Inverse Element Research Articles

An inverse boundary element method/genetic algorithm based approach for retrieval of multi-dimensional heat transfer coefficients within film cooling holes/slots

An inverse methodology is developed as a means of determining heat transfer coefficient distributions in film cooling holes/slots. Thermal conditions are over-specified at exposed surfaces amenable to measurement, while the temperature and surface heat flux distributions are unknown at the film cooling hole/slot walls. The latter are determined in an iterative manner by solving an inverse problem whose objective is to adjust the film-cooling hole/slot wall temperatures and heat flux distributions until the temperature and heat fluxes at the measurement surfaces are matched in an overall heat conduction solution. The heat conduction problem is solved using boundary element methods, and the inverse problem is solved using a genetic algorithm. The resulting film coefficient distributions are fit to a correlation reflecting dependency on position, the Prandtl and Reynolds numbers.

Reconstruction of vibroacoustic fields in half-space by using hybrid near-field acoustical holography

In this paper we examine the accuracy and efficiency of reconstructing the vibroacoustic quantities generated by a vibrating structure in half-space by using hybrid near-field acoustic holography (NAH) and modified Helmholtz equation least squares (HELS) formulations. In hybrid NAH, we combine modified HELS with an inverse boundary element method (IBEM) to reconstruct a vibroacoustic field. The main advantage of this approach is that the majority of the input data can be regenerated but not measured, thus the efficiency is greatly enhanced. In modified HELS, we expand the field acoustic pressure in terms of outgoing and incoming spherical waves and specify the corresponding expansion coefficients by solving a system of equations obtained by matching the assumed-form solution to the measured acoustic pressure. Here the system of equations is ill conditioned and Tikhonov regularization is implemented through singular value decomposition (SVD) and the generalized cross-validation (GCV) method. Numerical examples of a dilating and oscillating spheres and finite cylinder are demonstrated. Test results show that hybrid NAH can yield a more accurate reconstruction than does a modified HELS, but a modified HELS is more efficient than is hybrid NAH [Work supported by NSF].

On irreversibility in quantum mechanics

In connection with certain physical problems, Ginzburg [1] noted that the physical causes of a monotonic increase in the entropy of closed systems, as well as a corresponding irreversibility, are not yet clearly understood. A usual approach to irreversibility in quantum mechanics is as follows. Dynamic equations, including the Schrodinger equation, are time reversible. Based on this circumstance, one concludes that postulated quantum-mechanical schemes cannot lead to irreversibility in closed systems. For this reason, either a transition to open systems or a substantial change in the mathematical foundations of quantum mechanics and transition to the equipped Hilbert space is proposed in order to include irreversibility in quantum mechanics. Other proposals involve the inclusion of nonlinear and complex terms in the Schrodinger equation. Space‐time symmetries, which are mathematically expressed in terms of the theory of groups, i.e., sets with one operation where each element has an inverse element, are responsible for exact conservation laws. The Noether theorems establish a one-to-one correspondence [2] between conservation laws and grouptheoretical requirements imposed on physical theory, and, owing to the reversibility of equations, all propagators (matrices transforming solutions from one space‐time point to another) have inverse operators. Therefore, the satisfaction of conservation laws that follow from reversible equations leads to group-theoretical requirements for propagators, in particular, to the existence of inverse propagators; i.e., the reversibility of equations and the group-theoretical construction of a physical theory are mutually dependent [3]. The description of a physical system that includes irreversible equations is a sufficient condition of its irreversible evolution. Moreover, its description by only reversible equations is obviously a necessary condition of its reversible evolution. Is the latter condition

Homonuclear chemical shift correlation in rotating solids via RN?n symmetry-based adiabatic RF pulse schemes

The efficacy of RN(nu) (n) symmetry-based adiabatic Zero-Quantum (ZQ) dipolar recoupling schemes for obtaining chemical shift correlation data at moderate magic angle spinning frequencies has been evaluated. RN(nu) (n) sequences generally employ basic inversion elements that correspond to a net 180 degrees rotation about the rotating frame x-axis. It is shown here via numerical simulations and experimental measurements that it is also possible to achieve efficient ZQ dipolar recoupling via RN(nu) (n) schemes employing adiabatic pulses. Such an approach was successfully used for obtaining (13)C chemical shift correlation spectra of a uniformly labelled sample of (CUG)(97) - a triplet repeat expansion RNA that has been implicated in the neuromuscular disease myotonic dystrophy. An analysis of the (13)C sugar carbon chemical shifts suggests, in agreement with our recent (15)N MAS-NMR studies, that this RNA adopts an Alpha-helical conformation.

Robust Stability of Sequential Multi-input Multi-output Quantitative Feedback Theory Designs

This paper re-examines the stability of multi-input multi-output (MIMO) control systems designed using sequential MIMO quantitative feedback theory (QFT). In order to establish the results, recursive design equations for the SISO equivalent plants employed in a sequential MIMO QFT design are established. The equations apply to sequential MIMO QFT designs in both the direct plant domain, which employs the elements of plant in the design, and the inverse plant domain, which employs the elements of the plant inverse in the design. Stability theorems that employ necessary and sufficient conditions for robust closed-loop internal stability are developed for sequential MIMO QFT designs in both domains. The theorems and design equations facilitate less conservative designs and improved design transparency.

Boundary element analysis of contact problems using inverse techniques—linear and quadratic elements

This paper presents an inverse boundary element (BE) technique to reconstruct the boundary conditions in contact regions using photoelastic measurement data consisting of the differences of the principal stresses and their orientations at interior points. The separate individual Cartesian stress components are then obtained using the conventional ‘forward’ boundary element method (BEM). Numerical experiments show that using linear elements instead of quadratic elements can reduce the sensitivity of the inverse BEM to the errors of photoelastic measurements and gives better results. A smoothing displacement scheme is further introduced to improve the accuracy of the reconstructed tractions. When up to 5, 10 and 20 per cent random ‘noise’ was added to the simulated measurement data, the results of the inverse BE analysis still show good agreement with reference solutions. An example using real photoelastic measurements on a simple specimen is also presented and the results are found to be encouraging.

Nature of the Source Regions for Post-collisional, Potassic Magmatism in Southern and Northern Tibet from Geochemical Variations and Inverse Trace Element Modelling

Neogene potassic lavas in northern and southern Tibet have different isotopic (eNd(i) north, −5·5 to −10·3; south −8·8 to −18·1) and major element signatures suggesting derivation from separate sub-continental lithospheric mantle (SCLM) sources. Inverse trace-element modelling shows that the southern Tibet magmas were derived by 1–2% partial melting of a phlogopite and amphibole peridotite, and that the northern samples were derived by 3–4% partial melting of a phlogopite peridotite. In both cases, melting is inferred to take place in the spinel stability field. Both sources show large ion lithophile element (LILE) enrichment relative to the high field strength elements (HFSE), and heavy rare earth element (HREE) depletion relative to primitive mantle. LILE/HFSE enrichment suggests subduction-related metasomatism; HREE depletion is indicative of prior melt extraction. Extension postdates the earliest magmatism in southern and north–central Tibet by 7 Myr and 5 Myr, respectively, which, in combination with the shallow depths of melting inferred for the Tibetan samples, supports geodynamic models invoking thinning of the SCLM. The northern Tibetan magmatism and extension can be explained by convective removal of the lower SCLM; the older ages and arcuate distribution of the southern magmas are most consistent with the SCLM erosion following slab break-off.

Analysis of half-cell potential measurement for corrosion of reinforced concrete

Non-destructive evaluation techniques by the half-cell potential measurement are applied to estimate the corrosion of reinforcing steel-bars in concrete slabs under cyclic wet and dry conditions. The three-dimensional boundary element method (BEM) is applied to study the potential distributions and current flows of rebar. Then, the inverse boundary element method (IBEM) is applied to experimental results to identify the corrosion states. The influence of a void on the potential distribution and current flow is also investigated. Results show that the half-cell potential measurement is marginally successful, compared with analytical results of potential distribution and current flow by BEM. It is demonstrated that results by IBEM analysis identify clearly corroded areas.

境界観測および領域内観測を併用した静弾性境界値同定に対する交替境界要素逆解法の適用性に関する検討(OS4a 逆問題解析手法の開発と最新応用)

境界観測および領域内観測を併用した静弾性境界値同定に対する交替境界要素逆解法の適用性に関する検討(OS4a 逆問題解析手法の開発と最新応用)

Application of an Inverse BEM to the Modelling Fracturing Process at the Borehole Pillar by Excavation and Thermal Loading

ABSTRACT A two-dimensional boundary element code, FRACOD2D, has been developed to simulate brittle fracturing in rock-like material including fracture initiation, propagation and coalescence under tensile, shear and mixed mode. Since the code is based on the displacement discontinuity solution it is very difficult to implement standard thermo-mechanical boundary element algorithms in its formulation. To simulate the thermo-mechanical process without changing the current structure of the code, an alternative technique has been developed by reconstructing the stress field from other thermo-mechanical models without fracturing process. In this paper an inverse boundary element formulation is presented to reconstruct the complex stress fields by equivalent boundary conditions. Truncated singular value decomposition technique is used for inverse solution. Results from predictive modeling with the reconstructed stresses during the in-situ heater test between the deposition holes are also presented. With successful application, this approach can be a good alternative for modelling fracturing processes under complex loading conditions with boundary elements.

Shuffle on positive varieties of languages

We show there is a unique maximal positive variety of languages which does not contain the language (ab) ∗ . This variety is the unique maximal positive variety satisfying the two following conditions: it is strictly included in the class of rational languages and is closed under the shuffle operation. It is also the largest proper positive variety closed under length preserving morphisms. The ordered monoids of the corresponding variety of ordered monoids are characterized as follows: for every pair ( a, b) of mutually inverse elements, and for every element z of the minimal ideal of the submonoid generated by a and b, ( abzab) ω ⩽ ab. In particular this variety is decidable.

On the reconstruction of sound field using the equivalent source modeling

The sound field radiated from a vibrating structure is reconstructed by using the equivalent source modeling. In this method, the equivalent multipole sources which are similar to the spherical harmonics in the Helmholtz equation least-squares (HELS) method are distributed over or inside a vibrating surface. To improve the accuracy and usefulness, the effective independence (EfI) method is used to determine the optimal position of equivalent sources and the regularization scheme is adopted to determine the optimal expansion number of spherical harmonics and to suppress the high order poles. After regenerating field pressures using those optimized equivalent source modeling, the vibrating source is effectively reconstructed with minimal measurement combining the proposed method with the near-field acoustic holography (NAH) using the inverse boundary element method (BEM). In this study, an application example of a commercial vacuum cleaner using the equivalent source modeling will be demonstrated. [Work supported by the BK21 project and NRL.]

Sound source reconstruction using inverse boundary element calculations.

Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim in this work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form suited for solution by means of an inverse boundary element method. Since the numerical treatment of the inverse source reconstruction results in a discrete ill-posed problem, regularization is imposed to avoid unstable solutions dominated by errors. In the present work the emphasis is on Tikhonov regularization and parameter-choice methods not requiring an error-norm estimate for choosing the right amount of regularization. Several parameter-choice strategies have been presented lately, but it still remains to be seen how well these can handle industrial applications with real measurement data. In the present work it is demonstrated that the L-curve criterion is robust with respect to the errors in a real measurement situation. In particular, it is shown that the L-curve criterion is superior to the more conventional generalized cross-validation (GCV) approach for the present tire noise studies.

A BEM‐based genetic algorithm for identification of polarization curves in cathodic protection systems

AbstractThe purpose of this work is to apply an inverse boundary element formulation in order to develop efficient algorithms for identification of polarization curves in a cathodic protection system. The problem is to minimize an objective function measuring the difference between observed and BEM‐predicted surface potentials. The numerical formulation is based on the application of genetic algorithms, which are robust search techniques emulating the natural process of evolution as a means of progressing towards an optimum solution.Examples of application are included in the paper for different types of polarization curves in finite and infinite electrolytes. The accuracy and efficiency of the numerical results are verified by comparison with standard conjugate gradient techniques. As a result of this research, the genetic algorithm approach is shown to be more robust, independent of the position of the sensors and of initial guesses, and will be further developed for three‐dimensional applications. Copyright © 2002 John Wiley & Sons, Ltd.

On the Elasticity of the Perron Root of a Nonnegative Matrix

Let A=(ai,j) be an n × n nonnegative irreducible matrix whose Perron root is $\lambda$. The quantity $e_{i,j}=\frac{a_{i,j}}{\lam}\frac{\partial \lambda}{\partial a_{i,j}}$ is known as the elasticity of $\lambda$ with respect to ai,j. In this paper, we give two proofs of the fact that $\frac{\partial e_{i,j}}{\partial a_{i,j}} \geq 0$ so that ei,j is increasing as a function of ai,j. One proof uses ideas from symbolic dynamics, while the other, which is matrix theoretic, also yields a characterization of the case when $\frac{\partial e_{i,j}}{\partial a_{i,j}}=0$. We discuss a resulting connection between the elements of A and the elements of the group inverse of $\lambda I -A.$

Detection of Bacillus cereus in foods by colony hybridization using PCR-generated probe and characterization of isolates for toxins by PCR

Isolates of Bacillus cereus from traditional Indian foods were detected by colony hybridization using the PCR-generated phospholipase (PL-1) probe. In all, 29 isolates picked up by the probe were confirmed as B. cereus by conventional cultural and biochemical characteristics. All the isolates reacted positively in PCR with phospholipase (PL-1) primers. Among the native isolates, 11 of them showed the discontinuous pattern of haemolysin BL activity in gel diffusion assay. Though 14 isolates reacted positively in PCR with primers (Ha-1) specific to the B gene of haemolysin BL, only four of them showed both the presence of gene and haemolysin BL activity. More than 50% of the isolates indicated their potential enterotoxigenicity by reacting positively with primers specific for the BceT gene encoding for diarrhoeal enterotoxin. PCR with primers for different inverse (IS) repeat elements revealed that isolates carrying transposon IS 231–P 231-1 did not carry IS 240–P 240. Some of the isolates were devoid of these IS elements. The study demonstrated the potential of using of a PCR-generated labelled PL-1 probe for the direct detection of B. cereus in food samples and PCR for characterizing the toxigenic isolates.

Cramèr–Rao bounds for fractional Brownian motions

We obtain Cramèr–Rao bounds for parameters estimators of fractional Brownian motions. We point out the differences of behavior whether these processes are standard or not. The key-point of this study relies upon a linear algebra result we prove, exhibiting bounds for elements of inverse of localized matrices.

Development of new inverse boundary element techniques in photoelasticity

This paper presents a number of possible algorithms for inverse boundary element (BE) techniques applied to photoelastic analysis. The BE technique is shown to be an ideal companion to photoelastic analysis since, unlike the finite element (FE) method, the interior solutions can be represented by unconnected points rather than by discretized elements. From the photoelastic principal stress information obtained at a sufficient number of internal points, the unknown boundary conditions can be reconstructed using the inverse boundary element method (BEM). The inverse BE theory and numerical formulation are presented for problems involving Cartesian stress components and are then extended to photoelastic stress analysis. The inverse BE approach follows two stages. In stage 1, the photoelastic stress measurements of the differences in principal stresses and their directions at the interior points are used to compute the unknown boundary conditions on the surface. In stage 2, the individual stress components are calculated by the forward BEM using the computed boundary conditions from stage 1. The effect of scatter of the experimental results is also included in the analysis. A number of examples are presented in this paper and are shown to be in excellent agreement with other solutions.

ORDERS IN RINGS WITH INVOLUTION

In this paper we introduce a definition of order in a (notnecessarily unital) ring with involution in terms of the notions of Moore–Penrose inverse and *-cancellable element instead of those of group inverse and cancellable element. The main result states that if R is a Fountain–Gould order in a ring Q with Q semiprime and coinciding with its socle, then every involution * : R →R can be extended to a (unique) involution on Q in such a way that (R, *) is a *-order in (Q, *). And conversely, every *-order in an involution ring (Q, *) with Q semiprime and coinciding with its socle is a Fountain–Gould order inQ.

Kalman filter based 3d-stochastic inverse boundary element method for flaw identification and structural reliability prediction

A stochastic inverse boundary element method (SIEM) is developed for determination of three-dimensional (3D) flaws, stochastic boundary traction (load) and structural reliability parameters. SIBEM includes the direct solution of stochastic boundary element (SBEM) and the inverse analysis. Minimizing the difference of the initial guess and the objective values by Kalman filtering algorithm, makes it possible to predict the stochastic boundary loads, as well as to determinate the defects and the structural reliability. Two numerial examples, which show the effectiveness of this paper, including the determination of unknown defects and unknown parameter distribution of random boundary traction, are presented and discussed.