CN108416164B - Three-dimensional network-on-chip temperature reconstruction system based on limited number of temperature sensors - Google Patents

Three-dimensional network-on-chip temperature reconstruction system based on limited number of temperature sensors Download PDF

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CN108416164B
CN108416164B CN201810250930.0A CN201810250930A CN108416164B CN 108416164 B CN108416164 B CN 108416164B CN 201810250930 A CN201810250930 A CN 201810250930A CN 108416164 B CN108416164 B CN 108416164B
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李丽
傅玉祥
丰帆
潘红兵
何书专
李伟
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Nanjing University
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Abstract

The invention discloses a three-dimensional network-on-chip temperature reconstruction system based on a limited number of temperature sensors, which adopts a Gaussian sum filter to reconstruct the temperature of a three-dimensional network-on-chip, wherein the Gaussian sum filter is approximate to a non-Gaussian distribution by the weighted sum of a plurality of Gaussian distributions, so that a plurality of Gaussian term filtering results can be combined into an equivalent Gaussian term; the Gaussian sum filter hardware architecture is a reusable architecture which can realize the multiplexing of computing resources and storage resources, and comprises three parts: the controller, the storage resource and the computing unit array can be reused. The invention can effectively solve the problem of three-dimensional on-chip network temperature reconstruction under the conditions of limited number of temperature sensors and non-Gaussian noise, and the reusable Gaussian and filter hardware architecture can improve the utilization rate of computing resources and storage resources, and simultaneously reduce the area and the power consumption.

Description

Three-dimensional network-on-chip temperature reconstruction system based on limited number of temperature sensors
Technical Field
The invention belongs to the field of network-on-chips, and particularly relates to a three-dimensional network-on-chip temperature reconstruction system based on a limited number of temperature sensors.
Background
The three-dimensional network-on-chip system has higher throughput and lower average delay compared with the two-dimensional network-on-chip system, but the power consumption per unit area is higher due to the three-dimensional chip stacking, so that the three-dimensional network-on-chip system faces a severe temperature problem. In many multi-core or many-core chips, temperature control is a design consideration, and temperature sensors are the basis for developing temperature control. However, due to the cost, area, power consumption, and other overhead of the temperature sensors, generally, the number of temperature sensors that can be deployed on one chip is limited.
For a system with a limited number of temperature sensors, a temperature reconstruction technique is necessary because it ensures that the temperature of the entire chip can be reconstructed in real time from the observations of the temperature sensors. One problem in the application of the temperature reconstruction technology is that the temperature sensor measures noise, and the noise obviously has an important influence on the reconstruction accuracy. In practical situations, the accuracy of the temperature sensor to measure noise is affected by many factors, such as process variations, quantization errors, supply voltage fluctuations, and so on. In the existing literature, the measurement noise is usually assumed to be gaussian noise, which, although simple, introduces inaccuracies in most cases, since the true measurement noise is likely to be disturbed by anomalous factors and to appear non-gaussian. Therefore, it is a great challenge for designers how to accurately reconstruct the temperature under non-gaussian noise.
Disclosure of Invention
In order to solve the problems, the invention provides a three-dimensional network-on-chip temperature reconstruction framework based on a limited number of temperature sensors under non-Gaussian noise, which can effectively solve the temperature reconstruction problem of the three-dimensional network-on-chip under the conditions that the number of the temperature sensors is limited and the measured noise is non-Gaussian; the invention also aims to provide a three-dimensional network-on-chip temperature reconstruction hardware architecture based on a limited number of temperature sensors under high-energy-efficiency non-Gaussian noise, which is specifically realized by the following technical scheme:
the system reconstructs the temperature of a three-dimensional network-on-chip through a Gaussian sum filter, the Gaussian sum filter combines a plurality of Gaussian term filtering results into an equivalent Gaussian term, and the system comprises three stages: the system specifically comprises the following three parts:
a reusable controller that configures interconnections between the computing units and controls the process of the gaussians and the filters;
the storage resource consists of a constant memory and a data memory;
the computing unit array consists of common floating point computing units which are connected through a cross switch; in the prediction stage of the Gaussian sum filter, the system predicts the temperature according to the temperature state estimation value at the previous moment and calculates the corresponding error covariance, and the calculation process is as follows (1):
Figure GDA0003126559740000021
wherein A (k, k-1) and B are respectively a state transition matrix and an input matrix of the three-dimensional network-on-chip thermal model based on the state space, A (k, k-1)TIs the transpose of A (k, k-1), W is the covariance matrix of the process noise in the state space based thermal model, u (k) is the power consumption at time k for each node, is the input to the model,
Figure GDA0003126559740000022
the method comprises the following steps of respectively obtaining a posterior temperature estimation value at the k-1 moment, a prior temperature estimation value at the k moment and an error covariance corresponding to the posterior temperature estimation value and the prior temperature estimation value at the k moment;
in the updating stage of the Gaussian sum filter, the system combines a new observation value with the last predicted value to obtain an improved posterior estimated value, and the calculation process is as follows (2):
Figure GDA0003126559740000023
wherein, I is an identity matrix, K (k) is Kalman gain at the moment k, S (k) is an observed value of a temperature sensor at the moment k, H (k) is an output matrix at the moment k, and the position of a nonzero element of the output matrix indicates that the node can be measured, namely the temperature sensor exists at the point;
Figure GDA0003126559740000024
is the output value, P, of the temperature estimated at the previous moments(k | k-1) is the covariance of the merging errors of the l Gaussian terms, and the weight ω of the Gaussian terms is updated by the system during the weight update phase of the Gaussian sum filteri(k) Updating, wherein the process is as formula (3):
Figure GDA0003126559740000031
where | is the determinant of the matrix, aiIs the initialized weight factor, c (k) is the sum of all gaussian terms,
Figure GDA0003126559740000032
is the output estimate of the gaussian term i and the corresponding error covariance, l represents the number of gaussian terms.
The limited number of temperature sensor based three-dimensional network-on-chip temperature reconstruction system is further designed in that an arbitrary non-gaussian distribution is set according to equation (4) to be approximated by a limited number of gaussian sums,
Figure GDA0003126559740000033
where v (k) is a non-Gaussian distribution at time k, N (μ)i,Ri) Is a mean value of μiWith a covariance of RiThe initialized weight factor aiCorresponding to a mean value of μiWith a covariance of RiWherein the sum of the weights is 1;
the system performs filtering on each Gaussian term, and merges the filtering results of the Gaussian terms to obtain a state estimation and an error covariance, as shown in formula (5):
Figure GDA0003126559740000034
wherein R isiIs the covariance of the measurement noise of the gaussian term i.
The limited number temperature sensor-based three-dimensional network-on-chip temperature reconstruction system is further designed in such a way that the reusable Gaussian sum filter hardware module is externally connected with the dynamic temperature management controller, the temperature sensor and the power consumption estimator.
The limited number of temperature sensor based three-dimensional network-on-chip temperature reconstruction system is further designed in that the constant memory of the reusable gaussian sum filter is composed of 4 banks for storing the matrix parameters A, B, H.
The three-dimensional network-on-chip temperature reconstruction system based on the limited number of temperature sensors is further designed in that the data memory consists of 12 banks, an intermediate matrix stored in the calculation process, temperature sensor readings and power consumption estimated values serving as input data, and temperature estimated values serving as output data, the width of the memory bank is 32 bits, and the depth of the memory bank depends on the order number of the system.
The three-dimensional network-on-chip temperature reconstruction system based on the limited number of temperature sensors is further designed in that the computing unit array capable of reusing gaussians and filters is composed of common floating point operation units and comprises 4 adders, 4 multipliers, 1 divider and 1 exponent unit, and the 4 adders, the 4 multipliers, the 1 divider and the 1 exponent unit are connected through a cross switch.
The invention has the advantages that:
1) the framework can effectively solve the problem of temperature reconstruction of the three-dimensional network on chip under the condition that the number of temperature sensors is limited and the measurement noise is non-Gaussian.
2) The reusable Gaussian sum filter hardware architecture can improve the utilization rate of computing resources and storage resources, and simultaneously reduce the area and the power consumption.
In conclusion, the invention can effectively solve the problem of temperature reconstruction of the three-dimensional network on chip based on a limited number of temperature sensors under non-Gaussian noise, and has good practical application value.
Drawings
Fig. 1 is a schematic diagram of the gaussian sum filter structure of the present invention.
Fig. 2 is a gaussian sum filtering process and corresponding calculation unit of the present invention.
Fig. 3 is a diagram of the reusable gaussian sum filter hardware architecture of the present invention.
FIG. 4 is a schematic diagram of the internal architecture of the computational cell array in the reusable Gaussian sum filter hardware architecture of the present invention.
Detailed Description
The following describes the present invention in detail with reference to the accompanying drawings.
The gaussian sum filter structure of the present invention is schematically shown in fig. 1. The gaussian sum filter is a recursive process, and can be divided into three stages: prediction phase, updating phase and weight updating phase. The structures of the first, second and third in the figure are completely the same as the structure of the Kalman filter, and respectively correspond to a prediction process, an observed value estimation process and an updating process. The part of the figure except for the first, second and third is the place where the Gaussian sum filter of the invention is different from the Kalman filter, and the part is mainly the process of combining l Gaussian terms into an equivalent Gaussian term.
The gaussian sum filtering process and the corresponding calculation unit of the present invention are shown in fig. 2. The gaussian and filter process can be divided into 7 steps according to data dependency (the number of an equation in the summary of the invention is shown in parentheses), each step has data dependency with the previous step, and the calculation formulas have no data dependency in the same step, so that the data dependency can be processed in parallel. The right side of fig. 2 lists the required computational units corresponding to the computational steps on the left side of the figure. It can be seen that all steps use multipliers and adders, and dividers are used in the third and sixth steps, so that these arithmetic units can be shared between the calculation steps.
Further, in the prediction stage of the gauss sum filter, the system predicts the temperature according to the temperature state estimated value at the previous moment and calculates the corresponding error covariance, and the calculation process is as follows:
Figure GDA0003126559740000051
wherein, A and B are respectively a state transition matrix and an input matrix of the three-dimensional network-on-chip thermal model based on the state space, A (k, k-1)TIs the transpose of A (k, k-1), W is the covariance matrix of the process noise in the state space based thermal model, u (k) is the power consumption at time k for each node, is the input to the model,
Figure GDA0003126559740000052
the estimated value of posterior temperature at the time k-1, the estimated value of prior temperature at the time k and the error covariance corresponding to the two are respectively.
Further, in the updating stage of the gauss sum filter, the system combines a new observation value with the last predicted value to obtain an improved posterior estimated value, and the calculation process is as follows (2):
Figure GDA0003126559740000053
wherein, I is an identity matrix, K (k) is Kalman gain at the moment k, S is an observed value, H (k) is an output matrix at the moment k, and the position of a nonzero element of the output matrix indicates that the node can be measured, namely the node has a temperature sensor.
Further, in the weight updating stage of the Gaussian sum filter, the method comprises the following stepsSystem to gaussian term weight ωiUpdating, wherein the process is as formula (3):
Figure GDA0003126559740000061
where | is the determinant of the matrix, aiIs the initialized weight factor, c (k) is the sum of all gaussian terms,
Figure GDA0003126559740000062
is the output estimate of the gaussian term i and the corresponding error covariance.
An arbitrary non-gaussian distribution is set according to equation (4) to be approximated by a finite sum of gaussians,
Figure GDA0003126559740000063
where v (k) is a non-Gaussian distribution at time k, N (μ)i,Ri),aiRespectively mean value of muiWith a covariance of RiAnd its corresponding weight, wherein the sum of the weights is 1;
the system performs filtering on each Gaussian term, and merges the filtering results of the Gaussian terms to obtain a state estimation and an error covariance, as shown in formula (5):
Figure GDA0003126559740000064
wherein R isiIs the covariance, ω, of the measurement noise of the Gaussian term iiIs the weight of the corresponding gaussian term,
Figure GDA0003126559740000065
is the calculated value and error covariance, P, of the observed value corresponding to the Gaussian termsIs the covariance of the merging errors of the l gaussian terms.
The reusable gaussian and filter hardware architecture of the present invention benefits from the requirement of sequential execution of gaussian and filtering processes and the shareable nature of the computational units. The reusable gaussian sum filter hardware architecture of the present embodiment is shown in fig. 3, and the architecture includes the following three parts: the controller, the storage resource and the computing unit array can be reused. The reusable Gaussian sum filter hardware module is externally connected with the dynamic temperature management controller, the temperature sensor and the power consumption estimator. In the operation process of the chip, after each temperature sampling period begins, namely after the reading and the power consumption estimated value of the sensor are written into the memory, the dynamic temperature management controller sends a starting signal to the reusable controller, the reusable controller enters an internal state machine after receiving the starting signal, the configuration operation unit carries out the operation of Gaussian sum filtering process, the temperature estimated value obtained through final calculation is written into the memory, after the calculation is finished, the reusable controller sends an ending signal to the dynamic temperature management controller, and the dynamic temperature management controller reads the temperature estimated value obtained through calculation from a fixed position of the memory.
The reusable controller is responsible for configuring the interconnections between the computing units and controlling the process of the gaussian sum filter, and is the core of the hardware architecture of the reusable gaussian sum filter.
The storage resource of the reusable Gaussian sum filter hardware architecture is composed of a constant memory and a data memory, wherein the constant memory is composed of 4 banks, and the data memory is composed of 12 banks. Constant memory that can reuse gaussians and filters stores parameter matrices a, B, H, and data memory stores intermediate matrices, input data (temperature sensor readings, power consumption estimates) and output data (temperature estimates) during the calculation. The memory bank is 32 bits wide and the depth depends on the order of the system.
The computing unit array capable of reusing Gaussian and filter hardware architecture is composed of a plurality of common floating-point operation units, wherein each common floating-point operation unit comprises 4 adders, 4 multipliers, 1 divider and 1 exponent unit, and the operation units are connected through a cross switch. The reusable gaussian sum filter array of computing elements can be reconfigured as desired into complex modules, such as a multiply-accumulate (MAC) module built with multipliers and adders through a crossbar switch, the connection of which is controlled by a reusable controller, as shown in fig. 4.
In order to evaluate the beneficial effects of the present invention, a temperature sensor of a three-dimensional network-on-chip system with a scale of 4 × 4 × 3 is applied with non-gaussian noise (equivalent variance is about 16 degrees celsius) which is constructed by a weighted sum of gaussian noise and laplacian noise, and non-gaussian noise having different degrees of deviation from gaussian noise is constructed by adjusting the proportion of laplacian noise in the non-gaussian noise. The number of temperature sensors in the 4 x 3 three-dimensional network-on-chip system is less than the number of modules to be monitored, and the number of sensors is set to four cases of 14, 15, 16 and 17. After applying the architecture of the present invention, the Root Mean Square Error (RMSE) and the maximum Error (Max Error) of 144 reconstructed temperature values from the true temperature values are shown in table 1. Compared with the traditional Kalman filter, the root mean square error of the invention is reduced by 29.27-35%, and the maximum error is reduced by 33.26-40.6%.
TABLE 1 temperature reconstruction root mean square error and maximum error under non-Gaussian noise
Figure GDA0003126559740000081
The technical scope of the present invention is not limited to the contents of the specification, and any modifications, equivalents, improvements, etc. made within the spirit and scope of the present invention should be included in the scope of the present invention.

Claims (6)

1. A three-dimensional network-on-chip temperature reconstruction system based on a limited number of temperature sensors is characterized in that: the system reconstructs the temperature of a three-dimensional network-on-chip through a Gaussian sum filter, the Gaussian sum filter combines a plurality of Gaussian term filtering results into an equivalent Gaussian term, and the system comprises three stages: the system specifically comprises the following three parts:
a reusable controller that configures interconnections between the computing units and controls the process of the gaussians and the filters;
the storage resource consists of a constant memory and a data memory;
the computing unit array consists of common floating point computing units which are connected through a cross switch; in the prediction stage of the Gaussian sum filter, the system predicts the temperature according to the temperature state estimation value at the previous moment and calculates the corresponding error covariance, and the calculation process is as follows (1):
Figure FDA0003126559730000011
wherein A (k, k-1) and B are respectively a state transition matrix and an input matrix of the three-dimensional network-on-chip thermal model based on the state space, A (k, k-1)TIs the transpose of A (k, k-1), W is the covariance matrix of the process noise in the state space based thermal model, u (k) is the power consumption at time k for each node, is the input to the model,
Figure FDA0003126559730000012
the method comprises the following steps of respectively obtaining a posterior temperature estimation value at the k-1 moment, a prior temperature estimation value at the k moment and an error covariance corresponding to the posterior temperature estimation value and the prior temperature estimation value at the k moment;
in the updating stage of the Gaussian sum filter, the system combines a new observation value with the last predicted value to obtain an improved posterior estimated value, and the calculation process is as follows (2):
Figure FDA0003126559730000013
wherein, I is an identity matrix, K (k) is Kalman gain at the moment k, S (k) is an observed value of a temperature sensor at the moment k, H (k) is an output matrix at the moment k, and the position of a nonzero element of the output matrix indicates that the node can be measured, namely the node has the temperature sensor;
Figure FDA0003126559730000014
is the output value, P, of the temperature estimated at the previous moments(k | k-1) is the covariance of the merging errors of the l Gaussian terms, the weight updates in the Gaussian sum filtersPhase, weighting ω of the system to the Gaussian termi(k) Updating, wherein the process is as formula (3):
Figure FDA0003126559730000021
Figure FDA0003126559730000022
Figure FDA0003126559730000023
where | is the determinant of the matrix, aiIs the initialized weight factor, c (k) is the sum of all gaussian terms,
Figure FDA0003126559730000024
is the output estimate of the gaussian term i and the corresponding error covariance, l represents the number of gaussian terms.
2. The limited number of temperature sensor based three-dimensional network-on-chip temperature reconstruction system of claim 1, wherein: an arbitrary non-gaussian distribution is set according to equation (4) to be approximated by a finite sum of gaussians,
Figure FDA0003126559730000025
where v (k) is a non-Gaussian distribution at time k, N (μ)i,Ri) Is a mean value of μiWith a covariance of RiThe initialized weight factor aiCorresponding to a mean value of μiWith a covariance of RiWherein the sum of the weights is 1;
the system performs filtering on each Gaussian term, and merges the filtering results of the Gaussian terms to obtain a state estimation and an error covariance, as shown in formula (5):
Figure FDA0003126559730000026
Figure FDA0003126559730000027
Figure FDA0003126559730000028
Figure FDA0003126559730000029
wherein R isiIs the covariance of the measurement noise of the gaussian term i.
3. The limited number of temperature sensor based three-dimensional network-on-chip temperature reconstruction system of claim 1, wherein: the reusable Gaussian sum filter hardware module is externally connected with the dynamic temperature management controller, the temperature sensor and the power consumption estimator.
4. The limited number of temperature sensor based three-dimensional network-on-chip temperature reconstruction system of claim 1, wherein: the constant memory of the reusable gaussian sum filter consists of 4 banks for storing the matrix parameters A, B, H.
5. The limited number of temperature sensor based three-dimensional network-on-chip temperature reconstruction system of claim 1, wherein: the data memory consists of 12 banks, and stores an intermediate matrix in the calculation process, temperature sensor readings and power consumption estimated values as input data, and temperature estimated values as output data, wherein the width of the memory bank is 32 bits, and the depth of the memory bank depends on the order of the system.
6. The limited number of temperature sensor based three-dimensional network-on-chip temperature reconstruction system of claim 1, wherein: the computing unit array capable of reusing the Gauss sum filter is composed of a common floating point operation unit and comprises 4 adders, 4 multipliers, 1 divider and 1 exponent unit, and the 4 adders, the 4 multipliers, the 1 divider and the 1 exponent unit are connected through a cross switch.
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