Uncertainty quantification of inverse analysis for geomaterials using probabilistic programming

Uncertainty is an essentially challenging for safe construction and long-term stability of geotechnical engineering.The inverse analysis is commonly utilized to determine the physico-mechanical parameters.However,conventional inverse analysis cannot deal with uncertainty in geotechnical and geological systems.In this study,a framework was developed to evaluate and quantify uncertainty in inverse analysis based on the reduced-order model(ROM)and probabilistic programming.The ROM was utilized to capture the mechanical and deformation properties of surrounding rock mass in geomechanical problems.Probabilistic programming was employed to evaluate uncertainty during construction in geotechnical engineering.A circular tunnel was then used to illustrate the proposed framework using analytical and numerical solution.The results show that the geomechanical parameters and associated uncertainty can be properly obtained and the proposed framework can capture the mechanical behaviors under uncertainty.Then,a slope case was employed to demonstrate the performance of the developed framework.The results prove that the proposed framework provides a scientific,feasible,and effective tool to characterize the properties and physical mechanism of geomaterials under uncertainty in geotechnical engineering problems.

Rockfill material uncertainty inversion analysis of concrete-faced rockfill dams using stacking ensemble strategy and Jaya optimizer

Numerical simulation of concrete-faced rockfill dams(CFRDs)considering the spatial variability of rockfill has become a popular research topic in recent years.In order to determine uncertain rockfill properties efficiently and reliably,this study developed an uncertainty inversion analysis method for rockfill material parameters using the stacking ensemble strategy and Jaya optimizer.The comprehensive implementation process of the proposed model was described with an illustrative CFRD example.First,the surrogate model method using the stacking ensemble algorithm was used to conduct the Monte Carlo stochastic finite element calculations with reduced computational cost and improved accuracy.Afterwards,the Jaya algorithm was used to inversely calculate the combination of the coefficient of variation of rockfill material parameters.This optimizer obtained higher accuracy and more significant uncertainty reduction than traditional optimizers.Overall,the developed model effectively identified the random parameters of rockfill materials.This study provided scientific references for uncertainty analysis of CFRDs.In addition,the proposed method can be applied to other similar engineering structures.

Temperature Sensitivity of Soil Respiration Probed by Numerical Analysis of Field-Observed Data Sets

Temperature sensitivity of soil respiration is essential to predict possible changes in terrestrial carbon budget on various scenarios about atmospheric and soil climates. Although it is often evaluated by using respiratory quotient “Q10”, Q10 values of soil respiration seem to vary depending on methods or scales of evaluation. Aiming at probing how Q10 values of soil respiration are evaluated differently for a field, this study used a model of soil respiration rate, and numerically evaluated soil respiration rates along depth by fitting the model to depth distributions of CO2 concentration measured in a field. And temperature sensitivity of soil respiration rate was evaluated by comparing the determined soil respiration rates with atmospheric and soil temperatures measured in the field. The results showed that the relation between surface CO2 emission rates and atmospheric temperatures was represented by lower Q10 values than that between soil respiration rates and soil temperatures, presumably because the top soil layers had acclimatized in more extent to the existing thermal regime than the underlying deeper layers. Thus, for evaluating effects of long-term rise in atmospheric temperature on soil respiration, it is necessary to precisely predict the long-term change in depth distribution of soil temperature as well as to quantify temperature sensitivity of soil respiration along depth. The evaluated sensitivity of surface CO2 emission rate to atmospheric temperature showed hysteresis, implying the needs for more knowledge about temperature sensitivity of soil respiration evaluated in both warming and cooling processes for better understandings and predictions about terrestrial carbon cycling.

Surface wave inversion with unknown number of soil layers based on a hybrid learning procedure of deep learning and genetic algorithm

Surface wave inversion is a key step in the application of surface waves to soil velocity profiling.Currently,a common practice for the process of inversion is that the number of soil layers is assumed to be known before using heuristic search algorithms to compute the shear wave velocity profile or the number of soil layers is considered as an optimization variable.However,an improper selection of the number of layers may lead to an incorrect shear wave velocity profile.In this study,a deep learning and genetic algorithm hybrid learning procedure is proposed to perform the surface wave inversion without the need to assume the number of soil layers.First,a deep neural network is adapted to learn from a large number of synthetic dispersion curves for inferring the layer number.Then,the shear-wave velocity profile is determined by a genetic algorithm with the known layer number.By applying this procedure to both simulated and real-world cases,the results indicate that the proposed method is reliable and efficient for surface wave inversion.

Inverse analysis determining interfacial properties between metal film and ceramic substrate with an adhesive layer

In the present study, peel tests and inverse analysis were performed to determine the interracial mechanical parameters for the metal film/ceramic system with an epoxy interface layer between film and ceramic. Al films with a series of thicknesses between 20 and 250 μm and three peel angles of 90°, 135° and 180° were considered. A finite element model with the cohesive zone elements was used to simulate the peeling process. The finite element results were taken as the training data of a neural network in the inverse analysis. The interracial cohesive energy and the separation strength can be determined based on the inverse analysis and peel experimental result

An Inverse Analysis of the Comprehensive Medium Parameters and a Simulation of the Crustal Deformation of the Qinghai-Tibet Plateau

Based on the theory of finite element analysis, an inverse analysis model for the comprehensive medium parameters of the Qinghai-Tibet Plateau is set up. With the help of GPS velocity field, the comprehensive crustal medium parameters of the plateau are inversely analyzed and the characteristics of the related movement macroscopically simulated. It is then concluded that the tectonic deformation of the plateau is mainly in the form of a N-S compression accompanied by an E-W stretching, and the present tectonic setting of the plateau should be the result of the collision between the Indian and the Eurasian continents during the Cenozoic.

An efficient probabilistic design approach for tunnel face stability by inverse reliability analysis

In order to maintain the safety of underground constructions that significantly involve geo-material uncertainties,this paper delivers a new computation framework for conducting reliability-based design(RBD)of shallow tunnel face stability,utilizing a simplified inverse first-order reliability method(FORM).The limit state functions defining tunnel face stability are established for both collapse and blow-out modes of the tunnel face failure,respectively,and the deterministic results of the tunnel face support pressure are obtained through three-dimensional finite element limit analysis(FELA).Because the inverse reliability method can directly capture the design support pressure according to prescribed target reliability index,the computational cost for probabilistic design of tunnel face stability is greatly reduced.By comparison with Monte Carlo simulation results,the accuracy and feasibility of the proposed method are verified.Further,this study presents a series of reliability-based design charts for vividly understanding the limit support pressure on tunnel face in both cohesionless(sandy)soil and cohesive soil stratums,and their optimal support pressure ranges are highlighted.The results show that in the case of sandy soil stratum,the blowout failure of tunnel face is extremely unlikely,whereas the collapse is the only possible failure mode.The parametric study of various geotechnical uncertainties also reveals that ignoring the potential correlation between soil shear strength parameters will lead to over-designed support pressure,and the coefficient of variation of internal friction angle has a greater influence on the tunnel face failure probability than that of the cohesion.

Inverse analysis of laboratory data and observations for evaluation of backward erosion piping process

An inverse analysis procedure has been developed to interpret collected pore pressure data and observations during backward erosion piping(BEP)initiation and progression in sandy soils.The procedure has been applied to laboratory models designed to mimic the initiation and progression of BEP through a constricted vertical outlet.The inverse analysis uses three-dimensional(3D)finite element method(FEM)to successively produce models of the hydraulic head regime surrounding progressive stages of BEP based on observations at the sample surface and pore pressure measurements obtained from the laboratory models.The inverse analysis results in a series of 3D contour plots that represent the hydraulic-head regime at each stage of the BEP development,allowing for assessing the development of BEP mechanism as well as calculating the critical hydraulic conditions required for various BEP stages to initiate and progress.Interpretation of the results identified four significant stages of the piping process:(1)loosened zone initiation,(2)channel initiation and progression,(3)riser sand fluidization,and(4)loosened zone progression.Interpretation of the hydraulic head contour plots allows assessment of the critical hydraulic gradients needed to initiate and progress various components of the BEP development.

Wedge Splitting Test and Inverse Analysis on Fracture Behaviour of Fiber Reinforced and Regular High Performance Concretes

The fracture behaviour of three fiber reinforced and regular HPC （high performance concretes） is presented in this paper. Two mixes are based on optimization of HPC whereas the third mix was a commercial mix developed by CONTEC ApS （Denmark）. The wedge splitting test setup with 48 cubical specimens was used experimentally and the cracked non-linear hinge model based on the fictitious crack model was applied for the interpretation of the results. The stress-crack opening relationships were extracted by using inverse analysis algorithm for various multi-linear softening curves. This showed that the refinement of the softening curves reflects in improved accuracy of the WST （wedge splitting test） simulation in comparison with bi-linear softening curves with acceptable increase of computational time. Furthermore, the fracture mechanics parameters such as COD （crack opening displacement）, fracture energy and characteristic length were experimentally determined. Experiments were performed at 1, 3, 7 and 28 days. Fracture energy, Gf, was found to increase with age, while the characteristic length, Lch, was found to decrease.

Inverse displacement analysis of the general six degree-of-freedom serial robot based on optimization method

The paper presents a new solution of inverse displacement analysis of the general six degree-of-freedom serial robot.The inverse displacement analysis of the general serial robot is transformed into a minimization problem and then the optimization method is adopted to solve the nonlinear least squares problem with the analytic form of new Jacobian matrix.In this way,joint variables of the general serial robot can be searched out quickly under the desired precision when positions of the three non-collinear end effector points are given.Compared with the general Newton iterative method,the proposed algorithm can search out the solution when the robot is at the singular configuration and the initial configuration used in the optimization method may also be the singular configuration.So the convergence domain is bigger than that of the general Newton iterative method.Another advantage of the proposed algorithm is that positions of the three non-collinear end effector points are usually much easier to be measured than the orientation of the end effector.The inverse displacement analysis of the general 6R(six-revolute-joint) serial robot is illustrated as an example and the simulation results verify the efficiency of the proposed algorithm.Because the three non-collinear points can be selected at random,the method can be applied to any other types of serial robots.

Analysis and Inverse Substructuring Computation on Dynamic Quality of Mechanical Assembly

Mechanical assembly has its own dynamic quality directly affecting the dynamic quality of whole product and should be considered in quality inspection and estimation of mechanical assembly. Based on functional relations between dynamic characteristics involved in mechanical assembly, the effects of assembling process on dynamic characteristics of substructural components of an assembly system are investigated by substructuring analysis. Assembly-coupling dynamic stiffness is clarified as the dominant factor of the effects and can be used as a quantitative measure of assembly dynamic quality. Two computational schemes using frequency response functions（FRFs） to determine the stiffness are provided and discussed by inverse substructuring analysis, including their applicable conditions and implementation procedure in application. Eigenvalue analysis on matrix-ratios of FRFs before and after assembling is employed and well validates the analytical outcomes and the schemes via both a lumped-parameter model and its analogic experimental counterpart. Applying the two schemes to inspect the dynamic quality provides the message of dynamic performance of the assembly system, and therefore improves conventional quality inspection and estimation of mechanical assembly in completeness.

Methods for Force Analysis of Overconstrained Parallel Mechanisms： A Review

The force analysis of overconstrained PMs is relatively complex and difficult, for which the methods have always been a research hotspot. However, few liter- atures analyze the characteristics and application scopes of the various methods, which is not convenient for researchers and engineers to master and adopt them prop- erly. A review of the methods for force analysis of both passive and active overconstrained PMs is presented. The existing force analysis methods for these two kinds of overconstrained PMs are classified according to their main ideas. Each category is briefly demonstrated and evaluated from such aspects as the calculation amount, the compre- hensiveness of considering limbs＇ deformation, and the existence of explicit expressions of the solutions, which provides an important reference for researchers and engi- neers to quickly find a suitable method. The similarities and differences between the statically indeterminate prob- lem of passive overconstrained PMs and that of active overconstrained PMs are discussed, and a universal method for these two kinds of overconstrained PMs is pointed out. The existing deficiencies and development directions of the force analysis methods for overconstrained systems are indicated based on the overview.

Approach for Obtaining Material Mechanical Properties in Local Region of Structure Based on Accurate Analysis of Micro-indentation Test

The hot or cold processing would induce the change and the inhomogeneous of the material mechanical properties in the local processing region of the structure,and it is difficult to obtain the specific mechanical properties in these regions by using the traditional material tensile test.To accurately get actual material mechanical properties in the local region of structure,a micro-indentation test system incorporated by an electronic universal material test device has been established.An indenter displacement sensor and a group of special micro-indenter assemblies are estab-lished.A numerical indentation inversion analysis method by using ABAQUS software is also proposed in this study.Based on the above test system and analysis platform,an approach to obtaining material mechanical properties in the local region of structures is proposed and established.The ball indentation test is performed and combined with the energy method by using various changed mechanical properties of 316L austenitic stainless steel under differ-ent elongations.The investigated results indicate that the material mechanical properties and the micro-indentation morphological changes have evidently relevance.Compared with the tensile test results,the deviations of material mechanical parameters,such as hardness H,the hardening exponent n,the yield strength σy and others are within 5%obtained through the indentation test and the finite element analysis.It provides an effective and convenient method for obtaining the actual material mechanical properties in the local processing region of the structure.

Sensitivity and inverse analysis methods for parameter intervals

This paper proposes a sensitivity analysis method for engineering parameters using interval analyses.This method substantially extends the application of interval analysis method.In this scheme,parameter intervals and decision-making target intervals are determined using the interval analysis method.As an example,an inverse analysis method for uncertainty is presented.The intervals of unknown parameters can be obtained by sampling measured data.Even for limited measured data,robust results can also be obtained with the inverse analysis method,which can be intuitively evaluated by the uncertainty expressed in terms of an interval.For complex nonlinear problems,an iteratively optimized inverse analysis model is proposed.In a given set of loose parameter intervals,all the unknown parameter intervals that satisfy the measured information can be obtained by an iteratively optimized inverse analysis model.The influences of measured precisions and the number of parameters on the results of the inverse analysis are evaluated.Finally,the uniqueness of the interval inverse analysis method is discussed.

Measurement of the In-Plane Thermal Conductivity of Long Fiber Composites by Inverse Analysis

In the present work, inverse thermal analysis of heat conduction is carried out to estimate the in-plane thermal conductivity of composites. Numerical simulations were performed to determine the optimal configuration of the heating system to ensure a unidirectional heat transfer in the composite sample. Composite plates made of unsaturated polyester resin and unidirectional glass fibers were fabricated by injection to validate the methodology. A heating and cooling cycle is applied at the bottom and top surfaces of the sample. The thermal conductivity can be deduced from transient temperature measurements given by thermocouples positioned at three chosen locations along the fibers direction. The inverse analysis algorithm is initiated by solving the direct problem defined by the one-dimensional transient heat conduction equation using a first estimate of thermal conductivity. The integral in time of the square distance between the measured and predicted values is the criterion minimized in the inverse analysis algorithm. Finally, the evolution of the in-plane composite thermal conductivity can be deduced from the experimental results by the rule of mixture.

Parameter identification for a damage phase field model using a physics-informed neural network

This work applies concepts of artificial neural networks to identify the parameters of a mathematical model based on phase fields for damage and fracture.Damage mechanics is the part of the continuum mechanics that models the effects of micro-defect formation using state variables at the macroscopic level.The equations that define the model are derived from fundamental laws of physics and provide important relationships among state variables.Simulations using the model considered in this work produce good qualitative and quantitative results,but many parameters must be adjusted to reproduce certain material behavior.The identification of model parameters is considered by solving an inverse problem that uses pseudo-experimental data to find the best values that fit the data.We apply physics informed neural network and combine some classical estimation methods to identify the material parameters that appear in the damage equation of the model.Our strategy consists of a neural network that acts as an approximating function of the damage evolution with output regularized using the residue of the differential equation.Three stages of optimization seek the best possible values for the neural network and the material parameters.The training alternates between the fitting of only the pseudo-experimental data or the total loss that includes the regularizing terms.We test the robustness of the method to noisy data and its generalization capabilities using a simple physical case for the damage model.This procedure deals better with noisy data in comparison with a more standard PDE-constrained optimization method,and it also provides good approximations of the material parameters and the evolution of damage.

Deformation warning index for reinforced concrete dam based on structural health monitoring data and numerical simulation

The material mechanical parameters of the dam body and foundation will change when a dam is reinforced during the aging process.This causes significant changes in the structural state of the project and makes it difficult to ensure its structural safety.In this study,a new deformation warning index for reinforced concrete dams was developed according to the prototype monitoring data,statistical models,three-dimensional finite element model(FEM)numerical simulation,and the critical conditions of the dam structure.A statistical model was established to separate the water pressure component.Then,a three-dimensional FEM of the reinforced concrete dam was constructed to simulate the water pressure component.Furthermore,the deformation components that affected the mechanical parameters of the dam under the same amount of reservoir water level change were separated and quantified accurately.In addition,the method for inversion of comprehensive mechanical parameters after dam reinforcement was used.The influence mechanisms of the deformation behavior of concrete dams under the reservoir water level and temperature changes were investigated.A new deformation warning index was developed by combining the forward-simulated critical water pressure component and temperature component in the period of extreme temperature decrease with the aging component separated by the statistical model.The new deformation warning index considers the structural state of the dam before and after reinforcement and links the structural strength criterion and the deformation evolution mechanisms.It provides a theoretical foundation and decision support for long-term service and operation management of reinforced dams.

Deformation early-warning index for heightened gravity dam during impoundment period

The mechanical parameters of materials in a dam body and dam foundation tend to change when dams are reinforced in aging processes.It is important to use an early-warning index to reflect the safety status of dams,particularly of heightened projects in the impoundment period.Herein,a new method for monitoring the safety status of heightened dams is proposed based on the deformation monitoring data of a dam structure,a statistical model,and finite-element numerical simulation.First,a fast optimization inversion method for estimation of dam mechanical parameters was developed,which used the water pressure component extracted from a statistical model,an improved inversion objective function,and a genetic optimization iterative algorithm.Then,a finite element model of a heightened concrete gravity dam was established,and the deformation behavior of the dam with rising water levels in the impoundment period was simulated.Subsequently,mechanical parameters of aged dam parts were calculated using the fast optimization inversion method with simulated deformation and the water pressure deformation component obtained by the statistical model under the same conditions of water pressure change.Finally,a new earlywarning index of dam deformation was constructed by means of the forward-simulated deformation and other components of the statistical model.The early-warning index is useful for forecasting dam deformation under different water levels,especially high water levels.

Structural physical parameter identification based on evolutionary-simplex algorithm and structural dynamic response

Evolutionary computation based on the idea of biologic evolution is one type of global optimization algorithm that uses self-adaptation,self-organization and random searching to solve optimization problems.The evolutionary-simplex algorithm is introduced in this paper.It contains floating encoding which combines the evolutionary computation and the simplex algorithm to overcome the problems encountered in the genetic algorithm and evolutionary strategy methods. Numerical experiments are performed using seven typical functions to verify the algorithm.An inverse analysis method to identify structural physical parameters based on incomplete dynamic responses obtained from the analysis in the time domain is presented by using the evolutionary-simplex algorithm.The modal evolutionary-simplex algorithm converted from the time domain to the modal domain is proposed to improve the inverse efficiency.Numerical calculations for a 50-DOF system show that when compared with other methods,the evolutionary-simplex algorithm offers advantages of high precision, efficient searching ability,strong ability to resist noise,independence of initial value,and good adaptation to incomplete information conditions.