Blind-Kriging based natural frequency modeling of industrial Robot
01 Mar 2022-Precision Engineering-journal of The International Societies for Precision Engineering and Nanotechnology (Elsevier)-Vol. 74, pp 126-139
TL;DR: In this paper, a blind-Kriging-based natural frequency prediction of the industrial robot is proposed, utilizing the Latin Hypercube Sampling (LHS) technique, and a reliable dataset with 120 samples is generated for surrogate models based on the FEM.
Abstract: High-precision assembly conditions tend to necessitate consideration of the vibration modes of industrial robots. The modal characteristics of complex systems such as industrial robots are highly nonlinear. It means that mechanics experiments and finite element methods (FEM) to evaluate such features are usually expensive. Surrogate models combined with simulation-based design are widely used in engineering issues. However, few investigations apply surrogate models to industrial robots' modal analysis. We propose a practical scheme, i.e., the Blind-Kriging (KRG-B) based natural frequency prediction of the industrial robot, utilizing the Latin Hypercube Sampling (LHS) technique. A reliable dataset with 120 samples is generated for surrogate models based on the FEM. Then, the fourteen surrogate models with different optimization algorithms are evaluated to identify the optimal model for the natural frequency. In addition, the accuracy and robustness of the optimal surrogate model are investigated under different training samples. KRG-B model has better robustness (good fitting accuracy for both higher and lower order modes) and higher computational efficiency (1.133 s, the shortest time among all models). The proposed scheme mapping robot's joint angle and the natural frequency offers a valuable basis for further studying dynamic characteristics in industrial robotics.
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TL;DR: In this paper , the authors present a comprehensive summary review of structural health monitoring (SHM) for the prediction of modal frequency and the elimination of environment-induced masking effects based on the data normalization method.
Abstract: Modal frequencies are widely used for vibration‐based structural health monitoring (SHM) and for capturing the dynamics of a monitored structure to reveal possible failures. However, changing environmental and operational conditions (i.e., temperature, humidity, wind load, and traffic load) may submerge the modal variability induced by structural damage, thereby falsely identifying damage of interest. This paper presents a comprehensive summary review of SHM for the prediction of modal frequency and the elimination of environment‐induced masking effects based on the data normalization method. The influence mechanisms of external variations on modal frequencies extensively reported in the literature are first described. Next, the research progress in predicting and eliminating the operational modal variability is reviewed emphatically; this progress can be primarily divided into an input–output method that focuses on the establishment of the relationship model between structural frequency and environmental conditions and an output‐only method that separates the embedded environmental variable‐induced changes depending on whether the environmental measurements are measured. Finally, the conclusions and future studies are summarized and discussed. As an overview, the major contribution of this paper is to provide objective technical references for engineers and owners and to further evaluate structural safety conditions more effectively and in a timely manner.
14 citations
TL;DR: In this article , a new method is proposed by configuring the movement parameters of the flexible manipulator to reduce the residual vibration of the manipulator after the movement of the deceleration.
Abstract: There are three motion stages for an industrial robot manipulator, including the acceleration stage, the constant velocity stage, and the deceleration stage. Aiming at reducing the residual vibration of the manipulator after the movement of the deceleration, a new method is proposed by configuring the movement parameters of the flexible manipulator. Firstly, we conduct experiments to verify a numerical vibration model of the manipulator, and then, we analyze the vibration suppression effect under different conditions based on the numerical model. The results show that in the range of one movement, the residual vibration can be well suppressed when the acceleration and deceleration time are set as a positive integer to the natural period of the manipulator operation; otherwise, the vibration suppression effect is not obvious and proportional to the difference between the acceleration/deceleration time and the manipulator natural period.
2 citations
25 May 2022-Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
TL;DR: In this article , a dual-machine riveting system is developed, and the kinematic chain model and the lower-numbered body of the system structure are constructed sequentially, considering the interaction and coupling effect of the two machines in the actual riveting process, the relative stiffnesses of the dual machine in the resisting state are identified by loading tests.
Abstract: Automatic riveting systems play a crucial role in the field of aircraft manufacturing. In the riveting process, the machine tool bears a large axial squeezing force, and the resulting deformation will inevitably affect the riveting quality. In this paper, a dual-machine riveting system is developed first, the kinematic chain model and the lower-numbered body of the system structure are constructed sequentially. Then, considering the interaction and coupling effect of the two machines in the actual riveting process, the relative stiffnesses of the dual machine in the resisting state are identified by loading tests. Based on the stiffness data at a combination of postures within the workspace, a Kriging prediction model is established to describe the relationship between stiffness and postures. According to the prediction results, the influence of rotational and translational axes on the spatial stiffness distribution of the riveting system is revealed. Finally, the online deformation compensation is realized by modifying the displacement of the feed axis on both sides. A riveting experiment is carried out, and the results demonstrate that the riveting quality is significantly improved after compensation.
1 citations
References
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TL;DR: In this paper, two sampling plans are examined as alternatives to simple random sampling in Monte Carlo studies and they are shown to be improvements over simple sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function.
Abstract: Two types of sampling plans are examined as alternatives to simple random sampling in Monte Carlo studies. These plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function.
8,328 citations
TL;DR: This work represents the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error.
Abstract: We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error Several continuous and discrete processes are treated, and numerical examples show substantial speed-up compared to Monte Carlo simulations for low dimensional stochastic inputs
4,473 citations
Book•
02 Sep 2008
TL;DR: This chapter discusses the design and exploration of a Surrogate-based kriging model, and some of the techniques used in that process, as well as some new approaches to designing models based on the data presented.
Abstract: Preface. About the Authors. Foreword. Prologue. Part I: Fundamentals. 1. Sampling Plans. 1.1 The 'Curse of Dimensionality' and How to Avoid It. 1.2 Physical versus Computational Experiments. 1.3 Designing Preliminary Experiments (Screening). 1.3.1 Estimating the Distribution of Elementary Effects. 1.4 Designing a Sampling Plan. 1.4.1 Stratification. 1.4.2 Latin Squares and Random Latin Hypercubes. 1.4.3 Space-filling Latin Hypercubes. 1.4.4 Space-filling Subsets. 1.5 A Note on Harmonic Responses. 1.6 Some Pointers for Further Reading. References. 2. Constructing a Surrogate. 2.1 The Modelling Process. 2.1.1 Stage One: Preparing the Data and Choosing a Modelling Approach. 2.1.2 Stage Two: Parameter Estimation and Training. 2.1.3 Stage Three: Model Testing. 2.2 Polynomial Models. 2.2.1 Example One: Aerofoil Drag. 2.2.2 Example Two: a Multimodal Testcase. 2.2.3 What About the k -variable Case? 2.3 Radial Basis Function Models. 2.3.1 Fitting Noise-Free Data. 2.3.2 Radial Basis Function Models of Noisy Data. 2.4 Kriging. 2.4.1 Building the Kriging Model. 2.4.2 Kriging Prediction. 2.5 Support Vector Regression. 2.5.1 The Support Vector Predictor. 2.5.2 The Kernel Trick. 2.5.3 Finding the Support Vectors. 2.5.4 Finding . 2.5.5 Choosing C and epsilon. 2.5.6 Computing epsilon : v -SVR 71. 2.6 The Big(ger) Picture. References. 3. Exploring and Exploiting a Surrogate. 3.1 Searching the Surrogate. 3.2 Infill Criteria. 3.2.1 Prediction Based Exploitation. 3.2.2 Error Based Exploration. 3.2.3 Balanced Exploitation and Exploration. 3.2.4 Conditional Likelihood Approaches. 3.2.5 Other Methods. 3.3 Managing a Surrogate Based Optimization Process. 3.3.1 Which Surrogate for What Use? 3.3.2 How Many Sample Plan and Infill Points? 3.3.3 Convergence Criteria. 3.3.4 Search of the Vibration Isolator Geometry Feasibility Using Kriging Goal Seeking. References. Part II: Advanced Concepts. 4. Visualization. 4.1 Matrices of Contour Plots. 4.2 Nested Dimensions. Reference. 5. Constraints. 5.1 Satisfaction of Constraints by Construction. 5.2 Penalty Functions. 5.3 Example Constrained Problem. 5.3.1 Using a Kriging Model of the Constraint Function. 5.3.2 Using a Kriging Model of the Objective Function. 5.4 Expected Improvement Based Approaches. 5.4.1 Expected Improvement With Simple Penalty Function. 5.4.2 Constrained Expected Improvement. 5.5 Missing Data. 5.5.1 Imputing Data for Infeasible Designs. 5.6 Design of a Helical Compression Spring Using Constrained Expected Improvement. 5.7 Summary. References. 6. Infill Criteria With Noisy Data. 6.1 Regressing Kriging. 6.2 Searching the Regression Model. 6.2.1 Re-Interpolation. 6.2.2 Re-Interpolation With Conditional Likelihood Approaches. 6.3 A Note on Matrix Ill-Conditioning. 6.4 Summary. References. 7. Exploiting Gradient Information. 7.1 Obtaining Gradients. 7.1.1 Finite Differencing. 7.1.2 Complex Step Approximation. 7.1.3 Adjoint Methods and Algorithmic Differentiation. 7.2 Gradient-enhanced Modelling. 7.3 Hessian-enhanced Modelling. 7.4 Summary. References. 8. Multi-fidelity Analysis. 8.1 Co-Kriging. 8.2 One-variable Demonstration. 8.3 Choosing X c and X e . 8.4 Summary. References. 9. Multiple Design Objectives. 9.1 Pareto Optimization. 9.2 Multi-objective Expected Improvement. 9.3 Design of the Nowacki Cantilever Beam Using Multi-objective, Constrained Expected Improvement. 9.4 Design of a Helical Compression Spring Using Multi-objective, Constrained Expected Improvement. 9.5 Summary. References. Appendix: Example Problems. A.1 One-Variable Test Function. A.2 Branin Test Function. A.3 Aerofoil Design. A.4 The Nowacki Beam. A.5 Multi-objective, Constrained Optimal Design of a Helical Compression Spring. A.6 Novel Passive Vibration Isolator Feasibility. References. Index.
2,335 citations
TL;DR: This paper compares Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model’s parameters given its form and and an R 2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriged model, permitting the comparison of different forms of a k Riging model.
Abstract: The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread usage of kriging models appears to be hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model, (2) computationally efficient algorithms for estimating the model’s parameters, and (3) an effective method to assess the resulting model’s quality. In this paper, we compare (1) Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model’s parameters given its form and (2) and an R 2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriging model, permitting the comparison of different forms of a kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.
833 citations
TL;DR: Two broad families of surrogates namely response surface surrogates, which are statistical or empirical data‐driven models emulating the high‐fidelity model responses, and lower‐f fidelity physically based surrogates which are simplified models of the original system are detailed in this paper.
Abstract: [1] Surrogate modeling, also called metamodeling, has evolved and been extensively used over the past decades. A wide variety of methods and tools have been introduced for surrogate modeling aiming to develop and utilize computationally more efficient surrogates of high-fidelity models mostly in optimization frameworks. This paper reviews, analyzes, and categorizes research efforts on surrogate modeling and applications with an emphasis on the research accomplished in the water resources field. The review analyzes 48 references on surrogate modeling arising from water resources and also screens out more than 100 references from the broader research community. Two broad families of surrogates namely response surface surrogates, which are statistical or empirical data-driven models emulating the high-fidelity model responses, and lower-fidelity physically based surrogates, which are simplified models of the original system, are detailed in this paper. Taxonomies on surrogate modeling frameworks, practical details, advances, challenges, and limitations are outlined. Important observations and some guidance for surrogate modeling decisions are provided along with a list of important future research directions that would benefit the common sampling and search (optimization) analyses found in water resources.
663 citations