scholarly journals Analysis of Linear Inverse Problem for Static Light Scattering Particle Size Distribution Measurement by Singular Value Decomposition

2018 ◽  
Vol 55 (1) ◽  
pp. 13-19
Author(s):  
Hirosuke Sugasawa
Keyword(s):  
Inverse Problem ◽  
Particle Size ◽  
Light Scattering ◽  
Singular Value Decomposition ◽  
Particle Size Distribution ◽  
Singular Value ◽  
Linear Inverse Problem ◽  
Distribution Measurement ◽  
Particle Size Distribution Measurement ◽  
Value Decomposition

scholarly journals Observation and Inversion of Aerosol Particle Size Distribution over Yinchuan Area

Atmosphere ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 992
Author(s):  
Jiandong Mao ◽  
Yali Ren ◽  
Juan Li ◽  
Qiang Wang ◽  
Yi Zhang
Keyword(s):  
Particle Size ◽  
Singular Value Decomposition ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Aerosol Optical Depth ◽  
Optical Depth ◽  
Singular Value ◽  
Truncated Singular Value Decomposition ◽  
Regularization Algorithm ◽  
Value Decomposition

Particle size distribution is one of the important microphysical parameters to characterize the aerosol properties. The aerosol optical depth is used as the function of wavelength to study the particle size distribution of whole atmospheric column. However, the inversion equation of the particle size distribution from the aerosol optical depth belongs to the Fredholm integral equation of the first kind, which is usually ill-conditioned. To overcome this drawback, the integral equation is first discretized directly by using the complex trapezoid formula. Then, the corresponding parameters are selected by the L curve method. Finally the truncated singular value decomposition regularization method is employed to regularize the discrete equation and retrieve the particle size distribution. To verify the feasibility of the algorithm, the aerosol optical depths taken by a sun photometer CE318 over Yinchuan area in four seasons, as well as hazy, sunny, floating dusty and blowing dusty days, were used to retrieve the particle size distribution. In order to verify the effect of truncated singular value decomposition algorithm, the Tikhonov regularization algorithm was also adopted to retrieve the aerosol PSD. By comparing the errors of the two regularizations, the truncated singular value decomposition regularization algorithm has a better retrieval effect. Moreover, to understand intuitively the sources of aerosol particles, the backward trajectory was used to track the source. The experiment results show that the truncated singular value decomposition regularization method is an effective method to retrieve the particle size distribution from aerosol optical depth.

Application of artificial bee colony algorithm for particle size distribution measurement of suspended sediment based on focused ultrasonic sensor

2021 ◽  
pp. 014233122198911
Author(s):  
Yeming Li ◽  
Yidan Xia ◽  
Dailiang Xie ◽  
Ya Xu ◽  
Zhipeng Xu ◽  
...  
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Suspended Sediment ◽  
Artificial Bee Colony ◽  
Ultrasonic Sensor ◽  
Inversion Algorithm ◽  
Distribution Measurement ◽  
Bee Colony ◽  
Particle Size Distribution Measurement

A new focused ultrasonic sensor is proposed, based on which the measurement system for particle size distribution measurement of suspended sediment is established. Compared with the traditional ultrasonic sensors, the one used in this paper is equipped with piezoelectric transducer (PZT) on an arc-shaped shell, to concentrate ultrasonic beams on one measurement point. The sensor is used to measure the particle size distribution of suspended sediment. The experiments were carried out on water-sediment mixtures with different particle size distribution. Due to multiple parameters and non-linearity of the ultrasonic attenuation model, the artificial bee colony (ABC) inversion algorithm is used to estimate particle size distribution, thus improving measurement accuracy. The particle sizes obtained by sieving method are seen as reference values. The results indicate that whether the suspended particles are subject to a unimodal distribution, uniform distribution or random distribution, the particle size distribution obtained by ABC inversion algorithm is consistent with the result obtained by the sieve method. The results demonstrate that the method has good utility and accuracy within the low concentration range.

Inversion of tikhonov and truncated singular value decomposition regularization for noisy dynamic light scattering data

2018 ◽  
Vol 26 (9) ◽  
pp. 2269-2279
Author(s):  
王雅静 WANG Ya-jing ◽  
袁 曦 YUAN Xi ◽  
申 晋 SHEN Jin ◽  
窦震海 DOU Zhen-hai ◽  
孙贤明 SUN Xian-ming
Keyword(s):  
Light Scattering ◽  
Dynamic Light Scattering ◽  
Singular Value Decomposition ◽  
Singular Value ◽  
Scattering Data ◽  
Truncated Singular Value Decomposition ◽  
Value Decomposition ◽  
Dynamic Light Scattering Data

scholarly journals Singular-value decomposition analysis of source illumination in seismic interferometry by multidimensional deconvolution

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. Q25-Q34 ◽  
Author(s):  
Shohei Minato ◽  
Toshifumi Matsuoka ◽  
Takeshi Tsuji
Keyword(s):  
Inverse Problem ◽  
Numerical Modeling ◽  
Singular Value Decomposition ◽  
Decomposition Analysis ◽  
Incident Field ◽  
Singular Value ◽  
Source Distribution ◽  
Seismic Interferometry ◽  
Source Illumination ◽  
Value Decomposition

We have developed a method to analytically evaluate the relationship between the source-receiver configuration and the retrieved wavefield in seismic interferometry performed by multidimensional deconvolution (MDD). The MDD method retrieves the wavefield with the desired source-receiver configuration from the observed wavefield without source information. We used a singular-value decomposition (SVD) approach to solve the inverse problem of MDD. By introducing SVD into MDD, we obtained quantities that revealed the characteristics of the MDD inverse problem and interpreted the effect of the initial source-receiver configuration for a survey design. We numerically simulated the wavefield with a 2D model and investigated the rank of the incident field matrix of the MDD inverse problem. With a source array of identical length, a sparse and a dense source distribution resulted in an incident field matrix of the same rank and retrieved the same wavefield. Therefore, the optimum source distribution can be determined by analyzing the rank of the incident field matrix of the inverse problem. In addition, the introduction of scatterers into the model improved the source illumination and effectively increased the rank, enabling MDD to retrieve a better wavefield. We found that the ambiguity of the wavefield inferred from the model resolution matrix was a good measure of the amount of illumination of each receiver by the sources. We used the field data recorded at the two boreholes from the surface sources to support our results of the numerical modeling. We evaluated the rank of incident field matrix with the dense and sparse source distribution. We discovered that these two distributions resulted in an incident field matrix of almost the same rank and retrieved almost the same wavefield as the numerical modeling. This is crucial information for designing seismic experiments using the MDD-based approach.

Sign in / Sign up

Export Citation Format

Share Document