Design space reduction in optimization using generative topographic mapping

Dimension reduction in design optimization is an extensively researched area. The need arises in design problems dealing with very high dimensions, which increase the computational burden of the design process because the sample space required for the design search varies exponentially with the dimensions. This work describes the application of a latent variable method called Generative Topographic Mapping (GTM) in dimension reduction of a data set by transformation into a low-dimensional latent space. The attraction it presents is that the variables are not removed, but only transformed and hence there is no risk of missing out on information relating to all the variables. The method has been tested on the Branin test function initially and then on an aircraft wing weight problem. Ongoing work involves finding a suitable update strategy for adding infill points to the trained GTM in order to converge to the global optimum effectively. Three update methods tested on GTM so far are discussed

Dimension reduction for design optimization

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Dimension reduction for design optimization

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Multi-step transversal and tangential linearization methods applied to a class of nonlinear beam equations

AbstractA novel and continuously parameterized form of multi-step transversal linearization (MTrL) method is developed and numerically explored for solving nonlinear ordinary differential equations governing a class of boundary value problems (BVPs) of relevance in structural mechanics. A similar family of multi-step tangential linearization (MTnL) methods is also developed and applied to such BVP-s. Within the framework of MTrL and MTnL, a BVP is treated as a constrained dynamical system, i.e. a constrained initial value problem (IVP). While the MTrL requires the linearized solution manifold to transversally intersect the nonlinear solution manifold at a chosen set of points across the axis of the independent variable, the essential difference of the present MTrL method from its previous version [Roy, D., Kumar, R., 2005. A multistep transversal linearization (MTL) method in nonlinear structural dynamics. J. Sound Vib. 17, 829–852.] is that it has the flexibility of treating nonlinear damping and stiffness terms as time-variant damping and stiffness terms in the linearized system. The resulting time-variant linearized system is then solved using Magnus’ characterization [Magnus, W., 1954. On the exponential solution of differential equations for a linear operator. Commun. Pure Appl. Math., 7, 649–673.]. Towards numerical illustrations, response of a tip loaded cantilever beam (Elastica) is first obtained. Next, the response of a simply supported nonlinear Timoshenko beam is obtained using a variationally correct (VC) model for the beam [Marur, S., Prathap, G., 2005. Nonlinear beam vibration problems and simplification in finite element model. Comput. Mech. 35(5), 352–360.]. The new model does not involve any simplifications commonly employed in the finite element formulations in order to ease the computation of nonlinear stiffness terms from nonlinear strain energy terms. A comparison of results through MTrL and MTnL techniques consistently indicate a superior quality of approximations via the transversal linearization technique. While the usage of tangential system matrices is common in nonlinear finite element practices, it is demonstrated that the transversal version of linearization offers an easier and more general implementation, requires no computations of directional derivatives and leads to a consistently higher level of numerical accuracy. It is also observed that higher order versions of MTrL/MTnL with Lagrangian interpolations may not work satisfactorily and hence spline interpolations are suggested to overcome this problem

Constrained design optimization using generative topographic mapping

High-dimensional design-optimization problems involving complex and time-consuming solvers present computational challenges and are expensive to execute. Even though surrogate models can replace these expensive problems with simpler models, the initial design of experiment for constructing these models effectively is still exponential to the dimension of the problem. Traditional screening methods in optimization reduce the dimension of the problem by discarding variables, which is undesirable. In this paper, a latent variable model called generative topographic mapping is proposed to reduce the dimension of the problem so as to facilitate an optimization search in a low-dimensional space without removing any variables from the design problem. The method works by transforming high-dimensional data to be embedded on a low dimensional manifold. It is demonstrated on a two-dimensional Branin function subjected to nonlinear constraints and then applied to real engineering constrained optimization problems of an aircraft wing design and an aircraft compressor rotor. The model developed in this work proved to be more effective in dealing with constrained optimization problems by effectively learning the constraint boundary, hence finding feasible best designs when compared to other surrogate models like kriging

Performance Analysis of Cloud-based Health Care Data Privacy System Using Hybrid Techniques

At present, due to the various hacking approaches, the protection for any data transmitted through any channel or mode is one of the important issues. Nowadays, providing data security is satisfactory, developments are extended for obtaining data among the transceivers. Security level depends on the size of a symmetric key which is employed for encryption and decryption using various cryptography systems management and in modern approaches like block and RF codes including AES use a larger size of key simultaneously and there exists security problems due to hacking approaches. To illustrate the protection level and hacking problems, a new ECC is presented as well as by employing scalar duplication, the synchronous key is generated and consists of point doubling and point addition. The created focuses are encrypted before transmission by using ECC-Elgamal-Holomorphic (ECCEH) and transferred through a distant channel and encipher data is failed at the receiver using ECCEH which includes the reverse process. The unique standards of cryptography context have been generated by MATLAB; the defined framework has endeavored to the extent that speed, delay as well as control, and many others are accepted in MATLAB 2017a. The user of the sender, the original information is transformed into integer value by employing Holomorphic and encodes it by utilizing the Elgamal ECC algorithm which employs point doubling and point addition. The encoded information is uploaded into the cloud for storage, here www.thingspeak.com is utilized for storage. When the user presents at the receiver request the cloud to access from it, initially the cloud server authenticates the access control strategies of the requester, and then access is provided by the cloud server. If the user authenticates the strategies, then encoded data can download and the original data is decoded by synchronous key employing ECC- Elgamal algorithm. Using original and decrypted data, various performance factors are calculated in terms of execution time, packet delivery ratio, throughput, latency and compare these results with conventional methods and found to be 12%, 31%, 24%, and 8% progress concerned with packet delivery ratio, latency, outturn and execution time.</jats:p