Inverse Problem Of Identification Research Articles

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.

A gradient based numerical algorithm to solve inverse dynamic viscoelastic problems of multi-variable identification

A gradient based numerical method is put forward to solve the inverse dynamic viscoelastic problem with multi-variable identification for the constitutive and TKBC (third kind boundary conditions) related parameters. A three parameter model is employed to describe the time dependent TKBC concerned with structural interaction, and is formulated in the forward and inverse dynamic viscoelastic analysis. In addition to the reliable platform provided by TPAA-SBFEM to gain the solution of forward problems, a piecewise recursive adaptive algorithm is developed to obtain the derivatives required in the sensitivity analysis, which is able to provide a stable temporal solution accuracy for different step sizes. SBFEM (Scaled Boundary Finite Element Method) is stressed in the structural analysis with its own advantages, such as the efficient and convenient treatment of stress singularity problem and flexibility of mesh generation with polygonal elements and image based quadtree gridding. The inverse problem of identification is solved by the Levenberg-Marquardt method, and the regional inhomogeneity, crack, initial guess, location/number of measurement points, material contrast ratios, and noisy data are taken into account. Numerical examples are provided to verify the proposed approach, and the satisfactory results are achieved.

Coefficient identification in a SIS fractional-order modelling of economic losses in the propagation of COVID-19

A fractional-order SIS (Susceptible–Infectious–Susceptible) model with time-dependent coefficients is used to analyse some effects of the novel coronavirus 2019 (COVID-19). This generalized model is suitable for describing the COVID dynamics since it does not presume permanent immunity after contagion. The fractional derivative activates the memory property of the dynamics of the susceptible and infectious population time series. A coefficient identification inverse problem is posed, which consists of reconstructing the time-varying transmission and recovery rates, which are of paramount importance in practice for both medics and politicians.The inverse problem is reduced to a minimization problem, which is solved in a least squares sense. The iterative predictor–corrector algorithm reconstructs the time-dependent parameters in a piecewise-linear fashion. The economic losses emerging from social distancing using the calibrated model are also discussed. A comparison between the results obtained by the classical model and the fractional-order model is included, which is validated by ample tests with synthetic and real data.

Postflight Recovery of the Rotational Motion of a Small Space Vehicle from Solar Sensor Information

The use of the developed technology for solving inverse problems of parametric identification of the rotational motion of a spacecraft (SC) based on the accumulated sample of measurements of various compositions is expanded. On the example of processing telemetry data (measuring the direction vector to the Sun) of the BugSat-1 small spacecraft (SSC), the possibility of determining not only the characteristics of rotational motion but also its inertia coefficient is demonstrated. The rotational motion is determined based on the data obtained for five time intervals from January to May 2022, during which BugSat-1 made an uncontrolled movement around the direction vector toward the Sun. This type of motion does not allow applying traditional approaches to determine the dynamics of its rotation. In the process of data processing, a simplified model of the rotation of a SSC is used. At the same time, the initial conditions of rotational motion are estimated—the angular velocity vector and orientation angles, which made it possible to draw a conclusion about the precessional motion of a SSC. Using the analytical model of a regular precession, it is possible to estimate the inertia coefficient of a SSC. The results of flight information processing are presented and the errors of the obtained results are estimated.

Parameter Estimation Analysis in a Model of Honey Production

Honeybee losses are an extensive global problem. In this study, a new compartment model of honeybee population that mainly concerns honey production is developed. The model describes the interaction of the food stock with the brood (immature bees), adult bees and produced honey. In the present paper, the issue of an adequate model recovery is addressed and the parameter identification inverse problem is solved. An adjoint equation procedure to obtain the unknown parameter values by minimizing the functional error during a period of time is proposed. Numerical simulations with realistic data are discussed.

A hybrid algorithm to solve a nonlinear inverse problem of boundary conditions and damage identification

In this communication we present a method exploiting displacement data measured at accessible parts of solid’s boundary, for the solution of boundary conditions and damage identification problems encountered in mechanics. Targeted applications are made of materials presenting a nonlinear mechanical behavior with damage-based approaches. A hybrid algorithm has been developed in order to identify the missing data by minimizing a gap-functional. It takes into account the incremental mechanical behavior of the material and the damage evolution inside the solid via the concept of piloting. An application on a solid made of mortar with synthetic measurements is presented to illustrate the efficiency and robustness of the algorithm.

Stratifications and foliations in phase portraits of gene network models.

Periodic processes of gene network functioning are described with good precision by periodic trajectories (limit cycles) of multidimensional systems of kinetic-type differential equations. In the literature, such systems are often called dynamical, they are composed according to schemes of positive and negative feedback between components of these networks. The variables in these equations describe concentrations of these components as functions of time. In the preparation of numerical experiments with such mathematical models, it is useful to start with studies of qualitative behavior of ensembles of trajectories of the corresponding dynamical systems, in particular, to estimate the highest likelihood domain of the initial data, to solve inverse problems of parameter identification, to list the equilibrium points and their characteristics, to localize cycles in the phase portraits, to construct stratification of the phase portraits to subdomains with different qualities of trajectory behavior, etc. Such an à priori geometric analysis of the dynamical systems is quite analogous to the basic section "Investigation of functions and plot of their graphs" of Calculus, where the methods of qualitative studies of shapes of curves determined by equations are exposed. In the present paper, we construct ensembles of trajectories in phase portraits of some dynamical systems. These ensembles are 2-dimensional surfaces invariant with respect to shifts along the trajectories. This is analogous to classical construction in analytic mechanics, i. e. the level surfaces of motion integrals (energy, kinetic moment, etc.). Such surfaces compose foliations in phase portraits of dynamical systems of Hamiltonian mechanics. In contrast with this classical mechanical case, the foliations considered in this paper have singularities: all their leaves have a non-empty intersection, they contain limit cycles on their boundaries. Description of the phase portraits of these systems at the level of their stratifications, and that of ensembles of trajectories allows one to construct more realistic gene network models on the basis of methods of statistical physics and the theory of stochastic differential equations.

Simultaneous determination of the time‐dependent potential and force terms in a fourth‐order Rayleigh–Love equation

This paper considers an inverse coefficient problem of simultaneous determination of solely time‐dependent potential and force terms with the unknown longitudinal displacement from a Rayleigh–Love equation from two integral overdetermination measurements. Unique solvability of this theorem is investigated theoretically by using contraction principle. Although, the aforesaid inverse identification problem is ill‐posed but has a unique solution. We use the cubic B‐spline (CBS) collocation and Tikhonov regularization techniques to discretize the direct problem and to obtain stable as well as accurate solutions, respectively. The stability, for the discretized system of the direct problem, is also carried out by means of the von Neumann method. The acquired results demonstrate that accurate as well as stable solutions for the and are accessed for , when for both smooth and discontinuous potential and force terms. The stability analysis shows that the discretized system of the direct problem is unconditionally stable. Since the noisy data are introduced, the investigation and analysis model real circumstances where the practical quantities are naturally infested with noise. The technique establishes that accurate, as well as stable, solutions are obtained.

Reconstruction of a potential coefficient in the Rayleigh–Love equation with non-classical boundary condition

PurposeThe purpose of this paper is to reconstruct the potential numerically in the fourth-order Rayleigh–Love equation with boundary and nonclassical boundary conditions, from additional measurement.Design/methodology/approachAlthough, the aforesaid inverse identification problem is ill-posed but has a unique solution. The authors use the cubic B-spline (CBS) collocation and Tikhonov regularization techniques to discretize the direct problem and to obtain stable as well as accurate solutions, respectively. The stability, for the discretized system of the direct problem, is also carried out by means of the von Neumann method.FindingsThe acquired results demonstrate that accurate as well as stable solutions for the a(t) are accessed for {10–8, 10–7, 10–6, 10–5}, when p {0.01%, 0.1%} for both linear and nonlinear potential coefficient a(t). The stability analysis shows that the discretized system of the direct problem is unconditionally stable.Research limitations/implicationsSince the noisy data are introduced, the investigation and analysis model real circumstances where the practical quantities are naturally infested with noise.Practical implicationsThe acquired results demonstrate that accurate as well as stable solutions for the a(t) are accessed for {10–8, 10–7, 10–6, 10–5}, when p {0.01%, 0.1%} for both linear and nonlinear potential coefficient a(t). The stability analysis shows that the discretized system of the direct problem is unconditionally stable.Originality/valueThe potential term in the fourth-order Rayleigh–Love equation from additional measurement is reconstructed numerically, for the first time. The technique establishes that accurate, as well as stable solutions are obtained.

Hybrid identification method of material parameters based on genetic algorithm and improved homotopy algorithm

This paper proposes a hybrid identification method of material parameters based on genetic algorithm and improved homotopy algorithm. In this method, genetic algorithm is first used to perform a preliminary identification of the model parameters. Then, the results of the preliminary identification are used as the initial values for more precise parameter identification using the improved homotopy algorithm. Based on the Euler prediction-Newton correction homotopy algorithm, a curve prediction-Newton correction homotopy algorithm is proposed to improve the calculation accuracy and efficiency. The effectiveness and accuracy of the hybrid identification method are verified by numerical examples. The hybrid identification method is applied successfully to determine material characteristic parameters of FGH97. The results indicate that based on experimental data and numerical simulations, the hybrid identification method can rapidly obtain effective and reliable material parameters. This method reduces the calculation amount, avoids dependence on the selection of the initial population, and has a high calculation accuracy and efficiency for the inverse problem of parameter identification. It provides an effective method to accurately identify material parameters and can also be applied to parameter identification of other materials. • A hybrid identification method of material parameters based on genetic algorithm and improved homotopy algorithm is proposed. • Curve prediction-Newton correction homotopy algorithm is proposed to improve the calculation accuracy and efficiency. • The effectiveness and accuracy of the hybrid identification method are verified by numerical examples. • The hybrid identification method is applied successfully to determine material characteristic parameters of FGH97 • Hybrid identification method can also be applied to parameter identification of other materials.

Retraction Note: Solving algorithm for inverse problem of partial differential equation parameter identification based on IGEP

Retraction Note: Solving algorithm for inverse problem of partial differential equation parameter identification based on IGEP

Numerical Coefficient Reconstruction of Time-Depending Integer- and Fractional-Order SIR Models for Economic Analysis of COVID-19

In the present work, a fractional temporal SIR model is considered. The total population is divided into three compartments—susceptible, infected and removed individuals. It generalizes the classical SIR model and consists of three coupled time-fractional ordinary differential equations (ODEs). The fractional derivative is introduced to account for the subdiffusion process of confirmed, cured and deceased people dynamics. Although relatively basic, the model is robust and captures the real dynamics, helped by the memory property of the fractional system. In the paper, the issue of an adequate model reconstruction is addressed, and a coefficient identification inverse problem is solved; in particular, the transition and recovering rates, varying in time, are recovered. A least-squares cost functional is minimized for solving the problem. The time-dependent parameters are reconstructed with an iterative predictor–corrector algorithm. Its application is demonstrated via tests with synthetic and real data. What is more, an approach for economic impact assessment is proposed.

Structural system identification and damage detection using adaptive hybrid Jaya and differential evolution algorithm with mutation pool strategy

Engineering applications of swarm intelligence optimization algorithms have been widely employed to identify structural systems and damages owing to their merits of simplicity, flexibility, robustness etc., while they often suffer from the defects of slow efficiency, premature convergence or even trapping into local optima in solving the inverse problem of nonlinear optimization-based parameter identification with partial noise-contaminated measurements. To deal with this issue, an adaptive hybrid Jaya and differential evolution (AHJDE) algorithm is proposed based on Jaya algorithm and differential evolution (DE) by effectively combining the advantages of both algorithms. In the proposed AHJDE, four improvements including adaptive mutation strategy, dynamic mutation and crossover operators, sampling-based resizing search space and linear resizing population size are integrated. The effectiveness of the proposed method is verified using a numerical example of 20-DOF linear system by comparing its performance with particle swarm optimization, modified artificial bee colony algorithm, clustering tree seeds algorithm, improved butterfly optimization algorithm etc. considering known mass case and unknown mass case. In addition, numerical studies on a nonlinear single degree-of-freedom system with classical Bouc-Wen hysteretic model and improved Bouc-Wen model are implemented to investigate the applicability in the field of nonlinear system identification. Finally, a series of experimental tests on a five-story steel frame structure are conducted in the laboratory to further validate the performance of the proposed approach in damage identification. Identification results demonstrate the proposed AHJDE can accurately and effectively identify the unknown system parameters and damages with limited sensors and noise-polluted responses.

Machine learning-assisted parameter identification for constitutive models based on concatenated loading path sequences

A hybrid strategy for the identification of material parameters of constitutive models is presented. One main challenge in the context of classic optimisation-based parameter identification schemes is the generation of adequate starting values for the multi-objective optimisation procedure. We address this issue by employing an artificial neural network that is trained with data obtained from the material model, more precisely speaking, from different solutions of the direct problem for homogeneous states of deformation. As a result, a solution of the inverse problem of parameter identification can be approximated with the help of a neural network processing experimental data. This approximate solution is used as a starting value for a subsequent, classic optimisation-based parameter identification approach. One key advantage of this strategy is that a network only has to be trained once per material model and can subsequently be applied for different materials. A rather sophisticated material model, incorporating gradient-enhanced damage coupled to plasticity in a geometrically non-linear setting, is used to demonstrate the capabilities of this approach. Two different strategies for the generation of training data are investigated and compared, and the neural network’s hyperparameters are optimised for improved prediction capabilities. In view of the calibration of material parameters related to the non-locality of the model, the obtained set of parameters is again considered as a starting value for a final optimisation step, where we consider inhomogeneous states of deformation and digital image correlation data.

Duct mode identification in a statistical model via the Iterative Bayesian Focusing

The measurements of aero-engine fan noise are crucial to engine-noise reduction and silent-turbofan design. The duct mode identification is adpoted to decompose inner duct noises into spinning modes from acoustic pressure measured by a microphone array. However, modes identification of the aero-engine fan are difficult cause the number of modes is usually much larger than the number of microphones and leading to an ill-posed problem during the inverse process. A mode identification method based on Iterative Bayesian Focusing is used to solve this problem. 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 sparsity of the target acoustic modes is applied as a priori condition, and a Mode Aperture Function (MAF) is developed. The aperture width of the MAFis automatically updated and contracted through iterations, after which mode coefficients are contracted to a sparsest solution. The used mode identification method is firstly validated through numerical simulations, and the effects of the number of microphones and SNR on mode identification results are discussed. Then the Iterative Bayesian Focusing-based mode identification method is experimentally verified through a well designed Spinning Mode Synthesizer. Both numerical and experimentalresults indicate that target modes can be accurately identified when the number of microphones are much less than the number of all propagating modes.

Multiphysics-informed deep learning for swelling of pH/temperature sensitive cationic hydrogels and its inverse problem

This paper proposes a field theory of constrained swelling of pH/temperature sensitive cationic hydrogels in equilibrium with their chemical and mechanical environment. A general formulation is obtained based on a variational approach, yielding a set of governing equations coupling mechanical and chemical equilibrium conditions, which is employed to investigate some benchmark problems involving homogeneous and inhomogeneous swelling of the pH/temperature sensitive cationic hydrogels. The simulation results are compared with experimental data available in the literature to verify the present model. By encoding the underlying physical and chemical laws into the deep learning neural networks as prior information, we introduce the multiphysics-informed deep learning (MIDL) to investigate the effects of temperature and pH on the distributions of concentration of solvent and stresses in the hydrogel shell. In addition, the MIDL is extended to solve inverse identification problem of inhomogeneous swelling of core-shell hydrogels, which yields a reasonable identification accuracy even if the observed data is corrupted due to uncorrelated noise.

Inverse two-phase nonlinear Stefan and Cauchy-Stefan problems: A phase-wise approach

We develop a novel phase-wise sequential numerical approach based on the method of fundamental solutions (MFS) for inverse two-phase nonlinear Stefan and Cauchy-Stefan problems in one dimension (1D). By treating each phase independently, the inverse two-phase nonlinear Stefan problem splits into two single-phase inverse problems: an inverse nonlinear boundary identification problem and an inverse linear one-phase Stefan problem. Along with the reconstruction of boundary data, the simultaneous reconstruction of the boundary and initial data is also considered. Numerical investigations show the robustness and efficiency of the proposed method in reconstructing the data.

Regularized Least Squares Recursive Algorithm with Forgetting Factor for Identifying Parameters in the Grinding Process

This paper investigates a parameter identification problem in the grinding process. Due to the data saturated phenomenon and the ill-posed of parameter identification inverse problem, this paper presents a regularized least squares recursive algorithm with a forgetting factor (RLSRAFF), the basic idea of which is to combine the forgetting factor with regularization parameters. Moreover, based on RLSRAFF, this paper verifies the recursive calculation of criterion function, analyzes the effect of calculation error from the gain matrix and proves the convergence of the proposed algorithm. Finally, effectiveness of RLSRAFF is verified by simulation experiments and grinding data. Compared with other algorithms, RLSRAFF can give a more convergence rate to the real data and reduce the error from the true value.