Force Reconstruction Research Articles

A model-based deep learning approach to interpretable impact force localization and reconstruction

Model-based and deep learning-based methods have been widely studied for force identification. However, model-based methods usually have high computational complexity and face challenges in parameter setting, while the generic network structures in deep learning methods are mostly designed empirically. In this paper, a model-based deep learning network is proposed to simultaneously localize and reconstruct impact f[orces. The proposed network, dubbed NSC-Net, is obtained by unrolling the iterative shrinkage-thresholding algorithm (ISTA) for the non-negative sparse coding (NSC) model. NSC-Net combines the interpretability of the model-based ISTA with the powerful parameter learning capability of deep learning. The transfer matrix is embedded into the network as physical information through learnable scaling. The structure of NSC-Net is based on explicit theoretical analysis, which enhances its interpretability in terms of structural design. In contrast to ISTA, the parameters in NSC-Net can be trained end-to-end from the training data without manual setting. Simulations and experiments on composite panels are conducted to validate the performance of the proposed method. The results demonstrate that NSC-Net accurately localizes and reconstructs impact forces, outperforming both ISTA and learned iterative shrinkage-thresholding algorithm (LISTA) network. Additionally, NSC-Net exhibits excellent noise immunity. Furthermore, the systematic approach of constructing an algorithm unrolling network for impact force identification is summarized, aiming to facilitate further related research.

A Kalman-filter based strategy for space-frequency force reconstruction

This contribution presents a Kalman filtering strategy for space-frequency reconstruction of mechanical sources. The proposed approach is based on the definition of an appropriate state-space model, where the state equation assumes that the force vector follows a random walk behavior, while the observation equation is the classical linear relationship between the force and the measured response through the transfer function matrix of the considered structure. One of the main challenges of the proposed approach is the fine-tuning of the covariance matrix associated with the process noise. In this work, it is estimated and adapted at each frequency during the filtering procedure. A numerical experiment is performed on a simply supported beam excited by a broadband point mechanical force to evaluate the reconstruction performance of the proposed approach. Further comparisons with other regularization strategies are also proposed to provide a fair overview of the results obtained.

EasyCalib: Simple and Low-Cost In-Situ Calibration for Force Reconstruction With Vision-Based Tactile Sensors

EasyCalib: Simple and Low-Cost In-Situ Calibration for Force Reconstruction With Vision-Based Tactile Sensors

Impact Force Localization and Reconstruction via ADMM-based Sparse Regularization Method

In practice, simultaneous impact localization and time history reconstruction can hardly be achieved, due to the ill-posed and under-determined problems induced by the constrained and harsh measuring conditions. Although ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{1}$$\\end{document} regularization can be used to obtain sparse solutions, it tends to underestimate solution amplitudes as a biased estimator. To address this issue, a novel impact force identification method with ℓp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{p}$$\\end{document} regularization is proposed in this paper, using the alternating direction method of multipliers (ADMM). By decomposing the complex primal problem into sub-problems solvable in parallel via proximal operators, ADMM can address the challenge effectively. To mitigate the sensitivity to regularization parameters, an adaptive regularization parameter is derived based on the K-sparsity strategy. Then, an ADMM-based sparse regularization method is developed, which is capable of handling ℓp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{p}$$\\end{document} regularization with arbitrary p values using adaptively-updated parameters. The effectiveness and performance of the proposed method are validated on an aircraft skin-like composite structure. Additionally, an investigation into the optimal p value for achieving high-accuracy solutions via ℓp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{p}$$\\end{document} regularization is conducted. It turns out that ℓ0.6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{0.6}$$\\end{document} regularization consistently yields sparser and more accurate solutions for impact force identification compared to the classic ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell_{1}$$\\end{document} regularization method. The impact force identification method proposed in this paper can simultaneously reconstruct impact time history with high accuracy and accurately localize the impact using an under-determined sensor configuration.

Myological and osteological approaches to gape and bite force reconstruction in Smilodon fatalis

Myological and osteological approaches to gape and bite force reconstruction in <i>Smilodon fatalis</i>

The Piston Slap Force Reconstruction of Diesel Engine Using WOA-VMD and Deconvolution.

In a diesel engine, piston slap commonly occurs concurrently with fuel combustion and serves as the main source of excitation. Although combustion pressure can be measured using sensors, determining the slap force is difficult without conducting tests. In this study, we propose a method to identify the slap force of the piston to solve this difficult problem. The traditional VMD algorithm easily receives noise interference, which affects the value of parameter combination [k, α] and thus affects the extraction accuracy of the algorithm. First, we obtain the transfer function between the incentive and vibration response through percussion tests. Secondly, a variational modal decomposition method based on whale algorithm optimization is used to separate the slap response from the surface acceleration of the block. Finally, we calculated the slap force using the deconvolution method. Deconvolution is a typical inverse problem of mathematics, often prone to ill-conditioning, and the singular value decomposition and regularization method is used to overcome this flaw and improve accuracy. The proposed method provides an important means to evaluate the angular distribution of the slap force, identify the shock positions on the piston liner, and determine the peak value of the waveform which helps us analyze the vibration characteristics of the piston and optimize the structural design of the engine.

An iterative neural network approach applied to human-induced force reconstruction using a non-linear electrodynamic shaker

Human-induced force analysis plays an important role across a wide range of disciplines, including biomechanics, sport engineering, health monitoring or structural engineering. Specifically, this paper focuses on the replication of ground reaction forces (GRF) generated by humans during movement. They can provide critical information about human-mechanics and be used to optimize athletic performance, prevent and rehabilitate injuries and assess structural vibrations in engineering applications. It is presented an experimental approach that uses an electrodynamic shaker (APS 400) to replicate GRFs generated by humans during movement, with a high degree of accuracy. Successful force reconstruction implies a high fidelity in signal reproduction with the electrodynamic shaker, which leads to an inverse problem, where a reference signal must be replicated with a nonlinear and non-invertible system. The solution presented in this paper relies on the development of an iterative neural network and an inversion-free approach, which aims to generate the most effective drive signal that minimizes the error between the experimental force signal exerted by the shaker and the reference. After the optimization process, the weights of the neural network are updated to make the shaker behave as desired, achieving excellent results in both time and frequency domains.

A Novel Strategy for Hypersonic Vehicle With Complex Distributed No-Fly Zone Constraints

Aiming at solving trajectory planning problem with complex distributed no-fly zone constraints, this paper proposed a novel obstacle avoidance strategy. For longitudinal motion, an angle of attack adjustment method is employed to adjust lift and design the angle of attack profile, while adjusting the bank angle for range and altitude correction to meet terminal constraints. For lateral motion, this paper developed enhanced attractive, repulsive, and velocity potential fields. Combined with the proposed repulsive force reconstruction method, this effectively resolves the overmaneuvering problem of traditional artificial potential field methods (APFMs) for vehicle. In order to avoid mismatched magnitudes of attractive and repulsive forces, a complementary no-fly zone avoidance strategy based on minimum turn radius is introduced, updating the bank angle command during no-fly zone avoidance. Simulation results indicate that the proposed strategy can address the avoidance of sudden threat, proving to be feasible and effective for handling complex distributed no-fly zone avoidance problems.

Convex model-based regularization method for force reconstruction

In the process of reconstructing structural forces, the influence of measurement errors and inherent model inaccuracies cannot be ignored. These errors exhibit a degree of correlation, and the presence of such correlation inevitably affects the quantification of uncertainties in force reconstruction. Objectively, the inherent ill-posed nature of structural inverse problems makes it difficult to obtain the forces to be identified, subject to uncertainties and highly susceptible to perturbations. Consequently, this paper introduces a force reconstruction regularization approach that explicitly considers the correlation of uncertainty parameters based on the truncated singular value regularization method. The primary objective is to refine the influence of uncertainties on the reconstructed force bounds with greater precision. When determining robust regularization parameters, the generalized cross-validation method and convex modelling approach are introduced to consider the uncertainty and its correlation in solving inverse problems. The proposed approach is rigorously validated through a comprehensive numerical case study. Error indexes and dispersion indices are employed to analyze the impact of different levels of noise and correlation on force reconstruction results. The force bounds obtained using the proposed method are compared with Monte Carlo simulation results. Finally, the validity of the proposed method is verified by an experiment with a four-story shear frame.

Integrative and relational approaches to resilience in the NATO concept and action

The concept of resilience, suitable for specific operations, has been used within NATO since 2010. The particularity of the term resides in the characteristic phases of implementation in the allied operational environment, which generates appropriate conduct of identifying, analyzing, and avoiding risks, resistance to disruptive and impactful factors, recovery, restoration, and reconstruction of the initial force and action potential. The Alliance’s combatant forces will maintain integrity and adequate functionality, even under restrictive, difficult conditions, by implementing, at organizational and operational levels, the two components of layered resilience (operational or military and civil). In this way, a high level of protection, stability, and viability of combat structures of tactical and/or joint forces will be achieved, to face the threats and complex actions of unfriendly (enemy) forces. Through the findings, the present research includes a theoretical approach, with possibilities of concretization in applied resilience in NATO civilian and military fields, because it includes important programmatic details, related to the consequences of the Russian-Ukrainian armed confrontation, which started on February 24, 2022. From here, relevant elements resulted in the consolidation of action power of joint and tactical forces, meant to be engaged in national and multinational operations within the North Atlantic Alliance, against any hostile aggressive forces.

A New Conjugate Gradient Method for Impact Load Identification of Stochastic Composite Structures

This paper presents a novel conjugate gradient method to identify the impact force of stochastic composite structure. Firstly, the proposed method is established based on constructing a new gradient regularization operator, and its stability and global convergence are strictly proven. Moreover, the proposed method solves the deterministic inverse problem of composite laminated cylindrical shells. Then, using the matrix perturbation method, the uncertain inverse problem of the impact force reconstruction of stochastic structure is converted to definite inverse problems. At last, the statistical properties of the reconstructed impact load are also analyzed. Numerical simulations show that the proposed method performs well in identifying the impact force of composite laminated cylindrical shells with stochastic and non-stochastic properties.

An efficient impact force identification methodology via a single sensor utilizing the concept of generalized transmissibility

The issue of localizing and reconstructing the impact force through double-inverse approaches is widely recognized as an ill-posed and computationally demanding problem. Such a challenge has emerged as a prominent research topic of interest and great concern in the field of structural health monitoring. This study proposes a novel and efficient hierarchical methodology that is adept at ascertaining both the location and time history of an impact force through data obtained from a single accelerometer. The proposed methodology entails an efficient retrieval of uncorrected modal constants with a ratio function referred to as generalized transmissibility. The generalized transmissibility symbolizes the ratio of responses from identical accelerometer subjected to two distinct impacting scenarios, one excited at a yet-to-be-identified location and the other at a pre-determined reference location. The theoretical disclosure of the correlation between the generalized transmissibility at pole frequencies and retrieved uncorrected modal constants is demonstrated in details herein. These modal constants are then served as a signature to identify the impact location. Following localization, the force reconstruction problem is tackled by fitting a parametric model, wherein a gaussian basis function is employed to effectively approximate the time history of impact force. Experimental demonstrations on a metallic plate and a composite wing were carried out to validate the efficient and accurate localization as well as the rapid reconstruction capabilities in response to an impact force applied anywhere on a 2D structure.

The T-Blep: A Soft Optical Sensor for Stiffness and Contact Force Measurement.

This paper presents the Tactile Blep (T-Blep), an optical soft sensor that can measure the stiffness and force of different materials. The sensor consists of an inflatable membrane with an optical elements inside. The T-Blep can switch between stiffness detection and force detection modes, by changing the pattern followed by internal pressure of the membrane. Simulations reveal that a 1 mm-thick membrane enables differentiation of extra-soft, soft, and rigid targets. Furthermore, the sensitivity and FSO of the force estimation can be adjusted by varying the internal pressure. Force detection experiments exhibit a sixfold increase in detectable force range as internal pressure varies from 10 kPa to 40 kPa, with a force peak of 5.43 N and sensitivity up to 331 mV/N. A piecewise force reconstruction method provides accurate results even in challenging conditions (R2>0.994). Stiffness detection experiments reveal distinguishable patterns of pressure and voltage during indentation, resulting in a classification accuracy of 97%.

Evaluation, selection and validation of force reconstruction models for vision-based tactile sensors

Vision-based tactile sensors can provide robots with high-resolution distributed force applied to robots’ fingertips. They reconstruct the force distribution from the measured deformation of their elastic bodies based on force reconstruction models. The force reconstruction models are various mathematical expressions to approximate the deformation-force relationship of the elastic bodies. The force reconstruction models determine the force reconstruction accuracy, modeling cost, and computational consumption of the sensor. Therefore, selecting the force reconstruction model is an important issue in the studies of vision-based tactile sensors. This study focuses on the evaluation and selection of the force reconstruction models. A method for evaluating the nonlinearity phase of the elastic body is proposed. Then, three representative force reconstruction models are evaluated, validated, and compared theoretically and experimentally under various load conditions. This study provides quantitative and theoretical guidance for selecting the force reconstruction models and makes the model selection rigorous.

Volcanic forcing of high-latitude Northern Hemisphere eruptions

High-latitude explosive volcanic eruptions can cause substantial hemispheric cooling. Here, we use a whole-atmosphere chemistry-climate model to simulate Northern Hemisphere (NH) high-latitude volcanic eruptions of magnitude similar to the 1991 Mt. Pinatubo eruption. Our simulations reveal that the initial stability of the polar vortex strongly influences sulphur dioxide lifetime and aerosol growth by controlling the dispersion of injected gases after such eruptions in winter. Consequently, atmospheric variability introduces a spread in the cumulative aerosol radiative forcing of more than 20%. We test the aerosol evolution’s sensitivity to co-injection of sulphur and halogens, injection season, and altitude, and show how aerosol processes impact radiative forcing. Several of these sensitivities are of similar magnitude to the variability stemming from initial conditions, highlighting the significant influence of atmospheric variability. We compare the modelled volcanic sulphate deposition over the Greenland ice sheet with the relationship assumed in reconstructions of past NH eruptions. Our analysis yields an estimate of the Greenland transfer function for NH extratropical eruptions that, when applied to ice core data, produces volcanic stratospheric sulphur injections from NH extratropical eruptions 23% smaller than in currently used volcanic forcing reconstructions. Furthermore, the transfer function’s uncertainty, which propagates into the estimate of sulphur release, needs to be at least doubled to account for atmospheric variability and unknown eruption parameters. Our results offer insights into the processes shaping the climatic impacts of NH high-latitude eruptions and highlight the need for more accurate representation of these events in volcanic forcing reconstructions.

Reconstruction of shear force in Atomic Force Microscopy from measured displacement of the cone-shaped cantilever tip

&lt;abstract&gt;&lt;p&gt;We present a new comprehensive mathematical model of the cone-shaped cantilever tip-sample interaction in Atomic Force Microscopy (AFM). The importance of such AFMs with cone-shaped cantilevers can be appreciated when its ability to provide high-resolution information at the nanoscale is recalled. It is an indispensable tool in a wide range of scientific and industrial fields. The interaction of the cone-shaped cantilever tip with the surface of the specimen (sample) is modeled by the damped Euler-Bernoulli beam equation $ \rho_A(x)u_{tt} $ $ +\mu(x)u_{t}+(r(x)u_{xx}+\kappa(x)u_{xxt})_{xx} = 0 $, $ (x, t)\in (0, \ell)\times (0, T) $, subject to the following initial, $ u(x, 0) = 0 $, $ u_t(x, 0) = 0 $ and boundary, $ u(0, t) = 0 $, $ u_{x}(0, t) = 0 $, $ \left (r(x)u_{xx}(x, t)+\kappa(x)u_{xxt} \right)_{x = \ell} = M(t) $, $ \left (-(r(x)u_{xx}+\kappa(x)u_{xxt})_x\right)_{x = \ell} = g(t) $ conditions, where $ M(t): = 2h\cos \theta\, g(t)/\pi $ is the moment generated by the transverse shear force $ g(t) $. Based on this model, we propose an inversion algorithm for the reconstruction of an unknown shear force in the AFM cantilever. The measured displacement $ \nu(t): = u(\ell, t) $ is used as additional data for the reconstruction of the shear force $ g(t) $. The least square functional $ J(F) = \frac{1}{2}\Vert u(\ell, \cdot)-\nu \Vert_{L^2(0, T)}^2 $ is introduced and an explicit gradient formula for the Fréchet derivative of the cost functional is derived via the weak solution of the adjoint problem. Additionally, the geometric parameters of the cone-shaped tip are explicitly contained in this formula. This enables us to construct a gradient based numerical algorithm for the reconstructions of the shear force from noise free as well as from random noisy measured output $ \nu (t) $. Computational experiments show that the proposed algorithm is very fast and robust. This creates the basis for developing a numerical "gadget" for computational experiments with generic AFMs.&lt;/p&gt;&lt;/abstract&gt;

Impact force localization and reconstruction via gated temporal convolutional network

Techniques for identifying impact forces are crucial for improving the operational reliability and safety of aerospace composite structures. To address the challenges of theoretical modeling that arise from the complexity of composite structures, we propose a Gated Temporal Convolutional Network (GTCN) method. This method establishes inverse mapping relationships between structural vibration responses and impact forces. The GTCN increases the receptive field through dilated convolution, concurrently employing gating mechanisms to extract pivotal features from input signals in the vertical direction. Simulations and experiments are conducted to robustly validate the efficacy and applicability of the proposed impact force identification method. The simulation results demonstrate that the GTCN method is capable of obtaining robust impact force localization and reconstruction results, even amidst conditions of elevated noise levels. The average localization error of the GTCN is kept within 20 mm even at a noise level of 5 dB. Meanwhile, the GTCN method achieves satisfactory identification results for different types of impact forces (Gaussian, semi-cosine, and sawtooth), with an average localization accuracy above 95%. The applicability of the GTCN method to real-world structure is verified in the experiments. The average relative error of the reconstructed forces by GTCN is less than 15%. GTCN achieves stable identification of impact forces when the number of sensors is larger than 2. In both simulations and experiments, the GTCN performs better than Temporal Convolutional Network (TCN) and Convolutional Neural Network (CNN) with higher identification accuracy. The proposed method demonstrates considerable potential for application in the health monitoring of aircraft composite structures.

Interval strategy-based regularization approach for force reconstruction with multi-source uncertainties

A force reconstruction method for uncertain structures instead of direct measurement is proposed in this paper. Considering the multi-source uncertainties as unknown-but-bounded (UBB) parameters including unknown structural dynamics and measurement errors, this study proposed a novel force reconstruction method using an interval strategy-based regularization approach with truncated singular value decomposition (TSVD). To overcome the drawbacks of incompleted models and limited information, the overall modelling and inversion of the interval force are reconstructed based on the non-probabilistic uncertainty theory. First, The interval uncertainty-based kernel function for force inversion is deduced using the second-order interval perturbation method, in which the uncertainties of the reconstructed force originate from the uncertain singular values and measurement errors. Based on the regularization of the TSVD, the interval bounds of the singular values can be accurately obtained. Combining the two typical regularization approaches, a novel interval strategy-based regularization approach is proposed to optimize the best regularization parameter based on the uncertain interval distribution of singular values. This novel strategy can not only balance the two typical regularization approaches but also reduce the burden of force inversion. Two numerical examples including a truss and space capsule are applied to access the proposed method, and the estimated accurate force can prove the effectiveness.

Optimal calibration of optical tweezers with arbitrary integration time and sampling frequencies: a general framework [Invited

Optical tweezers (OT) have become an essential technique in several fields of physics, chemistry, and biology as precise micromanipulation tools and microscopic force transducers. Quantitative measurements require the accurate calibration of the trap stiffness of the optical trap and the diffusion constant of the optically trapped particle. This is typically done by statistical estimators constructed from the position signal of the particle, which is recorded by a digital camera or a quadrant photodiode. The finite integration time and sampling frequency of the detector need to be properly taken into account. Here, we present a general approach based on the joint probability density function of the sampled trajectory that corrects exactly the biases due to the detector's finite integration time and limited sampling frequency, providing theoretical formulas for the most widely employed calibration methods: equipartition, mean squared displacement, autocorrelation, power spectral density, and force reconstruction via maximum-likelihood-estimator analysis (FORMA). Our results, tested with experiments and Monte Carlo simulations, will permit users of OT to confidently estimate the trap stiffness and diffusion constant, extending their use to a broader set of experimental conditions.

Fiber alignment in 3D collagen networks as a biophysical marker for cell contractility

Cells cultured in 3D fibrous biopolymer matrices exert traction forces on their environment that induce deformations and remodeling of the fiber network. By measuring these deformations, the traction forces can be reconstructed if the mechanical properties of the matrix and the force-free matrix configuration are known. These requirements limit the applicability of traction force reconstruction in practice. In this study, we test whether force-induced matrix remodeling can instead be used as a proxy for cellular traction forces. We measure the traction forces of hepatic stellate cells and different glioblastoma cell lines and quantify matrix remodeling by measuring the fiber orientation and fiber density around these cells. In agreement with simulated fiber networks, we demonstrate that changes in local fiber orientation and density are directly related to cell forces. By resolving Rho-kinase (ROCK) inhibitor-induced changes of traction forces, fiber alignment, and fiber density in hepatic stellate cells, we show that the method is suitable for drug screening assays. We conclude that differences in local fiber orientation and density, which are easily measurable, can be used as a qualitative proxy for changes in traction forces. The method is available as an open-source Python package with a graphical user interface.