3.1. A priori Knowledge Neural Network Optimization Model Combining Multi-Node Matching with Q-Value Constraints and Multi-Objective Function Constraints
a) Analyze the reasons why the voltage standing wave ratio (VSWR) is limited for each structural segment of a temperature measuring antenna under octave conditions; improve the power transmission efficiency of the antenna by optimizing VSWR parameters; propose a Q-constrained multi-branch broadband matching method based on both Chebyshev and multi-branch matching theory.
According to Chebyshev’s waveguide matching theory, the matching node order N can be obtained by the following equation:
where
is the impedance ratio of the input and output ports of the waveguide,
ρ is the maximum VSWR of the waveguide. According to Equation (1), if
, the maximum VSWR
of the waveguide is less than 1.1 theoretically. According to Chebyshev impedance transformation theory:
Where and are the characteristic impedance of each matched branch, is the characteristic impedance at the waveguide input port and is the impedance ratio of the waveguide input and output port. and are the polynomial related to the fractional bandwidth parameter.
According to the equivalent principle of tuning loop, the fractional bandwidth
of multi-branch matching loop is:
Where s the reflection coefficient, is the quality factor. and are the tuning loop coefficient.
b) Explore the limitations of manual tuning antenna optimization; adopt the optimization algorithm of swarm intelligence fused with neural networks; optimize the major lobe beam, side lobe, and transition zone simultaneously as objectives; define the constraint range of multiple sub-objective functions; reallocate weights to improve the pointing performance of the temperature measurement antenna.
By assigning different weights to each optimization objective function, the proportion of optimization objectives is set, and the main indicators and secondary indicators are defined. The definition of the objective function is shown in Equation (4):
Where is the total fitness function value of the optimization objective. , , , are the fitness function values of the major lobe beam, transition zone, side lobe and respectively. , , , are the weights of the optimization objectives.
The expressions defined by
are shown in Equation (5) as follows:
Where is the target value, is the actual value, and is the th frequency point. For the major lobe beam, the optimization goal is to obtain a pencil beam distribution within the desired range. For the transition zone, , and , represent the angles corresponding to 90% and 30% of the maximum electromagnetic response on the E-plane and H-plane, respectively. The smaller the difference between the angles, the narrower the transition zone. For the side lobes, the goal is to minimize the difference between the optimized target and actual value. For the parameters, the optimization goal is to ensure that all maximum values within the operating frequency band are less than the target value.
c) To address the issue of the antenna structure’s inverse requiring excessive data, a neural network model based on prior knowledge is studied. As shown in
Figure 2, multiple sub-forward neural networks (forward neural networks, FNN) are taken as the structural parameter of antenna with prior knowledge inversion and multi-indexes, and finally a multi-index optimization system with extremely narrow pencil beam temperature measuring antenna is constructed.
The input of INN is electromagnetic response: , where represents the major lobe beam, represents the transition zone, and represents the side lobes, represents the . are the number of discrete points. The output is structural parameters written as , where is the number of structural parameters. The input of FNN is structural parameters, and the output is electromagnetic response. There are three hidden layers in total. The FNN corresponding to each optimization objective has two hidden layers. The output layer’s activation function is Tanh, while the hidden layer’s activation function is Relu. The inputs of the three sub-FNN are all the same set of structural parameters . The inputs of the three sub-FNNs are the same set of structural parameters. The outputs of the three sub-FNNs are different, namely the major lobe beam, transition zone, side lobe and . The loss function uses the MSE function to train the FNN to make the predicted electromagnetic response approach the real electromagnetic response.
3.2. Channel Phase Shifting Correction Algorithm and Calibration Link Uncertainty Calibration for Measuring Radiation Brightness Temperature Errors
a) Construct an error model of microwave radiation meter architecture with key indicators such as sensitivity and accuracy; analyze the expression of the influence mechanism of phase, amplitude, offset and other errors on radiometer output data; design a periodic phase-shifting error correction algorithm based on uniform polar circle in combination with phase modulation circuit to correct the detected output data.
To calculate the sensitivity of a phase modulation correlation radiometer, it is necessary to determine the output RMSF and the change in output mean value caused by the temperature variation of the target being measured. When SNR equals to 1, the sensitivity expression is:
Where, ,, is the equivalent bandwidth of the RF front end, is the integration time of the system, and are the root mean square of the gain and phase fluctuations, respectively. Equation (6) reveals that the sensitivity is affected by the gain fluctuations of the amplifier, the phase errors of the phase modulator, and the temperature difference between the target under test and the reference load. When the correlation radiometer operates in equilibrium, that is, , the sensitivity expression is the same as that of an ideal correlation radiometer. When the radiometer operates in a non-equilibrium state, that is, , the gain fluctuations of the amplifier have a significant impact on the sensitivity. In the case of relatively small phase modulation errors, when, the impact of phase modulation errors on this radiometer is not significant.
To determine the phase error of the radiometer, the demodulated output data is corrected using a periodic phase modulation method. The radiometer
r input end is modulated by a phase shift in steps. At each phase point, the sampled data of the
group output channels are collected and the average is calculated through digital integration. After obtaining the original sampled data of the output channels, the quadrant in which they belong is determined based on the sign of their symbols. First, the sum of squares of the sampled data of the output channels is calculated, then the square root is taken to obtain the demodulated voltage amplitude. Finally, under a fixed phase shift, the radiometer demodulated voltage amplitude is calculated, collecting the voltage amplitude and the corresponding phase difference values. The ideal radiometer I/Q channel output data is calculated based on the ideal situation data, and the measured output data of the I/Q channels are linearly fitted separately with the ideal situation data as reference. By the linear fitting method, the intercept and slope parameters are obtained, and the correction equations for the I/Q channel data can be derived as follows:
Where
and
are the corrected output voltage values of the I/Q channels,
is the phase modulation step size,
is the amplitude coefficient,
is the phase scanning times, and
is the actual mean phase error of the radiometer, as shown in Equation (9).
b) A finite element method based on forward and backward modeling theory is proposed to calibrate the scattering model of the calibration source, the control strategy of the electro-thermal performance of the calibration source is studied, the structure of the calibration source is improved, the influence of antenna beam on the transmission effect of the brightness temperature is analyzed from the perspective of the overall directional radiation temperature, the uncertainty of the calibration link is traced back, and the error of the transmission brightness temperature is corrected.
Among them, the radiation brightness temperature of the coated array calibration source can be obtained by calculating the directional radiation brightness temperature model, which is based on reciprocity under the condition of far-field, and can calculate the radiation brightness temperature perpendicular to the front direction of the calibration source. Usually, the calculation of directional brightness temperature is the cross integration along the three-dimensional direction, as shown in Equation (10). However, for the coating array type calibration source, the temperature distribution and local absorption distribution inside the cone coating mainly vary along the direction. Therefore, the process of directional brightness temperature calculation can be simplified to one-dimensional integration, as shown in Equation (11).
Where,
is the radiation brightness temperature perpendicular to the array surface,
is the total reflectance of the cone array,
is the normalized absorption ratio inside the cone coating at height,
is the average temperature inside the cone coating at height
,
is the ambient temperature, and
is the set reference temperature of the cone calibration source. Explore the boundary of the electro-thermal dual consideration characteristics of the calibration source, that is, approaching
. It can be seen from Equation (11) that the radiation brightness temperature is obtained by coupling the results of electromagnetic analysis and temperature analysis through integration. The scene of directional radiation brightness temperature calculation for the calibration source is shown in
Figure 3.
As shown in the above figure, when the finite cone array calibration source is operating in an open scene, assuming that the total power passing through the closed surface
surrounding the entire integration area is averaged as:
Where, , are the electromagnetic field distribution on the closed surface irradiated by the antenna (single-mode excitation), is the normal vector pointing outward of the closed surface, is the incident power on the antenna port cross-section, is the backscattered power on the antenna port cross-section, is the total leakage to the surrounding space in the open scene, including antenna leakage and leakage after scattering by the calibration source.
When the antenna is excited by a single mode, the absorbed power
in the target coating is:
Where, is the polarized absorption electric field in the volume element of the - calibration source coating when the antenna is excited by single mode. According to Equation (13), the key to obtaining the transfer brightness temperature is to calculate the local absorption power within each volume element of the calibration source coating.
The expression for the transfer brightness temperature received by the near-field antenna is
Where is the local temperature within the volume element, is the unit mode field power passing through the antenna port cross section under single-mode transmission. According to Equation (14), the transfer brightness temperature at the antenna port in the near-field calibration scenario is: the absorption power in the calibration source coating integrated after being weighted by the temperature distribution at the corresponding local position.
3.3. Incoherent Skin Tissue Radiation Forward Model and Objective Function Constrained Deep Learning Combined Inversion Method
a) Clarify the relationship between human skin tissue radiation brightness temperature and weight function; research the temperature distribution of human epidermis, dermis, subcutaneous tissue and muscle layer by using C, X and Ku frequency bands; obtain the mathematical representation of skin tissue heat transfer based on incoherent method; derive the estimation equation of apparent brightness temperature when human body transmissivity is 0.
The radiation brightness temperature
of skin tissue is a weighted contribution of the temperatures of each layer, which can be expressed as:
Where, and are the physical temperature and weighting function of each layer of tissue, and is the depth at which the measured tissue is located below the surface.
In the absence of scattering, the weighting function
can be expressed as:
Where is the transmissivity, is the absorption coefficient, and is the angle of incidence.
It can be seen from Equations (15) and (16) that brightness temperature is the sum of the vertical antenna aperture weighted skin tissue temperatures, and the weighting function directly affects the observation results. Therefore, in order to accurately describe the relationship between brightness temperature and the physical temperatures of various layers of skin tissue, it is necessary to establish a radiative transfer forward model to numerically calculate the weighting function.
Considering the scattering, the forward model of radiation transmission of incoherent skin tissue is established, as shown in
Figure 4.
As shown in
Figure 4(a), the microwave thermal radiation model between skin tissues includes epidermis layer, dermis layer, subcutaneous tissue layer and muscle layer. Considering the multiple reflections in the radiation transmission process of human tissues, the brightness temperature contribution of human tissues is divided into two parts: upward and downward. It is assumed that the brightness temperature emitted upward by the epidermis layer is
, the brightness temperature emitted downward by the epidermis layer is
, the brightness temperature emitted upward by the dermis layer is
, the brightness temperature emitted downward by the dermis layer is
, the brightness temperature emitted upward by the subcutaneous tissue layer is
, the brightness temperature emitted downward by the subcutaneous tissue layer is
, and the brightness temperature emitted upward by the muscle layer is
. Therefore, the total emitted brightness temperature
of the skin surface layer can be expressed as:
Assume that the brightness temperatures emitted by the epidermis layer, dermis layer, subcutaneous tissue layer, and muscle layer are
,
,
and
, respectively; the tissue loss factors of each layer are
,
,
and
; the reflectivity at the boundaries of each tissue layer are
,
and
respectively. Therefore, the upward and downward emitted brightness temperatures of each tissue layer can be expressed as:
Where,
is the absorption coefficient of each layer of organization. It can be represented as
by the attenuation constant
.
,
,
,
are the physical temperatures of the epidermis, dermis, subcutaneous tissue layer, and muscle layer, respectively. The specific values can be calculated using the Pennes bioheat transfer equation:
Where, , , are the skin tissue density, specific heat capacity, and thermal conductivity, , , are the blood perfusion rate, density, and specific heat capacity, is the blood arterial temperature, is the skin tissue layer temperature, and is the tissue metabolic heat.
As shown in
Figure 4(b), the apparent brightness temperature when the human body transmissivity equals 0 can be expressed as:
Where, is the skin brightness temperature of the human body, is the emissivity of the human body, is the transmissivity of the clothing, is the reflectance of the clothing, is the physical temperature of the human body, is the physical temperature of the clothing, is the ambient temperature, and is the equivalent ambient temperature.
b) Analyze the factors that affect the accuracy of temperature measurement under near-field condition; analyze the microwave radiation forward model of human skin tissue; calculate the constraint range of temperature difference between adjacent skin tissues in different areas of an individual driven by solving the contribution weight of brightness temperature of each layer of tissue; define the objective function of the penalty function correction algorithm.
When the microwave temperature measurement system is affected by the random disturbance of environment and equipment, the inversion result exceeds the reasonable distribution range of skin tissue temperature difference, so the limit value constraint objective function of temperature distribution is adopted. Assuming that for the
th sample, the temperature difference between the
th and (
+1)th layer of tissue is
, it should satisfy
which
and
are the minimum temperature difference and maximum temperature difference between the
th and (
+1)th layer of tissue. The predicted temperature difference between the ith and (
+1)th layer of tissue is
. When it exceeds the
,
range, the inversion algorithm is corrected by defining an appropriate penalty function to distribute the inversion prediction values within a reasonable temperature range. If the definition
oes not exceed the temperature difference distribution range, the value of the penalty function is zero; if
xceeds the temperature difference range, the value of the penalty function becomes non-zero, and with the increase of the deviation degree, the value of the penalty function increases according to the square trend. According to the relationship between the zero point of the quadratic function and the solution of the equation, the penalty function is defined as follows:
Where is the penalty function coefficient whose value ranges less than 1.
Equation (27) describes the predicted temperature difference penalty function between the
and (
+1)th layers. For the prediction of multi-layer structures, the penalty function should be the superposition of the predicted temperature difference losses of adjacent layers, namely:
Where, () are the predicted temperatures of the th layer of tissue and is the number of layers of tissue.
c) In order to optimize the accuracy, generalization and robustness of the inversion algorithm, a closed-loop high-precision forward and inversion modeling detection method for human tissue temperature measurement is proposed, as shown in
Figure 5. Firstly, the human tissue temperature data set and constraint conditions are constructed by the forward model, then the human simulated tissue fluid, skin tissue and other samples are tested, and the clinical data are collected to verify the inversion algorithm. Finally, the clinical experiment is guided by the test results and evaluation indicators, and the mathematical and physical relationship of the forward model is improved by comparing the clinical data with the simulation data, which further enhances the scientific nature of the method.