A Modification of the Monte Carlo Filtering Approach for Correcting Negative SEA Loss Factors
Abstract
:1. Introduction
- All elements off the main diagonal are negative.
- Elements on the main diagonal are positive and greater than the sum of the absolute values of the remaining elements for a given column.
- The present paper proposes a modification of the MCF method. The modification is called DESA (Diagonal Expansion of the Search Area), which is the main contribution to the experimental SEA field. DESA consists of applying a correction during the MCF, which causes a non-uniform expansion of the search area (Section 2.1). This novel approach expands the range of vibroacoustic systems that can be properly identified by MCF. It can be applied in the frequency bands for which correct results could not be obtained using the MCF method in the basic version (using a homogeneous expansion of the search area for the population with a normal distribution), as will be demonstrated by the example presented in Section 3.
- The effect of the expansion of the search area (parameter ) on the errors introduced into the loss factors was investigated. The so-called shift error was observed and related to the asymmetry present in the generated population of the energy matrices. We pointed out that the asymmetry of the population increases with an increase in .
- We introduced a new parameter describing the degree of asymmetry of the energy matrix population, the asymmetry index , and proposed two methods (A and B) for eliminating the shift error. Method A involves detecting matrices that introduce asymmetry and rejecting them from the calculation, while method B involves using a log-normal distribution when generating the energy matrix population. A common feature of both methods is the need to perform minimization.
2. Materials and Methods
2.1. Expansion of the Search Area (UESA and DESA)
2.2. Errors Associated with ESA
2.2.1. Population Asymmetry and Shift Error
2.2.2. Scaling Factor Minimization
2.2.3. Enforcing Symmetry of the Population
- Method A, which involves discarding from the calculation matrices that fall into the tail of the normal distribution.
- Method B, which involves generating a population with a log-normal distribution.
- The use of one of the presented SFM methods in combination with -minimization allows us to:
- Correct negative loss factors and replace them with factors that are free of offset error.
- Obtain results close to the original results in bands that do not require correction, which can be good in terms of the quality control of the applied methods.
- When , or equivalently , the result obtained will be free of both shift error and negative LF. Then, the identification result obtained by Method A can be considered correct, and occurs for the resulting population.
- When , or equivalently (which also means that ), all correct matrices will be discarded and the correction of negative LF coefficients will not take place. Method A is then ineffective. However, it is possible to take the LF coefficients determined for an asymmetric population of matrices as the final result. In such a situation, the result obtained will be affected by a shift error. However, this error will be minimized by using during the calculation (the distance between the matrices and the original matrix will be relatively small).
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Geometry | |
---|---|
Thickness | 20 mm |
Length | 80 mm |
Width | 500 mm |
Mechanical Parameters | |
Material | Steel |
Density | 7827 kg/m3 |
Young’s modulus | 205 GPa |
Poisson number | 0.3 |
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Nieradka, P.; Dobrucki, A. A Modification of the Monte Carlo Filtering Approach for Correcting Negative SEA Loss Factors. Acoustics 2022, 4, 1028-1044. https://doi.org/10.3390/acoustics4040063
Nieradka P, Dobrucki A. A Modification of the Monte Carlo Filtering Approach for Correcting Negative SEA Loss Factors. Acoustics. 2022; 4(4):1028-1044. https://doi.org/10.3390/acoustics4040063
Chicago/Turabian StyleNieradka, Paweł, and Andrzej Dobrucki. 2022. "A Modification of the Monte Carlo Filtering Approach for Correcting Negative SEA Loss Factors" Acoustics 4, no. 4: 1028-1044. https://doi.org/10.3390/acoustics4040063