Handbook of Technical Diagnostics: Fundamentals and Application to Structures and Systems

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The same should be true for complex industrial systems such as automobiles and high-pressure multi-stage compressors.

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  • Handbook of Technical Diagnostics.

The FFT VSA principles, while currently applied to a limited array of industrial equipment, are applicable to anything that shakes. This chapter introduces vibration theory, relevant vocabulary, tools of analysis, and their applications in predictive and diagnostic maintenance of complex machinery. It describes FFT VSA methodology for manufacturing quality, predictive and diagnostic maintenance, which can lead to longer, healthier lives for industrial equipment, ultimately enhancing cost, quality, and productivity.

This chapter presents the principles and applications of acoustic emission AE analysis to detect microscale symptoms and syndromes of faults and failures in technical structures and systems.

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  7. Non-destructive testing NDT methods are employed in the technical field as a precautionary to avoid accidence or emergency situations for the human and the environment. A risk situation in the technical field could happen if the load of a component is increasing and the wall thickness due to defect growth is decreasing until a critical defect situation. The result of such scenarios could be catastrophic breakdown of the component with sometimes severe aftermath for the human. Infrared thermography also commonly referred as thermal imaging , or simply thermography , is a nondestructive testing NDT technique that has received vast and growing attention for diagnostics and monitoring in the last few decades.

    This is mainly due to the fact that commercial infrared or thermal cameras, the main instrument for performing infrared thermography, are continuously improving in both sensibility and in spatial resolution, and they are getting faster and relatively less expensive. Every year or so, it is possible to acquire a better camera for about the same cost as the preceding model from the year before. Industrial radiology is typically applied for the volumetric inspection of industrial products and installations [1, 2].

    The basic setup consists of a radiation source in front of the object to be inspected and an area detector behind the object.

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    The classical detector is an X-ray film. New electronic area detectors are gradually substituting the film. The radiation source can be an X-ray generator, a gamma source or a particle emitter, generating e. Computed tomography CT with X- and Gamma-rays is a well-known imaging method, established first for medical use. Applications to non-destructive testing were published in the early s. CT offers the possibility to map non-invasively the three-dimensional local absorption of X-rays of samples and components, which correspond to the inner and outer structures.

    The result of a CT measurement is usually given in the form of a 3D image matrix. Each point represents a single volume element in the sample, a voxel. This chapter introduces the concept of structural health monitoring, gives an overview of state-of-the-art sensing techniques used for performance control and condition monitoring, and reviews topical applications from different industrial areas.

    Beyond classical X-ray techniques are used for the purpose of preferably short-term applications, but some supplementary X-ray and synchrotron techniques for higher resolution microdiagnostics take advantage of scattering effects. In contrast to directly imaging methods their resolution is only limited by the diffraction limit of the X-ray wavelength, far below the atomic dimensions.

    Their basic advantage over microscopic techniques is their potential for the non-destructive characterisation of materials, far from invasive sample treatments.

    Hydraulic drive of vibration stand for testing the robotic systems units by random vibration method

    They combine scattering and spatial resolution. This chapter describes relevant methods of micro- and nanosurface chemical analysis used in technical diagnostics. Informative case studies in diagnostics applied in a wide range of industrial technology are presented, too. Many performance properties of devices or interacting machine parts are related to superficial layers which often show completely different or at least modified microstructures compared to the bulk materials.

    Although various prescriptions for organization and performing failure analyses are existing in literature, up to the present no approach is consistent to the concept of technical systems in the Sects 2. Failure analysis is needed as a diagnostic tool to assess the sequence of primary, secondary and perhaps tertiary damage of different parts in a damaged system.

    This is a prerequisite to identify the contributing causes and the root cause for the causal failure. For as long as there have been machines, there have been maintenance issues, uncertainties regarding reliability, and failures. With an ever-increasing reliance on expensive and complex machines, machinery failures significantly affect company profits, largely due to the loss of equipment availability, the cost of spare parts, the risk of injury to people, and the possibility of damage to the environment.

    It formulates general principles for integrating and implementing measurement and signal processing technologies in the context of SHM to diagnose the condition, performance and health of a technical structure. Information and recommended methods for designing instrumentation, data acquisition, data processing and data analysis for any SHM application are offered. Diagnostics of buildings had not drawn attention until recent years. Steel and concrete structures were assumed to be strong enough during their life span.

    In some occasions, sensors were installed to verify the accuracy and appropriateness of design processes for large, tall or special building structures. Bridges have been the preferred structures where structural health monitoring SHM and performance assessment have been developed.

    Comprehensive methodologies are available already and good reference is provided in the literature health monitoring of bridges, Wenzel Practical application started in the s and has developed into a full life cycle engineering approach as desired now. Out of the initial desire to detect damage a methodology to optimise and manage the constructed infrastructure has developed and is being applied widely.

    Flowlines—pipelines or gas lines often cross hazardous environmental areas, from the point of view natural exposures such as landslides and earthquakes and from the point of view of third party influences such as vandalism or obstruction. These hazards can significantly change the original functioning of the flowline, leading to damaging, leakage and failure with serious economic and ecologic consequences.

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    Furthermore, the operational conditions of the pipeline itself can induce additional wearing or even damage due to corrosion, erosion and fatigue. This chapter presents methods, techniques and their application to structural health monitoring and performance control. Diagnosis of the operational condition of facilities in power stations and transmission networks is of significant importance to ensure their reliable operation. Using condensation or expansion, it is possible to compare a large analytical set of DOFs to a relatively small set of experimental DOFs.

    Reduction and expansion also play a very important role with regard to model updating. Consequently, the set of the tested DOFs requires reducing the number of DOFs of a large model without losing any information or characteristics of the dynamic system in the modelling process. Here the coordinates represent the location of sub-matrices in the original matrix. The reduction of the stiffness matrix is thus accomplished by identifying those degrees of freedom to be condensed or reduced as slave degrees of freedom, and to express them in terms of remaining master degrees-of-freedom.

    The dynamic equations of equilibrium for an undamped n degree-of-freedom model may be written as:.

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    The displacement response vector U t in Equation 4 can be expressed as shown in Equation 5 using the mode superposition method:. It is well known that the computation of the complete eigenvector matrix is not required for a large model. Therefore, modal truncation is usually used in the mode superposition technique Qu If p eigenvectors of the full model are used in the mode superposition, Equatioin 5 is rewritten as:. With the arrangement of the total degrees of freedom, Equation 6 may be partitioned as:.

    This is equivalent to two equations 8 and 9 :. Equation 8 provides a description of the displacement responses at the master DOFs in terms of the eigenvector matrix at these DOFs. Since the number of knowns in Equation 8 are greater than the number of unknowns, Equation 8 can be put into a normal form by transforming this equation as:. Substituting Equation 8 into Equation 10 produces:.

    Handbook of Technical Diagnostics

    Although the square coefficient matrix of p t will in general be of full rank and possess an inverse, the determining of the inverse of this matrix using standard methods may encounter some numerical difficulty, and singular-value decomposition solution is usually required.

    Symbolically p t could be solved from Equation 11 as:. Substituting Equation 10 into Equation 12 produces the general form of the solution of the modal coordinates in terms of physical coordinates and modal matrix as:. Equation 13 represents the "best" solution of the p variables given in Equation 8. For convenience, the solution q P t of Equation 8 can be approximated by qp t , Qu :. Substituting Equation 15 into Equation 9 leads to:. When the dynamic condensation matrix is available Equation 17 , the coordinate transformation matrix T may be given by the following Kammer :. The coordinate transformation matrix is obtained by substituting Equation 15 into Equation Using the coordinate transformation in Equation 20, the reduced system matrices are given by:.

    Udwadia discusses non-proportional damping in linearly damped vibrating systems in which the stiffness and damping matrices are not restricted to being symmetric and positive-definite in simple systems with two-degrees-of-freedom; they conclude that if the system has an active element, as commonly arises in the active control of a structure, the stability is more difficult to physically interpret, and their approximation by damping matrices that commute with the stiffness matrices needs to be carried out with considerable care and caution.

    In this study, as there is no active element, proportional damping is taken into consideration. The damping matrix is calculated using Rayleigh damping where the damping is defined as being proportional to the mass and the stiffness of the structure Chopra :.

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    The damping ratio for the n th mode of such a system is:. Expressing Equation 24 for these two modes in matrix form leads to:. Seeing that the damping matrix is proportional to the mass and stiffness matrices, the change in the damping matrix due to the change in the stiffness is taken into account. By plotting the Fourier amplitude spectra of the signals recorded, the frequencies associated with the modes of vibration of the structure are located at the corresponding vibration amplitude peak values. Optimisation technique. Multi-objective optimisation is a mathematical optimisation technique used to optimise more than one objective function simultaneously.

    In this study, a multi-objective optimisation technique is used to optimise the equation of motion used in the TPC technique. The maximum of is minimised by the unscaled goal attainment problem. The algorithm coded is used to find x to minimise the maximum of , where the weighting variables w t are a given positive value. The TPC technique finds the best stiffness value to satisfy the function given in Equation 2, as well as the corresponding frequencies.

    The initial inputs are as follows:. The reduced theoretical stiffness matrix. The reduced mass matrix. The acceleration, velocity and displacement vectors. The first mode and second modal frequencies. The damping ratios of the first two modal frequencies. A goal function value of zero is used in order to get the optimal value of K in the function given in Equation 2. Weighting function values of unity are used in this study. The technique uses the reduced theoretical stiffness matrix as a starting point where the solver finds the best stiffness matrix values that satisfy the equation of motion and the associated modal frequencies.

    The output of the solution process is the identified optimised stiffness matrix. K c is then used for comparison purposes to locate the damage.