Inverse Problems In Engineering Research Articles

Investigation of Compressor Cascade Flow Using Physics-Informed Neural Networks with Adaptive Learning Strategy

In this study, we utilize the emerging physics-informed neural networks (PINNs) approach for the first time to predict the flowfield of a compressor cascade. Different from conventional training methods, a new adaptive learning strategy that mitigates gradient imbalance through incorporating adaptive weights in conjunction with a dynamically adjusting learning rate is used during the training process to improve the convergence of PINNs. The performance of PINNs is assessed here by solving both the forward and inverse problems. In the forward problem, by encapsulating the physical relations among relevant variables, PINNs demonstrate their effectiveness in accurately forecasting the compressor’s flowfield. PINNs also show obvious advantages over the traditional computational fluid dynamics (CFD) approaches, particularly in scenarios lacking complete boundary conditions, as is often the case in inverse engineering problems. PINNs successfully reconstruct the flowfield of the compressor cascade solely based on partial velocity vectors and near-wall pressure information. Furthermore, PINNs show robust performance in the environment of various levels of aleatory uncertainties stemming from labeled data. This research provides evidence that PINNs can offer turbomachinery designers an additional and promising option alongside the current dominant CFD methods.

Modeling of Ultrasonic Flaw Detection Processes in the Task of Searching and Visualizing Internal Defects in Assemblies and Structures

Introduction. Inverse problems are a specific type of tasks where the consequences of phenomena are studied to identify their causes. They are widely used in scientific studies, specifically, those dealing with large amounts of experimental data. In the presented paper, inverse problems in mechanical engineering and structural diagnostics are considered. These areas require precise methods to identify internal defects in various materials, which can be critical to ensure the safety and efficiency of technical structures. Despite the many flaw detection methods available, there is a need for innovative developments that can provide higher accuracy and efficiency. This study integrates different scientific methods and technologies. It opens up new perspectives in nondestructive testing for the detection of internal defects in various materials and structures. Its objective is to develop and implement nondestructive testing methods based on a neural network device to improve the accuracy of defect identification, as well as to build a neural network model and evaluate its effectiveness for the refinement of ultrasonic visualization of internal defects in solid materials. In this regard, the task to be solved is to create a reliable tool for accurate visualization of sizes, shapes, location and orientation of internal defects in various materials.Materials and Methods. The technique of determining the geometric parameters of defects in materials through nondestructive testing is used. The approach combining modeling of ultrasonic wave propagation in acoustic medium and artificial neural network technologies is applied. This approach identifies nonlinear relationships between the geometry of defects and the amplitude-frequency and amplitude-time data obtained during signal analysis. Artificial neural networks are a model that can be trained on examples, which provides for an effective solution to problems that are difficult to express in traditional forms. The study uses the finite difference method in the time domain. It is applied to identify and visualize internal defects in materials using ultrasonic nondestructive testing and convolutional generative neural networks.Results. A convolutional neural network has been developed to visualize internal defects using ultrasonic nondestructive testing techniques. This neural network successfully determines the size of defects, their location, shape and orientation with high accuracy and reliability.Discussion and Conclusion. The authors highlight the key influence of defect size on the accuracy of ultrasonic imaging in various scenarios. The validation of the model for three different cases of defects with different mechanical parameters has shown that for successful visualization of defects, the wavelength of the ultrasonic pulse must be ten times smaller than the size of the defect. When analyzing the impact of defect size on the accuracy of the neural network, it is found that the visualization error increases for defects of smaller size. It has also been found that the relative speed of sound in materials has a greater effect on the accuracy of the method than the relative density of the material. Based on the results obtained by the authors, it can be argued that the developed methods and technical solutions are of great importance for future research in the field of flaw detection. They have significant potential for scientific and practical applications.

A Regularization-Free Scheme for Recovering Large External Forces of Higher-Order Nonlinear Evolution Equations

In this study, the inverse engineering problems of the Ostrovsky equation (OE), Kawahara equation (KE), modified Kawahara equation (mKE), and sixth-order Korteweg-de Vries (KdV) equation will be investigated numerically. An effective numerical approach to tackle these inverse Coriolis dispersion problems and the above-mentioned inverse problems are still not available. To use different boundary shape functions, we must deal with the boundary data, initial conditions, and terminal time conditions of the OE, KE, mKE, and sixth-order KdV equations. The unknown Coriolis dispersion of OE and unknown large external forces of those three equations can be retrieved through back-substitution of the solution into the OE, KE, mKE, and sixth-order KdV equations while we obtain the solution with the symmetry property by employing the boundary shape function scheme (BSFS). Five numerical experiments with noisy data are carefully validated and discussed.

Selected Papers from the 10th International Conference on Inverse Problems in Engineering (ICIPE 22)

Selected Papers from the 10th International Conference on Inverse Problems in Engineering (ICIPE 22)

An inverse mapping approach for process systems engineering using automatic differentiation and the implicit function theorem

AbstractThe objective in this work is to propose a novel approach for solving inverse problems from the output space to the input space using automatic differentiation coupled with the implicit function theorem and a path integration scheme. A common way of solving inverse problems in process systems engineering (PSE) and in science, technology, engineering and mathematics (STEM) in general is using nonlinear programming (NLP) tools, which may become computationally expensive when both the underlying process model complexity and dimensionality increase. The proposed approach takes advantage of recent advances in robust automatic differentiation packages to calculate the input space region by integration of governing differential equations of a given process. Such calculations are performed based on an initial starting point from the output space and are capable of maintaining accuracy and reducing computational time when compared to using NLP‐based approaches to obtain the inverse mapping. Two nonlinear case studies, namely a continuous stirred tank reactor (CSTR) and a membrane reactor for conversion of natural gas to value‐added chemicals are addressed using the proposed approach and compared against: (i) extensive (brute‐force) search for forward mapping and (ii) using NLP solvers for obtaining the inverse mapping. The obtained results show that the novel approach is in agreement with the typical approaches, while computational time and complexity are considerably reduced, indicating that a new direction for solving inverse problems is developed in this work.

10th International Conference on Inverse Problems in Engineering ICIPE 22

May 15-19, 2022 Francavilla al Mare (Chieti), ITALY Introduction This Proceedings of the Journal of Physics: Conference Series contains a subset of papers presented at the 10th International Conference on Inverse Problems in Engineering (ICIPE), hosted by the Department of Industrial and Information Engineering and Economics, University of L’Aquila, Italy, and held in Francavilla al Mare (Chieti), May 15 – 19, 2022.Due to Coronavirus emergency and to protect the health and safety to all our participants, the 10th Edition, scheduled during May 18-21, 2020, and then May 16-20, 2021, was postponed to May 15-19, 2022, and termed as ICIPE 22.Since the first ICIPE in 1993, this conference has served as the main international venue for collaboration and interaction between applied mathematicians who develop inverse analysis tools, and engineers who use these tools in many different disciplines of science such as manufacturing and machining processes, medical imaging, oil exploration, radar, sonar and seismology, space applications, non-destructive testing and so on. The 2022 meeting continued this tradition, with more than 50 delegates from many sub-disciplines of engineering, science, and applied mathematics. The number of participants was lower than the standard number of 80 – 120 due to both covid travel restrictions in some Asian and American countries and conflict in Ukraine.List of Dedication, References, Organizing Committee, Local Committee, Scientific Committee, List of Registrants, Sponsors and Logos are available in this pdf.

Stochastic asymptotical regularization for linear inverse problems

We introduce stochastic asymptotical regularization (SAR) methods for the uncertainty quantification of the stable approximate solution of ill-posed linear-operator equations, which are deterministic models for numerous inverse problems in science and engineering. We demonstrate that SAR can quantify the uncertainty in error estimates for inverse problems. We prove the regularizing properties of SAR with regard to mean-square convergence. We also show that SAR is an order-optimal regularization method for linear ill-posed problems provided that the terminating time of SAR is chosen according to the smoothness of the solution. This result is proven for both a priori and a posteriori stopping rules under general range-type source conditions. Furthermore, some converse results of SAR are verified. Two iterative schemes are developed for the numerical realization of SAR, and the convergence analyses of these two numerical schemes are also provided. A toy example and a real-world problem of biosensor tomography are studied to show the accuracy and the advantages of SAR: compared with the conventional deterministic regularization approaches for deterministic inverse problems, SAR can provide the uncertainty quantification of the quantity of interest, which can in turn be used to reveal and explicate the hidden information about real-world problems, usually obscured by the incomplete mathematical modeling and the ascendence of complex-structured noise.

Special Section: 10th International Conference on Inverse Problems in Engineering ICIPE 22, May 15–19, 2022, Francavilla al Mare (Chieti), Italy

Abstract This Special Section of the ASME Journal VVUQ contains two papers presented at the 10th International Conference on Inverse Problems in Engineering (ICIPE), hosted by the Department of Industrial and Information Engineering and Economics, University of L'Aquila, Italy, and held in Francavilla al Mare (Chieti), May 15 - 19, 2022.

Inverse problems in food engineering: A review

With the increase in the computational power, numerical simulations play an increasing role in designing, development, and optimization of various food processing operations. Inverse and ill-posed problems have been studied extensively in many branches of science and engineering, including mechanical, chemical, aerospace, biology, physics, and chemistry. The inverse techniques have been currently witnessing a growing trend in the food processing field for a decade. Inverse problems are usually performed when direct measurements of heat and mass transfer properties and boundary conditions, are not feasible. They are very sensitive to measurement errors; require optimization methods to tackle the inverse problem. It is necessary to consider the coupling heat and mass transfer for the solution of inverse problem since food process involves simultaneous heat and mass transfer within the food products. To date, inverse methods have been applied in few food processing operations, including drying, baking, freezing, and thermal processing. However, studies related to these areas on the estimation of unknown quantities for various fruits and vegetables, and food products are limited. This review covers the statistical concepts which include confidence interval, confidence region, model validation and minimization techniques discussed in detail. The optimal experimental design, D-optimality and Fisher Information Matrix, and sensitivity analysis are all extensively presented. The optimization techniques and their algorithms used in the area of food processing are explained. Finally, it mainly focuses on the inverse estimation of unknown quantities, namely, heat and mass transfer parameters in different food processing operations.

Solution to inverse natural convection problem using experimental data

Inverse problems arise in a wide range of practical systems and processes and, thus, form an important and well-known area of research in mathematics and physical sciences. The basic nature of an inverse problem is mathematically ill-posed and, as such, finding a unique, accurate, solution is challenging. A prime example of inverse problems in mechanical engineering is the inverse heat transfer problem where the desired solution is known and the boundary and initial conditions, or even material properties, are not. While the heat conduction problem has attracted the bulk of research due to its generally linear governing physics, inverse heat convection presents a greater challenge. The inclusion of fluid mechanics and the nonlinear nature of momentum and energy equations, combined with the previously mentioned ill-posed nature of the inverse problem, presents a challenging research topic. In this paper, a search-based inverse heat convection methodology, developed earlier, is tested against experimental data. The problem considered is a wall plume flow generated by a heat source, such as an electronic component or a fire, located on a vertical surface. This method shows that by measuring the temperatures at a limited number of points downstream of the heat source, the heat input and location of the source can be estimated within an acceptable range of accuracy. This paper continues the earlier work by including experimental data in the prediction of heat source strength and location. It is shown that the methodology introduced earlier is quite robust and can be used for a variety of important practical applications.

Structural engineering from an inverse problems perspective.

The field of structural engineering is vast, spanning areas from the design of new infrastructure to the assessment of existing infrastructure. From the onset, traditional entry-level university courses teach students to analyse structural responses given data including external forces, geometry, member sizes, restraint, etc.—characterizing a forward problem (structural causalities structural response). Shortly thereafter, junior engineers are introduced to structural design where they aim to, for example, select an appropriate structural form for members based on design criteria, which is the inverse of what they previously learned. Similar inverse realizations also hold true in structural health monitoring and a number of structural engineering sub-fields (response structural causalities). In this light, we aim to demonstrate that many structural engineering sub-fields may be fundamentally or partially viewed as inverse problems and thus benefit via the rich and established methodologies from the inverse problems community. To this end, we conclude that the future of inverse problems in structural engineering is inexorably linked to engineering education and machine learning developments.

An uncertainty inversion technique using two-way neural network for parameter identification of robot arms

Due to structural complexity of robot arms, constraints of experiments, especially uncertainty of design parameters, numerical models for dynamics analysis of robot arms can produce erroneous results, which can seriously affect the performance of the designed robot arms. Reliable parameter uncertainty identification for robot arms becomes important. The current methods for uncertainty analysis have double-layered processes, in which the inner layer is for uncertainty propagation and the outer layer is an iterative optimization process. Such a nested double-layered approach limits computational efficiency. This work proposes a novel inverse method for parameter uncertainty identification using a two-way neural network. First, an element (FE) model of a robot arm is established and validated experimentally. Sensitivity analysis is then conducted using the FE model to determine a set of major parameters to be identified. A two-way neural network is next established, and the explicit formulae of direct weight inversion (DWI) use to inverse these parameters of the robot arm. Finally, the inverse result is validated by experiments. Our study show that the present inverse method can greatly improve the computational efficiency. It provides a new avenue to tackle complex inverse problems in engineering and sciences.

An abstract approach toward the structural digital twin of ship hulls: A numerical study applied to a box girder geometry

Condition monitoring (CM) of ship hull structures is a promising field that has recently attracted the interested of researches. The main challenge behind CM is to develop a system that gets as input sensor readings from the structure and provide the damage locus as an output. In this regard, the current study proposes two alternative CM digital twin schemes for solving this inverse engineering problem. The first one is based on a Finite Element (FE) – Optimization cooperative framework that solves several times the model until the predicted strains match the measured ones and as such the damage location has been found. The other scheme is based on a cooperative framework of Artificial Neural Networks (ANNs) used for classification and fitting, that may be regarded as surrogated models which provide solutions instantaneously. The ANNs are trained through the numerical solutions provided by the FE model. A thin-walled hollow cantilever beam, that resembles a hull-girder subjected to principal stresses under vertical bending, has been adopted. The performed work has allowed for the selection and evaluation of the locations for sensor placement and the estimation of the damage sensitive area for monitoring. Both CM digital twin schemes have proven to be promising for the theoretical simplified examined case.

An application of conjugate gradient technique for determination of thermal conductivity as an inverse engineering problem

Inverse problems frequently occur when boundary conditions/thermal properties of a material are unknown, and are determined from known internal temperature measurements. A direct problem is the opposite of an inverse problem. For example, it would be the task of determining the temperature field within a material body, given boundary conditions and thermal properties. In an ill-posed, inverse problem, small variations in internal temperature measurement cause large variations in the estimated quantity such as boundary heat flux. Measured temperature variations may be due to noise, measurement error and instrumentation error, among other factors. There are various methods for solving inverse problems in materials engineering. In the paper, an inverse problem of estimating boundary heat flux for one-dimensional heat conduction is solved using the classical method of Beck and temperature dependent thermal conductivity is estimated using the more recent and advanced Conjugate Gradient method (CGM). The temperature values from the finite difference application to a direct heat transfer problem are used along with noise added to the data, in order to simulate real world, experimental conditions. The data is applied to the inverse problem of finding boundary heat flux and thermal conductivity. It is seen that Conjugate Gradient Method (CGM) along with sequential function specification method recovers the boundary heat flux and thermal conductivity quite accurately for noise levels of 1% and 2%. It is further observed that addition of future time steps stabilize the algorithm and increase accuracy of the desired results. It is also observed that CGM can recover the temperature dependent thermal conductivity quickly within few iterations, for different values of thermal conductivity function coefficients, k0 and k1. CGM is found to be fast and robust when applied to one-dimensional case and can be extended to complex geometries.

Wavefield reconstruction inversion: an example

Nonlinear least squares data-fitting driven by physical process simulation is a classic and widely successful technique for the solution of inverse problems in science and engineering. Known as ‘full waveform inversion (FWI)’ in application to seismology, it can extract detailed maps of earth structure from near-surface seismic observations, but also suffers from a defect not always encountered in other applications: the least squares error function at the heart of this method tends to develop a high degree of nonconvexity, so that local optimization methods (the only numerical methods feasible for field-scale problems) may fail to produce geophysically useful final estimates of earth structure, unless provided with initial estimates of a quality not always available. A number of alternative optimization principles have been advanced that promise some degree of release from the multimodality of FWI, amongst them wavefield reconstruction inversion (WRI), the focus of this paper. Applied to a simple 1D acoustic transmission problem, both full waveform and WRI methods reduce to minimization of explicitly computable functions, in an asymptotic sense. The analysis presented here shows explicitly how multiple local minima arise in FWI, and that WRI can be vulnerable to the same ‘cycle-skipping’ failure mode.

Simulation-based non-linear vibration model for damage detection in RC beams

This study presents a simulation-based method for damage detection in reinforced concrete beam-type structures. Reinforced concrete bridges are constantly exposed to dynamic loading, thus leading to deterioration before their design life. A novel damage assessment procedure has been presented, which uses the changes in non-linear vibration characteristics from computational model for damage assessment. A constitutive model is proposed, the parameters of which can be developed from compressive strength from laboratory test, and implemented in FE modelling of an RC beam. Incremental static damage is simulated in the beam, after which the non-linear behaviour is detected using harmonic excitation. The non-linear behaviour from simulation is characterised and used in proposing a damage detection method that does not rely on the baseline data of the structure. The methodology is validated experimentally and compared with conventional linear frequency-shift-based damage detection method. Resultantly, the proposed method is simple, computationally efficient, shows good agreement with the published studies on cracked vibration behaviour and has promising prospects in addressing inverse engineering problem in structural health monitoring of RC structures.

A study of transient wall plume and its application in the solution of inverse problems

Inverse engineering problems have many applications in various industries. While most of the research is focused on the steady state problems, transient heat transfer also has potential with regard to application and research. A detailed study of the forward transient wall plume is developed and the analytical results are used to build an inverse solution methodology. The goal of the inverse solution is to find the heat source location and energy input or strength using a few, limited, data points downstream. The methodology involves developing interpolating functions that relates transient features to plume strength and location at each location downstream of the plume and then using these functions to set up a system of equations. This system of equations is then solved to find the unknown variables. A search based optimization method, particle swarm optimization (PSO), is used to find the optimal sensor locations downstream of the plume in order to minimize the number of downstream data points needed for an accurate prediction.

A Novel Improved Maximum Entropy Regularization Technique and Application to Identification of Dynamic Loads on the Coal Rock

A new signal processing algorithm was proposed to identify the dynamic load acting on the coal-rock structure. First, the identification model for dynamic load is established through the relationship between the uncertain load vector, and the assembly matrix of the responses was measured by the machinery dynamic system. Then, the entropy item of maximum entropy regularization (MER) is redesigned using the robust estimation method, and the elongated penalty function according to the ill-posedness characteristics of load identification, which was named as a novel improved maximum entropy regularization (IMER) technique, was proposed to process the dynamic load signals. Finally, the load identification problem is transformed into an unconstrained optimization problem and an improved Newton iteration algorithm was proposed to solve the objective function. The result of IMER technique is compared with MER technique, and it is found that IMER technique is available for analyzing the dynamic load signals due to higher signal-noise ratio, lower restoration time, and fewer iterative steps. Experiments were performed to investigate the effect on the performance of dynamic load signals identification by different regularization parameters and calculation parameters, pi, respectively. Experimental results show that the identified dynamic load signals are closed to the actual load signals using IMER technique combined with the proposed PSO-L regularization parameter selection method. Selecting optimal calculated parameters pi is helpful to overcome the ill-condition of dynamic load signals identification and to obtain the stable and approximate solutions of inverse problems in practical engineering. Meanwhile, the proposed IMER technique can also play a guiding role for the coal-rock interface identification.

State-of-the-art review on Bayesian inference in structural system identification and damage assessment

Bayesian inference provides a powerful approach to system identification and damage assessment for structures. The application of Bayesian method is motivated by the fact that inverse problems in structural engineering, including structural health monitoring, are typically ill-conditioned and ill-posed when using noisy incomplete data because of various sources of modeling uncertainties. One should not just search for a single “optimal” value for the vector of model parameters but rather attempt to describe the whole family of plausible model parameters based on measured data using a Bayesian probabilistic framework. In this article, the fundamental principles of Bayesian analysis and computation are summarized; then a review is given of recent state-of-the-art practices of Bayesian inference in system identification and damage assessment for civil infrastructure. Discussions of the benefits and deficiencies of these approaches, as well as potentially useful avenues for future studies, are also provided. Our focus is on meeting challenges that arise from system identification and damage assessment for the civil infrastructure but our presented theories also have a considerably broader applicability for inverse problems in science and technology.

9th International Conference on Inverse Problems in Engineering (ICIPE)

IntroductionThis proceedings of the Journal of Physics: Conference Series contains a subset of papers presented at the 9th International Symposium on Inverse Problems in Engineering (ICIPE), held at the University of Waterloo, May 23-26 2017. Since the first ICIPE in 1993, this conference has served as the main international venue for collaboration and interaction between mathematical theorists who develop inverse analysis tools, and engineers who use these tools to solve today’s problems. Our meeting continued this tradition, with 80 delegates from many sub-disciplines of engineering, science, and applied mathematics.The conference and its proceedings are dedicated to Professor Graham Gladwell, FRSC. Graham played a key role in establishing this conference series, and was cross-appointed between the Faculties of Mathematics and Engineering during his career at the University of Waterloo, exemplifying the fact that inverse analysis lies at the intersection of these two areas. Sadly, Graham passed away on March 11th, 2017, only two months before our conference. We honoured his memory and spirit throughout the conference.List of Dedication, Conference Organizers, Sponsors and Conference Participants are available in this Pdf.