Navigation: Spectral Matching (QuakeMatch) >

Matching Criteria

General

Users may set the period or frequency range of matching as follows:

•Period Range (s)

•Frequency Range (Hz)

Adaptive: Recalculate Spectra after Each Step: applies only with mean and mean with dispersion spectral matching. Adaptive matching recalculates the targets after each step.

Users may also set the appropriate Number of Steps or passes that will be used to perform matching. The number of steps refers to the number of times spectral matching is performed. QuakeManager runs a spectral matching analysis for each of the steps. Using multiple steps can be helpful in cases where performing the spectral matching in a single step does not results in a good match.

QuakeManager can automatically generate the time/frequency steps using the Auto Generate Steps. Alternatively, the user may set and define the Tmin/Tmax or Fmin/Fmax manually by clicking in a specific period or frequency inside the box.

The "Periods to use" or "Frequencies to use" are the periods/frequencies at which the matching is performed/evaluated. The target design spectrum will be evaluated/interpolated at these periods or frequencies. Users may utilize one of the following:

•Target: The periods that are defined for the Target Design Spectrum Periods/Frequencies, falling within the defined range. For Code Design Spectra (e.g. IBC), the NGA periods are used.

•NGA: Predefined NGA Periods/Frequencies falling within the defined range

•Log Spacing: User may define the number of periods to match in the “Count” box and QuakeManager will generate logarithmically spaced values.

•Linear Spacing: User may define the number of periods to match in the “Count” box and QuakeManager will generate linearly spaced values.

•Custom: User-defined Periods/Frequencies. Users may enter their customized periods or paste them inside the “Periods” box. Periods may be separated by commas or spaces. All defined periods falling with the period range will be counted and added to the “Count” box.

In all cases, the number of periods/frequencies that fall within the matching range is shown in the “Count” box

Record Scaling

Prescale Records at Period: Scale factor used to linearly prescale the acceleration series and the response spectrum at the specified period prior to performing the spectral matching. Once Prescale Records box is clicked, users may specify the period at which to scale the PSa spectrum, and can choose to prescale records at the First Iteration Only or at Every iteration.

Additional Scale Factor: Apply an additional scale factor used to scale the initial acceleration time series prior spectral matching.

Advanced

Wavelet model:

•Model 1 - Reverse Acceleration Impulse Response Function: Wavelet used by Lilhanand and Tseng [13] [14]. This wavelet is very efficient in adjusting the response; however, it may corrupt the velocity and displacement time-history because the wavelet does not end with zero velocity or displacement ^a. This model perform spectral matching to the target acceleration response spectrum ^b.

•Model 6 - Tapered Cosine Function: This wavelet is an update of the wavelet used by Abrahamson [10]. This model preserves the non-stationery character of the acceleration time series, but it may results in drifted velocity and displacement time series. To overcome this problem, users are required to apply a baseline correction to the matched time series after each step/iteration to ensure zero final displacement ^a. This model perform spectral matching to the target acceleration response spectrum. a1, a2, f1 and f2 are parameters used in this model to define the frequency dependence of the taper [15].

•Model 7 - Improved Tapered Cosine Function: An improved model that results with zero drift in the velocity and displacement time series. One advantage of this model that it is not supposed to require applying baseline correction to the matched time series (though QuakeManager allows the user apply baseline correction if desired). It also provide stability and better results in terms of convergence and efficiency by using analytical integrations, though it generally runs slower than the other models [10]. Note that Model 7 perform pseudo-acceleration spectral matching [15].

Baseline Correction: Generally, baseline correction is required for the matched acceleration time series to correct the resulting drift in the velocity and displacement time series. Users may turn off this option so no correction is applied. Users can select the polynomial order from 0 to 15. QuakeManager enables applying a baseline correction at one of the different matching stages as follows:

•No: no baseline correction is applied

•After Each Iteration: baseline is applied after each iteration

•After Each Step: baseline is applied after each major step

•After Last Step: baseline is applied after finishing all steps 

Note that for model 7, baseline correction is generally not required, but may be used if the user chooses to.

Frequency Group size: Specify the number of spectral values to use in the matching subgroup. To solve spectral matching optimization problem more effectively, the algorithm breaks the matching frequencies/periods into multiple groups that are solved individually, instead of optimizing the whole period/frequency range at once.

Maximum number of iterations: Specify the maximum number of iterations for spectral matching convergence. QuakeManager keeps iterating until finding a solution or when the specified maximum number of iteration is reached.

Solution Convergence Tolerance: Set the convergence tolerance which represents the maximum mismatch as a fraction of the target spectral acceleration.