An adaptive learning method and system based on physical expressions

Abstract

The application discloses a kind of adaptive learning method and system based on physical expression, its method includes: obtaining the sampling data of current time and inputting it in physical expression module, to obtain the sampling output data of current time;Desired output data of current time and the sampling output data of current time are input into root mean square error module;Root mean square error module is based on the data of input to calculate the root mean square error corresponding to current time to judge;Adaptive learning algorithm module is calculated to obtain the weight value of next time according to the input root mean square error.The application method is simple, and high implementability;By introducing weight, adaptive algorithm and physical expression are closely combined together, by cyclically adjusting weight, so that physical expression is more close to engineering demand, and therefore algorithm model is more comprehensive and effective.

Description

Technical Field

[0001] This invention relates to the field of adaptive learning technology, and in particular to an adaptive learning method and system based on physical expressions. Background Technology

[0002] Data processing is involved in many research fields, including scientific experiments, computer image processing, and signal processing. To analyze relationships between things, predict future trends, and make reasonable decisions, data fitting is essential. Data fitting is widely used in many fields and has always been a popular topic. Essentially, it involves fitting given discrete data points to curves or surfaces, using smooth curves or surfaces to approximate these discrete points, thus improving the fitting effect. This is an important research topic in mathematics and other disciplines.

[0003] For input and output data with a clearly defined analytical expression relationship, a mathematical function analytical expression y = f(x, p, ..., q) consistent with the background patterns of the data is used to represent the dependency relationship between different input parameters x, p, ..., q (assuming a total of k) and the output data y. This y = f(x, p, ..., q) is called the theoretical mathematical model. Guided by this expression, the output data can be completely obtained from the input data through calculation. However, in the comparison between theoretical calculations and actual test results, the theoretical calculation results often do not match the test data well, meaning the expression cannot be directly used as a curve fitting function. There are various reasons for this phenomenon, such as the superposition of certain fixed parameters during the data acquisition process, the addition of coefficients due to amplifiers or attenuators, or the introduction of specific parameters by the testing instruments during the testing process. These reasons all prevent mathematical modeling based solely on physical expressions from meeting the design requirements. However, the system links are complex, the testing environment is limited, and it is impossible to investigate all causes individually; only the final test data results are known. Therefore, how to construct an accurate model becomes the key and challenging aspect of the design. Summary of the Invention

[0004] In view of this, the present invention provides an adaptive learning method and system based on physical expressions to solve the above-mentioned technical problems.

[0005] This invention discloses an adaptive learning method based on physical expressions, which includes the following steps:

[0006] Step 1: Obtain the sampling data at the current moment and input it into the physics expression module to obtain the sampling output data at the current moment;

[0007] Step 2: Input the expected output data at the current time and the sampled output data at the current time into the root mean square error module;

[0008] Step 3: The root mean square error module calculates the root mean square error corresponding to the current time based on the input data. Depending on whether the root mean square error meets the requirements, it determines whether to use the current sampled output data of the physical expression module as the final data output of the physical expression module, or to input the root mean square error into the adaptive learning algorithm module.

[0009] Step 4: The adaptive learning algorithm module calculates the weight value at the current time based on the input root mean square error, and calculates the weight value at the next time based on the weight value at the current time, and replaces the weight value in the physical expression module with the weight value at the next time.

[0010] Step 5: Use the sampled data of the next time moment as the sampled data of the current time moment, and repeat steps 1 to 5 until the root mean square error output by the root mean square error module meets the requirements.

[0011] Further, step 1 includes:

[0012] Let the sampled data at the current moment be (ak, bk, ..., qk), where (ak, bk, ..., qk) is the sampled data of a, b, ..., q at the k-th moment, i.e. the current moment; k is a positive integer, ranging from 1 to n;

[0013] The sampled data at the current moment is input into the domain-knowledge-based physical expression in the physical expression module to obtain the sampled output data at the current moment, i.e.:

[0014] zk=f(λ1×ak,λ2×bk,…,λm×qk)

[0015] Where f is an analytical expression with physical meaning, λ1, λ2, ..., λm are weight values, which are used to adjust the size of the sampled data at the current time; zk is the sampled output data at the current time.

[0016] Further, step 3 includes:

[0017] Step 31: When the root mean square error meets the requirements, the current sampled output data zk is used as the output of the physical expression module; when the root mean square error does not meet the requirements, the root mean square error e is... k Send it to the adaptive learning algorithm module;

[0018] Step 32: The adaptive learning algorithm module uses the mean squared error as the cost function, calculates the partial derivatives with respect to λ1, λ2, ..., λm, and then sets the partial derivatives to zero to obtain the extreme values ​​of MSE.

[0019] Step 33: Based on step 33, obtain the weight value for the next time step.

[0020] Furthermore, the root mean square error e k for:

[0021]

[0022] Furthermore, step 32 specifically includes:

[0023] The adaptive learning algorithm module uses mean squared error as the cost function:

[0024]

[0025] By taking the partial derivative of the above equation with respect to λ1, λ2, ..., λm, and then setting the partial derivative to zero, the extreme values ​​of MSE can be obtained.

[0026] Taking the partial derivative of the above equation, we get:

[0027]

[0028] in, It can be calculated based on the expression f(λ1×aj,λ2×bj,…,λn×qj); λ i (k) represents the i-th weight value at the current time, where i ranges from 1 to m.

[0029] Furthermore, step 33 specifically includes:

[0030]

[0031] Where η is a fixed parameter representing the learning efficiency, and λ i (k+1) represents the next time step, i.e., the i-th weight value at time k+1.

[0032] Furthermore, in step 4:

[0033] Replace the m weight values ​​of the domain-knowledge-based physical expression in the physical expression module with the m weight values ​​of the next time step.

[0034] This invention also discloses an adaptive learning system based on physical expressions, which includes:

[0035] The physical expression module is used to receive the sampled data at the current moment and obtain the sampled output data at the current moment; and to receive the feedback information that meets the requirements output by the root mean square error module; when the feedback information is received, the sampled output data at the current moment is used as its final data output; it is also used to use the sampled data of the next moment output by the adaptive learning algorithm module as the sampled data of the current moment.

[0036] The root mean square error module is used to calculate the root mean square error between the expected output data received at the current time and the sampled output data at the current time output by the physical expression module. When the root mean square error meets the requirements, it outputs feedback information that meets the requirements to the physical expression module; when the root mean square error does not meet the requirements, it inputs the root mean square error into the adaptive learning algorithm module.

[0037] The adaptive learning algorithm module is used to calculate the weight value at the current time step based on the received root mean square error, calculate the weight value at the next time step based on the weight value at the current time step, and replace the weight value in the physical expression module with the weight value at the next time step.

[0038] Due to the adoption of the above technical solution, the present invention has the following advantages: the method of the present invention is simple and highly implementable; by introducing weights, the adaptive algorithm is closely integrated with the physical expression, and by cyclically adjusting the weights, the physical expression is made closer to the engineering requirements, thus the algorithm model is more comprehensive and effective. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in the embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0040] Figure 1 This is a schematic diagram of an adaptive learning method framework based on physical expressions according to an embodiment of the present invention;

[0041] Figure 2 This is a schematic diagram of the sensitivity calculation and test values ​​in an embodiment of the present invention;

[0042] Figure 3 This is a schematic diagram of the average value curve of the UV function input parameters and the sensitivity error curve in an embodiment of the present invention;

[0043] Figure 4 This is a schematic diagram of the FM modulation sensitivity curve output by the adaptive learning algorithm based on physical expressions in an embodiment of the present invention. Detailed Implementation

[0044] The present invention will be further described in conjunction with the accompanying drawings and embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art should fall within the protection scope of the present invention.

[0045] See Figure 1This invention provides an embodiment of an adaptive learning method based on physical expressions, which includes the following steps:

[0046] Step 1: Obtain the sampling data at the current moment and input it into the physics expression module to obtain the sampling output data at the current moment;

[0047] Step 2: Input the expected output data at the current time and the sampled output data at the current time into the root mean square error module;

[0048] Step 3: The root mean square error module calculates the root mean square error corresponding to the current time based on the input data. Depending on whether the root mean square error meets the requirements, it determines whether to use the current sampled output data of the physical expression module as the final data output of the physical expression module, or to input the root mean square error into the adaptive learning algorithm module.

[0049] Step 4: The adaptive learning algorithm module calculates the weight value at the current time based on the input root mean square error, and calculates the weight value at the next time based on the weight value at the current time, and replaces the weight value in the physical expression module with the weight value at the next time.

[0050] Step 5: Use the sampled data of the next time moment as the sampled data of the current time moment, and repeat steps 1 to 5 until the root mean square error output by the root mean square error module meets the requirements.

[0051] In this embodiment, step 1 includes:

[0052] For applications requiring data fitting, assuming the input data from n samplings is (a1, b1, ..., q1), (a2, b2, ..., q2), ..., (ak, bk, ..., qk), ..., (an, bn, ..., qn), the desired output data is the target data y1, y2, ..., yk, ..., yn; where the input data is (ak, bk, ..., qk), the corresponding target data is yk. Here, a, b, ..., q represent n different input feature parameters. To obtain an accurate fitting curve for predicting the output of other sampling points, we aim to find a suitable function expression such that the input a, b, ..., q outputs the corresponding test output data y1, y2, ..., yk, ..., yn.

[0053] Let the sampling data at the current moment be (ak, bk, ..., qk), where (ak, bk, ..., qk) is the sampling data for a, b, ..., q at the k-th moment, i.e., the current moment; k is a positive integer representing the sampling point, with a value ranging from 1 to n;

[0054] The sampled data at the current moment is input into the domain-knowledge-based physical expression in the physical expression module to obtain the sampled output data at the current moment, i.e.:

[0055] zk=f(λ1×ak,λ2×bk,…,λm×qk)

[0056] Where f is an analytical expression with physical meaning, λ1, λ2, ..., λm are weight values, which are used to adjust the size of the sampled data at the current time; zk is the sampled output data at the current time.

[0057] In this embodiment, step 3 includes:

[0058] Step 31: When the root mean square error meets the requirements, the current sampled output data zk is used as the output of the physical expression module; when the root mean square error does not meet the requirements, the root mean square error e is... k Send it to the adaptive learning algorithm module;

[0059] Step 32: The adaptive learning algorithm module uses the mean squared error as the cost function, calculates the partial derivatives with respect to λ1, λ2, ..., λm, and then sets the partial derivatives to zero to obtain the extreme values ​​of MSE.

[0060] Step 33: Based on step 33, obtain the weight value for the next time step.

[0061] In this embodiment, the root mean square error e k for:

[0062]

[0063] In this embodiment, step 32 specifically includes:

[0064] The adaptive learning algorithm module uses mean squared error as the cost function:

[0065]

[0066] By taking the partial derivative of the above equation with respect to λ1, λ2, ..., λm, and then setting the partial derivative to zero, the extreme values ​​of MSE can be obtained.

[0067] Taking the partial derivative of the above equation, we get:

[0068]

[0069] in, It can be calculated based on the expression f(λ1×aj,λ2×bj,…,λn×qj); λ i (k) represents the i-th weight value at the current time, where i ranges from 1 to m.

[0070] In this embodiment, step 33 specifically includes:

[0071]

[0072] Where η is a fixed parameter representing the learning efficiency, and λ i (k+1) represents the next time step, i.e., the i-th weight value at time k+1.

[0073] In this embodiment, in step 4:

[0074] Replace the m weight values ​​of the domain-knowledge-based physical expression in the physical expression module with the m weight values ​​of the next time step. That is, replace the m weight values ​​of λ1(k+1), λ2(k+1), ... λ at the (k+1)th time step with the weight values ​​of λ1(k+1), ... λ2(k+1), ... λ3(k+1). m (k+1) Feedback enters the expression module, replacing the weight coefficients λ1(k), λ2(k), ... λ of the k-th sampling. m (k).

[0075] The present invention also provides an embodiment of an adaptive learning system based on physical expressions, comprising:

[0076] The physical expression module is used to receive the sampled data at the current moment and obtain the sampled output data at the current moment; and to receive the feedback information that meets the requirements output by the root mean square error module; when the feedback information is received, the sampled output data at the current moment is used as its final data output; it is also used to use the sampled data of the next moment output by the adaptive learning algorithm module as the sampled data of the current moment.

[0077] The root mean square error module is used to calculate the root mean square error between the expected output data received at the current time and the sampled output data at the current time output by the physical expression module. When the root mean square error meets the requirements, it outputs feedback information that meets the requirements to the physical expression module; when the root mean square error does not meet the requirements, it inputs the root mean square error into the adaptive learning algorithm module.

[0078] The adaptive learning algorithm module is used to calculate the weight value at the current time step based on the received root mean square error, calculate the weight value at the next time step based on the weight value at the current time step, and replace the weight value in the physical expression module with the weight value at the next time step.

[0079] In conjunction with specific application scenarios, the present invention also provides a specific embodiment:

[0080] Because integrated aviation electronic information equipment is a comprehensive system, with different functional units implemented by multiple modules, the core indicators of most functional units are determined by the indicators of multiple cascaded modules. Due to the complexity of the parameters of each module and the significant differences in the operating modes of modules within different functional units, the mapping relationship between core functional indicators and module indicators is complex and diverse, influenced by multiple factors such as their own operating modes, operating environment, and testing instruments. Therefore, this study delves into the relationship between core functional indicators and module indicators, explores their physical characteristics, constructs functions to calculate core functional indicators from module indicators, and, based on existing knowledge, gains a deeper understanding of the connections between modules. Furthermore, it explores the relationship between core indicators and module indicators by considering the characteristics of different modules.

[0081] Currently, taking aviation integrated electronic information equipment as the research object, we have selected the sensitivity functional unit of UV, which is representative in terms of business functions, to analyze the correlation between core functional indicators and corresponding module indicators, and established a digital model based on physical expression-based adaptive algorithm.

[0082] 1. The physical expression meaning of the sensitivity index:

[0083] For UV-enabled receiver units, sensitivity is a key parameter for evaluating receiver performance. It measures the receiver's ability to detect signals of a given level, especially small signals. Sensitivity depends on several factors, such as modulation scheme, temperature, intermediate frequency bandwidth, and the required signal-to-noise ratio (SNR) of the demodulator output. The relationship between these factors and receiver sensitivity can be expressed by the following formula:

[0084]

[0085] in: This refers to the required output signal-to-noise ratio during demodulation.

[0086] K: Boltzmann constant, 1.38 × 10⁻⁶ -23 J / K;

[0087] T: Represents absolute temperature, expressed as:

[0088] T = T0 + T K =20 + 273.15(K)

[0089] T0: Room temperature, usually 20°C;

[0090] TK: Absolute temperature, 273.15K;

[0091] B N : Indicates intermediate frequency bandwidth, in Hz;

[0092] NF: Noise figure of the cascaded system, in dB.

[0093] Among the above parameters Related to the modulation method and bit error rate, B N Related to baud rate and technical system, these two parameters remain basically unchanged for different data modulation formats. Therefore, P in the above equation... r The representation is as follows:

[0094]

[0095] For a given system, the bandwidth and signal-to-noise ratio of each signal are already determined, therefore P r The change in noise figure (NF) is mainly related to the cascaded noise figure of the system. This is because noise, which is usually greater than thermal noise, is superimposed in the circuitry of the receiving system. Therefore, circuit noise is often the main limiting factor when detecting small signals. Thus, the receiver's noise figure is a very important parameter and a measure of the magnitude of the additional noise in the receiver circuit. In functional design, the only way to improve sensitivity is to reduce the noise figure. The unit of NF is dB, i.e.:

[0096] NF = 10log 10 (F)

[0097] Where F is the noise factor, which for a receiver refers to the total noise from the antenna to the demodulator output port of the entire receiving circuit. Therefore, it is necessary to keep the noise figure of each stage in the signal link as low as possible. The cascade formula for the noise factor is as follows:

[0098]

[0099] Where F n Let A be the noise factor of the nth stage circuit. n-1 It is the gain factor for the n-1 stage circuit.

[0100] For UV receiving channels, the noise figure we usually refer to is before the nonlinear circuits, i.e., before the detector, including the high-frequency amplifier, frequency converter, and intermediate frequency amplifier. Its greatest impact generally refers to the first one or two stages of the circuitry. Therefore, the above expression can be written as:

[0101]

[0102] Where F UVPA F is the noise factor of the first-stage UVPA circuit. UVRT For the noise factor of the second-stage UVRT circuit, A UVPA This is the gain factor for the first-stage UVPA circuit.

[0103] Substituting the above equation into Pr The physical expression for sensitivity can then be obtained. The UV function sensitivity index is mainly related to the noise of the UVPA and UVRT circuits and the gain of the UVPA circuit.

[0104] 2. Sensitivity test data

[0105] The collected data are shown in Table 1. Each set of test data includes sensitivity data of core functional indicators, noise figure data of UVPA, gain data of UVPA, and noise figure data of UVRT at different frequencies. The data includes 8 sets under the same environment, and only one set is shown here.

[0106] Table 1. Correspondence between UV functional sensitivity indicators and module indicators

[0107]

[0108] 3. Expression analysis and calculation based on test data:

[0109] Using the physical expression, the sampled data is substituted into the calculation, where λ1, λ2, and λ3 are all set to 1:

[0110] According to the table above, the noise figure NF of the UVPA circuit was measured. UVPA The noise figure NF of the UVRT circuit UVTR Gain coefficient G of UVPA circuit UVPA , with F UVPA F UVRT and A UVPA The relationships are as follows:

[0111]

[0112] Multiplying the above equation by the weight coefficients yields λ1F. UVPA ,λ2F UVRT ,λ3A UVPA Substitute it into the noise factor expression:

[0113]

[0114] The noise figure is calculated as follows:

[0115] NF = 10log 10 (F)

[0116] Substitute NF into the sensitivity expression:

[0117]

[0118] 4. Error function:

[0119] Figure 2The test sensitivity Pr' and the calculated sensitivity Pr curve are given, along with the error curves of Pr' and Pr and F. UVPA F UVRT and A UVPA Values ​​such as Figure 3 As shown in the figure, all parameters will be input into the cross-correlation function module. Then we give the root mean square value of the error as 2.74. If this value does not meet the requirements, the data will be sent to the adaptive learning algorithm module.

[0120] 5. Adaptive Learning Algorithm Module:

[0121] According to the weighting coefficient adjustment rules:

[0122]

[0123] The resulting calculation expression is:

[0124]

[0125] 6. Weighting coefficient feedback:

[0126] The weighting coefficients λ1(n+1), λ2(n+1), and λ3(n+1) are obtained and fed back into the expression module to replace the weighting coefficients λ1(n), λ2(n), and λ3(n) of the nth sampling, and then the calculation is performed. This process continues iteratively until the mean square error output by the error module meets the user's requirements. The output result is as follows: Figure 4 As shown, compared with the original calculated curve, the output of this model is closer to the measured curve, and its root mean square error is reduced from 2.74 to 1.23, which meets the user's needs.

[0127] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method of adaptive learning based on physical expressions, characterized by, The method comprises the following steps: Step 1: obtaining the sampling data of the input and output of the UV module of the current time aviation integrated electronic information equipment and inputting the sampling data into the physical expression module to obtain the sampling output data of the current time; the input of the physical expression comprises a modulation mode, a temperature, a middle frequency bandwidth, a signal-to-noise ratio required by a demodulator output and a noise coefficient of a system cascade; the output of the physical expression comprises a sensitivity index of a receiver; Step 2: inputting the expected output data of the current time and the sampling output data of the current time into the root mean square error module; Step 3: the root mean square error module calculates the root mean square error corresponding to the current time based on the input data, and determines whether the sampling output data of the current time of the physical expression module is the final data output of the physical expression module according to whether the root mean square error meets the requirement, or the root mean square error is input into the adaptive learning algorithm module; Step 4: the adaptive learning algorithm module calculates the weight value of the current time according to the input root mean square error, and calculates the weight value of the next time according to the weight value of the current time, and replaces the weight value in the physical expression module with the weight value of the next time; Step 5: taking the sampling data of the next time as the sampling data of the current time, repeating steps 1 to 5 until the root mean square error output by the root mean square error module meets the requirement; The step 3 comprises: Step 31: When the root mean square error meets the requirement, the sampling output data z k of the current time is taken as the output of the physical expression module; when the root mean square error does not meet the requirement, the root mean square error e k is sent to the adaptive learning algorithm module; Step 32: The adaptive learning algorithm module takes the mean square error as a cost function, and obtains the optimal values of λ1, λ2, …, λ m The partial derivative is obtained, and the partial derivative is equal to zero to obtain the MSE extreme value; Step 33: obtaining the weight value of the next time according to step 33; The step 32 is specifically: The adaptive learning algorithm module takes the mean square error as a cost function: The above formula is applied to λ1, λ2, …, λ m The partial derivative is obtained, and the partial derivative is equal to zero to obtain the MSE extreme value; Taking the partial derivative of the above formula, we can get: wherein, The calculation can be performed according to the expression of f (λ1×aj, λ2×bj, …, λ m qj); λ i (k) is the i-th weight value at the current moment, and i ranges from 1 to m. The step 33 is specifically: wherein η is the learning efficiency, which is a fixed parameter, λ i (k+1) is the i-th weight value at the next time, i.e. at time k+1.

2. The method of claim 1, wherein, The step 1 comprises: Let the sampling data of the current time be (ak, bk, …, qk), wherein (ak, bk, …, qk) is the sampling data of a, b, …, q at the kth time, i.e. the current time; k is a positive integer, and the value range is 1 to n; Inputting the sampling data of the current time into the physical expression based on the domain knowledge in the physical expression module to obtain the sampling output data of the current time, i.e. z k = f(λ1×ak, λ2×bk,..., λ m ×qk) Wherein, f is an analytical expression with physical meaning, λ1, λ2, …, λ m is a weight value, through which the size of the sampling data at the current moment is adjusted; z k is the sampling output data at the current moment.

3. The method of claim 2, wherein, The root mean square error e k is:

4. The method of claim 1, wherein, In step 4: Replace the m weight values of the physical expression based on the domain knowledge in the physical expression module with the m weight values of the next time.

5. A physical expression based adaptive learning system implementing the method of any of claims 1-4, characterized by, Comprise: The physical expression module is used for receiving the sampling data of the current time and obtaining the sampling output data of the current time; And receiving the feedback information meeting the requirement output by the root mean square error module; When the feedback information is received, the sampling output data of the current time is taken as the final data output thereof; Also used for taking the sampling data of the next time output by the adaptive learning algorithm module as the sampling data of the current time; The root mean square error module is used for calculating the root mean square error of the expected output data of the current time and the sampling output data of the current time output by the physical expression module, and outputting the feedback information meeting the requirement to the physical expression module when the root mean square error meets the requirement; When the root mean square error does not meet the requirement, the root mean square error is input into the adaptive learning algorithm module; An adaptive learning algorithm module is configured to calculate the weight value at the current time according to the received root mean square error, and to calculate the weight value at the next time according to the weight value at the current time, and to replace the weight value in the physical expression module with the weight value at the next time.

Images