A particle energy spectrum inversion method and system based on double canonical coefficients

Abstract

The present application discloses a particle energy spectrum inversion method and system based on dual regularization coefficients, so as to achieve the purpose of inverting the electron and proton energy spectra at one time while using less detection equipment. The detector is a single detector that detects electrons and protons simultaneously. The method comprises: generating a first inversion model based on the detector; wherein the first inversion model includes a local relaxation coefficient and a dual regularization coefficient, and the dual regularization coefficient includes a first regularization coefficient corresponding to electrons and a second regularization coefficient corresponding to protons; presetting a local relaxation coefficient set and a dual regularization coefficient set of the dual regularization coefficients; based on the local relaxation coefficient set and the dual regularization coefficient set, iteratively calculating the first inversion model using a Boosted‑Gold algorithm based on the dual regularization coefficients, recording the energy spectrum norm and residual norm that meet the preset convergence conditions; generating an L curve based on the spectrum norm and the residual norm, and taking the inflection point of the L curve as the optimal inversion solution.

Description

Technical Field

[0001] The present application relates to the technical field of space high-energy particle detection, and in particular to a particle energy spectrum inversion method and system based on double canonical coefficients. Background Art

[0002] Charged particle radiation in the space environment is mainly composed of electrons and protons. Both types of particles use the mechanism of energy loss after the particles are incident and interact with the sensor material, generating ionization excitation in the material for detection. Without taking special measures, both electrons and protons will produce responses in the proton-electron load, that is, there is contamination between them. The inversion of high-energy electron energy spectrum faces multiple technical difficulties. First, the interference between electron and proton signals is one of the main challenges. The proton signal may be confused with the electron signal in the detector, affecting the inversion accuracy. Secondly, the energy deposition of high-energy electrons of a single energy in the detector has the uncertainty of Gaussian distribution, which leads to the overlap of the deposition energy spectra of electrons of different energies, increasing the complexity of the inversion.

[0003] Due to the limitations of the accelerator beam conditions, data acquisition across the entire energy range cannot be performed, requiring GEANT4 Monte Carlo simulation. Existing Monte Carlo simulation-based particle inversion relies on using separate detectors to collect electron and proton signals, then performing inversion separately. Summary of the Invention

[0004] The purpose of this application is to provide a particle energy spectrum inversion method and system based on double canonical coefficients, so as to achieve the purpose of inverting electron and proton energy spectra at one time with less detection equipment.

[0005] In a first aspect, the present application provides a particle energy spectrum inversion method based on a double canonical coefficient, wherein the detector is a single detector that detects electrons and protons simultaneously, and the method comprises:

[0006] Based on the detector, a first inversion model is generated; wherein the first inversion model includes a local relaxation coefficient and a double regularization coefficient, and the double regularization coefficient includes a first regularization coefficient corresponding to electrons and a second regularization coefficient corresponding to protons;

[0007] Presetting a local relaxation coefficient set of the local relaxation coefficient and a dual regularization coefficient set of the dual regularization coefficient, and based on the local relaxation coefficient set and the dual regularization coefficient set, using a Boosted-Gold algorithm based on the dual regularization coefficient to iteratively calculate the first inversion model, and recording an energy spectrum norm and a residual norm that meet a preset convergence condition;

[0008] An L curve is generated based on the spectral norm and the residual norm, and an inflection point of the L curve is used as an optimal inversion solution.

[0009] In a possible embodiment, the iterative calculation of the first inversion model based on the local relaxation coefficient set and the dual regularization coefficient set using the Boosted-Gold algorithm with dual regularization coefficients includes:

[0010] Traversing the set of biregular coefficients;

[0011] When traversing the set of double regularization coefficients, each time the current double regularization coefficient is selected, the local relaxation coefficient is iteratively calculated;

[0012] Iteratively updating the particle energy spectrum in the first inversion model according to a preset preliminary solution based on the current biregular coefficient and the current local relaxation coefficient calculated in each iteration;

[0013] Repeat the previous step until the energy spectrum norm and the residual norm that meet the preset convergence condition are obtained when the current regularization coefficient is selected, and record the energy spectrum norm and the residual norm that meet the preset convergence condition when the current regularization coefficient is selected.

[0014] In a possible embodiment, generating the first inversion model includes:

[0015] obtaining an electron response function and a proton response function of the detector;

[0016] determining a response matrix based on the electron response function and the proton response function;

[0017] determining the basic inversion model based on the response matrix and the detection value of the detector;

[0018] Performing transformation based on the basic inversion model to generate the first inversion model;

[0019] The preset preliminary solution of the first inversion model is determined.

[0020] In a possible embodiment, the response matrix is ​​as follows:

[0021] , (1)

[0022] in, is the total number of measurement energy levels, is the total number of electron incident energy channels, is the total number of proton incident energy channels; For electrons in the channel The response function, For protons in the channel Response function of is the number of the measurement energy level, is the number of the incident energy channel, The value range is 1 to The natural number, The value range is 1 to natural numbers;

[0023] The basic inversion model is as follows:

[0024] (2)

[0025] in, is the response matrix, is the electron spectrum or proton spectrum, is the measurement error, is the measured value.

[0026] In a possible embodiment, the first inversion model is formulated as follows:

[0027] (3)

[0028] Among them, A T is the inverse matrix of A; μ is the local relaxation coefficient, which is used to adjust the update amplitude of the solution. Each element is ; is the first regularization coefficient, is the second regularization coefficient; is the particle energy spectrum, is the electron energy spectrum, Proton spectrum.

[0029] In a second aspect, the present application provides a particle energy spectrum inversion system based on a dual canonical coefficient, wherein the detector is a single detector that simultaneously detects electrons and protons, comprising:

[0030] A model unit, configured to generate a first inversion model based on the detector; wherein the first inversion model includes a local relaxation coefficient and a double regularization coefficient, and the double regularization coefficient includes a first regularization coefficient corresponding to electrons and a second regularization coefficient corresponding to protons;

[0031] a processing unit, configured to preset a local relaxation coefficient set of the local relaxation coefficient and a dual regularization coefficient set of the dual regularization coefficient, perform iterative calculations on the first inversion model using a Boosted-Gold algorithm based on the dual regularization coefficients based on the local relaxation coefficient set and the dual regularization coefficient set, and record an energy spectrum norm and a residual norm that meet a preset convergence condition;

[0032] A result unit is used to generate an L curve based on the spectral norm and the residual norm, and take the inflection point of the L curve as the best inversion solution.

[0033] In a possible embodiment, the processing unit performs iterative calculation on the first inversion model, including:

[0034] Traversing the set of biregular coefficients;

[0035] When traversing the set of double regularization coefficients, each time the current double regularization coefficient is selected, the local relaxation coefficient is iteratively calculated;

[0036] Iteratively updating the particle energy spectrum in the first inversion model according to a preset preliminary solution based on the current biregular coefficient and the current local relaxation coefficient calculated in each iteration;

[0037] Repeat the previous step until the energy spectrum norm and the residual norm that meet the preset convergence condition are obtained when the current regularization coefficient is selected, and record the energy spectrum norm and the residual norm that meet the preset convergence condition when the current regularization coefficient is selected.

[0038] In a possible embodiment, the model unit generates the first inversion model, including:

[0039] obtaining an electron response function and a proton response function of the detector;

[0040] determining a response matrix based on the electron response function and the proton response function;

[0041] determining the basic inversion model based on the response matrix and the detection value of the detector;

[0042] Performing transformation based on the basic inversion model to generate the first inversion model;

[0043] The preset preliminary solution of the first inversion model is determined.

[0044] In a possible embodiment, the response matrix is ​​as follows:

[0045] , (1)

[0046] in, is the total number of measurement energy levels, is the total number of electron incident energy channels, is the total number of proton incident energy channels; For electrons in the channel The response function, For protons in the channel Response function of is the number of the measurement energy level, is the number of the incident energy channel, The value range is 1 to The natural number, The value range is 1 to natural numbers;

[0047] The basic inversion model is as follows:

[0048] (2)

[0049] in, is the response matrix, is the electron spectrum or proton spectrum, is the measurement error, is the measured value.

[0050] In a possible embodiment, the first inversion model is formulated as follows:

[0051] (3)

[0052] Among them, A T is the inverse matrix of A; μ is the local relaxation coefficient, which is used to adjust the update amplitude of the solution. Each element is ; is the first regularization coefficient, is the second regularization coefficient; is the particle energy spectrum, is the electron energy spectrum, Proton spectrum.

[0053] The particle energy spectrum inversion method and system based on dual regularization coefficients provided in the embodiments of the present application use a single detector in combination with a particle energy spectrum inversion method based on dual regularization coefficients, thereby reducing the number of detectors and being able to invert the electron and proton energy spectra at one time, thereby improving the inversion efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A flow chart of a particle energy spectrum inversion method based on dual canonical coefficients provided in an embodiment of the present application;

[0055] Figure 2 A flowchart of iterative calculation based on double regular coefficients provided in an embodiment of the present application;

[0056] Figure 3 A flowchart for generating a first inversion model provided in an embodiment of the present application;

[0057] Figure 4 A schematic diagram showing a mapping relationship between the incident energy spectrum and the measured energy spectrum of protons and electrons in a detector provided in an embodiment of the present application;

[0058] Figure 5 A schematic diagram of the L curve provided in an embodiment of the present application;

[0059] Figure 6 A more specific flow chart of the particle energy spectrum inversion method based on double canonical coefficients provided in an embodiment of the present application;

[0060] Figure 7 This is a structural diagram of the particle energy spectrum inversion system based on double canonical coefficients provided in an embodiment of the present application. DETAILED DESCRIPTION

[0061] To make the purpose, technical solutions, and advantages of the embodiments of this application more clear, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. Obviously, the described embodiments are part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0062] like Figure 1 As shown, an embodiment of the present application provides a particle energy spectrum inversion method based on a double canonical coefficient, wherein the detector is a single detector that detects electrons and protons simultaneously, and the method includes:

[0063] 101. Generate a first inversion model based on the detector; wherein the first inversion model includes a local relaxation coefficient and a double regularization coefficient, and the double regularization coefficient includes a first regularization coefficient corresponding to electrons and a second regularization coefficient corresponding to protons.

[0064] 102. A local relaxation coefficient set of a preset local relaxation coefficient and a dual regularization coefficient set of a preset dual regularization coefficient are preset. Based on the local relaxation coefficient set and the dual regularization coefficient set, a Boosted-Gold algorithm based on the dual regularization coefficient is used to iteratively calculate the first inversion model, and the energy spectrum norm and residual norm that meet the preset convergence conditions are recorded.

[0065] 103. Generate an L curve based on the spectral norm and the residual norm, and take the inflection point of the L curve as the best inversion solution.

[0066] In a possible embodiment, Figure 2 As shown, in step 102, based on the local relaxation coefficient set and the double regularization coefficient set, the Boosted-Gold algorithm with the double regularization coefficient is used to iteratively calculate the first inversion model, including:

[0067] 201. Traverse the set of biregular coefficients.

[0068] 202. When traversing the set of biregular coefficients, each time the current biregular coefficient is selected, the local relaxation coefficient is iteratively calculated.

[0069] 203. Based on the current bi-regular coefficient and the current local relaxation coefficient calculated in each iteration, iteratively update the particle energy spectrum in the first inversion model according to a preset preliminary solution.

[0070] 204. Repeat the previous step 203 until the energy spectrum norm and residual norm that meet the preset convergence condition are obtained when the current regularization coefficient is selected, and record the energy spectrum norm and residual norm that meet the preset convergence condition when the current regularization coefficient is selected.

[0071] In a possible embodiment, Figure 3 As shown, the first inversion model is generated, including:

[0072] 301. Obtaining the electron response function and the proton response function of the detector;

[0073] 302. Determine a response matrix based on the electron response function and the proton response function;

[0074] 303. Determine a basic inversion model based on the response matrix and the detection value of the detector;

[0075] 304. Perform transformation based on the basic inversion model to generate a first inversion model;

[0076] 304. Determine a preset preliminary solution of the first inversion model.

[0077] In a possible embodiment, the response matrix is ​​as follows:

[0078] , (1)

[0079] in, is the total number of measurement energy levels, is the total number of electron incident energy channels, is the total number of proton incident energy channels; For electrons in the channel The response function, For protons in the channel Response function. is the number of the measurement energy level, is the number of the incident energy channel, The value range is 1 to The natural number, The value range is 1 to natural numbers;

[0080] The basic inversion model is as follows:

[0081] (2)

[0082] in, is the response matrix, is the electron spectrum or proton spectrum, is the measurement error, is the measured value.

[0083] In a possible embodiment, the first inversion model is formulated as follows:

[0084] (3)

[0085] Among them, A T is the inverse matrix of A; μ is the local relaxation coefficient, which is used to adjust the update amplitude of the solution. Each element is ; is the first regularization coefficient, is the second regularization coefficient; is the particle energy spectrum, is the electron energy spectrum, Proton spectrum.

[0086] It should be noted that is the total number of measurement energy channels, and its value is 、 ,and Under certain circumstances, The number of iterations. In step 203, the specific iteration is based on the preliminary solution (denoted as ) as the starting point, Iterate.

[0087] In order to better understand the particle energy spectrum inversion method based on double regular coefficients provided by this application, combined with Figures 4 to 6 The detailed instructions are as follows:

[0088] like Figure 4 As shown, the proton spectrum It is incident on the high energy electron detector and the interfering proton response probability is , which interferes with proton counting ; Electron spectrum It is incident on the high energy electron detector, and according to the electron response probability (Probability of correct response + probability of incorrect response), which generates an electronic count . Instrument measurement results is the sum of interfering proton counts and electron counts, that is: = + ; Therefore, in high-energy electron detectors, there is a set of mapping relationships between the incident energy spectrum and the measured energy spectrum of protons and electrons.

[0089] To address the response characteristics of protons and electrons in the instrument, a single-instrument proton-electron matrix joint inversion method was used to invert the proton-electron energy spectrum. A Boosted-Gold algorithm based on dual regularization coefficients was proposed. In real-world scenarios, the equations can be simplified, as shown in Equation 2.

[0090] In formula 2 Used to adjust the update amplitude of the solution to avoid excessive updates that lead to unstable convergence.

[0091] Based on practical considerations, there may be two problems: First, the measurement data is often affected by noise, which may cause the inversion results to overfit the noise; second, when using a single instrument to perform proton and electron spectroscopy simultaneously, the system of equations for the spectrum solution is underdetermined, that is, the number of unknowns exceeds the number of equations. In this case, solving the system of equations is prone to numerical instability, resulting in unreliable results. Therefore, in order to obtain a stable solution, the problem is regularized, that is, an additional term is added to the problem to suppress overfitting and falling into local optimal solutions: . Also taking into account, the solution of the equations It is composed of the energy spectrum of electrons and the energy spectrum of protons, so two regularization coefficients are introduced for the actual situation and The purpose is to more flexibly control the stability and smoothness of each part of the solution by acting on the electron energy spectrum and proton energy spectrum respectively. The iterative formula obtained is the first inversion model, as shown in Formula 3:

[0092] (3)

[0093] Regularization coefficient corresponding to the expected result and The L-curve method is used to determine the regularization parameter. The L-curve method is a graphical method for selecting regularization parameters, which is widely used in dealing with underdetermined or ill-conditioned problems. The L-curve is an image drawn on a logarithmic scale. Figure 5 As shown in Figure 1, the horizontal axis is the norm of the solution, and the vertical axis is the norm of the fitting error. At the "corner" of the L-curve, the regularization parameter reaches a balance point. The regularization parameter corresponding to the corner point is generally considered optimal because it strikes the best balance between the norm of the solution (representing the complexity or smoothness of the solution) and the fitting error.

[0094] Based on the above description, combined with the method steps, Figure 6 A flowchart showing a more specific inversion process includes:

[0095] 601. Obtain the electron response function and proton response function of a single detector.

[0096] 602. Determine a response matrix.

[0097] The method includes determining a response matrix based on the electron response function and the proton response function. In a possible embodiment, the response matrix is ​​as shown in Formula 1.

[0098] 603. Determine the basic inversion model.

[0099] The method includes determining a basic inversion model based on the response matrix and the detection value of the detector. In a possible embodiment, the basic inversion model is as shown in Formula 2.

[0100] 604. Generate a first inversion model and determine a preliminary solution.

[0101] The method comprises transforming the basic inversion model, generating a first inversion model and determining a preliminary solution, wherein the first inversion model includes a local relaxation coefficient. , regularization coefficient and .

[0102] 605. Traverse the set of biregular coefficients.

[0103] 606. Each time the current biregular coefficient is selected, the local relaxation coefficient is iteratively calculated. .

[0104] 607. Iteratively update the particle energy spectrum in the first inversion model.

[0105] Including based on the current biregular coefficient and and the current local relaxation coefficient calculated at each iteration , the particle energy spectrum in the first inversion model is iteratively updated according to the preset preliminary solution.

[0106] 608. Check whether the convergence meets the preset conditions.

[0107] If the convergence meets the preset conditions, the energy spectrum norm and residual norm that meet the preset convergence conditions when the current regularization coefficient is recorded; if the convergence does not meet the preset conditions, the iterative calculation of the local relaxation coefficient in step 606 is performed. , until the current regularization coefficient is selected, the energy spectrum norm and residual norm that meet the preset convergence conditions are obtained, and the energy spectrum norm and residual norm that meet the preset convergence conditions when the current regularization coefficient is selected are recorded.

[0108] 609. Check whether the traversal of the double regular coefficient set is completed.

[0109] If yes, proceed to step 610 ; if no, proceed to step 606 .

[0110] 610. Generate an L curve and analyze the L curve to determine the best inversion solution. Norm and residual norm, generate L curve.

[0111] 611. Output energy spectrum.

[0112] like Figure 7 As shown, the present application provides a particle energy spectrum inversion system based on dual canonical coefficients, wherein the detector is a single detector that detects electrons and protons simultaneously, including:

[0113] A model unit 701 is configured to generate a first inversion model based on the detector, wherein the first inversion model includes a local relaxation coefficient and a double regularization coefficient, and the double regularization coefficient includes a first regularization coefficient corresponding to electrons and a second regularization coefficient corresponding to protons;

[0114] A processing unit 702 is configured to preset a local relaxation coefficient set of local relaxation coefficients and a dual regularization coefficient set of dual regularization coefficients, iteratively calculate a first inversion model using a Boosted-Gold algorithm based on the local relaxation coefficient set and the dual regularization coefficient set, and record an energy spectrum norm and a residual norm that meet a preset convergence condition;

[0115] The result unit 703 is used to generate an L curve based on the spectral norm and the residual norm, and use the inflection point of the L curve as the best inversion solution.

[0116] In a possible embodiment, the processing unit 702 performs iterative calculation on the first inversion model, including:

[0117] Traverse the set of biregular coefficients;

[0118] When traversing the set of biregular coefficients, each time the current biregular coefficient is selected, the local relaxation coefficient is iteratively calculated;

[0119] Iteratively updating the particle energy spectrum in the first inversion model according to a preset preliminary solution based on the current biregular coefficient and the current local relaxation coefficient calculated at each iteration;

[0120] Repeat the previous step until the energy spectrum norm and residual norm that meet the preset convergence conditions are obtained when the current regularization coefficient is selected, and record the energy spectrum norm and residual norm that meet the preset convergence conditions when the current regularization coefficient is selected.

[0121] In a possible embodiment, the model unit 701 generates the first inversion model, including:

[0122] Obtain the electron response function and proton response function of the detector;

[0123] Determine a response matrix based on the electron response function and the proton response function;

[0124] Determine the basic inversion model based on the response matrix and the detection value of the detector;

[0125] Performing transformation based on the basic inversion model to generate a first inversion model;

[0126] Determine a preset preliminary solution for the first inversion model.

[0127] In a possible embodiment, the response matrix is ​​as follows:

[0128] , (1)

[0129] in, is the total number of measurement energy levels, is the total number of electron incident energy channels, is the total number of proton incident energy channels; For electrons in the channel The response function, For protons in the channel Response function. is the number of the measurement energy level, is the number of the incident energy channel, The value range is 1 to The natural number, The value range is 1 to natural numbers;

[0130] The basic inversion model is as follows:

[0131] (2)

[0132] in, is the response matrix, is the electron spectrum or proton spectrum, is the measurement error, is the measured value.

[0133] In a possible embodiment, the first inversion model is formulated as follows:

[0134] (3)

[0135] Among them, A T is the inverse matrix of A; μ is the local relaxation coefficient, which is used to adjust the update amplitude of the solution. Each element is ; is the first regularization coefficient, is the second regularization coefficient; is the particle energy spectrum, is the electron energy spectrum, Proton spectrum.

[0136] The particle energy spectrum inversion method and system based on dual regularization coefficients provided in the embodiments of the present application use a single detector in combination with a particle energy spectrum inversion method based on dual regularization coefficients, thereby reducing the number of detectors and being able to invert the electron and proton energy spectra at one time, thereby improving the inversion efficiency.

[0137] It should be understood that the terms used in this application, such as "unit", are a method for distinguishing different components at different levels or different functional divisions. However, if other terms can achieve the same purpose, they may be used in this application to replace the above terms.

[0138] The terms "first" or "second" described in this application are only used to distinguish the relationship between the components, and do not limit them to be necessarily different. If other terms can achieve the same purpose, these other terms may be used in this application to replace the above terms.

[0139] Although the present application has been illustrated and described using specific embodiments, it should be appreciated that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Those skilled in the art should understand that the technical solutions described in the above embodiments may be modified, or some or all of the technical features therein may be replaced by equivalents, without departing from the spirit and scope of the present application. These modifications or replacements do not deviate from the essence of the corresponding technical solutions within the scope of the technical solutions of the embodiments of the present application. Therefore, this means that all such replacements and modifications within the scope of the present application are included in the appended claims.

Claims

1. A particle energy spectrum inversion method based on dual canonical coefficients, wherein the detector is a single detector that detects electrons and protons simultaneously, characterized in that: include: Based on the detector, a first inversion model is generated; wherein the first inversion model includes a local relaxation coefficient and a double regularization coefficient, and the double regularization coefficient includes a first regularization coefficient corresponding to electrons and a second regularization coefficient corresponding to protons; generating the first inversion model includes: obtaining an electron response function and a proton response function of the detector; determining a response matrix based on the electron response function and the proton response function; determining a basic inversion model based on the response matrix and a detection value of the detector; performing a transformation based on the basic inversion model to generate the first inversion model; and determining a preset preliminary solution of the first inversion model; the response matrix is ​​formulated as follows: ， （1） in, is the total number of measurement energy levels, is the total number of electron incident energy channels, is the total number of proton incident energy channels; For electrons in the channel The response function, For protons in the channel Response function of is the number of the measurement energy level, is the number of the incident energy channel, The value range is 1 to The natural number, The value range is 1 to natural numbers; The basic inversion model is as follows: （2） in, is the response matrix, is the electron spectrum or proton spectrum, is the measurement error, is the measured value; The first inversion model is formulated as follows: （3） Among them, A T is the inverse matrix of A; μ is the local relaxation coefficient, which is used to adjust the update amplitude of the solution. Each element is ; is the first regularization coefficient, is the second regularization coefficient; is the particle energy spectrum, is the electron energy spectrum, is the proton spectrum; Presetting a local relaxation coefficient set of the local relaxation coefficient and a dual regularization coefficient set of the dual regularization coefficient, and based on the local relaxation coefficient set and the dual regularization coefficient set, using a Boosted-Gold algorithm based on the dual regularization coefficient to iteratively calculate the first inversion model, and recording an energy spectrum norm and a residual norm that meet a preset convergence condition; An L curve is generated based on the spectral norm and the residual norm, and an inflection point of the L curve is used as an optimal inversion solution.

2. The particle energy spectrum inversion method based on double canonical coefficients according to claim 1, characterized in that: The iterative calculation of the first inversion model based on the local relaxation coefficient set and the dual regularization coefficient set using the Boosted-Gold algorithm with the dual regularization coefficients includes: Traversing the set of biregular coefficients; When traversing the set of double regularization coefficients, each time the current double regularization coefficient is selected, the local relaxation coefficient is iteratively calculated; Iteratively updating the particle energy spectrum in the first inversion model according to a preset preliminary solution based on the current biregular coefficient and the current local relaxation coefficient calculated in each iteration; Repeat the previous step until the energy spectrum norm and the residual norm that meet the preset convergence condition are obtained when the current regularization coefficient is selected, and record the energy spectrum norm and the residual norm that meet the preset convergence condition when the current regularization coefficient is selected.

3. A particle energy spectrum inversion system based on dual canonical coefficients, wherein the detector is a single detector that detects electrons and protons simultaneously, characterized in that: include: A model unit is configured to generate a first inversion model based on the detector; wherein the first inversion model includes a local relaxation coefficient and a double regularization coefficient, and the double regularization coefficient includes a first regularization coefficient corresponding to electrons and a second regularization coefficient corresponding to protons; the model unit generates the first inversion model by: obtaining an electron response function and a proton response function of the detector; determining a response matrix based on the electron response function and the proton response function; determining a basic inversion model based on the response matrix and a detection value of the detector; performing a transformation based on the basic inversion model to generate the first inversion model; and determining a preset preliminary solution of the first inversion model; the response matrix is ​​formulated as follows: ， （1） in, is the total number of measurement energy levels, is the total number of electron incident energy channels, is the total number of proton incident energy channels; For electrons in the channel The response function, For protons in the channel Response function of is the number of the measurement energy level, is the number of the incident energy channel, The value range is 1 to The natural number, The value range is 1 to natural numbers; The basic inversion model is as follows: （2） in, is the response matrix, is the electron spectrum or proton spectrum, is the measurement error, is the measured value; The first inversion model is formulated as follows: （3） Among them, A T is the inverse matrix of A; μ is the local relaxation coefficient, which is used to adjust the update amplitude of the solution. Each element is ; is the first regularization coefficient, is the second regularization coefficient; is the particle energy spectrum, is the electron energy spectrum, is the proton spectrum; a processing unit, configured to preset a local relaxation coefficient set of the local relaxation coefficient and a dual regularization coefficient set of the dual regularization coefficient, perform iterative calculations on the first inversion model using a Boosted-Gold algorithm based on the dual regularization coefficients based on the local relaxation coefficient set and the dual regularization coefficient set, and record an energy spectrum norm and a residual norm that meet a preset convergence condition; A result unit is used to generate an L curve based on the spectral norm and the residual norm, and take the inflection point of the L curve as the best inversion solution.

4. The particle energy spectrum inversion system based on dual canonical coefficients according to claim 3, characterized in that: The processing unit performs iterative calculation on the first inversion model, including: Traversing the set of biregular coefficients; When traversing the set of double regularization coefficients, each time the current double regularization coefficient is selected, the local relaxation coefficient is iteratively calculated; Iteratively updating the particle energy spectrum in the first inversion model according to a preset preliminary solution based on the current biregular coefficient and the current local relaxation coefficient calculated in each iteration; Repeat the previous step until the energy spectrum norm and the residual norm that meet the preset convergence condition are obtained when the current regularization coefficient is selected, and record the energy spectrum norm and the residual norm that meet the preset convergence condition when the current regularization coefficient is selected.

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