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    • 专利摘要:

    公开号:NL2003432A
    申请号:NL2003432
    申请日:2009-09-03
    公开日:2010-04-02
    发明作者:Franz Schreier；Adrian Doicu
    申请人:Deutsch Zentr Luft & Raumfahrt；
    IPC主号:
    专利说明:

    METHOD FOR DETERMINING CONCENTRATION, PRESSURE AND TEMPERATURE PROFILES IN ANY, PREFERRED GAS MEDIA
    The invention relates to a method for determining concentration, pressure and temperature profiles in arbitrary, preferably gaseous, media by contactless spectrometric radiation measurements, wherein a series of spectra in arbitrary spectra ranges are measured and simultaneously with respect to a "Global Fit" in a Compensation calculation method is evaluated, while the measuring vectors corresponding to an individual spectrum are combined into a total measuring vector.
    Measuring the state of the gaseous media, characterized by pressure, temperature, composition and the like, including their spatial distribution and variability over time, is one of the common scientific, industrial and governmental objectives.
    Temperature is a central variable of the earth's atmosphere and knowledge of the spatial temperature distribution (height, length and width) on the earth is an essential requirement for the numerical weather forecast. Analogously applies to pressure and water vapor. Furthermore, gathering the spatial distribution of trace gases and their development over time is an essential objective of atmospheric research (climate change, stratospheric ozone reduction, etc.) and meteorology.
    Determining the exhaust gases from combustion processes and also other chemical processes is important for the control and optimization of the respective devices or engines or aircraft drives (efficiency) and the observation with regard to undesired or prohibited components (exhaust gas regulations, emission safety requirements, etc.) ). Combustion products are often harmful to the environment and / or to health, and their registration is therefore of great importance for (health, environmental, ...) government as well as for research. The gas temperature is often of a decisive magnitude, since it influences both the efficiency of the combustion processes and also the composition of the exhaust gas.
    The measurement methods used can essentially be divided into two major classes, namely sampling and non-contact distance measurement methods.
    In the case of measurements by sampling, a sample is withdrawn from a defined space within the medium to be examined and subsequently the composition is analyzed, for example by gas chromatography or mass spectrometry. Pressure and / or temperature measurements are performed by corresponding sensors directly at the relevant room. A good spatial resolution can be obtained by scanning the medium as closely as possible.
    However, measurement methods through sampling are bound to all kinds of disadvantages. Sampling is time-consuming and expensive. Moreover, sampling methods are often gas-specific. A measurement with high spatial resolution of time-variable media can only be achieved by the simultaneous use of a plurality of sampling sensors. Falsifications of the gas medium by sampling can be avoided. In any case, changes in the medium must be taken into account, for example due to turbulence. In the case of an unstable gas, the composition must be determined immediately after or during sampling. Measurement methods by sampling are moreover not suitable for measuring in areas that are difficult or inaccessible, for example in very hot gases or in the medium to high atmosphere of earth.
    In addition to measuring methods by sampling, contactless measuring methods with distance measurement have been established, which are based on the measurement of gas-emitted and / or random electromagnetic radiation in the microwave, infrared, visible or ultraviolet spectral region. With suitable choice of the spectral region and the spectral resolution and also the measuring geometry, the spectrometric radiation measurement of the spatially resolved determination of pressure p, temperature T and gas concentration p (also more inhomogenous) of media of any composition is possible. Infrared spectroscopic measuring methods are particularly suitable for hot gases, because the interesting gases here have significant spectral absorption properties on the one hand, and also show strong thermal emissions at higher temperatures on the other.
    In atmospheric research, the distance measurement with spectroscopic methods facilitated by satellites counts as the most important method for determining the spatial pressure, temperature, gas concentration or aero-sol distribution. Compared to nadir reflecting sensors, horizontal probing sensors, so-called Limb-Sounder, have some substantial advantages. FIG. 1 shows in a schematic view the geometry of the atmospheric distance measurement by a horizontal probing instrument (Limb Sounder), which is arranged on a satellite orbiting the earth. Since the radiation (in absorption against the sun or in emission) is measured for a series of lines of sight tangential to the earth (Line of Sight), it allows a substantially higher vertical resolution, which is mainly due to the vertical distance of the tangential points and the finite magnitude of the field of view of the spectrometers (Field of View, FoV). On the basis of the lines of sight running horizontally through the earth's atmosphere, in comparison with a vertical probe, substantially longer-extending orbits result in the high range immediately above the tangent points. As a result, species with very small concentrations can also be measured. In FIG. 1, the earth radius is indicated by Re.
    Non-contact measurement methods of infrared spectroscopy have also proven themselves for examining exhaust gases, in particular jet drives or turbines. These make it possible to determine the exhaust gas component and, therefore, gases such as CO2, CO, NO2, SO2, H2O and also unburned hydrocarbons, particles or soot. For tomographic investigations of the spatial distribution of the exhaust gases and also of pressure and temperature, several measurements are required, whereby spectra are considered for a series of sight lines (preferably perpendicular to the exhaust gas jet). Here, the measurements can be carried out for a series of parallel shifted lines of sight, if applicable also in two directions perpendicular to each other, or for a series of lines of sight, which the exhaust gas jet at different viewing angles comparable to the horizontal axis of the earth atmosphere.
    FIG. 2 shows a schematic representation of the tomographic exhaust gas jet measurement through a series of parallel lines of sight. The direction of the exhaust gas jet, which does not necessarily have to be exactly circular in cross-section, is perpendicular to the drawing plane.
    FIG. 3 shows a schematic representation of the tomographic exhaust gas jet measurement through a series of differently oriented sight lines. The direction of the exhaust gas jet, which here also does not necessarily have to be exactly circular in cross-section, is here also perpendicular to the drawing plane.
    The so-called inversion, that is to say the analysis of the series of measured spectra for determining pressure, temperature, gas concentration and aerosol profiles, is based both on the scope of the atmospheric investigation and also on the scope of the investigation of exhaust gases. , as a rule on generally non-linear least squares fits (GauS compensating methods of the least error squares). In the remote atmospheric research, the so-called Onion-Peeling method, or sequential analysis of the spectra, starting with the outer spectra (i.e. the highest tangential point), is followed as much as possible by a simultaneous analysis of the spectra. Such a so-called "Global Fit" can also be laid down for analysis on the exhaust gas measurements.
    The following considerations concerning the state of the art are formulated in particular in the context of the horizontal sounding remote atmospheric investigation and can be applied to tomographic exhaust gas investigations in a technically known manner; the variable "tangential height" or viewing angle is correspondingly by displacement or angle, similar to FIG. 2 and FIG. 3, to be replaced.
    The analysis is based on the theory of radiation transport in gaseous media. When omitting the distribution (aerosols and scattering are irrelevant for further discussion and are therefore omitted in the following), the jet density (intensity) I observed by an observer at the site is described by the integral form of the Schwarzschild equation :

    Here, τ the transmission as a function of the wave number v, B (v, T) is the Planck function for temperature T, p, the pressure, kg and pg, the absorption cross-section and the particle density of the g-ste gas, and s' the trajectory coordinates along the line of sight rays. The sum in equation (2) spans all absorbed gases. To take into account instrumental effects, a suitable instrumental line profile function can be folded in the technically known manner. In an analogous manner, folding also includes the effect of the finite size of the instrumental field of view.
    With horizontally sounding sensors, instruments that measure in absorption (for example against the sun), as well as instruments that measure the self-emission of the atmosphere are common. Without limiting the generality, only the emission spectroscopy is dealt with below; in the case of the absorption spectroscopy only in equation (3) and the following equations is the vector of the measured intensity i (obs) and the (according to equation (1)) modulated intensity i ^ mod * by corresponding vectors (with bold typeface on data) for the measured and modulated transmission (according to equation (2)).
    Without limiting the generality, it will be assumed in the following that only one profile, for example the temperature or concentration of a gas, can be determined and all other profiles are known. The generalization in the case of several unknown profiles takes place in technically known ways.
    The profile to be determined by the measurement is in the simplest case a continuous function of the height z (relative to, for example, on the earth's surface), in the general case also a function of the geographical length and width. Without limiting the generality, length and width are omitted in the following. It follows, inter alia, that the atmospheric profiles p (s), T (s), p (s) occurring in the equations (1) and (2) as a function of the trajectory coordinates s can be clearly described as a function of the height z to be.
    Since only one finite number of parameters can be determined from one measurement, the unknown profile f (z) is discretized in a technically known manner, for example by applying a quadratisation method to calculate the weighing integral in the equations (1) and (2) ), so approximately
    or by developing into a suitable function system
    The n-dimensional parameter vector x representing the unknown profile f (z) is thus formed from the function values Xj = f (Zj) at the quadratisation nodes Zj or from the development coefficients Xj of the function development.
    For a discrete wave number (or frequency) Vi,. . in the measured spectrum
    by suitable variation of the parameter vectors x to be determined, a spectrum i (mod) modulated in accordance with equation (1) is changed such that the standard of the m-dimensional residue vectors is minimal:
    (3)
    Since the spectrum generally depends on the parameter vector x (or the profile represented by x) in a non-linear manner, this non-linear least squares problem is solved in a technically known manner by, for example, GauË-Newton or Levenberg-Marquardt. methods solved.
    In the case of horizontal subsidence, a complete measurement consists of a series of several spectra measured for various tangential heights
    On the basis of the error propagation unavoidable in the sequential analysis of such a measurement series (Onion Peeling), the simultaneous analysis of the spectra (Global Fit) results in the measurement vectors corresponding to the individual spectra of the length mi to become a total vector
    (4) of the length M = mi + ... + mL merged. Without limiting the generality, all spectra will have the same number of measurement points, so mi = m2 = ... = mL = m and also M = L * m. An analog model vector is formed and the unknown parameter vector x is generalized by comparison (3)
    (5) determined by a generally non-linear least squares fit.
    There are a number of drawbacks to the previously noted, currently applied methods for gas profile analysis: a) Inaccurate measurement geometry (angle, height,...).
    As explained above in connection with the state of the art considerations, a single measured value in the horizontal subsidence is a function of two variables, namely of the wave number v and the tangential height ht (respectively the angle of rise of the sensor). It is noted at this point that in the next section the tangential height is written with "t" as super script, when a loop index 1 is additionally required.
    In contrast to the wave numbers, the tangential height can only be determined with limited accuracy. The profiles derived from the measurements are therefore sometimes shifted in height or distorted. For this reason, when analyzing a horizontal subsidence measurement, it is often customary to also determine the tangential height from the measured spectra by least squares. The unknown parameter vector of the profile is thereby supplemented to
    and the minimization problem cited in the equation (5) correspondingly generalized. However, this results in a poorer conditioning number of the Jacobi-Matrix (linear dependence on the column vectors). This approach also ignores the distinctive nature of the independent variable wave number and tangential height.
    b) Consistency between the individual spectra
    With "Global Fit" methods, the individual elements of the total measuring vectors are considered to be independent of each other, that is, the m x L measured intensity values are considered as function independent measuring points.
    considered. Relations between the measuring points are thereby ignored, so for example functional coherence between the intensity of a certain wave number,
    In reality, however, it can be considered as a matrix with "matrix" independent variables and corresponding matrix dependent variables, similar to the equations (17) and (18) indicated later.
    c) Poorly arranged inversion problem
    Inverse problems, such as the determination of profiles from spectroscopic measurements, are often "poorly arranged", that is, in particular, that small changes of the measurement vectors lead to strong changes of the solution vectors. Standard solution methods of the least squares problem usually give physically "nonsense" solutions, for example negative temperatures and gas concentrations or highly oscillating profiles (their discretized representations respectively).
    d) Derivation to tangential height not analytical
    When solving a non-linear least squares problem such as in equations (3) or (5), the partial derivations of the model function to the components of the parameter vectors x to be determined are required (Jacobi matrix, in the case of the simple least squares fits of the equation (3), thus an mx n-matrix). While the leads to pressure, temperature or gas concentrations (especially the leads to the components of their discrete display vectors x) can easily be calculated from the analytical representation of the model spectra according to equations (1) and (2), the leads to the tangential heights are only extremely complex to be determined analytically and as a result are usually finite differentials
    (6) determined. However, the calculation of distractions due to malfunction is very time-consuming and error-prone. Moreover, since a faulty or inaccurate Jacobi matrix negatively influences the convergence behavior of the optimization problem, it leads to a further delay and, under certain circumstances, the fit does not converge.
    On the basis of the aforementioned disadvantages, "standard methods" lead to measurement of temperature, pressure and / or concentration distributions of gaseous media at increased computing power leading to poorer results, i.e., inaccuracies associated with forged spatial allocation.
    A standard method for the purpose of quantitative analysis of gas volumes, in particular of exhaust gases from combustion devices, by means of emission or absorption spectroscopy in a random spectral range is also known from EP 0.959.341 BI. A geometrically defined and reproducibly adjustable observation surface is defined here, which is each time perpendicular to the exhaust gas blast axis and along this axis. In a first measurement series, a number of a spectral measurements are carried out, the optical axis of a spectrometer always being in the relevant observation plane, but from one measurement to the next being moved in parallel over a first distance. In a second series of measurements, b measurements are then carried out, the optical axis, this time positioned perpendicular to the aforementioned optical axis, again lying in the observation plane and being displaced parallel to each other by a second distance from measurement to measurement. As a result of the placement of the optical axis in the observation plane, the (a + b) measurements result in two orthogonal radiation beam series, which form a grid with (a + b) cross-section volumes, their size being given by geometry. With the aid of the series of (a + b) measurements, the spectral transmission or the spectral emission results, which is integrated over the total gas volume in the beam of the field of view of the spectrometers. In this known method, multiple spectra can be measured and simultaneously analyzed for the purpose of a "Global Fit" in a least squares compensating method, wherein the measuring vectors corresponding to the individual spectra are combined into a total vector and the minimization condition is applied to this vector.
    The object of the present invention is to provide, in a method for measuring temperature, pressure and / or concentration distributions in gaseous or similar media, while avoiding the aforementioned disadvantages, an analysis of several spectra measured for different elevation angles or tangent heights in which it is taken into account that the observation geometry (angle and the like) is only known with finite accuracy and that the spectra of the measuring sequence are measured on the same wave number grid, additional information or boundary conditions are taken into account, which provides a stable, physically meaningful solution of the allow inverse problem, and derivations that are not easy to calculate analytically, are calculated by automatic differentiation methods instead of failure.
    According to the invention, which relates to a method according to the techniques mentioned in the opening paragraph, the object is advantageously achieved in that the searched profile function or the searched profile functions are respectively transformed into a state vector by a discretization rule, that with respect to a generally non-linear least squares method, the spectra models used for the compensation calculation are matched by variation of the state vectors (model parameter) to the corresponding measurement spectra until noise is matched be adjusted in such a way that in the compensation calculation with the different accuracies of the independent variables, namely the observation angle or the like on the one hand and the wave number on the other hand, are taken into account by orthogonal distance regression instead of standard-least squares and that derivations of the forward model (radiation transport ) are used by automatic differentiation methods.
    The method according to the present invention is of great significance in particular in the context of atmospheric / meteorological research or in the measurement of gases in combustion processes, exhaust gas flows or clouds.
    For example, a sequence of spectra can be measured by a horizontal probing instrument on a satellite or similar carriers for remote atmospheric research in any spectra region, preferably ultraviolet, infrared, or millimeter region, and is then measured according to a "Global Fit". single "measurement vector" brought together (merged).
    When formulating an inversion problem analysis of the series of measured spectra for determining the profile function or profile functions with respect to an orthogonal distance regression, the measurement uncertainties are advantageously considered by Pre-Whitening.
    In the iterative solution of the weighted orthogonal distance regression by GauS-Newton or Levenberg-Marquard methods, the conditioning of the Jacobi matrix forming one derivative matrix is advantageously improved by column standardization.
    In the so-called inverse problem describing the profile or profiles from the spectroscopic measurements, a numerically stable and physically meaningful solution is suitably provided by additional regulation by means of limitations, for example positivity, and / or by means of quadratic preconditions, for example smoothness, obtained.
    For analyzing a series of spectra for a measurement of engine exhaust gases, the method according to the invention is characterized in that the methods developed for the analysis of a series of Limb spectra in the context of an atmospheric distance measurement are applied analogously to comparable analysis problems.
    Advantageous and suitable further developments and embodiments of the method according to the present invention are indicated in the claims referring to patent claim 1.
    The invention is worked out in detail below with reference to figures. They show:
    FIG. 1 a geometry of remote atmospheric research, as explained above, by a horizontal sounding instrument (Limb Sounder),
    FIG. 2 is a schematic representation of a tomographic exhaust gas jet measurement through a series of parallel lines of sight, also in which the direction of the exhaust gas jet, which is not necessarily exactly circular in cross-section, extends perpendicular to the drawing plane,
    FIG. 3 is a diagrammatic representation of a tomographic exhaust gas jet measurement through a series of differently oriented sight lines, also in which the direction of the exhaust gas jet, which is not necessarily exactly circular in cross-section, extends perpendicular to the drawing plane,
    FIG. 4 a schematic representation of the usual least squares fit, and
    FIG. 5 is a schematic representation of the orthogonal distance regression ODR used in accordance with the invention.
    The method according to the invention uses the so-called orthogonal distance regression (ODR) instead of a simple least squares fit (Gaufi compensation methods). In the case of purely linear coherence, the so-called "Total Least Squares" is used instead of the normal "Least Squares".
    The basis of this compensation method is that, in addition to errors in the dependent variables y (in the present case, this is the intensity), errors in one or more of the independent variables are also taken into account. If f (x, t) is a model of the size y measured as a function of the independent variables x for different parameters t with errors ε, so f (x, ti) * yi + Ei for i = 1,. . ., m, then in the usually least squares methods (see Fig. 4) the n model parameters x are determined by minimizing the error squared:
    When applying the orthogonal distance regression ODR according to the invention, errors δ are also included in the measurement variables t and the minimization condition of the usual least squares methods indicated in equation (7) is shown in accordance with FIG. 5 replaced by:
    By applying the boundary condition in the minimalization condition one obtains:
    which represents a standard minimization problem without boundary conditions. The solution of this problem follows in a technically known manner by methods of the numerical linear algebra, using the special structure of the problem, to ensure an efficient and stable implementation. To this end, with the help of the definitions
    and the m + n vector
    (11) the equation (9) in a conventional least squares method
    (12) for m + n parameters and 2m equations described. It is crucial for the efficiency of the implementation that the block structure of the completed derivation matrix (Jacobi matrix)
    (13) is taken along with
    (14) (15)
    (16)
    In the method according to the invention, only the orthogonal distance regression ODR is advantageously applied to the analysis of horizontal support measurements. The measured spectra i <obs) correspond to the error rate y, and the modeling of the spectra according to equation (1) corresponds to f. The discretized representation for the atmosphere profile to be determined (temperature, gas concentration, etc. ...) is symbolized by x, as in the earlier elaborations. In the simplest case of the horizontal probe, in which only one spectral point is measured for all tangent heights (for example, the integral total intensity of a spectral line or spectral band of the gas to be determined), the independent variable t is included in the equation ( 8) and subsequent ones correspond to the error-prone tangent height ht (respectively the observation angle).
    In the general case of m measured intensity values per tangent height ht, the method according to the invention uses the possibility of orthogonal distance regression ODR to also analyze multidimensional data. The independent variable t and the dependent variable y thus correspond to measurement sizes from two-dimensional spaces, the space of t being stretched by wave numbers v and tangent heights ht,
    (17) and the space of the y is stretched by their transformation to intensity values I (v, ht),
    (18)
    This also advantageously incorporates the aforementioned facts, which relate to the relationship between the ankle spectra.
    When implementing the orthogonal distance regression ODR for the analysis of a sequence of Limb spectra, it is additionally to be taken into account that the dependent sizes y, f (here intensities) and independent sizes t, δ (here tangent heights respectively their errors) are physical quantities of different dimensions. The formulation of the least squares problem derived from the orthogonal distance regression ODR according to equation (9) can be independent of the choice of displaying the dependent sizes y, f (here intensities) and independent sizes t, δ (here tangent heights or their respective errors) (for example, intensity in W / (cm 2 sr cm -1) or erg / (s cm 2 sr cm -1) and tangent heights in kilometers or meters), while the sizes are related to their known measurement uncertainties. This can generally be done by weighting with covariance matrices of y and t, (if only a treasure value is known, for example due to the standard deviation, then the corresponding covariance matrix can be used as a product of this variance with a unit matrix of suitable dimension.) Whitening (multiplication of the measurement vector y and the vector f of the model function f (x, t) by the root of the covariance matrix) becomes the problem until the standard form according to equation (9).
    Furthermore, the conditioning of the least squares problem according to equation (7) or the ODR problem according to equation (8) depends essentially on the variation of the order of magnitude of the parameters x and t. For example, for gases whose volume-mixing ratios in the atmosphere decreases with increasing order of magnitude, it is more favorable to take the particle density n = V M R * nair as unknown x. In general, by introducing diagonal weight matrices for x and t, these parameters can be transformed into the comparable order of magnitude. The different physical dimensions and the different accuracies of the relevant quantities can therefore be taken into account by a weighted orthogonal distance regression ODR.
    For iteratively solving the orthogonal distance regression ODR or the non-linear least squares problem derived therefrom, the derivations to the atmosphere profiles to be determined (represented by the vector x) and to the tangent height ht with errors are required according to equation (13). Since these derivations can only be calculated analytically with great effort, automatic differentiation methods are used in the method according to the invention. Since the differentiation of mathematical functions can be performed by applying simple rules, as opposed to integration, this set of rules can also be applied to the differentiation of the functions implemented by programming languages such as C or Fortran. As a result, the calculation of the derivations of the radiation intensity of the corresponding radiation transport calculation program described by equations (1) and also (2) is transformed by a pre-processor into a program which, in addition to the function (intensity), simultaneously derives the derivation calculates thereof.
    The solution of the non-linear least squares problem derived from equation (8) according to equation (12) (respectively the usual non-linear least squares problem according to equation (7) takes place in a technically known manner iteratively, e.g. a GauS-Newton or Levenberg-Marquardt method Even with weighted orthogonal distance regression ODR, the derivation matrix (Jacobi matrix) can be approximate single (high condition number), so that when calculating the parameter update vector δη by QR factorization of the Jacobi matrix a aforementioned scaling is generally important for the norm of the columns of the Jacobi matrix.
    The introduction of additional information for stabilizing the solution (regularization) takes place in a technically known manner by extending the least squares problem according to equation (7) or the ODR problem according to equation (8) by quadratic boundary conditions (smoothness) and / or inequality preconditions, for example
    where Ω is the regularization matrix and λ is the regularization parameter. The determination of the regularization quantities and the solution of equation (19) takes place in a technically known manner, for example by means of L-curve methods or iteratively regulated Gaufi-Newton methods. This regularization provides physically meaningful solutions to inverse problems that are generally poorly set up.
    REFERENCE NUMBER LIST
    1 Vision line 2 Field of vision 3 Tangential height 4 Instrument (Limb Sounder) 5 Satellite 6 Earth
    Re Earth radius 7 Parallel sight lines 8 Exhaust gas stream 9 Different directional sight lines
    权利要求:
    Claims (5)
    [1]
    A method for determining concentration, pressure and temperature profiles in random, preferably gaseous, media by contactless spectrometric radiation measurements, wherein a series of spectra in random spectral ranges are measured and simultaneously with respect to a "Global Fit" in a Compensation calculation method is analyzed in which the measurement vectors corresponding to a single spectrum are brought together to form a total measurement vector, characterized in that the profile function or the profile functions sought are transformed by a discretization rule into a state vector, and that for the compensation calculation Spectrum models used with respect to a generally non-linear least squares fit method are adjusted by variation of the state vector (model parameter) to the corresponding measurement spectra until corresponding to the noise in such a way that with the compensation Calculation of the various accuracies of the independent variables, namely the observation angle or the like on the one hand and the wave number on the other hand, are settled by orthogonal distance regression instead of standard least squares and that derivations of the forward model (radiation transport) by automatic differentiation methods are implemented.
    [2]
    Method according to claim 1, characterized in that when formulating the analysis of the series of measured spectra for determining the profile function or profile functions with respect to an orthogonal distance regression, the measurement uncertainties are settled by Pre-Whitening.
    [3]
    Method according to claim 1 or 2, characterized in that in the iterative solution of a weighted orthogonal distance regression by Gauft-Newton or Leven-berg-Marquard methods, the conditioning of the Jacobi matrix forming a delineation matrix is improved by column standardization .
    [4]
    Method according to one of the preceding claims, characterized in that, in the case of a so-called inverse problem-forming determination of the profile or profiles, a numerically stable and physically meaningful solution from the spectroscopic measurements by additional regulation by means of limitations, e.g. sitivity, and / or by means of quadratic boundary conditions, for example smoothness.
    [5]
    Method according to any one of the preceding claims for analyzing a series of spectra for a measurement of engine exhaust gases, characterized in that the methods developed for the analysis of a series of Limb spectra in the context of an atmospheric distance measurement are based on comparable analysis problems are applied analogously. -o-o-o-o-o-o-o-
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    同族专利:
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    引用文献:
    公开号 | 申请日 | 公开日 | 申请人 | 专利标题
    EP0959341A1|1998-05-16|1999-11-24|Deutsches Zentrum für Luft- und Raumfahrt e.V.|Method for the quantitative analysis of volumina of gases, especially exhaust gases from combustion apparatus, and device for implementing the method|
    DE19840794C1|1998-09-08|2000-03-23|Deutsch Zentr Luft & Raumfahrt|Method and device for detecting infrared radiation properties of exhaust gases|
    DE102004001748A1|2004-01-12|2005-08-18|Deutsches Zentrum für Luft- und Raumfahrt e.V.|Analyzing random, preferably gaseous media, comprises displaying spectrum produced by IR spectrometer as time-dependent spectrum, and back-transforming interferogram into frequency region|
    DE102005060245B3|2005-12-14|2007-03-01|Deutsches Zentrum für Luft- und Raumfahrt e.V.|Gas concentration, pressure and temperature distributions determining method for use in e.g. motor vehicle, involves providing cubic polynomial as interpolating function, where interpolating function and mixed derivations are same|
    DE102010063539A1|2010-12-20|2012-06-21|Siemens Aktiengesellschaft|air conditioning unit|
    法律状态:
    2020-05-06| MM| Lapsed because of non-payment of the annual fee|Effective date: 20191001 |
    优先权:
    申请号 | 申请日 | 专利标题
    DE102008050046|2008-10-01|
    DE102008050046A|DE102008050046B3|2008-10-01|2008-10-01|Method for determining concentration, pressure and temperature profiles in exhaust gas of aircraft, involves implementing derivations of forward models based on equations for radiation transport by automatic differentiation process|
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