While research in multiple-input/multiple-output (MIMO) random vibration testing techniques, control methods, and test design has been increasing in recent years, research into specifications for these types of tests has not kept pace. This is perhaps due to the very particular requirement for most MIMO random vibration control specifications – they must be narrowband, fully populated cross-power spectral density matrices. This requirement puts constraints on the specification derivation process and restricts the application of many of the traditional techniques used to define single-axis random vibration specifications, such as averaging or straight-lining. This requirement also restricts the applicability of MIMO testing by requiring a very specific and rich field test data set to serve as the basis for the MIMO test specification. Here, frequency-warping and channel averaging techniques are proposed to soften the requirements for MIMO specifications with the goal of expanding the applicability of MIMO random vibration testing and enabling tests to be run in the absence of the necessary field test data.
Many in the structural dynamics community are currently researching a range of multiple-input/multiple-output problems and largely rely on commercially-available closed-loop controllers to execute their experiments. Generally, these commercially-available control systems are robust and prove adequate for a wide variety of testing. However, with the development of new techniques in this field, researchers will want to exercise these new techniques in laboratory tests. For example, modifying the control or input estimation method can have benefits to the accuracy of control, or provide higher response for a given input. Modification of the control methods is not typically possible in commercially-available control systems, therefore it is desirable to have some methodology available which allows researchers to synthesize input signals for multiple-input/multiple-output experiments. Here, methods for synthesizing multiply-correlated time histories based on desired cross spectral densities are demonstrated and then explored to understand effects of various parameters on the resulting signals, their statistics, and their relation to the specified cross spectral densities. This paper aims to provide researchers with a simple, step-by-step process which can be implemented to generate input signals for open-loop multiple-input/multiple-output experiments.
Multi-axis testing is growing in popularity in the testing community due to its ability to better match a complex three-dimensional excitation than a single-axis shaker test. However, with the ability to put a large number of shakers anywhere on the structure, the design space of such a test is enormous. This paper aims to investigate strategies for placement of shakers for a given test using a complex aerospace structure controlled to real environment data. Initially shakers are placed using engineering judgement, and this was found to perform reasonably well. To find shaker setups that improved upon engineering judgement, impact testing was performed at a large number of candidate excitation locations to generate frequency response functions that could be used to perform virtual control studies. In this way, a large number of shaker positions could be evaluated without needing to reposition the shakers each time. A brute force computation of all possible shaker setups was performed to find the set with the lowest error, but the computational cost of this approach is prohibitive for very large candidate shaker sets. Instead, an iterative approach was derived that found a suboptimal set that was nearly as good as the brute force calculation. Finally, an investigation into the number of shakers used for control was performed, which could help determine how many shakers might be necessary to perform a given test.
In the past decade, multi-axis vibration testing has progressed from its early research stages towards becoming a viable technology which can be used to simulate more realistic environmental conditions. The benefits of multi-axis vibration simulation over traditional uniaxial testing methods have been demonstrated by numerous authors. However, many challenges still exist to best utilize this new technology. Specifically, methods to obtain accurate and reliable multi-axis vibration specifications based on data acquired from field tests is of great interest. Traditional single axis derivation approaches may be inadequate for multi-axis vibration as they may not constrain profiles to adhere to proper cross-axis relationships—they may introduce behavior that is neither controllable nor representative of the field environment. A variety of numerical procedures have been developed and studied by previous authors. The intent of this research is to benchmark the performance of these different methods in a well-controlled lab setting to provide guidance for their usage in a general context. Through a combination of experimental and analytical work, the primary questions investigated are as follows: (1) In the absence of part-to-part variability and changes to the boundary condition, which specification derivation method performs the best? (2) Is it possible to optimize the sensor selection from field data to maximize the quality/accuracy of derived multi-axis vibration specifications? (3) Does the presence of response energy in field data which did not originate due to rigid body motion degrade the accuracy of multi-axis vibration specifications obtained via these derivation methods?
Random vibration tests have been conducted for over 5 decades using vibration machines which excite a test item in uniaxial motion. With the advent of multi shaker test systems, excitation in multiple axes and/or at multiple locations is feasible. For random vibration testing, both the auto spectrum of the individual controls and the cross spectrum, which defines the relationship between the controls, define the test environment. This is a striking contrast to uniaxial testing where only the control auto spectrum is defined. In a vibration test the energy flow proceeds from drive excitation voltages to control acceleration auto and cross spectral densities and finally, to response auto and cross spectral densities. This paper examines these relationships, which are encoded in the frequency response function. Following the presentation of a complete system diagram, examination of the relationships between the excitation and control spectral density matrices is clarified. It is generally assumed that the control auto spectra are known from field measurements, but the control cross spectra may be unknown or uncertain. Given these constraints, control algorithms often prioritize replication of the field auto spectrum. The system dynamics determine the cross spectrum. The Nearly Independent Drive Algorithm, described herein, is one approach. A further issue in Multi Input Multi Response testing is the link between cross spectrum at one set of locations and auto spectra at a second set of locations. The effect of excitation cross spectra on control auto spectra is one important case, encountered in every test. The effect of control cross spectra on response auto spectra is important since we may desire to adjust control cross spectra to achieve some desired response auto spectra. The relationships between cross spectra at one set of locations and auto spectra at another set of locations is examined with the goal of elucidating the advantages and limitations of using control cross spectra to define response auto spectra.
Six degree of freedom (6-DOF) subsystem/component testing is becoming a desirable method, for field test data and the stress environment can be better replicated with this technology. Unfortunately, it is a rare occasion where a field test can be sufficiently instrumented such that the subsystem/component 6-DOF inputs can be directly derived. However, a recent field test of a Sandia National Laboratory system was instrumented sufficiently such that the input could be directly derived for a particular subsystem. This input is compared to methods for deriving 6-DOF test inputs from field data with limited instrumentation. There are four methods in this study used for deriving 6-DOF input with limited instrumentation. In addition to input comparisons, response measurements during the flight are compared to the predicted response of each input derivation method. All these methods with limited instrumentation suffer from the need to inverse the transmissibility function.
Recent advances in 6DOF testing has made 6DOF subsystem/component testing a preferred method because field environments are inherently multidimensional and can be better replicated with this technology. Unfortunately, it is rare that there is sufficient instrumentation in a field test to derive 6DOF inputs. One of the most challenging aspects of the test inputs to derive is the cross spectra. Unfortunately, if cross spectra are poorly defined, it makes executing the tests on a shaker difficult. In this study, tests were carried out using the inputs derived by four different inverse methods, as described in a companion paper. The tests were run with all 6DOF as well with just the three translational degrees of freedom. To evaluate the best way to handle the cross spectra, three different sets of tests were run: with no cross terms defined, with only the coherence defined, and with the coherence and phase defined. All of the different tests were compared using a variety of metrics to assess the efficacy of the specification methods. The drive requirements for the different methods are also compared to evaluate how the specifications affect the shaker performance. A number of the inverse methods show great promise for being able to derive inputs to a 6DOF shaker to replicate the flight environments.
This paper presents a method for improved auscultation with an electronic stethoscope by estimating and removing the effects of unknown disturbance inputs. By replacing the single transducer in a stethoscope with a dual piezo transducer assembly, it is shown that an inverse dynamic mapping can be used to relate the two measured signals to original directional inputs acting on the stethoscope. Specifically, model inversion is used to estimate and remove physician handling noise from chest sound signals. An experimental test platform which uses a vibration shaker to simulate the desired auscultation signal is used to experimentally demonstrate the feasibility of the dual-piezo stethoscope approach in improving auscultation.
The vibration excitation mechanisms for structures in service are typically multi-directional. However, during product testing conducted in a lab setting the standard practice is to replicate these environments with three orthogonal single axis vibration tests. Recent advances in technology have made it possible to perform multi-axis simulations in the laboratory. Simultaneous multi-axis excitation can result in different stress states, rates of damage accumulation, and peak accelerations and strains than those resulting from sequential single axis testing. Accordingly, a series of experiments were run on a plate structure to investigate and quantify these differences. The experiments included single and multiple axis tests with different excitation amplitudes. The single axis tests were performed on both uniaxial and multiaxial shaker systems. The control levels, response energy, modal behavior, and peak accelerations were compared for each test condition. The data illustrates the differences between the structural response for single and multi-axis tests and enables an objective comparison between testing conducted on single and multiple axis shaker systems.