A Hybrid Design Optimization Method using Enriched Craig-Bampton Approach

A hybrid design optimization method is presented which combines a number of techniques such as Component Mode Synthesis (CMS), Design of Computer Experiments and Neural Networks for surrogate modeling with Genetic Algorithms and Sequential Quadratic Programming for optimization. In the method, the FE analysis is decomposed and reduced by a well-known CMS technique called the Craig-Bampton method. Since the optimization method requires CMS calculations of the updated model at each of its iterations due to the changes in the design variables, one can either reuse the reduction basis of the initial components or compute new reduction basis for the condensation of the system matrices. The first option usually leads to inaccurate results and the last one increases the omputation time. In the method, instead of using one of these options, the Enriched Craig-Bampton method, proposed by Masson et al., is employed for efficient optimization. New basis for the modified components are generated by extending the corresponding initial reduction basis with a set of static residual vectors which are calculated using prior knowledge of the initial component designs. Thus, time consuming complete component analyzes are prevented. A theoretical test problem is used for the demonstration of the method

Force limited random vibration testing: the computation of the semi-empirical constant C2 for a real test article and unknown supporting structure

To prevent over-testing of the test-item during random vibration testing Scharton proposed and discussed the force limited random vibration testing (FLVT) in a number of publications. Besides the random vibration specification, the total mass and the turn-over frequency of the test article (load), C2 is a very important parameter for FLVT. A number of computational methods to estimate C2 are described in the literature, i.e. the simple and the complex two degree of freedom system, STDFS and CTDFS, respectively. The motivation of this work is to evaluate the method for the computation of a realistic value of C2 to perform a representative random vibration test based on force limitation, when the description of the supporting structure (source) is more or less unknown. Marchand discussed the formal description of obtaining C2 , using the maximum PSD of the acceleration and maximum PSD of the force, both at the interface between test article and supporting structure. Stevens presented the coupled systems modal approach (CSMA), where simplified asparagus patch models (parallel-oscillator representation) of load and source are connected. The asparagus patch model consists of modal effective masses and spring stiffnesses associated with the natural frequencies. When the random acceleration vibration specification is given the CSMA method is suitable to compute the value of the parameter C2 . When no mathematical model of the source can be made available, estimations of the value C2 can be find in literature. In this paper a probabilistic mathematical representation of the unknown source is proposed, such that the asparagus patch model of the source can be approximated. The chosen probabilistic design parameters have a uniform distribution. The computation of the value C2 can be done in conjunction with the CSMA method, knowing the apparent mass of the load and the random acceleration specification at the interface between load and source, respectively. Data of two cases available from literature has been analyzed and discussed to get more knowledge about the applicability of the probabilistic metho

An optimization method for dynamics of structures with repetitive component patterns

The occurrence of dynamic problems during the operation of machinery may have devastating effects on a product. Therefore, design optimization of these products becomes essential in order to meet safety criteria. In this research, a hybrid design optimization method is proposed where attention is focused on structures having repeating patterns in their geometries. In the proposed method, the analysis is decomposed but the optimization problem itself is treated as a whole. The model of an entire structure is obtained without modeling all the repetitive components using the merits of the Component Mode Synthesis method. Backpropagation Neural Networks are used for surrogate modeling. The optimization is performed using two techniques: Genetic Algorithms (GAs) and Sequential Quadratic Programming (SQP). GAs are utilized to increase the chance of finding the location of the global optimum and since this optimum may not be exact, SQP is employed afterwards to improve the solution. A theoretical test problem is used to demonstrate the method

Characterization and synthesis of random acceleration vibration specifications

Random acceleration vibration specifications for subsystems, i.e. instruments,\ud equipment, are most times based on measurement during acoustic noise tests on system level, i.e. a spacecraft and measured by accelerometers, placed in the neighborhood of the interface between spacecraft and subsystem. Tuned finite element models can be used to predict the random acceleration power spectral densities at other locations than available via the power spectral density measurements of the acceleration. The measured and predicted power spectral densities do represent the modal response characteristics of the system and show many peaks and valleys. The equivalent random acceleration vibration test specification is a smoothed, enveloped, peak-clipped version of the measured and predicted power spectral densities of the acceleration spectrum.\ud The original acceleration vibration spectrum can be characterized by a different number response spectra: Shock Response Spectrum (SRS) , Extreme Response Spectrum (ERS), Vibration Response Spectrum (VRS), and Fatigue Damage Spectrum (FDS). An additional method of non-stationary random vibrations is based on the Rayleigh distribution of peaks. The response spectra represent the responses of series of SDOF systems excited at the base by random acceleration,\ud both in time and frequency domain. The synthesis of equivalent random acceleration vibration specifications can be done in a very structured manner and are more suitable than equivalent random acceleration vibration\ud specifications obtained by simple enveloping. In the synthesis process Miles’ equation plays a dominant role to invert the response spectra into equivalent random acceleration vibration spectra. A procedure is proposed to reduce the number of data point in the response spectra curve by dividing the curve in a numbers of fields. The synthesis to an equivalent random acceleration spectrum is performed on a reduced selected set of data points. The recalculated response\ud spectra curve envelops the original response spectra curves. A real life measured random acceleration spectrum (PSD) with quite a number of peaks and\ud valleys is taken to generate, applying response spectra SRS, ERS, VRS, FDS and the Rayleigh distribution of peaks, equivalent random acceleration vibration specifications. Computations are performed both in time and frequency domain

Force limited vibration testing: an evaluation of the computation of C2 for real load and probabilistic source

To prevent over-testing of the test-item during random vibration testing Scharton proposed and discussed the force limited random vibration testing (FLVT) in a number of publications. Besides the random vibration specification, the total mass and the turn-over frequency of the load (test item), is a very important parameter for FLVT. A number of computational methods to estimate are described in the literature, i.e., the simple and the complex two degrees of freedom system, STDFS and CTDFS, respectively. The motivation of this work is to evaluate the method for the computation of a realistic value of to perform a representative random vibration test based on force limitation, when the adjacent structure (source) description is more or less unknown. Marchand discussed the formal description of getting , using the maximum PSD of the acceleration and maximum PSD of the force, both at the interface between load and source. Stevens presented the coupled systems modal approach (CSMA), where simplified asparagus patch models (parallel-oscillator representation) of load and source are connected, consisting of modal effective masses and the spring stiffness's associated with the natural frequencies. When the random acceleration vibration specification is given the CSMA method is suitable to compute the value of the parameter . When no mathematical model of the source can be made available, estimations of the value can be find in literature. In this paper a probabilistic mathematical representation of the unknown source is proposed, such that the asparagus patch model of the source can be approximated. The chosen probabilistic design parameters have a uniform distribution. The computation of the value can be done in conjunction with the CSMA method, knowing the apparent mass of the load and the random acceleration specification at the interface between load and source, respectively. Data of two cases available from literature have been analyzed and discussed to get more knowledge about the applicability of the probabilistic metho

Design Optimization Utilizing Dynamic Substructuring and Artificial Intelligence Techniques

In mechanical and structural systems, resonance may cause large strains and stresses which can lead to the failure of the system. Since it is often not possible to change the frequency content of the external load excitation, the phenomenon can only be avoided by updating the design of the structure. In this paper, a design optimization strategy based on the integration of the Component Mode Synthesis (CMS) method with numerical optimization techniques is presented. For reasons of numerical efficiency, a Finite Element (FE) model is represented by a surrogate model which is a function of the design parameters. The surrogate model is obtained in four steps: First, the reduced FE models of the components are derived using the CMS method. Then the components are aassembled to obtain the entire structural response. Afterwards the dynamic behavior is determined for a number of design parameter settings. Finally, the surrogate model representing the dynamic behavior is obtained. In this research, the surrogate model is determined using the Backpropagation Neural Networks which is then optimized using the Genetic Algorithms and Sequential Quadratic Programming method. The application of the introduced techniques is demonstrated on a simple test problem