Inverse Problem Of Identification Research Articles

Dynamical analysis combined with parameter identification for a model of infection in honeybee colonies with social immunity

Several models on honeybee population dynamics have been considered in the past decades, which explain that the growth of beecolonies is highly dependent on the availability of food and social inhibition. The phenomenon of the Colony Collapse Disorder (CCD) and its exact causes remain unclear and here we are interested on the factor of social immunity. We work with the mathematical model in [1]. The core model, consisting of four nonlinear ordinary differential equations with unknown functions: brood and nurses B, iB, N and iN represent the number of healthy brood, infected brood, healthy nurses, and infected nurses, respectively. First, this model implements social segregation. High-risk individuals such as foragers are limited to contact only nectar-receivers, but not other vulnerable individuals (nurses and brood) inside the nest. Secondly, it includes the hygienic behavior, by which healthy nurses actively remove infected workers and brood from the colony. We aim to study the dynamics and the long-term behavior of the proposed model, as well as to discuss the effects of crucial parameters associated with the model. In the first stage, we study the model equilibria stability in dependence of the reproduction number. In the second stage, we investigate the inverse problem of parameters identification in the model based on finite number time measurements of the population size. The conjugate gradient method with explicit Frechet derivative of the cost functional is proposed for the numerical solution of the inverse problem. Computational results with synthetic and realistic data are performed and discussed.

Identification of spatially distributed rheological parameters for viscoplastic gravity currents

The rheology of a fluid is often difficult to measure in situ and in real time. This work investigates whether it is possible to recover rheological information from direct field observations. We present a closed-form analytical solution for inverse problem of identification of the mobility coefficient in gravity-driven fluid flowed down an inclined plane. The lubrication approximation is used to model the three-dimensional thin film of fluid and the governing equation is solved numerically by the explicit finite difference method to calculate the fluid thickness. We show in this study that using very straightforward measurements of fluid thickness at only a few points and only two successive instants, the mobility coefficient of fluid flow can be estimated accurately. Then as an important application in Bingham fluids we show that the knowledge of the mobility coefficient together with velocity measurement at only one point and instant enable us to estimate temperature-dependent viscosity and yield stress of the Bingham fluid. Unlike other methods, the proposed method allows the local identification of the rheology which is particularly useful when the rheological parameters are functions of the local temperature and/or composition. The proposed inverse analysis is a non-iterative approach with negligible computational cost since our analysis revealed closed form formulae relating the rheological parameters to the local flow depth, its derivatives, and the local free surface velocity.

Integration of Deep Learning with Vibration-Based Identification Method

The vibration-based identification method has long been used as an alternative to mechanical tests for material characterization. Its non-destructive nature, high efficiency in parameter identification of anisotropic materials and its ability to achieve structure-level homogenization make it very attractive for both academic community and industry. Due to the absence of explicit mapping from the result of vibration test to elastic constants, conventional vibration-based identification approaches generally rely on the minimization of a cost function built on modal properties or Frequency Response Function (FRF) curve. In this paper, a direct relation from FRFs to mechanical properties is established by deep neural network, which offers a new perspective to solve the inverse identification problem. Specifically, this mapping is approximately built with Multilayer Perceptrons (MLPs) and the network’s weights are learned from massive training data. The training data-i.e., the FRF curves, is generated by a finite element model whose input parameters are selected by Latin Hypercube Sampling (LHS). After training, the obtained model is validated by dataset unseen during training process and will be further used to predict mechanical properties of materials from FRFs obtained by vibration test. The effectiveness and efficiency of the developed method are demonstrated on the case study of an aluminum plate. Both the Young’s modulus and Poisson’s ratio are retrieved with high accuracy.

Inverse Problem of Parameter Identification for Extended Compositional Gradient Model

In this study we address simulation of initial distribution of fluid composition in hydrocarbon reservoirs, particularly in scenarios where slow vertical segregation in a low-permeability near-critical reservoir results in an incomplete relaxation to the quasi-equilibrium state. To effectively analyze these complex scenarios, we propose an extended compositional gradient model that takes into account incomplete system relaxation. Practical application of the method involves solution of the forward problem of compositional profiling, with the model parameters adjusted according to real fluid samples. We formulate the inverse problem of parameter identification for the extended compositional gradient model and solve it using gradient-free optimization methods. The adjusted parameters are specific enthalpies of fluid components and the relaxation parameter. The overarching goal of parameter identification is to closely match the predictions of the model with real data, thereby enhancing the reliability of forecasts regarding distribution of fluid composition. We believe that the results of this study will significantly influence both understanding and simulation techniques for distribution of hydrocarbon components in natural reservoirs, particularly in situations characterized by incomplete system relaxation.

Damage assessment in plate structures using an enhanced Jaya algorithm

The article proposes a new method called enhanced Jaya (EJaya) to identify and evaluate damage in plate structures. The method uses a nonlinear optimization task to solve the inverse damage identification problem. The damage magnitudes of the plate elements are taken as design variables, and the objective function to be minimized uses the variations in the plate flexibility matrix and includes a penalization term to avoid false alarm detection. EJaya is developed by incorporating three modifications in the traditional Jaya algorithm: generating an initial population of candidate solutions using prior knowledge of the damage scenario, integrating a component that takes into account the individual distribution through the search space, and implementing a new local search technique. The simulation results show that EJaya is efficient in both solution quality and computational effort and can detect and evaluate damage even in large-sized problems and under noisy data conditions.

Об особенностях идентификации переменных термомеханических характеристик функционально-градиентного прямоугольника

The inverse thermoelastic problem of identification of the variable properties of a functionally graded rectangle is studied. Unsteady vibrations are excited by applying mechanical and thermal loads to the upper side of the rectangle. To solve the direct problem in Laplace transforms, the method of separation of variables and the shooting method for harmonics are used. Transformants are inverted by expanding the origin in terms of shifted Legendre polynomials. The method proposed for solving the direct problem is verified by comparison with a finite element solution. The influence of the laws of change of variable characteristics on the boundary physical fields is analyzed. The displacement components give additional information on the mechanical loading, and the temperature measured on the upper side of the rectangle over a certain time interval – on the thermal loading. Assuming that the additional information admits expansion in Fourier series, the two-dimensional inverse problem is reduced to one-dimensional problems for various harmonics. The solution of the obtained nonlinear inverse problems is carried out on the basis of an iterative process, at each stage of which, in order to find corrections for thermomechanical characteristics, systems of Fredholm integral equations of the 1st kind are solved. The possibility of simultaneous reconstruction of several characteristics is investigated. The results of computational experiments on the phased reconstruction of thermomechanical characteristics are presented. The influence of the thermomechanical coupling parameter on the results of the thermal stress coefficient reconstruction was clarified.

The inverse problem of dipolar source identification from incomplete boundary measurements

We consider and combine two methods to solve the inverse problem of locating dipolar sources in a restricted domain from measurements of the Cauchy data on a part of the boundary for the Laplace equation. We begin by extending the boundary measurements, which are accessible only on a part of the boundary by solving an extremal bounded problem in an annulus. The inverse problem of source identification is then solved using the reciprocity gap concept applied to the completed data. In order to evaluate the effectiveness of source detection with regard to the expansion of the data, some numerical tests are provided.

Identification of cable tension through physical models and non-contact measurements

Determining the static and dynamic response of structural cables is a mechanical problem of theoretical and practical interest in many aspects of civil engineering. In particular, the cable tension is a fundamental variable to be assigned in direct design problems, as well as a fundamental unknown to be assessed in inverse identification problems. The present paper outlines an original analytical strategy for identifying the axial tension of inclined sagged cables in cable-stayed structures, based on static measurements. Starting from the classic formulation of an inextensible, perfectly flexible model of catenary suspended cables, a perturbation-based low-order polynomial approximation of the static configuration under self-weight is achieved (direct problem). The quadratic and cubic coefficients of the configurational function are tension-dependent quantities, whose analytical expressions can be mathematically inverted to define consistent parametric formulas for tension identification (inverse problem). The experimental assessment of the static cable configuration, which serves as input for the inverse problem, is provided by the geometric data acquired by modern and noninvasive techniques of non-contact measurement. The methodological advantage is that the laser scanner acquisition of point cloud models can efficiently and economically provide precise and redundant three-dimensional geometric descriptions of the cable configuration, which is suitable for a highly accurate and statistically robust data treatment. Lastly, the identification strategy is successfully applied to a real-scale structure, for tension identification in the stays of a cable-stayed footbridge. The results are discussed from a qualitative and quantitative viewpoint, and finally validated through a comparison with the outcomes of a dynamic identification procedure based on high-speed camera acquisitions.

Replacing voids and localized parameter changes with fictitious forcing terms in boundary-value problems

We present a general observation on how to replace changes of material properties in limited regions within a domain with fictitious forcing terms in initial- and boundary-value problems associated with wave propagation and diffusion. Then, by considering a paradigmatic heat conduction problem on a domain with a cavity, we prove that the presence of the void can be replaced by a fictitious heat source with support contained within the cavity. We illustrate this fact in a situation where the source term can be analytically recovered from the values of the temperature and heat flux at the boundary of the cavity. Our result provides a strategy to map the nonlinear geometric inverse problem of void identification into a more manageable one, that involves the identification of forcing terms given the knowledge of external boundary data. To set the stage for a systematic study of the inverse problem, we present algebraic reconstructions, based on a finite-element discretization of the domain, that give an approximation of the fictitious source from different sets of temperature measurements. We show how the accuracy of the reconstruction is reflected on the void identification.

On a Derivative-free Optimization Approach to Some Problems of Civil Engineering

Development of advanced materials and structures for civil engineering, due to the requirements of green and sustainable building, including the reduction of energy consumption and the balance between occupant comfort and environmental friendliness, needs proper analysis of related physical, chemical, etc. processes, whose mathematical description leads to direct, sensitivity and inverse initial and boundary value problems for nonlinear partial differential equations, analysed numerically using finite element, difference and similar techniques. Design optimization requires to implement a set of additional variable parameters into all related computations, which is very expensive or quite impossible in most cases. Thus realistic computational strategies work with the minimizations of some cost functions with unknown parameters using certain kind of numerical differentiation, like quasi-Newton, inexact Newton or conjugate gradient methods, some derivative-free approach, or, as a much-favoured alternative, some heuristic soft-computing algorithm. A reasonable compromise seems to be the exploitation of an algorithm coming from the non-gradient Nelder-Mead simplex approach. In this paper, referring to the experience with i) the direct problem of thermal design of a residential building and ii) the inverse problem of identification of material characteristics as thermal conductivity and diffusivity from well-advised laboratory experiments, after several remarks to the history and progress of the Nelder-Mead method and its improvements, we shall demonstrate some convergence properties of such approach, regardless of the highly cited evaluation of the original Nelder-Mead algorithm: “Mathematicians hate it because you cannot prove convergence; engineers seem to love it because it often works.”

Lipschitz stability estimate for the simultaneous recovery of two coefficients in the anisotropic Schrödinger type equation via local Cauchy data

We consider the inverse problem of the simultaneous identification of the coefficients σ and q of the equation div(σ∇u)+qu=0 from the knowledge of the Cauchy data set. We assume that σ=γA, where A is a given matrix function and γ and q are unknown piecewise affine scalar functions. No sign, nor spectrum condition on q is assumed. We derive a result of global Lipschitz stability in dimension n≥3. The proof relies on the method of singular solutions and on the quantitative estimates of unique continuation.

Synergistic integration of deep neural networks and finite element method with applications of nonlinear large deformation biomechanics

Patient-specific finite element analysis (FEA) holds great promise in advancing the prognosis of cardiovascular diseases by providing detailed biomechanical insights such as high-fidelity stress and deformation on a patient-specific basis. Albeit feasible, FEA that incorporates three-dimensional, complex patient-specific geometry can be time-consuming and unsuitable for time-sensitive clinical applications. To mitigate this challenge, machine learning (ML) models, e.g., deep neural networks (DNNs), have been increasingly utilized as potential alternatives to finite element method (FEM) for biomechanical analysis. So far, efforts have been made in two main directions: (1) learning the input-to-output mapping of traditional FEM solvers and replacing FEM with data-driven ML surrogate models; (2) solving equilibrium equations using physics-informed loss functions of neural networks. While these two existing strategies have shown improved performance in terms of speed or scalability, ML models have not yet provided practical advantages over traditional FEM due to generalization issues. This has led us to the question: instead of abandoning or replacing the traditional FEM framework that can reliably solve biomechanical problems, can we integrate FEM and DNNs to enhance performance?In this study, we propose a synergistic integration of DNNs and FEM to overcome their individual limitations. Using biomechanical analysis of the human aorta as the test bed, we demonstrated two novel integrative strategies in forward and inverse problems. For the forward problem, we developed DNNs with state-of-the-art architectures to predict a nodal displacement field, and this initial DNN solution was then updated by a FEM-based refinement process, yielding a fast and accurate computing framework. For the inverse problem of heterogeneous material parameter identification, our method employs DNN as a regularizer of the spatial distribution of material parameters, aiding the optimizer in locating the optimal solution. In our demonstrative examples, despite that the DNN-only forward models yielded small displacement errors in most test cases; stress errors were considerably large, and for some test cases, the peak stress errors were greater than 50%. Our DNN-FEM integration eliminated these non-negligible errors in DNN-only models and was magnitudes faster than the FEM-only approach. Additionally, compared to FEM-only inverse method with errors greater than 50%, our DNN-FEM inverse approach significantly improved the parameter identification accuracy and reduced the errors to less than 1%.

Discovering governing equations in discrete systems using PINNs

Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom. We illustrate the ability of a suitable adaptation of Physics-Informed Neural Networks (PINNs) to solve the inverse problem of parameter identification in such discrete, high-dimensional systems inspired by physical applications. The methodology is illustrated in a diverse array of examples including real-field ones (ϕ4 and sine-Gordon), as well as complex-field (discrete nonlinear Schrödinger equation) and going beyond Hamiltonian to dissipative cases (the discrete complex Ginzburg–Landau equation). Both the successes, as well as some limitations of the method are discussed along the way.

Identifying Parameters of Reactor Operation Digital Twin by Using Swarm and Evolutionary Algorithms

Digital twin (DT) technology is currently gaining popularity in a variety of industrial applications. Recently, the China Institute of Nuclear Power proposed a data driven by nuclear reactor digital twin. The digital twin solves the forward problem for physical field simulation and the inverse problem for parameter identification. The inverse problem can be viewed as a black-box optimization problem where the input parameters are identified by the Latin hypercube sampling (LHS) method based on a given partial observation. While LHS is relatively naive, in this paper, we proposed to apply swarm and evolutionary algorithms to solve the inverse problem. Specifically, we present an experimental comparative study for LHS and four popular SEAs, Particle Swarm Optimizer (PSO), Differential Evolution (DE), Evolutionary Strategy (ES), and evolution strategy with covariance matrix adaptation (CMA-ES). The results show that, for this inverse problem, SEAs are more accurate and efficient than LHS. We also investigate the comparative optimization algorithm’s searching capability under the conditions of noisy observations and no initial input parameter guesses. The experimental results show that DE and CMA-ES have strong robustness and high searching ability.

The inverse problem of permeability identification for multiphase flow in porous media

Estimating permeability heterogeneity is a key component in modeling multiphase flow in geological porous media such as aquifers and reservoirs. The inverse problem of identifying permeability has been thoroughly studied regarding single-phase flow, however, hardly in two-phase flow problems. In this work, we study the inverse problem of estimating the spatial distribution of permeability in two-phase flow, considering a known saturation distribution, and using an iterative method based on inverting the capillary pressure–permeability relationship. The method is evaluated considering many different problem parameters and shown to be accurate for many cases in both oil–water and CO2–water three-dimensional systems. Large errors are observed when there is significant water trapping due to capillary effects and when conditions are dominated by viscosity. A range of optimal parameters is determined in which the inverse method is most accurate. These parameters can be used in applications, for example, when designing coreflooding experiments for permeability estimation. The estimated permeability is then used to predict the saturation and pressure distributions of two-phase flow with different injection flow rates and fluid fractions. The models are shown to be accurate when permeability estimations are accurate. The results support the possibility of calibrating a numerical model to coreflooding experiments and then using it to replace additional experiments, e.g., for evaluating flow rate effects.

Lagrangian approach and shape gradient for inverse problem of breaking line identification in solid: contact with adhesion

A class of inverse identification problems constrained by variational inequalities is studied with respect to its shape differentiability. The specific problem appearing in failure analysis describes elastic bodies with a breaking line subject to simplified adhesive contact conditions between its faces. Based on the Lagrange multiplier approach and smooth Lavrentiev penalization, a semi-analytic formula for the shape gradient of the Lagrangian linearized on the solution is proved, which contains both primal and adjoint states. It is used for the descent direction in a gradient algorithm for identification of an optimal shape of the breaking line from boundary measurements. The theoretical result is supported by numerical simulation tests of destructive testing in 2D configuration with and without contact.

Вычисление коэффициентов определяющих соотношений нелинейно-упругих материалов с использованием эволюционных алгоритмов

Abstract. The possibility of parameter identification for constitutive relations of materials based on uniaxial stretching of a nonlinear-elastic prismatic sample and on inflating a hollow cylinder has been studied. The experiments are modeled using the semi-inverse method of nonlinear theory of elasticity. To describe the mechanical properties of the studied objects, the potentials of compressible nonlinearly elastic media - Blatz and Ko material, and Murnaghan model are used. In the first stage, a series of direct problems are solved. Analytical expressions for the load-elongation dependence are used for the stretching problem. The three-dimensional problem of a cylinder inflation is reduced to a nonlinear boundary value problem for an ordinary second-order differential equation for the function of the radial displacement of cylinder points. In all cases, load diagrams are constructed based on the specified parameters of the nonlinearly elastic models, which are subsequently considered as initial data for the inverse problem of parameter identification. The problem is reduced to finding the minimum of the objective function which is defined as a least squares function. Two evolutionary algorithms were used for analysis: the Squirrel search algorithm (SSA), based on the model of the foraging behaviour of southern flying squirrel population, and the differential evolution algorithm (DE) from the SciPy library. Reliable identification of material parameters of models was shown using evolutionary algorithms based on load diagrams of samples, including condition of artificial noise of "experimental" data.

A thermal load identification method based on physics-guided neural network for honeycomb sandwich structures

The identification of thermal load/thermal shock of aircraft during service is beneficial for collecting information of the service environment and avoiding risks. In the paper, a method based on multivariate information fusion and physics-guided neural network is developed for the inverse problem of thermal load identification of honeycomb sandwich structures. Two thermal feature parameters: temperature gradient and temperature variation rate are used to build the dataset. A 16-layers physics-guided neural network is presented to achieve the predicted results consistent with physical knowledge. In the work, laser irradiation is used as the thermal load, and two laser parameters are to be identified, i.e. spot diameter, power. Simulations and experiments are conducted to verify the effectiveness of the proposed method. The effects of physics-guided loss function and multivariate information fusion are discussed, and it is found that the results based on the proposed method are much better than the results based on the method without physical model. Besides, results based on multivariate information fusion are better than results based on single temperature response. Then, the effects of network models and hyper parameters on the proposed method are also discussed.

Sparse Bayesian Learning with hierarchical priors for duct mode identification of tonal noise

Fan noise has become an important noise component of civil aviation engines with the increasing bypass ratio. The mode identification method is the key to in-duct fan noise testing. The number of modes that can propagate through the duct increases dramatically for high-frequency in-duct fan noise, which requires a large number of microphones to measure the sound field in the duct. Since the number of modes is usually larger than the number of microphones, it is difficult to realize mode identification. A Sparse Bayesian Learning algorithm for mode identification is proposed to solve this problem in this paper. The in-duct sound field is described by a statistical model, and the inverse problem of mode identification is expressed in a Bayesian framework. The non-convex optimization problem of the cost function is considered, iteratively achieving the sparsest solution via a block coordinate descent algorithm in a majorization-minimization framework. The mode identification method based on Sparse Bayesian Learning has high sparsity and can achieve parameter adaptation. The effectiveness of the Sparse Bayesian Learning method for duct mode identification is verified by numerical simulations and experimental tests. The results show that the mode identification method of Sparse Bayesian Learning can accurately identify the target mode using fewer microphones.

Substructural damage identification using autoregressive moving average with exogenous inputs model and sparse regularization

Substructuring approaches possess many superiorities over traditional global approaches in damage identification because large-size global structures are replaced by small and manageable substructures. This paper proposes a substructural time series model for locating and quantifying the damage in complex systems. A substructural autoregressive moving average with exogenous inputs (ARMAX) model is established to extract the frequencies and mode shapes of substructures as indicators for damage detection. The detection of structural damage is essentially an inverse problem, and the damage in structure bears sparse properties. The inverse problem of substructural damage identification is efficiently solved via sparse regularization, and structural damage can be located and quantified through the nonzero terms in the solution vector. The accuracy of the proposed method is demonstrated by the numerical simulation of a frame structure and shaking table test of a shear building structure. As the substructural properties are more sensitive to local structural damage than the global properties, the substructural ARMAX model is quite accurate and efficient to be used in the damage identification of a complex system.