VALIDATION AND VERIFICATION

(1)We will regard MSE as essentially analogous to RMSE, and concentrate on comparisonsbetween RMSE and MAE. While the choice between these two metrics may seeminconsequential, there are cases where they would lead to conflicting interpretations duringvalidation, especially for pattern classification networks. The following example is from(Twomey and Smith 1993a, 1995). The pattern classification problem is a well known two classclassification problem depicted in Figure 1. Two Gaussian distributions are classes A and B,where class A has a mean of 0 and a standard deviation of 1 and class B has a mean of 0 and astandard deviation of 2. There is considerable overlap between the classes, making this is astraightforward “hard” pattern classification task. Both training and testing sets contained equalnumbers of observations from each class.Figure 1 here.Typically, networks are trained to decreasingly lower training tolerances in an attempt toachieve the “best” performing network. This assumes that lower training tolerances equate withimproved performance, which is certainly not always the case. To examine the relativedifferences between RMSE and MAE, several networks were trained and tested in order tomeasure the effects of lowering the training tolerance for the two pattern classification problemwhere the correct output for class A is 0 and the correct output for class B is 1.A total of 13 different networks were trained, each to a different training tolerance.Training tolerances ranged from 0.08 to 0.6 for normalized input between 0 and 1. Duringtraining, a response was considered correct if the output was within a pre-specified absolutetraining tolerance of the target value (0 or 1). Training iterations continued for each networkMSEn

. Page   In 1974, TRIMHX was verified using three numerical test problems. For the first two tests, analytic solutions were available for comparison.
In the third test, a series of static asymptotic calculations are used for comparison.
Each of these tests were characterized by the following attributes: • 2 energy groups • 1 to 6 delayed neutron families • six-fold sector symmetry in the horizontal plane • one mesh point per hex (horizontally) • ten mesh points per layer axially • a step change in reactivity at time 0 The first of these test problems considered a bare homogeneous reactor with a spatially uniform perturbation in production cross section.
The second test differed from the first onty in that the reactor modeled was heterogeneous.
The third test used a heterogeneous reactor perturbed by reducing the thewmal absorption cross section in the center of the reactor. This created an axially uniform step change in the reactivity at time 0.
The results of Experiment 1 are shown in Figure 1 and Table I, while the results of Exper:ment 2 are shown in Table I1. Both of these tests had exact solutions using point kinetics equations.
A comparison of these results is presented in Tables I and II which show TRIMHX was in excellent agreement with the exact solution at ali points (for the first test to within .5%). lt should be noted that during these tests it was foun3 that the use of the exponential transform in TRIMHX gave more accurate results. Since the point kinetics model solution was not valid for the third test, a dynamic reactivity was inferred from the asymptotic period found by using a calculated neutron lifetime. Figure 2 shows the radial distribution of the thermal flux between that calculated and measured. Agreement between the transient and asymptotic shape is excellent (<.1% error).
Results for Experiment 3 with and without the exponential transforms are presented in Table II1.
These experiments show that the TRIMHX solution method provides an effective means of analyzing multidimensional reactor problems accurately.

HTGR Benchmark 5
As part of the effort to verify GRIMHX, a benchmark problem was developed under the auspices of the Mathematics and Computations division of the American Nuclear Society.
The benchmark problem consisted of a HTGR core representation with 60-degree rotational symmetry in 2-D surrounded by a graphite reflector.
This benchmark was part of a cooperative effort between SRL, ORNL, and General Atomic (GAC) to verify their hexagonal finite difference codes.
The results of the benchmark are presented for the three codes GRIMHX(SRL), VENTURE(ORNL), and BUG180(GAC) in Table IV. These results show that GRIMHX is indeed solving the finite differenced neutron diffusion equation correctly.
The input data records for this benchmark currently exist on the author's dataset.

Comparison of TRIMHX to the Adiabatic Model 6
In 1988, Bi!l Graves made a 2-D, one-point per mesh, coarse mesh comparison of TRIMHX versus the adiabatic model for a mockup of the Fast Scram Shutdown System. The test involved modeling the injection of He-3 • into three hollow rods in the core and performing an analysis ignoring the temperature feedback.

WSRC-TR-90-594 Validation and Verification Summary Report
December 1990 for GRIMHX and TRIMHX (U) , The adiabatic model employs a static reactor code (GRIMHX) to prepare input for a point kinetics code which provides assembly power as a function of time. This amounts to assuming that the computed flux shapes are based on the delayed neutron precursors being at equilibrium. The adiabatic model produced results which differed from those calculated by TRIMHX by less than 1.0%.
The results for total reactor power as a function of time are shown in Table V. lt should be noted that TRIMHX produces edits of power as a function of time directly.

Pulsed Neutron Experiments 7
Pulsed neutron experiments were carried out in the Process Development • Pile (PDP) at SRL. The test involved a hexagonal core surrounded by a hexagonal reflector. Control assemblies and fuel assemblies (E-D charge) were representative of typical SRS lattices.
'This core was then pulsed by a 3H(d,n)4He accelerator source.
Two assumptions were incorporated into the TRIMHX analysis.
The first of these is that discrepancies between calculated and measured values are due to errors in input parameters and not the calculation method. Therefore, with a normalization procedure, these differences can be removed. This can be seen in Figures 3 and 4. The second assumption was that if the space-time response of the reactor is adequately calculated using normalized parameters, then static subcritical reactivity can be derived by using the same neutronics model and parameters (i.e. in the GRIMHX code). _ . The space-time calculational method is unaffected by the problems of ' kinetic distortion and prompt and delayed harmonics. Kinetic distortion results from spatial and spectral differences between the fundamental prompt and delayed neutron modes. To the extent 2-group treatment was adequate, the effects of delayed and prompt harmonics and kinetic distortions were directly included in the space-time calculation of the experiments.
Although the reflected lattice produced kinetic distortion and harmonic distortion which invalidates the conventional methods of determining reactivities, for illustration Table VI compares the conventional and space-time results.
The space-time results were found using data only after the fundamental mode had been established.
Comparisons of the calculated to measured data showed that after suitable normalization of the production cross sections the overall prompt neutron response to a pulsed source was well represented.
These comparisons were made against experiments at critical conditions and at varying degrees of subcriticality.
In ali cases there was good agreement between the measured and calculated kelf. The space-time method should be among the most accurate of methods proposed to date for deducing the J subcritical reactivity from pulsed neutron experiments.

2-D Experiments 8
In 1974 experiments were carried out to measure delayed neutron holdback in the PDP. The control and fuel (E-D charge) were representative of typical SRS lattices.
TRIMHX (2-D) was used to model the reactor response.
Two experiments were conducted; the first involved ' an initial flux shape peaked in the center, the second a flux shape dished in the center. Reactivity transients were initiated by dropping 2 or more 235U bearing rods into the lattice at selected perturbation sites in Gang 3 as this location maximized flux tilt. Gold pin activation was used to measure the radial flux shape.
Flux tilts between pairs of detectors were determined (i.e. tilt ( from the gold pin activation and from TRIMHX calculated fluxes and compared.
The geometry of Experiment 1 is shown in Figure 5. In this experiment the perturbation was initiated by dropping three perturbation rods into prepared fuel sites.
Four detectors were placed in interstitial positions, and TRIMHX was used to calculate the time response out to approximately 90% of the asymptotic value. Due to computing cost, GRIMHX was used to determine the asymptotic solution.
The geometry used in Experiment 2 is shown in Figure 6. In this case the perturbation was initiated by the dropping of two perturbation rods into prepared fuel sites. In this experiment, the number of detectors were doubled and the detectors were moved to actual fuel sites. Once again GRIMHX was used to calculate the asymptotic solution.
In the analysis of both experiments, the exponential transform option was used in TRIMHX. Also, the vT.,f value input to TRIMHX was adjusted to produce agreement with measured data such as static kelf, flux shape and perturbation worth, lt should be noted that the asymptotic flux distribution is not normalized even though the perturbation worth is.
The results from Experiment 1 (Figure 7) show that the tilt between detector pairs is well represented by GRIMHX/TRIMHX.
In particular the fraction of delayed neutron holdback in the total tilt has been calculated very accurately.
Some discrepancies remained in the absolute tilt with errors of as much as 4%. Much of this error may be attributable to the interstitial placement of the detectors.
Since the product of flux times volume at the cell level is the smallest spatial flux editable, TRIMHX is unable to compute values for the interstitial spaces directly, but instead they must be inferred from the flux in surrounding cells. As seen in Figure  8, Experiment 2 was found to be more accurate. This increased accuracy has been attributed to the placement of the detectors in fuel positions where the TRIMHX code can calculate the flux directly.
In addition to the flux tilts, the net reactivity addition to the lattice was calculated by GRIMHX to be 15.4 cents. The reactivity change was also found by inserting the measured stable period into the Inhour equation. The Inhour calculated value was also 15.4 cents.
This validation shows that TRIMHX/GRIMHX can accurately reproduce the flux shapes (as measured by tilt ratios), the reactivity worth of the perturbation and the thermal reactor response under transient conditions In 1977 zero power tests were performed in the PDP to allow further measurement of delayed neutron holdback. Control and fuel (E-D charge) were typical of SRS operation.
Three experiments, each initiated from stable critical reactor conditions, were conducted which measured neutron flux responses and used these to compute flux tilts. TRIMHX was used to model the reactor response, and the calculated flux tilts were compared to those measured.
Descriptions of the three experiments follow.
The reactivity perturbation in Experiment 1 was initiated by dropping • three rods (each containing 235U slugs on the bottom and 6Li on top) into the central hex of the core. This distorted the flux shape in the axial and radial dimensions, but not in the azimuthal. The space-time effect of delayed neutron holdback was relatively small in this transient as shown by the small difference between tiltsat the end of the rod insertion (5.1 sec) and the asymptotic tilts (see Figures 9, 10 and 11). Experiment 2 began from the same core configuration as Experiment 1 with the exception of three rods (235U slugs in the bottom and AI in the , top) being dropped into each of two hexes in Gang 3 (for a total of 6 rods). This produced a flux tilt in the axial, radial and azimuthal directions. The space-time effects of delayed neutron holdback was most pronounced in the radial and azimuthaA directions, but was small in the axial.
In Experiment 3, the reactivity perturbation was caused by pulling one full length Cadmium (Cd) rod from ali Gang 1 assemblies (about 20% of the core) at 3.05 cm/sec.
Due to the slow rate of withdrawal, the observed delayed neutron holdback was very small.  I I  I  III  II  I I IIII I III The /esults from Experiment 1 are shown in Figures 9, 10 and 11; results from Experiment 2 are shown in Figures 12, 13 and 14; results from Experiment 3 are shown in Figures 15, 16 and 17. In ali cases the exponential transform was used to accelerate convergence, and as they were in the 2-D experiments, the two-group macroscopic cross sections were normalized to better match the observed data. The results from these experiments showed that the measured tilts from detectors paired axially, radially and diagoriaXly were well represented by TRIMHX/GRIMHX. The influence of dela_,ed neutron holdback in the tilts was calculated accurately, however, small discrepancies in home of the individual tilts were evident. The largest discrepancy for e×periment 1 was 2.3%; for experiment 2 was 2.4%; and for experiment 3 was 4.8%. In ali comparisons, the tilt discrepancy was largest when a detector close to a region of positive reactivity was involved.
In addition to the flux tilts, an analysis of the _(t)/_(0) kinetic data was J calculated using the Inhour equation.
Perturbation reactivity worths compared well with those calculated by GRIMHX using normalized cross • sections. This can be seen in Figure 18.
These experiments demonstrate that TRIMHX accurately predicts the course of zero-power thermal reactor transients in 3-D. The time dependence and magr_itude of delayed neutron holdback were directly tested.

:_, VALIDATION AGAINST MCNP lO
In 1989 MCNP was used to validate GRIMHX for the determination of safety rod worths. Safety rod worths were computed by each code for a variety of initial flux shapes, rod configurations and material contents.
Since the original issue of this document, these results have been recomputed, and it is expected that the report will be reissued.
Until that time, the results and conclusions drawn from the first report will not be reported . here.

COMPARISONS OF PAST AND PRESENT CODE VERSIONS
In 1989 Gregory reran the HTGR benchmark problem on the current production version of GRIMHX. Tables VII and VIII show the results of this benchmark 11 were identical to those found when running the odginal version of the code. Eigenvalue, flux distribution and number of outer iterations were alp tested using the benchmark and found to be exactly the same as those determined earlier .
In 1990 this benchmark was run again by Trumble on GRIMHX and was also used to test the static solution of TRIMHX . Table IX shows the results of these calculations 12 with both , GRIMHX and TRIMHX converging to the same value as the original benchmark, As part of this later work, a consistency check was also run on the results of TRIMHX versus those fo_'_d via the adiabatic model (GR!MHX plus point kinetics). These results (Figure 19) show that TRIMHX models the core during a transient in an accurate and predictable manner.

QUALITY ASSURANCE
This report was generated under QA Task 90-044-1, Certification Plan for GRIMHX, TRIMHX and GILDA Codes.