技术领域technical field
本发明属芯片温度监控技术领域，具体涉及一种芯片动态热管理中热传感器温度实时校准的方法。The invention belongs to the technical field of chip temperature monitoring, and in particular relates to a method for real-time temperature calibration of a thermal sensor in chip dynamic thermal management.
背景技术Background technique
随着集成电路特征尺寸的缩小和性能需求的增加，其功率密度迅速上升，导致芯片温度不断升高。此外，为了提高处理器性能，芯片设计者不断提升处理器频率，导致其动态功耗不断增加。再者，随着集成电路制造技术的不断改进，门电路的阈值电压、氧化厚度以及通道长度进一步减小，致使漏电流不断增大，漏电功耗(即静态功耗)显著增加。目前研究显示，电路总功耗中静态功耗已经占据一半以上。值得注意的是，静态功耗不但与制造工艺有关，还和芯片温度存在一定关系。一方面，静态功耗随芯片温度的上升呈指数级增加；另一方面，增加的静态功耗反过来会进一步提高芯片温度，导致恶性循环，进而出现热失控。As integrated circuit feature sizes shrink and performance demands increase, their power densities rise rapidly, resulting in ever-increasing chip temperatures. In addition, in order to improve processor performance, chip designers continue to increase processor frequency, resulting in increasing dynamic power consumption. Furthermore, with the continuous improvement of integrated circuit manufacturing technology, the threshold voltage, oxide thickness and channel length of the gate circuit are further reduced, resulting in a continuous increase in leakage current and a significant increase in leakage power consumption (ie, static power consumption). Current research shows that static power consumption has accounted for more than half of the total power consumption of the circuit. It is worth noting that the static power consumption is not only related to the manufacturing process, but also has a certain relationship with the chip temperature. On the one hand, the static power consumption increases exponentially with the rise of the chip temperature; on the other hand, the increased static power consumption will in turn further increase the chip temperature, leading to a vicious circle and then thermal runaway.
近年来，高性能多核处理器普遍集成片上热传感器，采用动态热管理(DynamicThermal Management,DTM)技术对芯片实施连续温度监控，一旦温度超过警戒阈值，便采取调节手段使其恢复到安全范围内。然而，实际芯片中的热传感器不可避免地伴随有多种噪声，例如制造随机性噪声、电源电压噪声、温度与电路参数交叉耦合和非线性关系引起的噪声等等。这些噪声大部分是由于生产制造的不完美性和环境的不确定性造成的。具体来说，因为当前半导体工艺技术的客观限制，不可避免地存在生产制造的随机性，即在实际制造中各个器件不可能和设计的参数毫无出入。同时，在芯片上还存在电网噪声和交叉耦合效应。此外，热传感器的温度参数和芯片参数之间还存在一些非线性的限制关系问题。由于这些噪声源理论上不能被完全消除，即使不断提高半导体的制造工艺，努力提供稳定的运行环境，也只能减小噪声的产生，这就给动态热管理的运行埋下了隐患。如果不对片上热传感器温度读数进行降噪处理，热点误警率会显著增加，在一定程度上会加剧错误的预警和不必要的响应，使动态热管理的可靠性受到严重影响，给系统性能带来不必要的损失。一方面，过高的温度估计会引起错误的预警和触发不必要的热控制机制，导致动态热管理的使用次数增加；另一方面，过低的温度估计将极大降低处理器的可靠性，甚至导致芯片的损坏。In recent years, high-performance multi-core processors have generally integrated on-chip thermal sensors, using Dynamic Thermal Management (DTM) technology to continuously monitor the temperature of the chip. Once the temperature exceeds the warning threshold, it will take adjustment measures to restore it to a safe range. However, thermal sensors in practical chips are inevitably accompanied by various noises, such as manufacturing random noise, power supply voltage noise, noise caused by cross-coupling and nonlinear relationship between temperature and circuit parameters, and so on. Most of these noises are due to manufacturing imperfections and environmental uncertainties. Specifically, due to the objective limitations of current semiconductor process technology, there is inevitably a randomness in manufacturing, that is, it is impossible for each device to be completely different from the designed parameters in actual manufacturing. At the same time, there are grid noise and cross-coupling effects on the chip. In addition, there are some nonlinear constraints between the temperature parameters of the thermal sensor and the chip parameters. Since these noise sources cannot be completely eliminated in theory, even if the semiconductor manufacturing process is continuously improved and a stable operating environment is provided, the noise generation can only be reduced, which buries a hidden danger to the operation of dynamic thermal management. If the noise reduction processing is not performed on the temperature readings of the on-chip thermal sensor, the false alarm rate of hot spots will increase significantly, which will exacerbate false early warnings and unnecessary responses to a certain extent, seriously affect the reliability of dynamic thermal management, and reduce system performance. to unnecessary losses. On the one hand, too high temperature estimation will cause false warnings and trigger unnecessary thermal control mechanisms, resulting in increased usage of dynamic thermal management; on the other hand, too low temperature estimation will greatly reduce the reliability of the processor. even lead to chip damage.
实时有效的热传感器温度校准方法对芯片的性能、寿命、可靠性等影响至关重要，已成为一个新兴且极其重要的研究方向及一个迫切需要解决的问题。通过对现有技术文献检索发现，Yufu Zhang和Ankur Srivastava在2011年IEEE Transactions on Very LargeScale Integration(VLSI)Systems(IEEE超大规模集成电路系统)发表文章《AccurateTemperature Estimation Using Noisy Thermal Sensors for Gaussian and Non-Gaussian Cases》(对于含噪热传感器在高斯和非高斯噪声下的精确温度估计)，该文章对于芯片上含噪热传感器温度估计提出了一种统计学的处理方法，分别对单传感器和多传感器在高斯和非高斯噪声两种状态下的温度估计进行分析。其不足之处在于该方法首先需要模拟出芯片的先验功率密度信息，缺乏实时预测的能力，实用性较差。The real-time and effective thermal sensor temperature calibration method is very important to the performance, life and reliability of the chip, and has become an emerging and extremely important research direction and an urgent problem to be solved. Through searching the prior art literature, it was found that Yufu Zhang and Ankur Srivastava published the article "AccurateTemperature Estimation Using Noisy Thermal Sensors for Gaussian and Non-Gaussian" in 2011 IEEE Transactions on Very LargeScale Integration (VLSI) Systems (IEEE VLSI Systems). Cases" (for accurate temperature estimation of noisy thermal sensors under Gaussian and non-Gaussian noise), this paper proposes a statistical processing method for the temperature estimation of noisy thermal sensors on a chip. The temperature estimation in both states of Gaussian and non-Gaussian noise is analyzed. The disadvantage is that the method first needs to simulate the prior power density information of the chip, lacks the ability of real-time prediction, and has poor practicability.
发明内容SUMMARY OF THE INVENTION
为了克服现有技术的不足，本发明提供一种芯片动态热管理中热传感器温度实时校准的方法。本发明方法是一种基于平滑滤波和空间相关性的卡尔曼滤波估计方法：首先，利用多项式拟合热传感器温度和输出频率之间的非线性关系，获得温度观测值；然后，通过平滑滤波技术得到温度预测值，进而将温度观测值和预测值利用卡尔曼滤波进行融合；接着，建立多传感器空间相关性模型和观测温度校正算法，利用相关性对噪声温度观测值进行修正；最后，再次利用卡尔曼滤波将修正后的观测值和平滑滤波得到的预测值进行融合，给出最佳温度读数估计值。In order to overcome the deficiencies of the prior art, the present invention provides a method for real-time calibration of thermal sensor temperature in chip dynamic thermal management. The method of the invention is a Kalman filter estimation method based on smoothing filtering and spatial correlation: first, the nonlinear relationship between the temperature of the thermal sensor and the output frequency is fitted by a polynomial to obtain the temperature observation value; then, the smoothing filtering technology The temperature prediction value is obtained, and then the temperature observation value and the prediction value are fused by Kalman filter; then, the multi-sensor spatial correlation model and the observation temperature correction algorithm are established, and the noise temperature observation value is corrected by the correlation; The Kalman filter fuses the corrected observations with the predicted values obtained by smoothing filtering to give the best estimate of the temperature reading.
一种芯片动态热管理中热传感器温度实时校准的方法，其特征在于步骤如下：A method for real-time calibration of thermal sensor temperature in chip dynamic thermal management, characterized in that the steps are as follows:
步骤1：根据频率与温度的关系式模拟不同温度下对应的输出频率值，将模拟得到的温度和频率的数据集进行多项式拟合，通过拟合关系式将环形振荡器输出频率转换为热传感器温度观测值；Step 1: Simulate the corresponding output frequency values at different temperatures according to the relationship between frequency and temperature, perform polynomial fitting on the data sets of temperature and frequency obtained by the simulation, and convert the output frequency of the ring oscillator into a thermal sensor through the fitting relationship temperature observations;
步骤2：对所有当前时刻之前的温度校准值向量进行平滑滤波，得到热传感器的温度预测值向量Step 2: Perform smooth filtering on all the temperature calibration value vectors before the current time to obtain the temperature prediction value vector of the thermal sensor
其中，为温度预测值向量，k表示当前时刻，Ns为平滑滤波长度，Ns≤k-1，B为系统输入矩阵；in, is the temperature prediction value vector, k represents the current moment, Ns is the smoothing filter length, Ns ≤k-1, and B is the system input matrix;
步骤3：利用将步骤2得到的温度预测值向量和温度观测值向量S(k)进行卡尔曼滤波融合，得到热传感器的第一次温度校准值向量Step 3: Utilize Convert the temperature prediction vector obtained in step 2 Perform Kalman filter fusion with the temperature observation value vector S(k) to obtain the first temperature calibration value vector of the thermal sensor
其中，K(k)＝P(k|k-1)HT[H P(k|k-1)HT+R]-1为卡尔曼增益矩阵，H为系统输出矩阵，R为观测噪声向量υ(k)的协方差矩阵，P(k|k-1)＝B P(k-1|k-1)BT+Q为误差协方差矩阵，满足P(k|k)＝[I-K(k)H]P(k|k-1)，I为单位矩阵，Q为过程噪声向量ω(k)的协方差矩阵；Among them, K(k)=P(k|k-1)HT [HP(k|k-1)HT +R]-1 is the Kalman gain matrix, H is the system output matrix, and R is the observation noise vector The covariance matrix of υ(k), P(k|k-1)=BP(k-1|k-1)BT +Q is the error covariance matrix, satisfying P(k|k)=[IK(k )H]P(k|k-1), I is the identity matrix, Q is the covariance matrix of the process noise vector ω(k);
步骤4：利用计算两两传感器之间的相关性系数，其中，κ为第二类修正贝塞尔函数，Γ为伽马函数，v为两个传感器之间的空间距离，b和s为调节函数形状的两个实数参数，b,s＞0，ρ为相关性系数，下标i、j为传感器序号，i,j＝1,…,M，M为传感器个数；Step 4: Utilize Calculate the correlation coefficient between two sensors, where κ is the modified Bessel function of the second kind, Γ is the gamma function, v is the spatial distance between the two sensors, and b and s are the two parameters of the adjustment function shape. A real number parameter, b, s>0, ρ is the correlation coefficient, subscript i, j is the sensor serial number, i, j=1, ..., M, M is the number of sensors;
对于任一传感器m，如果其和所有其他传感器的相关性系数均满足ρm,i＜λ，i＝1,…,M且i≠m，λ为设定阈值，λ∈(0,1)，则按式(2)对该传感器的温度观测值Sm(k)进行修正，得到修正后的温度观测值向量For any sensor m, if its correlation coefficient with all other sensors satisfies ρm,i <λ, i=1,...,M and i≠m, λ is the set threshold, λ∈(0,1) ,but Correct the temperature observation value Sm (k) of the sensor according to formula (2), and obtain the corrected temperature observation value vector
其中，为传感器m修正后的温度观测值，也即修正后的温度观测值向量的第m个分量；Sm(k)为温度观测值向量S(k)的第m个分量；Sn(k)为温度观测值向量S(k)的第n个分量；为传感器m的第一次温度校准值，也即第一次温度校准值向量的第m个分量；为传感器n的第一次温度校准值，也即第一次温度校准值向量的第n个分量；n为满足ρm,n＞ρm,j,且j≠m,n的传感器序号；in, is the corrected temperature observation value of sensor m, that is, the mth component of the corrected temperature observation value vector; Sm (k) is the mth component of the temperature observation value vector S(k); Sn (k) is the nth component of the temperature observation vector S(k); is the first temperature calibration value of sensor m, that is, the first temperature calibration value vector the mth component of ; is the first temperature calibration value of sensor n, that is, the first temperature calibration value vector The nth component of ; n is satisfying ρm,n >ρm,j , And the sensor serial number of j≠m,n;
步骤5：按式(3)对修正后的温度观测值向量和温度预测值向量进行二次卡尔曼滤波，得到当前时刻热传感器最终的温度校准值向量T(k|k)：Step 5: According to formula (3), the corrected temperature observation value vector and a vector of temperature predicted values Perform secondary Kalman filtering to obtain the final temperature calibration value vector T(k|k) of the thermal sensor at the current moment:
本发明的有益效果是：由于采用基于平滑滤波的卡尔曼滤波，故热传感器温度的预测值将更加平稳贴近实际温度值，同时利用芯片热点温度之间的空间相关性对热传感器温度观测值进行修正，因此最终将得到更加准确的热传感器温度估计值。The beneficial effects of the present invention are: due to the Kalman filter based on smoothing filtering, the predicted value of the temperature of the thermal sensor will be more stable and close to the actual temperature value, and at the same time, the observed value of the temperature of the thermal sensor will be calculated by using the spatial correlation between the hot spot temperatures of the chip. correction, so you will end up with a more accurate thermal sensor temperature estimate.
附图说明Description of drawings
图1为本发明的一种芯片动态热管理中热传感器温度实时校准方法的流程图1 is a flowchart of a method for real-time calibration of thermal sensor temperature in chip dynamic thermal management according to the present invention
图2为含噪声时热传感器在不同温度下输出频率的概率密度函数图Figure 2 is a graph of the probability density function of the output frequency of the thermal sensor at different temperatures with noise
图3为热传感器输出频率和温度多项式拟合图Figure 3 is the polynomial fitting diagram of the output frequency and temperature of the thermal sensor
图4为热传感器相关性图Figure 4 is a thermal sensor correlation diagram
图5为实际温度曲线Figure 5 is the actual temperature curve
图6为加入噪声后的温度曲线Figure 6 is the temperature curve after adding noise
图7为卡尔曼滤波后的温度曲线Figure 7 is the temperature curve after Kalman filtering
图8为基于平滑滤波的卡尔曼滤波后的温度曲线Figure 8 shows the temperature curve after Kalman filtering based on smoothing filtering
图9为基于空间相关性和平滑滤波的卡尔曼滤波后的温度曲线Figure 9 is the temperature curve after Kalman filtering based on spatial correlation and smoothing filtering
具体实施方式Detailed ways
下面结合附图和实施例对本发明进一步说明，本发明包括但不仅限于下述实施例。The present invention will be further described below with reference to the accompanying drawings and embodiments, and the present invention includes but is not limited to the following embodiments.
本发明方法的主要思路为：对于卡尔曼滤波引入平滑滤波和相关性模型。首先，利用平滑滤波得到热传感器温度预测值；然后，通过卡尔曼滤波将温度预测值和观测值进行融合，得到第一次热传感器温度校准值；接着，利用第一次卡尔曼滤波得到的校准值和相关性系数判断热传感器观测值偏大或偏小，并对热传感器温度观测值进行校正；最后，再次利用卡尔曼滤波将校正后的观测值和平滑滤波得到的预测值进行融合。The main idea of the method of the present invention is to introduce smooth filtering and correlation model to Kalman filtering. First, the temperature prediction value of the thermal sensor is obtained by smoothing filtering; then, the temperature prediction value and the observed value are fused by Kalman filtering to obtain the first thermal sensor temperature calibration value; then, the calibration value obtained by the first Kalman filtering is used. The value and the correlation coefficient determine whether the observed value of the thermal sensor is too large or too small, and correct the observed value of the thermal sensor temperature; finally, Kalman filter is used again to fuse the corrected observed value and the predicted value obtained by smoothing filtering.
如图1所示，本发明的一种芯片动态热管理中热传感器温度实时校准方法，具体实现过程如下：As shown in FIG. 1, a real-time calibration method for thermal sensor temperature in chip dynamic thermal management of the present invention, the specific implementation process is as follows:
1、利用多项式拟合简化热传感器温度和频率之间的非线性关系，得到温度观测值。1. Simplify the nonlinear relationship between the temperature and frequency of the thermal sensor by using polynomial fitting, and obtain the temperature observation value.
目前，片上热传感器的组成结构主要采用环形振荡器的形式，其由奇数个反相器和一个计数器构成。反相器完成高低电平的转换需要一定的时间，计数器所输出的振荡频率由每个反相器的传播延迟决定。反相器从高电平转换到低电平的转换时间可以表示为：At present, the composition structure of the on-chip thermal sensor is mainly in the form of a ring oscillator, which is composed of an odd number of inverters and a counter. It takes a certain amount of time for the inverter to complete the conversion of high and low levels, and the oscillation frequency output by the counter is determined by the propagation delay of each inverter. The transition time of the inverter from high level to low level can be expressed as:
其中，μn为N型金属-氧化物-半导体(N-type Metal-Oxide-Semiconductor,NMOS)中电子的迁移率，(W/L)n为NMOS管的宽长比，Cox为单位门面积电容(Cox＝εox/Tox),C为驱动反相器的有效负载电容，VDD为电源电压，Vt为阈值电压。同理，可以得到反相器从低电平转换到高电平的转换时间tPLH，只需将μn和(W/L)n分别换成对应P型金属-氧化物-半导体(P-type Metal-Oxide-Semiconductor,PMOS)的μp和(W/L)p即可。因此，环形振荡器的输出频率可以表示为：Among them, μn is the mobility of electrons in N-type Metal-Oxide-Semiconductor (NMOS), (W/L)n is the width-to-length ratio of the NMOS tube, and Cox is the unit gate Area capacitance (Cox =εox /Tox ), C is the effective load capacitance of the drive inverter, VDD is the power supply voltage, and Vt is the threshold voltage. In the same way, the conversion time tPLH of the inverter from low level to high level can be obtained, just replace μn and (W/L)n with corresponding P-type metal-oxide-semiconductor (P- type Metal-Oxide-Semiconductor, PMOS) μp and (W/L)p are sufficient. Therefore, the output frequency of the ring oscillator can be expressed as:
由式(4)和(5)中可以看出，环形振荡器的输出频率受到阈值电压Vt以及MOS管中电子(或空穴)迁移率μn(或μp)的影响。然而，Vt和μn(或μp)对温度非常敏感，为了更加确切的描述温度效应，可以使用以下两个经验公式：It can be seen from equations (4) and (5) that the output frequency of the ring oscillator is affected by the threshold voltage Vt and the electron (or hole) mobility μn (or μp ) in the MOS tube. However, Vt and μn (or μp ) are very sensitive to temperature. In order to describe the temperature effect more precisely, the following two empirical formulas can be used:
Vt＝Vt0-0.002(T-T0) (6)Vt =Vt0 -0.002(TT0 ) (6)
μn/p＝μ0(T/T0)-1.5 (7)μn/p = μ0 (T/T0 )-1.5 (7)
其中，Vt0和μ0分别为Vt和μn(或μp)在室温T0下的标准值。由式(6)和(7)可知，温度每升高1℃，Vt就会减小2毫伏，μn(或μp)则会以一个更复杂的关系减小。由于在对反相器电平转换时间的影响中μn(或μp)占主导地位，因此，环形振荡器的输出频率随温度上升而下降。所以，片上热传感器可以利用环形振荡器的输出频率来测量芯片的温度。Wherein, Vt0 and μ0 are the standard values of Vt and μn (or μp ) at room temperature T0 , respectively. From equations (6) and (7), it can be known that for every 1°C increase in temperature, Vt will decrease by 2 mV, and μn (or μp ) will decrease in a more complex relationship. Since μn (or μp ) dominates the effect on the inverter level transition time, the output frequency of the ring oscillator decreases with increasing temperature. Therefore, the on-chip thermal sensor can use the output frequency of the ring oscillator to measure the temperature of the chip.
然而，由于生产制造的随机性和环境的不确定性，环形振荡器的输出频率易受到一些随机参数的影响，例如电源电压VDD的波动等。因此，热传感器所提供的温度读数具有很大的不确定性。针对表1所示的不同高斯分布的随机噪声参数特性，对环形振荡器的输出频率做不同温度下的蒙特卡洛模拟(图2所示)，温度范围从30℃到70℃(增量为10℃)，每组采样100000次。由图2可见，不同温度下输出频率的概率密度曲线发生了严重的重叠现象，这说明在噪声的影响下温度和输出频率并不是一一对应的关系。因此，噪声对热传感器的影响不能被忽略，不能盲目地相信热传感器所提供的温度读数。However, due to the randomness of manufacturing and the uncertainty of the environment, the output frequency of the ring oscillator is easily affected by some random parameters, such as the fluctuation of the power supply voltage VDD and so on. Therefore, the temperature readings provided by thermal sensors have large uncertainties. According to the random noise parameter characteristics of different Gaussian distributions shown in Table 1, the output frequency of the ring oscillator is subjected to Monte Carlo simulations at different temperatures (as shown in Figure 2), and the temperature range is from 30°C to 70°C (in increments of 10°C), 100,000 samples per group. It can be seen from Figure 2 that the probability density curves of output frequencies at different temperatures have a serious overlapping phenomenon, which shows that there is no one-to-one correspondence between temperature and output frequency under the influence of noise. Therefore, the effect of noise on thermal sensors cannot be ignored and the temperature readings provided by thermal sensors cannot be blindly trusted.
表1Table 1
因此，需要将温度和频率之间的关系进行简化。因此利用式(4)～(7)在MATLAB中模拟不同温度下对应的热传感器频率输出值。将模拟得到的温度和频率的数据集进行多项式拟合(如图3所示)，再通过拟合关系式将环形振荡器输出频率转换为热传感器温度观测值。Therefore, the relationship between temperature and frequency needs to be simplified. Therefore, formulas (4) to (7) are used to simulate the corresponding thermal sensor frequency output values at different temperatures in MATLAB. Polynomial fitting is performed on the data set of temperature and frequency obtained from the simulation (as shown in Figure 3), and then the ring oscillator output frequency is converted into the temperature observation value of the thermal sensor through the fitting relation.
2、利用平滑滤波得到热传感器温度预测值。2. Use smooth filtering to obtain the temperature prediction value of the thermal sensor.
利用卡尔曼滤波进行温度估计时，首先需要建立热传感器的预测和观测模型，如式(8)和(9)所示：When using Kalman filter for temperature estimation, the prediction and observation model of the thermal sensor needs to be established first, as shown in equations (8) and (9):
T(k)＝B T(k-1)+ω(k) (8)T(k)=B T(k-1)+ω(k) (8)
S(k)＝H T(k)+υ(k) (9)S(k)=HT(k)+υ(k) (9)
式(8)中，k表示当前时刻，T(k)为当前时刻热传感器温度值向量，T(k-1)为上一时刻温度预测值向量，B为系统输入矩阵，ω(k)为过程噪声向量。式(9)中，S(k)为热传感器温度观测值向量，H为系统输出矩阵，υ(k)为观测噪声向量。In formula (8), k represents the current moment, T(k) is the temperature value vector of the thermal sensor at the current moment, T(k-1) is the temperature prediction value vector at the previous moment, B is the system input matrix, and ω(k) is Process noise vector. In formula (9), S(k) is the temperature observation value vector of the thermal sensor, H is the system output matrix, and υ(k) is the observation noise vector.
基于短采样间隔片上温度不会发生突变的特性，可利用当前时刻之前的温度校准值通过平滑滤波建立更加精确的温度预测值，以最大化减少温度波动(毛刺)的影响，即：Based on the characteristic that the temperature on the chip with short sampling interval does not change abruptly, the temperature calibration value before the current time can be used to establish a more accurate temperature prediction value through smoothing filtering, so as to minimize the influence of temperature fluctuation (burr), namely:
其中，为温度预测值向量，Ns为平滑滤波长度，Ns≤k-1，本实施例中Ns＝5。in, is the temperature prediction value vector, Ns is the smoothing filter length, Ns ≤k-1, and Ns =5 in this embodiment.
3、将温度预测值和观测值利用卡尔曼滤波进行融合。3. Integrate the predicted temperature value and the observed value with Kalman filter.
将上一步平滑滤波得到热传感器温度预测值向量和温度观测值向量S(k)进行卡尔曼滤波融合，得到热传感器的第一次温度校准值向量具体过程如下：Smoothing and filtering the previous step to obtain a vector of thermal sensor temperature prediction values Perform Kalman filter fusion with the temperature observation value vector S(k) to obtain the first temperature calibration value vector of the thermal sensor The specific process is as follows:
P(k|k-1)＝B P(k-1|k-1)BT+Q (11)P(k|k-1)=BP(k-1|k-1)BT +Q (11)
K(k)＝P(k|k-1)HT[H P(k|k-1)HT+R]-1 (12)K(k)=P(k|k-1)HT [HP(k|k-1)HT +R]-1 (12)
P(k|k)＝[I-K(k)H]P(k|k-1) (14)P(k|k)=[I-K(k)H]P(k|k-1) (14)
其中，P(k|k-1)为误差协方差矩阵，Q为ω(k)的协方差矩阵，K(k)为卡尔曼增益矩阵，R为υ(k)的协方差矩阵，P(k|k)为更新后的误差协方差矩阵，本实施例中，P初值设为0.04的对角矩阵。Among them, P(k|k-1) is the error covariance matrix, Q is the covariance matrix of ω(k), K(k) is the Kalman gain matrix, R is the covariance matrix of υ(k), P( k|k) is the updated error covariance matrix. In this embodiment, the initial value of P is set as a diagonal matrix of 0.04.
4、计算热传感器两两之间相关性，并利用相关性和卡尔曼滤波值修正温度观测值。4. Calculate the correlation between the two thermal sensors, and use the correlation and Kalman filter value to correct the temperature observation value.
芯片上不同位置的温度变化具有相关性，距离越近相关性越高，利用相关性可以对热传感器噪声温度观测值进行修正，以提高温度估计的准确性。对于距离相差为v的两个热传感器，由于它们的协方差可以近似看作距离v的函数，因此，可建立如下所示的空间相关性模型：The temperature changes at different positions on the chip are correlated, and the closer the distance is, the higher the correlation is. Using the correlation, the noise temperature observation value of the thermal sensor can be corrected to improve the accuracy of temperature estimation. For two thermal sensors with a distance difference v, since their covariance can be approximately regarded as a function of the distance v, the spatial correlation model can be established as follows:
其中，κ为第二类修正贝塞尔函数，Γ为伽马函数，v为传感器之间的空间距离，b和s为调节函数形状的两个实数参数，b,s＞0，本实施例中b＝1，s＝8，ρ为相关性系数。图4为b和s不同取值下相关性图。Among them, κ is the second type of modified Bessel function, Γ is the gamma function, v is the spatial distance between the sensors, b and s are two real parameters that adjust the shape of the function, b, s>0, this embodiment where b=1, s=8, and ρ is the correlation coefficient. Figure 4 is a correlation diagram under different values of b and s.
利用相关性模型可以获得任意两个热传感器之间的相关性系数ρ，在此基础上，设定阈值λ(λ∈(0,1))，当相关性系数小于该阈值时(ρ＜λ)说明两个热传感器之间的相关性太低，则不进行修正，反之，则对观测值进行修正。本实施例中λ＝0.6。The correlation coefficient ρ between any two thermal sensors can be obtained by using the correlation model. On this basis, a threshold λ (λ∈(0,1)) is set. When the correlation coefficient is smaller than the threshold (ρ<λ ) indicates that the correlation between the two thermal sensors is too low, so no correction is made, otherwise, the observed value is corrected. In this embodiment, λ=0.6.
本实施例对三个热传感器(P1，P2，P3)进行温度校准，以热传感器P1为例，分别计算热传感器P1与热传感器P2、热传感器P1与热传感器P3之间的相关性系数ρP1,P2和ρP1,P3，如果ρP1,P2＞ρP1,P3且ρP1,P2＞λ，则选取热传感器P2对P1进行修正，具体流程为：This embodiment performs temperature calibration on three thermal sensors (P1, P2, P3). Taking thermal sensor P1 as an example, the correlation coefficient ρ between thermal sensor P1 and thermal sensor P2, and thermal sensor P1 and thermal sensor P3 is calculated respectively.P1,P2 and ρP1,P3 , if ρP1,P2 >ρP1,P3 and ρP1,P2 >λ, then select thermal sensor P2 to correct P1, the specific process is:
(1)利用基于平滑滤波的卡尔曼滤波对P1、P2两个热传感器温度进行第一次估(1) Use the Kalman filter based on smoothing filtering to estimate the temperature of the two thermal sensors P1 and P2 for the first time
计得到和count and
即为修正后的传感器P1的温度观测值。 That is, the corrected temperature observation value of the sensor P1.
对所有传感器均按上述过程进行相关性系数计算和修正，得到修正后的温度观测值向量The correlation coefficients are calculated and corrected for all sensors according to the above process, and the corrected temperature observation value vector is obtained.
5、对修正后的温度观测值和预测值进行二次卡尔曼滤波得到最终校准值。5. Perform a quadratic Kalman filter on the corrected temperature observations and predicted values to obtain the final calibration value.
修正后的热传感器温度观测值需再次通过卡尔曼滤波得到最终的温度校准值，即：The corrected thermal sensor temperature observation value needs to pass through Kalman filter again to obtain the final temperature calibration value, namely:
其中，为热传感器修正温度观测值向量，为平滑滤波得到的热传感器温度预测值向量，为卡尔曼滤波结果，即热传感器最终温度校准值。in, The vector of corrected temperature observations for the thermal sensor, is the vector of thermal sensor temperature prediction values obtained by smooth filtering, is the result of Kalman filtering, that is, the final temperature calibration value of the thermal sensor.
本实施例中对三个热传感器(P1、P2、P3)进行温度校准，每个热传感器采样3000个点，实际温度曲线如图5所示，然后对其加入高斯噪声，如图6所示。采用三种不同的滤波方案进行温度校准：方案一、卡尔曼滤波；方案二、基于平滑滤波的卡尔曼滤波；方案三、基于空间相关性和平滑滤波的卡尔曼滤波。图7-9分别为三种滤波方案后的温度曲线。In this embodiment, three thermal sensors (P1, P2, P3) are temperature calibrated, each thermal sensor samples 3000 points, the actual temperature curve is shown in Figure 5, and Gaussian noise is added to it, as shown in Figure 6 . Three different filtering schemes are used for temperature calibration: scheme one, Kalman filtering; scheme two, Kalman filtering based on smoothing filtering; scheme three, Kalman filtering based on spatial correlation and smoothing filtering. Figures 7-9 are the temperature curves after the three filtering schemes.
表2Table 2
表2为三种滤波方案的均方根误差和信噪比数据。可以看出，基于空间相关性和平滑滤波的卡尔曼滤波相比较单纯的卡尔曼滤波精确度大幅提升。经MATLAB仿真运行时间为90毫秒，平均每一次校正时间为0.03毫秒，远远小于采样间隔(17毫秒)，故可实现实时校正。Table 2 shows the root mean square error and signal-to-noise ratio data for the three filtering schemes. It can be seen that the accuracy of Kalman filtering based on spatial correlation and smoothing filtering is greatly improved compared to that of simple Kalman filtering. The running time of MATLAB simulation is 90 milliseconds, and the average correction time is 0.03 milliseconds, which is far less than the sampling interval (17 milliseconds), so real-time correction can be realized.
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