Obtaining Prior Information for Ultrasonic Signal Reconstruction from FRI Sparse Sampling Data

Finite rate of innovation sampling is a novel sub-Nyquist sampling method that can reconstruct a signal from sparse sampling data.The application of this method in ultrasonic testing greatly reduces the signal sampling rate and the quantity of sampling data.However,the pulse number of the signal must be known beforehand for the signal reconstruction procedure.The accuracy of this prior information directly affects the accuracy of the estimated parameters of the signal and influences the assessment of flaws,leading to a lower defect detection ratio.Although the pulse number can be pre-given by theoretical analysis,the process is still unable to assess actual complex random orientation defects.Therefore,this paper proposes a new method that uses singular value decomposition(SVD) for estimating the pulse number from sparse sampling data and avoids the shortcoming of providing the pulse number in advance for signal reconstruction.When the sparse sampling data have been acquired from the ultrasonic signal,these data are transformed to discrete Fourier coefficients.A Hankel matrix is then constructed from these coefficients,and SVD is performed on the matrix.The decomposition coefficients reserve the information of the pulse number.When the decomposition coefficients generated by noise according to noise level are removed,the number of the remaining decomposition coefficients is the signal pulse number.The feasibility of the proposed method was verified through simulation experiments.The applicability was tested in ultrasonic experiments by using sample flawed pipelines.Results from simulations and real experiments demonstrated the efficiency of this method.

Testability evaluation using prior information of multiple sources

Testability plays an important role in improving the readiness and decreasing the lifecycle cost of equipment. Testability demonstration and evaluation is of significance in measuring such testability indexes as fault detection rate（FDR） and fault isolation rate（FIR）, which is useful to the producer in mastering the testability level and improving the testability design, and helpful to the consumer in making purchase decisions. Aiming at the problems with a small sample of testability demonstration test data（TDTD） such as low evaluation confidence and inaccurate result, a testability evaluation method is proposed based on the prior information of multiple sources and Bayes theory. Firstly, the types of prior information are analyzed. The maximum entropy method is applied to the prior information with the mean and interval estimate forms on the testability index to obtain the parameters of prior probability density function（PDF）, and the empirical Bayesian method is used to get the parameters for the prior information with a success-fail form. Then, a parametrical data consistency check method is used to check the compatibility between all the sources of prior information and TDTD. For the prior information to pass the check, the prior credibility is calculated. A mixed prior distribution is formed based on the prior PDFs and the corresponding credibility. The Bayesian posterior distribution model is acquired with the mixed prior distribution and TDTD, based on which the point and interval estimates are calculated.Finally, examples of a flying control system are used to verify the proposed method. The results show that the proposed method is feasible and effective.

An image reconstruction algorithm of EIT based on pulmonary prior information

Using a CT scan of the pulmonary tissue,a human pulmonary model is established combined with the structure property of the human lung tissue using the software COMSOL.Combined with the conductivity contribution information of the human tissue and organ,an image reconstruction method of electrical impedance tomography based on pulmonary prior information is proposed using the conjugate gradient method.Simulation results show that the uniformity index of sensitivity distribution of the pulmonary model is 15.568,which is significantly reduced compared with 34.218 based on the round field.The proposed algorithm improves the uniformity of the sensing field,the image resolution of the conductivity distribution of pulmonary tissue and the quality of the reconstruction image based on pulmonary prior information.

Inversion of Moho Interface in Northeastern China with Prior Information

Non-uniqueness is always, by nature, the problem we face in inversion processes, and it is caused by the phenomenon of equivalence in field, erroneous, discrete, and finite features in obser- vation and the influence of other sources. Many authors have done lots of researches in this field in order to get more reliable outcomes, and joint inversion is a thriving one where different kinds of data are combined to derive certain information simultaneously or sequentially. One of these studies is that the prior information such as the geological, drilling and seismic data will be used as con- straints, while the inversion procedure can be controlled. In this article we use a new method with the goal of better obtaining the three-dimensional density contrast interface. This prior seismic data integrated in the inversion can play a constrained role in the procedure which means that the depth of the Moho interface at the seismic location will be restricted. It thus can provide a credible result. In order to test its effect, this program is applied in a field example--derivation of Moho geometry in Northeast China.

A new learning method using prior information of neural networks

In this paper, we present a new learning method using prior information for three-layered neural networks. Usually when neural networks are used for identification of systems, all of their weights are trained independently, without considering their interrelation of weight values. Thus the training results are not usually good. The reason for this is that each parameter has its influence on others during the learning. To overcome this problem, first, we give an exact mathematical equation that describes the relation between weight values given by a set of data conveying prior information. Then we present a new learning method that trains a part of the weights and calculates the others by using these exact mathematical equations. In almost all cases, this method keeps prior information given by a mathematical structure exactly during the learning. In addition, a learning method using prior information expressed by inequality is also presented. In any case, the degree of freedom of networks (the number of adjustable weights) is appropriately limited in order to speed up the learning and ensure small errors. Numerical computer simulation results are provided to support the present approaches.

Remaining useful life prediction based on nonlinear random coefficient regression model with fusing failure time data

Remaining useful life(RUL) prediction is one of the most crucial elements in prognostics and health management(PHM). Aiming at the imperfect prior information, this paper proposes an RUL prediction method based on a nonlinear random coefficient regression(RCR) model with fusing failure time data.Firstly, some interesting natures of parameters estimation based on the nonlinear RCR model are given. Based on these natures,the failure time data can be fused as the prior information reasonably. Specifically, the fixed parameters are calculated by the field degradation data of the evaluated equipment and the prior information of random coefficient is estimated with fusing the failure time data of congeneric equipment. Then, the prior information of the random coefficient is updated online under the Bayesian framework, the probability density function(PDF) of the RUL with considering the limitation of the failure threshold is performed. Finally, two case studies are used for experimental verification. Compared with the traditional Bayesian method, the proposed method can effectively reduce the influence of imperfect prior information and improve the accuracy of RUL prediction.

Prestack seismic stochastic inversion based on statistical characteristic parameters

In the conventional stochastic inversion method,the spatial structure information of underground strata is usually characterized by variograms.However,effectively characterizing the heterogeneity of complex strata is difficult.In this paper,multiple parameters are used to fully explore the underground formation information in the known seismic reflection and well log data.The spatial structure characteristics of complex underground reservoirs are described more comprehensively using multiple statistical characteristic parameters.We propose a prestack seismic stochastic inversion method based on prior information on statistical characteristic parameters.According to the random medium theory,this method obtains several statistical characteristic parameters from known seismic and logging data,constructs a prior information model that meets the spatial structure characteristics of the underground strata,and integrates multiparameter constraints into the likelihood function to construct the objective function.The very fast quantum annealing algorithm is used to optimize and update the objective function to obtain the fi nal inversion result.The model test shows that compared with the traditional prior information model construction method,the prior information model based on multiple parameters in this paper contains more detailed stratigraphic information,which can better describe complex underground reservoirs.A real data analysis shows that the stochastic inversion method proposed in this paper can effectively predict the geophysical characteristics of complex underground reservoirs and has a high resolution.

Incorporating genomic annotation into single-step genomic prediction with imputed whole-genome sequence data

Single-step genomic best linear unbiased prediction(ss GBLUP) is now intensively investigated and widely used in livestock breeding due to its beneficial feature of combining information from both genotyped and ungenotyped individuals in the single model. With the increasing accessibility of whole-genome sequence(WGS) data at the population level, more attention is being paid to the usage of WGS data in ss GBLUP. The predictive ability of ss GBLUP using WGS data might be improved by incorporating biological knowledge from public databases. Thus, we extended ss GBLUP, incorporated genomic annotation information into the model, and evaluated them using a yellow-feathered chicken population as the examples. The chicken population consisted of 1 338 birds with 23 traits, where imputed WGS data including 5 127 612 single nucleotide polymorphisms(SNPs) are available for 895 birds. Considering different combinations of annotation information and models, original ss GBLUP, haplotype-based ss GHBLUP, and four extended ss GBLUP incorporating genomic annotation models were evaluated. Based on the genomic annotation(GRCg6a) of chickens, 3 155 524 and 94 837 SNPs were mapped to genic and exonic regions, respectively. Extended ss GBLUP using genic/exonic SNPs outperformed other models with respect to predictive ability in 15 out of 23 traits, and their advantages ranged from 2.5 to 6.1% compared with original ss GBLUP. In addition, to further enhance the performance of genomic prediction with imputed WGS data, we investigated the genotyping strategies of reference population on ss GBLUP in the chicken population. Comparing two strategies of individual selection for genotyping in the reference population, the strategy of evenly selection by family(SBF) performed slightly better than random selection in most situations. Overall, we extended genomic prediction models that can comprehensively utilize WGS data and genomic annotation information in the framework of ss GBLUP, and validated the idea that properly handling the genomic annotation information and WGS data increased the predictive ability of ss GBLUP. Moreover, while using WGS data, the genotyping strategy of maximizing the expected genetic relationship between the reference and candidate population could further improve the predictive ability of ss GBLUP. The results from this study shed light on the comprehensive usage of genomic annotation information in WGS-based single-step genomic prediction.

Assessment Method of Heavy NC Machine Reliability Based on Bayes Theory

It is difficult to collect the prior information for small-sample machinery products when their reliability is assessed by using Bayes method. In this study, an improved Bayes method with gradient reliability(GR) results as prior information was proposed to solve the problem. A certain type of heavy NC boring and milling machine was considered as the research subject, and its reliability model was established on the basis of its functional and structural characteristics and working principle. According to the stress-intensity interference theory and the reliability model theory, the GR results of the host machine and its key components were obtained. Then the GR results were deemed as prior information to estimate the probabilistic reliability(PR) of the spindle box, the column and the host machine in the present method. The comparative studies demonstrated that the improved Bayes method was applicable in the reliability assessment of heavy NC machine tools.

The role of prior in image based 3D modeling： a survey

The prior knowledge is the significant supple- ment to image-based 3D modeling algorithms for refining the fragile consistency-based stereo. In this paper, we review the image-based 3D modeling problem according to prior cate- gories, i.e., classical priors and specific priors. The classical priors including smoothness, silhouette and illumination are well studied for improving the accuracy and robustness of the 3D reconstruction. In recent years, various specific priors which take advantage of Manhattan rule, geometry template and trained category features have been proposed to enhance the modeling performance. The advantages and limitations of both kinds of priors are discussed and evaluated in the paper. Finally, we discuss the trend and challenges of the prior studies in the future.

Individual Word Length Patterns for Fractional Factorial(Split-Plot)Designs

Fractional factorial(FF)designs are commonly used for factorial experiments in many fields.When some prior knowledge has shown that some factors are more likely to be significant than others,Li,et al.(2015)proposed a new pattern,called the individual word length pattern(IWLP),which,defined on a column of the design matrix,measures the aliasing of the effect assigned to this column and effects involving other factors.In this paper,the authors first investigate the relationships between the IWLP and other popular criteria for regular FF designs.As we know,fractional factorial split-plot(FFSP)designs are important both in theory and practice.So another contribution of this paper is extending the IWLP criterion from FF designs to FFSP designs.The authors propose the IWLP of a factor from the whole-plot(WP),or sub-plot(SP),denoted by the I_w WLP and Is WLP respectively,in the FFSP design.The authors further propose combined word length patterns C_(w) WLP and Cs WLP,in order to select good designs for different cases.The new criteria C_(w) WLP and Cs WLP apply to the situations that the potential important factors are in WP or SP,respectively.Some examples are presented to illustrate the selected designs based on the criteria established here.

Theory of Compressive Sensing via l1-Minimization:a Non-RIP Analysis and Extensions

Compressive sensing(CS)is an emerging methodology in computational signal processing that has recently attracted intensive research activities.At present,the basic CS theory includes recoverability and stability:the former quantifies the central fact that a sparse signal of length n can be exactly recovered from far fewer than n measurements via l1-minimization or other recovery techniques,while the latter specifies the stability of a recovery technique in the presence of measurement errors and inexact sparsity.So far,most analyses in CS rely heavily on the Restricted Isometry Property(RIP)for matrices.In this paper,we present an alternative,non-RIP analysis for CS via l1-minimization.Our purpose is three-fold:(a)to introduce an elementary and RIP-free treatment of the basic CS theory;(b)to extend the current recoverability and stability results so that prior knowledge can be utilized to enhance recovery via l1-minimization;and(c)to substantiate a property called uniform recoverability of l1-minimization;that is,for almost all random measurement matrices recoverability is asymptotically identical.With the aid of two classic results,the non-RIP approach enables us to quickly derive from scratch all basic results for the extended theory.

THE STUDY OF RETRIEVAL THEORY AND METHODS FROM SATELLITE REMOTE SENSING FOR METEOROLOGICAL PARAMETERS OVER EASTERN ASIA-PARTI:ISPRM AND SRRM

A review of ten-year's practice in developing the improved simultaneous physical retrieval method(ISPRM)is given in the hope that some creative ideas can be drawn from it.The improvement upon the SPRM is associated with the under-determinedness of this ill-posed inverse problem.In our experiment,the precondition is observed that prior information must be independent of the satellite measurements.The well-posed retrieval theory has told us that the forward process is fundamental for the retrieval,and it is the bridge between the input of satellite radiance and the output of retrievals.In order to obtain a better result from the forward process. the full advantage of every prior information available must be taken.It is necessary to turn the ill- posed inverse problem into the well-posed one.Then by using the Ridge regression or Bayes algorithm to find the optimal combination among the first guess,the theoretical analogue information and the satellite observations,the impact of the under-determinedness of this inverse problem on the numerical solution is minimized.

CT local reconstruction of solid rocket motor based on PI-POCS-TVM

In order to test the defects of solid rocket motor(SRM)accurately and efficiently,the computed tomography(CT)inspection scheme for SRM's defects was investigated and a CT local reconstruction algorithm called prior information-projection onto convex sets-total variation minimization(PI-POCS-TVM)was developed.The SRM was first inspected by industrial CT(ICT)to generate a low-resolution SRM image used as the prior information,then high-resolution local inspection was carried out for SRM's defects.To validate the effectiveness of the CT inspection scheme for SRM's defects,one SRM was inspected by a narrow fan beam ICT system.Filtered back projection(FBP)algorithm,POCS,POCS-TVM and PI-POCS-TVM algorithms were applied to reconstruct CT images.The performance of these algorithms was also compared.Results demonstrated the effectiveness of the CT inspection scheme for SRM's defects.Moreover,the PI-POCS-TVM algorithm has better local reconstruction image quality than the other three algorithms,showing great significance for accurate measurement of SRM's defects.

A Shrinkage Estimator for Combination of Bioassays

A shrinkage estimator and a maximum likelihood estimator are proposed in this paper for combination of bioassays. The shrinkage estimator is obtained in closed form which incorporates prior information just on the common log relative potency after the homogeneity test for combination of bioassays is accepted. It is a practical improvement over other estimators which require iterative procedure to obtain the estimator for the relative potency. A real data is also used to show the superiorities for the newly-proposed procedures.

Bayesian model predicts the aboveground biomass of Caragana microphylla in sandy lands better than OLS regression models

Aims In forest ecosystems,different types of regression models have been frequently used for the estimation of aboveground biomass,where Ordinary Least Squares(OLS)regression models are the most common prediction models.Yet,the relative performance of Bayesian and OLS models in predicting aboveground biomass of shrubs,especially multi-stem shrubs,has relatively been less studied in forests.Methods In this study,we developed the biomass prediction models for Caragana microphylla Lam.which is a widely distributed multi-stems shrub,and contributes to the decrease of wind erosion and the fixation of sand dunes in the Horqin Sand Land,one of the largest sand lands in China.We developed six types of formulations under the framework of the regression models,and then,selected the best model based on specific criteria.Consequently,we estimated the parameters of the best model with OLS and Bayesian methods with training and test data under different sample sizes with the bootstrap method.Lastly,we compared the performance of the OLS and Bayesian models in predicting the aboveground biomass of C.microphylla.Important Findings The performance of the allometric equation(power=1)was best among six types of equations,even though all of those models were significant.The results showed that mean squared error of test data with non-informative prior Bayesian method and the informative prior Bayesian method was lower than with the OLS method.Among the tested predictors(i.e.plant height and basal diameter),we found that basal diameter was not a significant predictor either in OLS or Bayesian methods,indicating that suitable predictors and well-fitted models should be seriously considered.This study highlights that Bayesian methods,the bootstrap method and the type of allometric equation could help to improve the model accuracy in predicting shrub biomass in sandy lands.