Prestressed concrete beam parameter identification method and device

Abstract

The invention relates to a prestressed concrete beam parameter identification method and device, and belongs to the technical field of artificial intelligence. The method comprises the following steps: S1, incrementing a beam column equation; s2, nondimensionalization of an incremental beam column equation is carried out; s3, a composite loss function, namely a dimensionless increment differential equation loss function, a boundary loss function and a deflection increment loss function, for the physical information neural network is constructed in cooperation with the dimensionless increment beam-column equation, and a network optimization method and an optimal hyper-parameter are adapted; and S4, guiding PINN training through the deflection increment and the minimum composite loss function to obtain the characteristic deflection and the dimensionless axial force, and inversely calculating the pre-stress and the rigidity. The advanced method and device for identifying the parameters of the prestressed concrete beam are provided in cooperation with the incremental beam column equation and the physical information neural network, the influences of the multi-scale effect, implicit time-varying functions (such as concrete shrinkage creep and steel strand relaxation) and inherent observation deviation can be avoided, and the prestress and rigidity can be accurately identified.

Description

Technical Field

[0001] The present invention belongs to the technical field of artificial intelligence, and relates to a method and device for identifying parameters of prestressed concrete beams. Background Art

[0002] The static deflection method is based on the second-order theory of compression and bending. Assuming that the prestress is an eccentric axial load acting at the beam end, it is a non-destructive testing method formed thereby. Its basic control equation is the beam-column equation (BCE). The prestress of a prestressed concrete beam under short-term load can be measured, and the prestress can be identified under the condition of known bending stiffness. However, since it is very difficult to obtain high-precision bending stiffness / prestress measured on site, if both long-term and short-term effects are considered, unless the bending stiffness and prestress are decoupled simultaneously, it is impossible to achieve high-precision parameter identification by solving the inverse problem of BCE.

[0003] Physics-Informed Neural Networks (PINN) embed (partial) differential equations into the loss function of neural networks and use automatic differentiation technology to seamlessly integrate the physical prior information from measurements and (partial) differential equations, expanding the usage scenarios of physical prior information, that is, using and integrating the basic physical processes encapsulated by physical equations and sparse observation data. Therefore, when dealing with the prestressed concrete beam parameter identification task dominated by BCE, it will promote the development of inverse problem solution schemes. However, considering that the deflection effect caused by prestress is not significant, it is still doubtful whether it can identify prestress and flexural stiffness simultaneously; and multi-dimensional BCE may face multi-scale and multi-physics problems, causing PINN to fall into unphysical pseudo-solutions.

[0004] The existing methods for identifying parameters of prestressed concrete beams can be generally divided into three types according to the principle: dynamic characteristic method, physical sensing method, and static deflection method, and their purpose is to determine the state of prestress loss. It is very difficult to identify the prestress of prestressed concrete beams based on the dynamic characteristic method and no consensus has been formed yet; the physical sensing method can identify the prestress of prestressed concrete beams to a certain extent, but there are problems such as being unable to detect old bridges, lacking overall evaluation (local / end detection), immature technology (remaining in the laboratory stage), and lacking sufficient accuracy; unless the bending stiffness and prestress are decoupled simultaneously, identifying the prestress of prestressed concrete beams based on the static characteristic method will be limited to laboratories or reinforcement projects (accurate bending stiffness can be obtained through destructive testing). Therefore, in order to achieve decoupled identification of prestress and bending stiffness of prestressed concrete beams, a multi-parameter identification method for solving inverse problems using limited observation data needs to be established. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a method and device for identifying parameters of a prestressed concrete beam, namely, a method and device for identifying parameters of a prestressed concrete beam by coordinating the incremental beam-column equation and PINN. This method and device use the characteristic points of the deflection increment of the prestressed concrete beam under incremental loads as inputs, and through the technical framework of coordinating the incremental beam-column equation and PINN, take the characteristic deflection and dimensionless axial force in the dimensionless and regularized standard physical system as outputs, and finally back-calculate the prestress and stiffness. Specifically, this solution includes the following four aspects: 1) Construct the non-homogeneous term of the BCE using easily observable parameters, and derive the incremental beam-column equation (Incremental Beam-Column Equation, iBCE) to avoid the influence of multi-scale effects, implicit time-varying functions (such as concrete shrinkage and creep, strand relaxation, structural self-weight, etc.) and inherent observation biases; 2) Derive the characteristic deflection and dimensionless axial force of the iBCE, and construct a dimensionless and regularized standard physical system that avoids multi-scale effects and is suitable for PINN solution; 3) Coordinate the dimensionless incremental beam-column equation to construct a composite loss function for PINN, namely, the dimensionless incremental differential equation loss function, boundary loss function, and deflection increment loss function, and adapt the network optimization method and optimal hyperparameters to avoid the limitations of solving the forward and inverse problems of incremental differential equations and transcendental equations; 4) Guide the training of PINN through the deflection increment and minimizing the composite loss function to obtain the characteristic deflection and dimensionless axial force, and back-calculate the prestress and stiffness.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for identifying parameters of a prestressed concrete beam, the method specifically includes the following steps:

[0008] S1: Incrementalization of the beam-column equation: Construct the non-homogeneous term of the beam-column equation using easily observable parameters, and derive the incremental beam-column equation to avoid the influence of multi-scale effects, implicit time-varying functions (such as concrete shrinkage and creep, strand relaxation, structural self-weight, etc.) and inherent observation biases;

[0009] S2: Dimensionlessization of the incremental beam-column equation: Derive the characteristic deflection and dimensionless axial force of the incremental beam-column equation, and construct a dimensionless and regularized standard physical system that avoids multi-scale effects and is suitable for solving by the physics-informed neural network;

[0010] S3: Coordinate the dimensionless incremental beam-column equation to construct a composite loss function for the physics-informed neural network, namely, the dimensionless incremental differential equation loss function, boundary loss function, and deflection increment loss function, and adapt the network optimization method and optimal hyperparameters;

[0011] S4: Guide the training of the physics-informed neural network through the deflection increment and minimizing the composite loss function to obtain the characteristic deflection and dimensionless axial force, and back-calculate the prestress and stiffness.

[0012] Further, in step S1, the specific steps of the incrementalization of the beam-column equation include:

[0013] S11: Construction of the beam-column model:

[0014] Refer to the beam-column model in Equation (1): The beam has a length L, bears a lateral distributed load q, and has a cross-sectional moment of inertia I; when the beam bears an axial compression force N and shear deformation is ignored, its lateral displacement w is controlled by the following equation:

[0015] EIw'' = M0 - Nw (1)

[0016] Where, M0 represents the moment caused by the lateral load q, Nw represents the second-order moment, and E is the Young's modulus;

[0017] S12: Construction of the general mechanical model of the prestressed concrete beam:

[0018] Regard the prestress (P>0) with an eccentricity e as the axial force, that is, N→P; establish a new reference model considering the self-weight q g and the equivalent lateral load q t ;

[0019] The non-homogeneous term M0 in Equation (1) can be expressed as Equation (2):

[0020] M0(x) = M q (x) - Pecosθ (2)

[0021] From this, the general mechanical model of the prestressed concrete beam as shown in Equation (3) can be derived:

[0022] EIw'' = M q (x) - Pecosθ - Pw (3)

[0023] Where, M q is the moment jointly caused by the prestress P and the lateral load q, and θ is the angle between the prestressed tendon and the cross-section normal;

[0024] S13: Construction of the general mechanical model considering the long-term effect:

[0025] Consider the long-term effect considering the second-order influence and regard it as a component of the initial deflection that changes with time, denoted as w lt ; Introduce w lt into the general mechanical model of the prestressed concrete beam and derive the general mechanical model considering the long-term effect, as shown in Equation (4):

[0026]

[0027] It should be particularly noted that after obtaining the solution w(x) of Equation (4), w lt cannot be ignored. Therefore, the total observed deflection W should be given by Equation (5):

[0028] W(x,t0) = w(x,t0) + w lt (x,t0) (5)

[0029] S14. Construction of a general mechanical model considering short-term loading:

[0030] Then, introduce the short-term effect considering the second-order influence, that is, the lateral load Q for the mid-span; in the half-span interval (0 ≤ x ≤ L / 2) at t = t0, the general mechanical model considering short-term loading can be derived by symmetry, as shown in Equation (6):

[0031]

[0032] S15. Incrementalization;

[0033] Because it can be assumed that w lt remains unchanged during the short-term loading process, the influence of the long-term deflection can be eliminated by using the invariance of the homogeneous solution of the differential equation. Specifically, for the half-span interval at t = t0, the inhomogeneous term associated with the initial deflection can be eliminated without cost through incrementalization; to distinguish between the long-term and short-term deflections, the total observed deflection W at t = t0 is defined respectively by Equation (7):

[0034]

[0035] After incremental operation, the deflection increment Δw under different loadings is obtained:

[0036] Δw = W2(x,t0) - W1(x,t0) = w2(x,t0) - w1(x,t0) (8)

[0037] From this, the incremental beam-column equation under the action of the short-term incremental load ΔQ in the incremental force system is derived:

[0038]

[0039] In fact, this process can also eliminate some constant systematic errors, such as the inherent spatial geometric error of measurement, the concrete surface roughness error, and the truncation error, etc. Equation (9) is a second-order linear inhomogeneous differential equation, which is similar in form to the classical beam-column equation. This equation emphasizes a physical system that does not need to consider the long-term effect (including self-weight and equivalent lateral load).

[0040] Furthermore, in step S2, the non-dimensionalization steps of the incremental beam-column equation include:

[0041] S21, Dimensionless Parameters and Dimensionlessization:

[0042] The dimensionless parameters are defined by Equation (10):

[0043]

[0044] where δ is the characteristic deflection, n is the dimensionless axial force, ξ is the dimensionless spatial axial coordinate, and ω is the dimensionless deflection;

[0045] The operator operation is carried out according to Equation (11):

[0046]

[0047] The obtained incremental beam-column equations and their simplified forms are Equations (12) and (13) respectively:

[0048]

[0049]

[0050] S22, Construction of the Standard Physical System:

[0051] At this time, Equation (14) can be reversely deduced through Equations (11) and (12) to establish the mapping relationship between the equation and the actual engineering scenario:

[0052]

[0053] Finally, a dimensionless and regularized standard physical system that avoids multi-scale effects and is suitable for PINN solution is constructed, as shown in Equation (15):

[0054]

[0055] Furthermore, in step S3, the construction steps of the composite loss function include:

[0056] S31, Construction of the Forward Problem Composite Loss Function:

[0057] After completing steps S1 and S2, considering the standard physical system under the incremental force system, that is, the iBCE of Equation (13), the solution Δw(x, t0) parameterized by λ is defined on the domain Ω as:

[0058]

[0059] And the boundary conditions are specified:

[0060]

[0061] To solve through the PINN proxy, first construct a neural network with trainable parameter η to approximate the solution Δω(x); use a set of collocation points within the domain and another set of collocation points on the boundary After that, define the forward problem composite loss function as:

[0062]

[0063] where k f and k b are weights and satisfy the following definitions:

[0064]

[0065] S32. Construction of the inverse problem composite loss function:

[0066] The same method can be used not only for the forward problem but also for solving the inverse problem of iBCE. To solve the inverse problem of iBCE, consider the deflection increment of the prestressed concrete beam induced by the incremental load ΔQ and record the corresponding deflection increment Δw for each group according to the graded loading standard, which is used to guide the additional measurement for the PINN to solve the inverse problem. That is, if the parameter λ in Equation (19) is unknown and there is additional measurement of Δw on a set of collocation points then define the inverse problem composite loss function as:

[0067]

[0068] where k m is the weight, and the observation loss of the deflection increment induced by the incremental load ΔQ is:

[0069]

[0070] S33. Optimization of the network structure and hyperparameters:

[0071] For the iBCE equation, Equation (20) is the composite loss function of the prestressed concrete beam in the incremental force system, consisting of the loss of the beam-column incremental equation the boundary loss the observation loss of the deflection increment Composite composition. If the PINN constructed in the incremental force system can accurately solve the forward and inverse problems of iBCE, it means that the gradients ▽ of each independent loss function and its composite loss function tend to zero, and it is also considered that the predicted values at each point in the backpropagation calculation of PINN tend to the true values. Therefore, solving the forward and inverse problems of the iBCE equation is transformed into optimizing the composite loss function, and using automatic differentiation technology to encapsulate the basic physical processes of S11, S12, S13, S14, S15, S21, S22, S31 and S32. The goal is to calculate the neural network parameter η* by minimizing the loss functions in equations (18) and (20). Among them, the hyperparameters are set as the loss weight k of the beam-column incremental equation f , the loss weight k of the boundary b , the loss weight k of the deflection increment observation m , the collocation points in the geometric domain the boundary training points the additional deflection increment observation points the learning rate lr, the number of neurons nn, the number of network layers nl; the optimization process is set as the optimizer Adam (or / and L-BFGS), the activation function Tanh, and the initialization strategy Xavier; the test index is set as the two-norm

[0072] Furthermore, in step S4, the training and parameter identification steps of the physics-informed neural network include:

[0073] S41. Embed the incremental beam-column equation into the physics-informed neural network:

[0074] The steps of embedding the incremental beam-column equation into the physics-informed neural network are divided into six steps: The first step is to determine the short-term incremental loading scheme for the prestressed concrete beam in the offline stage and record the deflection increment Δw under each working condition. The second step is to determine the variables x and Δw in the solution scheme, the unknown parameters EI or / and P to be identified, and the known parameters ΔQ and L. The third step is to convert each variable and parameter into the dimensionless form ξ, Δω, n and δ in the standard physical system. The fourth step is to determine the boundary conditions. The fifth step is to generate scattered points and integrate the deflection increment observation points (the collocation points in the geometric domain the boundary training points and the additional deflection increment observation points ). The sixth step is to establish a deep neural network for iBCE, and with the goal of minimizing the neural network parameter η*, optimize the network structure (learning rate lr, number of neurons nn) and hyperparameters (the loss weight k of the beam-column incremental equation f , the loss weight k of the boundary b , the loss weight k of the deflection increment observation m , the collocation points in the geometric domain the boundary training points and additional deflection increment observation points ) to obtain the least square norm under the specified optimization strategy (optimizer Adam, optimizer L-BFGS, activation function Tanh, and initialization strategy Xavier)

[0075] S42. Parameter identification of prestressed concrete beams:

[0076] Judge whether the maximum number of iterations has been reached. If so, continue to execute step S42. If not, return to step S33 and guide the iterative process of the physics-informed neural network with the composite loss function. In the optimal model under control, output the characteristic deflection δ and dimensionless axial force n, and back-calculate the prestress P and stiffness EI according to Equation (10). In the optimal model under control, output the characteristic deflection δ and dimensionless axial force n, and back-calculate the prestress P and stiffness EI according to Equation (10).

[0077] The present invention also provides a device for parameter identification of prestressed concrete beams, which includes:

[0078] An input data increment control module for calculating the deflection increment Δw of the prestressed concrete beam induced by the incremental load ΔQ and simultaneously serving as the input data for parameter identification;

[0079] A beam-column equation increment module for constructing the objective function and its parametric equation of PINN surrogate modeling;

[0080] An incremental beam-column equation dimensionless module for avoiding multi-scale effects and setting the parameters to be identified (characteristic deflection δ and dimensionless axial force n);

[0081] A boundary condition determination module for calculating and defining the floating-point precision at the boundary condition position, so that the determination returns True when the coordinate x = 0 and x = L, and returns False in other cases (returns True when located within the subdomain and returns False when located outside the subdomain);

[0082] A composite loss function calculation module for responding when the constraint conditions are met, that is, the input data increment control module, the beam-column equation increment module, the incremental beam-column equation dimensionless module, and the boundary condition determination module calculate the value of the composite loss function, judge whether the maximum number of iterations has been reached. If not, re-call the module and guide the iterative process of the physics-informed neural network with the value of the composite loss function and the two-norm;

[0083] An output parameter back-calculation module for responding when the maximum number of iterations is reached, taking the characteristic deflection δ, dimensionless axial force n, and deflection increment Δw identified in each iteration as the final required results, and realizing the parameter identification of the concrete beam based on the final required results.

[0084] The present invention also provides a prestressed concrete beam parameter identification system, which includes one or more processors, a memory, and one or more programs stored in the memory. The one or more programs include instructions for executing the prestressed concrete beam parameter identification method according to any one of claims 1-5.

[0085] The present invention also provides a computer-readable storage medium including one or more programs for execution by one or more processors of an electronic device. The one or more programs include instructions for executing the prestressed concrete beam parameter identification method according to any one of claims 1-5.

[0086] The beneficial effects of the present invention are as follows:

[0087] 1) The proposed incremental beam-column equation avoids the influence of implicit time-varying functions, and effectively eliminates the interference of time-varying effects including concrete shrinkage and creep, strand relaxation, structural self-weight, inherent observation deviation, and equivalent load in the incremental force system through quantification.

[0088] 2) The proposed dimensionless incremental beam-column equation avoids the influence of multi-scale effects, and can scale the prestressed concrete beam system under any loading scenario to a dimensionless and regularized standard physical system, and can further be extended to the general scenario of prestressed concrete parameter identification.

[0089] 3) The proposed collaborative incremental beam-column equation and the physical information neural network calculation method can achieve high-precision identification of single parameters and multi-parameters, and can specifically identify prestress and / or stiffness.

[0090] 4) The present invention does not rely on finite element programs, has high generalization ability, and is applicable to the remaining compression beam structures with the same physical control equations.

[0091] Other advantages, objectives, and features of the present invention will be described to some extent in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following specification. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in preferred detail below in conjunction with the drawings, where:

[0093] Figure 1 is the method flow chart of the present invention;

[0094] Figure 2 is the beam-column reference model of the present invention under axial compression load N and lateral load q;

[0095] Figure 3 This is a test case of a prestressed concrete beam in the present invention;

[0096] Figure 4 This is the structural form and measuring point layout scheme of the prestressed concrete beam in the present invention;

[0097] Figure 5 This is a beam-column reference model subjected to prestress P and lateral load q in the present invention;

[0098] Figure 6 This is the beam-column reference model under long-term and short-term effects in the present invention;

[0099] Figure 7 This is a reference model controlled by the incremental beam-column equation in the present invention;

[0100] Figure 8 This is the structural diagram of embedding the incremental beam-column equation into a physics-informed neural network in the present invention;

[0101] Figure 9 This is the device structural diagram in the present invention;

[0102] Figure 10 This is the parameter identification process and result diagram in the present invention. Detailed implementation manners

[0103] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0104] In this embodiment, a method for identifying parameters of a prestressed concrete beam by coordinating an incremental beam-column equation and a physics-informed neural network is provided. The deflection increment characteristic points of the prestressed concrete beam under incremental loads are used as inputs. Through the technical framework of coordinating the incremental beam-column equation and PINN, the characteristic deflection and dimensionless axial force in a dimensionless and normalized standard physical system are used as outputs, and finally the prestress and stiffness are calculated by back-calculation. The influence of multi-scale effects, implicit time-varying functions (such as concrete shrinkage and creep, strand relaxation, structural self-weight, etc.) and inherent observation deviations can be avoided, and the prestress and stiffness can be accurately identified. Figure 1 This is the method flow chart of the present invention.

[0105] In this embodiment, a typical structure of a prestressed concrete simply supported beam is taken as an example. As Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 , Figure 8 , Figure 9 and Figure 10 shown, after obtaining the deflection increment, the parameter identification of the prestressed concrete beam can be automatically calculated and realized.

[0106] Specifically, the method includes the following steps:

[0107] S1: Incrementalization of the beam-column equation: Construct the non-homogeneous term of the beam-column equation using easily observable parameters, and derive the incremental beam-column equation to avoid the influence of multi-scale effects, implicit time-varying functions (such as concrete shrinkage and creep, strand relaxation, structural self-weight, etc.), and inherent observation biases.

[0108] S2: Dimensionlessization of the incremental beam-column equation: Derive the characteristic deflection and dimensionless axial force of the incremental beam-column equation, and construct a dimensionless and regularized standard physical system that avoids multi-scale effects and is suitable for solution by a physics-informed neural network.

[0109] S3: Collaboratively construct a composite loss function for the physics-informed neural network using the dimensionless incremental beam-column equation, namely the dimensionless incremental differential equation loss function, boundary loss function, and deflection increment loss function, and adapt the network optimization method and optimal hyperparameters.

[0110] S4: Guide the training of the physics-informed neural network through the deflection increment and minimizing the composite loss function to obtain the characteristic deflection and dimensionless axial force, and back-calculate the prestress and stiffness.

[0111] The following details each step:

[0112] The specific steps of S1 are as follows:

[0113] S11: Construction of the beam-column model;

[0114] Refer to the beam-column model as shown in Equation (1) ( Figure 2 ). The beam has a length L, bears a lateral distributed load q, and has a sectional moment of inertia I. When the beam bears an axial compression N and shear deformation is ignored, its lateral displacement w is controlled by the following equation:

[0115] EIw'' = M0 - Nw (1)

[0116] where M0 represents the moment caused by the lateral load q, Nw represents the second-order moment, and E is the Young's modulus.

[0117] The prestressed concrete beam in the embodiment is as Figure 3 shown. The known conditions include the lateral displacement w j (j = 1, 2,..., 7, representing the displacement measurement values at seven equally divided points on the beam axis), the beam length L = 6.62 m, the sectional moment of inertia I = 1.3333×10 9 mm 4 , and the parameters to be identified are the prestress P and the flexural stiffness EI. Its structural form and measuring point layout scheme are as Figure 4 shown. Then, the flexural deformations at 7 characteristic points of the prestressed concrete beam were measured through 9 groups of short-term loading tests (Table 1).

[0118] Table 1 9 groups of short-term loading tests and their measurement results

[0119]

[0120]

[0121] S12. Construction of the general mechanical model of prestressed concrete beams;

[0122] Regarding the prestress (P>0) with an eccentricity of e as an axial force, i.e., N→P. Based on the equivalent load method, a new reference model considering the self-weight q g and the equivalent lateral load q t is established ( Figure 5 ).

[0123] The non-homogeneous term M0 in Equation (1) can be expressed as Equation (2):

[0124] M0(x) = M q (x) - Pecosθ (2)

[0125] From this, the general mechanical model of prestressed concrete beams as shown in Equation (3) can be derived:

[0126] EIw" = M q (x) - Pecosθ - Pw (3)

[0127] where M q is the bending moment jointly caused by the prestress P and the lateral load q, and θ is the angle between the prestressing tendon and the cross-section normal.

[0128] S13. Construction of the general mechanical model considering the long-term effect;

[0129] Considering the long-term effect of the second-order influence and regarding it as a component of the initial deflection varying with time, denoted as w lt . Introducing w lt into the general mechanical model of prestressed concrete beams and deriving the general mechanical model considering the long-term effect, as shown in Equation (4):

[0130]

[0131] It should be particularly noted that after obtaining the solution w(x) of Equation (4), w lt cannot be ignored. Therefore, the total observed deflection W should be as shown in Equation (5):

[0132] W(x,t0) = w(x,t0) + w lt (x,t0) (5)

[0133] S14. Construction of the general mechanical model considering short-term loading;

[0134] Then introduce the short-term effect considering the second-order influence, that is, the lateral load Q for the mid-span, as Figure 6 shown. In the half-span interval (0 ≤ x ≤ L / 2) at time t = t0, the general mechanical model considering short-term loading can be derived by symmetry, as shown in Equation (6):

[0135]

[0136] S15, Incrementalization;

[0137] Because it can be assumed that w lt remains unchanged during the short-term loading process, the influence of long-term deflection can be eliminated by using the invariance of the homogeneous solution of the differential equation. Specifically, for the half-span interval at time t = t0, the non-homogeneous term associated with the initial deflection can be eliminated without cost by incrementalization. To distinguish between long-term and short-term deflections, the total observed deflection W at time t = t0 is defined respectively according to Equation (7):

[0138]

[0139] After incremental operation, the deflection increment Δw under different loadings is obtained:

[0140] Δw = W2(x, t0) - W1(x, t0) = w2(x, t0) - w1(x, t0) (8)

[0141] From this, the incremental beam-column equation (IncrementalBeam-Column Equation, iBCE) under the action of the short-term incremental load ΔQ in the incremental force system is derived:

[0142]

[0143] Actually, this process can also eliminate some constant systematic errors, such as the inherent spatial geometric error of measurement, the concrete surface roughness error, and the truncation error, etc. Equation (9) is a second-order linear non-homogeneous differential equation, which is similar in form to the classical beam-column equation. This equation emphasizes a physical system that does not need to consider the long-term effect (including self-weight and equivalent lateral load), as Figure 7 shown.

[0144] The specific steps of S2 are as follows:

[0145] S21, Dimensionless parameters and dimensionlessization;

[0146] The dimensionless parameters are defined as Equation (10):

[0147]

[0148] Among them, δ is the characteristic deflection, n is the dimensionless axial force, ξ is the dimensionless spatial axial coordinate, and ω is the dimensionless deflection.

[0149] The operator operation is carried out according to Equation (11):

[0150]

[0151] The obtained incremental beam-column equations and their simplified forms are respectively Equation (12) and Equation (13):

[0152]

[0153]

[0154] S22. Construction of the standard physical system;

[0155] At this time, Equation (14) can be reversely deduced through Equation (11) and Equation (12) to establish the mapping relationship between the equation and the actual engineering scenario:

[0156]

[0157] Finally, a dimensionless and regularized standard physical system that avoids multi-scale effects and is suitable for PINN solution is constructed, as shown in Equation (15):

[0158]

[0159] According to the method of the present invention, the incremental and dimensionless results under 9 groups of test schemes in Table 2 can be calculated, including: the spatial dimensionless coordinate ξ, the deflection increment Δw, the dimensionless axial force n, and the characteristic deflection δ. At this time, the parameters to be identified are the dimensionless axial force n and the characteristic deflection δ.

[0160] Table 2 Incremental and dimensionless results under 9 groups of test schemes

[0161]

[0162]

[0163] The specific steps of S3 are as follows:

[0164] S31. Construction of the forward problem composite loss function;

[0165] After completing steps S1 and S2, considering the standard physical system under the incremental force system, that is, the iBCE of Equation (13), the solution Δw(x, t0) parameterized by λ is defined on the domain Ω as:

[0166]

[0167] And the boundary conditions are specified:

[0168]

[0169] To solve through the PINN proxy, first construct a neural network with trainable parameter η to approximate the solution Δω(x); use a set of collocation points within the domain and another set of collocation points on the boundary After that, define the forward problem composite loss function as:

[0170]

[0171] where k f and k b are weights. And they satisfy the following definitions:

[0172]

[0173] S32. Construction of the inverse problem composite loss function;

[0174] The same method can be used not only for the forward problem but also for solving the inverse problem of iBCE. To solve the inverse problem of iBCE, consider the deflection increment of the prestressed concrete beam induced by the incremental load ΔQ, and record the corresponding deflection increment Δw for each group according to the graded loading standard, which is used to guide the additional measurement for the PINN to solve the inverse problem. That is, if the parameter λ in Equation (19) is unknown, and there is an additional measurement of Δw on a set of collocation points then the inverse problem composite loss function can be defined as:

[0175]

[0176] where k m is the weight, and the observation loss for the deflection increment induced by the incremental load ΔQ is:

[0177]

[0178] S33. Optimization of the network structure and hyperparameters;

[0179] For the iBCE equation, Equation (20) is the composite loss function of the prestressed concrete beam in the incremental force system, consisting of the loss of the beam-column incremental equation the boundary loss and the observation loss of the deflection increment Composite composition. If the PINN constructed in the incremental force system can accurately solve the forward and inverse problems of iBCE, it means that the gradients ▽ of each independent loss function and its composite loss function tend to zero, and it is also considered that the predicted values at each point in the backpropagation calculation of PINN tend to the true values. Therefore, solving the forward and inverse problems of the iBCE equation is transformed into optimizing the composite loss function, and using automatic differentiation technology to encapsulate the basic physical processes of S11, S12, S13, S14, S15, S21, S22, S31, and S32. The goal is to calculate the neural network parameter η* by minimizing the loss functions in equations (18) and (20). Among them, the hyperparameters are set as the loss weight k of the beam-column incremental equation f , the loss weight k of the boundary b , the loss weight k of the deflection increment observation m , the collocation points in the geometric domain boundary training points additional deflection increment observation points learning rate lr, number of neurons nn, number of network layers nl; the optimization process is set as the optimizer Adam (or / and L-BFGS), activation function Tanh, initialization strategy Xavier; the test index is set as the two-norm L2.

[0180] Table 3 shows the shared PINN hyperparameters under 9 groups of test schemes, including: the loss weight k of the beam-column incremental equation f , the loss weight k of the boundary b , the loss weight k of the deflection increment observation m , the collocation points in the geometric domain boundary training points additional deflection increment observation points learning rate lr, number of neurons nn, number of network layers nl.

[0181] According to the method of the present invention, the shared hyperparameters of the 9 groups of test schemes in Table 3 can be obtained.

[0182] Table 3 Shared hyperparameters of 9 groups of test schemes

[0183]

[0184] The specific steps of S4 are as follows:

[0185] S41. Embed the incremental beam-column equation into the physics-informed neural network;

[0186] Figure 8 is the working process of embedding the incremental beam-column equation into the physics-informed neural network. In Figure 8In it, the construction of the prestressed concrete beam model is divided into six steps: First step, determine the short-term incremental loading scheme for the prestressed concrete beam in the offline stage, and record the deflection increment Δw under each working condition; Second step, determine the variables (x and Δw), unknown parameters to be identified (EI or / and P), and known parameters (ΔQ and L) in the solution scheme; Third step, convert each variable and parameter into the dimensionless form (ξ, Δω, n, and δ) in the standard physical system; Fourth step, determine the boundary conditions; Fifth step, generate scattered points and integrate the deflection increment observation points (geometric domain configuration points Boundary training points and additional deflection increment observation points ); Sixth step, establish a deep neural network for iBCE, and with the goal of minimizing the neural network parameters η*, optimize the network structure (learning rate lr, number of neurons nn) and hyperparameters (beam-column incremental equation loss weight k f , boundary loss weight k b , deflection increment observation loss weight k m , geometric domain configuration points Boundary training points and additional deflection increment observation points ), and obtain the least square norm under the specified optimization strategy (optimizer Adam, optimizer L-BFGS, activation function Tanh, and initialization strategy Xavier)

[0187] S42. Parameter identification of the prestressed concrete beam;

[0188] Judge whether the maximum number of iterations has been reached. If so, continue to execute step S42. If not, return to step S33, and guide the iterative process of the physics-informed neural network with the composite loss function. In the optimal model controlled by the least square norm , output the characteristic deflection δ and dimensionless axial force n, and back-calculate the prestress P and stiffness EI according to Equation (10).

[0189] When the above method is implemented in the form of software functional units and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs.

[0190] The present invention also provides a device for identifying parameters of a prestressed concrete beam that collaborates an incremental beam-column equation with a physics-informed neural network, as Figure 9 shown, including: an input data incrementation module for controlling input data; a beam-column equation incrementation module; an incremental beam-column equation non-dimensionalization module; a boundary condition determination module; a composite loss function calculation module; and an inverse calculation module for controlling output parameters. Among them, the input data incrementation module for controlling input data is used to calculate the deflection increment Δw of the prestressed concrete beam induced by the incremental load ΔQ and simultaneously use it as the input data during parameter identification; the beam-column equation incrementation module is used to construct the objective function and its parametric equation for PINN surrogate modeling; the incremental beam-column equation non-dimensionalization module is used to avoid multi-scale effects and set the parameters to be identified (characteristic deflection δ and non-dimensional axial force n); the boundary condition determination module is used to calculate and define the floating-point precision at the position of the boundary condition, so that the determination returns True when the coordinates are x = 0 and x = L, and returns False in other cases (returns True when located within the subdomain and returns False when located outside the subdomain); the composite loss function calculation module is used to respond when the constraint conditions are met, that is, the input data incrementation module for controlling input data, the beam-column equation incrementation module, the incremental beam-column equation non-dimensionalization module, and the boundary condition determination module calculate the value of the composite loss function, determine whether the maximum number of iterations has been reached, and if not, re-call the module and guide the iterative process of the physics-informed neural network with the value of the composite loss function and the two-norm; the inverse calculation module for controlling output parameters is used to respond when the maximum number of iterations is reached, take the characteristic deflection δ, non-dimensional axial force n, and deflection increment Δw identified in each iteration as the final required results, and realize the identification of the parameters of the concrete beam based on the final required results.

[0191] Figure 10It shows the parameter identification process and results of the present invention, that is, using the deflection increment characteristic points of the prestressed concrete beam under incremental load as the input, through the technical framework of the collaborative incremental beam-column equation and PINN, taking the characteristic deflection and dimensionless axial force in the dimensionless and normalized standard physical system as the output, and finally realizing the inverse calculation of prestress and stiffness with high precision. The comparative tests in Table 4 show that: in the tests of 9 groups of prestressed concrete beams of real structures, the present invention demonstrates significant multi-parameter identification ability. The maximum error of prestress identification is 27.2%, and the minimum error is -0.24%; the maximum error of flexural stiffness identification is -29.9%, and the minimum error is 0.34%. The comprehensive results show that: thanks to the prestressed concrete beam parameter identification method proposed by the present invention, the influence of multi-scale effects, implicit time-varying functions (such as concrete shrinkage and creep, strand relaxation, structural self-weight, etc.) and inherent observation deviations can be avoided, and the prestress and stiffness can be accurately identified.

[0192] Table 4 Multi-parameter identification results of 9 groups of prestressed concrete beam tests

[0193]

[0194] The present invention also provides a device for identifying parameters of a prestressed concrete beam by collaborating an incremental beam-column equation and a physics-informed neural network, including one or more processors, a memory, and one or more programs stored in the memory, and the one or more programs include instructions for performing the parameter identification of the prestressed concrete beam by collaborating the incremental beam-column equation and the physics-informed neural network as described above.

[0195] Those skilled in the art should understand that the embodiments of the present invention can provide a method, a system, or a computer program product. Therefore, the present invention can be implemented in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can be implemented in the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented in various computer languages, for example, object-oriented programming languages such as Java and interpreted scripting languages such as JavaScript.

[0196] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0197] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in one flow Figure 1 one flow or multiple flows and / or blocks Figure 1 or multiple blocks.

[0198] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified without departing from the spirit and scope of the present technical solution, and they should all be covered by the scope of the claims of the present invention.

Claims

1. A method for identifying parameters of a prestressed concrete beam, characterized in that: The method specifically includes the following steps: S1: Incrementalization of the beam-column equation: Construct the non-homogeneous term of the beam-column equation using easily observable parameters, and derive the incremental beam-column equation to avoid the influence of multi-scale effects, implicit time-varying functions, and inherent observation biases; S2: Dimensionlessization of the incremental beam-column equation: Derive the characteristic deflection and dimensionless axial force of the incremental beam-column equation, and construct a dimensionless and regularized standard physical system that avoids multi-scale effects and is suitable for solution by a physics-informed neural network; S3: Collaboratively construct a composite loss function for the physics-informed neural network using the dimensionless incremental beam-column equation, namely the dimensionless incremental differential equation loss function, the boundary loss function, and the deflection increment loss function, and adapt the network optimization method and optimal hyperparameters; S4: Guide the training of the physics-informed neural network through the deflection increment and minimizing the composite loss function to obtain the characteristic deflection and dimensionless axial force, and back-calculate the prestress and stiffness.

2. The parameter identification method of a prestressed concrete beam according to claim 1, characterized in that: In step S1, the specific steps of the incrementalization of the beam-column equation include: S11: Construction of the beam-column model: Refer to the beam-column model as shown in Equation (1): The beam has a length L, bears a lateral distributed load q, and has a sectional moment of inertia I; when the beam bears an axial compressive force N and shear deformation is ignored, its lateral displacement w is controlled by the following equation: EIw" = M0 - Nw (1) where, M0 represents the moment caused by the lateral load q, Nw represents the second-order moment, and E is the Young's modulus; S12: Construction of the general mechanical model of the prestressed concrete beam: The prestress with an eccentricity of e is regarded as an axial force, i.e., N→P; a new reference model considering the self-weight q g and the equivalent lateral load q t is established based on the equivalent load method; The non-homogeneous term M0 in Equation (1) can be expressed as Equation (2): M0(x) = M q (x) - Pecosθ (2) From this, the general mechanical model of the prestressed concrete beam as shown in Equation (3) can be derived: EIw" = M q (x) - Pecosθ - Pw (3) Among them, M q is the bending moment caused by the combined action of the prestress P and the lateral load q, and θ is the angle between the prestressing tendon and the section normal; S13: Construction of the general mechanical model considering the long-term effect: Consider the long-term effect of second-order influence and regard it as a component of the initial deflection that varies with time, denoted as w lt ; Introduce w lt into the general mechanical model of prestressed concrete beams and derive the general mechanical model considering the long-term effect, as shown in Equation (4): After obtaining the solution w(x) of Equation (4), w lt cannot be ignored. Therefore, the total observed deflection W should be as shown in Equation (5): W(x,t0) = w(x,t0) + w lt (x,t0) (5) S14: Construction of the general mechanical model considering short-term loading: In the half-span interval at t = t0, the general mechanical model considering short-term loading can be derived by symmetry, as shown in Equation (6): S15: Incrementalization; For the half-span interval at t = t0, the non-homogeneous term associated with the initial deflection can be eliminated without cost through incrementalization; to distinguish between long-term and short-term deflections, the total observed deflection W at t = t0 is defined respectively according to Equation (7): After incremental operation, the deflection increment Δw under different loadings is obtained: Δw = W2(x,t0) - W1(x,t0) = w2(x,t0) - w1(x,t0) (8) From this, the incremental beam-column equation under the action of the short-term incremental load ΔQ in the incremental force system is derived: Equation (9) is a second-order linear non-homogeneous differential equation, which is similar in form to the classical beam-column equation, and this equation emphasizes a physical system that does not need to consider the long-term effect.

3. A method for identifying parameters of a prestressed concrete beam according to claim 2, characterized in that: In step S2, the dimensionlessization steps of the incremental beam-column equation include: S21: Dimensionless parameters and dimensionlessization: The dimensionless parameters are defined as Equation (10): where, δ is the characteristic deflection, n is the dimensionless axial force, ξ is the dimensionless spatial axial coordinate, and ω is the dimensionless deflection; The operator operation is carried out according to Equation (11): The obtained incremental beam-column equation and its simplified form are respectively Equation (12) and Equation (13): S22: Construction of the standard physical system: At this time, Equation (14) can be deduced backward from Equations (11) and (12) to establish the mapping relationship between the equation and the actual engineering scenario: Finally, a dimensionless and regularized standard physical system that avoids multi-scale effects and is suitable for PINN solution is constructed as shown in Equation (15):

4. A method for identifying the parameters of a prestressed concrete beam according to claim 3, characterized in that: In step S3, the construction steps of the composite loss function include: S31. Construction of the forward problem composite loss function: After completing steps S1 and S2, consider the standard physical system under the incremental force system, that is, the iBCE of Equation (13). Define the solution Δw(x, t0) parameterized by λ on the domain Ω as: And specify the boundary conditions: For solving through the PINN proxy, first construct a neural network Δω(x; η) with trainable parameters η to approximate the solution Δω(x); use a set of collocation points within the domain and another set of collocation points C on the boundary b After that, define the composite loss function of the forward problem as: where k f and k b are weights and satisfy the following definitions: S32. Construction of the inverse problem composite loss function: To solve the inverse problem of iBCE, consider the deflection increment of a prestressed concrete beam induced by an incremental load ΔQ, and record the corresponding deflection increment Δw for each group according to the step loading criterion to guide the additional measurement for the PINN to solve the inverse problem. That is, if the parameter λ in Equation (19) is unknown and there is an additional measurement of Δw at a set of collocation points then the inverse problem composite loss function is defined as: where k m is the weight, and the observed loss of the deflection increment induced by the incremental load ΔQ is as follows: S33. Optimization of the network structure and hyperparameters: For the iBCE equation, Equation (20) is the composite loss function of a prestressed concrete beam in an incremental force system, which consists of the losses of the beam-column incremental equation Boundary loss Deflection increment observation loss L m and is composed of composites. If the PINN constructed in the incremental force system can accurately solve the forward and inverse problems of the iBCE, it means that the gradient ▽ of each independent loss function and its composite loss function tends to zero, and it is also considered that the predicted values at each point in the backpropagation calculation of the PINN tend to the true values. Therefore, solving the forward and inverse problems of the iBCE equation is transformed into optimizing the composite loss function, and using automatic differentiation technology to encapsulate the basic physical processes of S11, S12, S13, S14, S15, S21, S22, S31, and S32. The goal is to calculate the neural network parameter η* by minimizing the loss functions in Equations (18) and (20). Among them, the hyperparameters are set as the loss weight k of the beam-column incremental equation f , the boundary loss weight k b , the deflection increment observation loss weight k m , the geometric domain configuration points boundary training points additional deflection increment observation points learning rate lr, the number of neurons nn, the number of network layers nl; the optimization process is set as the optimizer Adam, the activation function Tanh, and the initialization strategy Xavier; the test index is set as the two-norm 5. A method for identifying parameters of a prestressed concrete beam according to claim 4, characterized in that: In step S4, the training and parameter identification steps of the physics-informed neural network include: S41. Embedding the incremental beam-column equation into the physics-informed neural network: The steps of embedding the incremental beam-column equation into a physics-informed neural network are divided into six steps: First, determine the short-term incremental loading scheme for prestressed concrete beams in the offline stage and record the deflection increment Δw under each condition; Second, determine the variables x and Δw in the solution scheme, the unknown parameters EI or / and P to be identified, and the known parameters ΔQ and L; Third, convert each variable and parameter into the dimensionless form ξ, Δω, n, and δ in the standard physical system; Fourth, determine the boundary conditions; Fifth, generate scattered points and integrate the deflection increment observation points; Sixth, establish a deep neural network for iBCE, and aim at minimizing the neural network parameter η*, optimize the network structure and hyperparameters, and obtain the least squares norm under the specified optimization strategy S42. Parameter identification of the prestressed concrete beam: Determine whether the maximum number of iterations has been reached. If so, continue to execute step S42. If not, return to step S33 and guide the iterative process of the physics-informed neural network with the composite loss function. In the optimal model controlled by the least square norm Output the characteristic deflection δ and the dimensionless axial force n, and calculate the prestress P and the stiffness EI by back-calculation according to Equation (10).

6. A device for identifying parameters of a prestressed concrete beam, characterized in that: The device includes: An input data increment control module for calculating the deflection increment Δw of the prestressed concrete beam induced by the incremental load ΔQ and simultaneously serving as the input data for parameter identification; A beam-column equation increment module for constructing the objective function and its parameterized equation of PINN surrogate modeling; An incremental beam-column equation dimensionless module for avoiding multi-scale effects and setting the parameters to be identified; A boundary condition determination module for calculating and defining the floating-point precision at the boundary condition position, so that the determination returns True when the coordinates are x = 0 and x = L, and returns False in other cases (returns True when located within the subdomain and returns False when located outside the subdomain); A composite loss function calculation module for responding when the constraint conditions are met, that is, the input data increment control module, the beam-column equation increment module, the incremental beam-column equation dimensionless module, and the boundary condition determination module calculate the value of the composite loss function, and determine whether the maximum number of iterations has been reached. If not, the module is called again, and the iteration process of the physics-informed neural network is guided by the value of the composite loss function and the two-norm; An output parameter inverse calculation module for responding when the maximum number of iterations is reached, taking the characteristic deflection δ, dimensionless axial force n, and deflection increment Δw identified in each iteration as the final required results, and realizing the parameter identification of the concrete beam based on the final required results.

7. A parameter identification system for prestressed concrete beams, characterized in that: The system includes one or more processors, a memory, and one or more programs stored in the memory. The one or more programs include instructions for executing the prestressed concrete beam parameter identification method according to any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, Including one or more programs executed by one or more processors of the electronic device. The one or more programs include instructions for executing the prestressed concrete beam parameter identification method according to any one of claims 1-5.

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