To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second...To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second stage impeller guide vanes.Moreover,the impeller blade outlet width,impeller inlet diameter,blade inclination angle,and number of blades were considered for orthogonal tests.Accordingly,nine groups of design solutions were formed,and then used as a basis for the execution of numerical simulations(CFD)aimed at obtaining the efficiency values and heads for each design solution group.The influence of impeller geometric parameters on the efficiency and head was explored,and the“weight”of each factor was obtained via a range analysis.Optimal structural parameters were finally chosen on the basis of the numerical simulation results,and the performances of the optimized model were verified accordingly(yet by means of CFD).Evidence is provided that the increase in the efficiency and head of the optimized model was 12.11%and 23.5 m,respectively,compared with those of the original model.展开更多
Room and pillar sizes are key factors for safe mining and ore recovery in open-stope mining. To investigate the influence of room and pillar configurations on stope stability in highly fractured and weakened areas, an...Room and pillar sizes are key factors for safe mining and ore recovery in open-stope mining. To investigate the influence of room and pillar configurations on stope stability in highly fractured and weakened areas, an orthogonal design with two factors, three levels and nine runs was proposed, followed by three-dimensional numerical simulation using ANSYS and FLAC3~. Results show that surface settlement after excavation is concentrically ringed, and increases with the decrease of pillar width and distances to stope gobs. In the meantime, the ore-control fault at the ore-rock boundary and the fractured argillaceous dolomite with intercalated slate at the hanging wall deteriorate the roof settlement. Additionally, stope stability is challenged due to pillar rheological yield and stress concentration, and both are induced by redistribution of stress and plastic zones after mining. Following an objective function and a constraint function, room and pillar configuration with widths of 14 m and 16 m, respectively, is presented as the optimization for improving the ore recovery rate while maintaining a safe working environment.展开更多
Wind barriers have attracted significant attention as an effective measure to ensure train safety under crosswinds.However,in past decades,the influence of structural parameters such as the height and ventilation rati...Wind barriers have attracted significant attention as an effective measure to ensure train safety under crosswinds.However,in past decades,the influence of structural parameters such as the height and ventilation ratio of wind barriers on the difference of the average pressure coefficient between the train windward and leeward surface(ΔCp)has not been fully investigated.To determine the influence of the interaction among the three factors,namely the wind barrier height(H),ventilation ratio(R),and distance to the train(D),twenty five numerical simulation cases with different structural parameters were considered based on an orthogonal design.The shear stress transfer(SST)k-ωturbulent model was employed to calculate the wind pressure coefficients,and the calculation accuracy was validated by using wind tunnel experiments.The results indicated that with an increase in R,ΔCp first decreased and then increased,andΔCp decreased while D increased.Moreover,with the increase in H,ΔCp first increased and then decreased.Therefore,these three factors must be considered during the installation of wind barriers.Furthermore,according to a range analysis(judging the relative importance of the three factors intuitively),the three factors were ranked in the following order:R>H>D.Based on a variance analysis,R was found to be of high significance toΔCp,followed by H,which was significant,whereas D had relatively insignificant influence.Finally,the optimal values of R and H were determined to be 20%and 110 mm,respectively.And when R=40%,H=85 mm,the train was relatively unsafe under these such conditions.The findings of this study provide significant guidance for the structural design of wind barriers.展开更多
In this paper, we show the construction of orthogonal wavelet basis on the interval [0, 1],using compactly supportted Daubechies function. Forwardly, we suggest a kind of method to deal with the differential operator ...In this paper, we show the construction of orthogonal wavelet basis on the interval [0, 1],using compactly supportted Daubechies function. Forwardly, we suggest a kind of method to deal with the differential operator in view of numerical analysis and derive the appoximation algorithm of wavelet ba-sis and differential operator, which affects on the basis, to functions belonging to L2 [0, 1 ]. Numerical computation indicate the stability and effectiveness of the algorithm.展开更多
A prototype centrifugal pump with a specific speed of 110 is used to investigate and optimize the performances of a turbine for power generation.Particular attention is given to the design of the internal impeller.The...A prototype centrifugal pump with a specific speed of 110 is used to investigate and optimize the performances of a turbine for power generation.Particular attention is given to the design of the internal impeller.The internal flow field is simulated in the framework of a commercial computational fluid dynamics software(ANSYS).Four geometrical parameters of the impeller are considered,i.e.,the inlet diameter,the inlet width,the blade number,and the blade angle.The optimization is carried out on the basis of a three-level approach relying on an orthogonal test method.The results of the numerical simulations show good agreement with the experimental tests under different flow conditions.In accordance with the L9(34)design table,the head and efficiency under the rated flow rate of the nine designed schemes are calculated and processed with the method of range analysis to obtain an optimized model.展开更多
Being aimed at the ground subsidence due to underground coal mining,a numerical model of rock was established and an appropriate method of numerical simulation was put forward.Using the measured subsidence data on the...Being aimed at the ground subsidence due to underground coal mining,a numerical model of rock was established and an appropriate method of numerical simulation was put forward.Using the measured subsidence data on the ground,the equivalent mechanical parameters of the rock stratums can be back-calculated by the properly treatment of coal excavation area,then the ground subsidence of other coal mining area can be predicted by FFM.It provided reference for the treatment of the buildings on the ground of this colliery.展开更多
During the compaction of a road subgrade, the mechanical parameters of the soil mass change in real time, but current research assumes that these parameters remain unchanged. In order to address this discrepancy, this...During the compaction of a road subgrade, the mechanical parameters of the soil mass change in real time, but current research assumes that these parameters remain unchanged. In order to address this discrepancy, this paper establishes a relationship between the degree of compaction K and strain ε. The relationship between the compaction degree K and the shear strength of soil(cohesion c and frictional angle φ) was clearly established through indoor experiments. The subroutine UMAT in ABAQUS finite element numerical software was developed to realize an accurate calculation of the subgrade soil compaction quality. This value was compared and analyzed against the assumed compaction value of the model, thereby verifying the accuracy of the intelligent compaction calculation results for subgrade soil. On this basis, orthogonal tests of the influential factors(frequency, amplitude, and quality) for the degree of compaction and sensitivity analysis were carried out. Finally, the ‘acceleration intelligent compaction value’, which is based on the acceleration signal, is proposed for a compaction meter value that indicates poor accuracy. The research results can provide guidance and basis for further research into the accurate control of compaction quality for roadbeds and pavements.展开更多
The inverse heat conduction method is one of methods to identify the casting simulation parameters. A new inverse method was presented according to the Tikhonov regularization theory. One appropriate regularized funct...The inverse heat conduction method is one of methods to identify the casting simulation parameters. A new inverse method was presented according to the Tikhonov regularization theory. One appropriate regularized functional was established, and the functional was solved by the sensitivity coefficient and Newtonaphson iteration method. Moreover, the orthogonal experimental design was used to estimate the appropriate initial value and variation domain of each variable to decrease the number of iteration and improve the identification accuracy and efficiency. It illustrated a detailed case of AlSiTMg sand mold casting and the temperature measurement experiment was done. The physical properties of sand mold and the interracial heat transfer coefficient were identified at the meantime. The results indicated that the new regularization method was efficient in overcoming the ill-posedness of the inverse heat conduction problem and improving the stability and accuracy of the solutions.展开更多
As a typical laser additive manufacturing technology,laser powder bed fusion(LPBF)has achieved demonstration applications in aerospace,biomedical and other fields.However,how to select process parameters quickly and r...As a typical laser additive manufacturing technology,laser powder bed fusion(LPBF)has achieved demonstration applications in aerospace,biomedical and other fields.However,how to select process parameters quickly and reasonably is still themain concern of LPBF production.In order to quantitatively analyze the influence of different process parameters(laser power,scanning speed,hatch space and layer thickness)on the LPBF process,the multilayer and multi-path forming process of LPBF was predicted based on the open-source discrete element method framework Yade and the open-source finite volume method framework OpenFOAM.Based on the design of experiments method,a four-factor three-level orthogonal test scheme was designed,and the porosity and surface roughness data of each calculation scheme were extracted.By analyzing the orthogonal test data,it was found that as the laser power increased,the porosity decreased,and as the scanning speed,hatch space,and layer thickness increased,the porosity increased.In addition,the influence of laser power and scanning speed on surface roughness showed a trend of decreasing first and then increasing,while the influence of scanning distance and layer thickness on surface roughness showed amonotonous increasing trend.The order of the influence of each process parameter on porosity was:scanning speed>laying thickness>laser power>hatch space,and the order of the influence of each process parameter on surface roughness was:hatch space>layer thickness>laser power>scanning speed.So the porosity of the part is most sensitive to scanning speed,and the surface roughness is the most sensitive to hatch space.The above conclusions are expected to provide process control basis for actual LPBF production of the 316L stainless steel alloy.展开更多
This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild slope equation in the orthogonal coordinate system. Two types of coordinate systems are stud...This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild slope equation in the orthogonal coordinate system. Two types of coordinate systems are studied: (a) a general form of orthogonal coordinate system and (b) the conformal system, a special form of orthogonal coordinate system. Two typical examples, namely, expanded breakwaters and a circular channel, are studied to validate the model. First, the examples are studied by use of the general orthogonal coordinates. Then the same examples are computed by use of the conformal system. The computational results show that the conformal coordinate system generally gives better predictions than the general orthogonal system. A numerical technique for generating the conformal grid is combined with the numerical model to improve the practicability of the model. The comparison between the result from the numerical grid system and that from the analytical grid system shows that reliable computational results can be obtained by use of the numerical conformal grid system.展开更多
The diagonal Pade' approximates for exp(x). tanx and tanhx are obtained in asimple manner by using the property of Legendre polynomials that on [ -1, 1] Pn (x)is orthogonal to every polynomial of lower degree. Gau...The diagonal Pade' approximates for exp(x). tanx and tanhx are obtained in asimple manner by using the property of Legendre polynomials that on [ -1, 1] Pn (x)is orthogonal to every polynomial of lower degree. Gauss's quadrature formula is used tofined the denomiators of some functions.展开更多
A biconical liner was optimized to improve its penetration ability. Its formation and pene- tration mechanism was studied through numerical simulation and experiments. And the influence of different liner geometry siz...A biconical liner was optimized to improve its penetration ability. Its formation and pene- tration mechanism was studied through numerical simulation and experiments. And the influence of different liner geometry sizes on the jet performance was analyzed using the orthogonal method. The liner formed the high-speed jet with an explosively formed projectile. The small angle 2a remarkably influenced the jet speed which was inversely proportional to 2a. And the liner thickness t' and large angle 2β had highly significant effect on the projectile speed. The liner was optimized at t' = 0. 14 cm, 2α = 50°, 2β = 135°, N = 0. 4 or 0. 5, when its jet speed respectively is at 6 613 m/s and 6 839 m/s and projectile speed is at 2 247 m/s and 2 095 m/s, steel target penetration is at 8. 24 cm and 8. 31 cm, and aperture is in 2.12 cm and 2.08 cm. The results show that target is penetrated by the high-speed jet and high-speed projectile resulting into double damages. The penetration ability is improved greatly.展开更多
An iron and steel company' s hot galvanizing technology was chosen as the object. An orthogonal experimental scheme with 5 factors of mixed level was designed, according to the various factors affecting the distribut...An iron and steel company' s hot galvanizing technology was chosen as the object. An orthogonal experimental scheme with 5 factors of mixed level was designed, according to the various factors affecting the distribution of slag. For each scheme, the amount of slag and slag height in different orthogonal schemes by simulation were obtained with FLUENT software. Then, range and variance analyses were selected to compare the trend of slag height in the different process parameters of the hot dip galvanizing process. Finally, the optimal combination of the process parameters was obtained.展开更多
In this paper we present a generalized perturbative approximate series expansion in terms of non-orthogonal component functions. The expansion is based on a perturbative formulation where, in the non-orthogonal case, ...In this paper we present a generalized perturbative approximate series expansion in terms of non-orthogonal component functions. The expansion is based on a perturbative formulation where, in the non-orthogonal case, the contribution of a given component function, at each point, in the time domain or frequency in the Fourier domain, is assumed to be perturbed by contributions from the other component functions in the set. In the case of orthogonal basis functions, the formulation reduces to the non-perturbative case approximate series expansion. Application of the series expansion is demonstrated in the context of two non-orthogonal component function sets. The technique is applied to a series of non-orthogonalized Bessel functions of the first kind that are used to construct a compound function for which the coefficients are determined utilizing the proposed approach. In a second application, the technique is applied to an example associated with the inverse problem in electrophysiology and is demonstrated through decomposition of a compound evoked potential from a peripheral nerve trunk in terms of contributing evoked potentials from individual nerve fibers of varying diameter. An additional application of the perturbative approximation is illustrated in the context of a trigonometric Fourier series representation of a continuous time signal where the technique is used to compute an approximation of the Fourier series coefficients. From these examples, it will be demonstrated that in the case of non-orthogonal component functions, the technique performs significantly better than the generalized Fourier series which can yield nonsensical results.展开更多
基金National Key R&D Program of China(Grant No.2020YFC1512404).
文摘To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second stage impeller guide vanes.Moreover,the impeller blade outlet width,impeller inlet diameter,blade inclination angle,and number of blades were considered for orthogonal tests.Accordingly,nine groups of design solutions were formed,and then used as a basis for the execution of numerical simulations(CFD)aimed at obtaining the efficiency values and heads for each design solution group.The influence of impeller geometric parameters on the efficiency and head was explored,and the“weight”of each factor was obtained via a range analysis.Optimal structural parameters were finally chosen on the basis of the numerical simulation results,and the performances of the optimized model were verified accordingly(yet by means of CFD).Evidence is provided that the increase in the efficiency and head of the optimized model was 12.11%and 23.5 m,respectively,compared with those of the original model.
基金Projects(50934002,51074013,51104100)supported by the National Natural Science Foundation of ChinaProject(IRT0950)supported by the Program for Changjiang Scholars and Innovative Research Team in University of China
文摘Room and pillar sizes are key factors for safe mining and ore recovery in open-stope mining. To investigate the influence of room and pillar configurations on stope stability in highly fractured and weakened areas, an orthogonal design with two factors, three levels and nine runs was proposed, followed by three-dimensional numerical simulation using ANSYS and FLAC3~. Results show that surface settlement after excavation is concentrically ringed, and increases with the decrease of pillar width and distances to stope gobs. In the meantime, the ore-control fault at the ore-rock boundary and the fractured argillaceous dolomite with intercalated slate at the hanging wall deteriorate the roof settlement. Additionally, stope stability is challenged due to pillar rheological yield and stress concentration, and both are induced by redistribution of stress and plastic zones after mining. Following an objective function and a constraint function, room and pillar configuration with widths of 14 m and 16 m, respectively, is presented as the optimization for improving the ore recovery rate while maintaining a safe working environment.
基金Project(51822803)supported by the National Natural Science Foundation of ChinaProject(2019JJ50688)supported by Hunan Provincial Natural Science Foundation,China+1 种基金Project(kq1905005)supported by Training Program for Excellent Young Innovators of Changsha,ChinaProject(CX20210775)supported by Hunan Provincial Innovative Foundation for Postgraduates,China。
文摘Wind barriers have attracted significant attention as an effective measure to ensure train safety under crosswinds.However,in past decades,the influence of structural parameters such as the height and ventilation ratio of wind barriers on the difference of the average pressure coefficient between the train windward and leeward surface(ΔCp)has not been fully investigated.To determine the influence of the interaction among the three factors,namely the wind barrier height(H),ventilation ratio(R),and distance to the train(D),twenty five numerical simulation cases with different structural parameters were considered based on an orthogonal design.The shear stress transfer(SST)k-ωturbulent model was employed to calculate the wind pressure coefficients,and the calculation accuracy was validated by using wind tunnel experiments.The results indicated that with an increase in R,ΔCp first decreased and then increased,andΔCp decreased while D increased.Moreover,with the increase in H,ΔCp first increased and then decreased.Therefore,these three factors must be considered during the installation of wind barriers.Furthermore,according to a range analysis(judging the relative importance of the three factors intuitively),the three factors were ranked in the following order:R>H>D.Based on a variance analysis,R was found to be of high significance toΔCp,followed by H,which was significant,whereas D had relatively insignificant influence.Finally,the optimal values of R and H were determined to be 20%and 110 mm,respectively.And when R=40%,H=85 mm,the train was relatively unsafe under these such conditions.The findings of this study provide significant guidance for the structural design of wind barriers.
文摘In this paper, we show the construction of orthogonal wavelet basis on the interval [0, 1],using compactly supportted Daubechies function. Forwardly, we suggest a kind of method to deal with the differential operator in view of numerical analysis and derive the appoximation algorithm of wavelet ba-sis and differential operator, which affects on the basis, to functions belonging to L2 [0, 1 ]. Numerical computation indicate the stability and effectiveness of the algorithm.
基金This work was supported by the National Natural Science Foundation of China under Grant 51605200the Senior Talent Start-up Foundation of Jiangsu University under Grant 14JDG145.
文摘A prototype centrifugal pump with a specific speed of 110 is used to investigate and optimize the performances of a turbine for power generation.Particular attention is given to the design of the internal impeller.The internal flow field is simulated in the framework of a commercial computational fluid dynamics software(ANSYS).Four geometrical parameters of the impeller are considered,i.e.,the inlet diameter,the inlet width,the blade number,and the blade angle.The optimization is carried out on the basis of a three-level approach relying on an orthogonal test method.The results of the numerical simulations show good agreement with the experimental tests under different flow conditions.In accordance with the L9(34)design table,the head and efficiency under the rated flow rate of the nine designed schemes are calculated and processed with the method of range analysis to obtain an optimized model.
文摘Being aimed at the ground subsidence due to underground coal mining,a numerical model of rock was established and an appropriate method of numerical simulation was put forward.Using the measured subsidence data on the ground,the equivalent mechanical parameters of the rock stratums can be back-calculated by the properly treatment of coal excavation area,then the ground subsidence of other coal mining area can be predicted by FFM.It provided reference for the treatment of the buildings on the ground of this colliery.
基金Project(51878164) supported by the National Natural Science Foundation of ChinaProjects(BK20161421, BK20140109) supported by the Natural Science Foundation of Jiangsu Province, China+4 种基金Project(141076) supported by the Huoyingdong Foundation of the Ministry of Education of ChinaProject(BZ2017011) supported by the Science and Technology Support Project of Jiangsu Province, ChinaProject(2242015R30027) supported by the Fundamental Research Funds for the Central Universities, ChinaProject(grant number KFJ170106) supported by the Changsha University of Science & Technology via Open Fund of National Engineering Laboratory of Highway Maintenance Technology, ChinaProject(2018B51) supported by the Science and Technology Support Project of Qilu Transportation Development Group, China。
文摘During the compaction of a road subgrade, the mechanical parameters of the soil mass change in real time, but current research assumes that these parameters remain unchanged. In order to address this discrepancy, this paper establishes a relationship between the degree of compaction K and strain ε. The relationship between the compaction degree K and the shear strength of soil(cohesion c and frictional angle φ) was clearly established through indoor experiments. The subroutine UMAT in ABAQUS finite element numerical software was developed to realize an accurate calculation of the subgrade soil compaction quality. This value was compared and analyzed against the assumed compaction value of the model, thereby verifying the accuracy of the intelligent compaction calculation results for subgrade soil. On this basis, orthogonal tests of the influential factors(frequency, amplitude, and quality) for the degree of compaction and sensitivity analysis were carried out. Finally, the ‘acceleration intelligent compaction value’, which is based on the acceleration signal, is proposed for a compaction meter value that indicates poor accuracy. The research results can provide guidance and basis for further research into the accurate control of compaction quality for roadbeds and pavements.
文摘The inverse heat conduction method is one of methods to identify the casting simulation parameters. A new inverse method was presented according to the Tikhonov regularization theory. One appropriate regularized functional was established, and the functional was solved by the sensitivity coefficient and Newtonaphson iteration method. Moreover, the orthogonal experimental design was used to estimate the appropriate initial value and variation domain of each variable to decrease the number of iteration and improve the identification accuracy and efficiency. It illustrated a detailed case of AlSiTMg sand mold casting and the temperature measurement experiment was done. The physical properties of sand mold and the interracial heat transfer coefficient were identified at the meantime. The results indicated that the new regularization method was efficient in overcoming the ill-posedness of the inverse heat conduction problem and improving the stability and accuracy of the solutions.
基金supported by the Natural Science Foundation of Guangdong Province(No.2019A1515012040).
文摘As a typical laser additive manufacturing technology,laser powder bed fusion(LPBF)has achieved demonstration applications in aerospace,biomedical and other fields.However,how to select process parameters quickly and reasonably is still themain concern of LPBF production.In order to quantitatively analyze the influence of different process parameters(laser power,scanning speed,hatch space and layer thickness)on the LPBF process,the multilayer and multi-path forming process of LPBF was predicted based on the open-source discrete element method framework Yade and the open-source finite volume method framework OpenFOAM.Based on the design of experiments method,a four-factor three-level orthogonal test scheme was designed,and the porosity and surface roughness data of each calculation scheme were extracted.By analyzing the orthogonal test data,it was found that as the laser power increased,the porosity decreased,and as the scanning speed,hatch space,and layer thickness increased,the porosity increased.In addition,the influence of laser power and scanning speed on surface roughness showed a trend of decreasing first and then increasing,while the influence of scanning distance and layer thickness on surface roughness showed amonotonous increasing trend.The order of the influence of each process parameter on porosity was:scanning speed>laying thickness>laser power>hatch space,and the order of the influence of each process parameter on surface roughness was:hatch space>layer thickness>laser power>scanning speed.So the porosity of the part is most sensitive to scanning speed,and the surface roughness is the most sensitive to hatch space.The above conclusions are expected to provide process control basis for actual LPBF production of the 316L stainless steel alloy.
文摘This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild slope equation in the orthogonal coordinate system. Two types of coordinate systems are studied: (a) a general form of orthogonal coordinate system and (b) the conformal system, a special form of orthogonal coordinate system. Two typical examples, namely, expanded breakwaters and a circular channel, are studied to validate the model. First, the examples are studied by use of the general orthogonal coordinates. Then the same examples are computed by use of the conformal system. The computational results show that the conformal coordinate system generally gives better predictions than the general orthogonal system. A numerical technique for generating the conformal grid is combined with the numerical model to improve the practicability of the model. The comparison between the result from the numerical grid system and that from the analytical grid system shows that reliable computational results can be obtained by use of the numerical conformal grid system.
文摘The diagonal Pade' approximates for exp(x). tanx and tanhx are obtained in asimple manner by using the property of Legendre polynomials that on [ -1, 1] Pn (x)is orthogonal to every polynomial of lower degree. Gauss's quadrature formula is used tofined the denomiators of some functions.
基金Supported by the National Natural Science Foundation of China(51174183)the Anhui Natural Science Foundation of China(1508085ME85)
文摘A biconical liner was optimized to improve its penetration ability. Its formation and pene- tration mechanism was studied through numerical simulation and experiments. And the influence of different liner geometry sizes on the jet performance was analyzed using the orthogonal method. The liner formed the high-speed jet with an explosively formed projectile. The small angle 2a remarkably influenced the jet speed which was inversely proportional to 2a. And the liner thickness t' and large angle 2β had highly significant effect on the projectile speed. The liner was optimized at t' = 0. 14 cm, 2α = 50°, 2β = 135°, N = 0. 4 or 0. 5, when its jet speed respectively is at 6 613 m/s and 6 839 m/s and projectile speed is at 2 247 m/s and 2 095 m/s, steel target penetration is at 8. 24 cm and 8. 31 cm, and aperture is in 2.12 cm and 2.08 cm. The results show that target is penetrated by the high-speed jet and high-speed projectile resulting into double damages. The penetration ability is improved greatly.
文摘An iron and steel company' s hot galvanizing technology was chosen as the object. An orthogonal experimental scheme with 5 factors of mixed level was designed, according to the various factors affecting the distribution of slag. For each scheme, the amount of slag and slag height in different orthogonal schemes by simulation were obtained with FLUENT software. Then, range and variance analyses were selected to compare the trend of slag height in the different process parameters of the hot dip galvanizing process. Finally, the optimal combination of the process parameters was obtained.
文摘In this paper we present a generalized perturbative approximate series expansion in terms of non-orthogonal component functions. The expansion is based on a perturbative formulation where, in the non-orthogonal case, the contribution of a given component function, at each point, in the time domain or frequency in the Fourier domain, is assumed to be perturbed by contributions from the other component functions in the set. In the case of orthogonal basis functions, the formulation reduces to the non-perturbative case approximate series expansion. Application of the series expansion is demonstrated in the context of two non-orthogonal component function sets. The technique is applied to a series of non-orthogonalized Bessel functions of the first kind that are used to construct a compound function for which the coefficients are determined utilizing the proposed approach. In a second application, the technique is applied to an example associated with the inverse problem in electrophysiology and is demonstrated through decomposition of a compound evoked potential from a peripheral nerve trunk in terms of contributing evoked potentials from individual nerve fibers of varying diameter. An additional application of the perturbative approximation is illustrated in the context of a trigonometric Fourier series representation of a continuous time signal where the technique is used to compute an approximation of the Fourier series coefficients. From these examples, it will be demonstrated that in the case of non-orthogonal component functions, the technique performs significantly better than the generalized Fourier series which can yield nonsensical results.