Side lobe level reduction(SLL)of antenna arrays significantly enhances the signal-to-interference ratio and improves the quality of service(QOS)in recent and future wireless communication systems starting from 5G up t...Side lobe level reduction(SLL)of antenna arrays significantly enhances the signal-to-interference ratio and improves the quality of service(QOS)in recent and future wireless communication systems starting from 5G up to 7G.Furthermore,it improves the array gain and directivity,increasing the detection range and angular resolution of radar systems.This study proposes two highly efficient SLL reduction techniques.These techniques are based on the hybridization between either the single convolution or the double convolution algorithms and the genetic algorithm(GA)to develop the Conv/GA andDConv/GA,respectively.The convolution process determines the element’s excitations while the GA optimizes the element spacing.For M elements linear antenna array(LAA),the convolution of the excitation coefficients vector by itself provides a new vector of excitations of length N=(2M−1).This new vector is divided into three different sets of excitations including the odd excitations,even excitations,and middle excitations of lengths M,M−1,andM,respectively.When the same element spacing as the original LAA is used,it is noticed that the odd and even excitations provide a much lower SLL than that of the LAA but with amuch wider half-power beamwidth(HPBW).While the middle excitations give the same HPBWas the original LAA with a relatively higher SLL.Tomitigate the increased HPBWof the odd and even excitations,the element spacing is optimized using the GA.Thereby,the synthesized arrays have the same HPBW as the original LAA with a two-fold reduction in the SLL.Furthermore,for extreme SLL reduction,the DConv/GA is introduced.In this technique,the same procedure of the aforementioned Conv/GA technique is performed on the resultant even and odd excitation vectors.It provides a relatively wider HPBWthan the original LAA with about quad-fold reduction in the SLL.展开更多
The control design, based on self-adaptive PID with genetic algorithms(GA) tuning on-line was investigated, for the temperature control of industrial microwave drying rotary device with the multi-layer(IMDRDWM) and wi...The control design, based on self-adaptive PID with genetic algorithms(GA) tuning on-line was investigated, for the temperature control of industrial microwave drying rotary device with the multi-layer(IMDRDWM) and with multivariable nonlinear interaction of microwave and materials. The conventional PID control strategy incorporated with optimization GA was put forward to maintain the optimum drying temperature in order to keep the moisture content below 1%, whose adaptation ability included the cost function of optimization GA according to the output change. Simulations on five different industrial process models and practical temperature process control system for selenium-enriched slag drying intensively by using IMDRDWM were carried out systematically, indicating the reliability and effectiveness of control design. The parameters of proposed control design are all on-line implemented without iterative predictive calculations, and the closed-loop system stability is guaranteed, which makes the developed scheme simpler in its synthesis and application, providing the practical guidelines for the control implementation and the parameter design.展开更多
Swarm intelligence in a bat algorithm(BA)provides social learning.Genetic operations for reproducing individuals in a genetic algorithm(GA)offer global search ability in solving complex optimization problems.Their int...Swarm intelligence in a bat algorithm(BA)provides social learning.Genetic operations for reproducing individuals in a genetic algorithm(GA)offer global search ability in solving complex optimization problems.Their integration provides an opportunity for improved search performance.However,existing studies adopt only one genetic operation of GA,or design hybrid algorithms that divide the overall population into multiple subpopulations that evolve in parallel with limited interactions only.Differing from them,this work proposes an improved self-adaptive bat algorithm with genetic operations(SBAGO)where GA and BA are combined in a highly integrated way.Specifically,SBAGO performs their genetic operations of GA on previous search information of BA solutions to produce new exemplars that are of high-diversity and high-quality.Guided by these exemplars,SBAGO improves both BA’s efficiency and global search capability.We evaluate this approach by using 29 widely-adopted problems from four test suites.SBAGO is also evaluated by a real-life optimization problem in mobile edge computing systems.Experimental results show that SBAGO outperforms its widely-used and recently proposed peers in terms of effectiveness,search accuracy,local optima avoidance,and robustness.展开更多
In recent years, immune genetic algorithm (IGA) is gaining popularity for finding the optimal solution for non-linear optimization problems in many engineering applications. However, IGA with deterministic mutation fa...In recent years, immune genetic algorithm (IGA) is gaining popularity for finding the optimal solution for non-linear optimization problems in many engineering applications. However, IGA with deterministic mutation factor suffers from the problem of premature convergence. In this study, a modified self-adaptive immune genetic algorithm (MSIGA) with two memory bases, in which immune concepts are applied to determine the mutation parameters, is proposed to improve the searching ability of the algorithm and maintain population diversity. Performance comparisons with other well-known population-based iterative algorithms show that the proposed method converges quickly to the global optimum and overcomes premature problem. This algorithm is applied to optimize a feed forward neural network to measure the content of products in the combustion side reaction of p-xylene oxidation, and satisfactory results are obtained.展开更多
In order to solve the problem between searching performance and convergence of genetic algorithms, a fast genetic algorithm generalized self-adaptive genetic algorithm (GSAGA) is presented. (1) Evenly distributed init...In order to solve the problem between searching performance and convergence of genetic algorithms, a fast genetic algorithm generalized self-adaptive genetic algorithm (GSAGA) is presented. (1) Evenly distributed initial population is generated. (2) Superior individuals are not broken because of crossover and mutation operation for they are sent to subgeneration directly. (3) High quality im- migrants are introduced according to the condition of the population schema. (4) Crossover and mutation are operated on self-adaptation. Therefore, GSAGA solves the coordination problem between convergence and searching performance. In GSAGA, the searching per- formance and global convergence are greatly improved compared with many existing genetic algorithms. Through simulation, the val- idity of this modified genetic algorithm is proved.展开更多
Evolutionary algorithms(EAs)have been used in high utility itemset mining(HUIM)to address the problem of discover-ing high utility itemsets(HUIs)in the exponential search space.EAs have good running and mining perform...Evolutionary algorithms(EAs)have been used in high utility itemset mining(HUIM)to address the problem of discover-ing high utility itemsets(HUIs)in the exponential search space.EAs have good running and mining performance,but they still require huge computational resource and may miss many HUIs.Due to the good combination of EA and graphics processing unit(GPU),we propose a parallel genetic algorithm(GA)based on the platform of GPU for mining HUIM(PHUI-GA).The evolution steps with improvements are performed in central processing unit(CPU)and the CPU intensive steps are sent to GPU to eva-luate with multi-threaded processors.Experiments show that the mining performance of PHUI-GA outperforms the existing EAs.When mining 90%HUIs,the PHUI-GA is up to 188 times better than the existing EAs and up to 36 times better than the CPU parallel approach.展开更多
Transmission of data over the internet has become a critical issue as a result of the advancement in technology, since it is possible for pirates to steal the intellectual property of content owners. This paper presen...Transmission of data over the internet has become a critical issue as a result of the advancement in technology, since it is possible for pirates to steal the intellectual property of content owners. This paper presents a new digital watermarking scheme that combines some operators of the Genetic Algorithm (GA) and the Residue Number (RN) System (RNS) to perform encryption on an image, which is embedded into a cover image for the purposes of watermarking. Thus, an image watermarking scheme uses an encrypted image. The secret image is embedded in decomposed frames of the cover image achieved by applying a three-level Discrete Wavelet Transform (DWT). This is to ensure that the secret information is not exposed even when there is a successful attack on the cover information. Content creators can prove ownership of the multimedia content by unveiling the secret information in a court of law. The proposed scheme was tested with sample data using MATLAB2022 and the results of the simulation show a great deal of imperceptibility and robustness as compared to similar existing schemes.展开更多
In microarray-based cancer classification, gene selection is an important issue owing to the large number of variables and small number of samples as well as its non-linearity. It is difficult to get satisfying result...In microarray-based cancer classification, gene selection is an important issue owing to the large number of variables and small number of samples as well as its non-linearity. It is difficult to get satisfying results by using conventional linear sta- tistical methods. Recursive feature elimination based on support vector machine (SVM RFE) is an effective algorithm for gene selection and cancer classification, which are integrated into a consistent framework. In this paper, we propose a new method to select parameters of the aforementioned algorithm implemented with Gaussian kernel SVMs as better alternatives to the common practice of selecting the apparently best parameters by using a genetic algorithm to search for a couple of optimal parameter. Fast implementation issues for this method are also discussed for pragmatic reasons. The proposed method was tested on two repre- sentative hereditary breast cancer and acute leukaemia datasets. The experimental results indicate that the proposed method per- forms well in selecting genes and achieves high classification accuracies with these genes.展开更多
Genetic Algorithm (GA) is a biologically inspired technique and widely used to solve numerous combinational optimization problems. It works on a population of individuals, not just one single solution. As a result, it...Genetic Algorithm (GA) is a biologically inspired technique and widely used to solve numerous combinational optimization problems. It works on a population of individuals, not just one single solution. As a result, it avoids converging to the local optimum. However, it takes too much CPU time in the late process of GA. On the other hand, in the late process Simulated Annealing (SA) converges faster than GA but it is easily trapped to local optimum. In this letter, a useful method that unifies GA and SA is introduced, which utilizes the advantage of the global search ability of GA and fast convergence of SA. The experimental results show that the proposed algorithm outperforms GA in terms of CPU time without degradation of performance. It also achieves highly comparable placement cost compared to the state-of-the-art results obtained by Versatile Place and Route (VPR) Tool.展开更多
Accurate prediction of chemical composition of vacuum gas oil (VGO) is essential for the routine operation of refineries. In this work, a new approach for auto-design of artificial neural networks (ANN) based on a...Accurate prediction of chemical composition of vacuum gas oil (VGO) is essential for the routine operation of refineries. In this work, a new approach for auto-design of artificial neural networks (ANN) based on a genetic algorithm (GA) is developed for predicting VGO saturates. The number of neurons in the hidden layer, the momentum and the learning rates are determined by using the genetic algorithm. The inputs for the artificial neural networks model are five physical properties, namely, average boiling point, density, molecular weight, viscosity and refractive index. It is verified that the genetic algorithm could find the optimal structural parameters and training parameters of ANN. In addition, an artificial neural networks model based on a genetic algorithm was tested and the results indicated that the VGO saturates can be efficiently predicted. Compared with conventional artificial neural networks models, this approach can improve the prediction accuracy.展开更多
The common failure mechanism for brittle rocks is known to be axial splitting which happens parallel to the direction of maximum compression. One of the mechanisms proposed for modelling of axial splitting is the slid...The common failure mechanism for brittle rocks is known to be axial splitting which happens parallel to the direction of maximum compression. One of the mechanisms proposed for modelling of axial splitting is the sliding crack or so called, “wing crack” model. Fairhurst-Cook model explains this specific type of failure which starts by a pre-crack and finally breaks the rock by propagating 2-D cracks under uniaxial compression. In this paper, optimization of this model has been considered and the process has been done by a complete sensitivity analysis on the main parameters of the model and excluding the trends of their changes and also their limits and “peak points”. Later on this paper, three artificial intelligence algorithms including Particle Swarm Intelligence (PSO), Ant Colony Optimization (ACO) and genetic algorithm (GA) has been used and compared in order to achieve optimized sets of parameters resulting in near-maximum or near-minimum amounts of wedging forces creating a wing crack.展开更多
Proper fixture design is crucial to obtain the better product quality according to the design specification during the workpiece fabrication. Locator layout planning is one of the most important tasks in the fixture ...Proper fixture design is crucial to obtain the better product quality according to the design specification during the workpiece fabrication. Locator layout planning is one of the most important tasks in the fixture design process. However, the design of a fixture relies heavily on the designerts expertise and experience up to now. Therefore, a new approach to loeator layout determination for workpieces with arbitrary complex surfaces is pro- posed for the first time. Firstly, based on the fuzzy judgment method, the proper locating reference and locator - numbers are determined with consideration of surface type, surface area and position tolerance. Secondly, the lo- cator positions are optimized by genetic algorithm(GA). Finally, a typical example shows that the approach is su- perior to the experiential method and can improve positioning accuracy effectively.展开更多
In order to derive the linac photon spectrum accurately both the prior constrained model and the genetic algorithm GA are employed using the measured percentage depth dose PDD data and the Monte Carlo simulated monoen...In order to derive the linac photon spectrum accurately both the prior constrained model and the genetic algorithm GA are employed using the measured percentage depth dose PDD data and the Monte Carlo simulated monoenergetic PDDs where two steps are involved.First the spectrum is modeled as a prior analytical function with two parameters αand Ep optimized with the GA.Secondly the linac photon spectrum is modeled as a discretization constrained model optimized with the GA. The solved analytical function in the first step is used to generate initial solutions for the GA’s first run in this step.The method is applied to the Varian iX linear accelerator to derive the energy spectra of its 6 and 15 MV photon beams.The experimental results show that both the reconstructed spectrums and the derived PDDs with the proposed method are in good agreement with those calculated using the Monte Carlo simulation.展开更多
基金Research Supporting Project Number(RSPD2023R 585),King Saud University,Riyadh,Saudi Arabia.
文摘Side lobe level reduction(SLL)of antenna arrays significantly enhances the signal-to-interference ratio and improves the quality of service(QOS)in recent and future wireless communication systems starting from 5G up to 7G.Furthermore,it improves the array gain and directivity,increasing the detection range and angular resolution of radar systems.This study proposes two highly efficient SLL reduction techniques.These techniques are based on the hybridization between either the single convolution or the double convolution algorithms and the genetic algorithm(GA)to develop the Conv/GA andDConv/GA,respectively.The convolution process determines the element’s excitations while the GA optimizes the element spacing.For M elements linear antenna array(LAA),the convolution of the excitation coefficients vector by itself provides a new vector of excitations of length N=(2M−1).This new vector is divided into three different sets of excitations including the odd excitations,even excitations,and middle excitations of lengths M,M−1,andM,respectively.When the same element spacing as the original LAA is used,it is noticed that the odd and even excitations provide a much lower SLL than that of the LAA but with amuch wider half-power beamwidth(HPBW).While the middle excitations give the same HPBWas the original LAA with a relatively higher SLL.Tomitigate the increased HPBWof the odd and even excitations,the element spacing is optimized using the GA.Thereby,the synthesized arrays have the same HPBW as the original LAA with a two-fold reduction in the SLL.Furthermore,for extreme SLL reduction,the DConv/GA is introduced.In this technique,the same procedure of the aforementioned Conv/GA technique is performed on the resultant even and odd excitation vectors.It provides a relatively wider HPBWthan the original LAA with about quad-fold reduction in the SLL.
基金Project(51090385) supported by the Major Program of National Natural Science Foundation of ChinaProject(2011IB001) supported by Yunnan Provincial Science and Technology Program,China+1 种基金Project(2012DFA70570) supported by the International Science & Technology Cooperation Program of ChinaProject(2011IA004) supported by the Yunnan Provincial International Cooperative Program,China
文摘The control design, based on self-adaptive PID with genetic algorithms(GA) tuning on-line was investigated, for the temperature control of industrial microwave drying rotary device with the multi-layer(IMDRDWM) and with multivariable nonlinear interaction of microwave and materials. The conventional PID control strategy incorporated with optimization GA was put forward to maintain the optimum drying temperature in order to keep the moisture content below 1%, whose adaptation ability included the cost function of optimization GA according to the output change. Simulations on five different industrial process models and practical temperature process control system for selenium-enriched slag drying intensively by using IMDRDWM were carried out systematically, indicating the reliability and effectiveness of control design. The parameters of proposed control design are all on-line implemented without iterative predictive calculations, and the closed-loop system stability is guaranteed, which makes the developed scheme simpler in its synthesis and application, providing the practical guidelines for the control implementation and the parameter design.
基金This work was supported in part by the Fundamental Research Funds for the Central Universities(YWF-22-L-1203)the National Natural Science Foundation of China(62173013,62073005)+1 种基金the National Key Research and Development Program of China(2020YFB1712203)U.S.National Science Foundation(CCF-0939370,CCF-1908308).
文摘Swarm intelligence in a bat algorithm(BA)provides social learning.Genetic operations for reproducing individuals in a genetic algorithm(GA)offer global search ability in solving complex optimization problems.Their integration provides an opportunity for improved search performance.However,existing studies adopt only one genetic operation of GA,or design hybrid algorithms that divide the overall population into multiple subpopulations that evolve in parallel with limited interactions only.Differing from them,this work proposes an improved self-adaptive bat algorithm with genetic operations(SBAGO)where GA and BA are combined in a highly integrated way.Specifically,SBAGO performs their genetic operations of GA on previous search information of BA solutions to produce new exemplars that are of high-diversity and high-quality.Guided by these exemplars,SBAGO improves both BA’s efficiency and global search capability.We evaluate this approach by using 29 widely-adopted problems from four test suites.SBAGO is also evaluated by a real-life optimization problem in mobile edge computing systems.Experimental results show that SBAGO outperforms its widely-used and recently proposed peers in terms of effectiveness,search accuracy,local optima avoidance,and robustness.
基金Supported by the Major State Basic Research Development Program of China (2012CB720500)the National Natural Science Foundation of China (Key Program: U1162202)+1 种基金the National Natural Science Foundation of China (General Program:61174118)Shanghai Leading Academic Discipline Project (B504)
文摘In recent years, immune genetic algorithm (IGA) is gaining popularity for finding the optimal solution for non-linear optimization problems in many engineering applications. However, IGA with deterministic mutation factor suffers from the problem of premature convergence. In this study, a modified self-adaptive immune genetic algorithm (MSIGA) with two memory bases, in which immune concepts are applied to determine the mutation parameters, is proposed to improve the searching ability of the algorithm and maintain population diversity. Performance comparisons with other well-known population-based iterative algorithms show that the proposed method converges quickly to the global optimum and overcomes premature problem. This algorithm is applied to optimize a feed forward neural network to measure the content of products in the combustion side reaction of p-xylene oxidation, and satisfactory results are obtained.
文摘In order to solve the problem between searching performance and convergence of genetic algorithms, a fast genetic algorithm generalized self-adaptive genetic algorithm (GSAGA) is presented. (1) Evenly distributed initial population is generated. (2) Superior individuals are not broken because of crossover and mutation operation for they are sent to subgeneration directly. (3) High quality im- migrants are introduced according to the condition of the population schema. (4) Crossover and mutation are operated on self-adaptation. Therefore, GSAGA solves the coordination problem between convergence and searching performance. In GSAGA, the searching per- formance and global convergence are greatly improved compared with many existing genetic algorithms. Through simulation, the val- idity of this modified genetic algorithm is proved.
基金This work was supported by the National Natural Science Foundation of China(62073155,62002137,62106088,62206113)the High-End Foreign Expert Recruitment Plan(G2023144007L)the Fundamental Research Funds for the Central Universities(JUSRP221028).
文摘Evolutionary algorithms(EAs)have been used in high utility itemset mining(HUIM)to address the problem of discover-ing high utility itemsets(HUIs)in the exponential search space.EAs have good running and mining performance,but they still require huge computational resource and may miss many HUIs.Due to the good combination of EA and graphics processing unit(GPU),we propose a parallel genetic algorithm(GA)based on the platform of GPU for mining HUIM(PHUI-GA).The evolution steps with improvements are performed in central processing unit(CPU)and the CPU intensive steps are sent to GPU to eva-luate with multi-threaded processors.Experiments show that the mining performance of PHUI-GA outperforms the existing EAs.When mining 90%HUIs,the PHUI-GA is up to 188 times better than the existing EAs and up to 36 times better than the CPU parallel approach.
文摘Transmission of data over the internet has become a critical issue as a result of the advancement in technology, since it is possible for pirates to steal the intellectual property of content owners. This paper presents a new digital watermarking scheme that combines some operators of the Genetic Algorithm (GA) and the Residue Number (RN) System (RNS) to perform encryption on an image, which is embedded into a cover image for the purposes of watermarking. Thus, an image watermarking scheme uses an encrypted image. The secret image is embedded in decomposed frames of the cover image achieved by applying a three-level Discrete Wavelet Transform (DWT). This is to ensure that the secret information is not exposed even when there is a successful attack on the cover information. Content creators can prove ownership of the multimedia content by unveiling the secret information in a court of law. The proposed scheme was tested with sample data using MATLAB2022 and the results of the simulation show a great deal of imperceptibility and robustness as compared to similar existing schemes.
基金Project supported by the National Basic Research Program (973) of China (No. 2002CB312200) and the Center for Bioinformatics Pro-gram Grant of Harvard Center of Neurodegeneration and Repair,Harvard Medical School, Harvard University, Boston, USA
文摘In microarray-based cancer classification, gene selection is an important issue owing to the large number of variables and small number of samples as well as its non-linearity. It is difficult to get satisfying results by using conventional linear sta- tistical methods. Recursive feature elimination based on support vector machine (SVM RFE) is an effective algorithm for gene selection and cancer classification, which are integrated into a consistent framework. In this paper, we propose a new method to select parameters of the aforementioned algorithm implemented with Gaussian kernel SVMs as better alternatives to the common practice of selecting the apparently best parameters by using a genetic algorithm to search for a couple of optimal parameter. Fast implementation issues for this method are also discussed for pragmatic reasons. The proposed method was tested on two repre- sentative hereditary breast cancer and acute leukaemia datasets. The experimental results indicate that the proposed method per- forms well in selecting genes and achieves high classification accuracies with these genes.
基金Supported by School of Engineering, Napier University, United Kingdom, and partially supported by the National Natural Science Foundation of China (No.60273093).
文摘Genetic Algorithm (GA) is a biologically inspired technique and widely used to solve numerous combinational optimization problems. It works on a population of individuals, not just one single solution. As a result, it avoids converging to the local optimum. However, it takes too much CPU time in the late process of GA. On the other hand, in the late process Simulated Annealing (SA) converges faster than GA but it is easily trapped to local optimum. In this letter, a useful method that unifies GA and SA is introduced, which utilizes the advantage of the global search ability of GA and fast convergence of SA. The experimental results show that the proposed algorithm outperforms GA in terms of CPU time without degradation of performance. It also achieves highly comparable placement cost compared to the state-of-the-art results obtained by Versatile Place and Route (VPR) Tool.
文摘Accurate prediction of chemical composition of vacuum gas oil (VGO) is essential for the routine operation of refineries. In this work, a new approach for auto-design of artificial neural networks (ANN) based on a genetic algorithm (GA) is developed for predicting VGO saturates. The number of neurons in the hidden layer, the momentum and the learning rates are determined by using the genetic algorithm. The inputs for the artificial neural networks model are five physical properties, namely, average boiling point, density, molecular weight, viscosity and refractive index. It is verified that the genetic algorithm could find the optimal structural parameters and training parameters of ANN. In addition, an artificial neural networks model based on a genetic algorithm was tested and the results indicated that the VGO saturates can be efficiently predicted. Compared with conventional artificial neural networks models, this approach can improve the prediction accuracy.
文摘The common failure mechanism for brittle rocks is known to be axial splitting which happens parallel to the direction of maximum compression. One of the mechanisms proposed for modelling of axial splitting is the sliding crack or so called, “wing crack” model. Fairhurst-Cook model explains this specific type of failure which starts by a pre-crack and finally breaks the rock by propagating 2-D cracks under uniaxial compression. In this paper, optimization of this model has been considered and the process has been done by a complete sensitivity analysis on the main parameters of the model and excluding the trends of their changes and also their limits and “peak points”. Later on this paper, three artificial intelligence algorithms including Particle Swarm Intelligence (PSO), Ant Colony Optimization (ACO) and genetic algorithm (GA) has been used and compared in order to achieve optimized sets of parameters resulting in near-maximum or near-minimum amounts of wedging forces creating a wing crack.
基金Supported by the Natural Science Foundation of Jiangxi Province(2009GZC0104)the Science and Technology Research Project of Jiangxi Provincial Department of Education(GJJ10521)~~
文摘Proper fixture design is crucial to obtain the better product quality according to the design specification during the workpiece fabrication. Locator layout planning is one of the most important tasks in the fixture design process. However, the design of a fixture relies heavily on the designerts expertise and experience up to now. Therefore, a new approach to loeator layout determination for workpieces with arbitrary complex surfaces is pro- posed for the first time. Firstly, based on the fuzzy judgment method, the proper locating reference and locator - numbers are determined with consideration of surface type, surface area and position tolerance. Secondly, the lo- cator positions are optimized by genetic algorithm(GA). Finally, a typical example shows that the approach is su- perior to the experiential method and can improve positioning accuracy effectively.
文摘In order to derive the linac photon spectrum accurately both the prior constrained model and the genetic algorithm GA are employed using the measured percentage depth dose PDD data and the Monte Carlo simulated monoenergetic PDDs where two steps are involved.First the spectrum is modeled as a prior analytical function with two parameters αand Ep optimized with the GA.Secondly the linac photon spectrum is modeled as a discretization constrained model optimized with the GA. The solved analytical function in the first step is used to generate initial solutions for the GA’s first run in this step.The method is applied to the Varian iX linear accelerator to derive the energy spectra of its 6 and 15 MV photon beams.The experimental results show that both the reconstructed spectrums and the derived PDDs with the proposed method are in good agreement with those calculated using the Monte Carlo simulation.