Concrete dam deformation behavior analysis method

Abstract

The invention discloses a concrete dam deformation behavior analysis method, which comprises the following steps: acquiring multi-source observation data, engineering information and a prior parameter set, and generating a preprocessing data packet and a model information packet; based on the data packet and the model information packet, evaluating an aging index representing the structural state of the dam and monitoring a condition number of an inversion problem; according to the aging index and the condition number, dynamically determining a regularization parameter, and constructing a self-adaptive objective function; a self-adaptive hybrid optimization strategy with a multi-index state machine switching mechanism is adopted, a self-adaptive objective function is solved, and an estimation parameter set is output; and generating an analysis result packet according to the estimation parameter set. According to the method, the inversion process can be adaptively constrained according to the aging state of the dam, the problem of discomfort of fractional order model parameter inversion is effectively solved, and the stability and precision of deformation analysis are improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of building deformation analysis, and particularly relates to a concrete dam deformation behavior analysis method. BACKGROUND

[0002] Under the action of long-term hydrostatic pressure, temperature change and self-weight load, the dam building materials (such as concrete and dam foundation rock mass) will exhibit complex rheological properties such as creep and creep, resulting in irreversible deformation of the dam body. Therefore, establishing a high-precision deformation analysis model to accurately predict the deformation behavior of the dam under future load conditions is the scientific basis for dam safety monitoring, operation state evaluation and maintenance strategy development, and has great engineering research significance.

[0003] Currently, the analysis method of concrete dam deformation behavior has developed from the traditional statistical model to the numerical simulation based on the combination of the constitutive model of physical mechanics and the finite element method. In the aspect of physical mechanics model, the viscoelastic constitutive model composed of integer order calculus elements (such as Kelvin-Voigt, Maxwell, Burgers, etc.) is widely used in the engineering field to describe the rheological properties of materials. In recent years, with the deepening of research, fractional calculus theory has been introduced into rheological mechanics, forming a fractional order constitutive model (such as fractional order Burgers model). Due to the memory and non-local characteristics of fractional derivative, the fractional order model has been proved to be able to more accurately describe the mechanical behavior of viscoelastic materials in a wide frequency range with fewer parameters. In the aspect of parameter determination, the existing technology usually uses various optimization algorithms (such as least squares method, standard genetic algorithm, quasi-Newton method, etc.) to perform inversion on the model parameters, so as to make the model calculation value fit the field multi-source observation data (such as displacement, crack opening degree, etc.).

[0004] However, although the fractional order constitutive model has superiority in theory, its parameter inversion process faces technical bottlenecks in engineering application, which limits the analysis accuracy and reliability of the existing scheme. These problems mainly manifest as: serious inversion ill-posedness problem caused by model complexity, and lack of model physical consistency caused by limitation of inversion strategy. SUMMARY

[0005] The application aims to provide a concrete dam deformation behavior analysis method to solve the above problems existing in the prior art.

[0006] Technical scheme, a concrete dam deformation behavior analysis method, comprising:

[0007] Obtaining multi-source observation data, engineering information and prior parameter set, generating pre-processing data package and model information package;

[0008] Based on the pre-processed data packet and the model information packet, an aging index representing the structural state of the dam is evaluated and the condition number of the inverse problem is monitored;

[0009] According to the aging index and the condition number, a regularization parameter is dynamically determined, and an adaptive objective function is constructed;

[0010] An adaptive hybrid optimization strategy with a multi-index state machine switching mechanism is used to solve the adaptive objective function, and an estimated parameter set is output;

[0011] According to the estimated parameter set, an analysis result packet is generated.

[0012] Beneficial effects, the present application can adaptively constrain the inversion process according to the aging state of the dam, effectively overcome the ill-posed problem of fractional order model parameter inversion, and improve the stability and precision of deformation analysis. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 A step flowchart of a concrete dam deformation behavior analysis method provided by the embodiment of the present application.

[0014] Figure 2 A step flowchart of constructing an adaptive objective function provided by the embodiment of the present application.

[0015] Figure 3 A step flowchart of refining an aging index provided by the embodiment of the present application.

[0016] Figure 4 A step flowchart of outputting an estimated parameter set provided by the embodiment of the present application. DETAILED DESCRIPTION

[0017] In order to enable the personnel in the technical field to better understand the present application scheme, the technical solutions in the embodiments of the present application will be described clearly and completely in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by the person skilled in the art without creative labor should belong to the scope of protection of the present application.

[0018] In the study, it is found that the parameters of the fractional model (such as the fractional order α, the viscosity coefficient η, etc.) are highly coupled and extremely sensitive to the observed data, resulting in an ill-posed problem of inversion. The existing technology generally uses the Tikhonov regularization method to alleviate this ill-posedness, but the regularization parameter λ is usually fixed according to experience or trial calculation. The defect of this static regularization strategy is that it cannot adapt to the dynamic physical process of the aging of dam materials over time. When the dam materials age and the model uncertainty increases, the degree of ill-posedness (i.e. the condition number) of the inversion problem will worsen. At this time, the fixed λ may be too small to suppress the oscillation of the solution; on the contrary, when the system is stable, the fixed λ may be too large to cause excessive smoothing, distorting the true physical parameters. The existing technology lacks an adaptive mechanism that can dynamically associate the regularization strength with the physical aging state of the system. Secondly, this static and blind regularization further leads to a lack of physical consistency in the spatial and temporal dimensions of the inversion results. In space, the conventional smoothing constraint (such as the Laplace regularization) will indiscriminately penalize the gradients of all parameters, leading to the over-smoothing of the parameter field at the interface mask where the material properties should physically change, such as the dam-body and dam-foundation interface, violating the physical reality. In time, the existing method is difficult to ensure that the fractional order α(t) evolved by the inversion strictly follows the physical law (such as monotonic aging) and is easily disturbed by data noise to produce meaningless oscillation. Finally, the above problems lead to the extremely complex, non-convex shape of the final optimization objective function (J total ), and there are many local minima. The standard optimization algorithm used in the existing technology is difficult to cope with: global search (such as the standard genetic algorithm) can jump out of the local area, but the convergence efficiency is low; local search (such as BFGS) converges fast, but is highly sensitive to the initial value and is prone to premature convergence. The existing technology lacks a hybrid optimization mechanism that can intelligently switch between global and local strategies according to the real-time state of the optimization process (such as population diversity, convergence speed, problem curvature), resulting in low efficiency and success rate of inversion.

[0019] For example, during long-term service, dam concrete and foundation rock exhibit rheological properties such as creep and slack deformation. Traditional deformation analysis methods often employ constitutive models composed of integer-order calculus elements (e.g., the Kelvin-Voigt model or the Maxwell model). However, such integer-order models often suffer from poor fitting of experimental data when describing the rheological properties of structures over a wide frequency range. To address this issue, fractional-order calculus theory has been introduced to construct fractional-order constitutive models (e.g., the fractional-order Burgers model). These models have clear physical meaning and can more accurately characterize the creep properties of concrete. However, fractional-order models introduce more undetermined parameters (such as the fractional order and viscosity coefficient), while dam deformation observation data are affected by various uncertainties. This makes it highly susceptible to ill-posed problems when using measured data to invert and determine these model parameters. The ill-posedness of the inversion results is characterized by their high sensitivity to small perturbations in the observation data and prior information (such as initial parameter values), which leads to unstable and non-unique inversion results, and may even violate physical laws, seriously affecting the accuracy and reliability of the analysis model.

[0020] Specifically, considering the characteristics of each working stage of a concrete dam structure, this study analyzes the changes in deformation behavior during the service life of a concrete dam and investigates the construction methods of constitutive models for different service stages, extending the integer-order mechanical models for different stages into fractional-order constitutive models. For high concrete dams, under long-term external loads, the stress level at any part of the dam is high, but usually does not exceed the proportional limit strength of the material. At this point, it is in the viscoelastic working stage, and the Kelvin-Voigt model and Maxwell model can be used to characterize the constitutive relationship. In the viscoelastic stage of the concrete dam, its rheological deformation can converge, exhibiting the behavior of a viscoelastic solid. Therefore, based on the Kelvin-Voigt constitutive model, a fractional-order constitutive model for the viscoelastic stage of the concrete dam is constructed. Under constant stress σ, ε(t) = J(t)σ = σE -1 ∑ k=0 ∞ (-1) k / Г(αk+α+1)((E / η)t α ) k+1Where ε(t) is the strain at time t; J(t) is the time-dependent creep function; E is the elastic modulus; k is the index variable in the summation symbol; Г() is the Gamma function; α is the fractional order; η is the viscosity coefficient; and t is the time variable. As the load increases, the dam stress is readjusted, and the compressive stress in the downstream area increases but remains within the proportional limit. The stress-strain relationship is basically quasi-viscoelastic. Referring to the unified rheological element model, the Burgers constitutive model can be expressed as: ε(t) = σ / E0(t) + σ / E1(t)(1-e (-E1(t) / η1(t))t )+ ∫0 t (σ / η3(t))dt; where E0(t) is the instantaneous elastic modulus; E1(t) is the delayed elastic modulus; η1(t) is the viscosity coefficient controlling the rate of delayed deformation; η3(t) is the viscosity coefficient controlling the rate of irreversible deformation; and e is the base of the natural logarithm. Under constant stress σ, ε(t) = J(t)σ = [1 / E K ∑ k=0 ∞ (((-1) k ((E K / η K )t α ) k+1 ) / Г(αk+α+1))+(1 / E M )+(1 / η M )(t α / Г(α+1))] σ; where E K η is the elastic modulus in the Kelvin-Voigt element. K E is the viscosity coefficient in the Kelvin-Voigt element. M η is the elastic modulus in a Maxwell element. M Here, represents the viscosity coefficient in the Maxwell element. Under three-dimensional stress, the fractional constitutive model of the rheological process of the dam concrete and foundation rock can be derived by replacing the axial stress σ in the fractional constitutive model of the rheological process under one-dimensional stress with the deviatoric stress S, according to the creep equation under uniaxial stress. ij By converting the rheological parameters into shear rheological parameters, a fractional-order rheological constitutive model under three-dimensional stress can be obtained. The viscoelastic model of the dam concrete can be represented by the fractional-order Burgers constitutive model, while the viscoelastic constitutive model of the dam foundation can be characterized by the fractional-order Kelvin constitutive model with a series of springs. A related program was developed, combining the inversion analysis mode of concrete dam deformation influence parameters. For the dam concrete, the viscoelastic constitutive model described by the fractional-order Burgers model under three-dimensional stress is: ε ij (t)=(σ m / 3K)δ ij +[1 / 2GK ∑ k=0 ∞ (((-1) k ((G K / η K )t α ) k+1 ) / Г(αk+α+1))+(1 / 2G M )+(1 / 2η M )(t α / Г(α+1))] S ij ; where ε ij σ is the strain tensor; m δ is the volume stress tensor; K is the bulk modulus; ij For the Kronecker function; G K G M S represents the shear modulus of the Kelvin-Voigt constitutive model and the Maxwell constitutive model, respectively, G = E / 2(1+μ), where μ is Poisson's ratio; S ij Let ε be the deviatoric stress tensor. For the dam foundation, the viscoelastic constitutive model described by the fractional-order Kelvin-Voigt constitutive model with series springs under three-dimensional stress state is: ε ij (t)=(σ m / 3K)δ ij +[1 / 2G K ∑ k=0 ∞ (((-1) k ((E K / η K )t α ) k+1 ) / Г(αk+α+1))+(1 / 2G0)] S ij Where G0 is the shear modulus.

[0021] like Figure 1 As shown, a method for analyzing the deformation behavior of concrete dams is proposed, including:

[0022] Acquire multi-source observation data, engineering information, and prior parameter sets to generate preprocessed data packages and model information packages.

[0023] In other words, we acquire multi-source observation data, engineering information, and prior parameter sets, and preprocess these data to obtain preprocessed data packages and model information packages.

[0024] In this embodiment, multi-source observation data may include, but is not limited to: the opening and closing degree of the joint gauges read from various sensors deployed on the concrete dam body and dam foundation (e.g., y). ce ), perpendicular measurements (e.g., y) pl), GNSS displacement (e.g., y gnss The data includes, but is not limited to: the dam's geometric model, finite element mesh, material zoning information, location masks (e.g., Γ) of construction joints and interfaces such as the dam heel / toe, and loads and environmental conditions during operation (e.g., reservoir water level, temperature field). The prior parameter set may include, but is not limited to: initial values ​​of material elastic parameters (e.g., elastic modulus), viscous parameters (e.g., viscosity coefficient), initial values ​​of fractional-order parameters, and reasonable physical upper and lower bounds for these parameters, preset based on engineering experience or laboratory tests. The process of generating the preprocessed data package and model information package involves formatting, cleaning, and organizing the aforementioned raw data for subsequent steps.

[0025] Based on the preprocessed data package and model information package, we evaluate aging indices that characterize the structural behavior of dams and monitor the condition number of the inversion problem.

[0026] Specifically, the aging index is used to quantify the degree of evolution (i.e., aging) of dam material properties over time. Evaluating this index allows for dynamic adjustments to the analysis strategy based on the dam's structural behavior. The condition number measures the ill-posedness of the inversion problem (i.e., the parameter identification problem). Monitoring the condition number allows for real-time assessment of the stability of the inversion solution.

[0027] Based on the aging index and condition number, the regularization parameter is dynamically determined, and an adaptive objective function is constructed.

[0028] In this embodiment, the regularization parameter (e.g., λ) is a key parameter used to balance the relationship between the model's predictions and the observed data's fit and the smoothness or stability of the parameters themselves within the objective function. Preferably, the regularization parameter λ is not fixed but dynamically and adaptively determined based on the evaluated aging index and the monitored condition number. The final constructed adaptive objective function (e.g., J...) total This will include both the data fitting term and this dynamic regularization term.

[0029] An adaptive hybrid optimization strategy with a multi-index state machine switching mechanism is adopted to solve the adaptive objective function and output the estimated parameter set.

[0030] Specifically, to efficiently and robustly solve the adaptive objective function, a hybrid optimization strategy is adopted. This strategy preferably combines a global search algorithm (such as the improved genetic algorithm IGA) and a local refinement algorithm (such as the BFGS quasi-Newton method). The strategy employs a multi-index state machine switching mechanism, meaning it no longer relies on a fixed number of iterations but instead determines when to automatically switch from global search to local refinement by real-time monitoring of multiple indices during the optimization process (such as population diversity, optimization improvement rate, problem curvature, etc.). The final result is to achieve an adaptive objective function J that... totalTo achieve the minimum combination of parameters, i.e., to estimate the parameter set (e.g., θ). hat ).

[0031] Based on the estimated parameter set, generate an analysis result package.

[0032] In this embodiment, the estimated parameter set θ is used. hat Perform forward computation to generate the model's predicted sequence (e.g., y). pred The system compares the results with observed data and calculates evaluation metrics such as the root mean square error (RMSE). It can also generate analysis reports including parameter confidence intervals and system stability diagnostic curves. Finally, all results (such as θ) are analyzed. hat y pred Package the analysis report and other data into deliverable packages (e.g., Deliverables).

[0033] This embodiment achieves dynamic adaptation of regularization parameters by introducing aging index and condition number monitoring, and improves the intelligence of hybrid optimization algorithm through state machine switching mechanism, thereby systematically solving the ill-posed problem in fractional-order model inversion.

[0034] In one possible implementation, the preprocessed data packet and the model information packet are generated, including:

[0035] The channel-level median absolute deviation of each data channel in the multi-source observation data is evaluated. Based on this channel-level median absolute deviation, an initial value for the whitening matrix is ​​constructed. Based on the initial value of the whitening matrix, engineering information, and prior parameter set, a preprocessing data package and a model information package are generated. Furthermore, the construction of the adaptive objective function and the evaluation of the aging index both depend on this initial value of the whitening matrix.

[0036] In this embodiment, when acquiring raw observation data (y obs After that, it undergoes a series of preprocessing steps to generate a preprocessed data packet (e.g., Y). preSpecifically: anomaly detection and missing data interpolation are performed. For example, windowed median absolute deviation (MAD) and two-sided thresholding are used to remove abnormal spikes. Neighborhood spline interpolation is used for short-term missing data segments, while regression interpolation based on the correlation of similar sensors can be used for long-term missing data segments. A unified time axis t is constructed using the highest sampling frequency or a common time resolution, and anti-aliasing low-pass filtering is applied to high-frequency channels before resampling to align all data in time. Based on the coordinate system configuration in the engineering information package, coordinate system registration and unit conversion (e.g., millimeters to meters, angles to radians) are completed for each channel's data to obtain normalized data. As a preferred implementation, before evaluating the channel-level median absolute deviation, i.e., after the above preprocessing, environmental covariate regression correction is also included to remove non-structural deformation drift caused by environmental factors (such as temperature, reservoir water level, seepage pressure, etc.) from the observed data. Specifically, normalized data and corresponding environmental covariate time series can be read, and a hierarchical regression model (e.g., a multiple regression model considering linear and lagged terms) can be established to fit the relationship between environmental quantities and deformation quantities. The fitted environmental effect portion is then subtracted from the observed data to obtain the environmentally corrected data series (e.g., Y). envcorr ).

[0037] Based on this, the absolute deviation of the channel-level median is evaluated. Preferably, this evaluation is performed on the environmentally corrected data sequence Y. envcorr This is performed (or for normalized data if environmental correction was not performed). For each data channel (e.g., individual components of seam gauge, plumb line, and GNSS), the median absolute deviation (MAD) of its time series is calculated. Median absolute deviation is a robust estimate of dispersion that is insensitive to outliers in the dataset. The MAD value for each channel is then converted to its equivalent standard deviation (e.g., σ) by multiplying it by a constant (e.g., 1.4826). ce , σ tilt , σ gnss (etc.). Initialize the whitening matrix W. y0 Construct a block-diagonal matrix, where the elements on the diagonal are the reciprocals of the equivalent standard deviation of the corresponding channel. For example, W y0 =blkdiag(σ ce -1 I, σ tilt -1 I, σ gnss -1 I), where I is the identity matrix and blkdiag is the block diagonal matrix. A robust MAD statistic is used instead of the traditional (outlier-prone) standard deviation to estimate the noise level, and an initial value W for the whitening matrix is ​​constructed. y0This reflects the noise levels of observation data from different sources, with different precision, and with different dimensions. This will be used in the subsequent construction of the adaptive objective function J. total At that time, the initial value W of the whitening matrix will be used. y0 The observation residuals are whitened. Whitening ensures that the residuals from different channels have the same variance (i.e., homoscedasticity), allowing higher-precision observations to receive greater weight than lower-precision observations during parameter inversion, thus resolving the heteroscedasticity problem. Simultaneously, the aging index I is subsequently evaluated. age The estimation will also be based on the whitened residual spectrum, and the initial value of the whitening matrix ensures the reliability of the spectrum estimation.

[0038] like Figure 2 As shown, according to one aspect of this application, an adaptive objective function is constructed, comprising:

[0039] By integrating preprocessed data packets and model information packets, aging indicators are extracted.

[0040] like Figure 3 As shown, in an optional implementation, aging metrics are extracted, including:

[0041] The preprocessed data packets and model information packets are calculated to obtain the whitened residual sequence.

[0042] In one exemplary embodiment, obtaining the whitening residual sequence includes:

[0043] Based on the initial value of the whitening matrix, the preprocessed data package, and the model information package, the initial draft of the residual is calculated, and based on the initial draft of the residual, the updated whitening matrix is ​​obtained.

[0044] Specifically, based on the initial value W of the whitening matrix y0 Preprocessed data packets Y pre And the model information package G1, using the model F(θ, α(t), G1) (which can use the prior parameter θ0 as the initial value), calculate the initial residual r0=Y pre -F(θ0, α(t), G1). Analyze the statistical characteristics of each channel in the initial residual r0 (e.g., recalculate the median absolute deviation), and obtain the updated whitening matrix W accordingly. y By adjusting the initial value W of the whitening matrix y0 Iterative optimizations were made to make it more consistent with the actual residual distribution under the current model framework.

[0045] The updated whitening matrix is ​​applied to process the discrepancy between the preprocessed data packet and the model information packet, and the whitening residual sequence is obtained.

[0046] Optionally, the whitened residual sequence r white It can be represented as: r white =W y ·(Ypre -F(θ, α(t), G1)); where θ is the parameter set of the current iteration.

[0047] Analyze the whitening residual sequence to determine the residual power spectrum of the whitening residual sequence within the preset frequency band; fit the logarithmic shape of the residual power spectrum to obtain the logarithmic slope of the power spectrum; and designate the logarithmic slope of the power spectrum as the aging index.

[0048] In this embodiment, the preset frequency band [ω l ω h The selection of [band name] can preferably be determined based on the main frequency range of the dam structure's response to environmental loads (such as annual or daily temperature variations) to cover the low-frequency band with a high signal-to-noise ratio. For example, if the main concern is annual cycle variation, the frequency band can be set to cover the angular frequency range corresponding to cycles of 0.5 to 5 years. The logarithmic form is log(S) in a log-log coordinate system. r The relationship between S(ω) and log(ω), where S r (ω) represents the residual power spectrum. Aging index I age This reflects the long-term correlation or color of the residual signal. For healthy systems with well-fitting models, the whitened residual sequence r... white It should approximate white noise, aging index I age The value approaches 0; however, when the system ages or the model mismatches, the whitened residual sequence r... white The model will retain long-term drift that is not explained by the model, leading to aging index I. age Increase (e.g., tend towards -1 or smaller).

[0049] Based on aging metrics, a condition number upper limit function is set.

[0050] Preferably, a dynamic upper limit function for the condition number is set, in the form: κ max (I age )=κ0 / (1+c·∣I age ∣); where κ0 is the upper limit of the baseline condition number, representing the aging index I. age When the condition number is close to 0 (indicating good dam structural behavior), the maximum condition number allowed for the inversion problem can be empirically set between 10³ and 10⁵. c is an adjustment factor that controls the upper limit function of the condition number, κ. max Follow | I age | An increased decay rate, for example, can be a value between 0.5 and 10. As system aging accelerates (|I age When the condition number κ increases, it means that the uncertainty of the model increases. At this time, the tolerance for the condition number κ should be actively reduced (i.e., κ should be reduced). max This reduces the regularization, forcing the algorithm to apply stronger regularization.

[0051] Establish an efficient Hessian approximation matrix to represent the condition number of the inversion problem.

[0052] Specifically, the effective Hessian approximation matrix can be approximated as: H eff =J T W y T W y J+λL T L; where J is the Jacobian matrix of model F for the inversion parameter θ, i.e., the sensitivity matrix of the model output to the parameter. J T W y T W y J is the Hessian matrix approximation term (data term) in the Gauss-Newton method. T This is the transpose. λL T L is the regularization term, and λ is the regularization parameter to be determined. T L originates from prior information about the parameters (such as the prior weighting matrix W). p (or subsequent space / time constraints).

[0053] The regularization parameter is automatically optimized so that the condition number of the effective Hessian approximation matrix is ​​constrained to a threshold determined by the upper limit function of the condition number.

[0054] For example, by means of binary search or small step trial, we find the minimum regularization parameter λ>0 such that the condition number κ(H) of the effective Hessian approximation matrix is... eff )=λ max (H eff ) / λ min (H eff )≤κ max (I age ), where λ max λ is the largest eigenvalue. min It is the smallest eigenvalue.

[0055] An adaptive objective function is constructed using the regularization parameters obtained through optimization.

[0056] In a preferred embodiment, the adaptive objective function J total =∣∣r white ||2 2 +λ·∣∣W p (θ-θ0)∣∣2 2 +β tv TV Γ (α)+η time ·∑Huber(α(t k )-α(t k-1 ))+μ phys ·Rphys (θ); where ||r white ||2 2 It is a data fitting term based on the whitening residual; λ·∣∣...∣∣2 2 It is a dynamically determined Tikhonov regularization term; W p It is a priori weighted matrix of parameters (used to balance parameters with different dimensions), θ0 is the prior parameter; β tv TV Γ (α) is the spatial smoothing regularization term; η time • ∑Huber(...) is a time-robust prior used to constrain the stationary evolution of α(t) over time. Preferably, the Huber loss function is used to resist abrupt changes or anomalies in the time series. The Huber threshold δ huber It can be adaptively determined, for example, by calculating α(t) k )-α(t k-1 The median absolute deviation (MAD) of the differenced sequence is used to robustly estimate its noise level, and this is used to set the Huber threshold δ. huber μ phys ·R phys (θ) is the penalty term in the physical feasible region, used to ensure parameters (such as α0, Δ) α λ (α0 > 0) remains within its physical range (e.g., α0 > 0). λ is dynamically adaptive. tv η time μ phys It's a hyperparameter. μ phys The penalty value is typically set to a sufficiently large value (e.g., 10⁸) to ensure physical constraints. β tv and η time The relative intensity used to balance spatial and temporal smoothing.

[0057] In a further embodiment, it also includes:

[0058] Based on the model information package and prior parameter set, a time-varying fractional order is constructed to characterize the aging behavior of materials.

[0059] Specifically, unlike traditional models that use a constant order, the preferred method for constructing a time-varying fractional order includes: constructing the time-varying fractional order as a function of low-dimensional aging parameters {α0, Δ}. α Functional form of τ} Where t represents the time elapsed since the dam began service (or the starting point of the model analysis); α(t) is the time-varying fractional order at time t, used to characterize the viscoelastic properties of the material at that time; α0 is the initial fractional order of the material (at t=0), whose physical meaning constrains its range of values, for example, α0∈(0,1); Δ αThe physical constraint Δ represents the maximum change in the fractional order over time due to aging effects. α ≥0; τ is the time constant characterizing the aging rate, τ>0, reflecting the time scale required for the material to reach its final aging state. This low-dimensional interpretable function form replaces the high-dimensional curve that treats the order of each moment or spatial location as independent degrees of freedom, reducing the degrees of freedom in the inversion problem and thus initially alleviating the ill-posedness problem. The low-dimensional aging parameters are incorporated into the estimated parameter set as the solution objective of the adaptive hybrid optimization strategy.

[0060] Based on the model constructed using time-varying fractional order, an effective Hessian approximation matrix is ​​established, and aging indicators are extracted.

[0061] In other words, the establishment of the effective Hessian approximation matrix and the extraction of aging indices are both based on models constructed using time-varying fractional order. Preferably, the model constructed based on time-varying fractional order is a forward model for concrete dam deformation analysis (e.g., the computational interface F(θ, α(t), G1) that couples the fractional-order Burgers constitutive model with the finite element model, where F() is the forward computational interface, θ is the set of estimated parameters, and G1 is the model information package).

[0062] Further implementation methods also include:

[0063] The interface mask is extracted from the model information package; based on the interface mask and the time-varying fractional order, an interface-friendly total variation regularization term is constructed; the interface-friendly total variation regularization term is integrated into the adaptive objective function to constrain the spatial smoothness of the adaptive hybrid optimization strategy.

[0064] Specifically, in the adaptive objective function J total In the middle, a spatial smoothing regularization term β was added. tv TV Γ (α). The interface mask Γ is geometric information extracted from engineering information (model information package) that identifies the interfaces between different materials or structures. For example, Γ can identify the contact surface between dam concrete and dam foundation rock, or the construction joint between different construction pouring blocks. Preferably, the interface-friendly total variation regularization term TV... Γ (α) is the total variation regularization term, whose smoothing constraint strength is spatially non-uniform. It treats the interface identified by the interface mask Γ in a friendly manner. When retrieving the spatial distribution of the time-varying fractional order α, it is generally desirable for α to be smooth within the same material domain (e.g., inside the dam foundation) (to suppress noise). However, at the interface between different materials (e.g., the dam-foundation interface Γ), α may be physically abruptly abrupt. Conventional smoothing constraints (such as standard TV or Laplace smoothing) indiscriminately penalize all gradients, causing real abrupt changes at the interface to be obscured. Interface-friendly total variation regularization term TVΓ (α) can achieve strong smoothing within the domain and weak smoothing at the interface.

[0065] In an optional implementation, the process of constructing the UI-friendly total variation regularization term specifically includes:

[0066] A spatial adjacency graph is established based on the model information package.

[0067] Specifically, the model information package can be a finite element mesh. Nodes i and j in the spatial adjacency graph can represent mesh elements or mesh nodes, and the edge (i, j) indicates that i and j are spatially adjacent.

[0068] Identify adjacency pairs that cross the interface mask in the spatial adjacency graph, and assign a first numerical weight to the first type of adjacency pairs identified.

[0069] Specifically, node i is located on one side of the interface mask Γ (e.g., the dam body), while node j is located on the other side of the interface mask Γ (e.g., the dam foundation). A first numerical weight w1 is assigned to the aforementioned first type of adjacency pair (i, j).

[0070] Identify adjacency pairs in the spatial adjacency graph that do not cross the interface mask and are located in the same domain, and assign a second numerical weight to the identified second type of adjacency pairs. The second numerical weight is higher than the first numerical weight.

[0071] For example, nodes i and j are both located within the dam body, or both within the dam foundation. For the second type of adjacency pair (i, j), a second numerical weight w2 is assigned. The second numerical weight w2 is set to be higher than the first numerical weight w1. For example, w1 can be set to 0.1 (weak smoothing weight), while w2 can be set to 1.0 (strong smoothing weight).

[0072] Based on the first and second numerical weights, the differences of the time-varying fractional order over all adjacency pairs are summed in a weighted manner to obtain the interface-friendly total variation regularization term.

[0073] In other words, the total variation of the user-friendliness regularization term TV Γ (α) is constructed as the difference of the time-varying fractional order α over all adjacency pairs (i, j) (e.g., |α) i -α j | or (α) i -α j ) 2 ), and apply a weighted summation with its corresponding numerical weight (w1 or w2).

[0074] For example, using the L1 norm form: TV Γ (α)=∑ (i，j)∈Domain 1 w2 |α i -αj ∣+∑ (i，j)∈Domain 2 w2 |α i -α j |+…+∑ (i，j)∈Interface Γ w1 |α i -α j |, where Domain 1 is the first homogeneous material region in the model, such as the dam concrete region; Domain 2 is the second homogeneous material region in the model, such as the dam foundation rock region; and Interface Γ is the interface mask Γ. Thus, the adaptive objective function J... total During optimization, parameter differences within the same domain are strongly penalized (applied w2) to force them to be smooth; however, parameter differences across interfaces are penalized less strongly (applied w1) to allow the inversion results to exhibit the necessary jumps at the physical interface Γ.

[0075] In a preferred embodiment, since the initial engineering information may deviate from the actual physical interface, the extraction of the interface mask Γ also includes a residual-guided refinement process. Specifically, this includes: performing rapid forward computation using the initial interface mask Γ and prior parameters θ0 to obtain a preliminary residual field r0; analyzing the gradient of the preliminary residual field r0 near the boundary of the interface mask Γ; if a systematic deviation of the gradient of the preliminary residual field r0 from the interface normal is found near the interface mask Γ, it indicates that the position of the interface mask Γ may be inaccurate; and fine-tuning the boundary of the interface mask Γ, for example, reassigning cells with abnormal residual gradients to neighboring material domains to produce a refined interface mask Γ. ref Using a refined interface mask ref Instead of using an interface mask to construct a TV Γ (α). This embodiment uses closed-loop feedback to correct the model (mask) using data (residuals), further improving the accuracy of spatial constraints.

[0076] like Figure 4 As shown, in one embodiment of this application, the output estimated parameter set includes:

[0077] Perform a global search on the adaptive objective function.

[0078] In this embodiment, the global search can employ an improved genetic algorithm. Unlike traditional genetic algorithms (GA) that use purely random initialization of the population, this embodiment preferably embodies an engineering prior-guided population initialization strategy. Specifically, this initialization strategy may include a combination of one or more of the following: based on engineering experience, applying reasonable, small-range random perturbations to the design parameters (such as elastic modulus and viscosity coefficient) in the prior parameter set θ0 to generate a subset of initial individuals; if parameter inversion results from historically similar projects exist, these results can be directly transferred to the initial population as elite individuals; within the physically feasible region of the parameters, using the Latin hypercube sampling (LHS) method to generate a subset of individuals to ensure that the initial population has good uniformity and representativeness across the entire parameter space; and mixing in a small number of completely randomly generated individuals to maintain population diversity and prevent early convergence. Through this initialization strategy, the global search phase can start from a higher-quality starting point, reducing the proportion of early invalid explorations and improving convergence efficiency.

[0079] During the global search, concurrent monitoring is performed on the triggering metrics used in the multi-metric state machine.

[0080] Specifically, while global search algorithms have strong exploration capabilities, their convergence speed is slow when approaching the optimal solution. Therefore, an intelligent mechanism is needed to determine when the global search has been sufficiently completed and when to switch to a faster local refinement algorithm. Preferably, a multi-index state machine is used instead of the traditional, fixed-number-of-iterations switching (e.g., N). act This enables data-driven adaptive switching. Optionally, the triggering metrics include at least two items selected from the following group: population diversity assessed based on the global search state; a measure of the dispersion among individuals in the current population. Specifically, this can be quantified by calculating the median absolute deviation (MAD) or standard deviation of each parameter in the population. When the population diversity metric σ... div Below the preset convergence threshold σ min Time (e.g., σ) min =10 -4 This indicates that the population has become highly saturated, making further global search less meaningful and triggering a switch. The relative improvement rate of the sliding window, evaluated based on optimization history, measures the rate of progress of the global search algorithm over a recent period. Specifically, a time window w (e.g., w=10 generations) can be set to calculate the current optimal objective function value J. best (k) relative to the optimal value J before generation w best The relative improvement rate ΔJ of (kw) w =∣J best (k)-J best (kw)∣ / ∣J best (k)∣。When the relative improvement rate of the sliding window ΔJw is below the stagnation threshold Ψ fTime (e.g., Ψ) f =10 -6 This indicates that the algorithm has stalled and a switch should be triggered. The curvature ratio, evaluated based on the effective Hessian approximation matrix, is used to assess the shape of the objective function in the region where the current optimal solution resides. The curvature ratio ρ can be derived from the effective Hessian approximation matrix H. eff Estimate, ρ=λ min (H eff ) / λ max (H eff When the curvature ratio ρ is below the ill-conditioned threshold ρ min (e.g., ρ) min =10 -8 When the condition is met, it indicates that the objective function is highly ill-conditioned or resembles a flat canyon in that region. The improved genetic algorithm may be difficult to optimize further, and a switch should be triggered to try using a local algorithm.

[0081] When the trigger indicator meets the preset threshold, a switching event is automatically generated, and the current optimal solution is captured as the initial value for local search.

[0082] In other words, when any of the above triggering indicators meets its preset threshold (e.g., σ), div <σ min or ΔJ w <Ψ f Automatically generate switching events and capture the best individual (i.e., the optimal solution) obtained from the current global search as the initial value x0 for the local search. local .

[0083] In response to the switching event, the local refinement stage is activated, and the adaptive objective function is optimized using the initial values ​​of the local search to obtain the estimated parameter set.

[0084] In this embodiment, preferably, the BFGS (Broyden-Fletcher-Goldfarb-Shanno) quasi-Newton method is used in the local refinement stage. As a preferred implementation, the BFGS algorithm employs a trust region strategy. In each iteration, not only is the BFGS search direction calculated, but also the trust region radius, which characterizes the reliable range of the current model approximation. If the BFGS step size exceeds this radius, a dogleg step, for example, is used to correct the step size, ensuring that the iterations are within the reliable range. Compared to traditional line search strategies, the trust region strategy is generally more robust when dealing with ill-conditioned or non-convex problems. In the local refinement stage, the physical feasibility of the parameters (e.g., α0∈(0,1), τ>0, etc.) must be strictly guaranteed. As a possible implementation, this constraint is guaranteed before optimization begins through reparameterization. For example, for a parameter τ that must be positive, τ = softplus(τ′) can be used to optimize the unconstrained aging time parameter τ′. For a parameter α0 that must be within (0, 1), we can let α0 = sigmoid(α0′) to optimize the unconstrained initial fractional order parameter α0′. In another alternative implementation, if a new solution x is obtained during iteration... new If the physical feasible region is violated, then the projection operator is used to project x. new Project back to the nearest point within the feasible region. As a preferred option to further improve robustness, an elite mutation bounce mechanism may also be included. If, during Local Fine Refinement (BFGS) process, the algorithm fails multiple times consecutively (e.g., the predicted improvement is less than or equal to the actual improvement ρ),... k If the value is less than the threshold twice consecutively, causing the trust region radius to shrink excessively, the bounce mechanism is triggered. This bounce mechanism applies a small random perturbation (mutation) to the current optimal solution (elite) and briefly reverts to the global search phase (e.g., performing several generations of improved genetic algorithm evolution) in order to escape the current ill-conditioned region or local minimum, and then re-triggers the state machine switching to enter a new local refinement process.

[0085] In one exemplary embodiment, before or during the activation of the local refinement phase, the method further includes:

[0086] Based on the Jacobian matrix and whitening matrix used to construct the effective Hessian approximation matrix, the sensitivity index of the model parameters is calculated.

[0087] In this embodiment, the sensitivity index is used to quantify how sensitive the model output (i.e., the predicted deformation) is to changes in each parameter to be inverted (particularly spatially distributed parameters, such as α for different regions). In a preferred implementation, this sensitivity index can be directly derived from the Hessian approximation J. T W y T W yJ is obtained. Specifically, its diagonal element diag(J) T W y T W y J) can be used as a sensitivity index for each parameter (or its corresponding spatial block). The larger the value, the greater the influence of the parameter on the whitening residual, and the higher the difficulty and importance of the inversion.

[0088] Identify sensitive areas where the sensitivity index exceeds a preset threshold.

[0089] Specifically, the sensitive region corresponds to the spatial block containing high-sensitivity index parameters. The preset threshold can be determined in several ways, including: arranging all parameters in descending order of sensitivity index and selecting the top p... percent The parameters, for example, selecting p percent =10% or 20% of the parameters; analyze the sensitivity index curves arranged in descending order, automatically find their inflection points, and select all high sensitivity parameters before the inflection point; set a fixed sensitivity threshold and select all parameters higher than the threshold.

[0090] For sensitive areas, targeted refinement is performed on the model information package to generate a refined model description.

[0091] Specifically, targeted refinement refers to not performing global, uniform refinement on the entire engineering model (e.g., the finite element mesh of the entire dam) (which would lead to a dramatic increase in computational load), but rather locally refining or subdividing the finite element mesh elements or parameter blocks corresponding to identified sensitive areas (e.g., stress concentration areas, material interface areas, etc.). For example, if a dam foundation element is identified as a sensitive area, that element is subdivided into eight smaller sub-elements. Limited computational resources are concentrated on the key areas that have the greatest impact on the inversion results and are the most uncertain. After refinement, the original model information package G1 is updated to the refined model description M. ref .

[0092] Based on the refined model description, the local refinement stage is activated.

[0093] In other words, the local refinement stage describes M based on this refined model. ref conduct.

[0094] In a further embodiment, when directional refinement is performed, for example, a parent unit is subdivided into multiple child units, this introduces new parametric degrees of freedom (e.g., the θ of the child units). child To ensure a smooth transition and physical consistency between the coarse and fine models, the following also applies:

[0095] Construct a cross-layer consistency penalty to punish the deviation between the newly added parameter degrees of freedom introduced by targeted refinement and their parent parameters.

[0096] Specifically, for the sub-parameter θ child When initializing new parameter degrees of freedom, affine extrapolation or interpolation based on parent values ​​is typically used (e.g., P(θ)). parent And stacked small perturbations. Cross-layer consistency penalty R prol It can be constructed as a quadratic penalty form: R prol =γ prol ·∑ child ||θ child -P(θ parent )∣∣2 2 ;wherein γ prol These are preset penalty weight coefficients used to control the degrees of freedom of child parameters deviating from the parent interpolation value; θ parent P(θ) is the parent parameter, and child is the child unit. parent ) is the parent value interpolation function.

[0097] A cross-layer consistency penalty is added to the adaptive objective function. For example, the updated adaptive objective function J... total_ref =J total +R prol .

[0098] In the local refinement stage, the focus shifts to optimizing the adaptive objective function that has been supplemented with cross-layer consistency penalties.

[0099] This embodiment ensures that when refining the model, the inversion results can still maintain continuity and consistency with the coarse model (global search stage), avoiding optimization oscillations caused by model mutations.

[0100] In a detailed embodiment, the experimental data came from creep tests on concrete specimens. Specifically, the specimens were 28-day-old concrete, placed in water during the test (100% humidity), and were cylinders with a diameter of 70 mm and a height of 280 mm. The applied axial stress during the test was 4.91 MPa. A fractional-order Burgers constitutive model was selected to simulate the experimental data. This is because the fractional-order Burgers model can be considered as a concatenation of the fractional-order Maxwell constitutive model (representing the characteristics of the fluid during concrete hydration and measuring irreversible deformation) and the fractional-order Kelvin-Voigt constitutive model (describing the mechanical properties of unhydrated cementitious particles, aggregates, etc., and measuring recoverable deformation). As a control, a traditional integer-order Burgers constitutive model (i.e., a degenerate form where α(t) is always equal to 1) was used to fit the experimental data. An improved genetic algorithm was used to determine the parameters. The fitting parameters corresponding to the obtained fitting results are: E M =86.41 GPa; E K =27.73 GPa; ηM =0.71 GPa·d; η K =11550.67 GPa·d; the order α is fixed at 1, and the final fitting residual is 1.43E-21. The fractional-order Burgers constitutive model of this application (in this embodiment, for simplification, α(t) is assumed to be a constant order α) is used to fit the same experimental data. The improved genetic algorithm is also used to determine the parameters. The fitting parameters corresponding to the obtained fitting results are: E M =70.13GPa; E K =26.90 GPa; η M =0.79 GPa·d; η K =5467.03 GPa·d; order α=0.78; the final fitting residual is 6.73E-22. By comparing the fitting residuals of the two groups (6.73E-22 is much smaller than 1.43E-21), it can be seen that the fractional-order Burgers constitutive model fits the experimental data significantly better than the integer-order Burgers constitutive model. This proves that the fractional-order constitutive model can more accurately characterize the creep characteristics of concrete over a wide frequency range.

[0101] According to one aspect of this application, generating an analysis results package includes the following steps:

[0102] Using the obtained optimal set of estimated parameters θ hat and time-varying fractional order field α field_hat The forward computation interface F(θ, α(t), G1) is called to perform a complete forward reconstruction computation and generate the model prediction sequence y. pred The model predicts the sequence y. pred With preprocessed observation data packet Y pre Compare and calculate the evaluation index set Eval. set Evaluation metrics set Eval set In addition to conventional goodness-of-fit metrics, such as root mean square error (RMSE), it preferably includes a series of diagnostic metrics: normalized residual spectrum: for y pred -Y pre Calculate the power spectrum to check if the residuals are close to white noise, or if there are still systematic biases in specific frequency bands (such as annual or daily cycles) that the model cannot explain. Gradient infinity norm: i.e., max(|▽J total |), used to check whether the optimization algorithm truly converges at a stationary point (gradient close to zero). Adjacency difference norm: for example, the L1 norm ||▽α||1, used to quantize the fractional-order field α obtained from the final inversion. field_hat Spatial smoothness, as a measure of TV Г (α) Posterior check of the effect of the regularization term.

[0103] Using the effective Hessian approximation matrix H of the final form obtained during the optimization process eff Preferably, the Laplace approximation method is used, by calculating H... eff The inverse matrix (H) eff -1 ), to approximate all the parameters to be inverted (θ) hat The posterior covariance matrix C θ From the posterior covariance matrix C θ The diagonal elements can be used to extract the posterior variance of each parameter. Based on this, key low-dimensional aging parameters (such as α0, Δ) can be extracted. α The confidence intervals (e.g., 95% confidence intervals) for the parameter inversion results are calculated using the parameters (τ) and key material parameters. This provides engineers with a measure of the reliability of the parameter inversion results. The parameter uncertainty (i.e., the posterior covariance matrix C) is then considered. θ Uncertainty propagation is achieved through a forward model F(θ, α(t), G1). For example, it can be achieved through Monte Carlo sampling (from C... θ By sampling from a defined multidimensional normal distribution or using first / second moment methods, the uncertainty of the parameters is propagated to the model output (such as displacement and stress). The result is no longer a single predicted curve y. pred Instead, it represents an uncertainty envelope or risk section. For example, it can generate a risk assessment report showing that the dam crest displacement has a 95% probability of falling within the [X, Y] interval over the next 10 years, which is of great value for dam safety monitoring and decision support. The diagnostic data recorded in all iteration steps throughout the adaptive optimization process are summarized. Preferably, I is generated. age –κ–λ correlation curve. This curve shows the correlation between aging index I and λ. age The change in the condition number (ill-conditioned change) and how the condition number conservation strategy automatically adjusts the regularization parameter λ and successfully increases the effective Hessian condition number κ(H) eff Constraints on the dynamic upper limit κ max (I age (below)

[0104] All generated results, including: the estimated parameter set θ hat Fractional order field α field_hat Model predicted sequence y pred Evaluation indicator set Eval set And an analysis report dataset containing confidence intervals, uncertainty envelopes, and diagnostic curves. set They are then integrated and packaged to form the final deliverable package.

[0105] As a preferred implementation, the deliverable package should also include necessary metadata, such as: the version number of the algorithm used, and the hyperparameters used (e.g., σ). min, ψ f p percent (etc.), calculate timestamps, and the raw data on which they depend (Y) pre The hash value of G1 makes the entire analysis process traceable and reproducible.

[0106] In another embodiment of this application, the adaptive objective function can also be:

[0107] Read and update project information and prior parameter package, and define the fractional order as... Constraints α0∈(0,1), Δ α ≥0, τ>0, forming a time-varying order parameter set α param ={α0,Δ α Read the updated engineering information and time-varying order parameter set, inject the fractional order into the original fractional viscoelastic constitutive framework using a reparameterization method, and couple it with the load / boundary time sequence to construct the model interface. Read the prior parameter package, reparameterize the elastic modulus, viscosity, fractional order, etc. using softplus / sigmoid, and form physical soft constraint rules for subsequent optimization and projection. Read the interface mask and updated engineering information, set the adjacency weights (weak interface smoothing, strong intra-domain smoothing) according to the mesh scale, stress level, and interface type to obtain the weight map. Read the time axis of the preprocessed observation data package and perform a reparameterization of the difference sequence α(t) k )-α(t k-1 The median absolute deviation is estimated, the Huber threshold is calculated, and a time prior configuration is formed. The initial values ​​of the parameter prior weighting matrix and the weight map are read, and the initial values ​​of the parameter prior weighting matrix are corrected to be consistent with the spatial scale of the total variation in user interface friendliness; the TV of the total variation in user interface friendliness is assembled. Γ (α)=Σ (i，j) w ij |α i -α j | and encapsulate the prior components = {interface-friendly total variation, time prior configuration, physical soft constraint rules}. Read the preprocessed observation data package, the initial value of the whitening matrix, and the model interface. Obtain the initial draft of the residuals through short-iteration forward prediction, update the equivalent standard deviation of each channel, and construct the whitening matrix. Read the whitening matrix, the preprocessed observation data package, and the model interface. Calculate the whitening observation residual = whitening matrix * (preprocessed observation data package - model interface), and perform window function shaping to avoid spectral leakage, obtaining the whitening residual. Read the whitening residual in the frequency band [ω l ω h Internal calculation of power spectrum S r (ω), for logS r(ω) The slope of the linear fitting is used to obtain the aging index, and the frequency band and fitting error are recorded for traceability. The model interface, whitening matrix, and prior component / parameter prior weighting matrix are read. The Jacobian J is obtained through analytical or numerical perturbation, and the effective Hessian draft H0=J is calculated. T W y T W y *J, where W y This is the whitening matrix. Read the aging index I. age , set κ max (I age )=κ0 / (1+c·∣I age |), thus obtaining the upper limit function of the condition number κ. max Read the valid Hessian draft, the prior weighted matrix of parameters, and the upper bound function of the condition number. Find the minimum regularization parameter λ such that κ(H) is minimized through binary search / small-step trial and error. eff )= κ(J T W y T W y J + λ L T L) ≤κ max (I age (L is determined by the prior weighting matrix and prior components), outputting the regularization parameter and the updated effective Hessian approximation matrix H. eff The whitening observation residual r white Whitening matrix, prior weighted matrix W p Prior components and regularization parameters are integrated into an adaptive objective function J. total =∣∣r white ||2 2 +λ·∣∣W p (θ-θ0)∣∣2 2 +β tv TV Γ (α)+η time ·∑Huber(α(t k )-α(t k-1 ))+μ phys ·R phys (θ); where β tv η time μ phys For fixed or configurable rights.

[0108] In another implementation of this application, the output estimated parameter set can also be:

[0109] Read the adaptive objective function, prior parameter package, updated project information, and time-varying order parameter set. Use a hierarchical strategy to generate the initial population: design parameter perturbation, similar project migration, Latin hypercube, and a small amount of randomness, ensuring all individuals satisfy the physical feasible region and interface mask Γ constraints. This yields the initial population P0 and its fitness evaluation Fit0=J. total (P0). Read the adaptive objective function and the current population P. k Calculate population diversity σ using historical best values. div =medianMAD(P k ) Improvement ΔJ compared to sliding windows w =∣J best (k)-J best (kw)∣ / ∣J best (k)∣, yielding the first state variable, where median is the median and MAD is the absolute deviation of the median. Reading the effective Hessian approximation matrix, the eigenvalue ratio is obtained using the Lanczos approximation, yielding the curvature ratio ρ=λ. min (H eff ) / λ max (H eff This forms the second state variable. Read the first and second state variables; when σ... div <σ min or ΔJ w <Ψ f or ρ < ρ min If the current best individual is frozen as a local initial value and a switching event is generated, the improved genetic algorithm (IGA) evolution continues. The adaptive objective function and whitening matrix are read, and the sensitivity index diag(J) is calculated. T W y T W y *J) and select the first p in descending order. percent The blocks are then refined to obtain a candidate set for refinement. The candidate set and the current parameter field are read, and mesh / parameter refinement is performed on the candidate blocks. The newly added degrees of freedom are initialized using parent value affine extrapolation and small perturbations to obtain the refined model description and initial refinement values. The current parameter field and initial refinement values ​​are read, and a cross-layer consistency penalty term R is added to the objective function. prol =γ prol ·∑ child ||θ child -P(θ parent )∣∣2 2The prior components are updated. The adaptive objective function or refined objective function, local initial values, and effective Hessian approximation matrix are read to construct the BFGS direction. When the step size exceeds the radius, the dogleg approximation solution is used to obtain candidate search steps. The candidate search steps and physical feasibility rules are read, and an Armijo-Wolfe line search is performed to obtain the step size. The out-of-bounds solution is projected onto the feasible region to form a new parameter solution. The new parameter solution and the old solution are read, and the predicted / actual improvement ratio ρ is calculated. k If ρ k If the threshold is exceeded, the radius is reduced and (if necessary) a brief elite mutation is triggered to bounce back to the global stage and then back to the local stage; otherwise, the radius is expanded. After satisfying the convergence criterion, candidate optimal solutions, fractional-order field, and optimization diagnostic increments are output. The optimization diagnostic increments are summarized, and convergence conditions (gradient infinity norm and relative target reduction) are evaluated. If satisfied, the estimated parameter set and fractional-order field are output; if not satisfied, the process reverts to the initial population generation step using the minimum improvement strategy and continues iterating.

[0110] This invention extracts an aging index characterizing the physical state of a system from the power spectrum of the whitened observation residuals using an adaptive regularization mechanism. A dynamically changing upper limit function for the condition number is set based on this aging index. During the inversion process, the minimum regularization parameter is automatically optimized and determined, ensuring that the condition number of the effective Hessian approximation matrix of the actual inversion problem is always constrained within the threshold determined by this dynamic upper limit. The regularization strength is dynamically coupled with the ill-conditioning degree of the system (i.e., the aging state) in real time, overcoming the ill-posedness problem caused by static regularization strategies. By constraining from both spatial and temporal dimensions, the lack of physical consistency in the inversion results is addressed. Specifically, in the spatial dimension, an interface-friendly total variation regularization term is introduced. This involves extracting an interface mask from the model information package and applying a lower first numerical weight to adjacency relationships crossing this mask (such as the dam-base boundary), while applying a higher second numerical weight to adjacency relationships within the same material domain. This suppresses noise while preserving the true parameter jumps that should exist at the physical interface, avoiding the ambiguity effect caused by traditional smoothing constraints. In the time dimension, the fractional-order parameter is parameterized as a time-varying function with clear physical meaning, controlled by low-dimensional aging parameters. This allows the inversion results to evolve smoothly according to physical laws, eliminating non-physical oscillations that may be caused by data noise. An adaptive hybrid optimization strategy is adopted to solve the problem of difficulty in optimizing the objective function caused by complex models. Specifically, instead of relying on fixed iteration counts or empirical judgments, a multi-index state machine switching mechanism is used for intelligent switching. This state machine monitors multiple trigger indicators in real time during the optimization process, such as population diversity, relative improvement rate of the sliding window, and curvature ratio (evaluated based on an effective Hessian approximation matrix). When any indicator meets a preset threshold, the algorithm automatically switches from the global search stage (such as an improved genetic algorithm) to the local refinement stage (such as the BFGS quasi-Newton method) and captures the current optimal solution as the initial value for the local search. This effectively avoids the inefficiency and premature convergence problems of traditional algorithms, improving the robustness and efficiency of solving complex non-convex objective functions.

[0111] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for analyzing the deformation behavior of concrete dams, characterized in that, include: Acquire multi-source observation data, engineering information, and prior parameter sets to generate preprocessed data packages and model information packages; Based on the preprocessed data package and model information package, we evaluate the aging index that characterizes the structural behavior of the dam and monitor the condition number of the inversion problem. Based on aging indicators and condition numbers, regularization parameters are dynamically determined, and an adaptive objective function is constructed. An adaptive hybrid optimization strategy with a multi-index state machine switching mechanism is adopted to solve the adaptive objective function and output the estimated parameter set. Based on the estimated parameter set, generate an analysis result package.

2. The method according to claim 1, characterized in that, Constructing an adaptive objective function includes: By integrating preprocessed data packets and model information packets, aging indicators are extracted. Based on aging indicators, set an upper limit function for the condition number; Establish an efficient Hessian approximation matrix representing the condition number of the inversion problem; The regularization parameter is automatically optimized so that the condition number of the effective Hessian approximation matrix is ​​constrained to a threshold determined by the upper limit function of the condition number. An adaptive objective function is constructed using the regularization parameters obtained through optimization.

3. The method according to claim 2, characterized in that, The aging indicators include: The preprocessed data packet and model information packet are calculated to obtain the whitened residual sequence; Analyze the whitened residual sequence to determine its residual power spectrum within a preset frequency band; By fitting the logarithmic shape of the residual power spectrum, the logarithmic slope of the power spectrum can be obtained; The logarithmic slope of the power spectrum is designated as the aging index.

4. The method according to claim 2, characterized in that, The extraction of aging indicators also includes: Based on the model information package and prior parameter set, a time-varying fractional order is constructed. Based on the model constructed using time-varying fractional order, an effective Hessian approximation matrix is ​​established, and aging indicators are extracted.

5. The method according to claim 4, characterized in that, The process of constructing a time-varying fractional order includes: The time-varying fractional order is constructed from the low-dimensional aging parameters {α0, Δ}. α Functional form of τ} Where t represents the time elapsed since the dam began operation; α(t) is the time-varying fractional order at time t; α0 is the initial fractional order of the material; Δ α τ represents the maximum change in the fractional order of the aging process over time due to the aging effect; τ is a time constant characterizing the aging rate. The low-dimensional aging parameters are incorporated into the estimated parameter set and used as the solution objective of the adaptive hybrid optimization strategy.

6. The method according to claim 2, characterized in that, The output estimated parameter set includes: Perform a global search on the adaptive objective function; During the global search, concurrent monitoring is performed on the triggering metrics used in the multi-metric state machine; When the trigger indicator meets the preset threshold, a switching event is automatically generated, and the current optimal solution is captured as the initial value for local search. In response to the switching event, the local refinement stage is activated, and the adaptive objective function is optimized using the initial values ​​of the local search to obtain the estimated parameter set.

7. The method according to claim 6, characterized in that, Triggering indicators include at least two items selected from the following groups: Population diversity was assessed based on the global search status. Based on the relative improvement rate of the sliding window in the historical evaluation; Curvature ratio evaluated based on the effective Hessian approximation matrix.

8. The method according to claim 4, characterized in that, Constructing an adaptive objective function also includes: Extract the interface mask from the model information package; Based on the interface mask and the time-varying fractional order, a regularization term for the total variation with a user-friendly interface is constructed. A user-friendly total variation regularization term is integrated into the adaptive objective function to constrain the spatial smoothness of the adaptive hybrid optimization strategy.

9. The method according to claim 8, characterized in that, Construct a regular expression for the total variation in user interface friendliness, including: Establish a spatial adjacency graph based on model information packets; Identify adjacency pairs that cross the interface mask in the spatial adjacency graph and assign them a first numerical weight. Identify adjacency pairs in the spatial adjacency graph that do not cross the interface mask and are located in the same domain, and assign them a second numerical weight, which is higher than the first numerical weight. Based on the first and second numerical weights, the differences of the time-varying fractional order over all adjacency pairs are summed in a weighted manner to obtain the interface-friendly total variation regularization term.

10. The method according to claim 6, characterized in that, Before or during the activation of the local refinement phase, it also includes: Based on the Jacobian matrix and whitening matrix used to construct the effective Hessian approximation matrix, the sensitivity index of the model parameters is calculated. Identify sensitive areas where the sensitivity index exceeds a preset threshold; For sensitive areas, targeted refinement is performed on the model information package to generate a refined model description; Based on the refined model description, the local refinement stage is activated.

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