Verify, refine, save and make one defensible change
核验、细化、保存并做一项可辩护的修改
COMSOL 6.4 desktop instructions. Each numbered card tells you where to click, what to enter, and how to check it. Complete one card before moving down. English menu labels are retained beside the Chinese explanation.
本教程使用 COMSOL 6.4 桌面界面。每张编号卡明确点击位置、输入内容和核对办法；做完一张再向下。英文菜单名称与中文解释并列保留。
A · Complete Model A’s gas sweep and accepted refinements
A · 完成模型 A 气体扫描与验收细化
You now have working models. Before interpreting them, reproduce the independent controls. Keep the original solved practice file and perform each control in a Save As copy or a separate study. The final A file contains five 3D components and seven stored study solutions; the external strongest-gas time/mesh controls are additional verification files.
模型可运行后，先复现独立对照再作解释。保留原有已解练习文件；每项对照在另存副本或独立研究中进行。最终 A 文件包含五个三维组件与七组存储研究解；最强气体的独立时间／网格对照另存为核验文件。
01 Run all seven gas input cases
运行全部七个气体输入情形
Open your complete Model A practice file. Click the cG study’s Time Dependent step. Expand Study Extensions, enable Auxiliary sweep, add gasCase with the list below. Keep the geometry/mesh fixed: the gas matching radius is 110 μm and the local mesh size is the fixed 12.9260865 μm from M1. Compute only that study. Keep the accepted 25 ns solver settings for this baseline.
打开自己的完整模型 A，点击 cG 研究的 Time Dependent。展开 Study Extensions，启用 Auxiliary sweep，添加下面 gasCase 参数列表。保持几何／网格固定：匹配半径 110 μm，局部网格尺寸为 M1 固定的 12.9260865 μm。只 Compute 该研究，基线保持 25 ns 求解设置。
| Field / 字段 | Select or enter exactly / 精确选择或输入 |
|---|---|
| Parameter name | gasCase |
| Parameter value list | 0 1 2 3 4 5 6 |
| Parameter unit | 1 |
You should see: Seven cases ×321 output times =2247 parameter/time states. Select gasCase=3 in the result plot to compare the strongest sampled case.
应当看到：七情形 ×321 输出时刻 =2247 个参数／时间状态；结果图选择 gasCase=3 比较最强采样情形。
02 Add the accepted small-gas correction study
添加已验收的小气体修正研究
Right-click model root → Add Study → Time Dependent → Add Study. Label = Small gas correction. In its step, enable Solve for only cG’s two interfaces. Add an Auxiliary sweep gasCase=0. Set the output list below, then Show Default Solver and apply M1’s scaling/Direct/Fully Coupled procedure with the refined step below. Compute this study.
右击模型根节点 → Add Study → Time Dependent → Add Study，Label = Small gas correction。步骤中只求解 cG 两个接口；添加 gasCase=0 辅助扫描，设置下列输出。Show Default Solver，按 M1 手动缩放／直接／全耦合方法配置，并用下列细时间步；只 Compute 当前研究。
| Field / 字段 | Select or enter exactly / 精确选择或输入 |
|---|---|
| Output times | range(0,12.5[ns],8[us]) |
| gasCase list | 0 |
| Relative tolerance | 2e-5 |
| Method | Generalized alpha |
| Steps taken by solver | Manual |
| Time step | 6.25[ns] |
| Amplification for high frequency | 0.75 |
You should see: 641 output states; refined case-0 peak≈31.1535 kPa. The old 25 ns case-0 waveform failed the selected error gate and is superseded.
应当看到：641 个输出状态；细化情形 0 峰值约 31.1535 kPa。旧 25 ns 情形 0 波形未通过误差门槛，须由此修正替代。
03 Add the refined uniform diagnostic study
添加细化均匀诊断研究
Add another Time Dependent study, Label = Uniform diagnostic refinement. Enable Solve for only the cU PDE/global interfaces, no auxiliary sweep. Generate its solver and repeat the Direct/Fully Coupled/manual scaling steps, using the refined settings below.
再添加 Time Dependent 研究，Label = Uniform diagnostic refinement，仅求解 cU 的 PDE／全局接口，不添加辅助扫描。生成求解器，重复直接／全耦合／手动缩放步骤，使用下面细化设置。
| Field / 字段 | Select or enter exactly / 精确选择或输入 |
|---|---|
| Output times | range(0,12.5[ns],8[us]) |
| Relative tolerance | 2e-6 |
| Method | Generalized alpha |
| Steps taken by solver | Manual |
| Time step | 6.25[ns] |
| Amplification for high frequency | 0.75 |
You should see: 641 states, diagnostic receiver peak≈16.6514 kPa; numerical convergence does not accept the physical closure.
应当看到：641 个状态，诊断接收峰值约 16.6514 kPa；数值收敛不代表物理闭合被接受。
04 Add maximum operator maxpopcU
添加Maximum算子 maxpopcU
Right-click Component → Definitions → Nonlocal Couplings → Maximum. Change the actual Operator name field, then choose the geometric level and named selection below. Renaming only the tree Label does not rename the operator.
右击 Component → Definitions → Nonlocal Couplings（非局部耦合）→ Maximum。修改真正的 Operator name（算子名称） 字段，再选择几何层级与命名选择。只改树上的 Label 不会修改算子名。
| Field / 字段 | Select or enter exactly / 精确选择或输入 |
|---|---|
| Operator name | maxpopcU |
| Geometric entity level | Domain |
| Selection | populationcU |
You should see: maxpopcU appears as the operator name. The highlighted entities match populationcU.
应当看到：算子名称为 maxpopcU；高亮实体与 populationcU 相符。
Why this choice: An integral over the right selection turns a local field into a scalar available to the global equations.
为何这样设置：在正确选择上积分，将局部场转换为全局方程可用的标量。
If this does not work / 如果这一步不成功
If the named selection is missing, check its entity level. A boundary selection cannot be used as a domain selection.
如果下拉框中没有对应选择，先检查其几何层级；边界选择不能用于域选择。
05 Add minimum operator minpopcU
添加Minimum算子 minpopcU
Right-click Component → Definitions → Nonlocal Couplings → Minimum. Change the actual Operator name field, then choose the geometric level and named selection below. Renaming only the tree Label does not rename the operator.
右击 Component → Definitions → Nonlocal Couplings（非局部耦合）→ Minimum。修改真正的 Operator name（算子名称） 字段，再选择几何层级与命名选择。只改树上的 Label 不会修改算子名。
| Field / 字段 | Select or enter exactly / 精确选择或输入 |
|---|---|
| Operator name | minpopcU |
| Geometric entity level | Domain |
| Selection | populationcU |
You should see: minpopcU appears as the operator name. The highlighted entities match populationcU.
应当看到：算子名称为 minpopcU；高亮实体与 populationcU 相符。
Why this choice: An integral over the right selection turns a local field into a scalar available to the global equations.
为何这样设置：在正确选择上积分，将局部场转换为全局方程可用的标量。
If this does not work / 如果这一步不成功
If the named selection is missing, check its entity level. A boundary selection cannot be used as a domain selection.
如果下拉框中没有对应选择，先检查其几何层级；边界选择不能用于域选择。
06 Evaluate the uniform-closure failure
计算均匀闭合的失效指标
In Global Evaluation choose the refined cU dataset and add the expressions below. If operators were added after solving, right-click this study → Update Solution before evaluating. Inspect extrema over all times, not just the receiver peak.
在 Global Evaluation 选择细化 cU 数据集，添加下面表达式。若求解后才添加算子，先右击研究 → Update Solution。检查全部时刻的极值，不能只看接收峰值。
You should see: Local pressure differs strongly from the population average; the negative local absolute pressure invalidates the assumed common-state liquid closure.
应当看到：局部压力大幅偏离泡群平均值；局部绝对压力为负，违背假定的共同状态液体闭合。
| Expression | Unit | Meaning / 含义 |
|---|---|---|
cU.maxpopcU(cU.pAc)-cU.ipcU(cU.pAc)/cU.ipcU(1) | kPa | Positive local feedback deviation / 正局部反馈偏离 |
cU.ipcU(cU.pAc)/cU.ipcU(1)-cU.minpopcU(cU.pAc) | kPa | Negative local feedback deviation / 负局部反馈偏离 |
DP+cU.minpopcU(cU.pAc) | kPa | Minimum local absolute pressure / 最小局部绝对压力 |
07 Save a checkpoint
保存检查点
Choose File → Save As. Save as Model_A_verified_my_rebuild.mph in your own practice folder. For subsequent cards use Ctrl+S. Keep the accepted delivered models as reference files.
选择 File → Save As（另存为），在自己的练习文件夹保存为 Model_A_verified_my_rebuild.mph。后续操作用 Ctrl+S 保存。保留已经交付的模型作为参考。
You should see: Five components and all seven primary/correction studies are preserved.
应当看到：保留五个组件及七个主／修正研究解。
B · Separate time, mesh and outer-domain checks
B · 分离时间、网格与外域检验
08 Refine the strongest gas case in a copy
在副本中细化最强气体情形
Save As Model_A_gas_time_check.mph. In the gas study use an Auxiliary sweep containing only gasCase=3. Set Output times = range(0,12.5[ns],8[us]); set the actual generalized-alpha Time step =12.5[ns], relative tolerance=2e-5 and high-frequency amplification=0.75. Keep every geometry and mesh size unchanged. Compute.
另存为 Model_A_gas_time_check.mph。气体辅助扫描只保留 gasCase=3，Output times = range(0,12.5[ns],8[us])，真正的广义 α 时间步 =12.5[ns]，相对容差=2e-5，高频放大因子=0.75。全部几何／网格尺寸保持原值，Compute。
You should see: Peak≈89.610251 kPa versus baseline≈89.587 kPa; relative peak change≈0.02594%. Maximum normalized energy residual≈0.10289%.
应当看到：峰值约 89.610251 kPa，对比基线约 89.587 kPa；相对峰值变化约 0.02594%，最大归一化能量残差约 0.10289%。
09 Refine the strongest gas mesh in a different copy
在另一个副本中细化最强气体网格
Reopen the original 25 ns gas baseline, Save As Model_A_gas_mesh_check.mph. Keep gasCase=3 and 25 ns. In Mesh → Size set global Maximum element size=100[um]. In the source boundary Size set Maximum element size below. Build All mesh, Compute, then compare to the 25 ns baseline.
重新打开原 25 ns 气体基线，另存为 Model_A_gas_mesh_check.mph。保持 gasCase=3 与 25 ns。全局 Mesh → Size 的 Maximum element size=100[um]；源面局部 Size 的最大尺寸改为下值。Build All 网格，Compute，与 25 ns 基线比较。
| Field / 字段 | Select or enter exactly / 精确选择或输入 |
|---|---|
| Global maximum element size | 100[um] |
| Source boundary maximum element size | 6.4630432580431044e-06[m] |
You should see: Peak≈89.5931 kPa; change from the baseline≈0.00684%.
应当看到：峰值约 89.5931 kPa，与基线变化约 0.00684%。
Why this choice: Changing one discretization at a time tells you which error is being reduced.
为何这样设置：每次只改变一种离散设置，才能识别减少的是哪种误差。
10 Check the five-source outer boundary distance
检查五源外边界距离
Use a Save As copy of Model A. Change Lout=1.2[mm]. In the c5 component Build All geometry and mesh, check the detector/source/far selections again, and Compute only c5 with the original 25 ns settings. Changing global Lout affects other geometries too, so keep this as a separate control file.
另存模型 A 副本，Lout=1.2[mm]。在 c5 组件 Build All 几何与网格，重新核对 detector／source／far 选择，只用原 25 ns 设置求解 c5。全局 Lout 会影响其他几何，因此保留为独立对照文件。
You should see: Five-source peak≈4.69031 kPa; change≈0.25155%.
应当看到：五源峰值约 4.69031 kPa，变化约 0.25155%。
11 Make a 3D pressure plot from the correct component
从正确组件制作三维压力图
Right-click Results → Datasets → Cut Plane. Data = the desired cP/c5 solution dataset. For cP use Plane type = Quick, Plane = xz, y=0; for c5 use xy, z=0. Right-click Results → 3D Plot Group, Data = this Cut Plane; add Surface and set the corresponding pAc expression below. Choose t=5.025[us] for cP or 3.275[us] for c5 and Plot.
右击 Results → Datasets（数据集）→ Cut Plane（截平面），Data 选 cP 或 c5 的解。cP 使用 Quick 平面 xz、y=0；c5 使用 xy、z=0。新建 3D Plot Group，以截平面为 Data，添加 Surface，填写下列对应 pAc。cP 选择 t=5.025[us]，c5 选择 3.275[us]，Plot。
| Field / 字段 | Select or enter exactly / 精确选择或输入 |
|---|---|
| Single-PFP expression | cP.pAc |
| Five-PFP expression | c5.pAc |
| Unit | kPa |
You should see: The geometry belongs to the selected component, with one or five matching holes. pAc is unfiltered gauge pressure; pdet*DP is the filtered scalar receiver result.
应当看到：图形属于选定组件，有一个或五个匹配孔。pAc 是未滤波表压，pdet*DP 才是滤波标量接收结果。
C · Independent 3D gel controls and mesh checks
C · 独立三维凝胶对照与网格检查
12 Create the elastic-pressure control copy
创建弹性压力对照副本
Open your B baseline, Save As Model_B_elastic_control.mph. Disable the Global ODEs and DAEs interface in this control study. In Boundary Load replace pLP-p0 by pLoad. In Parameters choose lam=1.2 first; keep sigTest=sigLL and pLoad=G/2*(5-4/lam-lam^(-4))+2*sigTest/(a*lam). Create a Stationary control study with an Auxiliary sweep lam=1.2 1.5 2 2.1 2.5; solve only Solid Mechanics, reuse solutions.
打开 B 基线，另存为 Model_B_elastic_control.mph。此对照研究中禁用全局 ODE 接口。Boundary Load 将 pLP-p0 换成 pLoad。Parameters 先设 lam=1.2，保留 sigTest=sigLL 及 pLoad=G/2*(5-4/lam-lam^(-4))+2*sigTest/(a*lam)。新建 Stationary 对照研究，辅助扫描 lam=1.2 1.5 2 2.1 2.5，只求解 Solid Mechanics、重复使用上一解。
You should see: Pressure is imposed; displacement remains free. This is an analytic elasticity/surface-force control rather than a PFP phase solve.
应当看到：施加已知压力，位移仍然自由；此项检验弹性与表面力，不求 PFP 相态。
Why this choice: A pressure-driven cavity must recover the established infinite incompressible spherical law when the finite outer domain and compressibility errors are small.
为何这样设置：在有限外域及可压误差小时，压力驱动空腔应恢复无限不可压球形参考规律。
13 Evaluate the independent elastic laws
计算独立弹性规律
Use the same manual scaling and fully coupled/PARDISO stationary solver as M2, except the ODE field is not solved. Compute the control and add the expressions below to Global Evaluation. Use Rfree/a as the actual solved stretch in the reference laws.
使用 M2 同样的手动缩放、全耦合／PARDISO 稳态求解器，但不求 ODE 场。求解后在 Global Evaluation 加入下列表达式，参考规律中的伸长使用实际求解的 Rfree/a。
You should see: Analytic pressure/work discrepancies are small. The accepted phase-model controls had ≈0.01845% pressure and ≈0.02770% work differences.
应当看到：解析压力／功差异应小；已验收相态模型对照的压力差约 0.01845%，功差约 0.02770%。
| Expression | Unit | Purpose / 目的 |
|---|---|---|
c.Rfree/a | 1 | Solved stretch / 求解伸长 |
pLoad-2*sigTest/c.Rfree | kPa | Native elastic reaction / 原生弹性反力 |
G/2*(5-4/(c.Rfree/a)-(c.Rfree/a)^(-4)) | kPa | Infinite-domain pressure / 无限域压力 |
c.iv(c.solid.Ws) | pJ | Native elastic work / 原生弹性功 |
2*pi*G*a^3*(5*(c.Rfree/a)^3/3-2*(c.Rfree/a)^2+1/(c.Rfree/a)-2/3) | pJ | Independent analytic work / 独立解析功 |
14 Reproduce the B coarse-mesh comparison
复现 B 粗网格比较
Reopen the accepted B phase baseline and Save As Model_B_coarse_check.mph. Keep all phase equations, energy values and free boundaries. In global Size set hmax=B*a/4, hmin=a/4, growth=1.6 and curvature=0.25. In cavity Size set Maximum element size=a/3. Build All mesh, compute the original Qdep sweep, then compare the same columns to the fine-mesh results.
重开已验收 B 相态基线，另存为 Model_B_coarse_check.mph。保持相态方程、能量和自由边界。全局 Size 设 hmax=B*a/4、hmin=a/4、growth=1.6、curvature=0.25；空腔面 Size 最大尺寸=a/3。Build All 网格，求原 Qdep 扫描，比较粗细网格对应列。
You should see: The accepted equivalent-stretch mesh change was ≈0.033555%, but the local principal-stretch change was ≈1.7538%. The 11.75 pJ verdict therefore remains borderline.
应当看到：已验收等效伸长网格变化约 0.033555%，但局部主伸长变化约 1.7538%；因此 11.75 pJ 判断仍属边缘。
D · Four B sensitivities at fixed retained energy
D · 固定保留能量的四组 B 敏感性
15 Return to the fine B baseline
回到 B 细网格基线
Open your Model_B_baseline_solved_my_rebuild.mph. Save As Model_B_with_sensitivities.mph. Keep the fine mesh from M2. Add caseIndex=0 to Parameters. Do not use the coarse/control file.
打开 Model_B_baseline_solved_my_rebuild.mph，另存为 Model_B_with_sensitivities.mph。保持 M2 细网格，在 Parameters 添加 caseIndex=0，不使用粗网格或弹性对照文件。
| Field / 字段 | Select or enter exactly / 精确选择或输入 |
|---|---|
| New parameter caseIndex | 0 |
You should see: The original five Qdep solution states remain saved.
应当看到：原有五个 Qdep 解状态仍已保存。
16 Create sensitivity function Gcase
创建敏感性函数 Gcase
Right-click Global Definitions → Functions → Interpolation. Data source = Local table. Set Function name=Gcase, argument unit=1, function unit=Pa, interpolation=Linear; enter the four rows below or load GUI_Gcase_table.txt.
右击 Global Definitions → Functions → Interpolation，Data source = Local table，Function name=Gcase、参数单位=1、函数单位=Pa、插值=Linear。输入下面四行或加载 GUI_Gcase_table.txt。
You should see: Only indices 0–3 are used in the admissible four-case sweep.
应当看到：有效四情形扫描只使用索引 0—3。
| t / index | f(t) / value |
|---|---|
| 0 | 10000 |
| 1 | 10000 |
| 2 | 10000 |
| 3 | 27027.027027 |
17 Create sensitivity function LLcase
创建敏感性函数 LLcase
Right-click Global Definitions → Functions → Interpolation. Data source = Local table. Set Function name=LLcase, argument unit=1, function unit=N/m, interpolation=Linear; enter the four rows below or load GUI_LLcase_table.txt.
右击 Global Definitions → Functions → Interpolation，Data source = Local table，Function name=LLcase、参数单位=1、函数单位=N/m、插值=Linear。输入下面四行或加载 GUI_LLcase_table.txt。
You should see: Only indices 0–3 are used in the admissible four-case sweep.
应当看到：有效四情形扫描只使用索引 0—3。
| t / index | f(t) / value |
|---|---|
| 0 | 0.053999999999999999 |
| 1 | 0.053999999999999999 |
| 2 | 0.053999999999999999 |
| 3 | 0.053999999999999999 |
18 Create sensitivity function LVcase
创建敏感性函数 LVcase
Right-click Global Definitions → Functions → Interpolation. Data source = Local table. Set Function name=LVcase, argument unit=1, function unit=N/m, interpolation=Linear; enter the four rows below or load GUI_LVcase_table.txt.
右击 Global Definitions → Functions → Interpolation，Data source = Local table，Function name=LVcase、参数单位=1、函数单位=N/m、插值=Linear。输入下面四行或加载 GUI_LVcase_table.txt。
You should see: Only indices 0–3 are used in the admissible four-case sweep.
应当看到：有效四情形扫描只使用索引 0—3。
| t / index | f(t) / value |
|---|---|
| 0 | 0.00941 |
| 1 | 0.0080000000000000002 |
| 2 | 0.014 |
| 3 | 0.00941 |
19 Create sensitivity function rhoColdCase
创建敏感性函数 rhoColdCase
Right-click Global Definitions → Functions → Interpolation. Data source = Local table. Set Function name=rhoColdCase, argument unit=1, function unit=kg/m^3, interpolation=Linear; enter the four rows below or load GUI_rhoColdCase_table.txt.
右击 Global Definitions → Functions → Interpolation，Data source = Local table，Function name=rhoColdCase、参数单位=1、函数单位=kg/m^3、插值=Linear。输入下面四行或加载 GUI_rhoColdCase_table.txt。
You should see: Only indices 0–3 are used in the admissible four-case sweep.
应当看到：有效四情形扫描只使用索引 0—3。
| t / index | f(t) / value |
|---|---|
| 0 | 1623.3028161533516 |
| 1 | 1623.3028161533516 |
| 2 | 1623.3028161533516 |
| 3 | 1623.3028161533516 |
20 Use the material/interface case functions
采用材料／界面情形函数
In Parameters replace only the four expressions below, and change lam to the new initial-guess value. Keep a, B and BK unchanged. In Global Equations 1 replace only the three Initial value entries below; their equations remain the same.
在 Parameters 只替换下列四个表达式，并修改 lam 初猜。a、B、BK 保持不变。Global Equations 1 中只修改下面三个 Initial value，方程保持原值。
| Field / 字段 | Select or enter exactly / 精确选择或输入 |
|---|---|
| G | Gcase(caseIndex) |
| sigLL | LLcase(caseIndex) |
| sigLV | LVcase(caseIndex) |
| rhoD | rhoColdCase(caseIndex) |
| lam | 2.5441334743639912 |
| theta initial value | 1.1398107875349053 |
| qL initial value | -0.093845518489624163 |
| qV initial value | 1.3349352599864706 |
You should see: Only the inputs and initial guesses change; cavity displacement remains unconstrained.
应当看到：只有输入与初猜改变，空腔位移仍不受规定。
21 Create and solve the sensitivity study
创建并求解敏感性研究
Add a new Stationary study. Enable both c.solid and c.ge, include geometric nonlinearity. Enable Auxiliary sweep and choose Specified combinations; add both rows below. Reuse solution from previous step=Yes. Show Default Solver, use manual scales a/G/1, Fully Coupled with maximum iterations=12, PARDISO and relative tolerance=1e-7, then Compute this new study.
新建 Stationary 研究，启用 c.solid、c.ge，启用几何非线性。辅助扫描选择 Specified combinations（指定组合），添加下面两行，Reuse solution from previous step=Yes。Show Default Solver，缩放 a／G／1，全耦合最大迭代数=12、PARDISO、相对容差=1e-7，然后只求新研究。
| Field / 字段 | Select or enter exactly / 精确选择或输入 |
|---|---|
| caseIndex: values; unit | 0 1 2 3; 1 |
| Qdep: values; unit | 13 13 13 13; pJ |
| Combination rule | Specified combinations |
You should see: Four states at 13 pJ. All exceed the chosen local stretch proxy; case 3 uses G≈27.027 kPa.
应当看到：四个 13 pJ 状态；全部超过所选局部伸长替代判据，第 3 情形 G≈27.027 kPa。
If this does not work / 如果这一步不成功
All combinations would create 16 duplicated states rather than four specified pairs. Do not add the coated-interface cases 4/5: those native solves were unconverged and are not accepted final states.
All combinations 会产生 16 个重复状态，不是四个指定配对。不要添加涂层界面情形 4／5；原生计算未收敛，不属于验收最终状态。
22 Save a checkpoint
保存检查点
Choose File → Save As. Save as Model_B_verified_my_rebuild.mph in your own practice folder. For subsequent cards use Ctrl+S. Keep the accepted delivered models as reference files.
选择 File → Save As（另存为），在自己的练习文件夹保存为 Model_B_verified_my_rebuild.mph。后续操作用 Ctrl+S 保存。保留已经交付的模型作为参考。
You should see: Five baseline plus four sensitivity states are retained with their separate datasets.
应当看到：五个基线与四个敏感性状态通过独立数据集保存。
E · One change you must predict and then test
E · 先预测，再检验一项修改
23 Choose one controlled change and predict its effect
选择一项可控制的修改，先预测影响
For the first independent exercise, use H0 and increase G from 10[kPa] to 20[kPa] while holding R0, viscosity, gas law and xinit fixed. Before Compute, calculate the new Ks and w0 from the parameter expressions, and predict whether the oscillation period increases or decreases. Save as a separate file, then solve and plot against your original H0.
首次独立练习使用 H0：G 从 10[kPa] 增至 20[kPa]，保持 R0、黏度、气体定律、xinit 不变。Compute 前由参数表达式算新 Ks、w0，预测振荡周期变长还是变短。另存文件、求解，并与原 H0 比较。
You should see: Your prediction, input change and measured period form a consistent explanation. Do not change multiple inputs or only edit a plot legend.
应当看到：预测、输入修改、实测周期构成一致解释；不要一次改多个输入，也不能只改图例。
For a complete rebuild demonstration, show your own Model Builder tree, input tables, solved observables, one refinement comparison and a saved file that reopens with its solution. I will check one stage at a time. No learner mastery is recorded until you demonstrate these operations.
完整独立重建证明包括：自己的节点树、输入表、求解观测量、一项细化比较、可重开且含解的保存文件。我会逐阶段检查；只有完成操作证明后才记录掌握。
