A method and system for calculating electrical performance of phased array antenna considering array element posture

Abstract

The present invention discloses a method and system for calculating the electrical performance of a phased array antenna taking into account the position and posture of an array element. The method comprises: constructing a coupling model of electromechanical and thermal multi-source uncertainty factors of a phased array antenna according to the uncertain influencing factors of the position and posture of the array element of the phased array antenna and the uncertain influencing factors of the excitation current; performing a solution calculation to obtain an uncertainty expression of the field strength pattern of the phased array antenna under interval representation; determining the power pattern of the phased array antenna based on the uncertainty expression of the field strength pattern of the phased array antenna under interval representation, performing electrical performance calculation of the phased array antenna, and obtaining the calculation result of the electrical performance of the phased array antenna. The present invention can quickly and accurately analyze the influence of uncertainty factors on the electrical performance of the phased array antenna, thereby improving the calculation efficiency of the electrical performance of the phased array antenna and the accuracy of the calculation result. As a method and system for calculating the electrical performance of a phased array antenna taking into account the position and posture of an array element, the present invention can be widely used in the field of radar antenna technology.

Description

Technical Field

[0001] The present invention relates to the field of radar antenna technology, and in particular to a method and system for calculating the electrical performance of a phased array antenna taking array element positions into consideration. Background Art

[0002] With the requirements of high gain, narrow beam, and low sidelobe, active phased array antennas (APAA) have gradually improved their status in modern communications, measurement, control, and anti-missile fields due to their flexible and agile beam, fast scanning speed, and good anti-interference ability, and have been more widely used. In order to analyze the impact of uncertainty factors on phased array antennas, it is necessary to model the coupling interval of array element posture and excitation current uncertainty factors based on the traditional electromechanical coupling model of active phased array antennas; and on this basis, quickly solve the coupling model to analyze the impact of various uncertainty factors on the electrical performance of active phased array antennas.

[0003] Related methods include using interval analysis methods to optimize the basic dimensions and tolerance bands of the array structure of phased array antennas, analyzing the uncertainty propagation of parameters in electromagnetic fields, and analyzing the influence of uncertainty parameters on the amplitude and phase of T / R components; also include a method for determining the electrical performance interval of active phased array antennas based on a proxy model, a priori knowledge algorithm for quickly calculating the electrical performance interval of active phased array antennas, and a statistical method based on interval analysis, which is used to analyze the influence of random errors and tolerances of the excitation amplitude and phase of phased array antenna elements on the radiation pattern.

[0004] However, the research on uncertainty factors of phased array antennas in related methods mainly focuses on the impact of analytical errors on antenna performance, and does not deeply explore the impact mechanism of other uncertainty factors, resulting in the failure to establish a suitable electromechanical thermal coupling model of uncertainty factors and to achieve rapid calculation of the electrical performance of active phased array antennas under the influence of array element position and excitation current uncertainty. This makes it impossible to design antennas based on the changes in electrical performance under the actual service environment of the antenna, and it is necessary to simulate the performance of multiple aspects of the antenna in multiple simulation software. As a result, the antenna design steps that consider the influence of array element position and excitation current uncertainty on electrical performance in related methods are cumbersome, computationally intensive, and inefficient, which is not conducive to the development of antenna design work. Summary of the invention

[0005] In order to solve the above technical problems, the purpose of the present invention is to provide a method and system for calculating the electrical performance of a phased array antenna taking into account the array element posture, which can quickly and accurately analyze the impact of uncertainty factors on the electrical performance of the phased array antenna, thereby improving the calculation efficiency of the electrical performance of the phased array antenna and the accuracy of the calculation results.

[0006] The first technical solution adopted by the present invention is: a method for calculating the electrical performance of a phased array antenna taking into account the array element posture, comprising the following steps:

[0007] According to the uncertain influencing factors of the element position and the excitation current of the phased array antenna, a coupling model of the electromechanical and thermal multi-source uncertainty factors of the phased array antenna is constructed;

[0008] The coupled model of electromechanical and thermal uncertainty factors of phased array antenna is solved and calculated, and the uncertainty expression of the field intensity pattern of phased array antenna is obtained under interval representation.

[0009] Based on the uncertainty expression of the field strength pattern of the phased array antenna under interval representation, the power pattern of the phased array antenna is determined, the electrical performance of the phased array antenna is calculated, and the calculation results of the electrical performance of the phased array antenna are obtained.

[0010] Furthermore, the step of constructing a coupling model of electromechanical and thermal multi-source uncertainty factors of the phased array antenna according to the uncertainty influencing factors of the element posture of the phased array antenna and the uncertainty influencing factors of the excitation current of the phased array antenna specifically includes:

[0011] According to the electromagnetic wave superposition principle of the phased array antenna, an ideal field strength pattern of the phased array antenna is constructed, wherein the phased array antenna has a plurality of array elements;

[0012] According to the ideal field strength pattern of the phased array antenna, determine the influencing parameters of the final pattern of the phased array antenna;

[0013] According to the influencing parameters of the final radiation pattern of the phased array antenna, the influencing factors of the uncertainty of the element position of the phased array antenna and the influencing factors of the uncertainty of the excitation current of the phased array antenna are determined;

[0014] Combining the uncertain influencing factors of the element posture of the phased array antenna and the uncertain influencing factors of the excitation current of the phased array antenna, a coupling model of multi-source uncertainty factors of the electromechanical and thermal phased array antenna is constructed.

[0015] Furthermore, the expression of the ideal field strength pattern of the phased array antenna is specifically as follows:

[0016] ;

[0017] In the above formula, represents the ideal field strength pattern of the phased array antenna, represents the number of elements of the phased array antenna, Indicates Array element number, Indicates The spatial phase distribution factor of the array element is Indicates The radiation pattern of the array element is Indicates The excitation current of the array element is represents the amplitude of the excitation current, represents the phase of the excitation current, Represents the line between the far-field observation point and the coordinate origin and The angle between the axes, Indicates that the line between the far-field observation point and the coordinate origin is Projection on a plane The angle between the axes, Represents an imaginary unit.

[0018] Further, the step of determining the influencing factors of the element position uncertainty of the phased array antenna and the influencing factors of the excitation current uncertainty of the phased array antenna according to the influencing parameters of the final radiation pattern of the phased array antenna specifically includes:

[0019] Obtaining influencing parameters of a final radiation pattern of a phased array antenna, wherein the influencing parameters of the final radiation pattern of the phased array antenna include array element uncertainty influencing factors and excitation current uncertainty influencing factors, wherein the array element uncertainty influencing factors include array element position uncertainty factors and array element deflection amount uncertainty influencing factors in the coordinate axis direction, and the excitation current uncertainty influencing factors include excitation current amplitude uncertainty influencing factors and excitation current phase uncertainty influencing factors;

[0020] The uncertainty factor of the array element position is expressed by intervals, and the uncertainty expression of the phase distribution of the phased array antenna aperture field is obtained;

[0021] The uncertainty influencing factors of the deflection of the array element in the coordinate axis direction are expressed in the form of intervals, and the uncertainty expression of the radiation pattern of the phased array antenna element is obtained;

[0022] Integrate the uncertainty expression of the phase distribution of the phased array antenna aperture field and the uncertainty expression of the radiation pattern of the phased array antenna element to obtain the uncertainty influencing factors of the phased array antenna element posture;

[0023] The uncertain influencing factors of the excitation current amplitude and the uncertain influencing factors of the excitation current phase are respectively expressed in the form of intervals, and the excitation current amplitude interval quantity and the excitation current phase interval quantity are obtained;

[0024] The excitation current amplitude interval and the excitation current phase interval are integrated to obtain the uncertain influencing factors of the excitation current of the phased array antenna.

[0025] Furthermore, the expression of the coupling model of the electromechanical and thermal multi-source uncertainty factors of the phased array antenna is specifically as follows:

[0026] ;

[0027] In the above formula, Represents the coupled model of multi-source uncertainty factors of phased array antenna electromechanical and thermal, represents the number of elements of the phased array antenna, Indicates Array element number, Indicates The spatial phase distribution factor of the array element is represents the structural design variables of the phased array antenna, represents the temperature load on the phased array antenna surface, represents the random assembly uncertainty, represents the uncertainty load, It represents the spatial phase distribution interval caused by the uncertainty of the array element position caused by the multi-source uncertainty factors of the active phased array antenna. They represent the current amplitude interval and current phase interval caused by the uncertainty of the excitation current, Indicates The radiation pattern of the array element is represents the radiation pattern under the influence of array element pointing uncertainty, Indicates that the array element has interval deflection in the direction of the coordinate axis, Indicates The position vector of the array element, Indicates The initial position vector of the array element, Indicates The change in the position vector of the array element is Represents the line between the far-field observation point and the coordinate origin and The angle between the axes, Indicates that the line between the far-field observation point and the coordinate origin is Projection on a plane The angle between the axes, Represents an imaginary unit.

[0028] Furthermore, the step of solving and calculating the coupled model of electromechanical and thermal multi-source uncertainty factors of the phased array antenna to obtain the uncertainty expression of the field intensity pattern of the phased array antenna under interval representation specifically includes:

[0029] The coupled model of multi-source uncertainty factors of phased array antenna electromechanical and thermal is divided and processed to obtain amplitude terms and phase terms.

[0030] Based on the uncertainty of amplitude term, the coupled model of electromechanical and thermal multi-source uncertainty factors of phased array antenna is solved and calculated, and the upper and lower bounds of the uncertainty of amplitude term of phased array antenna are obtained.

[0031] Based on the uncertainty factors of the phase term, the rectangular grid array element arrangement calculation is performed on the coupled model of the electromechanical and thermal multi-source uncertainty factors of the phased array antenna, and the upper and lower bounds of the uncertainty of the phase term of the phased array antenna are obtained.

[0032] Combining the interval upper and lower bounds of the uncertainty of the amplitude term of the phased array antenna with the interval upper and lower bounds of the uncertainty of the phase term of the phased array antenna, the uncertainty expression of the field strength pattern of the phased array antenna in interval representation is obtained.

[0033] Furthermore, the uncertainty expression of the field intensity pattern of the phased array antenna under the interval representation is specifically as follows:

[0034] ;

[0035] In the above formula, represents the uncertainty expression of the field strength pattern of the phased array antenna under interval representation, represents the upper bound of the interval of the phased array antenna field strength pattern, represents the lower bound of the interval of the phased array antenna field strength pattern, represents the upper bound of the uncertainty of the amplitude term of the phased array antenna, represents the lower bound of the uncertainty of the amplitude term of the phased array antenna, represents the upper bound of the uncertainty of the phase term of the phased array antenna, represents the lower bound of the uncertainty of the phase term of the phased array antenna, Indicates the maximum number of rows of array elements on the array plane. Indicates the maximum number of columns of array elements on the array plane. Indicates the row number of the current array element. Indicates the column number of the current array element. Indicates Row, No. The array element amplitude term of the column, Indicates Row, No. The array element phase term of the column, Represents the line between the far-field observation point and the coordinate origin and The angle between the axes, Indicates that the line between the far-field observation point and the coordinate origin is Projection on a plane The angle between the axes, Represents an imaginary unit.

[0036] Further, the step of determining the power pattern of the phased array antenna based on the uncertainty expression of the field strength pattern of the phased array antenna under the interval representation, performing electrical performance calculation of the phased array antenna, and obtaining the electrical performance calculation result of the phased array antenna specifically includes:

[0037] The uncertainty expression of the field intensity pattern of the phased array antenna under the interval representation is squared to obtain the power pattern of the phased array antenna.

[0038] The power pattern of the phased array antenna is represented by an interval, and the uncertainty expression of the power pattern under the interval representation is obtained;

[0039] Substitute the power pattern uncertainty expression under interval representation into the phased array antenna field strength pattern uncertainty expression based on interval representation to build a phased array antenna electrical performance calculation model;

[0040] The electrical performance calculation model of the phased array antenna is solved to obtain the electrical performance calculation results of the phased array antenna.

[0041] Furthermore, the expression of the power pattern of the phased array antenna is specifically as follows:

[0042] ;

[0043] In the above formula, represents the power pattern of the phased array antenna, represents the uncertainty expression of the field strength pattern of the phased array antenna under interval representation, represents the conjugate expression of the uncertainty of the phased array antenna field strength pattern in interval representation, Indicates the maximum number of rows of array elements on the array plane. Indicates the maximum number of columns of array elements on the array plane. Indicates the row number of the current array element. Indicates the column number of the current array element. Represents the line between the far-field observation point and the coordinate origin and The angle between the axes, Indicates that the line between the far-field observation point and the coordinate origin is Projection on a plane The angle between the axes.

[0044] The second technical solution adopted by the present invention is: a phased array antenna electrical performance calculation system considering array element posture, comprising:

[0045] The first module is used to construct a coupling model of electromechanical and thermal multi-source uncertainty factors of phased array antennas based on the uncertain influencing factors of the array element posture of the phased array antenna and the uncertain influencing factors of the excitation current of the phased array antenna;

[0046] The second module is used to solve and calculate the coupled model of the electromechanical and thermal multi-source uncertainty factors of the phased array antenna, and obtain the uncertainty expression of the field strength pattern of the phased array antenna under interval representation;

[0047] The third module is used to determine the power pattern of the phased array antenna based on the uncertainty expression of the field strength pattern of the phased array antenna under interval representation, calculate the electrical performance of the phased array antenna, and obtain the calculation results of the electrical performance of the phased array antenna.

[0048] The beneficial effects of the method and system of the present invention are as follows: the present invention is more in line with engineering practice by considering the uncertain influencing factors of the element posture of the phased array antenna and the uncertain influencing factors of the excitation current of the phased array antenna, thereby ensuring the accuracy of the electrical performance calculation results and improving the design efficiency of the active phased array antenna, and then constructing a coupling model of the electromechanical and thermal multi-source uncertainty factors of the phased array antenna, and solving and calculating the coupling model of the electromechanical and thermal multi-source uncertainty factors of the phased array antenna, obtaining the uncertainty expression of the field strength radiation pattern of the phased array antenna under the interval representation, and performing the electrical performance calculation of the phased array antenna, thereby realizing the rapid and accurate analysis of the influence of uncertainty factors on the electrical performance of the active phased array antenna, and improving the efficiency of targeted regulation of antenna performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flowchart of the steps of a method for calculating the electrical performance of a phased array antenna taking into account the position and posture of the array element of the present invention;

[0050] Figure 2 It is a structural block diagram of a phased array antenna electrical performance calculation system considering array element posture according to the present invention;

[0051] Figure 3 It is a schematic diagram of an active phased array antenna element position error interval provided by a specific embodiment of the present invention;

[0052] Figure 4 It is a schematic diagram of the pointing deflection of an active phased array antenna element provided by a specific embodiment of the present invention;

[0053] Figure 5 It is a schematic diagram of array element distribution of a rectangular grid array of an active phased array antenna provided by a specific embodiment of the present invention;

[0054] Figure 6 It is a schematic diagram of an enlarged local position of a rectangular grid array of an active phased array antenna provided in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0055] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only provided for the convenience of explanation and description, and the order between the steps is not limited in any way. The execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0056] Reference Figure 1 The present invention provides a method for calculating the electrical performance of a phased array antenna taking into account the array element posture, the method comprising the following steps:

[0057] S100, constructing a coupling model of electromechanical and thermal multi-source uncertainty factors of phased array antennas according to the uncertainty influencing factors of the element position and the excitation current of the phased array antennas;

[0058] Specifically, based on the ideal field strength calculation process of the active phased array antenna, the parameters of the active phased array antenna affected by the array element and the excitation current are obtained respectively; the uncertainty of the array element position is expressed in an interval manner, and the uncertainty expression of the phase distribution of the aperture field of the active phased array antenna is calculated; the uncertainty of the deflection of the array element in the coordinate axis direction is expressed in an interval manner, and the uncertainty expression of the array element radiation pattern is calculated; the uncertainty expression of the excitation current amplitude and phase under the influence of temperature uncertainty is obtained; the influence of the uncertainty of the active phased array antenna element posture and the excitation current is integrated to establish a coupling model of antenna electromechanical and thermal multi-source uncertainty factors.

[0059] S110, constructing an ideal field intensity pattern of a phased array antenna according to the electromagnetic wave superposition principle of the phased array antenna, wherein the phased array antenna has a plurality of array elements;

[0060] Specifically, for an active phased array antenna with N array elements, according to the electromagnetic wave superposition principle of the array antenna, without considering the mutual coupling of the array elements, the ideal field strength pattern of the active phased array antenna can be expressed as:

[0061] ;

[0062] In the above formula, represents the ideal field strength pattern of the phased array antenna, represents the number of elements of the phased array antenna, Indicates Array element number, Indicates The spatial phase distribution factor of the array element is: Indicates The radiation pattern of the array element is Indicates The excitation current of the array element is represents the amplitude of the excitation current, represents the phase of the excitation current, Represents the line between the far-field observation point and the coordinate origin and The angle between the axes, Indicates that the line between the far-field observation point and the coordinate origin is Projection on a plane The angle between the axes, Represents an imaginary unit.

[0063] It should also be noted that in the above formula, Figure 2 As shown, Far field observation point The line connecting the origin and The angle of the axis, Indicates connection exist Projection on a plane The angle of the axis.

[0064] Among them, Figure 3 As shown, it should be noted that:

[0065] ;

[0066] In the above formula, represents the wave constant, Far-field observation point The unit vector of .

[0067] S120, determining influencing parameters of a final directional pattern of the phased array antenna according to an ideal field strength directional pattern of the phased array antenna;

[0068] Specifically, based on the calculation process of the ideal field strength in step S110, the factors affecting the final radiation pattern of the active phased array antenna are analyzed. The main array element influences include the spatial phase distribution factor , Radiation pattern ; The main excitation current influences include the excitation current amplitude and excitation current phase In more detail, and The main impact is the amplitude distribution of the antenna aperture field. and The main influence is the phase distribution of the aperture field, and and Affected by the deviation of array element position and orientation, and It is mainly affected by temperature factors.

[0069] S130, determining the influencing factors of the element position uncertainty of the phased array antenna and the influencing factors of the excitation current uncertainty of the phased array antenna according to the influencing parameters of the final radiation pattern of the phased array antenna;

[0070] Specifically, the influencing parameters of the final radiation pattern of the phased array antenna are obtained, and the influencing parameters of the final radiation pattern of the phased array antenna include array element uncertainty influencing factors and excitation current uncertainty influencing factors, the array element uncertainty influencing factors include array element position uncertainty factors and array element deflection amount uncertainty influencing factors in the coordinate axis direction, and the excitation current uncertainty influencing factors include excitation current amplitude uncertainty influencing factors and excitation current phase uncertainty influencing factors; the array element position uncertainty factors are represented by intervals to obtain an uncertainty expression of the phase distribution of the phased array antenna aperture field; the uncertainty influencing factors of the deflection amount of the array element in the coordinate axis direction are represented by intervals to obtain an uncertainty expression of the radiation pattern of the phased array antenna element; the uncertainty expression of the phase distribution of the phased array antenna aperture field and the uncertainty expression of the radiation pattern of the phased array antenna element are integrated to obtain the uncertainty influencing factors of the phased array antenna element position; the excitation current amplitude uncertainty influencing factors and the excitation current phase uncertainty influencing factors are represented by intervals respectively to obtain the excitation current amplitude interval quantity and the excitation current phase interval quantity; the excitation current amplitude interval quantity and the excitation current phase interval quantity are integrated to obtain the excitation current uncertainty influencing factors of the phased array antenna.

[0071] In this embodiment, based on the influencing factors analyzed in step S120, the uncertainty of the array element position is expressed in an interval manner, and the uncertainty expression of the phase distribution of the aperture field of the active phased array antenna is calculated. When the array element of the active phased array antenna is affected by uncertainty factors such as environmental load, array surface temperature load and random assembly error, the array element will have a certain position error interval, which will cause new changes in the spatial phase of the antenna aperture field. Assume that the array element position interval is , then the expression of the phase distribution change of the aperture field is:

[0072] ;

[0073] In the above formula, represents the displacement of the array element structure caused by various uncertainties of the antenna, Represents the structural design variables of the antenna, including size, shape, type, etc. represents the temperature load on the antenna surface, represents the random assembly uncertainty, Represents loads and other uncertain loads.

[0074] Further Figure 4As shown, the uncertainty of the deflection amount of the array element in the coordinate axis direction is expressed in an interval manner, and the uncertainty expression of the array element radiation pattern is calculated.

[0075] Furthermore, suppose that the array element has an interval deflection in the direction of the coordinate axis and , then the expression of the radiation pattern of the array element is:

[0076] ;

[0077] The active phased array antenna will cause uneven temperature field distribution on the antenna array surface due to the high-density assembly of array elements and high thermal power consumption of array elements under high-power operation, which will lead to changes in the amplitude and phase of the array element excitation current. The expression of the excitation current amplitude interval under the influence of temperature uncertainty is:

[0078] ;

[0079] The expression of the excitation current phase interval is:

[0080] ;

[0081] In the above formula, They represent the current amplitude interval and current phase interval caused by the uncertainty of the excitation current, represents the upper limit of the excitation current amplitude range, represents the lower bound of the excitation current amplitude range, represents the upper bound of the excitation current phase interval, Represents the lower bound of the excitation current phase interval.

[0082] S140. Combining the uncertainty influencing factors of the element posture of the phased array antenna and the uncertainty influencing factors of the excitation current of the phased array antenna, a coupling model of the electromechanical and thermal multi-source uncertainty factors of the phased array antenna is constructed.

[0083] Specifically, the uncertainty factor of the array element position pointing mainly affects the array element term in the pattern function, and the uncertainty factor of the excitation current amplitude phase mainly affects the excitation current term in the pattern function. In more detail, the uncertainty of the array element pointing and the uncertainty of the excitation current amplitude affect the amplitude term in the pattern function, and the uncertainty of the array element position and the uncertainty of the excitation current phase affect the phase term in the pattern function. Combining the uncertainty influence of the active phased array antenna element posture and the excitation current obtained in the above steps, the coupling model of the multi-source uncertainty factors of the antenna electromechanical and thermal is established as follows:

[0084] ;

[0085] In the above formula, Represents the coupled model of multi-source uncertainty factors of phased array antenna electromechanical and thermal, represents the number of elements of the phased array antenna, Indicates Array element number, Indicates The spatial phase distribution factor of the array element is represents the structural design variables of the phased array antenna, represents the temperature load on the phased array antenna surface, represents the random assembly uncertainty, represents the uncertainty load, It represents the spatial phase distribution interval caused by the uncertainty of the array element position caused by the multi-source uncertainty factors of the active phased array antenna. They represent the current amplitude interval and current phase interval caused by the uncertainty of the excitation current, Indicates The radiation pattern of the array element is represents the radiation pattern under the influence of array element pointing uncertainty, Indicates that the array element has interval deflection in the direction of the coordinate axis, Indicates The position vector of the array element, Indicates The initial position vector of the array element, Indicates The change in the position vector of the array element is Represents the line between the far-field observation point and the coordinate origin and The angle between the axes, Indicates that the line between the far-field observation point and the coordinate origin is Projection on a plane The angle between the axes, Represents an imaginary unit.

[0086] Similarly, if Figure 2 As shown, Far-field observation point The line connecting the origin and The angle of the axis, Indicates connection exist Projection on a plane The angle of the axis.

[0087] S200, solving and calculating the coupled model of electromechanical and thermal multi-source uncertainty factors of the phased array antenna, and obtaining the uncertainty expression of the field strength pattern of the phased array antenna under interval representation;

[0088] S210, dividing and processing the coupling model of electromechanical and thermal multi-source uncertainty factors of the phased array antenna to obtain amplitude terms and phase terms;

[0089] Specifically, the calculation items of each array element in the coupling model of electromechanical and thermal multi-source uncertainty factors of active phased array antenna can be divided into amplitude terms and phase terms. and Under the influence of uncertain factors, it is expressed as an interval quantity.

[0090] S220, based on the influence of amplitude uncertainty, the coupled model of electromechanical and thermal multi-source uncertainty factors of the phased array antenna is solved and calculated to obtain the upper and lower bounds of the uncertainty of the amplitude term of the phased array antenna;

[0091] Specifically, based on the multi-source uncertainty coupling model and the amplitude term division in step S210, the upper and lower bounds of the antenna field strength pattern interval are calculated under the interval quantity representation of the amplitude term uncertainty.

[0092] when When the uncertainty of array element pointing and excitation current is determined, the influence of uncertainty can be regarded as an error interval imposed on the amplitude term of the pattern function. In actual situations, the array element pattern and excitation current are both known quantities, so the expression of the interval upper and lower bounds of the uncertainty of the amplitude term of the phased array antenna is:

[0093] ;

[0094] in

[0095] ;

[0096] In the above formula, represents the upper bound of the uncertainty of the amplitude term of the phased array antenna, represents the lower bound of the uncertainty of the amplitude term of the phased array antenna, represents the upper bound of the uncertainty of the amplitude term of the phased array antenna, The lower bound of the interval representing the uncertainty of the amplitude term of the phased array antenna.

[0097] S230, based on the phase term uncertainty influencing factors, the rectangular grid array element arrangement calculation is performed on the phased array antenna electromechanical thermal multi-source uncertainty factor coupling model to obtain the interval upper and lower bounds of the phase term uncertainty of the phased array antenna;

[0098] Specifically, the phase term in the antenna electromechanical thermal multi-source uncertainty factor coupling model of step S210 is and The interval quantity Directly determine, but There will be different expressions depending on the different array element distribution forms. Taking the rectangular grid commonly used in the active phased array antenna element distribution as an example, the corresponding interval quantity expression is derived, and the upper and lower bounds of the interval representing the uncertainty of its phase term are calculated.

[0099] For Figure 5 and Figure 6 shown The unit spacing is and The active phased array antenna is arranged in a rectangular grid, and the array elements Respectively There is an interval displacement in the direction , and , then according to the relative geometric relationship of the array elements, relative to the coordinate origin array element, the The actual spatial phase generated by an array element on the aperture field is:

[0100] ;

[0101] Substituting the upper and lower bounds of the interval displacement, the upper and lower bounds of the actual space phase interval are obtained as follows:

[0102] ;

[0103] In the above formula, For viewing direction The direction cosines of the above rectangular grid array element arrangement, the interval quantity and upper and lower bounds of the uncertainty of the phase term of the pattern function can be expressed as:

[0104] ;

[0105] In the above formula, reference Figure 5 , Indicates Row, No. The upper bound of the uncertainty of the phase term of the phased array antenna element is Indicates Row, No. The lower bound of the uncertainty of the phase term of the phased array antenna element Indicates Row, No. The supremum of the actual spatial phase generated by the array elements on the aperture field, Indicates Row, No. The supremum of the phase interval of the array element excitation current of the series, express The unit spacing in the axial direction, Represents array element exist The supremum of the interval displacement in the axial direction, Represents array element exist The lower bound of the interval displacement in the axial direction, express The unit spacing in the axial direction, Represents array element exist The supremum of the interval displacement in the axial direction, Represents array element exist The lower bound of the interval displacement in the axial direction, Represents array element exist The supremum of the interval displacement in the axial direction, Represents array element exist The lower bound of the interval displacement in the axial direction, Indicates Row, No. The lower bound of the uncertainty of the phase term of the phased array antenna element is Indicates the Row, No. The infimum of the actual spatial phase generated by the array elements in the aperture field is Indicates the Row, No. The lower bound of the phase interval of the array element excitation current is Represents array element exist The lower bound of the interval displacement in the axial direction, Represents array element exist The supremum of the interval displacement in the axial direction, Represents array element exist The lower bound of the interval displacement in the axial direction, Represents array element exist The supremum of the interval displacement in the axial direction, Represents array element exist The lower bound of the interval displacement in the axial direction, Represents array element exist The supremum of the interval displacement in the axial direction.

[0106] S240. Combining the interval upper and lower bounds of the uncertainty of the phased array antenna amplitude term with the interval upper and lower bounds of the uncertainty of the phased array antenna phase term, an uncertainty expression of the phased array antenna field strength pattern in interval representation is obtained.

[0107] Specifically, the calculation of the upper and lower bounds of the phase term interval and the uncertainty expression of the amplitude term give the uncertainty expression of the antenna field strength pattern under interval representation:

[0108] ;

[0109] In the above formula, represents the uncertainty expression of the field strength pattern of the phased array antenna under interval representation, represents the upper bound of the interval of the phased array antenna field strength pattern, represents the lower bound of the interval of the phased array antenna field strength pattern, represents the upper bound of the uncertainty of the amplitude term of the phased array antenna, represents the lower bound of the uncertainty of the amplitude term of the phased array antenna, represents the upper bound of the uncertainty of the phase term of the phased array antenna, represents the lower bound of the uncertainty of the phase term of the phased array antenna, Indicates the maximum number of rows of array elements on the array plane. Indicates the maximum number of columns of array elements on the array plane. Indicates the row number of the current array element. Indicates the column number of the current array element. Indicates Row, No. The array element amplitude term of the column, Indicates Row, No. The array element phase term of the column, Represents the line between the far-field observation point and the coordinate origin and The angle between the axes, Indicates that the line between the far-field observation point and the coordinate origin is Projection on a plane The angle between the axes, Represents an imaginary unit.

[0110] S300, based on the uncertainty expression of the field strength pattern of the phased array antenna under the interval representation, determine the power pattern of the phased array antenna, perform electrical performance calculation of the phased array antenna, and obtain the electrical performance calculation result of the phased array antenna.

[0111] S310, performing square calculation of the uncertainty expression of the field intensity pattern of the phased array antenna under the interval representation to obtain the power pattern of the phased array antenna;

[0112] Specifically, the power pattern of the antenna can be expressed as the square of the modulus of the field strength pattern, as shown below:

[0113] ;

[0114] The field intensity pattern is the sum of a series of complex exponentials, so the above formula is transformed into:

[0115] ;

[0116] The antenna power pattern expression based on the coupling model of antenna electromechanical thermal multi-source uncertainty factors is:

[0117] ;

[0118] In the above formula, represents the power pattern of the phased array antenna, represents the uncertainty expression of the field strength pattern of the phased array antenna under interval representation, represents the conjugate expression of the uncertainty of the phased array antenna field strength pattern in interval representation, Indicates the maximum number of rows of array elements on the array plane. Indicates the maximum number of columns of array elements on the array plane. Indicates the row number of the current array element. Indicates the column number of the current array element. Represents the line between the far-field observation point and the coordinate origin and The angle between the axes, Indicates that the line between the far-field observation point and the coordinate origin is Projection on a plane The angle between the axes.

[0119] S320, expressing the power pattern of the phased array antenna in an interval manner, and obtaining an uncertainty expression of the power pattern under the interval representation;

[0120] Specifically, the uncertainty expression of the power pattern under interval representation is:

[0121] ;

[0122] In the above formula, Indicates Row, No. The array element phase term of the column, Indicates Row, No. The array element phase term of the column, Indicates Row, No. The array element amplitude term of the column, Indicates Row, No. The array element amplitude terms of the column.

[0123] S330, substituting the power pattern uncertainty expression under the interval representation into the phased array antenna field strength pattern uncertainty expression based on the interval representation, and constructing a phased array antenna electrical performance calculation model;

[0124] S340, solving the phased array antenna electrical performance calculation model to obtain the phased array antenna electrical performance calculation results.

[0125] Specifically, based on the antenna field strength pattern interval quantity obtained in step S320, the monotonicity of the function is comprehensively considered, and the phased array Tianan electrical performance fast calculation formula considering the uncertainty of the array element posture and the excitation current is obtained as follows:

[0126] 1) When When:

[0127] ;

[0128] (2) When When:

[0129] ;

[0130] (3) When For other values, there are:

[0131] ;

[0132] In the above formula, Indicates Row, No. The phase term of the array element in the first Row, No. The difference in the phase terms of the array elements of the columns, Indicates Row, No. The supremum of the interval of the array element amplitude terms of the column, Indicates Row, No. The supremum of the interval of the array element amplitude terms of the column, Indicates Row, No. The supremum of the interval of the array element phase term of the column, Indicates Row, No. The infimum of the interval of the array element phase term of the column, Indicates Row, No. The lower bound of the interval of the array element amplitude terms of the column, Indicates Row, No. The lower bound of the interval of the array element amplitude terms of the column, Indicates Row, No. The infimum of the interval of the array element phase term of the column, Indicates Row, No. The supremum of the interval of the array element phase terms of the column.

[0133] Reference Figure 2 , a phased array antenna electrical performance calculation system considering array element position and posture, comprising:

[0134] The first module 201 is used to construct a coupling model of electromechanical and thermal multi-source uncertainty factors of the phased array antenna according to the uncertainty influencing factors of the element posture of the phased array antenna and the uncertainty influencing factors of the excitation current of the phased array antenna;

[0135] The second module 202 is used to solve and calculate the coupled model of electromechanical and thermal multi-source uncertainty factors of the phased array antenna to obtain the uncertainty expression of the field intensity pattern of the phased array antenna under interval representation;

[0136] The third module 203 is used to determine the power pattern of the phased array antenna based on the uncertainty expression of the field strength pattern of the phased array antenna under the interval representation, perform electrical performance calculation of the phased array antenna, and obtain the electrical performance calculation result of the phased array antenna.

[0137] The contents of the above method embodiments are all applicable to the present system embodiments. The functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0138] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A method for calculating the electrical performance of a phased array antenna taking into account the position and posture of the array element, characterized in that: The following steps are involved: According to the uncertain influencing factors of the element position and the excitation current of the phased array antenna, a coupling model of the electromechanical and thermal multi-source uncertainty factors of the phased array antenna is constructed; The coupled model of multi-source uncertainty factors of phased array antenna electromechanical and thermal is divided and processed to obtain amplitude terms and phase terms. Based on the uncertainty of amplitude term, the coupled model of electromechanical and thermal multi-source uncertainty factors of phased array antenna is solved and calculated, and the upper and lower bounds of the uncertainty of amplitude term of phased array antenna are obtained. Based on the uncertainty factors of the phase term, the rectangular grid array element arrangement calculation is performed on the coupled model of the electromechanical and thermal multi-source uncertainty factors of the phased array antenna, and the upper and lower bounds of the uncertainty of the phase term of the phased array antenna are obtained. Combining the interval upper and lower bounds of the uncertainty of the phased array antenna amplitude term with the interval upper and lower bounds of the uncertainty of the phased array antenna phase term, the uncertainty expression of the phased array antenna field strength pattern in interval representation is obtained; The uncertainty expression of the phased array antenna field strength pattern under the interval representation is specifically as follows: ； In the above formula, represents the uncertainty expression of the field strength pattern of the phased array antenna under interval representation, represents the upper bound of the interval of the phased array antenna field strength pattern, represents the lower bound of the interval of the phased array antenna field strength pattern, represents the upper bound of the uncertainty of the amplitude term of the phased array antenna, represents the lower bound of the uncertainty of the amplitude term of the phased array antenna, represents the upper bound of the uncertainty of the phase term of the phased array antenna, represents the lower bound of the uncertainty of the phase term of the phased array antenna, Indicates the maximum number of rows of array elements on the array plane. Indicates the maximum number of columns of array elements on the array plane. Indicates the row number of the current array element. Indicates the column number of the current array element. Indicates Row, No. The array element amplitude term of the column, Indicates Row, No. The array element phase term of the column, Represents the line between the far-field observation point and the coordinate origin and The angle between the axes, Indicates that the line between the far-field observation point and the coordinate origin is Projection on a plane The angle between the axes, represents an imaginary unit; Based on the uncertainty expression of the field strength pattern of the phased array antenna under interval representation, the power pattern of the phased array antenna is determined, the electrical performance of the phased array antenna is calculated, and the calculation results of the electrical performance of the phased array antenna are obtained.

2. According to claim 1, a method for calculating electrical performance of a phased array antenna taking into account the position and posture of the array element, characterized in that: The step of constructing a coupling model of electromechanical and thermal multi-source uncertainty factors of the phased array antenna according to the uncertainty influencing factors of the element posture of the phased array antenna and the uncertainty influencing factors of the excitation current of the phased array antenna specifically includes: According to the electromagnetic wave superposition principle of the phased array antenna, an ideal field intensity pattern of the phased array antenna is constructed, wherein the phased array antenna has a plurality of array elements; According to the ideal field strength pattern of the phased array antenna, determine the influencing parameters of the final pattern of the phased array antenna; According to the influencing parameters of the final radiation pattern of the phased array antenna, the influencing factors of the uncertainty of the element position of the phased array antenna and the influencing factors of the uncertainty of the excitation current of the phased array antenna are determined; Combining the uncertain influencing factors of the element posture of the phased array antenna and the uncertain influencing factors of the excitation current of the phased array antenna, a coupling model of multi-source uncertainty factors of the electromechanical and thermal phased array antenna is constructed.

3. According to claim 2, a method for calculating electrical performance of a phased array antenna taking into account the position and posture of the array element, characterized in that: The expression of the ideal field strength pattern of the phased array antenna is specifically as follows: ； In the above formula, represents the ideal field strength pattern of the phased array antenna, represents the number of elements of the phased array antenna, Indicates Array element number, Indicates The spatial phase distribution factor of the array element is Indicates The radiation pattern of the array element is Indicates The excitation current of the array element is represents the amplitude of the excitation current, represents the phase of the excitation current, Represents the line between the far-field observation point and the coordinate origin and The angle between the axes, Indicates that the line between the far-field observation point and the coordinate origin is Projection on a plane The angle between the axes, Represents an imaginary unit.

4. According to claim 3, a method for calculating electrical performance of a phased array antenna taking into account the position and posture of the array element is characterized in that: The step of determining the influencing factors of the element position uncertainty of the phased array antenna and the influencing factors of the excitation current uncertainty of the phased array antenna according to the influencing parameters of the final radiation pattern of the phased array antenna specifically includes: Obtaining influencing parameters of a final radiation pattern of a phased array antenna, wherein the influencing parameters of the final radiation pattern of the phased array antenna include array element uncertainty influencing factors and excitation current uncertainty influencing factors, wherein the array element uncertainty influencing factors include array element position uncertainty factors and array element deflection amount uncertainty influencing factors in the coordinate axis direction, and the excitation current uncertainty influencing factors include excitation current amplitude uncertainty influencing factors and excitation current phase uncertainty influencing factors; The uncertainty factor of the array element position is expressed by intervals, and the uncertainty expression of the phase distribution of the phased array antenna aperture field is obtained; The uncertainty influencing factors of the deflection of the array element in the coordinate axis direction are expressed in the form of intervals, and the uncertainty expression of the radiation pattern of the phased array antenna element is obtained; Integrate the uncertainty expression of the phase distribution of the phased array antenna aperture field and the uncertainty expression of the radiation pattern of the phased array antenna element to obtain the uncertainty influencing factors of the phased array antenna element posture; The uncertain influencing factors of the excitation current amplitude and the uncertain influencing factors of the excitation current phase are respectively expressed in the form of intervals, and the excitation current amplitude interval quantity and the excitation current phase interval quantity are obtained; The excitation current amplitude interval and the excitation current phase interval are integrated to obtain the uncertain influencing factors of the excitation current of the phased array antenna.

5. The method for calculating electrical performance of a phased array antenna taking into account the position and posture of an array element according to claim 4, characterized in that: The expression of the coupling model of the electromechanical and thermal multi-source uncertainty factors of the phased array antenna is specifically as follows: ； In the above formula, Represents the coupled model of multi-source uncertainty factors of phased array antenna electromechanical and thermal, represents the number of elements of the phased array antenna, Indicates Array element number, Indicates The spatial phase distribution factor of the array element is represents the structural design variables of the phased array antenna, represents the temperature load on the phased array antenna surface, represents the random assembly uncertainty, represents the uncertainty load, It represents the spatial phase distribution interval caused by the uncertainty of the array element position caused by the multi-source uncertainty factors of the active phased array antenna. They represent the current amplitude interval and current phase interval caused by the uncertainty of the excitation current, Indicates The radiation pattern of the array element is represents the radiation pattern under the influence of array element pointing uncertainty, Indicates that the array element has interval deflection in the direction of the coordinate axis, Indicates The position vector of the array element, Indicates The initial position vector of the array element, Indicates The change in the position vector of the array element is Represents the line between the far-field observation point and the coordinate origin and The angle between the axes, Indicates that the line between the far-field observation point and the coordinate origin is Projection on a plane The angle between the axes, Represents an imaginary unit.

6. According to claim 5, a method for calculating electrical performance of a phased array antenna taking into account the position and posture of the array element, characterized in that: The step of determining the power pattern of the phased array antenna based on the uncertainty expression of the field strength pattern of the phased array antenna under the interval representation, performing electrical performance calculation of the phased array antenna, and obtaining the electrical performance calculation result of the phased array antenna specifically includes: The uncertainty expression of the field intensity pattern of the phased array antenna under the interval representation is squared to obtain the power pattern of the phased array antenna. The power pattern of the phased array antenna is represented by an interval, and the uncertainty expression of the power pattern under the interval representation is obtained; Substitute the power pattern uncertainty expression under interval representation into the phased array antenna field strength pattern uncertainty expression based on interval representation to build a phased array antenna electrical performance calculation model; The electrical performance calculation model of the phased array antenna is solved to obtain the electrical performance calculation results of the phased array antenna.

7. The method for calculating electrical performance of a phased array antenna taking into account the position and posture of an array element according to claim 6, characterized in that: The expression of the power pattern of the phased array antenna is specifically as follows: ； In the above formula, represents the power pattern of the phased array antenna, represents the uncertainty expression of the field strength pattern of the phased array antenna under interval representation, represents the conjugate expression of the uncertainty of the phased array antenna field strength pattern in interval representation, Indicates the maximum number of rows of array elements on the array plane. Indicates the maximum number of columns of array elements on the array plane. Indicates the row number of the current array element. Indicates the column number of the current array element. Represents the line between the far-field observation point and the coordinate origin and The angle between the axes, Indicates that the line between the far-field observation point and the coordinate origin is Projection on a plane The angle between the axes.

8. A phased array antenna electrical performance calculation system considering array element position, characterized in that: Includes the following modules: The first module is used to construct a coupling model of electromechanical and thermal multi-source uncertainty factors of phased array antennas based on the uncertain influencing factors of the array element posture of the phased array antenna and the uncertain influencing factors of the excitation current of the phased array antenna; The second module is used to divide and process the coupled model of multi-source uncertainty factors of phased array antenna electromechanical and thermal to obtain amplitude terms and phase terms; Based on the uncertainty of amplitude term, the coupled model of electromechanical and thermal multi-source uncertainty factors of phased array antenna is solved and calculated, and the upper and lower bounds of the uncertainty of amplitude term of phased array antenna are obtained. Based on the uncertainty factors of the phase term, the rectangular grid array element arrangement calculation is performed on the coupled model of the electromechanical and thermal multi-source uncertainty factors of the phased array antenna, and the upper and lower bounds of the uncertainty of the phase term of the phased array antenna are obtained. Combining the interval upper and lower bounds of the uncertainty of the phased array antenna amplitude term with the interval upper and lower bounds of the uncertainty of the phased array antenna phase term, the uncertainty expression of the phased array antenna field strength pattern in interval representation is obtained; The uncertainty expression of the phased array antenna field strength pattern under the interval representation is specifically as follows: ； In the above formula, represents the uncertainty expression of the field strength pattern of the phased array antenna under interval representation, represents the upper bound of the interval of the phased array antenna field strength pattern, represents the lower bound of the interval of the phased array antenna field strength pattern, represents the upper bound of the uncertainty of the amplitude term of the phased array antenna, represents the lower bound of the uncertainty of the amplitude term of the phased array antenna, represents the upper bound of the uncertainty of the phase term of the phased array antenna, represents the lower bound of the uncertainty of the phase term of the phased array antenna, Indicates the maximum number of rows of array elements on the array plane. Indicates the maximum number of columns of array elements on the array plane. Indicates the row number of the current array element. Indicates the column number of the current array element. Indicates Row, No. The array element amplitude term of the column, Indicates Row, No. The array element phase term of the column, Represents the line between the far-field observation point and the coordinate origin and The angle between the axes, Indicates that the line between the far-field observation point and the coordinate origin is Projection on a plane The angle between the axes, represents an imaginary unit; The third module is used to determine the power pattern of the phased array antenna based on the uncertainty expression of the field strength pattern of the phased array antenna under interval representation, calculate the electrical performance of the phased array antenna, and obtain the calculation results of the electrical performance of the phased array antenna.

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