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CalibratedSystemModel[…]

表示从 SystemModelCalibrate 获得的符号校准系统模型.

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CalibratedSystemModel

CalibratedSystemModel[…]

表示从 SystemModelCalibrate 获得的符号校准系统模型.

更多信息

  • CalibratedSystemModel 由函数 SystemModelCalibrate 生成，并提供总结、探索和提取校准结果的方法.
  • CalibratedSystemModel[…] 对象 csm 可用于通过 csm["property"] 提取属性.
  • csm["Properties"] 给出可用属性的列表. 有关属性的其他详细信息列于 SystemModelCalibrate 的页面.
  • 典型属性包括：
  • "CalibratedModel"具有校准参数的新模型
    "CalibratedParameters"参数估计
    "ParameterConfidence"参数置信度信息
    "MeanPredictionBandsPlot"具有校准数据的平均预测置信带图
    "SinglePredictionBandsPlot"带有校准数据的基于单次观察的置信带图
  • 其他规范包括：
  • {p1,…,pn}获取属性值 pi
    "Summary"获取校准摘要
    "Dataset"获取作为 Dataset 的属性名称和值
    "PropertyAssociation"获取作为 Association 的属性名称和值

范例

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基本范例  (1)

使用由输入信号生成的数据校准校准 StateSpaceModel：

Wolfram Language code: ssm = StateSpaceModel[{{{0, b}, {-a, -b}}, {{0}, {1}}, {{-1, 2}}, {{0}}}, SamplingPeriod -> None, SystemsModelLabels -> None];

校准，指定模型输入，并创建一个 CalibratedSystemModel：

Wolfram Language code: csmodel = SystemModelCalibrate[<|1 -> {...}|>, ssm, {{a, 1}, {b, 1}}, <|"Inputs" -> {1 -> Tanh}|>, "CalibratedSystemModel"]

提取单个预测带的图：

Wolfram Language code: csmodel["SinglePredictionBandsPlot"]//First

提取属性列表：

Wolfram Language code: csmodel[{"CalibratedModel", "RMSE"}]

范围  (1)

属性  (1)

查找可用属性列表：

Wolfram Language code: assm = AffineStateSpaceModel[{{a*Cos[Subscript[x, 2]] - 0.5*a*Cos[Subscript[x, 1]*Subscript[x, 2]], -Cos[1 + Subscript[x, 2]] + Subscript[x, 1]}, {{1}, {0}}, {-Subscript[x, 1]}, {{0}}}, {Subscript[x, 1], Subscript[x, 2]}, {{u, 0}}, {Automatic}, Automatic, SamplingPeriod -> None];
Wolfram Language code: datay = {...};
Wolfram Language code: csmodel = SystemModelCalibrate[<|1 -> datay|>, assm, {{a, 1}}, "CalibratedSystemModel"];
Wolfram Language code: csmodel["Properties"]

提取单个预测带图：

Wolfram Language code: csmodel["SinglePredictionBandsPlot"]//First

提取具有自定义置信水平的单个预测带图：

Wolfram Language code: csmodel["SinglePredictionBandsPlot", ConfidenceLevel -> 0.5]//First

使用自定义方差估计函数提取单个预测带图：

Wolfram Language code: csmodel["SinglePredictionBandsPlot", VarianceEstimatorFunction -> (Mean[Abs[#]]&)]//First

提取校准后的模型和校准后的参数：

Wolfram Language code: csmodel[{"CalibratedModel", "CalibratedParameters"}]

提取单个预测带：

Wolfram Language code: csmodel["SinglePredictionBands"]//Short

提取在时间 t 运算的单个预测带：

Wolfram Language code: csmodel["SinglePredictionBands", t]//Short

提取每个校准变量的均方根误差：

Wolfram Language code: csmodel["MSE"]

提取每个校准变量的均方根误差，提供验证集：

Wolfram Language code: csmodel["MSE", ValidationSet -> <|1 -> {{0., 0.0900606}, {0.8, -0.724928}, {1.6, -1.50223}, {2.4, -2.31546}, {3.2, -0.999419}, {4., -0.779318}, {4.8, -0.815785}, {5.6, -0.915279}, {6.4, -0.923541}, {7.2, -1.01274}, {8., -0.961467}, {8.8, -0.993205}, {9.6, -0.999874}}|>]

提取参数置信度信息，包括估计值、标准误差、置信区间、参数估计值的

    • 统计量和参数 统计量的 值：

    Wolfram Language code: csmodel["ParameterConfidence"]

    提取属性数据集：

    Wolfram Language code: csmodel["Dataset"]

    应用  (1)

    使用两种物质浓度的多次测量来校准和验证化学反应模型：

    Wolfram Language code: concentrationsB = TemporalData[Automatic, {{{4.874784194344632, 4.283297652264419, 3.1205024488164392, 2.329517151958408, 1.9031820282345848, 1.6975228434320357, 1.6048935104244846, 1.565176685317381, 1.5488008434700962, 1.5422728074746261, 1.5397502930532 ... 5514239254004418, 1.5491758486499458, 1.5481025177266265, 1.5475916053843106}}, {{6, 20, 1}}, 50, {"Discrete", 50}, {"Discrete", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 0}, ValueDimensions -> 1}}, False, 13.3];
    Wolfram Language code: concentrationsC = TemporalData[Automatic, {{{1.9649533322063364, 4.482418102637959, 6.094357166033274, 6.941461728642186, 7.344174951901256, 7.523754626838695, 7.600165058547569, 7.63146865710425, 7.6438756398306635, 7.648643379128127, 7.650420029310113, 7 ... 7.7565552565173395, 7.758371965351636, 7.759236105324548, 7.759646289003896}}, {{6, 20, 1}}, 50, {"Discrete", 50}, {"Discrete", 1}, 1, {ResamplingMethod -> {"Interpolation", InterpolationOrder -> 0}, ValueDimensions -> 1}}, False, 13.3];

    选择模型，指定反应系数作为校准参数并引入参数约束：

    Wolfram Language code: model = [image];
    Wolfram Language code: reactionCoefs = {"k1", "k2", "k3"};
    Wolfram Language code: constraints = 0.01 < "k1" < 10 && 0.01 < "k2" < 10 && 0.01 < "k3" < 10;

    聚合大多数测量的数据点以用作校准数据：

    Wolfram Language code: caliCsB = SortBy[Join@@concentrationsB["Path", ;; -2], First];
    Wolfram Language code: caliCsC = SortBy[Join@@concentrationsC["Path", ;; -2], First];

    校准模型，指示浓度变量和模拟区间的数据：

    Wolfram Language code: csmodel = SystemModelCalibrate[<|"B.c" -> caliCsB, "C.c" -> caliCsC|>, {model, constraints}, reactionCoefs, <|"SimulationInterval" -> {0, 20}|>, "CalibratedSystemModel"]

    提取单个预测带的图：

    Wolfram Language code: csmodel["SinglePredictionBandsPlot"]//Dataset

    计算均方根误差，使用剩余数据路径作为验证数据：

    Wolfram Language code: csmodel["RMSE", ValidationSet -> <|"B.c" -> concentrationsB["Path", -1], "C.c" -> concentrationsC["Path", -1]|>]
    Wolfram Research (2023)，CalibratedSystemModel，Wolfram 语言函数，https://reference.wolfram.com/language/ref/CalibratedSystemModel.html.

    文本

    Wolfram Research (2023)，CalibratedSystemModel，Wolfram 语言函数，https://reference.wolfram.com/language/ref/CalibratedSystemModel.html.

    CMS

    Wolfram 语言. 2023. "CalibratedSystemModel." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/CalibratedSystemModel.html.

    APA

    Wolfram 语言. (2023). CalibratedSystemModel. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/CalibratedSystemModel.html 年

    BibTeX

    @misc{reference.wolfram_2026_calibratedsystemmodel, author="Wolfram Research", title="{CalibratedSystemModel}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/CalibratedSystemModel.html}", note=[Accessed: 06-July-2026]}

    BibLaTeX

    @online{reference.wolfram_2026_calibratedsystemmodel, organization={Wolfram Research}, title={CalibratedSystemModel}, year={2023}, url={https://reference.wolfram.com/language/ref/CalibratedSystemModel.html}, note=[Accessed: 06-July-2026]}