Transformer fractional order parameter online identification method based on adam-sgd fractional order neural network

Abstract

The application discloses an online identification method for fractional order parameters of a transformer based on an Adam-SGD fractional order neural network, and comprises the following steps: acquiring a fractional order state equation representing dynamic characteristics of capacitors and inductors of a DC-DC transformer; establishing a fractional order discrete recursive model based on GL fractional order calculus definition; constructing a neural network structure according to a recursive relationship of capacitor voltage and inductor current in the discrete model, taking actually collected voltage and current values as reference values, taking neural network output as estimated values, and constructing a mean square error loss function; performing gradient calculation and weight updating on the loss function by using an Adam-SGD optimization algorithm, and online adjusting neural network weights; and calculating and outputting parameters of the capacitors and the inductors in real time according to the established fractional order discrete model and the obtained weights. When the weights are updated, the application adopts an adaptive switching mechanism of Adam-SGD, and has the rapid convergence ability of Adam and the stable and fine optimization ability of SGD, so that the efficiency and reliability of online training of the fractional order neural network are significantly improved.

Description

Technical Field

[0001] This invention relates to the field of power electronics technology, and in particular to an online identification method for converter fractional parameters based on Adam-SGD fractional neural network. This method is based on fractional neural network online estimation technology and can achieve high-precision parameter identification under the steady-state normal operation conditions of the system. Background Technology

[0002] With the increasing global emphasis on sustainable energy solutions, renewable energy technologies have made significant progress. In modern energy infrastructure, the grid-connected scale of photovoltaic power generation systems, wind power generation systems, and electric vehicle power systems continues to expand, making DC-DC converters an indispensable and crucial component. Their performance—especially efficiency and stability—largely depends on the condition of core components such as capacitors. As easily aging components, capacitors exhibit gradual changes in their capacitance (C), equivalent series resistance (ESR), and even fractional-order characteristics that characterize non-ideal dynamic behavior during operation. Without effective monitoring, such degradation can lead to increased ripple voltage, decreased efficiency, and even system failure. Therefore, capacitor parameter identification research has received considerable attention in recent years and is of great significance for improving system operational reliability.

[0003] Capacitor identification methods can be broadly categorized into online and offline methods. While offline methods can achieve high-precision parameter measurements, they require system shutdown, making them unsuitable for scenarios demanding continuous operation. For example, some methods utilize impedance vector analysis under sinusoidal voltage excitation to determine ESR and capacitance values; others are based on the charging / discharging circuit structure and employ the LMS algorithm to achieve offline estimation of capacitance parameters. Furthermore, since capacitor aging often dynamically changes with actual operating conditions such as temperature and ripple current, offline methods cannot track their degradation trends in real time. This limitation significantly affects their applicability in practical engineering.

[0004] Against this backdrop, online parameter identification technology has become a key path to achieving "on-the-fly diagnosis." In recent years, research has proposed online fractional-order parameter identification methods based on neural networks. However, existing technologies only combine gradient descent algorithms for online parameter identification, which presents certain problems under steady-state normal operating conditions. During steady-state normal operation, variables such as input voltage, load current, and duty cycle change slowly, the excitation signal is weak, and the signal-to-noise ratio of the neural network input data is low. Traditional gradient descent algorithms are more prone to getting stuck in local convergence or convergence stagnation, leading to distorted identification results or failure to converge.

[0005] Meanwhile, although the Adam (Adaptive Moment Estimation) optimization algorithm has been widely proven in the field of deep learning to possess advantages such as adaptive learning rate, momentum accumulation, and second-order moment correction in non-convex optimization, effectively improving convergence speed and stability, its application in online fractional-order parameter identification of power electronic systems has not yet been explored. Especially under the stringent conditions of not requiring external excitation and relying solely on steady-state operating data, how to synergistically integrate Adam and SGD to construct a hybrid optimization mechanism that combines "fast global convergence" and "fine-grained local search" remains a technological gap that urgently needs to be overcome in this field.

[0006] In summary, while existing technologies have achieved initial breakthroughs in "undisturbed fractional-order parameter identification under steady-state conditions," they remain limited by the singularity and static nature of optimization algorithms, making it difficult to achieve fast, stable, and high-precision online identification under complex operating conditions characterized by low excitation, high noise, and multi-parameter coupling. Therefore, a novel online identification method integrating fractional-order modeling and the Adam-SGD hybrid optimization mechanism is urgently needed to achieve adaptive, robust, and real-time joint estimation of the four-dimensional parameters (Cα, α, Lβ, β) of fractional-order capacitance and inductance without interfering with normal system operation. Summary of the Invention

[0007] To address the problems of existing technologies, this invention proposes an online identification method for fractional-order parameters of DC-DC converters based on an Adam-SGD fractional-order neural network. This method enables simultaneous online identification of capacitor and inductor parameters of DC-DC converters during steady-state operation. The hybrid optimization strategy combining Adam and SGD utilizes the Adam algorithm for rapid approximation in the early stages of training, and automatically switches to the SGD algorithm for fine-tuning when the optimal solution is approached. This collaboratively resolves the contradiction between convergence speed and convergence stability.

[0008] The technical solution adopted by this invention to solve its technical problem is:

[0009] An online method for identifying fractional-order parameters of a DC-DC converter based on an Adam-SGD fractional-order neural network can achieve parameter identification under the condition of steady-state normal operation of the DC-DC converter. The method includes:

[0010] For the DC-DC converter, a fractional-order equivalent circuit model is established for modal analysis to obtain fractional-order state equations characterizing the dynamic characteristics of capacitors and inductors.

[0011] Based on the fractional-order state equation and the definition of fractional-order calculus in GL, a fractional-order discretized recursive model of the DC-DC converter is established.

[0012] Based on the recursive relationship between capacitor voltage and current in the fractional-order discretized recursive model, a fractional-order encoded neural network is constructed. The actual collected voltage and current data are used as reference values, and the voltage and current output by the neural network are used as predicted values. A loss function based on the mean square error of the predicted values ​​and reference values ​​is constructed.

[0013] Taking the partial derivative of the loss function yields the gradient expressions for each weight in the neural network. A strategy combining the Adaptive Moments Estimation Method (Adam) and the Stochastic Gradient Descent Method (SGD) is employed to achieve rapid online updates of the neural network weights. Specifically, when the gradient descent distance G is greater than a preset threshold ρ, the Adam method is used iteratively to quickly reduce the loss function; otherwise, the system automatically switches to the Stochastic Gradient Descent Method (SGD) with momentum for precise fine-tuning until the convergence condition is met.

[0014] Based on the established fractional-order discretized recursive model and the identified weight parameters, the capacitance and order of the fractional-order capacitor, as well as the inductance and order of the fractional-order inductor, are calculated and output in real time.

[0015] Preferably, in the Adam adaptive moment estimation method, the weight parameters... The iterative update expression is as follows:

[0016] ;

[0017] in, This represents the weight in the (k+1)th iteration; This represents the weight in the k-th iteration; This represents Adam's learning rate. The value range is [1x10]. -6 1x10 -2 ]; This represents the first-order moment estimate after bias correction in the k-th iteration; This represents the second-order moment estimate after bias correction in the k-th iteration; It is a small constant added for numerical stability;

[0018] The bias-corrected first-order moment estimates and bias-corrected second-order moment estimates are expressed as follows:

[0019] ;

[0020] in, This represents the first-moment estimate in the (k-1)th iteration; This represents the second-order moment estimate for the (k-1)th iteration; and denoted as the exponential decay rates of the first-moment estimate and the second-moment estimate, respectively;

[0021] The first-order moment estimate and the second-order moment estimate are expressed as follows:

[0022] ;

[0023] in, This represents the first-order moment estimate for the k-th iteration; This represents the second-order moment estimate for the k-th iteration; Indicates J to The partial derivative of .

[0024] Preferred, and The values ​​of are all in the range [0.9, 0.999]; the values ​​of ε are in the range [1x10]. -10 1x10 -4 ].

[0025] Preferably, the preset threshold ρ ranges from [1x10] to

[10] . -4 1x10 -3 ].

[0026] Preferably, in the stochastic gradient descent (SGD) method, each weight parameter... The iterative update expression is as follows:

[0027] ;

[0028] in, This represents the weight in the (k+1)th iteration; This represents the weight in the k-th iteration; This represents the learning rate of SGD. The value range is [1x10]. -6 1x10 -2 ]; Indicates J to The partial derivative of .

[0029] Preferably, taking a DC-DC converter as the object, and the inductor current i L and capacitor voltage V c For the state variables, the fractional-order state equations are established as follows:

[0030] ;

[0031] Among them, i L and V in These are the inductor current and the input voltage, respectively. and These represent the capacitance value and order of a fractional capacitor, respectively. and represents the inductance and order of the fractional inductor, respectively; R is the resistance of the load resistor in the DC-DC circuit; D is the duty cycle and 0≤D≤1; t is the time variable.

[0032] Preferably, the fractional-order discretized recursive model of the DC-DC converter, based on the fractional-order state equation and the definition of fractional-order calculus in GL, is expressed as follows:

[0033] ;

[0034] Among them, i L (k+1), V c (k+1) and i L (k), V c (k) represents the average value of inductor current and capacitor voltage in the (k+1)th switching cycle and the average value of inductor current and output voltage in the kth switching cycle, respectively; T is the sampling period; j is an integer in the range [0, k]. is the coefficient of Newton's generalized binomial; N is the memory length.

[0035] As can be seen from the above description of the present invention, compared with the prior art, the present invention has the following beneficial effects:

[0036] (1) Adam-SGD Optimized Fractional Neural Network: This invention proposes a hybrid optimization strategy combining Adam and SGD. This strategy, through an adaptive switching mechanism, combines the fast convergence capability of Adam with the stable and fine optimization capability of SGD, thereby improving the fast convergence and fine optimization capability in the fractional identification process of the entire DC-DC converter. This significantly improves the efficiency and reliability of online training of fractional neural networks. Traditional SGD methods have slow convergence speed in the early stage of training and require a large number of iterations to approach the optimal solution, which is difficult to meet the real-time requirements of online identification. Compared with simply using SGD for parameter identification, the Adam-SGD hybrid strategy proposed in this invention uses the Adam algorithm to achieve fast convergence in the early stage of training. After the gradient descent distance reaches the threshold, it automatically switches to SGD for fine-tuning, which overcomes the slow convergence of SGD and avoids the oscillation problem that Adam may cause in the fine-tuning stage.

[0037] (2) Non-invasive high-precision identification: No special test signal or system interruption is required. High-precision parameter estimation can be achieved using only the voltage and current data during normal operation. This overcomes the limitations of traditional online identification methods that rely on system dynamics or external injection. It is low-cost, easy to integrate, and has high identification accuracy.

[0038] (3) Steady-state operation and identification coordination: The parameter identification process is carried out synchronously with the steady-state operation of the system. No additional excitation signal is required, and the normal operation of the converter is not affected. The computational burden is significantly reduced, and effective technical support is provided for component status monitoring, aging assessment and online tuning of control parameters.

[0039] (4) Engineering practicality and scalability: The proposed method has a clear structure and is easy to implement on existing digital control platforms such as DSP. It does not require hardware modification and can be extended to various DC-DC converter topologies, thus having broad engineering application prospects. Attached Figure Description

[0040] Figure 1 This is a topology diagram of the fractional-order equivalent circuit model of the Buck converter according to an embodiment of the present invention;

[0041] Figure 2 This is a control and parameter identification structure diagram of the Buck converter according to an embodiment of the present invention;

[0042] Figure 3 This is a flowchart illustrating the parameter identification process in an embodiment of the present invention.

[0043] Figure 4 The following are schematic diagrams of simulation results for embodiments of the present invention: (a) capacitor voltage convergence curve; (b) capacitance value identification result; (c) order identification result;

[0044] Where S: the switching transistor in the Buck circuit, and D: the diode in the Buck circuit. Fractional inductance in a Buck circuit R: Fractional capacitance of the Buck circuit; V: Resistance of the Buck circuit load resistor. in Input voltage, V c : Capacitor voltage. Detailed Implementation

[0045] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0046] In the description of this invention, it should be noted that the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0047] like Figure 1 As shown in this embodiment, an online identification method for fractional-order converter parameters based on the Adam-SGD fractional-order neural network can achieve parameter identification under the condition that the system (including DC-DC converters, such as photovoltaic power generation systems, wind power generation systems, and electric vehicle power systems) maintains steady-state normal operation. The method includes:

[0048] For the DC-DC converter, a fractional-order equivalent circuit model is established for modal analysis to obtain fractional-order state equations characterizing the dynamic characteristics of capacitors and inductors.

[0049] Based on the fractional-order state equation and the definition of fractional-order calculus in GL, a fractional-order discretized recursive model of the DC-DC converter is established.

[0050] Based on the recursive relationship between capacitor voltage and current in the fractional-order discretized recursive model, a fractional-order encoded neural network is constructed. The actual collected voltage and current data are used as reference values, and the voltage and current output by the neural network are used as predicted values. A loss function based on the mean square error of the predicted values ​​and reference values ​​is constructed.

[0051] Taking the partial derivative of the loss function yields the gradient expressions for each weight in the neural network. A strategy combining the Adaptive Moments Estimation Method (Adam) and the Stochastic Gradient Descent Method (SGD) is employed to achieve rapid online updates of the neural network weights. Specifically, when the gradient descent distance G is greater than a preset threshold ρ, the Adam method is used iteratively to quickly reduce the loss function; otherwise, the system automatically switches to the Stochastic Gradient Descent Method (SGD) with momentum for precise fine-tuning until the convergence condition is met.

[0052] Based on the established fractional-order discretized recursive model and the identified weight parameters, the capacitance and order of the fractional-order capacitor, as well as the inductance and order of the fractional-order inductor, are calculated and output in real time.

[0053] Specifically, such as Figure 1As shown, this embodiment uses a Buck converter as an example for illustration. The fractional-order model of the Buck converter circuit consists of a voltage source V in Switch S, diode D, fractional-order inductor Fractional capacitance C α It consists of a load resistor R and a switching transistor S. One end of the switching transistor S is connected to a voltage source V. in One end is at the positive terminal; the other end is at the negative terminal of diode D and the fractional-order inductor. One end of the fractional inductor is connected to the other end of the fractional capacitor C. α One end is connected to a fractional capacitor C. α The other end is simultaneously connected to the positive terminal of diode D and the voltage source V. in The negative terminal connection; the subsequent inverter and the fractional capacitor C α Parallel connection; wherein, the switching transistor S can be a switching device such as a MOSFET or an IGBT.

[0054] like Figure 2 The diagram illustrates an integrated control and parameter identification structure for a Buck converter circuit. This circuit employs a voltage-based single-loop control strategy. While maintaining steady-state system operation, it directly utilizes real-time voltage and current data acquired during the closed-loop control process for parameter identification, achieving a high degree of coordination between operation and identification. This method eliminates the need to interrupt normal system operation or introduce additional test signals, thus enabling high-precision parameter identification during steady-state operation and providing effective support for Buck converter state monitoring and controller optimization.

[0055] like Figure 3 The flowchart illustrating the parameter identification process in this embodiment is shown below, and includes the following steps.

[0056] S1. Buck Transformer Initialization. In the initialization phase, the neural network weights are first set. The initial values ​​are then set, followed by configuration of key algorithm parameters, including memory length N, Adam learning rate λ1 and SGD learning rate λ2, Adam and SGD switching threshold ρ, first-moment estimation exponential decay rate β1 and second-moment estimation exponential decay rate β2, convergence threshold σ, and the number of consecutive convergences n. Finally, the iteration counter count and the first-moment estimate m are set. i (k) and the second moment estimate v i (k) is initialized to 0, completing all preparations before the algorithm starts.

[0057] S2. Data Acquisition and Preprocessing.

[0058] In each switching cycle k, the induced current i generated by the system during steady-state operation is acquired in real time. L (k) Capacitor voltage V c(k) Input voltage V in (k) and duty cycle D data; by performing real-time filtering preprocessing on the above steady-state operating data, noise interference is effectively suppressed while ensuring that the data used is consistent with the steady-state characteristics of the system, providing high-quality input that is directly related to the actual dynamic operation of the system for subsequent parameter identification.

[0059] Specifically, taking the Buck converter as an example, and the inductor current i L and capacitor voltage V c For the state variables, the fractional-order state equations are established as follows:

[0060] ;

[0061] Among them, i L and V in These are the inductor current and the input voltage, respectively. and These represent the capacitance value and order of a fractional capacitor, respectively. and represents the inductance and order of the fractional inductor, respectively; R is the resistance of the load resistor in the DC-DC circuit; D is the duty cycle and 0≤D≤1; t is the time variable.

[0062] Based on the fractional-order state equations and the definition of fractional-order calculus in GL, the fractional-order discretized recursive model of the DC-DC converter is established as follows:

[0063] ;

[0064] Among them, i L (k+1), V c (k+1) and i L (k), V c (k) represents the average value of inductor current and capacitor voltage in the (k+1)th switching cycle and the average value of inductor current and output voltage in the kth switching cycle, respectively; T is the sampling period; j is an integer in the range [0, k]. is the coefficient of Newton's generalized binomial; N is the memory length.

[0065] S3. Forward computation of neural networks.

[0066] Based on the fractional-order discretized recursive model of the Buck converter circuit and the relationship between the input and output of the neural network, the predicted value of the capacitor voltage V is obtained. c * (k+1) and the predicted inductor current i L * The expression for (k+1) is:

[0067] ;

[0068] in, =T α / C α , =α-T α / (RC α ), =(-1) j+1 , =β, =- T β / L β , =DT β / L β , =(-1) j+1 .

[0069] S4. Loss function calculation.

[0070] by and i L The loss function is constructed from the mean squared errors of the predicted and actual values. ,as follows:

[0071] .

[0072] S5. Gradient calculation and weight update.

[0073] To improve the training efficiency and convergence stability of neural networks, this embodiment employs a novel hybrid optimization strategy combining the Adam algorithm and stochastic gradient descent (SGD). This hybrid optimizer uses a two-stage training scheme: first, Adam is used to achieve fast initial convergence, followed by precise fine-tuning using SGD with dynamic range. This method effectively mitigates the potential convergence instability problem of Adam while retaining its adaptive learning rate advantage.

[0074] According to the chain rule, J is related to... The partial derivative can be expressed as:

[0075] ;

[0076] For C α For the identification of α, the range of values ​​for i is 1 ≤ i ≤ N+1, therefore:

[0077] ;

[0078] For neural networks, the output, calculated as the gradient with respect to each weight, is the corresponding input quantity, i.e.:

[0079] ;

[0080] Combining J pairs The partial derivatives yield:

[0081] ;

[0082] For L β For the identification of β, the range of values ​​for i is N+2≤i≤2N+3, therefore:

[0083] ;

[0084] In the Adam algorithm, the first moment estimate (the mean of the gradient) m i (k) and the second moment estimate (unbiased variance of the gradient) v i (k) Update according to the following formula:

[0085] ;

[0086] in, and β1 and β2 represent the exponential decay rates of the first-order and second-order moment estimates, respectively. β1 ranges from [0.9, 0.999]. The closer β1 is to 1, the greater the influence of historical gradient directions, resulting in stronger inertia and helping to accelerate along stable gradient directions, but potentially slowing down the response to changes in gradient direction. β2 ranges from [0.9, 0.9999]. The closer β2 is to 1, the stronger the dependence on the squared values ​​of past gradients, used to adaptively adjust the learning rate of each parameter, making it more stable for sparse features. After updating the moment estimates, bias correction is used to offset their initial zero bias. This process can be expressed by the following mathematical formula:

[0087] ;

[0088] As the iteration number k increases, both (1-β1ᵏ) and (1-β2ᵏ) asymptotically approach 1. At this point, the parameter update formula for the Adam algorithm can be simplified to:

[0089] ;

[0090] Where λ1 represents the Adam learning rate, and its value ranges from [1x10]. -6 1x10 -2 The specific value is adjusted according to the actual neural network training results; ε is a small constant added for numerical stability, and its value range is...

[0091] [1x10] -10 1x10 -4 In practice, it is usually taken as 1x10. -8 .

[0092] The descent distance G along the gradient direction in each iteration can be expressed as:

[0093] ;

[0094] When the gradient magnitude G falls below a preset threshold ρ, the algorithm automatically switches from Adam optimization to SGD optimization. This adaptive switching mechanism fully leverages the advantages of the two optimizers at different convergence stages, thereby ensuring that the training process always maintains optimal dynamic performance.

[0095] In this embodiment, the preset threshold ρ ranges from [1x10] to

[10] . -4 1x10 -3 This range is determined based on the gradient magnitude characteristics of fractional neural networks in steady-state identification tasks: the gradient magnitude G is within 10 during the initial iteration phase. -3 ~10 -2 The magnitude is so large that Adam needs to lead the convergence quickly; after entering the neighborhood of the optimal solution, G drops to 10. -4 Next, switch to SGD fine-tuning. If ρ > 10 -3 Switching too early will cause the convergence speed to decrease by about 40%, if ρ < 10. -4 If the switching is too late, the recognition accuracy will deteriorate by about 30%. Therefore, this range is a key design parameter for achieving fast Adam convergence and stable SGD optimization adaptive switching.

[0096] In the SGD algorithm, the iterative update expression for each weight parameter at step k can be expressed mathematically as follows:

[0097] ;

[0098] in, This represents the learning rate of SGD. The value range is [1x10]. -6 1x10 -2 ].

[0099] S6. Parameter inverse solution and output.

[0100] After obtaining the weights, through and (Choose any two that contain the parameters to be identified) The expression (that is) is sufficient. and By performing an inverse solution, we can obtain estimates of the capacitance and order:

[0101] ;

[0102] pass and L can be solved in reverse β The estimated values ​​for β are:

[0103] ;

[0104] S7. Convergence judgment.

[0105] To avoid coincidences, a counter is set. When the iterative descent distance G is less than the set error σ, the counter is incremented by one. The iteration stops only when G < σ for n consecutive times.

[0106] The fractional-order simulation parameters of the Buck circuit are shown in Table 1, with the input voltage V... in =50V, fractional inductance L β =0.001 fractional capacitance C α =0.3899 Switching frequency f s The frequency is 10kHz, the sampling period is T=0.00001s, and the capacitor voltage is V. c =30V, maintain steady-state operation when the Buck circuit is running normally, and start online identification of inductor and capacitor parameters according to the above steps at a certain moment while the inverter operating state remains unchanged.

[0107] like Figure 4 The figure shown is a schematic diagram of the simulation results of an embodiment of the present invention. Figure 4 (a) shows the actual capacitor voltage V. c Compared with the predicted value The convergence process is described. Simulation results show that the predicted output voltage is 0 at the initial moment, and this method utilizes the difference between this initial predicted value and the actual measured value to achieve parameter identification. Waveform analysis further confirms that the bus voltage remains stable during normal system operation. This parameter identification program maintains reliable initialization capability in all steady-state operation phases of the converter. Figure 4 (b) and Figure 4 (c) shows the parameter C respectively. α The identification results for α and C are given. Before the identification algorithm starts, the program is inactive, and both parameters retain their initial values. After starting the identification, the algorithm converges after 30 iterations (equivalent to 0.003 seconds). α And α are stable at approximately 0.3928. The values ​​are 0.3447 and 0.3447, corresponding to relative errors of 0.74% and 0.61%, respectively. In the initial stage of the identification process, V... c and There was a significant error between the two curves; however, as the number of iterations increased, this error gradually decreased, and the two curves eventually converged. After stabilization, the voltage deviation remained within 20mV for most of the operating time.

[0108] Table 1. Simulation parameters of the fractional-order model;

[0109]

[0110] The above embodiments illustrate the basic principles and implementation methods of the present invention, aiming to help understand the core concept and key steps of the invention. It should be understood that these embodiments are merely examples and do not limit the scope of application of the present invention. Those skilled in the art, based on their understanding of the concept of the present invention, can make various equivalent improvements to specific steps, parameter configurations, or system structures. These improvements also fall within the protection scope of the present invention, as defined in the appended claims.

[0111] The above embodiments illustrate the basic principles and implementation methods of the present invention, aiming to help understand the core concept and key steps of the invention. It should be understood that these embodiments are merely examples and do not limit the scope of application of the present invention. Those skilled in the art, based on their understanding of the concept of the present invention, can make various equivalent improvements to specific steps, parameter configurations, or system structures. These improvements also fall within the protection scope of the present invention, as defined in the appended claims.

Claims

1. A method for online identification of fractional-order parameters of a converter based on an Adam-SGD fractional-order neural network, characterized in that, Parameter identification can be achieved under the condition that the system maintains steady-state normal operation. Methods include: For the DC-DC converter, a fractional-order equivalent circuit model is established for modal analysis to obtain fractional-order state equations characterizing the dynamic characteristics of capacitors and inductors. Based on the fractional-order state equation and the definition of fractional-order calculus in GL, a fractional-order discretized recursive model of the DC-DC converter is established. Based on the recursive relationship between capacitor voltage and current in the fractional-order discretized recursive model, a fractional-order encoded neural network is constructed. The actual collected voltage and current data are used as reference values, and the voltage and current output by the neural network are used as predicted values. A loss function based on the mean square error of the predicted values ​​and reference values ​​is constructed. Taking the partial derivative of the loss function yields the gradient expressions for each weight in the neural network. A strategy combining the Adaptive Moments Estimation Method (Adam) and the Stochastic Gradient Descent Method (SGD) is employed to achieve rapid online updates of the neural network weights. Specifically, when the gradient descent distance G is greater than a preset threshold ρ, the Adam method is used iteratively to quickly reduce the loss function; otherwise, the system automatically switches to the Stochastic Gradient Descent Method (SGD) with momentum for precise fine-tuning until the convergence condition is met. Based on the established fractional-order discretized recursive model and the identified weight parameters, the capacitance and order of the fractional-order capacitor, as well as the inductance and order of the fractional-order inductor, are calculated and output in real time.

2. The online identification method for converter fractional-order parameters based on Adam-SGD fractional-order neural network according to claim 1, characterized in that, In the Adam adaptive moment estimation method, the weight parameters The iterative update expression is as follows: ； in, This represents the weight in the (k+1)th iteration; This represents the weight in the k-th iteration; This represents Adam's learning rate. The value range is [1x10]. -6 1x10 -2 ]; This represents the first-order moment estimate after bias correction in the k-th iteration; This represents the second-order moment estimate after bias correction in the k-th iteration; It is a small constant added for numerical stability; The bias-corrected first-order moment estimates and bias-corrected second-order moment estimates are expressed as follows: ； in, This represents the first-moment estimate in the (k-1)th iteration; This represents the second-order moment estimate for the (k-1)th iteration; and denoted as the exponential decay rates of the first-moment estimate and the second-moment estimate, respectively; The first-order moment estimate and the second-order moment estimate are expressed as follows: ； in, This represents the first-order moment estimate for the k-th iteration; This represents the second-order moment estimate for the k-th iteration; Indicates J to The partial derivative of .

3. The online identification method for converter fractional-order parameters based on Adam-SGD fractional-order neural network according to claim 2, characterized in that, and The values ​​of are all in the range [0.9, 0.999]; the values ​​of ε are in the range [1x10]. -10 1x10 -4 ].

4. The online identification method for converter fractional-order parameters based on Adam-SGD fractional-order neural network according to claim 1, characterized in that, The preset threshold ρ has a value range of [1x10]. -4 1x10 -3 ].

5. The online identification method for converter fractional-order parameters based on Adam-SGD fractional-order neural network according to claim 1, characterized in that, The stochastic gradient descent (SGD) method, with its various weight parameters... The iterative update expression is as follows: ； in, This represents the weight in the (k+1)th iteration; This represents the weight in the k-th iteration; This represents the learning rate of SGD. The value range is [1x10]. -6 1x10 -2 ]; Indicates J to The partial derivative of .

6. The online identification method for converter fractional-order parameters based on Adam-SGD fractional-order neural network according to claim 1, characterized in that, Taking a DC-DC converter as an example, and the inductor current i L and capacitor voltage V c For the state variables, the fractional-order state equations are established as follows: ； Among them, i L and V in These are the inductor current and the input voltage, respectively. and These represent the capacitance value and order of a fractional capacitor, respectively. and represents the inductance and order of the fractional inductor, respectively; R is the resistance of the load resistor in the DC-DC circuit; D is the duty cycle and 0≤D≤1; t is the time variable.

7. The online identification method for converter fractional-order parameters based on Adam-SGD fractional-order neural network according to claim 1, characterized in that, Based on the fractional-order state equations and the definition of fractional-order calculus in GL, the fractional-order discretized recursive model of the DC-DC converter is established as follows: ； Among them, i L (k+1), V c (k+1) and i L (k), V c (k) represents the average value of inductor current and capacitor voltage in the (k+1)th switching cycle and the average value of inductor current and output voltage in the kth switching cycle, respectively; T is the sampling period; j is an integer in the range [0, k]. is the coefficient of Newton's generalized binomial; N is the memory length.

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