​and theoretical values, the parameters of the algorithm model are adjusted to obtain atmospheric parameter calculation values ​​with acceptable errors. Finally, the algorithm model is evaluated based on these calculation values. This method supports research on the impact of the number of pressure measurement points on measurement accuracy, thereby supporting FADS algorithm optimization research; it can meet the fault tolerance requirements for various error terms and fault types in the FADS system algorithm, which is an important step in FADS algorithm verification; it can use a pressure sequence over a continuous time period for calculation, recalculating measurement data in actual applications to verify the reliability of the FADS algorithm. Compared with existing technologies, the technical solution of this invention can solve the technical problems of existing technologies that cannot evaluate the impact of algorithm error introduction and faulty pressure measurement point isolation on the accuracy of atmospheric parameter calculation.

[0066] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0067] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0068] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A simulation and evaluation method for atmospheric parameters of a FADS system, characterized in that, The method includes: S1: Read the pressure data of each pressure measuring point of the FADS system from the memory for a single time or a continuous period of time. Determine the correctness of the pressure measurement data of each pressure measuring point through the status word. If there is incorrect pressure measurement data, proceed to S2. If all are correct, proceed to S3. S2, determine the pressure measurement point corresponding to the incorrect pressure measurement data as the faulty pressure measurement point, load the fault model of the faulty pressure measurement point, and remove the pressure measurement data of the faulty pressure measurement point; S3, sort the correct pressure measurement data according to the pressure measurement point number, and configure the state matrix for the sorted pressure measurement data to obtain the pressure measurement data after troubleshooting; S4, Load the FADS system atmospheric parameter algorithm model and import the various parameters in the FADS system atmospheric parameter algorithm model; S5, determine whether to add an error term. If yes, go to S6; otherwise, go to S7. S6, add an error term to the pressure measurement data after troubleshooting to obtain pressure measurement data containing the error term; S7, determine whether to use a filter. If yes, go to S8; otherwise, go to S9. S8. The pressure measurement data after troubleshooting obtained in S3 or the pressure measurement data containing error terms obtained in S6 are filtered to obtain filtered pressure measurement data. S9, based on the algorithm model loaded in S4 and the imported parameters, uses the pressure measurement data after troubleshooting obtained in S3, the pressure measurement data with error terms obtained in S6, or the filtered pressure measurement data obtained in S8 to calculate the calculated values ​​of atmospheric parameters. S10, calculate the difference between the calculated value of the atmospheric parameters and the theoretical value of the atmospheric parameters as the solution error of the algorithm model, determine whether the solution error meets the design requirements, if not, adjust the parameters in the algorithm model and go to S5, if yes, go to S11; S11, end the simulation and evaluate the algorithm model based on the solution results.

2. The method according to claim 1, characterized in that, The atmospheric parameter algorithm models of the FADS system include: the FADS algorithm without stagnant points, the three-point FADS algorithm, the neural network algorithm, and the neural network algorithm based on the aerodynamic model.

3. The method according to claim 2, characterized in that, The error terms include pressure sensor noise value, average pressure measurement error, and pressure measuring hole position error.

4. The method according to claim 3, characterized in that, The atmospheric parameters include static pressure, total pressure, Mach number, angle of attack, sideslip angle, and pressure altitude.

5. The method according to claim 4, characterized in that, The method further includes: after S2 and before S3, selecting all or part of the pressure measurement points from the non-faulty pressure measurement points, and using the pressure measurement data corresponding to the selected pressure measurement points as the pressure measurement data sorted in S3.

6. A simulation and evaluation system for atmospheric parameters in a FADS system, characterized in that, The evaluation system includes a fault diagnosis and processing module, an algorithm module, an error module, a filtering module, an error calculation module, and an evaluation module. The fault judgment and processing module is used to read pressure data of each pressure measurement point of the FADS system from the memory for a single time or a continuous period of time, judge the correctness of the pressure measurement data of each pressure measurement point through the status word, identify the pressure measurement point corresponding to the incorrect pressure measurement data as the fault pressure measurement point, load the fault model of the fault pressure measurement point, and remove the pressure measurement data of the fault pressure measurement point. The correct pressure measurement data is sorted according to the pressure measurement point number, and a status matrix is ​​configured for the sorted pressure measurement data to obtain the pressure measurement data after the fault is eliminated. The algorithm module is used to load the FADS system atmospheric parameter algorithm model and import the various parameters in the FADS system atmospheric parameter algorithm model; The error module is used to determine whether to add an error term, and when it is determined that an error term should be added, an error term is added to the pressure measurement data after troubleshooting to obtain pressure measurement data containing the error term; The filtering module is used to determine whether to use a filter, and when it is determined that a filter should be used, the filter is used to filter the pressure measurement data after troubleshooting or the pressure measurement data containing error terms to obtain the filtered pressure measurement data. The algorithm module is also used to calculate atmospheric parameters based on the loaded algorithm model and imported parameters, using pressure measurement data after troubleshooting, pressure measurement data with error terms, or filtered pressure measurement data. The error calculation module is used to calculate the difference between the calculated value of the atmospheric parameters and the theoretical value of the atmospheric parameters as the solution error of the algorithm model, and to determine whether the solution error meets the design requirements. The algorithm module is also used to adjust the parameters in the algorithm model when the solution error does not meet the design requirements; The evaluation module is used to output evaluation results when the solution error meets the design requirements.

7. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 5.

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