Inverse Solution Research Articles

Seismic swarm intelligence inversion with sparse probability distribution of reflectivity

Seismic inversion, such as velocity and impedance, is an ill-posed problem. To solve this problem, swarm intelligence (SI) algorithms have been increasingly applied as the global optimization approach, such as differential evolution (DE) and particle swarm optimization (PSO). Based on the well logs, the sparse probability distribution (PD) of the reflectivity distribution is spatial stationarity. Therefore, we proposed a general SI scheme with constrained by a priori sparse distribution of the reflectivity, which helps to provide more accurate potential solutions for the seismic inversion. In the proposed scheme, as two key operations, the creating of probability density function library and probability transformation are inserted into standard SI algorithms. In particular, two targeted DE-PD and PSO-PD algorithms are implemented. Numerical example of Marmousi2 model and field example of gas hydrates show that the DE-PD and PSO-PD estimate better inversion solutions than the results of the original DE and PSO. In particular, the DE-PD is the best performer both in terms of mean error and fitness value of velocity and impendence inversion. Overall, the proposed SI with sparse distribution scheme is feasible and effective for seismic inversion.

Simultaneous Inversion of the Space-Dependent Source Term and the Initial Value in a Time-Fractional Diffusion Equation

Abstract The inverse problem for simultaneously identifying the space-dependent source term and the initial value in a time-fractional diffusion equation is studied in this paper. The simultaneous inversion is formulated into a system of two operator equations based on the Fourier method to the time-fractional diffusion equation. Under some suitable assumptions, the conditional stability of simultaneous inversion solutions is established, and the exponential Tikhonov regularization method is proposed to obtain the good approximations of simultaneous inversion solutions. Then the convergence estimations of inversion solutions are presented for a priori and a posteriori selections of regularization parameters. Finally, numerical experiments are conducted to illustrate effectiveness of the proposed method.

Solving an Inverse Problem for Time-Series-Valued Computer Simulators via Multiple Contour Estimation

Computer simulators are often used as a substitute of complex real-life phenomena, which are either expensive or infeasible to experiment with. This paper focuses on how to efficiently solve the inverse problem for an expensive to evaluate time-series-valued computer simulator. The research is motivated by a hydrological simulator which has to be tuned for generating realistic rainfall–runoff measurements in Athens, Georgia, USA. Assuming that the simulator returns g(x, t) over L time points for a given input x, the proposed methodology begins with a careful construction of a discretization (time-) point set of size $$k \ll L$$ , achieved by adopting a regression spline approximation of the target response series at k optimal knot locations $$\{t_1^*, t_2^*,\ldots ,t_k^*\}$$ . Subsequently, we solve k scalar-valued inverse problems for simulator $$g(x,t_j^*)$$ via the contour estimation method. The proposed approach, named MSCE, also facilitates the uncertainty quantification of the inverse solution. Extensive simulation study is used to demonstrate the performance comparison of the proposed method with the popular competitors for several test-function-based computer simulators and a real-life rainfall–runoff measurement model.

An inverse kinematics framework of mobile manipulator based on unique domain constraint

This paper presents the collision-free solution to the inverse kinematics of a mobile manipulator. The main contribution is to propose a novel inverse kinematics solution framework combining unique domains. The inverse kinematics problem is formulated as an optimization problem in this work. Firstly, the objective function is simplified by the kinematics decoupling method based on improved disconnection and re-connection. Then, the joint variables are decoupled and constrained, and an approach to initialize the variables is proposed. An inverse kinematic solution framework for the manipulator body to avoid obstacles is further presented, and CMA-ES is applied to the framework. Finally, the simulation results demonstrate the effectiveness of the proposed method.

Matrix Chain Multiplication and Equivalent Reduced-Order Parallel Calculation Method for a Robotic Arm

Intelligence development has put forward increasing requirements of real-time planning and dynamic feedback in controlling robotic arms. It has become essential in engineering applications to complete the kinematics calculation of complex manipulators in real time. This paper proposes a matrix cascading multiplication equivalent reduced-order parallel computing method for the multiplication of homogeneous matrices in the process of forward and inverse kinematics solutions, which reduces the order of the matrix according to the distribution of zero vectors in the homogeneous matrix calculations. The method removes the unnecessary multiplication in joint homogeneous matrixes containing zero vectors. It obtains the optimal calculation order of the cascade matrix multiplication through dynamic planning searches, improving the efficiency of effective dot product calculation by parallel computation. Calculation processes and specific examples are presented in this paper. Compared with the previous algorithms, the proposed algorithm reduces the calculation cycle by 90%, effectively improving the real-time calculation efficiency in the complex control process.

Inverse Source Solutions With Huygens’ Surface Conforming Distributed Directive Spherical Harmonics Expansions

Time-harmonic inverse source solutions are commonly working with electric and magnetic surface current densities defined and discretized on appropriately chosen Huygens’ surfaces. An efficient meshless alternative are spherical harmonics expansions of low-order distributed along the chosen Huygens’ surface, which still possess pretty good spatial localization properties. Similar to expansions with electric and magnetic surface current densities, distributed expansions with Cartesian spherical harmonics (SHCs) or standard vector spherical harmonics (SHVs) are redundant when they are placed on Huygens’ surfaces. This redundancy is reduced by allowing only spherical harmonics, which can be excited by surface current density distributions in a specific plane, and by forming directive spherical harmonics. This results in a considerable reduction of the necessary number of unknowns for representing the sources and improved conditioning of the discretized integral equations. Inspired by the Huygens’ radiator concept, appropriate directive harmonics on the basis of SHCs and SHVs are derived, implemented, and compared in terms of their performances. The validity of the presented techniques is confirmed via inverse source solutions for synthetic and real measurement data.

A practical method for the deformation of long‐stroke hydraulic manipulators in grasping‐handling tasks

AbstractLong‐stroke hydraulic manipulators are utilized in various grasping‐handling tasks, and the flexible deformation of these manipulators is the primary obstacle that affects precise position control of the end‐effectors in Cartesian space. This deformation is manifested in the following three aspects: joint deformation, structural deformation and clearance variation. Due to deformation uncertainty, methods that model the hydraulic manipulator as a combination of flexible multibody systems and hydraulic actuators are unsuitable. In this article, we propose an incremental inverse kinematics model (IIKM) as a new approach to solving the above deformation difficulties. The projection method is used to obtain the inverse kinematic analytical solution of long‐stroke hydraulic manipulators, which is based on the manipulator deformation in the current configuration (current configuration refers to the arrangement of the manipulator links when the manipulator starts to move to the target position). The proposed method avoids complex flexible multibody modeling and parameter identification, allowing long‐stroke hydraulic manipulators to be accurately controlled within a certain neighborhood. An evaluation coefficient is proposed to analyze the calculation accuracy of the IIKM in combination with the success rate obtained from 190 grasping experiments. Through these experiments, we determine the optimal calculation height range of the IIKM in the vertical direction and the optimal calculation position area in the horizontal direction and prove that the IIKM result can guarantee the success of grasping‐handling tasks when the end‐effector is within the optimal calculation height range.

Three-Dimensional Direct Current Resistivity Finite Element Method Forward Modelling Based on Jacobi Preconditioned Conjugate Gradient Algorithm

The calculation speed and accuracy of resistivity forward model are important for direct current exploration. This study proposes a calculation method for the forward model. First, we structured the unstructured grid to enable dissection of the three-dimensional finite element space. We then solved the large sparse linear equations, using the preconditioned conjugate gradient method. The diagonal matrix in the Jacobi iteration was used as the pre-processed matrix, which had the characteristics of a convenient inversion solution and consumed less memory; therefore, it substantially increased the speed to solve large linear equations. The forward modelling performed using synthetic data shows that the preconditioned conjugate gradient algorithm exhibits fast calculation speed and high accuracy. These results are in accordance with the potential distribution rule of the underground electric field. The results have value for three-dimensional direct current exploration in the field of engineering. Furthermore, it provides a reference for solving large linear equations of the finite element method in other fields.

Improvement of FFD parametric approach in the application of a lifting body

AbstractFFD (free-form deformation method) is one of the most commonly used parameterisation methods at present. It places the parameterised objects inside the control volume through coordinate system transformation, and controls the control volume through control points, thus realising the deformation control of its internal objects. Firstly, this paper systematically analyses and compares the characteristics and technical requirements of Bernstein, B-spline and NURBS (non-uniform rational b-splines) basic functions that can be adopted by FFD, and uses the minimum number of control points required to achieve the specified control effect threshold to express the control capability. Aiming at the problem of discontinuity at the right end in the actual calculation of B-spline basis function, a method of adding a small epsilon is proposed to solve it. Then, three basic functions are applied to the FFD parameterisation method, respectively, and the differences are compared from two aspects of the accurate expression of the model and the ability of deformation control. It is found that the BFFD (b-spline free-form deformation) approach owns better comprehensive performance when the control points are distributed correctly. In this paper, the BFFD method is improved, and a p-BFFD (reverse solution points based BFFD) method based on inverse solution is proposed to realise the free distribution of control points under the specified topology. Further, for the lifting body configuration, the control points of the p-BFFD method are brought closer to the airframe forming the EDGE-p-BFFD (edge constraints based p-BFFD) method. For the case in this paper, the proposed EDGE-p-BFFD method not only has fairly high parameterisation accuracy, but also reduces the expression error from 1.01E-3 to 1.25E-4, which is nearly ten times. It can also achieve effective lifting body guideline constraints, and has the ability of local deformation adapting to the configuration characteristics. In terms of the proportion of effective control points, the EDGE-p-BFFD method increases the proportion of effective control points from 36.7% to 50%, and the more control points, the more obvious the proportion increase effect. The new method also has better effect on the continuity of geometric deformation. At the same time, this paper introduces the independent deformation method of the upper and lower surfaces based on the double control body frames, which effectively avoids the deformation coupling problem of the simultaneous change of the upper and lower surfaces caused by the movement of control points in the traditional single control framework.

Estimating the chemical composition of municipal solid waste using the inverse method

This research aims to perform and implement an inverse solution method in waste-to-energy power plants for carrying out solid waste analysis without sampling. For this purpose, a simple simulated experiment is defined to evaluate the stability and accuracy of the method, which is investigated by adding random errors to the results of the direct problem conducted by the Monte Carlo method. The inverse problem solution procedure is solved by obtaining data categories for measuring parameters. In addition, the coefficient matrix is created and the linearization method is employed. By assuming a 0.5 percent nitrogen content in municipal solid waste, the number of unknown parameters is reduced, and the problem is solvable. The regularization method is applied to obtain the stability of the answer. The procedure is done for a municipal solid waste analysis with different regularization parameters. The mean value error and variance of the obtained solution from each analysis are evaluated and the acceptable range for regularization parameters is determined. Also, the identified matrix parameters between 1 and 100 are examined in the constant regularization parameter, and the acceptable parameters are determined. The error in validation by simulated experiment for carbon, oxygen, hydrogen, sulfur, moisture, and ash content of municipal solid waste is 1.47, 3.81, 0.91, 0.22, 7.32, and 1.57 percent, respectively. In the next step, the developed procedure is applied to the Aradkooh waste-to-energy power plant in Tehran, Iran. The operating data are gathered from the power plant, and the municipal solid waste composition is estimated. Results indicate the feasibility of the proposed method, and the municipal solid waste composition and mass flow rate can be predicted indirectly by the flue gas analysis and some other measurements without needing to sample the municipal solid waste. According to the results, the carbon, oxygen, hydrogen, sulfur, moisture, and ash content of municipal solid waste in the Aradkooh power plant is 21.13, 41.96, 5.70, 0.01, 25.06, and 5.63 percent, respectively. Further, the mass flow rate of municipal solid waste and air are 0.53 and 2.5 kg per second. Finally, the sensitivity of the estimated municipal solid waste composition to errors is evaluated by error analysis.

Multi-Branch Cellular Space Robot Mechanism Design and Climbing Behavior Research

Abstract Current space engineering projects such as large space structure erection and spacecraft maintenance tasks require robots with space truss climbing capability. To adapt to the complex climbing environment, this paper developed a multi-branch reconfigurable robot suitable for space truss climbing by using a cellular space robot (CSR). In different climbing environments, the robot can switch between different motion modes by changing the modules’ states. Considering the kinematic modeling problem after module reconfiguration, this paper analyzes the kinematics of the CSR based on the screw theory and extends it to any multi-branch configuration. Meanwhile, for the problem that it is difficult to obtain the inverse kinematic analytical solution of the multi-branch robot climbing mode with planar continuous three-parallel joints, the kinematic analytical algorithm for different configurations is given by combining algebraic and geometric methods. Besides, a 3D truss climbing environment is built, and the kinematic characteristics of the robot joint drive force, working space, and motion energy consumption under different motion modes of the multi-branched robot are analyzed. The results indicate that the developed multi-branched robot has good 3D space truss climbing capability and provides a basis for selecting its working mode in orbit. This study can help to broaden the application field of CSRs in orbit.

Performance Analysis of Hybrid Kinematic Mechanism for Fusion Reactor Maintenance

The hybrid kinematic mechanism (HKM) as an alternative remote handling subsystem of the Demonstration Fusion Power Plant (DEMO) breeding blanket (BB) is undergoing extensive theoretical analysis and feasibility verification. In this paper, the forward and inverse kinematic models of the HKM are derived by combining the Newtonian iterative method and the analytical method. Cartesian space trajectory planning is designed based on the trajectories of the HKM lifting of inboard and outboard BBs. The continuous smooth inverse kinematic solutions in the HKM joint space are obtained based on the polynomial interpolation method. For the characteristics of the HKM piston thread driving, the end-effector position error caused by the degradation of the spherical joint into a universal joint is analyzed and calculated. During the lifting of the left inboard BB, there is a maximum absolute error ∆P = 3.1 mm, and as the error continues to expand to the bottom of the BB it causes a risk of collision. Combining the overall effects of driving control, rigid–flexible coupling, etc., on position accuracy, an open-loop variable parameter error compensation plan based on the Levenberg–Marquardt (LM) nonlinear damping least-squares algorithm is proposed and validated in this paper. The simulation results show that the maximum absolute error after compensation is less than 1 mm as the mesh density increases, and the absolute position accuracy can be further improved by local mesh encryption. This study verifies the feasibility of the HKM as a BB remote handling subsystem and provides an option for high-precision control of the HKM.

Water-table response to extreme precipitation events

Extreme precipitation events (EPEs) will play a significant role in influencing soil–water and groundwater storage worldwide. We examined water-table depth (WTD) response to EPEs for 17 cases representative of soils and climate settings across the United States. Precipitation data from NOAA’s Precipitation Frequency Data Server were used for each case to characterize 1-day extreme precipitation events (EPEs) with annual exceedance probabilities of 0.1 % over an average baseline date range of 1981–2011. The inverse solution in the HYDRUS-1D modeling software was used to obtain the soil–water retention curve for each case. Non-EPE and EPE scenarios were modeled and compared to examine water-table displacement (ΔWTD) and recession time (trec). The ΔWTD ranged from 0.6 to 2.4 m across cases and were not directly controlled by EPE amount; instead, ΔWTD was inversely related to available porosity. Soils with low available porosity experienced large ΔWTD compared to soils with higher available porosity. In cases with larger diffusivity values, the modeled water table receded faster than in cases with smaller diffusivity values. This was because water-table recession times, trec, were inversely related to hydraulic diffusivity. For all cases, recession back to pre-EPE levels ranged from months to years suggesting an increased role by the unsaturated zone in buffering EPEs that should be considered in future EPE-groundwater modeling studies.

Influence of iron oxide layer on intensification of heat dissipation from the surface of a horizontal plate cooled with a water nozzle

The paper presents the changes in the heat transfer coefficient (HTC) and heat flux (HF) during the water spray cooling of the metal plate on the surface of which the thickness of the oxidized layer changed. The experimental investigations consisted in measuring the temperature changes inside the plate during spray cooling with water from 700 °C to the ambient temperature. The plate was made of the material (Armco iron), the surface of which had been oxidized during heating. Three measurements were made for three different thickness of the oxidized layer. The size of the area related with the directed impact of the spray water on the surface (high impingement zone) and the size of the secondary water flow zone (horizontal flow zone) that was placed beyond the high impingement zone were assessed. The distribution of the water flux density over the cooled surface was determined as well as the increase in the thickness of the oxidized layer with the heating time. The experimental investigations allowed identify HTC and HF by using the inverse method. The uncertainty tests that allowed determine the accuracy of the inverse solution were performed. The obtained results shows that the development of the boiling process on the surface covered with the oxidized layer is local. In the high impingement zone, the increase in the thickness of the oxidized layer from 0.018 to 0.035 mm significantly influences the changes of HF and HTC during each boiling phase. The increase in the thickness of the oxidized layer caused a shift of the maximum HF and the beginning of the transition boiling towards a higher surface temperature. Outside the high impingement zone the influence of the increase in the thickness of the oxidized layer is small during film boiling phase. The obtained results were compared with those obtained for the surface characterized by a low oxidation state, obtaining 35% lower maximum values of HF in relation to the oxidized surface.

Full Waveform Inversion Based on an Asymptotic Solution of Helmholtz Equation

This study considers the full waveform inversion (FWI) method based on the asymptotic solution of the Helmholtz equation. We provide frequency-dependent ray tracing to obtain the wave field used to compute the FWI gradient and calculate the modeled data. With a comparable quality of the inverse problem solution as applied to the standard finite difference approach, the speed of the calculations in the asymptotic method is an order of magnitude higher. A series of numerical experiments demonstrate the approach’s effectiveness in reconstructing the macro velocity structure of complex media for low frequencies.

Algorytmy konstrukcji obrazów w systemach tomografii procesowej

Tomography is one of the methods used to obtain cross-sectional images of the analysed object. This imaging technique has been used for many years in medicine, providing significantly higher efficiency of patient’s diagnosis. In recent years, the imaging method has also found application for visualization of industrial processes. The article describes the tomographic image construction methods used in the modules of monitoring of dynamic industrial processes. Introduction to methods of the inverse problems solutions in tomography systems, from a practical point of view, was presented, with particular emphasis on the electrical capacitance tomography. It was shown how based on the mathematical theorems and knowledge about physics rules, concerning the behaviour of measurement signal in tomography sensor, is possible to construct cross-sectional image of industrial process. In article the image construction steps were explained and discussion on the impact of various factors on the quality and speed of imaging was conducted.

Inverse Methods in Thermal Radiation Analysis and Experiment

Abstract Most thermal radiation problems are analyzed in a “forward” manner, in which the aim is to predict the response of a system based on well-defined boundary conditions. In practice, however, many thermal radiation problems are inverse problems. For example, the goal of many furnace design problems is to find a configuration that realizes a particular irradiation profile on a target, while in measurement problems, transmitted or reflected radiation measured with sensors at a boundary may be used to infer the properties of matter within the boundary. Such inverse problems are often mathematically ill-posed because they may have multiple solutions or no solution at all. Consequently, analyzing these types of problems is more complex than is required for forward problems. In this review, we examine the various types and characteristics of inverse problems, outline standard inverse solution methods for them, and review the historical and contemporary literature.

Dynamic simulation analysis and experimental verification of transmission tower climbing robot

In order to replace the climbing work of the first climbers of the transmission tower without safety ropes, a transmission tower climbing robot is designed in this paper. First of all, this paper designs the structure of the robot by imitating the silkworm crawling on the branches through the principle of bionics. On this basis, through the inverse kinetics solution method, under the premise of planning the gait of the robot first, the dynamic simulation analysis of the robot is carried out according to the gait, so as to obtain the torque required for each joint motion. At the same time, according to the simulation results, the experimental test of the robot is carried out. Experiments have shown that the robot can climb to the top of a 50 m high transmission tower in 70 min with a load of 10 kg. The research results show that the transmission tower robot can replace the manual climbing operation of the transmission tower, and the mechanization and intelligence of the high-altitude operation of the transmission tower is highly feasible.

Control of Precalciner Temperature in the Cement Industry: A Novel Method of Hammerstein Model Predictive Control with ISSA

As the most critical equipment in the pre-calcination process of dry cement production, the temperature of the precalciner is an essential factor affecting the quality of cement. However, the cement calcination system is time-delayed, nonlinear, and multi-disturbance, which makes it difficult to predict and control the precalciner temperature. In this study, a deep learning-based Hammerstein model is proposed, and a model predictive control system is built to predict and control the precalciner temperature. In the prediction model, the CNN-GRU network architecture is used to extract the operating states of the precalciner, and an attention mechanism is employed to find and emphasize the important historical information in the extracted states. Then, an ARX model is built to predict the temperature of the precalciner using the extracted operating state information. The complex nonlinear model solution in the control system is formed into a linear control problem and an inverse solution problem. The generalized predictive control (GPC) is used for linear control, and the improved sparrow search algorithm (ISSA) is used for the problem of an inverse solution. Tested with data from a cement plant in Hebei, China, the prediction accuracy of the model proposed in this paper is 99%, and the established control algorithm has less overshoot compared to PID and better stability in anti-disturbance tests. It is demonstrated that the prediction model developed in this study has better accuracy and the control strategy based on this model has good robustness.

Analytical solutions for film stress and bending deformation of coated optical lenses

Axisymmetric film/substrate systems are irreplaceable for many applications, owing to special structural requirements. Stoney's formula is widely used to analyze the thin plate film/substrate system. Many researches have been presented to relax limitations of Stoney's formula, which considered the substrate as a thin plate without any curvature. For the optical lens, the axisymmetric thin shell substrate with different curvatures on its upper and lower surfaces is common due to the need of optical focusing. The film stress of the optical lens needs to be optimized and measured due to its effects on system deformations and optical performances. However, the optical lens cannot be solved by Stoney's formula and its extensions due to the curvatures. In this paper, analytical solutions for the thin shell optical lens with different curvatures on upper and lower substrate surfaces are developed by the thin shell theory with the axisymmetric distribution film stress resultant (FSR) in consideration. The FSR is modeled by thermal stress equivalent method, which allows the calculation for the axisymmetric distribution FSR induced by many factors. The forward and inverse solutions between the FSR and the bending deformation are provided in the form of simple formulas with correction coefficient vectors depending on the global substrate thickness, which enables its feasibility in practical applications. Moreover, the two solutions are verified by the finite element method considering the deformation normal to the substrate surface measured by the interferometer in inverse solution, and small errors are found when the optical lens conforms to the assumptions of the method in this paper. The proposed method is efficient to predict the optical lens’ bending deformations, and extends the usage of curvature-based techniques from plates to shells with different curvatures on upper and lower surfaces in the film stress measurement, which makes great significance to the thin film/substrate application.