High arch dam deformation state fractional order numerical analysis physical and mechanical parameter inversion method and module

Abstract

The invention relates to the technical field of hydraulic structure service behavior analysis and computational mechanics, and particularly discloses a high arch dam deformation behavior fractional order numerical analysis physical and mechanical parameter inversion method and module. A viscoplasticity parameter inversion method is provided based on a Levenberg-Marquardt method by using rheological test data. Optimizing to obtain a to-be-inverted parameter sample combination by means of central composite design; constructing an elastic and viscoelastic parameter inversion objective function in combination with deformation in-situ monitoring data; based on a multiple-input-multiple-output support vector machine, establishing an elastic and viscoelastic parameter inversion agent model; a random inertia weight, an asynchronous change learning factor, golden sine disturbance and differential evolution variation disturbance are introduced to improve a particle swarm algorithm, so that a parameter optimal inversion value search strategy is established. The method aims at improving the accuracy and objectivity of numerical analysis of the deformation state of the high arch dam, provides technical support for in-service engineering safety monitoring and dangerous case early warning, and has wide application prospects and markets.

Description

Technical Field

[0001] The invention belongs to the technical field of service performance analysis and computational mechanics of hydraulic structures, and specifically relates to a physical and mechanical parameter inversion method and module for fractional-order numerical analysis of deformation performance of a high arch dam. Background Art

[0002] The giant project is located in a mountainous canyon area. Its service process is affected by many factors. Its safe operation faces severe challenges. Once it fails, it will cause huge casualties and property losses downstream. Deformation change is a comprehensive reflection of the structural state changes of the high arch dam body and dam foundation. It is an important indicator to measure the safety of the project. It is urgent to establish scientific and effective high arch dam deformation state analysis theory, methods and technology to grasp the real working state of the dam.

[0003] The deformation behavior of high arch dams is closely related to the physical and mechanical properties of the structure. When the external load state changes, the high arch dam first undergoes instantaneous deformation. Under the continuous action of the load, due to the rheological effect of the dam body and the dam foundation, the high arch dam undergoes time-dependent deformation. Scientific characterization of the physical and mechanical properties of high arch dams is the premise and basis for objective quantitative analysis of the deformation behavior of high arch dams. The physical and mechanical properties of high arch dams include elasticity, plasticity, viscoelasticity, viscoplasticity and viscoelastic-plasticity. At present, the analysis model can be summarized as empirical model, component model and theoretical model. Among them, the component model is widely used in practical engineering because of its simple configuration and clear physical meaning. The traditional component model is constructed based on the theory of integer-order calculus, and the series-parallel combination of springs, viscosity pots and sliders is used to characterize the above physical and mechanical properties. Although it has been successfully applied in many fields, it still has certain defects. For example, in order to better fit the rheological test results, the integer-order component model requires more parameters; likewise, the Newton viscosity pot only describes the linear rheological process. It is difficult to characterize the complex nonlinear rheological effects of high arch dams only by using integer-order rheological component models. Fractional-order calculus is a calculus theory that studies the operation order of fractions. The fractional-order rheological component model established based on this theory not only retains the advantages of the classical component model, but also can describe the rheological behavior of high arch dams within a wide frequency range. Based on the fractional-order model, combined with modern research methods and technologies, it is expected to provide an effective way for deformation behavior analysis and monitoring of high arch dams.

[0004] The values ​​of the physical and mechanical parameters of the fractional rheological mechanics element model have a great influence on the correctness and objectivity of the numerical analysis results. The physical and mechanical parameters to be determined include: elastic parameters (such as the instantaneous elastic modulus in the Hooke body), viscoelastic parameters (such as the viscosity coefficient and delayed elastic modulus that characterize the decaying rheology in the fractional Kelvin body) and viscoplastic parameters (such as the viscosity coefficient that characterizes the steady-state rheology and accelerated rheology in the fractional Bingham body). When conducting numerical analysis, the value of the instantaneous elastic modulus has a great influence on the simulation results of the instantaneous deformation of the high arch dam, while the parameters such as the delayed elastic modulus and the viscosity coefficient mainly affect the simulation results of the time-dependent deformation of the high arch dam. At present, there are two ways to invert the physical and mechanical parameters of concrete dams, namely: ① inversion based on rheological test data; ② inversion based on in-situ deformation monitoring data. Summarizing the existing research results, there are relatively few inversion methods for the physical and mechanical parameters of the fractional rheological mechanics element model, and they are concentrated on the inversion of rheological test data. During the operation stage, the physical and mechanical parameters of the dam often differ greatly from the design values ​​and test values. It is not enough to use only the test data for inversion. The integration of rheological tests and in-situ deformation monitoring can determine the physical and mechanical parameters more objectively. During the service process, the high arch dam is in an elastic or viscoelastic state, and may be in a viscoplastic state under special circumstances. Therefore, the viscoplastic parameters can be inverted with the help of rheological test data, and the elastic and viscoelastic parameters can be preliminarily obtained. On this basis, the elastic and viscoelastic parameters can be inverted based on the in-situ deformation monitoring data.

[0005] In summary, combining rheological test data with in-situ deformation monitoring data, applying modern mathematics, mechanics and dam engineering theory, and studying and constructing a physical and mechanical parameter inversion method and module for fractional-order numerical analysis of the deformation properties of high arch dams are key scientific issues and technical bottlenecks that technicians in the field of service performance analysis and computational mechanics of hydraulic structures urgently need to study and solve. Summary of the invention

[0006] In view of this, the present invention provides a physical and mechanical parameter inversion method and module for fractional-order numerical analysis of deformation behavior of high arch dams to solve the bottleneck problem existing in the background technology.

[0007] To achieve the above object, the present invention provides the following technical solutions.

[0008] On the one hand, a method for inversion of physical and mechanical parameters of fractional-order numerical analysis of deformation behavior of high arch dams is provided, including:

[0009] S1. Using Hooke body, fractional Kelvin body, fractional village body, fractional Bingham body and variable parameter fractional Bingham body, a fractional rheological mechanical element model of high arch dam body and foundation is constructed;

[0010] S2. Using rheological test data and based on the Levenberg-Marquardt method, the viscoplastic parameters of the fractional-order rheological mechanical element model are inverted, including:

[0011] S21. Using the attenuated rheological test data and based on the Levenberg-Marquardt method, the elastic and viscoelastic parameters of the Hooke body, fractional Kelvin body, and fractional Murasaki body are preliminarily inverted;

[0012] S22. Using steady-state rheological test data, the viscoplastic parameters of fractional Bingham bodies are inverted based on the Levenberg-Marquardt method.

[0013] S23, using the accelerated rheological test data, based on the Levenberg-Marquardt method, the acceleration parameters of the parameterized fractional Bingham body are inverted;

[0014] S3. Based on the deformation in-situ monitoring data, the elastic parameters of the fractional-order rheological mechanical element model are inverted, including:

[0015] S31. Adopt central composite design to optimize the sample combination of elastic parameters to be inverted, apply reservoir water load using fractional numerical analysis, and simulate the deformation change law of the dam under the sample combination of design parameters;

[0016] S32. Construct a deformation behavior analysis model for the high arch dam body and foundation, and separate the deformation water pressure component from the deformation in-situ monitoring data;

[0017] S33, using the deformation water pressure component, in the order of dam foundation first and dam body later, constructing the elastic parameter inversion objective function of the fractional-order rheological mechanics element model;

[0018] S34, constructing an elastic parameter inversion proxy model using a multi-input multi-output support vector machine;

[0019] S35, introducing random inertia weight, asynchronous change learning factor, golden sine perturbation and differential evolution mutation perturbation, and proposing an improved particle swarm algorithm, thereby establishing a search strategy for the optimal inversion value of elastic parameters;

[0020] S4. Based on the in-situ deformation monitoring data, the viscoelastic parameters of the fractional-order rheological element model are inverted, including:

[0021] S41. Adopt central composite design to optimize the sample combination of viscoelastic parameters to be inverted, apply the main loads borne during operation by fractional numerical analysis, and simulate the deformation change law of the dam under the sample combination of design parameters;

[0022] S42. Using the deformation in-situ monitoring data, construct the viscoelastic parameter inversion objective function of the fractional-order rheological element model of the high arch dam body and foundation;

[0023] S43, using multi-input multi-output support vector machine to construct a viscoelastic parameter inversion proxy model;

[0024] S44. Based on the improved particle swarm algorithm, a search strategy for the optimal inversion value of viscoelastic parameters is established.

[0025] On the other hand, a physical and mechanical parameter inversion module for fractional-order numerical analysis of deformation behavior of high arch dams is provided, including:

[0026] The model building unit is based on the parallel structure design and includes a dam body fractional-order rheological mechanics element model subunit and a dam foundation fractional-order rheological mechanics element model subunit;

[0027] The viscoplastic parameter inversion unit is designed based on a series structure and includes a decaying rheological inversion subunit, a steady-state rheological inversion subunit, and an accelerated rheological inversion subunit;

[0028] The elastic parameter inversion unit is based on the serial structure design and includes the dam body deformation behavior analysis model subunit, the dam foundation deformation behavior analysis model subunit, the elastic parameter sample combination optimization design subunit, the elastic deformation fractional numerical analysis subunit, the elastic parameter inversion proxy model subunit, and the elastic parameter optimal inversion value search subunit;

[0029] The viscoelastic parameter inversion unit is designed based on a series structure and includes a viscoelastic parameter sample combination optimization design subunit, a viscous deformation fractional-order numerical analysis subunit, a viscoelastic parameter inversion proxy model subunit, and a viscoelastic parameter optimal inversion value search subunit;

[0030] The visual display unit outputs results including viscoplastic parameters, elastic parameters, viscoelastic parameters, total deformation, instantaneous deformation, time-dependent deformation, stress and strain, which are presented to the operator in the form of tables, cloud maps, contour maps, distribution maps and process lines.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] (1) Comprehensively utilizing rheological tests and in-situ deformation monitoring data, based on modern mechanics, mathematics and dam engineering theory, a method for inversion of elastic, viscoelastic and viscoplastic parameters for fractional-order numerical analysis of deformation behavior of high arch dams was proposed. Compared with conventional methods, i.e., inversion using test data or in-situ monitoring data, the accuracy of parameter inversion has been improved.

[0033] (2) Based on the central composite design, the sample combination of parameters to be inverted was optimized and obtained. Fractional-order numerical analysis was used to simulate the deformation change law of the dam under the design parameter sample combination. Based on this, a parameter inversion proxy model was constructed using a multi-input and multi-output support vector machine. Compared with conventional methods, this technical method not only ensures the accuracy of the inversion results, but also reduces the workload of finite element calculations.

[0034] (3) Random inertia weights and asynchronous change learning factors realize the adaptive transformation of the particle swarm algorithm from global fast search to local precise search; golden sine perturbations and differential evolution mutation perturbations improve the local escape ability of the algorithm as a whole, greatly reducing the probability of falling into the local optimum; the optimal inversion value search strategy for parameters established on this basis has greatly improved performance;

[0035] (4) The present invention improves the accuracy and objectivity of numerical analysis of deformation properties of high arch dams, provides technical support for safety monitoring of in-service projects and early warning of dangerous situations, and has broad application prospects and markets. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 The implementation process of the physical and mechanical parameter inversion method for fractional-order numerical analysis of deformation behavior of high arch dams provided by the present invention;

[0037] Figure 2 The fractional-order rheological mechanics element model of the dam body provided by the present invention;

[0038] Figure 3 The fractional-order rheological mechanics element model of the dam foundation provided by the present invention;

[0039] Figure 4 The sample combination of parameters to be inverted obtained by optimizing the central composite design with three variables and two levels provided by the present invention;

[0040] Figure 5 The elastic parameter inversion process provided by the present invention;

[0041] Figure 6 The viscoelastic parameter inversion process provided by the present invention;

[0042] Figure 7 The physical and mechanical parameter inversion module architecture of the fractional-order numerical analysis of the deformation behavior of the high arch dam provided by the present invention;

[0043] Figure 8 A three-dimensional finite element model of the Jiagao arch dam provided by the present invention;

[0044] Fig. 9 The material partitioning of the Jiagao arch dam provided by the present invention;

[0045] Fig.10The vertical monitoring point arrangement of the Jiagao arch dam provided by the present invention;

[0046] Fig.11 The deformation water pressure components of IP13-1 and IP16-1 provided by the present invention;

[0047] Fig.12 The relationship curve between the calculated values ​​of the deformation water pressure components of IP13-1 and IP16-1 and the reservoir water level provided by the present invention;

[0048] Fig.13 The relationship between the calculated values ​​of the deformation increments of IP13-1 and IP16-1 provided by the present invention and the instantaneous elastic modulus of the dam foundation;

[0049] Fig.14 The IPSO iteration process provided by the present invention;

[0050] Fig.15 The deformation water pressure components of PL13-1 and PL16-1 provided by the present invention;

[0051] Fig.16 The relationship curve between the calculated values ​​of deformation and hydraulic separation of PL13-1 and PL16-1 and the reservoir water level provided by the present invention;

[0052] Fig.17 Comparison between the separation value of the deformation water pressure component of PL13-1 provided by the present invention and the calculated value;

[0053] Fig.18 The deformation monitoring value process line of PL16-5 and IP16-1 provided by the present invention;

[0054] Fig.19 Comparison between the deformation monitoring value and the calculated value of PL16-5 provided by the present invention;

[0055] Fig. 20 The deformation monitoring value and calculated value of IP16-1 provided by the present invention are compared. DETAILED DESCRIPTION

[0056] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0057] The embodiment of the present invention discloses a method for inversion of physical and mechanical parameters of fractional-order numerical analysis of deformation behavior of high arch dams. The implementation process is as follows: Figure 1 shown.

[0058] S1. Using Hooke body, fractional Kelvin body, fractional Murasaki body, fractional Bingham body and variable parameter fractional Bingham body, a fractional rheological mechanical element model of the high arch dam body and foundation is constructed.

[0059] The fractional-order rheological element model of the dam body adopts a series combination of Hooke body, fractional-order Kelvin body and variable-parameter fractional-order Bingham body, such as Figure 2 As shown, the expression is:

[0060]

[0061] The fractional-order rheological mechanical element model of the dam foundation adopts a series combination of Hooke body, fractional-order Murasaki body and variable-parameter fractional-order Bingham body, such as Figure 3 As shown, the expression is:

[0062]

[0063] In formulas (1) and (2), σ is the total stress; σ s1 is the stress threshold for attenuation flow; σ s2 is the stress threshold for steady-state flow; α 2 is the acceleration parameter; η 1 is the viscosity coefficient that characterizes the decay rheology; η 2 is the viscosity coefficient that characterizes steady-state rheology and accelerated rheology; γ 1 is the order of decay rheology; γ 2 E is the order of steady-state rheology and accelerated rheology; 0 is the instantaneous elastic modulus that characterizes elastic deformation; E 1 is the delayed elastic modulus that characterizes the decay rheology; ε vp is the viscoplastic strain; is the viscoplastic strain when accelerated flow occurs; k is a non-negative integer variable; Γ(·) is the Gamma function; t is time; t s To accelerate the time when rheology occurs.

[0064] S2. Using rheological test data and based on the Levenberg-Marquardt method, the viscoplastic parameters of the fractional-order rheological element model are inverted.

[0065] S21. Using the attenuated rheological test data and based on the Levenberg-Marquardt method, the elastic and viscoelastic parameters of the Hooke body, fractional Kelvin body, and fractional Murasaki body are preliminarily inverted.

[0066] When the fractional Kelvin body is used to characterize the decay rheology, the strain calculation value is:

[0067]

[0068] In formula (3): is the calculated strain value; the meanings of other parameters are consistent with those in equations (1) and (2).

[0069] Residual r(t i )for:

[0070]

[0071] Introducing the Mittag-Leffler function, we get:

[0072]

[0073] In formula (4) and (5): t i is a certain moment; ε(t i ) is t obtained through experiments i moment strain value; t i Calculated value of strain at each moment; is a two-parameter Mittag-Leffler function; the meanings of the other parameters are consistent with those of equations (1) and (2).

[0074] The total residual sum of squares is:

[0075]

[0076] In formula (6), F is the total residual sum of squares; the meanings of other parameters are consistent with formulas (4) and (5).

[0077] The parameters that minimize equation (6) are the preliminary inversion values ​​of the elastic parameters of the Hooke body and fractional Kelvin body.

[0078] The Levenberg-Marquardt method is used to search for the minimum value of formula (6). The steps of the Levenberg-Marquardt method are not described here. Please refer to the relevant literature.

[0079] When using fractional order mass flow to describe the attenuation rheological process, it is first necessary to determine the stress threshold σ at which the attenuation rheology occurs: s1 .

[0080] Select two sets of decay rheological curves, the stress is σ 1 and σ 2 , for t ∞ At this moment, both rheological processes converge, minus the initial instantaneous strain and After that, we get t ∞ The viscoelastic strain at this moment is:

[0081]

[0082]

[0083] In formulas (7) and (8): t ∞ Momentary stress σ 1 viscoelastic strain under t ∞ Momentary stress σ 2 The meanings of other parameters are consistent with those of equations (1) and (2).

[0084] Combining equations (7) and (8), we get:

[0085]

[0086] The meanings of the parameters in formula (9) are consistent with those in formulas (7) and (8).

[0087] Get σ s1 After that, the elastic parameters of the fractional-order mountain are inverted using the Levenberg-Marquardt method. The process is the same as above and will not be repeated here.

[0088] S22. Using steady-state rheological test data, the viscoplastic parameters of the fractional Bingham body are inverted based on the Levenberg-Marquardt method.

[0089] First, determine the viscoplastic stress threshold σ for steady-state flow s2 .

[0090] Two sets of steady-state rheological curves are selected, and the stresses are σ 3 and σ 4 , the sum of the instantaneous strain and the viscoelastic strain at time t is calculated by formula (3), namely and Then the viscoplastic strain is separated and Right now:

[0091]

[0092]

[0093] In formulas (10) and (11): is the stress σ at time t 3 viscoplastic strain under ; is the stress σ at time t 4 The meanings of other parameters are consistent with those of equations (1) and (2).

[0094] Combining (10) and (11), we get:

[0095]

[0096] The meanings of the parameters in formula (12) are consistent with those in formulas (10) and (11).

[0097] Get σ s2 Then, the Levenberg-Marquardt method is used to invert the viscoplastic parameters of the fractional-order Bingham body. The process is the same as above and will not be repeated here.

[0098] S23. Using the accelerated rheological test data and based on the Levenberg-Marquardt method, the acceleration parameters of the parameterized fractional Bingham body are inverted.

[0099] Select the accelerated rheological curve, and calculate the strain ε(t) at time t using the third formula of formula (1) or the fourth formula of formula (2). 0 、E 1 , η 1 , γ 1 , η 2 , γ 2 , σ s1 , σ s2 Substituting this into the equation, and then using the Levenberg-Marquardt method, we can invert the acceleration parameter α 2 The process is the same as above and will not be repeated here.

[0100] Through the above analysis, the viscoplastic parameters of the fractional-order rheological element model are inverted, and the elastic and viscoelastic parameters are preliminarily obtained.

[0101] S3. Based on the in-situ deformation monitoring data, the elastic parameters of the fractional-order rheological mechanics element model are inverted.

[0102] S31. Central composite design is adopted to optimize the sample combination of elastic parameters to be inverted. Fractional numerical analysis is used to apply reservoir water load and simulate the deformation variation law of the dam under the sample combination of design parameters.

[0103] Note X 1 , X 2 , …, X i , …, X n For the parameters to be inverted, the central composite design process is as follows;

[0104] make:

[0105]

[0106]

[0107] Where: i is an integer variable, with values ​​of 1, 2, ..., n; n is the number of parameters to be inverted; X i,min For X i The minimum value of X i,max For X i The maximum value of .

[0108] According to the central composite design, the optimized parameter sample combination is as follows: ① Central sample point For a central composite design with 3 variables and 2 levels, Figure 4 The black dot in the center of the cube; ②Axial sample point in, e is the number of factorial sample points, for a central composite design with 3 variables and 2 levels, it is Figure 4 Black dots on the coordinate axes of the cube; ③ Factorial sample points in, For a central composite design with 3 variables and 2 levels, Figure 4 The vertices of the cube.

[0109] Based on the central composite design, K = 2 n +2n+1 sample points.

[0110] Fractional order numerical analysis is used to simulate the deformation variation of high arch dams under sample combinations of design parameters.

[0111] S32. Construct a deformation behavior analysis model for the high arch dam body and foundation, and separate the deformation water pressure component from the in-situ deformation monitoring data.

[0112] Based on the mixed mode, the deformation water pressure component δ H Build as:

[0113]

[0114] In formula (15): H is the upstream reservoir water level; δ′ H is δ H The finite element calculation value; X is the adjustment coefficient; i is an integer variable, which can be 1, 2, 3 or 4; a i is the coefficient to be determined.

[0115] Deformation temperature component δ T Build as:

[0116]

[0117] In formula (16), m is the number of simple harmonic groups, which is determined according to the temperature data. When the temperature fluctuates with a yearly period, m = 1; when the temperature fluctuates with a half-year period, m = 2; τ is the monitoring time; i is an integer variable, which can be 1 or 2; b 1i and b 2i is the coefficient to be determined.

[0118] Deformation aging component δ θ Build as:

[0119] δ θ =c1 θ+c 2 lnθ(17)

[0120] In formula (17): τ is the monitoring time; c 1 and c 2 is the coefficient to be determined.

[0121] The deformation δ of the dam body and foundation is constructed as:

[0122]

[0123] In formula (18): a 0 is a constant term to be determined; the meanings of the other parameters are consistent with those in equations (15) to (17).

[0124] The generalized least squares method is used to estimate the unknown coefficients of the model. The accuracy of model parameter estimation is evaluated based on the complex correlation coefficient and the residual standard deviation, thereby separating the deformation water pressure, temperature and aging components.

[0125] S33. Using the deformation water pressure component, the order of dam foundation first and then dam body is adopted to construct the elastic parameter inversion objective function of the fractional-order rheological mechanics element model.

[0126] Based on the deformation water pressure component of the dam foundation measuring points, the elastic parameter inversion objective function of the fractional-order rheological mechanics element model of the dam foundation is established.

[0127] Elastic parameter inversion objective function Q of fractional-order rheological element model of dam foundation 1 for:

[0128]

[0129] In formula (19): a r is the dam foundation measuring point number; m r is the total number of measuring points at the dam foundation; is the dam foundation measuring point a r The deformation water pressure component of is the dam foundation measuring point a r Finite element calculation value of deformation water pressure component; M r is the total number of dam foundation material partitions; For the dam foundation r The instantaneous elastic modulus of the material region characterizing the elastic deformation; r =1,2,…,M r .

[0130] Make Q 1 The parameter combination that reaches the minimum value is the optimal inversion value of the elastic parameters of the dam foundation fractional rheological mechanics element model.

[0131] After the elastic parameters of the dam foundation are obtained by inversion, the elastic parameter inversion objective function of the dam body fractional-order rheological mechanics element model is constructed based on the deformation water pressure components of the dam body measuring points.

[0132] Elastic parameter inversion objective function Q of fractional-order rheological element model of dam body 2 for:

[0133]

[0134] In formula (20): a b is the measuring point number of the dam body; m b is the total number of measuring points on the dam body; is the dam body measuring point a b The deformation water pressure component of is the dam body measuring point a b Finite element calculation value of deformation water pressure component; M b is the total number of dam material partitions; The dam body is b The instantaneous elastic modulus of the material region characterizing the elastic deformation; b =1,2,…,M b .

[0135] Make Q 2 The parameter combination that reaches the minimum value is the optimal inversion value of the elastic parameters of the dam body fractional rheological mechanics element model.

[0136] S34. Use a multi-input and multi-output support vector machine to construct an elastic parameter inversion proxy model.

[0137] Based on the multi-input and multi-output support vector machine (MSVM), the relationship between the calculated deformation value of the high arch dam and the parameters to be inverted is expressed as follows:

[0138]

[0139] In formula (21): f i (x) is the calculated deformation value of the high arch dam; x is the physical and mechanical parameter to be inverted; k(x·x i ) is the kernel function; and is the Lagrange multiplier; bi is the bias coefficient; n is the total number of parameters to be inverted; x i is the i-th group of parameter sample combinations obtained by the central composite design.

[0140] The kernel function uses Gaussian radial basis function, that is:

[0141]

[0142] In formula (22): k(x·x i ) is the kernel function; υ is the width of the kernel function; xi is the i-th group of physical and mechanical parameters obtained by central composite design; exp[·] is the exponential function; x is the physical and mechanical parameter to be inverted.

[0143] Based on MSVM, the elastic parameter inversion proxy model is constructed as follows.

[0144] Combined with formula (19), the proxy model Q for the inversion of dam foundation elastic parameters is 1 ′ is expressed as:

[0145]

[0146] In formula (23): The instantaneous elastic modulus of each area of ​​the high arch dam foundation is When the MSVM outputs the dam foundation measurement point a r Calculated value of deformation water pressure component; the meanings of other parameters are consistent with formula (19).

[0147] Make Q 1 The parameter combination that reaches the minimum value is the optimal inversion value of the elastic parameters of the fractional-order rheological mechanics element model of the dam foundation.

[0148] Combined with formula (20), the proxy model Q for the inversion of dam elastic parameters is 2 ′ is expressed as:

[0149]

[0150] In formula (24): The instantaneous elastic modulus of each area of ​​the high arch dam is When the MSVM model outputs the dam body measurement point a b Calculated value of deformation water pressure component; the meanings of other parameters are consistent with formula (20).

[0151] Make Q 2 The parameter combination that reaches the minimum value is the optimal inversion value of the elastic parameters of the dam body fractional rheological mechanics element model.

[0152] S35. Random inertia weight, asynchronous change learning factor, golden sine perturbation and differential evolution mutation perturbation are introduced, and an improved particle swarm algorithm is proposed to establish a search strategy for the optimal inversion value of elastic parameters.

[0153] Aiming at the shortcomings of particle swarm optimization (PSO), an improved PSO (IPSO) is established below.

[0154] In order to improve the algorithm search performance, random inertia weights and asynchronous change learning factors are introduced.

[0155] The random inertia weight ω is constructed as:

[0156]

[0157] In formula (25), μ is the translation parameter; μ min and μ max are the minimum and maximum values ​​of μ; ξ is the variance; N(0,1) is a random number that follows a standard normal distribution; Rand(0,1) is a random number between [0,1].

[0158] Asynchronous change learning factor d 1 and d 2 Build as:

[0159]

[0160] In formula (26): d 1s is d 1 The initial value of d 2s is d 2 The initial value of d 1e is d 1 The final value of the iteration; d 2e is d 2 The final value of the iteration; φ is the current iteration number; φ max is the maximum number of iterations.

[0161] In order to improve the algorithm's premature maturation problem, golden sine perturbation and differential evolution mutation perturbation are introduced.

[0162] The expression of the golden sine perturbation is:

[0163]

[0164]

[0165]

[0166] In formulas (27) to (29): is the position after the golden sine perturbation; X(φ) is the position of a particle at the φth iteration; r 1 is a random number in [0,2π]; r 2 is a random number in [0,π]; c and b are the golden section coefficients; φ is the current iteration number; is the golden ratio, which is 0.618033; α and β are the search intervals, which are -π and π respectively; X pbest (φ) is the global optimal position of the φth iteration; X rand (φ) is a random position at the φth iteration.

[0167] The expression of differential evolution mutation disturbance is:

[0168]

[0169] In formula (30): is the position after differential evolution mutation disturbance; X o (φ), X p (φ) and X q (φ) are three different random positions in the φth iteration; φ is the current iteration number; S is the scaling factor.

[0170] Let f be the individual fitness and the average fitness f avg =∑f / K, where K is the total number of particles. If f<f avg , perform golden sine perturbation, otherwise, implement differential evolution mutation perturbation.

[0171] If the disturbed position is better than the original position, the original position is replaced by the disturbed position; otherwise, the original position remains unchanged.

[0172] The elastic parameter inversion process is as follows: Figure 5 shown.

[0173] S4. Based on the in-situ deformation monitoring data, the viscoelastic parameters of the fractional-order rheological element model are inverted.

[0174] S41, using central composite design, optimize the combination of viscoelastic parameter samples to be inverted, use fractional numerical analysis, apply the main loads borne during operation, and simulate the deformation change law of the dam under the combination of design parameter samples. The key technology of this step is consistent with S31 and will not be repeated.

[0175] S42. Using the in-situ deformation monitoring data, the objective function for inversion of viscoelastic parameters of the fractional-order rheological mechanics element model of the high arch dam body and foundation is constructed.

[0176] Viscoelastic parameter inversion objective function Q 3 for:

[0177]

[0178] In formula (31): m c is the number of deformation monitoring points; τ is the monitoring time; T is the total monitoring time; δ a,τ is the deformation monitoring value of measuring point a at time τ; is the calculated value of deformation of measuring point a at time τ; The dam body is b The delayed elastic modulus of the material zone characterizes the decaying rheology; The dam body is b The viscosity coefficient of the material zone characterizes the decay rheology; The dam body is b The material region characterizes the order of decay rheology; M bis the total number of dam material partitions; b =1,2,…,M b ; For the dam foundation r The delayed elastic modulus of the material zone characterizes the decaying rheology; For the dam foundation r The viscosity coefficient of the material zone characterizes the decay rheology; For the dam foundation r The material region characterizes the order of decay rheology; M r is the total number of dam foundation material partitions; r =1,2,…,M r .

[0179] Make Q 3 The parameter combination that reaches the minimum value is the optimal inversion value of the viscoelastic parameters of the fractional-order rheological mechanics element model of the dam body and dam foundation.

[0180] S43. Use multi-input and multi-output support vector machines to construct a viscoelastic parameter inversion proxy model.

[0181] Based on MSVM and combined with formula (31), the viscoelastic parameter inversion proxy model Q 3 ′ is expressed as:

[0182]

[0183] In formula (32): The viscoelastic parameters of the dam body are The viscoelastic parameters of the dam foundation are When , the deformation calculation value of measuring point a output by MSVM; the meanings of the other parameter values ​​are consistent with formula (31).

[0184] Make Q 3 The parameter combination that achieves the minimum value of ′ is the optimal inversion value of the viscoelastic parameters of the fractional-order rheological mechanics element model of the dam body and dam foundation.

[0185] S44, based on the improved particle swarm algorithm, establish the optimal inversion value search strategy of viscoelastic parameters. The key technology of this step is consistent with S35 and will not be repeated here.

[0186] The inversion process of viscoelastic parameters is as follows: Figure 6 shown.

[0187] Specifically, based on the above method, a physical and mechanical parameter inversion module for fractional-order numerical analysis of deformation behavior of high arch dams is provided below. Figure 7 As shown, including:

[0188] The model building unit is based on the parallel structure design and includes a dam body fractional-order rheological mechanics element model subunit and a dam foundation fractional-order rheological mechanics element model subunit;

[0189] The viscoplastic parameter inversion unit is designed based on a series structure and includes a decaying rheological inversion subunit, a steady-state rheological inversion subunit, and an accelerated rheological inversion subunit;

[0190] The elastic parameter inversion unit is based on the serial structure design and includes the dam body deformation behavior analysis model subunit, the dam foundation deformation behavior analysis model subunit, the elastic parameter sample combination optimization design subunit, the elastic deformation fractional numerical analysis subunit, the elastic parameter inversion proxy model subunit, and the elastic parameter optimal inversion value search subunit;

[0191] The viscoelastic parameter inversion unit is designed based on a series structure and includes a viscoelastic parameter sample combination optimization design subunit, a viscous deformation fractional-order numerical analysis subunit, a viscoelastic parameter inversion proxy model subunit, and a viscoelastic parameter optimal inversion value search subunit;

[0192] The visual display unit outputs results including viscoplastic parameters, elastic parameters, viscoelastic parameters, total deformation, instantaneous deformation, time-dependent deformation, stress and strain, which are presented to the operator in the form of tables, cloud maps, contour maps, distribution maps and process lines.

[0193] An embodiment is introduced below to further illustrate the method of the present invention.

[0194] The Jiagao arch dam has a crest elevation of 1885m, a maximum dam height of 305m, a crest width of 16m, a crest centerline arc length of 552.23m, a maximum span of 480m, a minimum foundation elevation of 1580m, and a dam bottom thickness of 63m. The river valley is a typical deep V-shaped valley with a width-to-height ratio of 1.57, a normal water storage level of 1880m, and a dead water level of 1800m. Figure 8 This is the three-dimensional finite element model of the dam after completion. Fig. 9 The dam body material is divided into different zones. Fig.10 It is the location of the vertical monitoring point of the dam.

[0195] The design values ​​of elastic parameters of the dam body and dam foundation are shown in Table 1. Based on the test data, the viscoelastic parameters and viscoplastic parameters obtained by inversion are as follows. Dam body: E 1 =70GPa,η 1 =2×10 3 GPa·d,η 2 =1.5×10 4 GPa·d, γ 1 =0.7,γ 2 =0.8,σ s1 Take 0.15 times the instantaneous strength of concrete, σ s2 Take 0.8 times the instantaneous strength of concrete, α 2 Take 0.003h -1 . Dam foundation: E1 =50GPa,η 1 =3×10 3 GPa·d,η 2 =1.5×10 4 GPa·d, γ 1 =0.7,γ 2 =0.8,σ s1 Take 0.15 times the instantaneous strength of rock, σ s2 Take 0.8 times the instantaneous strength of rock, α 2 Take 0.003h -1 .

[0196] Table 1 Design values ​​of elastic parameters

[0197]

[0198] a. Inversion of dam foundation elastic parameters

[0199] Based on the IP13-1 and IP16-1 radial deformation monitoring data, the instantaneous elastic modulus of the dam foundation fractional rheological element model was inverted. The deformation analysis model modeling period was selected from 2015 / 7 / 1 to 2016 / 12 / 31, and the separated deformation water pressure components were as follows: Fig.11 As shown, during the period from 2016 / 6 / 10 to 2016 / 9 / 24, the water level in front of the dam was stored from 1800m to 1880m, and the increments of the deformation water pressure components of IP13-1 and IP16-1 were 2.4mm and 2.5mm respectively.

[0200] The reservoir water level calculation conditions are: 1800m, 1810m, 1820m, 1830m, 1840m, 1850m, 1860m, ​​1870m, 1880m. When the instantaneous elastic modulus of the dam foundation is taken as the design value, the relationship between the calculated values ​​of the deformation water pressure components of IP13-1 and IP16-1 and the reservoir water level is as follows: Fig.12 According to the central composite design, the instantaneous elastic modulus of the dam foundation is selected as 9GPa, 10GPa, ..., 18GPa, and 19GPa. When the reservoir water level changes from 1800m to 1880m, based on the fractional numerical analysis, the relationship between the calculated deformation increment of IP13-1 and IP16-1 and the instantaneous elastic modulus of the dam foundation is as follows: Fig.13 shown.

[0201] After obtaining the finite element calculation results, the design parameter sample combination is used as the input, and the IP13-1 and IP16-1 radial deformation calculation value increments are used as the output to train the MSVM. The initial position of the particle swarm is set to the parameter design value, the maximum number of iterations is set to 200, the population size is set to 100, and μ max =0.95, μ min =0.5,d 1s=2,d 1e =0.5,d 2s =0.5,d 2e =2, the convergence accuracy ε is set to 1×10 -4 The IPSO optimization process is as follows: Fig.14 As shown in Table 2, the algorithm converges after 70 iterations.

[0202] Table 2 Inversion results of dam foundation instantaneous elastic modulus

[0203]

[0204] b. Inversion of dam body elastic parameters

[0205] After obtaining the instantaneous elastic modulus of the dam foundation, the elastic parameters of the fractional-order rheological element model of the dam body were inverted based on the radial deformation monitoring data of PL13-1 and PL16-1. The modeling period of the deformation analysis model was from July 1, 2015 to December 31, 2016. The separated deformation water pressure components are as follows: Fig.15 As shown in the figure, during the period from 2016 / 6 / 10 to 2016 / 9 / 24, the water level in front of the dam was stored from 1800m to 1880m, and the hydraulic deformation increments of PL13-1 and PL16-1 were 37.27mm and 23.81mm respectively.

[0206] The instantaneous elastic modulus of the dam body is the design value, the instantaneous elastic modulus of the dam foundation is the inversion value, and the reservoir water level calculation conditions are selected as: 1800m, 1810m, 1820m, 1830m, 1840m, 1850m, 1860m, ​​1870m, 1880m. The relationship between the calculated values ​​of the hydraulic deformation of PL13-1 and PL16-1 and the reservoir water level is as follows: Fig.16 As shown. Dam 1 area E 0,b,1 The range of variation is [29GPa, 39GPa], dam body zone 2 E 0,b,2 The range of variation is [29GPa, 39GPa], dam body zone 3 E 0,b,3 The variation range is [25 GPa, 35 GPa]. Using central composite design, the elastic parameter design sample combination is obtained, as shown in Table 3.

[0207] Table 3 Sample combination of dam body instantaneous elastic modulus obtained based on central composite design (unit: GPa)

[0208]

[0209] When the reservoir water level changes from 1800m to 1880m, the deformation increments of PL13-1 and PL16-1 are calculated based on fractional numerical analysis. After obtaining the finite element calculation results, the design parameter sample combination is used as the input, and the calculated values ​​of the deformation increments of PL13-1 and PL16-1 are used as the output to train the MSVM. The initial position of the particle swarm is set to the parameter design value, the maximum number of iterations is set to 200, the particle swarm size is set to 100, and μ max =0.95, μ min =0.5,d 1s =2,d 1e =0.5,d 2s =0.5,d 2e =2, the iterative convergence accuracy ε is set to 1×10 -4 After 133 iterations, the solution converged and the inversion results are shown in Table 4.

[0210] Table 4 Inversion results of dam body instantaneous elastic modulus

[0211]

[0212] In order to verify the validity of the inversion results, the radial deformation of PL13-1 under the action of reservoir water pressure from 2016 / 4 / 1 to 2016 / 12 / 31 was calculated using the inversion values ​​of elastic parameters. Fig.17 As shown in the figure, the calculated results fit the monitoring data well, so the inversion results of the instantaneous elastic modulus are valid.

[0213] c. Inversion of viscoelastic parameters

[0214] After the elastic parameters are obtained by inversion, the viscoelastic parameters are inverted based on the radial deformation in-situ monitoring data of IP16-1 and PL16-5. Since there are many parameters, this embodiment takes the dam body area 1 and the dam foundation area 1 as examples. The calculation period is selected from 2014 / 1 / 1 (1st day) to 2015 / 3 / 31 (455th day). The radial deformation process lines of IP16-1 and PL16-5 during this period are as follows: Fig.18 The viscoelastic parameter range of the dam foundation is: γ 1,r,1 ∈[0,1],E 1,r,1 ∈[30GPa,70GPa],η 1,r,1 ∈[1×10 3 GPa·d,4×10 3 GPa·d]; the range of viscoelastic parameters of the dam is: γ 1,b,1 ∈[0,1],E 1,b,1 ∈[40GPa,90GPa],η 1,b,1 ∈[1×10 3 GPa·d,4×10 3GPa·d]. The central composite design is used to obtain the sample combination of viscoelastic parameters to be inverted, and the parameter sample design process will not be repeated. After obtaining the design parameter sample combination, the radial deformation values ​​of IP16-1 and PL16-5 during the analysis period are calculated based on fractional-order numerical analysis. The viscoelastic parameter design parameter sample combination is used as the input, and the calculated radial deformation values ​​of IP16-1 and PL16-5 are used as the output (with an interval of 20 days). The MSVM is trained, and then the IPSO is used to invert the viscoelastic parameters of the dam body and dam foundation, as shown in Table 5. The radial deformation values ​​of IP16-1 and PL16-5 during the period from 2014 / 1 / 1 to 2015 / 3 / 31 are calculated, as shown in Table 5. Fig.19 and 20 As shown in the figure, the calculated results fit well with the monitored values, so the inversion results of viscoelastic parameters are valid.

[0215] Table 5 Inversion results of viscoelastic parameters

[0216]

[0217] This example is based on the physical and mechanical parameter inversion method and module for fractional-order numerical analysis of the deformation properties of high arch dams. Taking the A-type high arch dam as an example, the elastic and viscoelastic parameters are inverted. On this basis, the deformation change law of the dam is analyzed. The calculation results generally reflect the actual situation and verify the feasibility of the present invention.

[0218] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for inversion of physical and mechanical parameters of fractional-order numerical analysis of deformation behavior of high arch dams, characterized in that: First, the viscoplastic parameters are inverted using the rheological test data, then the elastic parameters are inverted using the in-situ deformation monitoring data, and finally the viscoelastic parameters are inverted using the in-situ deformation monitoring data. S1. Using Hooke body, fractional Kelvin body, fractional village body, fractional Bingham body and variable parameter fractional Bingham body, a fractional rheological mechanical element model of high arch dam body and foundation is constructed; S2. Using rheological test data and based on the Levenberg-Marquardt method, the viscoplastic parameters of the fractional-order rheological mechanical element model are inverted, including: S21. Using the attenuated rheological test data and based on the Levenberg-Marquardt method, the elastic and viscoelastic parameters of the Hooke body, fractional Kelvin body, and fractional Murasaki body are preliminarily inverted; S22. Using steady-state rheological test data, the viscoplastic parameters of fractional Bingham bodies are inverted based on the Levenberg-Marquardt method. S23, using the accelerated rheological test data, based on the Levenberg-Marquardt method, the acceleration parameters of the parameterized fractional Bingham body are inverted; S3. Based on the deformation in-situ monitoring data, the elastic parameters of the fractional-order rheological mechanical element model are inverted, including: S31. Adopt central composite design to optimize the sample combination of elastic parameters to be inverted, apply reservoir water load using fractional numerical analysis, and simulate the deformation change law of the dam under the sample combination of design parameters; S32. Construct a deformation behavior analysis model for the high arch dam body and foundation, and separate the deformation water pressure component from the deformation in-situ monitoring data; S33, using the deformation water pressure component, in the order of dam foundation first and dam body later, constructing the elastic parameter inversion objective function of the fractional-order rheological mechanics element model; S34, constructing an elastic parameter inversion proxy model using a multi-input multi-output support vector machine; S35, introducing random inertia weight, asynchronous change learning factor, golden sine perturbation and differential evolution mutation perturbation, and proposing an improved particle swarm algorithm, thereby establishing a search strategy for the optimal inversion value of elastic parameters; S4. Based on the in-situ deformation monitoring data, the viscoelastic parameters of the fractional-order rheological element model are inverted, including: S41. Adopt central composite design to optimize the sample combination of viscoelastic parameters to be inverted, apply the main loads borne during operation by fractional numerical analysis, and simulate the deformation change law of the dam under the sample combination of design parameters; S42. Using the deformation in-situ monitoring data, construct the viscoelastic parameter inversion objective function of the fractional-order rheological element model of the high arch dam body and foundation; S43, using multi-input multi-output support vector machine to construct a viscoelastic parameter inversion proxy model; S44. Based on the improved particle swarm algorithm, a search strategy for the optimal inversion value of viscoelastic parameters is established.

2. According to claim 1, a method for inversion of physical and mechanical parameters of fractional-order numerical analysis of deformation behavior of high arch dams is characterized by: In step S1, the fractional-order rheological element model of the high arch dam body and foundation is constructed as follows: The fractional-order rheological mechanical element model of the dam body adopts a series combination of Hooke body, fractional-order Kelvin body and variable parameter fractional-order Bingham body, and the expression is: The fractional-order rheological mechanical element model of the dam foundation adopts a series combination of Hooke body, fractional-order Murasaki body and variable-parameter fractional-order Bingham body, and the expression is: Where: σ is the total stress; σ s1 is the stress threshold for attenuation flow; σ s2 is the stress threshold for steady-state flow; α2 is the acceleration parameter; η1 is the viscosity coefficient that characterizes the decay rheology; η2 is the viscosity coefficient that characterizes steady-state rheology and accelerated rheology; γ1 is the order that characterizes decay rheology; γ2 is the order that characterizes steady-state rheology and accelerated rheology; E0 is the instantaneous elastic modulus that characterizes elastic deformation; E1 is the delayed elastic modulus that characterizes decay rheology; ε vp is the viscoplastic strain; is the viscoplastic strain when accelerated flow occurs; k is a non-negative integer variable; Γ(·) is the Gamma function; t is time; t s To accelerate the time when rheology occurs.

3. The method for inversion of physical and mechanical parameters of fractional-order numerical analysis of deformation behavior of high arch dam according to claim 1 is characterized in that: In steps S31 and S41, a central composite design is used to optimize and obtain a sample combination of parameters to be inverted; Let X1, X2, ..., X i , …, X n For the parameters to be inverted, the central composite design process is as follows; make: Where: i is an integer variable, with values ​​of 1, 2, ..., n; n is the number of parameters to be inverted; X i,min For X i The minimum value of X i,max For X i The maximum value of According to the central composite design, the optimized parameter sample combination is as follows: ① Central sample point ②Axial sample points in, e is the number of factorial sample points; ③ factorial sample points in, Based on the central composite design, K = 2 n +2n+1 sample points; Fractional order numerical analysis is used to simulate the deformation variation of high arch dams under sample combinations of design parameters.

4. The method for inversion of physical and mechanical parameters of fractional-order numerical analysis of deformation behavior of high arch dam according to claim 1 is characterized in that: In step S32, the deformation behavior analysis model of the high arch dam body and dam foundation is constructed as follows: Based on the mixed mode, the deformation water pressure component δ H Build as: Where: H is the upstream reservoir water level; δ′ H is δ H The finite element calculation value; X is the adjustment coefficient; i is an integer variable, which can be 1, 2, 3 or 4; a i is the coefficient to be determined; Deformation temperature component δ T Build as: Where: m is the number of simple harmonic groups, and its value is determined according to the temperature data. When the temperature fluctuates with a yearly cycle, m=1; when the temperature fluctuates with a half-year cycle, m=2; τ is the monitoring time; i is an integer variable, which can be 1 or 2; b 1i and b 2i is the coefficient to be determined; Deformation aging component δ θ Build as: d θ =c1θ+c2lnθ Where: τ is the monitoring time; c1 and c2 are unknown coefficients; The deformation δ of the dam body and foundation is constructed as: Where: a0 is a constant term to be determined; the meanings of the other parameters are consistent with those in the expressions of deformation water pressure, temperature and aging components; The generalized least squares method is used to estimate the unknown coefficients of the model. The accuracy of model parameter estimation is evaluated based on the complex correlation coefficient and the residual standard deviation, thereby separating the deformation water pressure, temperature and aging components.

5. The method for inversion of physical and mechanical parameters of fractional-order numerical analysis of deformation behavior of high arch dam according to claim 1 is characterized in that: In step S33, the elastic parameter inversion objective function of the fractional-order rheological mechanical element model of the dam foundation and the dam body is constructed as follows: Based on the deformation water pressure component of the dam foundation measuring point, the elastic parameter inversion objective function Q1 of the dam foundation fractional-order rheological element model is: Where: a r is the dam foundation measuring point number; m r is the total number of measuring points at the dam foundation; is the dam foundation measuring point a r The deformation water pressure component of is the dam foundation measuring point a r Finite element calculation value of deformation water pressure component; M r is the total number of dam foundation material partitions; For the dam foundation r The instantaneous elastic modulus of the material region characterizing the elastic deformation; r =1,2,…,M r ; The parameter combination that makes Q1 reach the minimum value is the optimal inversion value of the elastic parameters of the dam foundation fractional rheological mechanics element model; Based on the deformation water pressure component of the dam body measuring point, the elastic parameter inversion objective function Q2 of the dam body fractional-order rheological element model is: Where: a b is the measuring point number of the dam body; m b is the total number of measuring points on the dam body; is the dam body measuring point a b The deformation water pressure component of is the dam body measuring point a b Finite element calculation value of deformation water pressure component; M b is the total number of dam material partitions; The dam body is b The instantaneous elastic modulus of the material region characterizing the elastic deformation; b =1,2,…,M b ; The parameter combination that minimizes Q2 is the optimal inversion value of the elastic parameters of the dam body fractional rheological element model.

6. The method for inversion of physical and mechanical parameters of fractional-order numerical analysis of deformation behavior of high arch dam according to claim 1 is characterized in that: In step S34, based on the multi-input multi-output support vector machine, the elastic parameter inversion proxy model is constructed as follows; Combined with the elastic parameter inversion objective function Q1 of the dam foundation fractional-order rheological element model, the dam foundation elastic parameter inversion proxy model Q1′ is expressed as: Where: The instantaneous elastic modulus of each area of ​​the high arch dam foundation is When the MSVM outputs the dam foundation measurement point a r Calculated value of deformation water pressure component; the meaning of other parameters is consistent with the elastic parameter inversion objective function Q1 of the dam foundation fractional rheological element model; The parameter combination that makes Q1′ reach the minimum value is the optimal inversion value of the elastic parameters of the dam foundation fractional rheological mechanics element model; Combined with the elastic parameter inversion objective function Q2 of the dam body fractional-order rheological element model, the dam body elastic parameter inversion proxy model Q2′ is expressed as: Where: The instantaneous elastic modulus of each area of ​​the high arch dam is When the MSVM model outputs the dam body measurement point a b Calculated value of deformation water pressure component; the meaning of other parameters is consistent with the elastic parameter inversion objective function Q2 of the dam body fractional-order rheological element model; The parameter combination that makes Q2′ reach the minimum value is the optimal inversion value of the elastic parameters of the dam body fractional rheological mechanics element model.

7. The method for inversion of physical and mechanical parameters of fractional-order numerical analysis of deformation behavior of high arch dam according to claim 1 is characterized in that: In step S42, using the deformation in-situ monitoring data, the viscoelastic parameter inversion objective function Q3 of the fractional-order rheological mechanical element model of the high arch dam body and foundation is constructed as follows: Where: m c is the number of deformation monitoring points; τ is the monitoring time; T is the total monitoring time; δ a,τ is the deformation monitoring value of measuring point a at time τ; is the calculated value of deformation of measuring point a at time τ; The dam body is b The delayed elastic modulus of the material zone characterizes the decaying rheology; The dam body is b The viscosity coefficient of the material zone characterizes the decay rheology; The dam body is b The material region characterizes the order of decay rheology; M b is the total number of dam material partitions; b =1,2,…,M b ; For the dam foundation r The delayed elastic modulus of the material zone characterizes the decaying rheology; For the dam foundation r The viscosity coefficient of the material zone characterizes the decay rheology; For the dam foundation r The material region characterizes the order of decay rheology; M r is the total number of dam foundation material partitions; r =1,2,…,M r ; The parameter combination that minimizes Q3 is the optimal inversion value of the viscoelastic parameters of the fractional-order rheological mechanics element model of the dam body and foundation.

8. The method for inversion of physical and mechanical parameters of fractional-order numerical analysis of deformation behavior of high arch dams according to claim 1 is characterized in that: In step S43, based on the multi-input multi-output support vector machine, the viscoelastic parameter inversion proxy model is constructed as follows; Combined with the viscoelastic parameter inversion objective function Q3, the viscoelastic parameter inversion proxy model Q3′ is expressed as: Where: The viscoelastic parameters of the dam body are The viscoelastic parameters of the dam foundation are When , the deformation calculation value of the measuring point a output by MSVM; the meanings of the other parameter values ​​are consistent with the viscoelastic parameter inversion objective function Q3; The parameter combination that makes Q3′ reach the minimum value is the optimal inversion value of the viscoelastic parameters of the fractional-order rheological mechanics element model of the dam body and dam foundation.

9. The method for inversion of physical and mechanical parameters of fractional-order numerical analysis of deformation behavior of high arch dam according to claim 1 is characterized in that: In steps S35 and S44, the improved method of the particle swarm algorithm is as follows; In order to improve the algorithm search performance, random inertia weights and asynchronous change learning factors are introduced; The random inertia weight ω is constructed as: Where: μ is the translation parameter; μ min and μ max are the minimum and maximum values ​​of μ; ξ is the variance; N(0,1) is a random number that follows a standard normal distribution; Rand(0,1) is a random number between [0,1]; The asynchronous variation learning factors d1 and d2 are established as: Where: d 1s is the initial value of d1; d 2s is the initial value of d2; d 1e is the final iteration value of d1; d 2e is the final iteration value of d2; φ is the current iteration number; φ max is the maximum number of iterations; In order to improve the algorithm's premature maturity problem, golden sine perturbation and differential evolution mutation perturbation are introduced; The expression of the golden sine perturbation is: Where: is the position after the golden sine perturbation; X(φ) is the position of a particle at the φth iteration; r1 is a random number in [0,2π]; r2 is a random number in [0,π]; c and b are the golden section coefficients; φ is the current iteration number; is the golden ratio, which is 0.618033; α and β are the search intervals, which are -π and π respectively; X pbest (φ) is the global optimal position of the φth iteration; X rand (φ) is a random position at the φth iteration; The expression of differential evolution mutation disturbance is: Where: is the position after differential evolution mutation disturbance; X o (φ), X p (φ) and X q (φ) are three different random positions in the φth iteration; φ is the current iteration number; S is the scaling factor; Let f be the individual fitness and the average fitness f avg =∑f / K, where K is the total number of particles. If f<f avg , perform golden sine perturbation, otherwise, implement differential evolution mutation perturbation; If the disturbed position is better than the original position, the original position is replaced by the disturbed position; otherwise, the original position remains unchanged.

10. A physical and mechanical parameter inversion module for fractional-order numerical analysis of deformation behavior of high arch dams, characterized in that: A method for inversion of physical and mechanical parameters of fractional-order numerical analysis of deformation behavior of a high arch dam according to any one of claims 1 to 9 is applied, comprising: The model building unit is based on the parallel structure design and includes a dam body fractional-order rheological mechanics element model subunit and a dam foundation fractional-order rheological mechanics element model subunit; The viscoplastic parameter inversion unit is designed based on a series structure and includes a decaying rheological inversion subunit, a steady-state rheological inversion subunit, and an accelerated rheological inversion subunit; The elastic parameter inversion unit is based on the serial structure design and includes the dam body deformation behavior analysis model subunit, the dam foundation deformation behavior analysis model subunit, the elastic parameter sample combination optimization design subunit, the elastic deformation fractional numerical analysis subunit, the elastic parameter inversion proxy model subunit, and the elastic parameter optimal inversion value search subunit; The viscoelastic parameter inversion unit is designed based on a series structure and includes a viscoelastic parameter sample combination optimization design subunit, a viscous deformation fractional-order numerical analysis subunit, a viscoelastic parameter inversion proxy model subunit, and a viscoelastic parameter optimal inversion value search subunit; The visual display unit outputs results including viscoplastic parameters, elastic parameters, viscoelastic parameters, total deformation, instantaneous deformation, time-dependent deformation, stress and strain, which are presented to the operator in the form of tables, cloud maps, contour maps, distribution maps and process lines.

Images