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GM Fitting Criteria

Acceptable Scale Factors

Define the acceptable scale factor range (minimum and maximum). Resulting records will be scaled by factors within the defined range; selected scale will never fall outside the range (SFmin , SFmax).

See the Ground Motion Scaling Code Requirements section for information on code requirements.

Period Range

Input the period range over which records will be scaled and optimized. This is the range over which the error between the suite an target spectra will be calculated, and is defined by a number of points and the suitable spacing (linear/logarithmic).

The Period Range can be defined using three different options:

1.Period Range (Uniform Weight)

2.Weight v/s Period

3.Weight v/s Frequency

If the Period Range (Uniform Weight) is selected, users may define the maximum and minimum periods (Tmax and Tmin). In case the second option is chosen, Weight v/s Period, users may define the period range in addition to weights. Same applies for the Weight v/s Frequency option.

Npoints: Number of points to match in the selection process. By default, Npoint=50, which means that 50 points within the specified period range will be matched. Note that using small number of points might result in a bad selection, and increasing number of points might enhance the results, but will consume much more time. 

Spacing: Logarithmic or Linear spacing of points

Error Measure

An advanced option allows the user to specify the method of calculation of the error and the spectral variable to be used (Sa, Sv, Sd, etc) and whether the spectral value of its Log are to be used in the calculation (Linear/Log). The fitting error measure is computed for entire suite while performing the Ground Motion Suite Selection, and it is also calculated for individual records when fitting records within the Search Panel.

The following error measure calculation options are available :

•Absolute Difference Sum

•Absolute Difference Integral

•Square Sum (SSE)

•Square Integral

For suite selection, the Match Objective can be set to one of the following:

•Suite Mean: the resulting Mean of a suite of records will be matched to the target

•Suite Mean + Dispersion: the resulting Mean of a suite and Dispersion will be matched to the target (recommended)

•Top Records: match each record individually to match the target

Users can select the “Top Records” feature to match top records (records with smallest errors) individually to the defined target spectrum (without optimizing the overall suite statistics). This feature is similar to matching using Search Panel, but while matching the additional constraints defined in the GM Suite Selection dialog, and may be used to select record seed candidates for further modification (such as spectral matching).

Suite Mean and Suite Mean + Dispersion options optimizes the resulting mean of the suite to match the target spectrum, where the error is measured as the difference between the resulting mean spectrum of the suite and target spectra. However, the Top Records option optimizes each record individually to match the defined target spectra, and the error measure is calculated as the difference between each record and the target spectrum and averaged by the sum of errors of the records in the suite.

The mean of the generated records using the Top Records option should not necessary have a good fit compared to the target spectrum; however, individually the generated records are the best. On the contrary, the records generated using the Suite Mean and Suite Mean + Dispersion have the best resulting mean spectrum.

Users are able to choose the Suite Mean Calculation method: either arithmetically or using the Geomean method.

If the Suite Mean + Dispersion option was selected in the Match Objective, then the Suite Dispersion Calculation method may be selected as Standard Deviation or LogSigma.

After setting the Suite Dispersion Calculation method, users may set the Dispersion Objective using one of the following mathematical equality or inequalities:

•Equals Target Standard Deviation

•Greater or Equals Target Standard Deviation

•Lesser or Equal Target Standard Deviation

It is also possible to specify the weight for the Standard Deviation Error term relative to Mean Error term for a specific Suite(s).

As an example if the weight is set to 1, then mean error and dispersion error are given equal weight when optimizing the suite record selection and scaling.

Suite Mean Limit Constraint

Adjust the suite scaling constraint (none/enveloping). None is the default option. However, the constraint can be enveloped by:

•Greater or equal to x*Target

•Less or equal to x*Target

where x is an input factor.

Adjusting the scaling constraint is useful to scale the records such that the average of the generated records does not fall above or below the "x, input factor" from the target spectrum. For example, to prevent the average of the suite from falling by more than 10% from the target spectrum over the period range (which is for example required by ASCE 7-16 and other codes), the user can choose the "Greater or equal to x*Target" option, with x set equal to 0.9.

Record Peak Limits Constraint

Adjust the scaling constraint by limiting peaks and valleys. This option will attempt to prevent any records peaks (or valleys) from falling above (or below) the target spectrum by more than the specified number of (Log) standard deviations.