diff --git a/eqpalg/utility/expression_engine.cpp b/eqpalg/utility/expression_engine.cpp
index c1e8dd8..4687336 100644
--- a/eqpalg/utility/expression_engine.cpp
+++ b/eqpalg/utility/expression_engine.cpp
@@ -7,7 +7,33 @@
 
 ExpressionEngine::ExpressionEngine(std::map<std::string, double>& mm_vars,
                                    std::vector<std::string>& m_tags)
-    : mm_vars_(mm_vars), m_tags_(m_tags) {}
+    : mm_vars_(mm_vars), m_tags_(m_tags) {
+  // 预初始化变量，等效于原 ExpModule::init()：
+  // 确保 mm_vars 中有 tagN/pN/pvN/now 等键，防止后续表达式求值时变量缺失
+  if (!m_tags_.empty()) {
+    ensureVarCache(var_cache_, m_tags_.size());
+    auto now = std::chrono::system_clock::now();
+    for (size_t i = 0; i < m_tags_.size(); i++) {
+      double value = 0.0;
+      try {
+        value = SingletonTemplate<GlobaltemSharedMemory>::GetInstance()[m_tags_[i]];
+      } catch (...) {
+        value = 0.0;
+      }
+      mm_vars_[var_cache_.p_keys[i]] = value;
+      mm_vars_[var_cache_.tag_keys[i]] = value;
+      for (size_t j = 0; j < PV_NUM; j++) {
+        mm_vars_[var_cache_.pv_keys[i][j]] = value;
+      }
+    }
+    mm_vars_["now"] = std::chrono::duration_cast<std::chrono::milliseconds>(
+                          now.time_since_epoch())
+                          .count();
+    mm_vars_["stime"] = 0;
+    mm_vars_["etime"] = 0;
+    mm_vars_["time"] = 0;
+  }
+}
 
 // 惰性初始化 VarsCache（首次变量刷新时调用）
 static void ensureVarCache(VarsCache& vc, size_t tag_count) {