refactor(nmNum): 将 LM 形状阶段改为逐参数单轮调整

- 移除时间窗口选参、三参数上限及子集枚举，每步联合调整全部有效非井储表皮参数
- 连续两次改善不足后刷新灵敏度，仅做一次全局联合确认，累计有效改善门槛设为 10%
- 放宽形状扩步条件，取消实际与预测改善比值限制，保留预测下降、步长和边界约束
- 确认步求解失败时有限重试，避免将失败误判为收敛
- 同步拟合轨迹元数据、尝试次数日志及中文翻译

Bin/Config/Lang/cn/nmNum_cn.ts

@@ -1277,24 +1277,24 @@ 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 completed shape rounds, %2 total-stage iterations, %3 total evaluations.</source>
-        <translation>自适应拟合统计：已完成 %1 轮形状搜索，整体阶段迭代 %2 次，累计评估 %3 次。</translation>
+        <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: adaptive shape search; confirm stagnation after 2 complete rounds without significant improvement.</source>
-        <translation>LM 阶段2：自适应形状搜索；连续两轮完整搜索无显著改善后确认停滞。</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>
         <translation>LM 起点误差：%1；整体阶段独立评估预算：%2</translation>
     </message>
     <message>
-        <source>Shape search round %1: shape error=%2, improvement=%3, required=%4.</source>
-        <translation>形状搜索第 %1 轮：形状误差=%2，改善量=%3，所需改善量=%4。</translation>
+        <source>Shape search step %1: shape error=%2, accumulated improvement=%3, required=%4.</source>
+        <translation>形状尝试 %1：形状误差=%2，累计改善=%3，有效改善门槛=%4。</translation>
     </message>
     <message>
         <source>Total-stage budget starts now: %1 iterations, %2 evaluations; pre-adjustment is counted separately.</source>
@@ -1305,16 +1305,16 @@ Reason: %1</source>
         <translation>无法建立有效的形状灵敏度模型。</translation>
     </message>
     <message>
-        <source>confirm stagnation after 2 complete shape rounds</source>
-        <translation>完成两轮形状搜索后确认停滞</translation>
+        <source>confirm shape stagnation after 2 ineffective steps</source>
+        <translation>连续两次形状改善不足，刷新灵敏度确认停滞</translation>
     </message>
     <message>
         <source>full sensitivity at total-stage entry</source>
         <translation>进入整体阶段时建立完整灵敏度</translation>
     </message>
     <message>
-        <source>no significant improvement in a complete round after fresh sensitivity confirmation</source>
-        <translation>重建灵敏度确认后，完整一轮搜索仍无显著改善</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>

Src/nmNum/nmCalculation/nmCalculationAutoFitLM.cpp

@@ -594,95 +594,6 @@ static QVector<TrustRegionFisher> buildTrustRegionFisher(
     return information;
 }
 
-static int nextTrustRegionWindow(
-        const QVector<AutoFitTimeWindowLM>& windows,
-        const QVector<bool>& attempted)
-{
-    // 每次都按当前误差能量重新排序；本轮无效的窗口暂时跳过，-1 表示全局回退。
-    int selected = -1;
-    double largestEnergy = 0.0;
-    for(int k = 0; k < windows.size(); ++k) {
-        if(!attempted[k] && isFiniteNumber(windows[k].energy) &&
-                windows[k].energy > largestEnergy) {
-            largestEnergy = windows[k].energy;
-            selected = k;
-        }
-    }
-    return selected;
-}
-
-static QVector<int> selectTrustRegionFisherColumns(
-        const TrustRegionFisher& local,
-        const TrustRegionFisher& global,
-        const QVector<bool>& columnValid,
-        const QVector<double>& coordinates,
-        double minimumStep)
-{
-    // g^2/F 衡量修正当前残差的潜力，避免仅按影响强度选中无助于降误差的参数。
-    const int dimensions = columnValid.size();
-    double maximumDiagonal = 0.0;
-    for(int p = 0; p < dimensions; ++p) {
-        if(columnValid[p] && isFiniteNumber(local.matrix[p][p])) {
-            maximumDiagonal = qMax(maximumDiagonal, local.matrix[p][p]);
-        }
-    }
-    const double diagonalFloor = qMax(1.0e-30, maximumDiagonal * 1.0e-12);
-    QVector<double> scores(dimensions, 0.0);
-    double maximumScore = 0.0;
-    for(int p = 0; p < dimensions; ++p) {
-        if(!columnValid[p] || local.matrix[p][p] <= diagonalFloor ||
-                !isFiniteNumber(local.matrix[p][p]) ||
-                !isFiniteNumber(local.gradient[p]) ||
-                !isFiniteNumber(global.gradient[p])) {
-            continue;
-        }
-        // 全局下降方向指向边界外时暂不选该参数，避免它挤占可移动参数的位置。
-        if((coordinates[p] <= minimumStep && global.gradient[p] > 0.0) ||
-                (coordinates[p] >= 1.0 - minimumStep && global.gradient[p] < 0.0)) {
-            continue;
-        }
-        double scaledGradient = local.gradient[p] /
-            qSqrt(local.matrix[p][p] + diagonalFloor);
-        double score = scaledGradient * scaledGradient;
-        if(isFiniteNumber(score)) {
-            scores[p] = score;
-            maximumScore = qMax(maximumScore, score);
-        }
-    }
-
-    QVector<int> selected;
-    for(int selection = 0; selection < qMin(3, dimensions); ++selection) {
-        int best = -1;
-        double bestScore = maximumScore * 1.0e-12;
-        for(int p = 0; p < dimensions; ++p) {
-            if(selected.contains(p) || scores[p] <= bestScore) {
-                continue;
-            }
-            // 沿用现有全局 0.995 共线限制，不因单个窗口内响应相似而冻结参数。
-            bool correlated = false;
-            for(int i = 0; i < selected.size(); ++i) {
-                int q = selected[i];
-                double denominator = qSqrt(global.matrix[p][p]) *
-                    qSqrt(global.matrix[q][q]);
-                if(denominator > 0.0 &&
-                        qAbs(global.matrix[p][q]) / denominator > 0.995) {
-                    correlated = true;
-                    break;
-                }
-            }
-            if(!correlated) {
-                best = p;
-                bestScore = scores[p];
-            }
-        }
-        if(best < 0) {
-            break;
-        }
-        selected.append(best);
-    }
-    return selected;
-}
-
 static bool buildTrustRegionFisherStep(
         const TrustRegionFisher& global,
         const QVector<int>& selected,
@@ -760,6 +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,
@@ -780,7 +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,
@@ -1212,7 +1147,7 @@ void nmCalculationAutoFitLM::writeTraceMetaFile()
 
     QTextStream out(&metaFile);
     out << "{\n";
-    out << "  \"schema_version\": 31,\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";
@@ -1227,11 +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 reliable shape direction, up to 2x when actual rho exceeds 0.75; retain ordinary step on failure\",\n";
-    out << "  \"shape_global_parameter_selection\": \"all_valid_non_wellbore_columns_with_positive_response\",\n";
-    out << "  \"stage2_budget\": \"adaptive, no fixed iteration or evaluation quota; full window/global rounds, 2 ineffective rounds then fresh-J confirmation\",\n";
-    out << "  \"shape_round_improvement_threshold\": \"max(0.0001, 1% of round entry shape loss)\",\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";
@@ -2013,6 +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;
@@ -2033,7 +1972,6 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
     const char* rebuildReason = QT_TR_NOOP("initial sensitivity model");
     bool modelRebuiltAtMinimumRadius = false;
     bool stagnationConfirmationRequested = false;
-    QVector<bool> attemptedWindows(kAutoFitTimeWindowCount, false);
     bool globalFallbackAttempted = false;
     StopReasonLM stopReason = LM_MAX_ITERATIONS;
 
@@ -2210,14 +2148,16 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
 
     if(m_shouldStop) return LM_USER_STOPPED;
 
-    // 第二阶段不按迭代比例截断；普通形状按完整搜索轮次判断是否仍有显著改善。
+    // 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 shapeRoundBaseline = current.breakdown.shapeLoss;
-    int shapeRoundNumber = 0;
-    int ineffectiveShapeRounds = 0;
-    bool shapeConfirmationRequested = false;
+    bool singleShapeStarted = false;
+    int shapeStepCount = 0;
+    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;
@@ -2283,7 +2223,7 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
         restoreEvaluationState(current);
     };
     emit logMessageGenerated(shapeStage
-        ? tr("LM stage 2: adaptive shape search; confirm stagnation after 2 complete rounds without significant improvement.")
+        ? 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
@@ -2328,7 +2268,6 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
         consecutivePoorPredictions = 0;
         modelRebuiltAtMinimumRadius = false;
         stagnationConfirmationRequested = false;
-        attemptedWindows.fill(false);
         globalFallbackAttempted = false;
         fullDataRejections = 0;
         effectiveImprovementBaseline = stageError(current);
@@ -2357,9 +2296,8 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
         consecutiveRejectedSteps = 0;
         consecutiveSolverFailures = 0;
         stagnationConfirmationRequested = false;
-        attemptedWindows.fill(false);
         globalFallbackAttempted = false;
-        trustRadius = 0.12;
+        trustRadius = shapeStage && !earlyShapeStage ? initialShapeTrustRadius : 0.12;
         damping = 0.01;
     };
     auto enterTotalStage = [&](const QString& reason) {
@@ -2454,37 +2392,37 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
                       true, 0, "early_wellbore_to_shape", &current.breakdown);
     };
 
-    auto completeShapeSearchRound = [&]() {
-        if(!shapeStage || earlyShapeStage || !globalFallbackAttempted) return;
-        if(m_shouldStop) return;
-        const double required = qMax(1.0e-4, 0.01 * shapeRoundBaseline);
-        const double improvement = shapeRoundBaseline - current.breakdown.shapeLoss;
-        const bool improved = improvement >= required;
-        ++shapeRoundNumber;
-        if(improved) {
-            ineffectiveShapeRounds = 0;
-            shapeConfirmationRequested = false;
-        } else ++ineffectiveShapeRounds;
-        writeTraceRow(m_currentIteration, -1, "shape_round_end", current.parameters, current.fitness,
-            true, 0, QString(improved ? "improved_round_%1" : "ineffective_round_%1").arg(shapeRoundNumber), &current.breakdown);
-        emit logMessageGenerated(tr("Shape search round %1: shape error=%2, improvement=%3, required=%4.")
-            .arg(shapeRoundNumber).arg(current.breakdown.shapeLoss, 0, 'g', 6)
-            .arg(improvement, 0, 'g', 6).arg(required, 0, 'g', 6));
-        if(!improved && shapeConfirmationRequested) {
-            finishShapeStage(tr("no significant improvement in a complete round after fresh sensitivity confirmation"));
-            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);
         }
-        // 下一轮重新覆盖窗口和全部有效参数的全局步；单步小改善不重置本轮进度。
-        shapeRoundBaseline = current.breakdown.shapeLoss;
-        attemptedWindows.fill(false);
-        globalFallbackAttempted = false;
-        if(!improved && ineffectiveShapeRounds >= 2) {
-            jacobian.clear();
-            reuseSensitivityForNextStage();
-            rebuildRequested = true;
-            rebuildReason = QT_TR_NOOP("confirm stagnation after 2 complete shape rounds");
-            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 {
@@ -2498,8 +2436,7 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
             return false;
         }
 
-        // 有效改善后重新开放全部窗口，并按新工作点的能量排序。
-        attemptedWindows.fill(false);
+        // 有效改善后更新累计基准，并清除停滞计数。
         globalFallbackAttempted = false;
         effectiveImprovementBaseline = fitness;
         consecutiveIneffectiveSteps = 0;
@@ -2507,11 +2444,11 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
         return true;
     };
 
-    // 无效尝试仍累计，但所有窗口及一次全局回退尝试完毕前，不触发停滞收敛。
-    // 完整一轮仍无改善时沿用原有重建确认，避免某个难处理窗口提前终止拟合。
+    // 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) {
-            completeShapeSearchRound();
+            completeShapeSearchStep(false);
             return false;
         }
         ++consecutiveIneffectiveSteps;
@@ -2524,7 +2461,6 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
         if(!globalFallbackAttempted) {
             return false;
         }
-        attemptedWindows.fill(false);
         globalFallbackAttempted = false;
         if(consecutiveIneffectiveSteps < maximumIneffectiveSteps) {
             return false;
@@ -2680,9 +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;
@@ -2702,14 +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;
@@ -2769,14 +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;
-            shapeRoundBaseline = 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;
@@ -2834,13 +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;
-        // 每轮从最新 J 和当前残差重算窗口 Fisher，包含有限差分与割线更新的变化。
+        // 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);
@@ -2854,10 +2791,6 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
             objectiveCoordinates.clear();
             for(int i = 0; i < 73; ++i) objectiveCoordinates.append((i + 4.0) / 80.0);
         }
-        const QVector<AutoFitTimeWindowLM> objectiveWindows = shapeStage
-            ? calculateAutoFitTimeWindows(objectiveResidual, m_comparisonTimeMin, m_comparisonTimeMax,
-                                          objectiveCoordinates, autoFitLogTimeWeights(objectiveCoordinates))
-            : current.breakdown.timeWindows;
         const QVector<TrustRegionFisher> information = buildTrustRegionFisher(
             objectiveJacobian, objectiveResidual, jacobianColumnValid, objectiveCoordinates);
         const TrustRegionFisher& global = information[kAutoFitTimeWindowCount];
@@ -2870,98 +2803,86 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
         QVector<int> selectedColumns;
         QVector<double> coordinateStep;
         double predictedReduction = 0.0;
-        int selectedWindow = -1;
-
-        if(!shapeStage) {
-            // 整体阶段联合求解全部有效自由列，不按窗口得分、三参数上限或共线阈值删列。
-            // 边界列也参与耦合求解，是否向内移动由联合解及其边界投影决定。
-            for(int column = 0; column < dimensions; ++column) {
-                // 仅跳过完全没有总残差响应的列，保留弱敏感列及相互相关的列。
-                if(stageColumnValid[column] && global.matrix[column][column] > 0.0)
-                    selectedColumns.append(column);
+        const int selectedWindow = earlyShapeStage ? 0 : -1;
+
+        // 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);
+        }
+        if(earlyShapeStage) {
+            double earlyStepRadius = trustRadius;
+            if(!earlyShapeHasImproved && selectedColumns.size() == 1) {
+                // 首次调整沿用小步起调，形状变差时由后面的同向扩步循环处理。
+                const int column = selectedColumns[0];
+                const int parameterIndex = m_enabledParamIndices[column];
+                const double lower = m_parameterLower[parameterIndex];
+                const double upper = m_parameterUpper[parameterIndex];
+                const double smallStep = useTrustRegionLogScale(parameterIndex, lower, upper)
+                    ? qLn(1.05) / (qLn(upper) - qLn(lower))
+                    : (parameterIndex == 1 ? 0.02 * qMax(0.1, qAbs(current.parameters[column]))
+                                          : 0.05 * qMax(1.0e-8, qAbs(current.parameters[column]))) / (upper - lower);
+                earlyStepRadius = qMin(trustRadius, smallStep);
             }
-            // 当前候选已使用全局信息，停滞判断无需再逐一尝试窗口子集。
-            attemptedWindows.fill(true);
-            globalFallbackAttempted = true;
-            if(selectedColumns.isEmpty() || !buildTrustRegionFisherStep(
-                    global, selectedColumns, current.coordinates, damping,
-                    trustRadius, minimumCoordinateStep, &coordinateStep, &predictedReduction)) {
+            if(selectedColumns.isEmpty() || !buildEarlyGapGuidedStep(
+                    stepInformation, selectedColumns, current.coordinates, earlyGapDirection,
+                    damping, earlyStepRadius, minimumCoordinateStep, &coordinateStep, &predictedReduction)) {
                 selectedColumns.clear();
             }
-        }
-        // 形状阶段先覆盖局部窗口，再用全部有效自由列求一次全局联合步。
-        while(shapeStage && selectedColumns.isEmpty()) {
-            selectedWindow = earlyShapeStage ? 0 : nextTrustRegionWindow(
-                objectiveWindows, attemptedWindows);
-            if(selectedWindow >= 0) {
-                attemptedWindows[selectedWindow] = true;
-            } else {
-                globalFallbackAttempted = true;
-            }
-            const TrustRegionFisher& local = selectedWindow >= 0
-                ? information[selectedWindow] : global;
-            QVector<int> proposed;
-            if(earlyShapeStage) {
-                // 前期只开放当前的井储或表皮参数。
-                for(int column = 0; column < dimensions; ++column) {
-                    if(stageColumnValid[column]) proposed.append(column);
+        } 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]);
                 }
-            } else if(selectedWindow < 0) {
-                // 全局步保留弱敏感及相关列，避免参数长期被窗口前三名或共线筛选排除。
-                for(int column = 0; column < dimensions; ++column) {
-                    if(stageColumnValid[column] && global.matrix[column][column] > 0.0)
-                        proposed.append(column);
-                }
-            } else {
-                proposed = selectTrustRegionFisherColumns(
-                    local, global, stageColumnValid,
-                    current.coordinates, minimumCoordinateStep);
-            }
-            // 局部窗口至多三列，比较非空子集；全局只求完整组合，不枚举全部参数子集。
-            const bool fullJointStep = !earlyShapeStage && selectedWindow < 0;
-            const int combinationCount = proposed.isEmpty() ? 0 : (fullJointStep ? 1 : (1 << proposed.size()) - 1);
-            for(int combination = 1; combination <= combinationCount; ++combination) {
-                QVector<int> columns;
-                if(fullJointStep) columns = proposed;
-                else {
-                    for(int i = 0; i < proposed.size(); ++i) {
-                        if(combination & (1 << i)) columns.append(proposed[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;
                 }
-                QVector<double> step;
-                double reduction = 0.0;
-                double earlyStepRadius = trustRadius;
-                if(earlyShapeStage && !earlyShapeHasImproved && columns.size() == 1) {
-                    // 确定方向后先小步：井储最多 1.05 倍，表皮为局部尺度的 2%。
-                    // 首次形状变差由后面的扩步循环处理，首次接受后恢复正常 LM 幅度。
-                    const int column = columns[0];
-                    const int parameterIndex = m_enabledParamIndices[column];
-                    const double lower = m_parameterLower[parameterIndex];
-                    const double upper = m_parameterUpper[parameterIndex];
-                    const double smallStep = useTrustRegionLogScale(parameterIndex, lower, upper)
-                        ? qLn(1.05) / (qLn(upper) - qLn(lower))
-                        : (parameterIndex == 1 ? 0.02 * qMax(0.1, qAbs(current.parameters[column]))
-                                              : 0.05 * qMax(1.0e-8, qAbs(current.parameters[column]))) / (upper - lower);
-                    earlyStepRadius = qMin(trustRadius, smallStep);
-                }
-                // 井储、表皮沿间距确定的方向调整；其他阶段保持原来的 LM 求步。
-                const bool stepBuilt = earlyShapeStage
-                    ? buildEarlyGapGuidedStep(stepInformation, columns, current.coordinates, earlyGapDirection,
-                        damping, earlyStepRadius, minimumCoordinateStep, &step, &reduction)
-                    : buildTrustRegionFisherStep(stepInformation, columns, current.coordinates,
-                        damping, trustRadius, minimumCoordinateStep, &step, &reduction);
-                if(!stepBuilt) continue;
-                const double tolerance = 1.0e-12 * qMax(predictedReduction, reduction);
-                if(selectedColumns.isEmpty() || reduction > predictedReduction + tolerance ||
-                        (qAbs(reduction - predictedReduction) <= tolerance &&
-                         columns.size() < selectedColumns.size())) {
-                    selectedColumns = columns;
-                    coordinateStep = step;
-                    predictedReduction = reduction;
+            } 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;
             }
-            if(earlyShapeStage || selectedWindow < 0) {
-                break;
+        } else {
+            // 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,
+                    trustRadius, minimumCoordinateStep, &coordinateStep, &predictedReduction)) {
+                selectedColumns.clear();
             }
         }
 
@@ -2973,11 +2894,6 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
                 --iteration;
                 continue;
             }
-            if(shapeStage) {
-                completeShapeSearchRound();
-                --iteration;
-                continue;
-            }
             if(trustRadius <= minimumTrustRadius * 1.01 &&
                     modelRebuiltAtMinimumRadius) {
                 if(promoteSampling(false)) continue;
@@ -3088,7 +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");
             }
@@ -3104,41 +3020,6 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
             continue;
         }
 
-        // 普通形状步真实表现可靠时，沿同一联合方向最多扩步试算一次，不区分参数类型。
-        // 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()) {
-            const double ordinaryEnergy = 0.5 * trustRegionSquaredNorm(objectiveResidual);
-            const double ordinaryReduction = ordinaryEnergy - 0.5 * trustRegionSquaredNorm(candidate.breakdown.shapeResiduals);
-            const double predictionFloor = qMax(1.0e-14, ordinaryEnergy * 1.0e-8);
-            QVector<double> expandedStep;
-            double expandedPrediction = 0.0;
-            if(predictedReduction > predictionFloor && ordinaryReduction / predictedReduction > 0.75 &&
-                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;
@@ -3168,7 +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");
         }
@@ -3189,21 +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");
             }
@@ -3259,6 +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;
 
@@ -3291,8 +3179,8 @@ StopReasonLM nmCalculationAutoFitLM::runTrustRegionFitting()
         m_currentIteration = completedIterations - 1;
     }
     restoreEvaluationState(current);
-    emit logMessageGenerated(tr("Adaptive fitting counts: %1 completed shape rounds, %2 total-stage iterations, %3 total evaluations.")
-        .arg(shapeRoundNumber).arg(totalIterations).arg(m_totalEvaluations));
+    emit logMessageGenerated(tr("Adaptive fitting counts: %1 shape attempts, %2 total-stage iterations, %3 total evaluations.")
+        .arg(shapeStepCount).arg(totalIterations).arg(m_totalEvaluations));
 
     if(m_shouldStop) {
         return LM_USER_STOPPED;