The topic of force reconstruction has been studied quite extensively but most of the existing research work that has been done are in the domain of structural and civil engineering construction like bridges and beams. Considerable work in force reconstruction has also being done in fabrication of machines and structures like aircrafts, gear boxes etc. The topic of force reconstruction of the cutting forces during a machining process like turning or milling machines is a recent line of research to suffice the requirement of proactive monitoring of forces generated during the operation of the machine tool. The forces causing vibrations while machining if detected and monitored can enhance system productivity and efficiency of the process. The objective of this study was to investigate the algorithms available in literature for inverse force reconstruction and apply for reconstruction of cutting forces while machining on a computer numerically controlled (CNC) machine. This study has applied inverse force reconstruction technique algorithms 1) Deconvolution method, 2) Kalman filter recursive least square and 3) augmented Kalman filter for inverse reconstruction of forces for multi degree of freedom systems. Results from experiments conducted as part of this thesis work shows the effectiveness of the methods of force reconstruction to monitor the forces generated during the machining process on machine tools in real time without employing dynamometers which are expensive and complex to set-up. This study for developing a cost-effective method of force reconstruction will be instrumental in applications for improving machining efficiency and proactive preventive maintenance. / Graduate

The regularization of linear ill-posed problems is based on their conditional well-posedness when restricting the problem to certain classes of solutions. Given such class one may consider several related real-valued functions, which measure the wellposedness of the problem on such class. Among those functions the modulus of continuity is best studied. For solution classes which enjoy the additional feature of being star-shaped at zero, the authors develop a series of results with focus on continuity properties of the modulus of continuity. In particular it is highlighted that the problem is conditionally well-posed if and only if the modulus of continuity is right-continuous at zero. Those results are then applied to smoothness classes in Hilbert space. This study concludes with a new perspective on a concavity problem for the modulus of continuity, recently addressed by two of the authors in "Some note on the modulus of continuity for ill-posed problems in Hilbert space", 2011.

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Heat flux and heat conductance at the metal mold interface plays a key role in controlling the final metal casting strength. It is difficult to obtain these parameters through direct measurement because of the required placement of sensors, however they can be obtained through inverse heat conduction calculations. Existing inverse heat conduction methods are analyzed and classified into three categories, i.e., direct inverse methods, observer-based methods and optimization methods. The solution of the direct inverse methods is based on the linear relationship between heat flux and temperature (either in the time domain or in the frequency domain) and is calculated in batch mode. The observer-based method consists on the application of observer theory to the inverse heat conduction problem. The prominent characteristic in this category is online estimation, but the methods in this category show weak robustness. Transforming estimation problems into optimization problems forms the methods in the third category. The methods in third category show very good robustness property and can be easily extended to multidimensional and nonlinear problems. The unknown parameters in some inverse heat conduction methods can be obtained by a proposed calibration procedure. A two-index property evaluation (accuracy and robustness) is also proposed to evaluate inverse heat conduction methods and thus determine which method is suitable for a given situation. The thermocouple dynamics effect on inverse calculation is also analyzed. If the thermocouple dynamics is omitted in the inverse calculation, the time constant of thermocouple should be as small as possible. Finally, a simple model is provided simulating the temperature measurement using a thermocouple. FEA (Finite Element Analysis) is employed to simulate temperature measurement.

No description available.

There are various ways to regularize ill-posed operator equations in Hilbert space. If the underlying operator is accretive then Lavrentiev regularization (singular perturbation) is an immediate choice. The corresponding convergence rates for the regularization error depend on the given smoothness assumptions, and for general accretive operators these may be both with respect to the operator or its adjoint. Previous analysis revealed different convergence rates, and their optimality was unclear, specifically for adjoint source conditions. Based on the fundamental study by T. Kato, Fractional powers of dissipative operators. J. Math. Soc. Japan, 13(3):247--274, 1961, we establish power type convergence rates for this case. By measuring the optimality of such rates in terms on limit orders we exhibit optimality properties of the convergence rates, for general accretive operators under direct and adjoint source conditions, but also for the subclass of nonnegative selfadjoint operators.

By manipulating constraints and goals, this study had generated some ill-posed problems in "Fractions" which were packed into 2 mathematical tasks for teacher uses in an intended exploration of their perceived effectiveness of teaching mathematical problem-solving against their student responses through the lens of the theory of formative assessment. Each ill-posed problem was characterized by certain descriptive "instability" that users would have to define own sets of mathematical assumptions for problem-solving inquiries. 3 highly qualified, experienced, and trained mathematics teachers were purposefully recruited, and instructed to acquire and mark student responses without any prior teaching and intervention. Each of these teachers' perceptions of ill-posed problems was acquired through a semi-structured clinical case-interview. All teachers in common demonstrated only individual singular mathematical problem-solving inquiries as major instructional adjustments during evaluation, even though individuals had ample opportunities in manipulating the described intention of each problem. Although some could realize inquiries from students being alternative to own used, not all would intend to change initial instructional plans of each problem and could design dedicated tasks in extending given problem-solving contexts for subsequent teaching and maintaining the described problem-solving intentions merely because of evaluation purposes. The resulting thick teacher perceptions were then analyzed by the Mayring's (2015) Qualitative Content Analysis (QCA) method for exploring particularly those who could intend to influence and get influenced by students' used mathematical assumptions in interviews. Certain unanticipated uses of assumptions of student individuals and groups were evidently found to have influenced cognitively some teachers' further problem-solving inquiries at some interview instants and stimulated their perception changes. In the lack of subject implementation in mathematics education for the theory of "formative" assessment (Black & Wiliam, 2009), based on its definition, these instants should be put as their potential creations of and/or capitalizations upon certain asynchronous moments of contingency according to their planning of instructional adjustments for more comprehensive learning and definite growths of mathematical inquiries of students according to individuals' needs of problem-solving. Due to QCA, these perception changes might be characterized by four certain inductively formed categories of scenarios of perceptions, which were summarized as 1) Evaluation Perception, 2) Assumption Expansion Perception, 3) Assumption Collection Perception, and 4) Intention Indecision Perception. These scenarios of perceptions might be used to explore teachers' intentions, actions, and coherency in accounting for students' used assumptions in mathematical inquiries for given problem-solving contexts and extensions of given intentions of mathematical inquiries, particularly in their designs of mathematical tasks. Teacher uses of ill-posed problems were shown to have provided certain evidences in implementing formative assessments which should substantiate a subject implementation of its theory in the discipline of mathematics education. Methodologically, the current study also substantiate how theory-guided designs of ill-posed problems as well as generic plain text analysis through QCA have facilitate effectiveness comparisons of instructional adjustments within a teacher, across different teachers, decided prior knowledge, students of prior mathematical learning experiences, and students in different levels of schooling and class size.

We prove some sufficient conditions for obtaining convergence rates in regularization of linear ill-posed problems in a Hilbert space setting and show that these conditions are directly related with the conditional stability in several concrete inverse problems for partial differential equations.

The authors study parameter choice strategies for Tikhonov regularization of nonlinear ill-posed problems in Banach spaces. The effectiveness of any parameter choice for obtaining convergence rates depend on the interplay of the solution smoothness and the nonlinearity structure, and it can be expressed concisely in terms of variational inequalities. Such inequalities are link conditions between the penalty term, the norm misfit and the corresponding error measure. The parameter choices under consideration include an a priori choice, the discrepancy principle as well as the Lepskii principle. For the convenience of the reader the authors review in an appendix a few instances where the validity of a variational inequality can be established.

Ill-posed inverse problems with quadratic structure are introduced, studied and solved. As an example an inverse problem appearing in laser optics is solved numerically based on a new regularized inversion algorithm. In addition, the theory of sparsity promoting regularization is extended to situations in which sparsity cannot be expected and also to equations with non-injective operators.