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The purpose of this paper is to analyze the sensitivity of the motion error parameters in microassembly process, thereby improving the assembly accuracy. The motion errors of the precision motion stages directly affect the final assembly quality after the machine visual alignment.

This paper presents the error parameters of the in-house microassembly system with coaxial alignment function, builds the error transfer model by the multi-body system theory, analyzes the error sensitivity on the sensitive direction using the Sobol method, which was based on variance, and then gets the ones which made a great degree of influence. Before the sensitivity analyzing, parts of the error sources have been measured to obtain their distribution ranges.

The results of the sensitivity analysis by the Sobol method, which was based on variance, are coincident with the theoretical analysis. Besides, the results provide a reference for the error compensation in control process, for the selection of the precision motion stages and for the installation index of the motion stages of the assembly system with coaxial alignment.

This kind of error sensitivity analysis method is of great significance for improving the assembly accuracy after visual system positioning, and increasing efficiency from the initial motion stage selection to final error compensation for designers. It is suitable for general precision motion systems be of multi-degree of freedom, for the method of modeling, measuring and analyzing used in this paper are all universal and applicative.

Localization accuracy is a key concern in the design of a fixture to specify a locating scheme and tolerance allocation. This paper presents an analysis describing the impact of localization source errors on the potential datum‐related geometric errors of machined features. The analysis reveals the error sensitivity and error characteristics of critical points of multiple manufacturing features. It shows the importance to consider the overall error among the multiple critical points in fixture layout design. This paper also suggests an optimal approach to the locator configuration design for reducing geometric variations at the critical points of machined features.

Starting from the identification of some theoretically driven instructional principles, this paper presents a set of empirical cases based on strategies to learn from errors. The purpose of this paper is to provide first evidence about the feasibility and the effectiveness for learning of video-enhanced error-based strategies in vocational education and training.

Four different cases are presented. All of them share the same design-based research perspective, in which teachers and researchers co-designed an (iterative) intervention in the field. Two cases are preliminary investigations, while the other two profit from a quasi-experimental design with at least one experimental condition based on error treatment and a control group.

The four cases show the effectiveness of learning from error (and from error analysis). More specifically, they show the validity and flexible adoption of the specific instructional principles derived from the literature review: the use of inductive strategies and in particular, of worked-out examples; the reference to a concrete, possibly personal, experience for the analysis task; the use of prompted writing to elicit self-explanations and reflection; and the use of video for recording and annotating the situation to be analysed.

The four cases constitute only a starting point for further research into the use of errors for procedural learning. Moreover, the cases presented are focused on learning in the domain of procedural knowledge and not in that of declarative knowledge. Further studies in the vocational education and training sector might serve this research area.

The paper provides concrete indications and directions to implement effective instructional strategies for procedural learning from errors, especially within vocational education.

Errors are often identified with and attributed to (individual) failures. In both learning institutions and the workplace, this can engender an intolerant and closed climate towards mistakes, preventing real professional development and personal growth. Interventions on learning from errors in schools and workplaces can play a role in changing such a culture and in creating a tolerant and positive attitude towards them.

The majority of studies about learning from errors are focused on disciplinary learning in academic contexts. The present set of cases contributed to filling in the gap related to initial vocational education, because they deal with learning from errors in dual vocational training in the field of procedural knowledge development. Moreover, a specific contribution of the presented cases relies on the use of video annotation as a support that specifically enhances error analysis within working procedures.

The purpose is to reduce round-off errors in numerical simulations. In the numerical simulation, different kinds of errors may be created during analysis. Round-off error is one of the sources of errors. In numerical analysis, sometimes handling numerical errors is challenging. However, by applying appropriate algorithms, these errors are manageable and can be reduced. In this study, five novel topological algorithms were proposed in setting up a structural flexibility matrix, and five different examples were used in applying the proposed algorithms. In doing so round-off errors were reduced remarkably.

Five new algorithms were proposed in order to optimize the conditioning of structural matrices. Along with decreasing the size and duration of analyses, minimizing analytical errors is a critical factor in the optimal computer analysis of skeletal structures. Appropriate matrices with a greater number of zeros (sparse), a well structure and a well condition are advantageous for this objective. As a result, a problem of optimization with various goals will be addressed. This study seeks to minimize analytical errors such as rounding errors in skeletal structural flexibility matrixes via the use of more consistent and appropriate mathematical methods. These errors become more pronounced in particular designs with ill-suited flexibility matrixes; structures with varying stiffness are a frequent example of this. Due to the usage of weak elements, the flexibility matrix has a large number of non-diagonal terms, resulting in analytical errors. In numerical analysis, the ill-condition of a matrix may be resolved by moving or substituting rows; this study examined the definition and execution of these modifications prior to creating the flexibility matrix. Simple topological and algebraic features have been mostly utilized in this study to find fundamental cycle bases with particular characteristics. In conclusion, appropriately conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.

(1) Five new algorithms were proposed in order to optimize the conditioning of structural flexibility matrices. (2) A JAVA programming language was written for all five algorithms and a friendly GUI software tool is developed to visualize sub-optimal cycle bases. (3) Topological and algebraic features of the structures were utilized in this study.

This is a multi-objective optimization problem which means that sparsity and well conditioning of a matrix cannot be optimized simultaneously. In conclusion, well-conditioned flexibility matrices are obtained, and analytical errors are reduced accordingly.

Engineers always finding mathematical modeling of real-world problems and make them as simple as possible. In doing so, lots of errors will be created and these errors could cause the mathematical models useless. Applying decent algorithms could make the mathematical model as precise as possible.

Errors in numerical simulations should reduce due to the fact that they are toxic for real-world applications and problems.

This is an original research. This paper proposes five novel topological mathematical algorithms in order to optimize the structural flexibility matrix.

Human error data in the form of human error probabilities should ideally form the corner‐stone of human reliability theory and practice. In the history of human reliability assessment, however, the collection and generation of valid and usable data have been remarkably elusive. In part the problem appears to extend from the requirement for a technique to assemble the data into meaningful assessments. There have been attempts to achieve this, THERP being one workable example of a (quasi) database which enables the data to be used meaningfully. However, in recent years more attention has been focused on the PerformanceShaping Factors (PSF) associated with human reliability. A “database for today” should therefore be developed in terms of PSF, as well as task/ behavioural descriptors, and possibly even psychological error mechanisms. However, this presumes that data on incidents and accidents are collected and categorised in terms of the PSF contributing to the incident, and such classification systems in practice are rare. The collection and generation of a small working database, based on incident records are outlined. This has been possible because the incident‐recording system at BNFL Sellafield does give information on PSF. Furthermore, the data have been integrated into the Human Reliability Management System which is a PSF‐based human reliability assessment system. Some of the data generated are presented, as well as the PSF associated with them, and an outline of the incident collection system is given. Lastly, aspects of human common mode failure or human dependent failures, particularly at the lower human error probability range, are discussed, as these are unlikely to be elicited from data collection studies, yet are important in human reliability assessment. One possible approach to the treatment of human dependent failures, the utilisation of human performance‐limiting values, is described.

An extension of the concept of error on constitutive relation is proposed to the case of Mindlin plate finite element computations. The error of the performed analysis is estimated from the incompatibility in relation with the constitutive equation of admissible fields calculated from the finite element results. In a first stage, loads and moments densities leading to the equilibrium of each element are computed on the element edges as the sums of densities derived from the finite element solution and of densities with a resultant equal to zero on each element edge. Then strictly statically admissible stress resultants are calculated within each element. Both of the two stages allow an optimization for the statically admissible field in order to get a more accurate error. The calculations are local which is very interesting especially in case of complex structure analyses with a large number of degrees of freedom for which adaptivity is an important feature. A set of examples shows the efficiency of the proposed estimator and the good adaptation of the error on constitutive law method to Mindlin plate analysis.

The purpose of this paper is to describe a novel error‐ranking methodology and two compensation strategies for hybrid parallel kinematic machines (HPKMs).

The paper outlines an error analysis methodology developed for HPKMs and applies the technique to a typical industrial HPKM. Based on the results of this, two compensation strategies are developed and implemented, for both mass‐induced and thermal errors.

The paper demonstrates and quantifies the performance improvements possible with appropriate error compensation strategies.

The paper introduces a novel and generic methodology for error source analysis and describes two fully implemented compensation strategies which result in a significantly improved level of system performance.

This study aims to accurately evaluate the influence of various error intervals on the performance of the wiper.

The wiper structural system is decomposed into classical four-link planar for kinematics analysis, and it was modeled respectively by using interval method, universal grey number theory and enumeration approach depending on the nature of uncertainty.

The universal grey number theory is a viable methodology for the accurate analysis of uncertain structural system.

(1) The model of uncertain wiper structural system is established. (2) Universal grey number theory and new parameters are adopted to analyze the presence of uncertain wiper structural system. (3) Comparative analysis of response quantities is obtained by interval method, universal grey number theory and enumeration method.

The purpose of this paper is to address error‐controlled adaptive finite element (FE) method for thin and thick plates. A procedure is presented for determining the most suitable plate model (among available hierarchical plate models) for each particular FE of the selected mesh, that is provided as the final output of the mesh adaptivity procedure.

The model adaptivity procedure can be seen as an appropriate extension to model adaptivity for linear elastic plates of so‐called equilibrated boundary traction approach error estimates, previously proposed for 2D/3D linear elasticity. Model error indicator is based on a posteriori element‐wise computation of improved (continuous) equilibrated boundary stress resultants, and on a set of hierarchical plate models. The paper illustrates the details of proposed model adaptivity procedure for choosing between two most frequently used plate models: the one of Kirchhoff and the other of Reissner‐Mindlin. The implementation details are provided for a particular case of the discrete Kirchhoff quadrilateral four‐node plate FE and the corresponding Reissner‐Mindlin quadrilateral with the same number of nodes. The key feature for those elements that they both provide the same quality of the discretization space (and thus the same discretization error) is the one which justifies uncoupling of the proposed model adaptivity from the mesh adaptivity.

Several numerical examples are presented in order to illustrate a very satisfying performance of the proposed methodology in guiding the final choice of the optimal model and mesh in analysis of complex plate structures.

The paper confirms that one can make an automatic selection of the most appropriate plate model for thin and thick plates on the basis of proposed model adaptivity procedure.

Based on the asymptotic solution for predicted natural frequencies of a two‐dimensional elastodynamic problem from the finite element analysis, presents the concept of the asymptotic error, which is an approximate error but tends to the exact error when the characteristic length of elements approaches zero, and a practical error estimator. The present practical error estimator contains two criteria: one is the error estimator criterion, the other the finite element mesh design criterion. Using this practical error estimator, not only can the accuracy of a finite element solution for natural frequencies of a two‐dimensional elastodynamic problem be directly evaluated without any further finite element calculation, but also a new target finite element mesh for the desired accuracy of solution can be immediately designed from the relevant information of an original finite element solution. Generally, for the purpose of designing a new target finite element mesh, this original finite element solution is obtainable from a very coarse mesh of a few elements and usually does not satisfy the accuracy requirement. Since the new target finite element mesh could result in a finite element solution with a desire accuracy, the finite element solution so obtained can be used for a structural design in engineering practice. The related numerical results from vibration problems of three representative plates of different shapes under plane stress conditions have demonstrated the correctness and applicability of the present practical error estimator.