Program(TP, FpinP, L; pout="vacuum", time_unit="min")

Construct the structure Program with conventional formulation (see function conventional_program in GasChromatographySimulator.jl) of programs for the case without a thermal gradient.

Arguments

• TP: conventional formulation of a temperature program.
• FpinP: conventional formulation of a Flow (in m³/s) resp. inlet pressure (in Pa(a)) program.
• L: Length of the capillary measured in m (meter).
• pout: Outlet pressure, "vacuum" (default), "atmosphere" or the outlet pressure in Pa(a).
• time_unit: unit of time in the programs, "min"` (default) times are measured in minutes, "s" times are measured in seconds.

The argument L is used to construct the temperature interpolation T_itp(x,t).

Examples

julia> Program((40.0, 1.0, 5.0, 280.0, 2.0, 20.0, 320.0, 2.0),
                (400000.0, 10.0, 5000.0, 500000.0, 20.0),
                10.0)

check_measurement(meas, col_input; min_th=0.1, loss_th=1.0, se_col=true)

Similar to method_m1 (method_m1) estimate the three retention parameters $T_{char}$, $θ_{char}$ and $ΔC_p$ including standard errors, see stderror. In addition, if the found optimized minima is above a threshold min_th, it is flagged and the squared differences of single measured retention times and calculated retention times above another threshold loss_th are recorded.

Arguments

• meas ... Tuple with the loaded measurement data, see load_chromatograms.
• col_input ... Named tuple with col_input.L the column length in m and col_input.d the column diameter in mm. If this parameter is not gicen, than these parameters are taken from meas.
• se_col=true ... If true the standard errors (from the Hessian matrix, see stderror) of the estimated parameters are added as separate columns to the result dataframe. If false the standard errors are added to the values as Masurement type.

Output

• check ... Boolean. true if all values are below the thresholds, false if not.
• msg ... String. Description of check
• df_flag ... Dataframe containing name of the flagged measurements, solutes and the corresponding mesured and calculated retention times.
• index_flag ... Indices of flagged results
• res ... Dataframe with the optimized parameters and the found minima.
• Telu_max ... The maximum of elution temperatures every solute experiences in the measured programs.

elution_temperature(tRs, prog)

Calculate the elution temperatures from retention times tRs and GC programs prog.

estimate_parameters()

Calculate the estimates for the K-centric parameters and (optional) the column diameter.

Arguments

• chrom ... Tuple of the loaded chromatogram, see load_chromatograms

Options

• method=NewtonTrustRegion() ... used optimization method
• opt=std_opt ... general options, std_opt = GasChromatographySimulator.Options(abstol=1e-8, reltol=1e-5, ng=true, odesys=false)
• maxiters=10000 ... maximum number of iterations for every single optimization
• maxtime=600.0 ... maximum time for every single optimization
• mode="dKcentric" ... mode of the estimation. Possible options:
  • "Kcentric_single" ... optimization for the three K-centric retention parameters separatly for every solute
  • "Kcentric" ... optimization for the three K-centric retention parameters together for all solutes
  • "dKcentric_single" ... optimization for the column diameter and the three K-centric retention parameters separatly for every solute
  • "dKcentric" ... optimization for the column diameter and the three K-centric retention parameters together for all solutes
• metric="squared" ... used metric for the loss function ("squared" or "abs")

Output

• df ... DataFrame with the columns Name (solute names), d (estimated column diameter, optional), Tchar (estimated Tchar), θchar (estimated θchar), ΔCp (estimated ΔCp) and min (value of the loss function at the found optima)
• sol ... Array of SciMLBase.OptimizationSolution with the results of the optimization with some additional informations.

estimate_start_parameter(tRs::DataFrame, col, prog; time_unit="min", control="Pressure")

Estimation of initial parameters for Tchar, θchar and ΔCp based on the elution temperatures calculated from the retention times tR and GC programs prog for column col. The initial value of Tchar is estimated from the elution temperatures of the measurements. Based on this estimated Tchar estimates for the initial values of θchar and ΔCp are calculated as $\theta_{char,init} = 22 \left(\frac{T_{char,init}}{T_{st}}\right)^{0.7} \left(1000\frac{d_f}{d}\right)^{0.09} °C$ and $\Delta C_p = (-52 + 0.34 T_{char,init}) \mathrm{J mol^{-1} K^{-1}}$

Output

• Tchar_est ... estimate for initial guess of the characteristic temperature
• θchar_est ... estimate for initial guess of θchar
• ΔCp_est ... estimate for initial guess of ΔCp
• Telu_max ... the maximum of the calculated elution temperatures of the solutes

estimate_start_parameter_mean_elu_temp(tRs::DataFrame, col, prog; time_unit="min", control="Pressure")

Estimation of initial parameters for Tchar, θchar and ΔCp based on the elution temperatures calculated from the retention times tR and GC programs prog for column col. This function is used, if the temperature program is not a single ramp heating program. The elution temperatures of all measurements are calculated and the mean value of the elution temperatures is used as the initial characteristic temperature of a substance. Based on this estimated Tchar estimates for the initial values of θchar and ΔCp are calculated as $\theta_{char,init} = 22 \left(\frac{T_{char,init}}{T_{st}}\right)^{0.7} \left(1000\frac{d_f}{d}\right)^{0.09} °C$ and $\Delta C_p = (-52 + 0.34 T_{char,init}) \mathrm{J mol^{-1} K^{-1}}$

Output

• Tchar_est ... estimate for initial guess of the characteristic temperature
• θchar_est ... estimate for initial guess of θchar
• ΔCp_est ... estimate for initial guess of ΔCp
• Telu_max ... the maximum of the calculated elution temperatures of the solutes

estimate_start_parameter_single_ramp(tRs::DataFrame, col, prog; time_unit="min", control="Pressure")

Estimation of initial parameters for Tchar, θchar and ΔCp based on the elution temperatures calculated from the retention times tR and GC programs prog for column col. For this function it is assumed, that single ramp heating programs are used. The elution temperatures of all measurements are calculated and than interpolated over the heating rates. For a dimensionless heating rate of 0.6 the elution temperature and the characteristic temperature of a substance are nearly equal. Based on this estimated Tchar estimates for the initial values of θchar and ΔCp are calculated as $\theta_{char,init} = 22 \left(\frac{T_{char,init}}{T_{st}}\right)^{0.7} \left(1000\frac{d_f}{d}\right)^{0.09} °C$ and $\Delta C_p = (-180 + 0.63 T_{char,init}) \mathrm{J mol^{-1} K^{-1}}$

Output

• Tchar_est ... estimate for initial guess of the characteristic temperature
• θchar_est ... estimate for initial guess of θchar
• ΔCp_est ... estimate for initial guess of ΔCp
• Telu_max ... the maximum of the calculated elution temperatures of the solutes

load_chromatograms(file; delim=";")

Loading of the chromatographic data (column information, GC program information, retention time information, see also "Structure of input data") from a file.

Arguments

• file ... path to the file.
• delim=";" ... Delimiter for the imported .csv file.

Output

A tuple of the following quantities:

• col ... settings of the column as GasChromatographySimulator.Column structure.
• prog ... Array of the GC programs as GasChromatographySimulator.Program structure.
• tRs ... DataFrame of the retention times.
• solute_names ... Vector of the solute names.
• pout ... outlet pressure (detector pressure), "vacuum" or "atmospheric".
• time_unit ... unit of time scale used in the retention times and GC programs, "min" or "s".

load_chromatograms(file::Dict{Any, Any}; path=joinpath(dirname(pwd()), "data", "exp_pro"))

Loading of the chromatographic data (column information, GC program information, retention time information, see also "Structure of input data") from a file selected by the FilePicker in a Pluto notebook.

Arguments

• file ... file dictionary from the FilePicker.
• path ... if the temperature programs are defined by measured temperatures over time, define the path to these files.

Output

A tuple of the following quantities:

• col ... settings of the column as GasChromatographySimulator.Column structure.
• prog ... Array of the GC programs as GasChromatographySimulator.Program structure.
• tRs ... DataFrame of the retention times.
• solute_names ... Vector of the solute names.
• pout ... outlet pressure (detector pressure), "vacuum" or "atmospheric".
• time_unit ... unit of time scale used in the retention times and GC programs, "min" or "s".

loss(tR, Tchar, θchar, ΔCp, L, d, prog, gas; opt=std_opt, metric="squared")

Loss function as sum of squares of the residuals between the measured and calculated retention times.

Arguments

• tR ... mxn-array of the measured retention times in seconds.
• Tchar ... n-array of characteristic temperatures in K.
• θchar ... n-array of characteristic constants in °C.
• ΔCp ... n-array of the change of adiabatic heat capacity in J mol^-1 K^-1.
• L ... number of the length of the column in m.
• d ... number of the diameters of the column in m.
• prog ... m-array of structure GasChromatographySimulator.Programs containing the definition of the GC-programs.
• gas ... string of name of the mobile phase gas.

Output

The output is a tuple of the following quantites:

• sum((tR.-tRcalc).^2) ... sum of the squared residuals over m GC-programs and n solutes.

loss(tR::Array{T, 1}, Tchar, θchar, ΔCp, substance_list::Array{String, 1}, L, d, prog::Array{GasChromatographySimulator.Program, 1}, gas; opt=std_opt, metric="squared") where T<:Number

Calculates the loss between the measured retention times tR and the calculated retention times tRcalc for a list (vector) of substances.

Arguments

• tR::Array{T, 1}: Array of measured retention times.
• Tchar: Array of characteristic temperatures for each substance.
• θchar: Array of characteristic parameters for each substance.
• ΔCp: Array of heat capacity changes for each substance.
• substance_list::Array{String, 1}: List of substances.
• L: Length of the column.
• d: Diameter of the column.
• prog::Array{GasChromatographySimulator.Program, 1}: Array of programs for gas chromatography.
• gas: The gas used.
• opt=std_opt: (Optional) Options for calculating retention times.
• metric="squared": (Optional) The loss metric to use. Can be "abs" for absolute loss or "squared" for squared loss.

Return Value

• l: The calculated loss value.

Errors

• Throws an error if the lengths of tR, substance_list, and prog do not match.

method_m1(meas, col_input; se_col=true)

Estimation of the three retention parameters $T_{char}$, $θ_{char}$ and $ΔC_p$ including standard errors, see stderror.

Arguments

• meas ... Tuple with the loaded measurement data, see load_chromatograms.
• col_input ... Named tuple with col_input.L the column length in m and col_input.d the column diameter in mm.
• se_col=true ... If true the standard errors (from the Hessian matrix, see stderror) of the estimated parameters are added as separate columns to the result dataframe. If false the standard errors are added to the values as Masurement type.

Output

• res ... Dataframe with the optimized parameters and the found minima.
• Telu_max ... The maximum of elution temperatures every solute experiences in the measured programs.

method_m2(meas; se_col=true)

Estimation of the column diameter $d$ and three retention parameters $T_{char}$, $θ_{char}$ and $Δ C_p$ including standard errors, see stderror. In a first run all four parameters are estimated for every substance separatly, resulting in different optimized column diameters. The mean value of the column diameter is used for a second optimization using this mean diameter and optimize the remainig thre retention parameters $T_{char}$, $θ_{char}$ and $Δ C_p$.

Arguments

• meas ... Tuple with the loaded measurement data, see load_chromatograms.
• se_col=true ... If true the standard errors (from the Hessian matrix, see stderror) of the estimated parameters are added as separate columns to the result dataframe. If false the standard errors are added to the values as Masurement type.

Output

• res ... Dataframe with the optimized parameters and the found minima.
• Telu_max ... The maximum of elution temperatures every solute experiences in the measured programs.

method_m3(meas; se_col=true)

Estimation of the column diameter $d$ and three retention parameters $T_{char}$, $θ_{char}$ and $Δ C_p$ including standard errors, see stderror. Brute-force method, where all parameters (3n+1 for n substances) are estimate in one optimization.

ATTENTION: This method can take long time to finish. The more substances, the longer it takes.

Arguments

• meas ... Tuple with the loaded measurement data, see load_chromatograms.
• se_col=true ... If true the standard errors (from the Hessian matrix, see stderror) of the estimated parameters are added as separate columns to the result dataframe. If false the standard errors are added to the values as Masurement type.

Output

• res ... Dataframe with the optimized parameters and the found minima.
• Telu_max ... The maximum of elution temperatures every solute experiences in the measured programs.

opt_Kcentric(x, p)

Function used for optimization of the loss-function in regards to the three K-centric parameters.

Arguments

• x ... 3n-vector of the three K-centric parameters of n solutes. Elements 1:n are Tchar, n+1:2n are θchar and 2n+1:3n are ΔCp values.
• p ... vector containing the fixed parameters:
  • tR = p[1] ... vector of the measured retention times in seconds.
  • substance_list = p[2] ... vector of the names of the solutes related to tR and prog.
  • L = p[3] ... number of the length of the column in m.
  • d = p[4] ... number of the diameters of the column in m.
  • prog = p[5] ... vector of structure GasChromatographySimulator.Programs containing the definition of the GC-programs.
  • opt = p[6] ... struture GasChromatographySimulator.Options containing the settings for options for the simulation.
  • gas = p[7] ... string of name of the mobile phase gas.
  • metric = p[8] ... string of the metric used for the loss function (squared or abs).

Output

• sum((tR.-tRcalc).^2) ... sum of the squared residuals over m GC-programs and n solutes.

opt_dKcentric(x, p)

Function used for optimization of the loss-function in regards to the colum diameter and the three K-centric parameters.

Arguments

• x ... 1+3n-vector of column diameter and the three K-centric parameters of n solutes. Element 1 is the diameter, 2:n+1 are Tchar, n+2:2n+1 are θchar and 2n+2:3n+1 are ΔCp values.
• p ... vector containing the fixed parameters:
  • tR = p[1] ... vector of the measured retention times in seconds.
  • substance_list = p[2] ... vector of the names of the solutes related to tR and prog.
  • L = p[3] ... number of the length of the column in m.
  • prog = p[4] ... vector of structure GasChromatographySimulator.Programs containing the definition of the GC-programs.
  • opt = p[5] ... struture GasChromatographySimulator.Options containing the settings for options for the simulation.
  • gas = p[6] ... string of name of the mobile phase gas.
  • metric = p[7] ... string of the metric used for the loss function (squared or abs).

Output

• sum((tR.-tRcalc).^2) ... sum of the squared residuals over m GC-programs and n solutes.

optimize_Kcentric(tR::Vector{T}, substance_list, col, prog, Tchar_e::Vector{T}, θchar_e::Vector{T}, ΔCp_e::Vector{T}; method=RetentionParameterEstimator.NewtonTrustRegion(), opt=RetentionParameterEstimator.std_opt, maxiters=10000, maxtime=600.0, metric="squared") where T<:Number

Optimize the K-centric retention parameters for a given set of substances, measured retention times and used programs.

Arguments

• tR::Vector{T}: Vector of retention times.
• substance_list: List of substances to be optimized.
• col: Column characteristics including length L, diameter d, and gas type gas.
• prog: Program conditions.
• Tchar_e::Vector{T}: Initial estimates for characteristic temperatures.
• θchar_e::Vector{T}: Initial estimates for characteristic phase ratios.
• ΔCp_e::Vector{T}: Initial estimates for heat capacity changes.
• method: Optimization method to be used (default: RetentionParameterEstimator.NewtonTrustRegion()).
• opt: Optimization options (default: RetentionParameterEstimator.std_opt).
• maxiters: Maximum number of iterations (default: 10000).
• maxtime: Maximum time allowed for optimization in seconds (default: 600.0).
• metric: Metric to be used for optimization (default: "squared").

Returns

• opt_sol: The solution of the optimization problem.

optimize_dKcentric(tR::Vector{T}, substance_list, col, prog, Tchar_e::Vector{T}, θchar_e::Vector{T}, ΔCp_e::Vector{T}; method=RetentionParameterEstimator.NewtonTrustRegion(), opt=RetentionParameterEstimator.std_opt, maxiters=10000, maxtime=600.0, metric="squared") where T<:Number

Optimize the column diameter and K-centric retention parameters for a given set of substances, measured retention times and used programs.

Arguments

• tR::Vector{T}: Vector of retention times.
• substance_list: List of substances to be optimized.
• col: Column characteristics including length L and gas type gas.
• prog: Program conditions.
• Tchar_e::Vector{T}: Initial estimates for characteristic temperatures.
• θchar_e::Vector{T}: Initial estimates for characteristic phase ratios.
• ΔCp_e::Vector{T}: Initial estimates for heat capacity changes.
• method: Optimization method to be used (default: RetentionParameterEstimator.NewtonTrustRegion()).
• opt: Optimization options (default: RetentionParameterEstimator.std_opt).
• maxiters: Maximum number of iterations (default: 10000).
• maxtime: Maximum time allowed for optimization in seconds (default: 600.0).
• metric: Metric to be used for optimization (default: "squared").

Returns

• opt_sol: The solution of the optimization problem.

prog_list(prog, tRs)

Generate a vector of program conditions, excluding rows with missing values in tRs.

Arguments

• prog: A program condition to be repeated.
• tRs: A 2D array where each row corresponds to a set of retention times and columns to different substances.

Returns

• A vector of program conditions corresponding to non-missing rows in tRs.

reference_holdup_time(prog, L, d, gas; control="Pressure")

Calculate the reference holdup time for the GC program prog for a column with length L and diameter d and gas as mobile phase. The reference holdup time is the holdup time at the reference temperature 150°C.

separate_error_columns(res)

If the result dataframe res contains columns with Measurements typed values, these columns will be split in two. The first column contains the value and uses the original column name. The second column contains the uncertainty and the name of the column is the original name with an added "_uncertainty". If the column is not of the Measurements type, it will be copied as is for the new dataframe.

stderror(meas, res)

Calculation of the standard error of the found optimized parameters using the hessian matrix at the optima.

Attention

The used loss-function is hard coded in the function opt_Kcentric and has to be changed if another loss-function is used.

Arguments

• meas ... Tuple with the loaded measurement data, see load_chromatograms.
• res ... Dataframe with the result of the optimization, see estimate_parameters.

Optional parameters

• col_input ... Named tuple with col_input.L the column length in m and col_input.d the column diameter in mm. If this parameter is not gicen, than these parameters are taken from meas.

Output

• stderrors ... Dataframe with the standard errors of the optimized parameters.
• Hessian ... The hessian matrix at the found optims.

substance_list(substance_names, tRs)

Generate a vector of substance names, excluding rows with missing values in tRs.

Arguments

• substance_names: A vector of substance names.
• tRs: A 2D array where each row corresponds to a set of retention times and columns to different substances.

Returns

• A vector of substance names corresponding to non-missing rows in tRs.

tR_calc(Tchar, θchar, ΔCp, L, d, prog, gas; opt=std_opt)

Calculates the retention time tR for a solute with the K-centric parameters Tchar θchar and ΔCp for a column with length L, internal diameter d, the (conventional) program prog, options opt and mobile phase gas. For this calculation only the ODE for the migration of a solute in a GC column is solved, using the function GasChromatographySimulator.solving_migration.

tR_τR_calc(Tchar, θchar, ΔCp, L, d, df, prog, Cag, t₀, τ₀, gas; opt=std_opt)

Calculates the retention time tR for a solute with the K-centric parameters Tchar θchar and ΔCp for a column with length L, internal diameter d, film thickness df, the (conventional) program prog, diffusirivity coefficient Cag, start time t₀, initial peak width τ₀, options opt and mobile phase gas. For this calculation the ODE-system for the migration of a solute and peak width in a GC column is solved, using the function GasChromatographySimulator.solving_odesystem_r. The result is a tuple of retention time tR and peak width τR.