From 452123b06a1abdfe9040b7c31889aafea0b3dd75 Mon Sep 17 00:00:00 2001
From: lvjunjie <lvjunjie@abc.com>
Date: Tue, 22 Sep 2026 10:09:10 +0800
Subject: [PATCH] =?UTF-8?q?refactor(nmNum):=20=E5=B0=86=20LM=20=E5=BD=A2?=
 =?UTF-8?q?=E7=8A=B6=E9=98=B6=E6=AE=B5=E6=94=B9=E4=B8=BA=E9=80=90=E5=8F=82?=
 =?UTF-8?q?=E6=95=B0=E5=8D=95=E8=BD=AE=E8=B0=83=E6=95=B4?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 Bin/Config/Lang/cn/nmNum_cn.qm                | Bin 147250 -> 147243 bytes
 Bin/Config/Lang/cn/nmNum_cn.ts                |  12 +-
 .../nmCalculation/nmCalculationAutoFitLM.cpp  | 267 ++++++++++--------
 3 files changed, 162 insertions(+), 117 deletions(-)

diff --git a/Bin/Config/Lang/cn/nmNum_cn.qm b/Bin/Config/Lang/cn/nmNum_cn.qm
index 776d7652a03136f518578c753c99f83aeb04808f..a0b706a0031440ddad072be980c7a0d71e81241e 100644
GIT binary patch
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diff --git a/Bin/Config/Lang/cn/nmNum_cn.ts b/Bin/Config/Lang/cn/nmNum_cn.ts
index 6515933d..623ec74d 100644
--- a/Bin/Config/Lang/cn/nmNum_cn.ts
+++ b/Bin/Config/Lang/cn/nmNum_cn.ts
@@ -1277,16 +1277,16 @@ Reason: %1</source>
         <translation>接受灵敏度探针：形状误差=%1</translation>
     </message>
     <message>
-        <source>fresh sensitivity at joint shape entry</source>
-        <translation>进入联合形状调整时重建灵敏度</translation>
+        <source>fresh sensitivity at single-parameter shape entry</source>
+        <translation>进入单参数形状调整时重建灵敏度</translation>
     </message>
     <message>
         <source>Adaptive fitting counts: %1 shape attempts, %2 total-stage iterations, %3 total evaluations.</source>
         <translation>自适应拟合统计：形状尝试 %1 次，整体阶段迭代 %2 次，累计评估 %3 次。</translation>
     </message>
     <message>
-        <source>LM stage 2: joint shape search; after 2 ineffective steps, refresh sensitivity and confirm with one global step.</source>
-        <translation>LM 第二阶段：联合调整全部可调形状参数；连续两次改善不足后，刷新灵敏度并用一次全局联合调整确认。</translation>
+        <source>LM stage 2: adjust each shape parameter once; double the step after improvement, halve it after rejection, and switch after 3 consecutive rejections.</source>
+        <translation>LM 第二阶段：逐个调整形状参数，每个参数只调一轮；改善后步长翻倍，拒绝后减半，连续拒绝三次后换下一个参数。</translation>
     </message>
     <message>
         <source>LM starting point error: %1; independent total-stage evaluation budget: %2</source>
@@ -1313,8 +1313,8 @@ Reason: %1</source>
         <translation>进入整体阶段时建立完整灵敏度</translation>
     </message>
     <message>
-        <source>no significant shape improvement after fresh sensitivity and one global step</source>
-        <translation>刷新灵敏度并进行一次全局联合调整后，形状仍无显著改善</translation>
+        <source>all shape parameters visited once</source>
+        <translation>所有形状参数均已完成一轮调整</translation>
     </message>
     <message>
         <source>no valid early sensitivity model</source>
diff --git a/Src/nmNum/nmCalculation/nmCalculationAutoFitLM.cpp b/Src/nmNum/nmCalculation/nmCalculationAutoFitLM.cpp
index 78ab27e9..55d8c7a6 100644
--- a/Src/nmNum/nmCalculation/nmCalculationAutoFitLM.cpp
+++ b/Src/nmNum/nmCalculation/nmCalculationAutoFitLM.cpp
@@ -671,6 +671,30 @@ static bool buildTrustRegionFisherStep(
     return projectAndPredict();
 }
 
+// 为每个可调参数独立求解 LM 步，按边界投影后的预测下降量选择一个参数。
+static bool buildBestSingleParameterStep(const TrustRegionFisher& information,
+        const QVector<int>& available, const QVector<double>& coordinates,
+        double damping, double trustRadius, double minimumStep,
+        QVector<int>* selected, QVector<double>* step, double* predictedReduction)
+{
+    selected->clear();
+    step->fill(0.0, coordinates.size());
+    *predictedReduction = 0.0;
+    for(int i = 0; i < available.size(); ++i) {
+        QVector<int> singleColumn(1, available[i]);
+        QVector<double> trialStep;
+        double trialPrediction = 0.0;
+        if(buildTrustRegionFisherStep(information, singleColumn, coordinates,
+                damping, trustRadius, minimumStep, &trialStep, &trialPrediction) &&
+                trialPrediction > *predictedReduction) {
+            *selected = singleColumn;
+            *step = trialStep;
+            *predictedReduction = trialPrediction;
+        }
+    }
+    return !selected->isEmpty();
+}
+
 // 前期每次只调一个参数：间距锁定符号，形状 LM 提供幅度和后续验收依据。
 static bool buildEarlyGapGuidedStep(const TrustRegionFisher& shapeInformation,
         const QVector<int>& selected, const QVector<double>& coordinates, double direction,
@@ -691,7 +715,7 @@ static bool buildEarlyGapGuidedStep(const TrustRegionFisher& shapeInformation,
 }
 
 // 放大当前方向，仍受传入的最大半径和参数边界限制。
-// 普通形状步要求预测下降；前期初始探路可跨过预测上坡区，最终仍按真实形状验收。
+// 前期初始探路可跨过预测上坡区，最终仍按真实形状验收。
 static bool buildExpandedTrustRegionStep(const TrustRegionFisher& information,
         const QVector<double>& coordinates, const QVector<double>& originalStep,
         double maximumRadius, QVector<double>* expandedStep, double* prediction,
@@ -1123,7 +1147,7 @@ void nmCalculationAutoFitLM::writeTraceMetaFile()
 
     QTextStream out(&metaFile);
     out << "{\n";
-    out << "  \"schema_version\": 36,\n";
+    out << "  \"schema_version\": 39,\n";
     out << "  \"strategy\": \"permeability_height_then_shape_then_joint_lm\",\n";
     out << "  \"height_acceptance\": \"reliable_vertical_loss_decrease; no_shape_or_total_loss_constraint\",\n";
     out << "  \"shape_priority\": \"storage_then_skin_then_shape_without_wellbore_then_optional_wellbore_recheck\",\n";
@@ -1138,11 +1162,12 @@ void nmCalculationAutoFitLM::writeTraceMetaFile()
     out << "  \"early_wellbore_total_constraint\": false,\n";
     out << "  \"shape_stage_total_constraint\": false,\n";
     out << "  \"shape_wellbore_parameters_frozen\": true,\n";
-    out << "  \"shape_sensitivity_refresh\": \"non_wellbore_columns_only at joint shape entry and stagnation confirmation; full Jacobian rebuilt at total-stage entry\",\n";
-    out << "  \"shape_expansion_policy\": \"one expansion per accepted shape direction, up to 2x with predicted descent and parameter bounds; no_rho_gate; retain ordinary step on failure\",\n";
-    out << "  \"shape_global_parameter_selection\": \"all_valid_non_wellbore_columns_with_positive_response_at_every_shape_step; no_window_selection\",\n";
-    out << "  \"stage2_budget\": \"adaptive, no fixed iteration or evaluation quota; 2 ineffective shape attempts then one fresh-J global confirmation\",\n";
-    out << "  \"shape_step_improvement_threshold\": \"max(0.0001, 10% of last effective shape loss); accumulate small improvements\",\n";
+    out << "  \"shape_sensitivity_refresh\": \"non_wellbore_columns_once_at_sweep_entry; secant updates during sweep; full Jacobian rebuilt at total-stage entry\",\n";
+    out << "  \"shape_expansion_policy\": \"lock parameter and direction; after each strict shape decrease double next coordinate step from accepted point; otherwise retain point and halve step\",\n";
+    out << "  \"shape_radius_policy\": \"initial LM step capped at 0.24; subsequent coordinate steps capped at 0.60; no prediction-ratio gate\",\n";
+    out << "  \"shape_global_parameter_selection\": \"largest predicted reduction among unvisited non-wellbore parameters; finish current parameter before selecting next; each parameter visited once\",\n";
+    out << "  \"stage2_budget\": \"one parameter sweep; each parameter stops after 3 consecutive non-improving trials, a bound, or minimum step; existing solver failure limit retained\",\n";
+    out << "  \"shape_step_improvement_threshold\": \"any strict shape loss decrease; no cumulative improvement threshold\",\n";
     out << "  \"iteration_count_scope\": \"max_iterations applies to total-stage LM; trace iteration remains cumulative\",\n";
     out << "  \"wellbore_recheck_trigger\": \"early loss exceeds initial early-stage exit by max(0.0001, 10%)\",\n";
     out << "  \"wellbore_recheck_acceptance\": \"early decrease with fixed entry shape limit max(0.0001, 5%); no_total_loss_constraint\",\n";
@@ -1924,6 +1949,9 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
     const double minimumCoordinateStep = 1.0e-5;
     const double minimumTrustRadius = 2.0e-3;
     const double maximumTrustRadius = 0.30;
+    // 第二阶段整体形状允许更大步幅；第三阶段继续使用原来的半径和预测验收规则。
+    const double initialShapeTrustRadius = 0.24;
+    const double maximumShapeTrustRadius = 0.60;
     // 误差下降至少达到绝对 1e-5 且相对当前有效基准 0.2% 才算有效改善。
     // 更小的下降仍保留为最佳解，但不能反复清除停滞状态、延长拟合时间。
     const double effectiveRelativeImprovement = 2.0e-3;
@@ -2120,14 +2148,16 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
 
     if(m_shouldStop) return LM_USER_STOPPED;
 
-    // 第二阶段不按迭代比例截断；连续两次改善不足后，刷新灵敏度并仅做一次全局联合确认。
+    // 第二阶段先测灵敏度，再逐个调完非井筒参数；每个参数只访问一次。
     // 普通形状调整冻结井储、表皮，只按形状验收；总误差达标只在第三阶段判断。
     bool shapeStage = true;
-    bool jointShapeStarted = false;
-    double shapeImprovementBaseline = current.breakdown.shapeLoss;
+    bool singleShapeStarted = false;
     int shapeStepCount = 0;
-    int ineffectiveShapeSteps = 0;
-    bool shapeConfirmationRequested = false;
+    QVector<bool> shapeParameterFinished(dimensions, false);
+    int activeShapeColumn = -1;
+    double shapeCoordinateStep = 0.0;
+    int consecutiveShapeRejections = 0;
+    const int maximumShapeRejections = 3;
     const int storageColumn = m_enabledParamIndices.indexOf(2);
     const int skinColumn = m_enabledParamIndices.indexOf(1);
     bool hasRemainingShapeParameters = false;
@@ -2193,7 +2223,7 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
         restoreEvaluationState(current);
     };
     emit logMessageGenerated(shapeStage
-        ? tr("LM stage 2: joint shape search; after 2 ineffective steps, refresh sensitivity and confirm with one global step.")
+        ? tr("LM stage 2: adjust each shape parameter once; double the step after improvement, halve it after rejection, and switch after 3 consecutive rejections.")
         : tr("LM stage 3: original LM fitting; accept by total error only."));
     if(earlyShapeStage) {
         emit logMessageGenerated(earlyShapeParameter == 2
@@ -2267,7 +2297,7 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
         consecutiveSolverFailures = 0;
         stagnationConfirmationRequested = false;
         globalFallbackAttempted = false;
-        trustRadius = 0.12;
+        trustRadius = shapeStage && !earlyShapeStage ? initialShapeTrustRadius : 0.12;
         damping = 0.01;
     };
     auto enterTotalStage = [&](const QString& reason) {
@@ -2362,38 +2392,37 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
                       true, 0, "early_wellbore_to_shape", &current.breakdown);
     };
 
-    auto completeShapeSearchStep = [&]() {
-        if(!shapeStage || earlyShapeStage || m_shouldStop) return;
-        // 改善相对上一次有效改善累计，避免单次小步被立即否定；不再等待完整窗口轮次。
-        const double required = qMax(1.0e-4, 0.10 * shapeImprovementBaseline);
-        const double improvement = shapeImprovementBaseline - current.breakdown.shapeLoss;
-        const bool improved = improvement >= required;
-        ++shapeStepCount;
-        writeTraceRow(m_currentIteration, -1, "shape_step_end", current.parameters, current.fitness,
-            true, 0, QString(improved ? "improved_step_%1" : "ineffective_step_%1").arg(shapeStepCount), &current.breakdown);
-        emit logMessageGenerated(tr("Shape search step %1: shape error=%2, accumulated improvement=%3, required=%4.")
-            .arg(shapeStepCount).arg(current.breakdown.shapeLoss, 0, 'g', 6)
-            .arg(improvement, 0, 'g', 6).arg(required, 0, 'g', 6));
-        // 每次形状调整都是全局联合步，结束后清除本次尝试标记。
-        globalFallbackAttempted = false;
-        if(improved) {
-            shapeImprovementBaseline = current.breakdown.shapeLoss;
-            ineffectiveShapeSteps = 0;
-            shapeConfirmationRequested = false;
-            return;
-        }
-        ++ineffectiveShapeSteps;
-        if(shapeConfirmationRequested) {
-            finishShapeStage(tr("no significant shape improvement after fresh sensitivity and one global step"));
-            return;
+    auto finishShapeParameter = [&](const QString& reason) {
+        // 已完成的参数不再参与后续选优，保证所有可调参数只扫一遍。
+        if(activeShapeColumn >= 0) {
+            shapeParameterFinished[activeShapeColumn] = true;
+            writeTraceRow(m_currentIteration, activeShapeColumn, "shape_parameter_end",
+                current.parameters, current.fitness, true, 0, reason, &current.breakdown);
         }
-        if(ineffectiveShapeSteps >= 2) {
-            jacobian.clear();
-            reuseSensitivityForNextStage();
-            rebuildRequested = true;
-            rebuildReason = QT_TR_NOOP("confirm shape stagnation after 2 ineffective steps");
-            shapeConfirmationRequested = true;
+        activeShapeColumn = -1;
+        shapeCoordinateStep = 0.0;
+        consecutiveShapeRejections = 0;
+        for(int column = 0; column < dimensions; ++column) {
+            if(parameterAllowedInStage(column) && !shapeParameterFinished[column]) return;
         }
+        finishShapeStage(tr("all shape parameters visited once"));
+    };
+    auto completeShapeSearchStep = [&](bool accepted) {
+        if(!shapeStage || earlyShapeStage || m_shouldStop) return;
+        // 只按本次真实下降控制实际步长；不再使用累计 10% 门槛提前结束整轮。
+        ++shapeStepCount;
+        consecutiveShapeRejections = accepted ? 0 : consecutiveShapeRejections + 1;
+        shapeCoordinateStep = qBound(-maximumShapeTrustRadius,
+            shapeCoordinateStep * (accepted ? 2.0 : 0.5), maximumShapeTrustRadius);
+        writeTraceRow(m_currentIteration, activeShapeColumn, "shape_step_end", current.parameters,
+            current.fitness, true, 0,
+            QString("%1_step_%2_rejections_%3_next_delta_%4")
+                .arg(accepted ? "improved" : "rejected").arg(shapeStepCount)
+                .arg(consecutiveShapeRejections).arg(shapeCoordinateStep, 0, 'g', 12), &current.breakdown);
+        if(consecutiveShapeRejections >= maximumShapeRejections)
+            finishShapeParameter("3_consecutive_non_improving_trials");
+        else if(qAbs(shapeCoordinateStep) < minimumCoordinateStep)
+            finishShapeParameter("minimum_coordinate_step");
     };
 
     auto registerEffectiveImprovement = [&](double fitness) -> bool {
@@ -2415,11 +2444,11 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
         return true;
     };
 
-    // 普通形状按连续尝试判断停滞，并用新灵敏度下的全局联合步确认；
+    // 普通形状的失败试算缩步并累计当前参数的拒绝次数；
     // 前期井储、表皮与整体 LM 沿用各自的无效次数处理。
     auto recordIneffectiveStep = [&]() -> bool {
         if(shapeStage && !earlyShapeStage) {
-            completeShapeSearchStep();
+            completeShapeSearchStep(false);
             return false;
         }
         ++consecutiveIneffectiveSteps;
@@ -2587,9 +2616,11 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
                     jacobianColumnValid[column] = true;
                     columnBuilt = true;
 
+                    // 后半段形状探针仅用于灵敏度，正式调整必须经过单参数 LM 预测选优。
                     // 前期同时测井储和表皮，但缓存探针不能绕过当前子阶段的选参限制。
                     // 前期首次正式调整必须从小步开始，测形状灵敏度的大探针不能提前成为工作点。
-                    if((!earlyShapeStage || earlyShapeHasImproved) &&
+                    if((!shapeStage || earlyShapeStage) &&
+                            (!earlyShapeStage || earlyShapeHasImproved) &&
                             parameterAllowedInStage(column) && acceptable(probe, base) &&
                             (!bestProbe.valid || stageError(probe) < stageError(bestProbe))) {
                         bestProbe = probe;
@@ -2609,14 +2640,14 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
                 if(parameterAllowedInStage(i)) hasActiveSensitivity = true;
             }
         }
-        // 冻结列成功不能掩盖所有可调形状列的求解失败；有效零梯度仍由停滞逻辑处理。
+        // 冻结列成功不能掩盖所有可调形状列的求解失败；有效零梯度交给逐参数选步处理。
         if(validColumnCount == 0 || (shapeStage && !earlyShapeStage && !hasActiveSensitivity) || m_shouldStop) {
             restoreEvaluationState(base);
             return false;
         }
 
-        // 灵敏度试算本身若找到更优真实解也应保留。所有列先基于同一个 base
-        // 建完，再用该已知割线把 Jacobian 平移到新工作点，避免边算边移动基点。
+        // 前期井储/表皮和整体阶段仍可接受更优缓存探针；后半段形状只由 LM 选步。
+        // 所有列先基于同一个 base 建完，再用已知割线平移 Jacobian，避免边算边移动基点。
         if(bestProbe.valid && bestProbeColumn >= 0) {
             QVector<double> acceptedStep(dimensions, 0.0);
             acceptedStep[bestProbeColumn] = bestProbeDelta;
@@ -2676,14 +2707,13 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
         if(wellboreRecheck && current.breakdown.earlyParallelLoss <=
                 earlyWellboreBaseline + qMax(1.0e-4, 0.10 * earlyWellboreBaseline))
             enterTotalStage(tr("early shape error restored within tolerance"));
-        if(shapeStage && !earlyShapeStage && !jointShapeStarted) {
-            jointShapeStarted = true;
-            shapeImprovementBaseline = current.breakdown.shapeLoss;
+        if(shapeStage && !earlyShapeStage && !singleShapeStarted) {
+            singleShapeStarted = true;
             // 初调已改变井储/表皮，普通形状必须在新的工作点重测其余可调参数的响应。
             jacobian.clear();
             reuseSensitivityForNextStage();
             rebuildRequested = true;
-            rebuildReason = QT_TR_NOOP("fresh sensitivity at joint shape entry");
+            rebuildReason = QT_TR_NOOP("fresh sensitivity at single-parameter shape entry");
         }
         if(m_shouldStop) break;
         if(!shapeStage && (totalIterations >= m_maxIterations || m_totalEvaluations >= maximumEvaluations)) break;
@@ -2741,13 +2771,13 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
                 --iteration;
                 continue;
             }
-            // 单列探针没有改善不代表联合步无效；重建后继续真实候选评价，再确认停滞。
+            // 差分探针不等于 LM 候选；重建后继续按当前阶段求步并真实评价，再确认停滞。
             registerEffectiveImprovement(stageError(current));
         }
 
         // 第三阶段独立计数；方向不可行也消耗一次局部尝试，不能无限缩步循环。
         if(!shapeStage) ++totalIterations;
-        // 每次从最新 J 和当前阶段残差重算 Fisher，联合步使用全局信息。
+        // 每次从最新 J 和当前阶段残差重算全局信息，供单参数或联合 LM 求步。
         const QVector<double> objectiveResidual = earlyShapeStage
             ? current.breakdown.earlyParallelResiduals
             : (shapeStage ? current.breakdown.shapeResiduals : current.breakdown.residualVector);
@@ -2775,8 +2805,8 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
         double predictedReduction = 0.0;
         const int selectedWindow = earlyShapeStage ? 0 : -1;
 
-        // 前期只开放当前井储或表皮；普通形状和整体 LM 都联合求解全部有效自由列。
-        // 保留弱敏感、相关及边界列，让参数相互配合；窗口只保留作误差诊断。
+        // 前期只开放当前井储或表皮；后半段形状从有效自由列中选一个，整体 LM 仍联合求解。
+        // 保留弱敏感、相关及边界列供预测比较；窗口只保留作误差诊断。
         for(int column = 0; column < dimensions; ++column) {
             if(stageColumnValid[column] && (earlyShapeStage || global.matrix[column][column] > 0.0))
                 selectedColumns.append(column);
@@ -2800,8 +2830,54 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
                     damping, earlyStepRadius, minimumCoordinateStep, &coordinateStep, &predictedReduction)) {
                 selectedColumns.clear();
             }
+        } else if(shapeStage) {
+            // 首步由灵敏度选出尚未调过的参数；后续锁定方向，直接使用扩缩后的步长。
+            if(activeShapeColumn < 0) {
+                QVector<int> availableColumns;
+                for(int i = 0; i < selectedColumns.size(); ++i) {
+                    if(!shapeParameterFinished[selectedColumns[i]]) availableColumns.append(selectedColumns[i]);
+                }
+                buildBestSingleParameterStep(global, availableColumns, current.coordinates,
+                    0.01, initialShapeTrustRadius, minimumCoordinateStep,
+                    &selectedColumns, &coordinateStep, &predictedReduction);
+                if(!selectedColumns.isEmpty()) {
+                    activeShapeColumn = selectedColumns[0];
+                    shapeCoordinateStep = coordinateStep[activeShapeColumn];
+                    consecutiveShapeRejections = 0;
+                    writeTraceRow(m_currentIteration, activeShapeColumn, "shape_parameter_start",
+                        current.parameters, current.fitness, true, 0,
+                        "largest_predicted_reduction_unvisited", &current.breakdown);
+                } else {
+                    // 剩余参数均无可行预测下降步时逐项记录，不能重复选择已完成参数。
+                    for(int column = 0; column < dimensions; ++column) {
+                        if(!parameterAllowedInStage(column) || shapeParameterFinished[column]) continue;
+                        activeShapeColumn = column;
+                        finishShapeParameter(jacobianColumnValid[column]
+                            ? "no_feasible_descent_step" : "invalid_sensitivity");
+                        if(!shapeStage || earlyShapeStage) break;
+                    }
+                    --iteration;
+                    continue;
+                }
+            } else {
+                selectedColumns.clear();
+                selectedColumns.append(activeShapeColumn);
+                coordinateStep.fill(0.0, dimensions);
+                shapeCoordinateStep = qBound(0.0,
+                    current.coordinates[activeShapeColumn] + shapeCoordinateStep, 1.0)
+                    - current.coordinates[activeShapeColumn];
+                if(qAbs(shapeCoordinateStep) < minimumCoordinateStep) {
+                    finishShapeParameter("parameter_bound_or_minimum_step");
+                    --iteration;
+                    continue;
+                }
+                coordinateStep[activeShapeColumn] = shapeCoordinateStep;
+                predictedReduction = -global.gradient[activeShapeColumn] * shapeCoordinateStep
+                    - 0.5 * global.matrix[activeShapeColumn][activeShapeColumn]
+                        * shapeCoordinateStep * shapeCoordinateStep;
+            }
         } else {
-            // 普通调整和停滞确认共用全局联合方向，不再遍历窗口或枚举三参数子集。
+            // 第三阶段保持全部有效自由参数的联合 LM 调整。
             globalFallbackAttempted = true;
             if(selectedColumns.isEmpty() || !buildTrustRegionFisherStep(
                     global, selectedColumns, current.coordinates, damping,
@@ -2818,11 +2894,6 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
                 --iteration;
                 continue;
             }
-            if(shapeStage) {
-                completeShapeSearchStep();
-                --iteration;
-                continue;
-            }
             if(trustRadius <= minimumTrustRadius * 1.01 &&
                     modelRebuiltAtMinimumRadius) {
                 if(promoteSampling(false)) continue;
@@ -2933,7 +3004,7 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
                           "solver_invalid_" + selectionName,
                           nullptr);
             restoreEvaluationState(current);
-            if(consecutiveSolverFailures >= 2) {
+            if(consecutiveSolverFailures >= 2 && (!shapeStage || earlyShapeStage)) {
                 rebuildRequested = true;
                 rebuildReason = QT_TR_NOOP("2 consecutive solver failures");
             }
@@ -2941,8 +3012,6 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
                 stopReason = LM_CONSECUTIVE_FAILURES;
                 break;
             }
-            // 确认步求解失败不代表形状已收敛，沿用有限重试后按求解失败退出。
-            if(shapeStage && !earlyShapeStage && shapeConfirmationRequested) continue;
             if(recordIneffectiveStep()) {
                 if(promoteSampling(false)) continue;
                 stopReason = LM_LOCAL_OPTIMUM;
@@ -2951,37 +3020,6 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
             continue;
         }
 
-        // 普通形状步真实改善后，沿同一联合方向最多扩步一次，不再用预测兑现比例拦截。
-        // 扩步只按整体形状验收，优于原步才替换，否则保留原候选。
-        if(shapeStage && !earlyShapeStage && acceptable(candidate, current) && processPauseAndStop()) {
-            QVector<double> expandedStep;
-            double expandedPrediction = 0.0;
-            if(buildExpandedTrustRegionStep(stepInformation, current.coordinates, coordinateStep,
-                    maximumTrustRadius, &expandedStep, &expandedPrediction)) {
-                writeTraceRow(m_currentIteration, -1, "shape_step_base", candidate.parameters,
-                    candidate.fitness, true, candidate.elapsedMs, "eligible_for_expansion", &candidate.breakdown);
-                TrustRegionEvaluation expanded;
-                expanded.coordinates = current.coordinates;
-                for(int i = 0; i < dimensions; ++i) expanded.coordinates[i] += expandedStep[i];
-                expanded.parameters = parametersFromCoordinates(expanded.coordinates);
-                expanded.valid = evaluateTrustRegionPoint(expanded.parameters, &expanded.fitness,
-                    &expanded.breakdown, &expanded.curve, &expanded.elapsedMs);
-                const bool useExpanded = acceptable(expanded, current) && expanded.breakdown.shapeLoss < candidate.breakdown.shapeLoss;
-                writeTraceRow(m_currentIteration, -1, "shape_step_expanded", expanded.parameters,
-                    expanded.fitness, expanded.valid, expanded.elapsedMs, useExpanded ? "selected_expanded" : "retain_ordinary",
-                    expanded.valid ? &expanded.breakdown : nullptr);
-                if(useExpanded) {
-                    candidate = expanded;
-                    coordinateStep = expandedStep;
-                    predictedReduction = expandedPrediction;
-                    stepNorm = qSqrt(trustRegionSquaredNorm(coordinateStep));
-                    selectionName += "_expanded";
-                }
-                // 两次真实调用已分别记录，下方候选行只记录最终决策，避免重复统计耗时。
-                candidate.elapsedMs = -1;
-                restoreEvaluationState(current);
-            }
-        }
         if(m_shouldStop) {
             restoreEvaluationState(current);
             stopReason = LM_USER_STOPPED;
@@ -3011,7 +3049,7 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
         const bool poorPrediction = predictedReduction > predictionFloor &&
             (!isFiniteNumber(reductionRatio) || reductionRatio < 0.25);
         consecutivePoorPredictions = poorPrediction ? consecutivePoorPredictions + 1 : 0;
-        if(consecutivePoorPredictions >= 2) {
+        if(consecutivePoorPredictions >= 2 && (!shapeStage || earlyShapeStage)) {
             rebuildRequested = true;
             rebuildReason = QT_TR_NOOP("2 consecutive steps with actual improvement below 25% of prediction");
         }
@@ -3032,21 +3070,24 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
             ++acceptedSinceRebuild;
             consecutiveRejectedSteps = 0;
 
-            if(reductionRatio > 0.75) {
-                damping = qMax(1.0e-8, damping * 0.5);
-                if(stepNorm >= trustRadius * 0.8) {
-                    trustRadius = qMin(
-                        maximumTrustRadius, trustRadius * 1.6);
+            // 井筒调整及第三阶段保留原 LM 控制；逐参数粗调在步末直接扩缩实际步长。
+            if(!shapeStage || earlyShapeStage) {
+                if(reductionRatio > 0.75) {
+                    damping = qMax(1.0e-8, damping * 0.5);
+                    if(stepNorm >= trustRadius * 0.8) {
+                        trustRadius = qMin(
+                            maximumTrustRadius, trustRadius * 1.6);
+                    }
+                } else if(reductionRatio > 0.25) {
+                    damping = qMax(1.0e-8, damping * 0.8);
+                } else {
+                    damping = qMin(1.0e8, damping * 2.0);
+                    trustRadius = qMax(
+                        minimumTrustRadius, trustRadius * 0.75);
                 }
-            } else if(reductionRatio > 0.25) {
-                damping = qMax(1.0e-8, damping * 0.8);
-            } else {
-                damping = qMin(1.0e8, damping * 2.0);
-                trustRadius = qMax(
-                    minimumTrustRadius, trustRadius * 0.75);
             }
 
-            if(acceptedSinceRebuild >= 10 && !rebuildRequested) {
+            if(acceptedSinceRebuild >= 10 && !rebuildRequested && (!shapeStage || earlyShapeStage)) {
                 rebuildRequested = true;
                 rebuildReason = QT_TR_NOOP("10 accepted steps since last rebuild");
             }
@@ -3102,6 +3143,10 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
             finishEarlyShapeStage(tr("initial same-direction expansion reached the parameter bound without early shape improvement"));
             continue;
         }
+        if(shapeStage && !earlyShapeStage) {
+            completeShapeSearchStep(accepted);
+            continue;
+        }
         const bool effectiveImprovement = registerEffectiveImprovement(stageError(current));
         if(!effectiveImprovement && recordIneffectiveStep()) stopReason = LM_LOCAL_OPTIMUM;