76 results about "Numerical methodology" patented technology

The invention relates to a wellbore multiphase flow model numerical solution and gas-liquid distribution state inversion method and system, and belongs to the technical field of petroleum engineering, and the method comprises the steps: 1, constructing and training a physical information neural network for drilling wellbore multiphase flow dynamic simulation and overflow gas distribution state inversion; determining input and output of the physical information neural network; determining a loss function of the physical information neural network; training a physical information neural network; 2, designing an adaptive optimization algorithm, optimizing the final solution precision and convergence speed of the physical information neural network, and obtaining an adaptive physical information neural network; designing an adaptive activation function; designing a self-adaptive sampling mechanism based on residual errors; 3, based on the self-adaptive physical information neural network, numerical solution and gas-liquid distribution state inversion of the shaft multiphase flow model are achieved. According to the method, the problem that a traditional numerical method usually needs high-precision grid division and a large number of computing resources is effectively solved.

The invention discloses a mixed analytic-numerical method for solving soil-structure nonlinear interaction, and belongs to the technical field of geotechnical engineering and structural engineering. According to the method, a soil-structure nonlinear resistance curve is subjected to quasi-linearization, and numerical iteration is carried out by utilizing a matrix analytic solution of a multi-section elastic foundation beam theory, so that the internal force and displacement response of the structure is solved. The hybrid analytic-numerical method for solving soil-structure nonlinear interaction provided by the invention can truly simulate a mechanical behavior path of nonlinear resistance without depending on a traditional difference format. According to the method, absolute stability is kept in the solving process, better precision is achieved under the same calculation efficiency, meanwhile, precision improvement is based on fine adjustment of a small number of key variables, and the transparency and interpretability of the algorithm are guaranteed.

The invention relates to the technical field of numerical calculation and data analysis, in particular to a data interpolation and fitting analysis system which comprises a data processing module, a depth generation interpolation module, an uncertainty quantification module, an interpretability optimization module, a multi-source heterogeneous data processing module and a hybrid calculation acceleration module. In the prior art, a traditional interpolation method is easy to generate over-fitting or under-fitting in a complex data distribution and high noise scene, and a single deep learning model is insufficient in generalization ability in a small sample or data sparse region; through the dynamic fusion architecture of the depth generation interpolation module, the advantages of a traditional numerical method and deep learning are combined, the weight is automatically adjusted based on data characteristics, the prediction error under noise data is remarkably reduced, the adaptability to complex distribution is improved, and the stability of a data sparse region is enhanced; the problems of insufficient precision and weak generalization ability of a single model of a traditional method are effectively solved.

According to the FPGA real-time simulation method and device based on the self-adaptive base value and the variable step size and the readable storage medium of the FPGA real-time simulation method and device, the mapping relation between the system state and the per-unit base value is trained through a machine learning model, the initial value of the base value is output and subjected to PID dynamic fine adjustment, the step size is automatically adjusted in combination with a high-order numerical method containing error estimation and the dynamic range of the base value, and the simulation accuracy is improved. And performing parallel execution on the FPGA. The method has the advantages of automatic base value selection, intelligent step length adjustment, efficient reuse of computing resources and the like, can improve the simulation precision and efficiency of a complex system, and is suitable for strong nonlinear scenes such as new energy power.

The invention provides a numerical method for immiscible solution drop swallowing behavior in limited shear flow, and relates to the technical field of immiscible solution drop swallowing behavior, a simulation task based on a phase field model and a Navier-Stokes equation is established, a computational domain is discretized through a finite element method, a physical field is initialized, and in each time step, the physical field of the immiscible solution drop swallowing behavior in limited shear flow is calculated. Updated velocity field and phase field data are obtained through coupling solution, the interface curvature change rate and the flow field vorticity intensity are comprehensively calculated, a global index representing the dynamic intensity of the system is generated, the index is compared with a preset threshold value, and the dynamic intensity of the system is calculated. When the index is higher than a threshold value, a smaller step length and a higher grid resolution are adopted, otherwise, a larger step length and a lower resolution are adopted, finally, solver configuration is automatically reconstructed according to the selected parameters, solving is continued under a new adjusting strategy, a self-adaptive numerical simulation cycle is formed, and a new time step is obtained. And completing simulation and outputting complete field data of the liquid drop swallowing process.

The invention discloses a structural dynamic response method of a physical information radial basis Kolmogorov-Arnold network, and belongs to the technical field of anti-seismic engineering. The method comprises the following steps: acquiring a data supervision range of structural dynamic response under seismic excitation, and acquiring engineering dynamic parameters in the data supervision range in real time according to a timeline; according to the method, the mechanical preciseness of a traditional numerical method is inherited through kinetic equation constraint, and the efficiency and generalization bottlenecks of the traditional method are broken through by means of the self-adaptive learning capability of the RBF network; the analysis limitation of a traditional method under non-stationary seismic excitation is solved, dependence on artificial experience is reduced through an automatic process, and a novel structural dynamic response analysis normal form with precision, reliability and practicability is provided for the field of seismic engineering. And the technology upgrade of the field from empirical driving to data-physical dual driving is promoted.

The invention relates to the technical field of multi-physics field coupling, in particular to a PINN-based multi-domain physics field parameterization prediction method and device and a storage medium, and the method comprises the steps: obtaining a control equation and boundary conditions of a multi-domain physics field and independent feature parameters of each sub-domain; constructing a trunk branch framework model of a multi-domain physical field through a physical information neural network; the space coordinates and the characteristic parameters of the multi-domain physical field are input into the main branch frame model, and predicted values of a velocity field and a pressure field are generated; carrying out training point sampling on the multi-domain physical field, and training a trunk branch frame model by using point data obtained by sampling to obtain a parameterized model; and predicting a multi-domain actual physical field through the parameterized model. According to the method, the PINN, parameterization input and the control equation of the multi-domain physical field are combined, the actual multi-domain physical field can be efficiently and accurately predicted, the calculation complexity of a traditional numerical method is reduced, and the method is suitable for rapid prediction of the complex parameterization physical field.

The invention discloses a stable support analysis method for a tunnel face of a shield tunnel in a composite stratum, which relates to the technical field of support analysis, and comprises the following steps of: dividing the tunnel face and a front area thereof, classifying the areas with similar deformation tendency or instability tendency into the same kind, and setting differentiated support control targets for each area, the method comprises the following steps: constructing a balanced scheduling framework of support and settlement, extracting related risk characteristics before entering a risk working condition, inputting the related risk characteristics into a safety evaluation model, performing preventive correction on a tunnel face pressure regulation amplitude, a propulsion rate change slope and a grouting strategy according to an evaluation result, and in the whole analysis and control process, performing safety evaluation on the tunnel face pressure regulation amplitude and the propulsion rate change slope. And performing cross check by using a numerical method of different dimensions and field measurement, feeding back to the equilibrium scheduling framework when a difference is found, and re-correcting a support strategy. According to the analysis method, a scheduling framework is constructed through real-time data and partition classification, safety evaluation and cross checking are combined, the defects of composite stratum analysis are overcome, and the stability of the tunnel face and the construction safety are improved.

Embodiments perform neural network based behavior determination of physical objects. One such embodiment processes a three-dimensional (3D) numerical-method model representing a physical object to extract (i) 3D geometric data associated with the physical object and (ii) simulation data. The extracted 3D geometric data and simulation data are transformed into a 3D multi-graph. The 3D multi-graph is processed with one or more deep neural network (DNN) and one or more operators to determine behavior of the physical object.

The invention provides an urban rail transit tunnel flooding situation prediction method and system, and the method comprises the steps: obtaining the spatial geometric parameters of an urban rail transit tunnel, constructing a three-dimensional digital model of the urban rail transit tunnel, converting the model into a numerical calculation model, and calculating the flooding situation of the urban rail transit tunnel. The method comprises the following steps: carrying out analogue simulation on an urban rail transit tunnel flooding process under different water inflow conditions based on a numerical method, and forming a data set by simulated monitoring quantities; training a machine learning prediction model by using the data set; and utilizing the trained machine learning prediction model to predict the flooding height and the flow of different monitoring points at different moments, and carrying out risk assessment based on a prediction result. According to the method, numerical simulation and machine learning are combined, efficient, rapid and accurate prediction of the urban rail transit tunnel flooding development situation is achieved, a dynamic evaluation result of the urban rail transit tunnel flooding risk is given, and a scientific basis is provided for regulation and control decisions of the urban rail transit tunnel flooding risk.

This paper proposes an FPGA real-time simulation method, device, and readable storage medium based on adaptive base values ​​and variable step sizes. This method uses a machine learning model to train the mapping between system states and normalized base values, outputs an initial base value, and dynamically fine-tunes it using PID control. The method then automatically adjusts the step size by combining high-order numerical methods with error estimation and the base value's dynamic range. The method is executed in parallel on an FPGA. This method offers advantages such as automated base value selection, intelligent step size adjustment, and efficient reuse of computing resources. It can improve the accuracy and efficiency of complex system simulations and is suitable for highly nonlinear scenarios such as renewable energy power.

The invention discloses a two-way rocket launching window searching method, system and device and a medium, and the method comprises the steps: rapidly calculating two nearest launching windows of an ascending orbit and a descending orbit of a rocket according to the attributes of a central body, target orbit plane parameters, the geographic coordinates of launching points and the flight duration of the rocket; according to the method, the problem is converted into numerical calculation based on space geometry, the crossing moment is directly solved by using the geometrical relationship between the normal vector of the orbital plane and the inertial position vector of the launching point location and adopting efficient numerical methods such as dichotomy and the like, and complex dynamic iteration is avoided. According to the method, the calculated amount is greatly reduced, rapid searching of the launching window is achieved, the method is suitable for an interstellar detection task scene needing rapid response or multiple times of calculation, and the real-time performance of task planning is remarkably improved.

The invention discloses an HB-AFT-based shell-rotor system model rapid solving method, which comprises the following steps of: establishing a kinetic model of a complex shell-rotating shaft-motor coupling system, firstly performing primary model order reduction based on an intrinsic orthogonal decomposition (POD) method, and then performing model rapid solving based on the HB-AFT method. According to the method, the rotor system has higher calculation efficiency, the complex nonlinear vibration problem can be rapidly solved, and the dynamic behavior mechanism of the core cabin of the complex underwater vehicle can be clarified. Compared with a traditional numerical method, the method has the advantages that an unstable solution can be obtained through the semi-analysis and semi-numerical method, so that researchers are helped to better analyze the vibration phenomenon of the underwater vehicle core cabin system, and then optimization design is conducted on the underwater vehicle core cabin system.

The invention provides a numerical method and system for high-precision prediction of gas-driven piston motion in a powder dense-phase conveying process, and the method comprises the following steps: 1, taking a powder fuel supply system as a research object, setting an initial field of the research object, obtaining the physical properties and transportation conditions of a powder layer under the initial field of the research object, and calculating the physical properties of the powder layer; the initial static state of the piston is set as a starting point; 2, on the basis of a pre-constructed mesoscale solid phase corresponding force model, the total gas-solid resistance borne by the piston in the static state of the piston is obtained through calculation; 3, based on the gas-solid total resistance borne by the piston, the piston starting critical condition is set; 4, performing numerical simulation on piston motion based on a piston starting critical condition; according to the method, the actual stress environment of the piston is combined, solid phase corresponding force sudden change and the friction effect after powder deformation are comprehensively considered, the whole-process motion characteristic prediction of the piston from static state to dynamic stability has high credibility, and the problem of simulation distortion caused by inaccurate motion characteristics of a traditional model is solved.

The invention discloses a three-dimensional flow field prediction method based on deep learning, and the method constructs a novel deep learning network RKAN-3D through collaborative integration of a nonlinear learnable activation function module and an attention-enhanced residual convolution module in combination with an indirect prediction strategy, and achieves the precise modeling of a complex three-dimensional flow field. Wherein the non-linear learnable activation function module can adaptively capture multi-scale non-linear features in a three-dimensional flow field, and the expression ability of the model to a complex flow phenomenon is enhanced; the attention enhancement residual convolution module effectively improves the perception and modeling precision of the model on local flow characteristics in a three-dimensional space structure by focusing a key flow field area. In order to overcome the high-dimensional challenge of directly predicting the state of the whole flow field, an incremental learning mechanism is introduced, and the capturing capability and generalization performance of the model on complex flow characteristics are effectively improved by gradually evolving the dynamic process of the flow field. Experimental results show that the reasoning speed of the proposed network is improved by two orders of magnitude compared with that of a traditional numerical method, and the network shows excellent prediction precision and robustness in typical three-dimensional flow field prediction tasks such as spheres and cylinders.

The invention provides an airfoil profile streaming flow field rapid prediction method based on a Fourier neural operator, and belongs to the field of intelligent fluid mechanics. According to the method, machine learning and computational fluid mechanics are deeply fused, the future flow field state is rapidly predicted through a series of input and output data, and the calculation efficiency of the method is far higher than that of a traditional numerical method. According to the method, the calculation task of several hours or even several days of traditional computational fluid mechanics simulation can be shortened to the second level, the optimization iteration period of aircraft appearance design is greatly accelerated, and the dependence and cost of research and development on wind tunnel tests and high-performance calculation are remarkably reduced.

The invention discloses a method for analyzing the reliability and failure mechanism of advanced heterogeneous integrated hybrid bonding interconnection. The method comprises the following steps: (1) calculating the contact resistance of a bonding interface based on an advanced heterogeneous integrated hybrid bonding process condition; (2) taking the bonding interface contact resistance as the input of electromigration simulation, and simulating a vacancy evolution multi-physical process induced by electromigration in interconnection by using a numerical method; and (3) analyzing an interconnection failure position based on a simulation result. The provided method for analyzing the reliability and failure mechanism of the advanced heterogeneous integrated hybrid bonding interconnection can provide theoretical guidance for interconnection design optimization and future research on multi-physical processes in complex circuits and systems.

The present application relates to the field of intelligent control and optimization, and discloses a kind of energy consumption dynamic management method, comprising the following steps: S1, the mathematical model of energy system is constructed, and the state space and control space of energy system are defined;S2, and the stability of energy system state is analyzed by Lyapunov function;S3, the optimal control law of system is obtained by solving HJB equation;S4, design Kalman type state estimator;S5, model parameters are converted between micro and macro levels, for the consistency of energy and constraint conditions between scales;S6, the HJB equation is discretized and solved using numerical method;S7, the performance of the system is verified by simulation and experiment.The effect of automatic avoidance of high electricity price operation interval, budget overrun warning and adaptive cost optimization is achieved by constructing stochastic dynamics energy consumption model, HJB optimal control solution and cross-scale energy consumption mapping, dynamic prediction and optimal scheduling control of energy consumption behavior under different loads, different electricity prices and different budget upper limits.

The invention relates to a pipe network division method and system for urban infrastructure simulation, and the method comprises the steps: S1, building a pipe network structure model for a target region, and enabling the pipe network structure model to comprise the topological structure information of pipe network segments and the attribute information of each pipe network segment; wherein the pipe network section between any two connection nodes is regarded as a to-be-dispersed pipe network section, and S2, performing grid division on each to-be-dispersed pipe network section in the pipe network structure model until a division cut-off condition is met. According to the method, on the basis of ensuring the solving precision and convergence, the human experience dependence and unnecessary modeling debugging time are remarkably reduced, and a scientific and rapid spatial discrete scheme is provided for engineering tasks such as urban pipe network digital twinning, transmission and distribution system simulation optimization and operation condition prediction; the method is suitable for fluid transmission and distribution process simulation based on numerical methods such as a finite volume method and a finite difference method.

The application discloses a method for obtaining C / C composite ablation morphology based on physical information neural network, and relates to the field of aerospace, comprising the following steps: taking the coordinate data of a C / C composite three-dimensional space model under a Cartesian coordinate system, an ablation time, a dimensionless parameter Sh and a dimensionless parameter A as inputs of a pre-trained multilayer perceptron network, outputting oxygen molar concentration and solid volume fraction through the pre-trained multilayer perceptron network; solving a gas phase diffusion equation and a solid phase evolution equation through the oxygen molar concentration and the solid volume fraction output by the multilayer perceptron network to obtain the C / C composite ablation morphology. The method can efficiently and accurately solve the gas-solid coupling equation, overcome the limitations of traditional numerical methods, accurately obtain the ablation morphology of the C / C composite under the gas-solid coupling effect at a low calculation cost, and provide strong theoretical support and technical support for the application of the C / C composite in the field of aerospace and the like.

The invention discloses a pungent-keeping finite element solving method for dynamic response of a structure under a Hamiltonian system. According to the method, a finite element method is applied to a Hamiltonian equation, a Pocking finite element method is deduced, and it is proved that the Pocking finite element method is of a strict Pocking structure. And on the other hand, programmed solution of a high-order iteration format is realized by utilizing mathematical calculation software. In addition, the flexibility of the pungency-preserving finite element method to the linear Hamiltonian system is also discussed. A plurality of numerical examples verify the excellent performance of the Pocking finite element method in the structural dynamic response problem, and prove the capability of keeping energy conservation and excellent stability of the Pocking finite element method in the long-term dynamic simulation process, and compared with a traditional numerical method, the Pocking finite element method has remarkable advantages.

The application discloses a transient multiphase flow numerical simulation method of a high-temperature structure water-entry boiling mechanism, which designs a motion-flow-heat transfer-phase change synchronous calculation method for the high-temperature structure, realizes real-time solving of a flow field and a cavity shape in a high-temperature phase change process through joint solving of a motion equation, a multiphase flow equation and an energy equation, designs a boiling state determination method based on wall surface superheat, simultaneously calculates the flow, the high-temperature phase change, the heat transfer and the rigid body motion by using the same set of numerical methods, makes the cavity shape, the drag coefficient and the heat flux consistent in the physical mechanism and the numerical results, and can accurately reflect the influence of the steam film on the cavity shape, the water-entry motion and the drag characteristics by analyzing the quantitative correlation between the steam film and the stress and motion response of the structure, thereby improving the reliability of water-entry cavity evolution, water-entry trajectory and drag reduction prediction results, and providing a theoretical basis for the research on the material and motion control of the high-temperature structure.

The invention discloses a numerical method for predicting aerodynamic force of a large-span bridge through a vortex structure around a flow field, and belongs to the field of bridge wind engineering. The method comprises the following steps of: simulating and generating a velocity field and vortex structure information around a flow field by utilizing computational fluid mechanics; determining geometric boundary conditions based on a vortex force diagram method, constructing and solving a hypothetical potential equation, and calculating a vortex force vector; finally, the additional mass force, the vortex pressure, the viscosity pressure and the friction force are calculated through integration, and the total aerodynamic force is synthesized. The method combines flow field information and aerodynamic force, can analyze contribution of different vortex structures, is suitable for a single box girder bridge and a multi-box girder bridge, has the advantages of being accurate in result, high in efficiency and small in resource occupation, can be used for flow separation aerodynamic force mechanism analysis, and solves the problem that a traditional pressure integral method cannot analyze the influence of a flow field.

This invention relates to the field of space debris environment modeling technology, specifically to a short-term evolution method for continuum disintegration debris based on numerical methods. The method includes: Step 1, establishing an initial distribution model of disintegration debris, including a disintegration debris velocity increment model and a numerical model of the initial distribution of disintegration debris; Step 2, sampling feature points of the continuum using a gradient-based sampling method, selecting the top N samples with the highest L2 norm scores of the gradient vectors as feature points of the continuum to be evolved; Step 3, processing the continuum equations using numerical solutions, considering the six orbital roots and four perturbation factors to perform short-term evolution of feature points; Step 4, reconstructing the final state distribution of disintegration debris using a Student's t-mix model. This invention fills the gap in previous research in this field, which only focused on ultra-short-term and long-term evolution, and has the beneficial technical effects of requiring fewer samples, having lower computational costs, shorter computation time, higher result accuracy, and stronger robustness.

The application provides a wharf rock-embedded pile critical pile length calculation method and system, relates to the critical pile length calculation technical field, through the deep integration and data calibration of numerical simulation and physical test, a high-fidelity comprehensive parameter database is constructed, and a continuous mapping relationship of the critical length-diameter ratio about the base rock strength and the inclination is established. First, numerical analysis is carried out under multiple working conditions, then physical model test is carried out under representative working conditions, the test data are used to construct a correction model to calibrate all simulation results, so that the accuracy of the end resistance ratio prediction is significantly improved. The application effectively solves the dual limitations that the pure numerical method lacks entity verification and the pure theoretical method is difficult to simulate the complex pile-rock contact behavior, through systematically diffusing the discrete test information into the comprehensive simulation data, the stress mechanism of the inclined rock-embedded pile is accurately described, and it is ensured that the mapping relationship established subsequently can truly reflect the physical law under the multi-factor coupling.

The present application relates to the technical field of numerical simulation of hydraulic engineering, and particularly relates to a dam-break simulation method and system based on Pinn, which comprises the following steps: constructing a data set and training a first prediction model by numerically simulating different river channels, constructing an error matrix based on the model prediction results and fitting the correlation between time and space and error, using the relationship to construct an error-weighted quadratic training loss function to optimize and train the model, and finally screening the best dam-break simulation model to achieve accurate prediction of dam-break water flow and water depth in the target scene. The present application combines physical information neural network with numerical simulation data, physical constraints and error-weighted quadratic training, which not only gets rid of the grid dependence of traditional numerical methods, improves the calculation efficiency and scene adaptability, but also solves the problem of physical deviation caused by data scarcity, significantly improving the prediction accuracy and reliability under extreme dam-break working conditions.

The present invention relates to the technical field of optimized control of centrifugal pumps, and specifically, to an intelligent scheduling method, system, device and medium for coordinated operation of a variable-speed multi-pump parallel system; the method first calls numerical methods to simulate and calculate the performance characteristics of parallel centrifugal pumps and the pipeline loss characteristics of the variable-speed multi-pump parallel system to obtain digital characteristic curves; secondly, with the minimum total shaft power as the objective function, an intelligent regulation mathematical model of the variable-speed multi-pump parallel system is established under the given demand targets and various constraint conditions of the variable-speed multi-pump parallel system; then, the particle swarm optimization algorithm is improved according to the golden sine algorithm to solve and obtain operation data; and a surrogate model is established by calling a feedforward artificial neural network to regress and predict the operation data; finally, according to the prediction results of the surrogate model, an optimal regulation scheme for the variable-speed multi-pump parallel system is obtained, which improves the energy efficiency and stability of the variable-speed multi-pump parallel system while achieving more accurate prediction of the scheduling results.

The invention discloses a subsurface erosion simulation numerical method based on a semi-implicit two-phase substance point method, and relates to the technical field of geotechnical engineering numerical simulation, and the method comprises the following steps: generalizing unsaturated easily subsurface-eroded accumulated soil into a two-phase multi-component medium based on a mixture theory; establishing a solid-liquid double-phase double-layer grid system; establishing a core control equation of seepage subsurface erosion in the soil body; transferring the material point information of the solid phase and the liquid phase to corresponding background grid nodes in the double-layer grid system; applying a boundary condition on a background grid of the double-layer grid system, and carrying out semi-implicit solution on the core control equation; mapping the obtained node speed to a substance point; judging whether the relative velocity of the solid phase and the liquid phase exceeds a seepage velocity threshold value or not; state variable information carried by the two-phase substance points is updated; correcting permeability and saturation; and judging and calculating whether the specified time is up or whether the soil body reaches the yield limit. The method provided by the invention has important theoretical and engineering practical values for solving the difficulty in simulating the subsurface erosion disaster of the accumulated soil.

This paper proposes an efficient numerical method for simulating cross-basin flows of near-space vehicles. The method sequentially generates physical and velocity space grids based on vehicle geometry and incoming flow parameters, sets initial flow field variables, calculates interface fluxes, implicitly solves macroscopic adjoint equations to obtain estimated macroscopic quantities, implicitly solves the Boltzmann equation to obtain the distribution function for the next iteration, and uses the distribution function to update the flow field variables, achieving iterative flow field calculations. By coupling the implicit solution of the Boltzmann equation with the corresponding macroscopic governing equations and constructing multi-scale macroscopic fluxes, the method improves the efficiency of cross-basin flow simulations while maintaining simulation accuracy.

The present invention provides a method for analyzing the horizontal displacement of free-end pile foundations in a dual-parameter foundation model. The boundary conditions of pile foundations such as friction piles and isolation piles can be simplified to free-end pile foundations. Combined with the Fourier series method, a method for analyzing the horizontal displacement of free-end pile foundations in a dual-parameter foundation model is proposed. The method is used to calculate the horizontal displacement and internal force of pile foundations caused by shield construction adjacent to pile foundations. Compared with the numerical simulation method, the physical quantities required for calculation can be obtained by substituting the corresponding calculation parameters. The calculation process is simple. Compared with the theoretical method using the numerical method, the method only needs to solve the horizontal displacement of the pile end. w O 、 w L The related two-variable linear equation can be used to further obtain other unknown coefficients, which has high calculation efficiency and provides an effective theoretical method for the safety risk assessment of existing structures in shield construction adjacent to pile foundations.